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/srv/reproducible-results/rbuild-debian/r-b-build.TxJuHbUB/b1/macaulay2_1.25.06+ds-2_amd64.changes vs.
/srv/reproducible-results/rbuild-debian/r-b-build.TxJuHbUB/b2/macaulay2_1.25.06+ds-2_amd64.changes
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1 ·e94ec9ee1cd6da6dfd3517379d921cf5·62592·editors·optional·elpa-macaulay2_1.25.06+ds-2_all.deb1 ·e94ec9ee1cd6da6dfd3517379d921cf5·62592·editors·optional·elpa-macaulay2_1.25.06+ds-2_all.deb
2 ·21604df1099d682bc04d9ee2d5408271·30654100·math·optional·macaulay2-common_1.25.06+ds-2_all.deb 
3 ·1e1979b1efeabb1540a22ab7147f4510·49717108·debug·optional·macaulay2-dbgsym_1.25.06+ds-2_amd64.deb 
4 ·3b4cdfc846dba4367b9299868cb320e9·2621556·math·optional·macaulay2_1.25.06+ds-2_amd64.deb2 ·56b4e8648c1195210d9bb3e295a38ef6·30656412·math·optional·macaulay2-common_1.25.06+ds-2_all.deb
 3 ·e465a9c3ac041c4232cac89f7d3c5322·49713684·debug·optional·macaulay2-dbgsym_1.25.06+ds-2_amd64.deb
 4 ·fab6216197ff0e8efe7dc76c450b72b0·2621008·math·optional·macaulay2_1.25.06+ds-2_amd64.deb
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macaulay2-common_1.25.06+ds-2_all.deb
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1 -rw-r--r--···0········0········0········4·2025-06-02·16:39:21.000000·debian-binary1 -rw-r--r--···0········0········0········4·2025-06-02·16:39:21.000000·debian-binary
2 -rw-r--r--···0········0········0···515524·2025-06-02·16:39:21.000000·control.tar.xz2 -rw-r--r--···0········0········0···515584·2025-06-02·16:39:21.000000·control.tar.xz
3 -rw-r--r--···0········0········0·30138384·2025-06-02·16:39:21.000000·data.tar.xz3 -rw-r--r--···0········0········0·30140636·2025-06-02·16:39:21.000000·data.tar.xz
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1 Package:·macaulay2-common1 Package:·macaulay2-common
2 Source:·macaulay22 Source:·macaulay2
3 Version:·1.25.06+ds-23 Version:·1.25.06+ds-2
4 Architecture:·all4 Architecture:·all
5 Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org>5 Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org>
6 Installed-Size:·2954736 Installed-Size:·295488
7 Depends:·fonts-glyphicons-halflings·(>=·1.009~3.4.1+dfsg),·fonts-katex·(>=·0.16.10+~cs6.1.0),·libjs-bootsidemenu·(>=·1.0.0),·libjs-bootstrap·(>=·3.4.1+dfsg),·libjs-d3·(>=·3.5.17),·libjs-jquery·(>=·3.6.1+dfsg+~3.5.14),·libjs-katex·(>=·0.16.10+~cs6.1.0),·libjs-nouislider·(>=·15.8.1+ds),·libjs-three·(>=·111+dfsg1),·node-clipboard·(>=·2.0.11+ds+~cs9.6.11)7 Depends:·fonts-glyphicons-halflings·(>=·1.009~3.4.1+dfsg),·fonts-katex·(>=·0.16.10+~cs6.1.0),·libjs-bootsidemenu·(>=·1.0.0),·libjs-bootstrap·(>=·3.4.1+dfsg),·libjs-d3·(>=·3.5.17),·libjs-jquery·(>=·3.6.1+dfsg+~3.5.14),·libjs-katex·(>=·0.16.10+~cs6.1.0),·libjs-nouislider·(>=·15.8.1+ds),·libjs-three·(>=·111+dfsg1),·node-clipboard·(>=·2.0.11+ds+~cs9.6.11)
8 Section:·math8 Section:·math
9 Priority:·optional9 Priority:·optional
10 Multi-Arch:·foreign10 Multi-Arch:·foreign
11 Homepage:·http://macaulay2.com11 Homepage:·http://macaulay2.com
12 Description:·Software·system·for·algebraic·geometry·research·(common·files)12 Description:·Software·system·for·algebraic·geometry·research·(common·files)
13 ·Macaulay·2·is·a·software·system·for·algebraic·geometry·research,·written·by13 ·Macaulay·2·is·a·software·system·for·algebraic·geometry·research,·written·by
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./md5sums
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2877 -rw-r--r--···0·root·········(0)·root·········(0)·····9657·2025-06-02·16:39:21.000000·./usr/share/doc/Macaulay2/AInfinity/html/_display__Blocks.html2877 -rw-r--r--···0·root·········(0)·root·········(0)·····9657·2025-06-02·16:39:21.000000·./usr/share/doc/Macaulay2/AInfinity/html/_display__Blocks.html
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2973 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/doc/Macaulay2/AdjunctionForSurfaces/dump/2973 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/doc/Macaulay2/AdjunctionForSurfaces/dump/
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10 o2·=·cokernel·|·a·b·c·|10 o2·=·cokernel·|·a·b·c·|
  
11 ····························111 ····························1
12 o2·:·R-module,·quotient·of·R12 o2·:·R-module,·quotient·of·R
  
13 i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)13 i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)
14 ·--·2.15574s·elapsed14 ·--·3.5009s·elapsed
  
15 ······1······3······9······27······81······243······729······218715 ······1······3······9······27······81······243······729······2187
16 o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R16 o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R
17 ·····························································17 ·····························································
18 ·····0······1······2······3·······4·······5········6········718 ·····0······1······2······3·······4·······5········6········7
  
19 o3·:·Complex19 o3·:·Complex
  
20 i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)20 i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)
21 ·--·2.13967s·elapsed21 ·--·5.17538s·elapsed
  
22 ······1······3······9······27······81······243······729······218722 ······1······3······9······27······81······243······729······2187
23 o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R23 o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R
24 ·····························································24 ·····························································
25 ·····0······1······2······3·······4·······5········6········725 ·····0······1······2······3·······4·······5········6········7
  
26 o4·:·Complex26 o4·:·Complex
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90 ····························190 ····························1
91 o2·:·R-module,·quotient·of·R</code></pre>91 o2·:·R-module,·quotient·of·R</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)96 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)
97 ·--·2.15574s·elapsed97 ·--·3.5009s·elapsed
  
98 ······1······3······9······27······81······243······729······218798 ······1······3······9······27······81······243······729······2187
99 o3·=·R··&lt;--·R··&lt;--·R··&lt;--·R···&lt;--·R···&lt;--·R····&lt;--·R····&lt;--·R99 o3·=·R··&lt;--·R··&lt;--·R··&lt;--·R···&lt;--·R···&lt;--·R····&lt;--·R····&lt;--·R
100 ·····························································100 ·····························································
101 ·····0······1······2······3·······4·······5········6········7101 ·····0······1······2······3·······4·······5········6········7
  
102 o3·:·Complex</code></pre>102 o3·:·Complex</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)107 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)
108 ·--·2.13967s·elapsed108 ·--·5.17538s·elapsed
  
109 ······1······3······9······27······81······243······729······2187109 ······1······3······9······27······81······243······729······2187
110 o4·=·R··&lt;--·R··&lt;--·R··&lt;--·R···&lt;--·R···&lt;--·R····&lt;--·R····&lt;--·R110 o4·=·R··&lt;--·R··&lt;--·R··&lt;--·R···&lt;--·R···&lt;--·R····&lt;--·R····&lt;--·R
111 ·····························································111 ·····························································
112 ·····0······1······2······3·······4·······5········6········7112 ·····0······1······2······3·······4·······5········6········7
  
113 o4·:·Complex</code></pre>113 o4·:·Complex</code></pre>
781 B
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Offset 23, 24 lines modifiedOffset 23, 24 lines modified
23 i2·:·M·=·coker·vars·R23 i2·:·M·=·coker·vars·R
  
24 o2·=·cokernel·|·a·b·c·|24 o2·=·cokernel·|·a·b·c·|
  
25 ····························125 ····························1
26 o2·:·R-module,·quotient·of·R26 o2·:·R-module,·quotient·of·R
27 i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)27 i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)
28 ·--·2.15574s·elapsed28 ·--·3.5009s·elapsed
  
29 ······1······3······9······27······81······243······729······218729 ······1······3······9······27······81······243······729······2187
30 o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R30 o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R
  
31 ·····0······1······2······3·······4·······5········6········731 ·····0······1······2······3·······4·······5········6········7
  
32 o3·:·Complex32 o3·:·Complex
33 i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)33 i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)
34 ·--·2.13967s·elapsed34 ·--·5.17538s·elapsed
  
35 ······1······3······9······27······81······243······729······218735 ······1······3······9······27······81······243······729······2187
36 o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R36 o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R
  
37 ·····0······1······2······3·······4·······5········6········737 ·····0······1······2······3·······4·······5········6········7
  
38 o4·:·Complex38 o4·:·Complex
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11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmYWNldHMsQWJzdHJhY3RTaW1wbGljaWFsQ29tcGxl11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmYWNldHMsQWJzdHJhY3RTaW1wbGljaWFsQ29tcGxl
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9 #:len=3799 #:len=379
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibGlua3MgYWJzdHJhY3Qgc2ltcGxpY2lh10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibGlua3MgYWJzdHJhY3Qgc2ltcGxpY2lh
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2 #:version=1.12 #:version=1.1
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8 dHJhY2VNYXRyaXgoSWRlYWwsTWF0cml4KQ==8 dHJhY2VNYXRyaXgoSWRlYWwsTWF0cml4KQ==
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTE2MCwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTE2MCwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodHJhY2VNYXRyaXgsSWRlYWwsTWF0cml4KSwidHJh11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodHJhY2VNYXRyaXgsSWRlYWwsTWF0cml4KSwidHJh
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2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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8 YWRqdW5jdGlvblByb2Nlc3MoSWRlYWwsWlop8 YWRqdW5jdGlvblByb2Nlc3MoSWRlYWwsWlop
9 #:len=3109 #:len=310
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjc4LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjc4LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGp1bmN0aW9uUHJvY2VzcyxJZGVhbCxaWiksImFk11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGp1bmN0aW9uUHJvY2VzcyxJZGVhbCxaWiksImFk
533 B
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49 o8·:·BettiTally49 o8·:·BettiTally
  
50 i9·:·c=codim·I50 i9·:·c=codim·I
  
51 o9·=·451 o9·=·4
  
52 i10·:·elapsedTime·fI=res·I52 i10·:·elapsedTime·fI=res·I
53 ·--·.0170367s·elapsed53 ·--·.0335028s·elapsed
  
54 ········1·······14·······33·······28·······854 ········1·······14·······33·······28·······8
55 o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·055 o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0
56 ··················································56 ··················································
57 ······0·······1········2········3········4·······557 ······0·······1········2········3········4·······5
  
58 o10·:·ChainComplex58 o10·:·ChainComplex
795 B
./usr/share/doc/Macaulay2/AdjunctionForSurfaces/example-output/_adjunction__Process.out
    
Offset 87, 30 lines modifiedOffset 87, 30 lines modified
87 o13·:·BettiTally87 o13·:·BettiTally
  
88 i14·:·phi=map(P2,Pn,H);88 i14·:·phi=map(P2,Pn,H);
  
89 o14·:·RingMap·P2·<--·Pn89 o14·:·RingMap·P2·<--·Pn
  
90 i15·:·elapsedTime·betti(I'=trim·ker·phi)90 i15·:·elapsedTime·betti(I'=trim·ker·phi)
91 ·--·.4974s·elapsed91 ·--·1.09821s·elapsed
  
92 ·············0··192 ·············0··1
93 o15·=·total:·1·1193 o15·=·total:·1·11
94 ··········0:·1··.94 ··········0:·1··.
95 ··········1:·.··395 ··········1:·.··3
96 ··········2:·.··896 ··········2:·.··8
  
97 o15·:·BettiTally97 o15·:·BettiTally
  
98 i16·:·I'==·I98 i16·:·I'==·I
  
99 o16·=·true99 o16·=·true
  
100 i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;100 i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
101 ·--·4.88457s·elapsed101 ·--·11.6238s·elapsed
  
102 i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))102 i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))
  
103 ··························0·1103 ··························0·1
104 o18·=·Tally{(1,·1,·total:·1·2)·=>·5}104 o18·=·Tally{(1,·1,·total:·1·2)·=>·5}
105 ·······················0:·1·2105 ·······················0:·1·2
106 ··························0·1106 ··························0·1
985 B
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Offset 79, 40 lines modifiedOffset 79, 40 lines modified
79 ··········1:·.·.79 ··········1:·.·.
80 ··········2:·.·.80 ··········2:·.·.
81 ··········3:·.·881 ··········3:·.·8
  
82 o13·:·BettiTally82 o13·:·BettiTally
  
83 i14·:·elapsedTime·sub(I,H)83 i14·:·elapsedTime·sub(I,H)
84 ·--·.0100355s·elapsed84 ·--·.0203652s·elapsed
  
85 o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)85 o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)
  
86 o14·:·Ideal·of·P286 o14·:·Ideal·of·P2
  
87 i15·:·phi=map(P2,Pn,H);87 i15·:·phi=map(P2,Pn,H);
  
88 o15·:·RingMap·P2·<--·Pn88 o15·:·RingMap·P2·<--·Pn
  
89 i16·:·elapsedTime·betti(I'=trim·ker·phi)89 i16·:·elapsedTime·betti(I'=trim·ker·phi)
90 ·--·.0509251s·elapsed90 ·--·.0569185s·elapsed
  
91 ·············0··191 ·············0··1
92 o16·=·total:·1·1292 o16·=·total:·1·12
93 ··········0:·1··.93 ··········0:·1··.
94 ··········1:·.·1294 ··········1:·.·12
  
95 o16·:·BettiTally95 o16·:·BettiTally
  
96 i17·:·I'==·I96 i17·:·I'==·I
  
97 o17·=·true97 o17·=·true
  
98 i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;98 i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
99 ·--·1.59406s·elapsed99 ·--·4.04921s·elapsed
  
100 i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))100 i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))
  
101 ···························0··1101 ···························0··1
102 o19·=·Tally{(0,·34,·total:·1·15)·=>·1}102 o19·=·Tally{(0,·34,·total:·1·15)·=>·1}
103 ························0:·1··.103 ························0:·1··.
104 ························1:·.··.104 ························1:·.··.
1000 B
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149 o9·=·4</code></pre>149 o9·=·4</code></pre>
150 ············</td>150 ············</td>
151 ··········</tr>151 ··········</tr>
152 ··········<tr>152 ··········<tr>
153 ············<td>153 ············<td>
154 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I154 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I
155 ·--·.0170367s·elapsed155 ·--·.0335028s·elapsed
  
156 ········1·······14·······33·······28·······8156 ········1·······14·······33·······28·······8
157 o10·=·Pn··&lt;--·Pn···&lt;--·Pn···&lt;--·Pn···&lt;--·Pn··&lt;--·0157 o10·=·Pn··&lt;--·Pn···&lt;--·Pn···&lt;--·Pn···&lt;--·Pn··&lt;--·0
158 ··················································158 ··················································
159 ······0·······1········2········3········4·······5159 ······0·······1········2········3········4·······5
  
160 o10·:·ChainComplex</code></pre>160 o10·:·ChainComplex</code></pre>
357 B
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54 ·········2:·.·1254 ·········2:·.·12
  
55 o8·:·BettiTally55 o8·:·BettiTally
56 i9·:·c=codim·I56 i9·:·c=codim·I
  
57 o9·=·457 o9·=·4
58 i10·:·elapsedTime·fI=res·I58 i10·:·elapsedTime·fI=res·I
59 ·--·.0170367s·elapsed59 ·--·.0335028s·elapsed
  
60 ········1·······14·······33·······28·······860 ········1·······14·······33·······28·······8
61 o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·061 o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0
  
62 ······0·······1········2········3········4·······562 ······0·······1········2········3········4·······5
  
63 o10·:·ChainComplex63 o10·:·ChainComplex
1.69 KB
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Offset 217, 15 lines modifiedOffset 217, 15 lines modified
  
217 o14·:·RingMap·P2·&lt;--·Pn</code></pre>217 o14·:·RingMap·P2·&lt;--·Pn</code></pre>
218 ············</td>218 ············</td>
219 ··········</tr>219 ··········</tr>
220 ··········<tr>220 ··········<tr>
221 ············<td>221 ············<td>
222 ··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi)222 ··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi)
223 ·--·.4974s·elapsed223 ·--·1.09821s·elapsed
  
224 ·············0··1224 ·············0··1
225 o15·=·total:·1·11225 o15·=·total:·1·11
226 ··········0:·1··.226 ··········0:·1··.
227 ··········1:·.··3227 ··········1:·.··3
228 ··········2:·.··8228 ··········2:·.··8
  
Offset 238, 15 lines modifiedOffset 238, 15 lines modified
  
238 o16·=·true</code></pre>238 o16·=·true</code></pre>
239 ············</td>239 ············</td>
240 ··········</tr>240 ··········</tr>
241 ··········<tr>241 ··········<tr>
242 ············<td>242 ············<td>
243 ··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;243 ··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
244 ·--·4.88457s·elapsed</code></pre>244 ·--·11.6238s·elapsed</code></pre>
245 ············</td>245 ············</td>
246 ··········</tr>246 ··········</tr>
247 ··········<tr>247 ··········<tr>
248 ············<td>248 ············<td>
249 ··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))249 ··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))
  
250 ··························0·1250 ··························0·1
694 B
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110 ··········6:·.·7110 ··········6:·.·7
  
111 o13·:·BettiTally111 o13·:·BettiTally
112 i14·:·phi=map(P2,Pn,H);112 i14·:·phi=map(P2,Pn,H);
  
113 o14·:·RingMap·P2·<--·Pn113 o14·:·RingMap·P2·<--·Pn
114 i15·:·elapsedTime·betti(I'=trim·ker·phi)114 i15·:·elapsedTime·betti(I'=trim·ker·phi)
115 ·--·.4974s·elapsed115 ·--·1.09821s·elapsed
  
116 ·············0··1116 ·············0··1
117 o15·=·total:·1·11117 o15·=·total:·1·11
118 ··········0:·1··.118 ··········0:·1··.
119 ··········1:·.··3119 ··········1:·.··3
120 ··········2:·.··8120 ··········2:·.··8
  
121 o15·:·BettiTally121 o15·:·BettiTally
122 i16·:·I'==·I122 i16·:·I'==·I
  
123 o16·=·true123 o16·=·true
124 i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;124 i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
125 ·--·4.88457s·elapsed125 ·--·11.6238s·elapsed
126 i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))126 i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))
  
127 ··························0·1127 ··························0·1
128 o18·=·Tally{(1,·1,·total:·1·2)·=>·5}128 o18·=·Tally{(1,·1,·total:·1·2)·=>·5}
129 ·······················0:·1·2129 ·······················0:·1·2
130 ··························0·1130 ··························0·1
131 ············(1,·3,·total:·1·3)·=>·8131 ············(1,·3,·total:·1·3)·=>·8
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./usr/share/doc/Macaulay2/AdjunctionForSurfaces/html/_parametrization.html
    
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193 o13·:·BettiTally</code></pre>193 o13·:·BettiTally</code></pre>
194 ············</td>194 ············</td>
195 ··········</tr>195 ··········</tr>
196 ··········<tr>196 ··········<tr>
197 ············<td>197 ············<td>
198 ··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H)198 ··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H)
199 ·--·.0100355s·elapsed199 ·--·.0203652s·elapsed
  
200 o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)200 o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)
  
201 o14·:·Ideal·of·P2</code></pre>201 o14·:·Ideal·of·P2</code></pre>
202 ············</td>202 ············</td>
203 ··········</tr>203 ··········</tr>
204 ··········<tr>204 ··········<tr>
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210 o15·:·RingMap·P2·&lt;--·Pn</code></pre>210 o15·:·RingMap·P2·&lt;--·Pn</code></pre>
211 ············</td>211 ············</td>
212 ··········</tr>212 ··········</tr>
213 ··········<tr>213 ··········<tr>
214 ············<td>214 ············<td>
215 ··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi)215 ··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi)
216 ·--·.0509251s·elapsed216 ·--·.0569185s·elapsed
  
217 ·············0··1217 ·············0··1
218 o16·=·total:·1·12218 o16·=·total:·1·12
219 ··········0:·1··.219 ··········0:·1··.
220 ··········1:·.·12220 ··········1:·.·12
  
221 o16·:·BettiTally</code></pre>221 o16·:·BettiTally</code></pre>
Offset 230, 15 lines modifiedOffset 230, 15 lines modified
  
230 o17·=·true</code></pre>230 o17·=·true</code></pre>
231 ············</td>231 ············</td>
232 ··········</tr>232 ··········</tr>
233 ··········<tr>233 ··········<tr>
234 ············<td>234 ············<td>
235 ··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;235 ··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
236 ·--·1.59406s·elapsed</code></pre>236 ·--·4.04921s·elapsed</code></pre>
237 ············</td>237 ············</td>
238 ··········</tr>238 ··········</tr>
239 ··········<tr>239 ··········<tr>
240 ············<td>240 ············<td>
241 ··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))241 ··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))
  
242 ···························0··1242 ···························0··1
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82 ··········0:·1·.82 ··········0:·1·.
83 ··········1:·.·.83 ··········1:·.·.
84 ··········2:·.·.84 ··········2:·.·.
85 ··········3:·.·885 ··········3:·.·8
  
86 o13·:·BettiTally86 o13·:·BettiTally
87 i14·:·elapsedTime·sub(I,H)87 i14·:·elapsedTime·sub(I,H)
88 ·--·.0100355s·elapsed88 ·--·.0203652s·elapsed
  
89 o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)89 o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)
  
90 o14·:·Ideal·of·P290 o14·:·Ideal·of·P2
91 i15·:·phi=map(P2,Pn,H);91 i15·:·phi=map(P2,Pn,H);
  
92 o15·:·RingMap·P2·<--·Pn92 o15·:·RingMap·P2·<--·Pn
93 i16·:·elapsedTime·betti(I'=trim·ker·phi)93 i16·:·elapsedTime·betti(I'=trim·ker·phi)
94 ·--·.0509251s·elapsed94 ·--·.0569185s·elapsed
  
95 ·············0··195 ·············0··1
96 o16·=·total:·1·1296 o16·=·total:·1·12
97 ··········0:·1··.97 ··········0:·1··.
98 ··········1:·.·1298 ··········1:·.·12
  
99 o16·:·BettiTally99 o16·:·BettiTally
100 i17·:·I'==·I100 i17·:·I'==·I
  
101 o17·=·true101 o17·=·true
102 i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;102 i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
103 ·--·1.59406s·elapsed103 ·--·4.04921s·elapsed
104 i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))104 i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))
  
105 ···························0··1105 ···························0··1
106 o19·=·Tally{(0,·34,·total:·1·15)·=>·1}106 o19·=·Tally{(0,·34,·total:·1·15)·=>·1}
107 ························0:·1··.107 ························0:·1··.
108 ························1:·.··.108 ························1:·.··.
109 ························2:·.··.109 ························2:·.··.
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114 ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··|114 ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··|
115 ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··|115 ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··|
  
116 ··············4······4116 ··············4······4
117 o13·:·Matrix·A··<--·A117 o13·:·Matrix·A··<--·A
  
118 i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))118 i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))
119 ·--·used·0.366117s·(cpu);·0.321284s·(thread);·0s·(gc)119 ·--·used·0.385182s·(cpu);·0.327751s·(thread);·0s·(gc)
  
120 ·············0·1·2120 ·············0·1·2
121 o14·=·total:·3·6·3121 o14·=·total:·3·6·3
122 ··········0:·3·.·.122 ··········0:·3·.·.
123 ··········1:·.·6·.123 ··········1:·.·6·.
124 ··········2:·.·.·3124 ··········2:·.·.·3
  
125 o14·:·BettiTally125 o14·:·BettiTally
  
126 i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))126 i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))
127 ·--·used·0.507425s·(cpu);·0.402506s·(thread);·0s·(gc)127 ·--·used·0.621438s·(cpu);·0.451515s·(thread);·0s·(gc)
  
128 ·············0·1·2128 ·············0·1·2
129 o15·=·total:·3·6·3129 o15·=·total:·3·6·3
130 ··········0:·3·.·.130 ··········0:·3·.·.
131 ··········1:·.·6·.131 ··········1:·.·6·.
132 ··········2:·.·.·3132 ··········2:·.·.·3
  
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253 ··············4······4253 ··············4······4
254 o13·:·Matrix·A··&lt;--·A</code></pre>254 o13·:·Matrix·A··&lt;--·A</code></pre>
255 ············</td>255 ············</td>
256 ··········</tr>256 ··········</tr>
257 ··········<tr>257 ··········<tr>
258 ············<td>258 ············<td>
259 ··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))259 ··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))
260 ·--·used·0.366117s·(cpu);·0.321284s·(thread);·0s·(gc)260 ·--·used·0.385182s·(cpu);·0.327751s·(thread);·0s·(gc)
  
261 ·············0·1·2261 ·············0·1·2
262 o14·=·total:·3·6·3262 o14·=·total:·3·6·3
263 ··········0:·3·.·.263 ··········0:·3·.·.
264 ··········1:·.·6·.264 ··········1:·.·6·.
265 ··········2:·.·.·3265 ··········2:·.·.·3
  
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272 ········<div>272 ········<div>
273 ··········<p>With·the·form·<span·class="tt">pureResolution(p,q,D)</span>·we·can·directly·create·the·situation·of·<span·class="tt">pureResolution(M,D)</span>·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of·linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables·of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in·A·this·runs·much·faster·than·taking·a·random·matrix·M.</p>273 ··········<p>With·the·form·<span·class="tt">pureResolution(p,q,D)</span>·we·can·directly·create·the·situation·of·<span·class="tt">pureResolution(M,D)</span>·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of·linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables·of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in·A·this·runs·much·faster·than·taking·a·random·matrix·M.</p>
274 ········</div>274 ········</div>
275 ········<table·class="examples">275 ········<table·class="examples">
276 ··········<tr>276 ··········<tr>
277 ············<td>277 ············<td>
278 ··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))278 ··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))
279 ·--·used·0.507425s·(cpu);·0.402506s·(thread);·0s·(gc)279 ·--·used·0.621438s·(cpu);·0.451515s·(thread);·0s·(gc)
  
280 ·············0·1·2280 ·············0·1·2
281 o15·=·total:·3·6·3281 o15·=·total:·3·6·3
282 ··········0:·3·.·.282 ··········0:·3·.·.
283 ··········1:·.·6·.283 ··········1:·.·6·.
284 ··········2:·.·.·3284 ··········2:·.·.·3
  
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161 ······|·-30a-29b·-29a-24b·-47a-39b·38a+2b···|161 ······|·-30a-29b·-29a-24b·-47a-39b·38a+2b···|
162 ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··|162 ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··|
163 ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··|163 ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··|
  
164 ··············4······4164 ··············4······4
165 o13·:·Matrix·A··<--·A165 o13·:·Matrix·A··<--·A
166 i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))166 i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))
167 ·--·used·0.366117s·(cpu);·0.321284s·(thread);·0s·(gc)167 ·--·used·0.385182s·(cpu);·0.327751s·(thread);·0s·(gc)
  
168 ·············0·1·2168 ·············0·1·2
169 o14·=·total:·3·6·3169 o14·=·total:·3·6·3
170 ··········0:·3·.·.170 ··········0:·3·.·.
171 ··········1:·.·6·.171 ··········1:·.·6·.
172 ··········2:·.·.·3172 ··········2:·.·.·3
  
173 o14·:·BettiTally173 o14·:·BettiTally
174 With·the·form·pureResolution(p,q,D)·we·can·directly·create·the·situation·of174 With·the·form·pureResolution(p,q,D)·we·can·directly·create·the·situation·of
175 pureResolution(M,D)·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of175 pureResolution(M,D)·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of
176 linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables176 linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables
177 of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in177 of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in
178 A·this·runs·much·faster·than·taking·a·random·matrix·M.178 A·this·runs·much·faster·than·taking·a·random·matrix·M.
179 i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))179 i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))
180 ·--·used·0.507425s·(cpu);·0.402506s·(thread);·0s·(gc)180 ·--·used·0.621438s·(cpu);·0.451515s·(thread);·0s·(gc)
  
181 ·············0·1·2181 ·············0·1·2
182 o15·=·total:·3·6·3182 o15·=·total:·3·6·3
183 ··········0:·3·.·.183 ··········0:·3·.·.
184 ··········1:·.·6·.184 ··········1:·.·6·.
185 ··········2:·.·.·3185 ··········2:·.·.·3
  
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1 --·-*-·M2-comint·-*-·hash:·13305455765671 --·-*-·M2-comint·-*-·hash:·1330545576567
  
2 i1·:·runBenchmarks·"res39"2 i1·:·runBenchmarks·"res39"
3 --·beginning·computation·Thu·Jun··5·22:57:40·-12·20253 --·beginning·computation·Fri·Jul·10·10:36:24·+14·2026
4 --·Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.140-1·(2025-05-22)·x86_64·GNU/Linux4 --·Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux
5 --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·2196.688··5 --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·1996.250··
6 --·Macaulay2·1.25.06,·compiled·with·gcc·14.2.06 --·Macaulay2·1.25.06,·compiled·with·gcc·14.2.0
7 --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.108607·seconds7 --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.140042·seconds
  
8 i2·:·8 i2·:·
3.2 KB
./usr/share/doc/Macaulay2/Benchmark/html/_run__Benchmarks.html
    
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75 ········<div>75 ········<div>
76 ··········<p>The·tests·available·are:·<br>&quot;deg2generic&quot;·--·gb·of·a·generic·ideal·of·codimension·2·and·degree·2<br>&quot;gb4by4comm&quot;·--·gb·of·the·ideal·of·generic·commuting·4·by·4·matrices·over·ZZ/101<br>&quot;gb3445&quot;·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables<br>&quot;gbB148&quot;·--·gb·of·Bayesian·graph·ideal·#148<br>&quot;res39&quot;·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101<br>&quot;resG25&quot;·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)<br>&quot;yang-gb1&quot;·--·an·example·of·Yang-Hui·He·arising·in·string·theory<br>&quot;yang-subring&quot;·--·an·example·of·Yang-Hui·He<br></p>76 ··········<p>The·tests·available·are:·<br>&quot;deg2generic&quot;·--·gb·of·a·generic·ideal·of·codimension·2·and·degree·2<br>&quot;gb4by4comm&quot;·--·gb·of·the·ideal·of·generic·commuting·4·by·4·matrices·over·ZZ/101<br>&quot;gb3445&quot;·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables<br>&quot;gbB148&quot;·--·gb·of·Bayesian·graph·ideal·#148<br>&quot;res39&quot;·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101<br>&quot;resG25&quot;·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)<br>&quot;yang-gb1&quot;·--·an·example·of·Yang-Hui·He·arising·in·string·theory<br>&quot;yang-subring&quot;·--·an·example·of·Yang-Hui·He<br></p>
77 ········</div>77 ········</div>
78 ········<table·class="examples">78 ········<table·class="examples">
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·&quot;res39&quot;81 ··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·&quot;res39&quot;
82 --·beginning·computation·Thu·Jun··5·22:57:40·-12·202582 --·beginning·computation·Fri·Jul·10·10:36:24·+14·2026
83 --·Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.140-1·(2025-05-22)·x86_64·GNU/Linux83 --·Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux
84 --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·2196.688··84 --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·1996.250··
85 --·Macaulay2·1.25.06,·compiled·with·gcc·14.2.085 --·Macaulay2·1.25.06,·compiled·with·gcc·14.2.0
86 --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.108607·seconds</code></pre>86 --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.140042·seconds</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ········</table>89 ········</table>
90 ······</div>90 ······</div>
91 ······<div>91 ······<div>
92 ········<div·class="waystouse">92 ········<div·class="waystouse">
93 ··········<h2>For·the·programmer</h2>93 ··········<h2>For·the·programmer</h2>
1.42 KB
html2text {}
    
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23 "gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables23 "gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables
24 "gbB148"·--·gb·of·Bayesian·graph·ideal·#14824 "gbB148"·--·gb·of·Bayesian·graph·ideal·#148
25 "res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/10125 "res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101
26 "resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)26 "resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)
27 "yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory27 "yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory
28 "yang-subring"·--·an·example·of·Yang-Hui·He28 "yang-subring"·--·an·example·of·Yang-Hui·He
29 i1·:·runBenchmarks·"res39"29 i1·:·runBenchmarks·"res39"
30 --·beginning·computation·Thu·Jun··5·22:57:40·-12·2025 
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33 --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·2196.68833 --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·1996.250
34 --·Macaulay2·1.25.06,·compiled·with·gcc·14.2.034 --·Macaulay2·1.25.06,·compiled·with·gcc·14.2.0
35 --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.108607·seconds35 --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.140042·seconds
36 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*36 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
37 The·object·_\x8r_\x8u_\x8n_\x8B_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k_\x8s·is·a·_\x8c_\x8o_\x8m_\x8m_\x8a_\x8n_\x8d.37 The·object·_\x8r_\x8u_\x8n_\x8B_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k_\x8s·is·a·_\x8c_\x8o_\x8m_\x8m_\x8a_\x8n_\x8d.
38 ===============================================================================38 ===============================================================================
39 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-39 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
40 1.25.06+ds/M2/Macaulay2/packages/Benchmark.m2:297:0.40 1.25.06+ds/M2/Macaulay2/packages/Benchmark.m2:297:0.
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72 ············<li><span><a·title="an·option·to·group·variables·and·use·multihomogeneous·homotopies"·href="___Variable_spgroups.html">HomVariableGroup</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·to·group·variables·and·use·multihomogeneous·homotopies</span></span></li>72 ············<li><span><a·title="an·option·to·group·variables·and·use·multihomogeneous·homotopies"·href="___Variable_spgroups.html">HomVariableGroup</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·to·group·variables·and·use·multihomogeneous·homotopies</span></span></li>
73 ············<li><span><span·class="tt">M2Precision</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·M2Precision]-->73 ············<li><span><span·class="tt">M2Precision</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·M2Precision]-->
74 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·53</span>,·<span></span></span></li>74 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·53</span>,·<span></span></span></li>
75 ············<li><span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]-->75 ············<li><span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]-->
76 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;OutPoints&quot;</span>,·<span></span></span></li>76 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;OutPoints&quot;</span>,·<span></span></span></li>
77 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>77 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>
78 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>78 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>
79 ············<li><span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;/tmp/M2-1209936-0/0&quot;</span>,·<span>Option·to·change·directory·for·file·storage.</span></span></li>79 ············<li><span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;/tmp/M2-1227713-0/0&quot;</span>,·<span>Option·to·change·directory·for·file·storage.</span></span></li>
80 ············<li><span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span></li>80 ············<li><span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span></li>
81 ··········</ul>81 ··········</ul>
82 ········</li>82 ········</li>
83 ········<li>Outputs:··········<ul>83 ········<li>Outputs:··········<ul>
84 ············<li><span><span·class="tt">S</span>,·<span>a·<a·title="the·class·of·all·lists·--·{...}"·href="../../Macaulay2Doc/html/___List.html">list</a></span>,·a·list·whose·entries·are·lists·of·solutions·for·each·target·system</span></li>84 ············<li><span><span·class="tt">S</span>,·<span>a·<a·title="the·class·of·all·lists·--·{...}"·href="../../Macaulay2Doc/html/___List.html">list</a></span>,·a·list·whose·entries·are·lists·of·solutions·for·each·target·system</span></li>
85 ··········</ul>85 ··········</ul>
86 ········</li>86 ········</li>
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26 ············"OutPoints",26 ············"OutPoints",
27 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates27 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates
28 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real28 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real
29 ············number·or·random·complex·number29 ············number·or·random·complex·number
30 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates30 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates
31 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real31 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real
32 ············number·or·random·complex·number32 ············number·or·random·complex·number
33 ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-1209936-0/0",·Option·to33 ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-1227713-0/0",·Option·to
34 ············change·directory·for·file·storage.34 ············change·directory·for·file·storage.
35 ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional35 ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional
36 ············output36 ············output
37 ····*·Outputs:37 ····*·Outputs:
38 ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·whose·entries·are·lists·of·solutions·for·each38 ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·whose·entries·are·lists·of·solutions·for·each
39 ············target·system39 ············target·system
40 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*40 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
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77 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·53</span>,·<span></span></span></li>77 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·53</span>,·<span></span></span></li>
78 ············<li><span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·OutputStyle]-->78 ············<li><span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·OutputStyle]-->
79 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;OutPoints&quot;</span>,·<span></span></span></li>79 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;OutPoints&quot;</span>,·<span></span></span></li>
80 ············<li><span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]-->80 ············<li><span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]-->
81 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span></li>81 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span></li>
82 ············<li><span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]-->82 ············<li><span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]-->
83 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span></li>83 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span></li>
84 ············<li><span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;/tmp/M2-1209936-0/0&quot;</span>,·<span>Option·to·change·directory·for·file·storage.</span></span></li>84 ············<li><span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;/tmp/M2-1227713-0/0&quot;</span>,·<span>Option·to·change·directory·for·file·storage.</span></span></li>
85 ············<li><span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span></li>85 ············<li><span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span></li>
86 ··········</ul>86 ··········</ul>
87 ········</li>87 ········</li>
88 ········<li>Outputs:··········<ul>88 ········<li>Outputs:··········<ul>
89 ············<li><span><span·class="tt">S0</span>,·<span>a·<a·title="the·class·of·all·lists·--·{...}"·href="../../Macaulay2Doc/html/___List.html">list</a></span>,·a·list·of·solutions·to·the·target·system</span></li>89 ············<li><span><span·class="tt">S0</span>,·<span>a·<a·title="the·class·of·all·lists·--·{...}"·href="../../Macaulay2Doc/html/___List.html">list</a></span>,·a·list·of·solutions·to·the·target·system</span></li>
90 ··········</ul>90 ··········</ul>
91 ········</li>91 ········</li>
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21 ············value·{},21 ············value·{},
22 ··········o·HomVariableGroup·(missing·documentation)·=>·...,·default·value·{},22 ··········o·HomVariableGroup·(missing·documentation)·=>·...,·default·value·{},
23 ··········o·M2Precision·(missing·documentation)·=>·...,·default·value·53,23 ··········o·M2Precision·(missing·documentation)·=>·...,·default·value·53,
24 ··········o·OutputStyle·(missing·documentation)·=>·...,·default·value24 ··········o·OutputStyle·(missing·documentation)·=>·...,·default·value
25 ············"OutPoints",25 ············"OutPoints",
26 ··········o·RandomComplex·(missing·documentation)·=>·...,·default·value·{},26 ··········o·RandomComplex·(missing·documentation)·=>·...,·default·value·{},
27 ··········o·RandomReal·(missing·documentation)·=>·...,·default·value·{},27 ··········o·RandomReal·(missing·documentation)·=>·...,·default·value·{},
28 ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-1209936-0/0",·Option·to28 ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-1227713-0/0",·Option·to
29 ············change·directory·for·file·storage.29 ············change·directory·for·file·storage.
30 ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional30 ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional
31 ············output31 ············output
32 ····*·Outputs:32 ····*·Outputs:
33 ··········o·S0,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·solutions·to·the·target·system33 ··········o·S0,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·solutions·to·the·target·system
34 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*34 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
35 This·method·calls·Bertini·to·track·a·user-defined·homotopy.·The·user·needs·to35 This·method·calls·Bertini·to·track·a·user-defined·homotopy.·The·user·needs·to
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79 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;main_data&quot;</span>,·<span></span></span></li>79 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;main_data&quot;</span>,·<span></span></span></li>
80 ············<li><span><span·class="tt">NameSolutionsFile</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·NameSolutionsFile]-->80 ············<li><span><span·class="tt">NameSolutionsFile</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·NameSolutionsFile]-->
81 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;raw_solutions&quot;</span>,·<span></span></span></li>81 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;raw_solutions&quot;</span>,·<span></span></span></li>
82 ············<li><span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]-->82 ············<li><span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]-->
83 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;OutPoints&quot;</span>,·<span></span></span></li>83 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;OutPoints&quot;</span>,·<span></span></span></li>
84 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>84 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>
85 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>85 ············<li><span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span></li>
86 ············<li><span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;/tmp/M2-1209936-0/0&quot;</span>,·<span>Option·to·change·directory·for·file·storage.</span></span></li>86 ············<li><span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·&quot;/tmp/M2-1227713-0/0&quot;</span>,·<span>Option·to·change·directory·for·file·storage.</span></span></li>
87 ············<li><span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]-->87 ············<li><span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]-->
88 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span></li>88 <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span></li>
89 ············<li><span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span></li>89 ············<li><span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span></li>
90 ··········</ul>90 ··········</ul>
91 ········</li>91 ········</li>
92 ········<li>Outputs:··········<ul>92 ········<li>Outputs:··········<ul>
93 ············<li><span><span·class="tt">S</span>,·<span>a·<a·title="the·class·of·all·lists·--·{...}"·href="../../Macaulay2Doc/html/___List.html">list</a></span>,·a·list·of·points·that·are·contained·in·the·variety·of·F</span></li>93 ············<li><span><span·class="tt">S</span>,·<span>a·<a·title="the·class·of·all·lists·--·{...}"·href="../../Macaulay2Doc/html/___List.html">list</a></span>,·a·list·of·points·that·are·contained·in·the·variety·of·F</span></li>
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32 ············"OutPoints",32 ············"OutPoints",
33 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates33 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates
34 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real34 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real
35 ············number·or·random·complex·number35 ············number·or·random·complex·number
36 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates36 ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates
37 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real37 ············symbols/strings/variables·that·will·be·set·to·be·a·random·real
38 ············number·or·random·complex·number38 ············number·or·random·complex·number
39 ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-1209936-0/0",·Option·to39 ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-1227713-0/0",·Option·to
40 ············change·directory·for·file·storage.40 ············change·directory·for·file·storage.
41 ··········o·UseRegeneration·(missing·documentation)·=>·...,·default·value·-1,41 ··········o·UseRegeneration·(missing·documentation)·=>·...,·default·value·-1,
42 ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional42 ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional
43 ············output43 ············output
44 ····*·Outputs:44 ····*·Outputs:
45 ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·points·that·are·contained·in·the·variety·of·F45 ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·points·that·are·contained·in·the·variety·of·F
46 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*46 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
759 B
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=317 #:len=31
8 aW52ZXJzZVJpbmdBY3RvcnMoLi4uLFN1Yj0+Li4uKQ==8 aW52ZXJzZVJpbmdBY3RvcnMoLi4uLFN1Yj0+Li4uKQ==
9 #:len=2649 #:len=264
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjg0Niwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjg0Niwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaW52ZXJzZVJpbmdBY3RvcnMsU3ViXSwiaW52ZXJz11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaW52ZXJzZVJpbmdBY3RvcnMsU3ViXSwiaW52ZXJz
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76 i8·:·A·=·action(RI,S7)76 i8·:·A·=·action(RI,S7)
  
77 o8·=·Complex·with·15·actors77 o8·=·Complex·with·15·actors
  
78 o8·:·ActionOnComplex78 o8·:·ActionOnComplex
  
79 i9·:·elapsedTime·c·=·character·A79 i9·:·elapsedTime·c·=·character·A
80 ·--·.463062s·elapsed80 ·--·1.43588s·elapsed
  
81 o9·=·Character·over·R81 o9·=·Character·over·R
82 ······82 ······
83 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·|83 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·|
84 ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·|84 ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·|
85 ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·|85 ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·|
86 ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·|86 ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·|
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Offset 100, 15 lines modifiedOffset 100, 15 lines modified
100 i6·:·A=action(RI,S6)100 i6·:·A=action(RI,S6)
  
101 o6·=·Complex·with·11·actors101 o6·=·Complex·with·11·actors
  
102 o6·:·ActionOnComplex102 o6·:·ActionOnComplex
  
103 i7·:·elapsedTime·c=character·A103 i7·:·elapsedTime·c=character·A
104 ·--·.316343s·elapsed104 ·--·1.31834s·elapsed
  
105 o7·=·Character·over·R105 o7·=·Character·over·R
106 ······106 ······
107 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·|107 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·|
108 ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·|108 ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·|
109 ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·|109 ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·|
110 ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·|110 ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·|
1.16 KB
./usr/share/doc/Macaulay2/BettiCharacters/example-output/___Betti__Characters_sp__Example_sp3.out
    
Offset 187, 27 lines modifiedOffset 187, 27 lines modified
187 i19·:·A2·=·action(RI2,G,Sub=>false)187 i19·:·A2·=·action(RI2,G,Sub=>false)
  
188 o19·=·Complex·with·6·actors188 o19·=·Complex·with·6·actors
  
189 o19·:·ActionOnComplex189 o19·:·ActionOnComplex
  
190 i20·:·elapsedTime·a1·=·character·A1190 i20·:·elapsedTime·a1·=·character·A1
191 ·--·.640405s·elapsed191 ·--·2.13683s·elapsed
  
192 o20·=·Character·over·R192 o20·=·Character·over·R
193 ·······193 ·······
194 ······(0,·{0})·=>·|·1·1·1·1·1·1·|194 ······(0,·{0})·=>·|·1·1·1·1·1·1·|
195 ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|195 ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
196 ······(2,·{11})·=>·|·1·1·1·1·1·1·|196 ······(2,·{11})·=>·|·1·1·1·1·1·1·|
197 ······(2,·{13})·=>·|·1·1·1·1·1·1·|197 ······(2,·{13})·=>·|·1·1·1·1·1·1·|
  
198 o20·:·Character198 o20·:·Character
  
199 i21·:·elapsedTime·a2·=·character·A2199 i21·:·elapsedTime·a2·=·character·A2
200 ·--·33.3238s·elapsed200 ·--·64.7245s·elapsed
  
201 o21·=·Character·over·R201 o21·=·Character·over·R
202 ·······202 ·······
203 ······(0,·{0})·=>·|·1·1·1·1·1·1·|203 ······(0,·{0})·=>·|·1·1·1·1·1·1·|
204 ······(1,·{16})·=>·|·6·2·0·0·-1·-1·|204 ······(1,·{16})·=>·|·6·2·0·0·-1·-1·|
205 ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|205 ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
206 ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|206 ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
Offset 297, 15 lines modifiedOffset 297, 15 lines modified
297 i31·:·B·=·action(M,G,Sub=>false)297 i31·:·B·=·action(M,G,Sub=>false)
  
298 o31·=·Module·with·6·actors298 o31·=·Module·with·6·actors
  
299 o31·:·ActionOnGradedModule299 o31·:·ActionOnGradedModule
  
300 i32·:·elapsedTime·b·=·character(B,21)300 i32·:·elapsedTime·b·=·character(B,21)
301 ·--·19.2392s·elapsed301 ·--·29.1991s·elapsed
  
302 o32·=·Character·over·R302 o32·=·Character·over·R
303 ·······303 ·······
304 ······(0,·{21})·=>·|·1·1·1·1·1·1·|304 ······(0,·{21})·=>·|·1·1·1·1·1·1·|
  
305 o32·:·Character305 o32·:·Character
  
1.14 KB
./usr/share/doc/Macaulay2/BettiCharacters/html/___Betti__Characters_sp__Example_sp1.html
    
Offset 162, 15 lines modifiedOffset 162, 15 lines modified
  
162 o8·:·ActionOnComplex</code></pre>162 o8·:·ActionOnComplex</code></pre>
163 ············</td>163 ············</td>
164 ··········</tr>164 ··········</tr>
165 ··········<tr>165 ··········<tr>
166 ············<td>166 ············<td>
167 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·c·=·character·A167 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·c·=·character·A
168 ·--·.463062s·elapsed168 ·--·1.43588s·elapsed
  
169 o9·=·Character·over·R169 o9·=·Character·over·R
170 ······170 ······
171 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·|171 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·|
172 ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·|172 ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·|
173 ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·|173 ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·|
174 ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·|174 ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·|
467 B
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Offset 91, 15 lines modifiedOffset 91, 15 lines modified
91 o7·:·List91 o7·:·List
92 i8·:·A·=·action(RI,S7)92 i8·:·A·=·action(RI,S7)
  
93 o8·=·Complex·with·15·actors93 o8·=·Complex·with·15·actors
  
94 o8·:·ActionOnComplex94 o8·:·ActionOnComplex
95 i9·:·elapsedTime·c·=·character·A95 i9·:·elapsedTime·c·=·character·A
96 ·--·.463062s·elapsed96 ·--·1.43588s·elapsed
  
97 o9·=·Character·over·R97 o9·=·Character·over·R
  
98 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·|98 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·|
99 ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·|99 ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·|
100 ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·|100 ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·|
101 ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·|101 ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·|
1.04 KB
./usr/share/doc/Macaulay2/BettiCharacters/html/___Betti__Characters_sp__Example_sp2.html
    
Offset 180, 15 lines modifiedOffset 180, 15 lines modified
  
180 o6·:·ActionOnComplex</code></pre>180 o6·:·ActionOnComplex</code></pre>
181 ············</td>181 ············</td>
182 ··········</tr>182 ··········</tr>
183 ··········<tr>183 ··········<tr>
184 ············<td>184 ············<td>
185 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·c=character·A185 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·c=character·A
186 ·--·.316343s·elapsed186 ·--·1.31834s·elapsed
  
187 o7·=·Character·over·R187 o7·=·Character·over·R
188 ······188 ······
189 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·|189 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·|
190 ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·|190 ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·|
191 ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·|191 ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·|
192 ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·|192 ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·|
416 B
html2text {}
    
Offset 113, 15 lines modifiedOffset 113, 15 lines modified
113 o5·:·List113 o5·:·List
114 i6·:·A=action(RI,S6)114 i6·:·A=action(RI,S6)
  
115 o6·=·Complex·with·11·actors115 o6·=·Complex·with·11·actors
  
116 o6·:·ActionOnComplex116 o6·:·ActionOnComplex
117 i7·:·elapsedTime·c=character·A117 i7·:·elapsedTime·c=character·A
118 ·--·.316343s·elapsed118 ·--·1.31834s·elapsed
  
119 o7·=·Character·over·R119 o7·=·Character·over·R
  
120 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·|120 ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·|
121 ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·|121 ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·|
122 ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·|122 ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·|
123 ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·|123 ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·|
2.46 KB
./usr/share/doc/Macaulay2/BettiCharacters/html/___Betti__Characters_sp__Example_sp3.html
    
Offset 310, 30 lines modifiedOffset 310, 30 lines modified
  
310 o19·:·ActionOnComplex</code></pre>310 o19·:·ActionOnComplex</code></pre>
311 ············</td>311 ············</td>
312 ··········</tr>312 ··········</tr>
313 ··········<tr>313 ··········<tr>
314 ············<td>314 ············<td>
315 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·a1·=·character·A1315 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·a1·=·character·A1
316 ·--·.640405s·elapsed316 ·--·2.13683s·elapsed
  
317 o20·=·Character·over·R317 o20·=·Character·over·R
318 ·······318 ·······
319 ······(0,·{0})·=>·|·1·1·1·1·1·1·|319 ······(0,·{0})·=>·|·1·1·1·1·1·1·|
320 ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|320 ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
321 ······(2,·{11})·=>·|·1·1·1·1·1·1·|321 ······(2,·{11})·=>·|·1·1·1·1·1·1·|
322 ······(2,·{13})·=>·|·1·1·1·1·1·1·|322 ······(2,·{13})·=>·|·1·1·1·1·1·1·|
  
323 o20·:·Character</code></pre>323 o20·:·Character</code></pre>
324 ············</td>324 ············</td>
325 ··········</tr>325 ··········</tr>
326 ··········<tr>326 ··········<tr>
327 ············<td>327 ············<td>
328 ··············<pre><code·class="language-macaulay2">i21·:·elapsedTime·a2·=·character·A2328 ··············<pre><code·class="language-macaulay2">i21·:·elapsedTime·a2·=·character·A2
329 ·--·33.3238s·elapsed329 ·--·64.7245s·elapsed
  
330 o21·=·Character·over·R330 o21·=·Character·over·R
331 ·······331 ·······
332 ······(0,·{0})·=>·|·1·1·1·1·1·1·|332 ······(0,·{0})·=>·|·1·1·1·1·1·1·|
333 ······(1,·{16})·=>·|·6·2·0·0·-1·-1·|333 ······(1,·{16})·=>·|·6·2·0·0·-1·-1·|
334 ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|334 ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
335 ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|335 ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
Offset 467, 15 lines modifiedOffset 467, 15 lines modified
  
467 o31·:·ActionOnGradedModule</code></pre>467 o31·:·ActionOnGradedModule</code></pre>
468 ············</td>468 ············</td>
469 ··········</tr>469 ··········</tr>
470 ··········<tr>470 ··········<tr>
471 ············<td>471 ············<td>
472 ··············<pre><code·class="language-macaulay2">i32·:·elapsedTime·b·=·character(B,21)472 ··············<pre><code·class="language-macaulay2">i32·:·elapsedTime·b·=·character(B,21)
473 ·--·19.2392s·elapsed473 ·--·29.1991s·elapsed
  
474 o32·=·Character·over·R474 o32·=·Character·over·R
475 ·······475 ·······
476 ······(0,·{21})·=>·|·1·1·1·1·1·1·|476 ······(0,·{21})·=>·|·1·1·1·1·1·1·|
  
477 o32·:·Character</code></pre>477 o32·:·Character</code></pre>
478 ············</td>478 ············</td>
1.02 KB
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Offset 192, 26 lines modifiedOffset 192, 26 lines modified
192 o18·:·ActionOnComplex192 o18·:·ActionOnComplex
193 i19·:·A2·=·action(RI2,G,Sub=>false)193 i19·:·A2·=·action(RI2,G,Sub=>false)
  
194 o19·=·Complex·with·6·actors194 o19·=·Complex·with·6·actors
  
195 o19·:·ActionOnComplex195 o19·:·ActionOnComplex
196 i20·:·elapsedTime·a1·=·character·A1196 i20·:·elapsedTime·a1·=·character·A1
197 ·--·.640405s·elapsed197 ·--·2.13683s·elapsed
  
198 o20·=·Character·over·R198 o20·=·Character·over·R
  
199 ······(0,·{0})·=>·|·1·1·1·1·1·1·|199 ······(0,·{0})·=>·|·1·1·1·1·1·1·|
200 ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|200 ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
201 ······(2,·{11})·=>·|·1·1·1·1·1·1·|201 ······(2,·{11})·=>·|·1·1·1·1·1·1·|
202 ······(2,·{13})·=>·|·1·1·1·1·1·1·|202 ······(2,·{13})·=>·|·1·1·1·1·1·1·|
  
203 o20·:·Character203 o20·:·Character
204 i21·:·elapsedTime·a2·=·character·A2204 i21·:·elapsedTime·a2·=·character·A2
205 ·--·33.3238s·elapsed205 ·--·64.7245s·elapsed
  
206 o21·=·Character·over·R206 o21·=·Character·over·R
  
207 ······(0,·{0})·=>·|·1·1·1·1·1·1·|207 ······(0,·{0})·=>·|·1·1·1·1·1·1·|
208 ······(1,·{16})·=>·|·6·2·0·0·-1·-1·|208 ······(1,·{16})·=>·|·6·2·0·0·-1·-1·|
209 ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|209 ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
210 ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|210 ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·|
Offset 308, 15 lines modifiedOffset 308, 15 lines modified
308 i30·:·M·=·Is2·/·I2;308 i30·:·M·=·Is2·/·I2;
309 i31·:·B·=·action(M,G,Sub=>false)309 i31·:·B·=·action(M,G,Sub=>false)
  
310 o31·=·Module·with·6·actors310 o31·=·Module·with·6·actors
  
311 o31·:·ActionOnGradedModule311 o31·:·ActionOnGradedModule
312 i32·:·elapsedTime·b·=·character(B,21)312 i32·:·elapsedTime·b·=·character(B,21)
313 ·--·19.2392s·elapsed313 ·--·29.1991s·elapsed
  
314 o32·=·Character·over·R314 o32·=·Character·over·R
  
315 ······(0,·{21})·=>·|·1·1·1·1·1·1·|315 ······(0,·{21})·=>·|·1·1·1·1·1·1·|
  
316 o32·:·Character316 o32·:·Character
317 i33·:·b/T317 i33·:·b/T
724 B
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724 B
./usr/share/doc/Macaulay2/Binomials/dump/rawdocumentation.dump
    
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741 B
./usr/share/doc/Macaulay2/BoijSoederberg/dump/rawdocumentation.dump
    
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762 B
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728 B
./usr/share/doc/Macaulay2/BooleanGB/dump/rawdocumentation.dump
    
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723 B
./usr/share/doc/Macaulay2/Bruns/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/Bruns/example-output/_bruns.out
    
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230 ··········0:·1·.·.·.·.230 ··········0:·1·.·.·.·.
231 ··········1:·.·4·2·.·.231 ··········1:·.·4·2·.·.
232 ··········2:·.·1·6·5·1232 ··········2:·.·1·6·5·1
  
233 o22·:·BettiTally233 o22·:·BettiTally
  
234 i23·:·time·j=bruns·F.dd_3;234 i23·:·time·j=bruns·F.dd_3;
235 ·--·used·0.177725s·(cpu);·0.148017s·(thread);·0s·(gc)235 ·--·used·0.226441s·(cpu);·0.176114s·(thread);·0s·(gc)
  
236 o23·:·Ideal·of·S236 o23·:·Ideal·of·S
  
237 i24·:·betti·res·j237 i24·:·betti·res·j
  
238 ·············0·1·2·3·4238 ·············0·1·2·3·4
239 o24·=·total:·1·3·6·5·1239 o24·=·total:·1·3·6·5·1
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./usr/share/doc/Macaulay2/Bruns/html/_bruns.html
    
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380 o22·:·BettiTally</code></pre>380 o22·:·BettiTally</code></pre>
381 ············</td>381 ············</td>
382 ··········</tr>382 ··········</tr>
383 ··········<tr>383 ··········<tr>
384 ············<td>384 ············<td>
385 ··············<pre><code·class="language-macaulay2">i23·:·time·j=bruns·F.dd_3;385 ··············<pre><code·class="language-macaulay2">i23·:·time·j=bruns·F.dd_3;
386 ·--·used·0.177725s·(cpu);·0.148017s·(thread);·0s·(gc)386 ·--·used·0.226441s·(cpu);·0.176114s·(thread);·0s·(gc)
  
387 o23·:·Ideal·of·S</code></pre>387 o23·:·Ideal·of·S</code></pre>
388 ············</td>388 ············</td>
389 ··········</tr>389 ··········</tr>
390 ··········<tr>390 ··········<tr>
391 ············<td>391 ············<td>
392 ··············<pre><code·class="language-macaulay2">i24·:·betti·res·j392 ··············<pre><code·class="language-macaulay2">i24·:·betti·res·j
413 B
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230 o22·=·total:·1·5·8·5·1230 o22·=·total:·1·5·8·5·1
231 ··········0:·1·.·.·.·.231 ··········0:·1·.·.·.·.
232 ··········1:·.·4·2·.·.232 ··········1:·.·4·2·.·.
233 ··········2:·.·1·6·5·1233 ··········2:·.·1·6·5·1
  
234 o22·:·BettiTally234 o22·:·BettiTally
235 i23·:·time·j=bruns·F.dd_3;235 i23·:·time·j=bruns·F.dd_3;
236 ·--·used·0.177725s·(cpu);·0.148017s·(thread);·0s·(gc)236 ·--·used·0.226441s·(cpu);·0.176114s·(thread);·0s·(gc)
  
237 o23·:·Ideal·of·S237 o23·:·Ideal·of·S
238 i24·:·betti·res·j238 i24·:·betti·res·j
  
239 ·············0·1·2·3·4239 ·············0·1·2·3·4
240 o24·=·total:·1·3·6·5·1240 o24·=·total:·1·3·6·5·1
241 ··········0:·1·.·.·.·.241 ··········0:·1·.·.·.·.
763 B
./usr/share/doc/Macaulay2/CellularResolutions/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/CellularResolutions/example-output/_cell__Complex_lp__Ring_cm__Polyhedral__Complex_rp.out
    
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12 i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4};12 i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4};
  
13 i7·:·C·=·cellComplex(R,F);13 i7·:·C·=·cellComplex(R,F);
  
14 i8·:·facePoset·C14 i8·:·facePoset·C
  
15 o8·=·Relation·Matrix:·|·1·0·0·0·0·0·1·0·1·0·0·1·0·0·0·1·1·|15 o8·=·Relation·Matrix:·|·1·0·0·0·0·1·0·0·1·0·1·0·0·0·1·0·1·|
 16 ······················|·0·1·0·0·0·0·1·0·1·0·0·1·0·0·0·1·1·|
16 ······················|·0·1·0·0·0·0·0·1·0·1·1·1·0·1·1·1·1·|17 ······················|·0·0·1·0·0·0·0·1·0·1·1·1·0·1·1·1·1·|
17 ······················|·0·0·1·0·0·1·0·1·0·0·0·0·1·1·1·0·0·|18 ······················|·0·0·0·1·0·1·0·1·0·0·0·0·1·1·1·0·0·|
18 ······················|·0·0·0·1·0·0·1·0·0·1·0·0·1·1·0·1·0·|19 ······················|·0·0·0·0·1·0·1·0·0·1·0·0·1·1·0·1·0·|
19 ······················|·0·0·0·0·1·1·0·0·1·0·1·0·0·0·1·0·1·| 
20 ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·0·|20 ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·0·|
21 ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·|21 ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·|
22 ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·1·1·0·0·|22 ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·1·1·0·0·|
23 ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·1·|23 ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·1·|
24 ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·0·|24 ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·0·|
25 ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·|25 ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·|
26 ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·1·|26 ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·1·|
621 B
./usr/share/doc/Macaulay2/CellularResolutions/example-output/_cells_lp__Z__Z_cm__Cell__Complex_rp.out
    
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10 i5·:·exy·=·newSimplexCell·{vx,vy};10 i5·:·exy·=·newSimplexCell·{vx,vy};
  
11 i6·:·C·=·cellComplex(R,{exy,vz});11 i6·:·C·=·cellComplex(R,{exy,vz});
  
12 i7·:·cells(0,C)12 i7·:·cells(0,C)
  
13 o7·=·{Cell·of·dimension·0·with·label·z,·Cell·of·dimension·0·with·label·x,13 o7·=·{Cell·of·dimension·0·with·label·x,·Cell·of·dimension·0·with·label·z,
14 ·····------------------------------------------------------------------------14 ·····------------------------------------------------------------------------
15 ·····Cell·of·dimension·0·with·label·y}15 ·····Cell·of·dimension·0·with·label·y}
  
16 o7·:·List16 o7·:·List
  
17 i8·:·cells(1,C)17 i8·:·cells(1,C)
  
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./usr/share/doc/Macaulay2/CellularResolutions/html/_cell__Complex_lp__Ring_cm__Polyhedral__Complex_rp.html
    
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112 ··············<pre><code·class="language-macaulay2">i7·:·C·=·cellComplex(R,F);</code></pre>112 ··············<pre><code·class="language-macaulay2">i7·:·C·=·cellComplex(R,F);</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i8·:·facePoset·C117 ··············<pre><code·class="language-macaulay2">i8·:·facePoset·C
  
118 o8·=·Relation·Matrix:·|·1·0·0·0·0·0·1·0·1·0·0·1·0·0·0·1·1·|118 o8·=·Relation·Matrix:·|·1·0·0·0·0·1·0·0·1·0·1·0·0·0·1·0·1·|
 119 ······················|·0·1·0·0·0·0·1·0·1·0·0·1·0·0·0·1·1·|
119 ······················|·0·1·0·0·0·0·0·1·0·1·1·1·0·1·1·1·1·|120 ······················|·0·0·1·0·0·0·0·1·0·1·1·1·0·1·1·1·1·|
120 ······················|·0·0·1·0·0·1·0·1·0·0·0·0·1·1·1·0·0·|121 ······················|·0·0·0·1·0·1·0·1·0·0·0·0·1·1·1·0·0·|
121 ······················|·0·0·0·1·0·0·1·0·0·1·0·0·1·1·0·1·0·|122 ······················|·0·0·0·0·1·0·1·0·0·1·0·0·1·1·0·1·0·|
122 ······················|·0·0·0·0·1·1·0·0·1·0·1·0·0·0·1·0·1·| 
123 ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·0·|123 ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·0·|
124 ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·|124 ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·|
125 ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·1·1·0·0·|125 ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·1·1·0·0·|
126 ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·1·|126 ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·1·|
127 ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·0·|127 ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·0·|
128 ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·|128 ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·|
129 ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·1·|129 ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·1·|
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html2text {}
    
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26 i3·:·P2·=·convexHull·matrix·{{2,-2,0},{1,1,0}};26 i3·:·P2·=·convexHull·matrix·{{2,-2,0},{1,1,0}};
27 i4·:·P3·=·convexHull·matrix·{{-2,-2,0},{1,-1,0}};27 i4·:·P3·=·convexHull·matrix·{{-2,-2,0},{1,-1,0}};
28 i5·:·P4·=·convexHull·matrix·{{-2,2,0},{-1,-1,0}};28 i5·:·P4·=·convexHull·matrix·{{-2,2,0},{-1,-1,0}};
29 i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4};29 i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4};
30 i7·:·C·=·cellComplex(R,F);30 i7·:·C·=·cellComplex(R,F);
31 i8·:·facePoset·C31 i8·:·facePoset·C
  
32 o8·=·Relation·Matrix:·|·1·0·0·0·0·0·1·0·1·0·0·1·0·0·0·1·1·|32 o8·=·Relation·Matrix:·|·1·0·0·0·0·1·0·0·1·0·1·0·0·0·1·0·1·|
 33 ······················|·0·1·0·0·0·0·1·0·1·0·0·1·0·0·0·1·1·|
33 ······················|·0·1·0·0·0·0·0·1·0·1·1·1·0·1·1·1·1·|34 ······················|·0·0·1·0·0·0·0·1·0·1·1·1·0·1·1·1·1·|
34 ······················|·0·0·1·0·0·1·0·1·0·0·0·0·1·1·1·0·0·|35 ······················|·0·0·0·1·0·1·0·1·0·0·0·0·1·1·1·0·0·|
35 ······················|·0·0·0·1·0·0·1·0·0·1·0·0·1·1·0·1·0·|36 ······················|·0·0·0·0·1·0·1·0·0·1·0·0·1·1·0·1·0·|
36 ······················|·0·0·0·0·1·1·0·0·1·0·1·0·0·0·1·0·1·| 
37 ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·0·|37 ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·0·|
38 ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·|38 ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·0·|
39 ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·1·1·0·0·|39 ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·1·1·0·0·|
40 ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·1·|40 ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·1·|
41 ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·0·|41 ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·0·|
42 ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·|42 ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·0·1·|
43 ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·1·|43 ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·1·1·|
1.34 KB
./usr/share/doc/Macaulay2/CellularResolutions/html/_cells_lp__Z__Z_cm__Cell__Complex_rp.html
    
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103 ··············<pre><code·class="language-macaulay2">i6·:·C·=·cellComplex(R,{exy,vz});</code></pre>103 ··············<pre><code·class="language-macaulay2">i6·:·C·=·cellComplex(R,{exy,vz});</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i7·:·cells(0,C)108 ··············<pre><code·class="language-macaulay2">i7·:·cells(0,C)
  
109 o7·=·{Cell·of·dimension·0·with·label·z,·Cell·of·dimension·0·with·label·x,109 o7·=·{Cell·of·dimension·0·with·label·x,·Cell·of·dimension·0·with·label·z,
110 ·····------------------------------------------------------------------------110 ·····------------------------------------------------------------------------
111 ·····Cell·of·dimension·0·with·label·y}111 ·····Cell·of·dimension·0·with·label·y}
  
112 o7·:·List</code></pre>112 o7·:·List</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
577 B
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Offset 19, 15 lines modifiedOffset 19, 15 lines modified
19 i2·:·vx·=·newSimplexCell({},x);19 i2·:·vx·=·newSimplexCell({},x);
20 i3·:·vy·=·newSimplexCell({},y);20 i3·:·vy·=·newSimplexCell({},y);
21 i4·:·vz·=·newSimplexCell({},z);21 i4·:·vz·=·newSimplexCell({},z);
22 i5·:·exy·=·newSimplexCell·{vx,vy};22 i5·:·exy·=·newSimplexCell·{vx,vy};
23 i6·:·C·=·cellComplex(R,{exy,vz});23 i6·:·C·=·cellComplex(R,{exy,vz});
24 i7·:·cells(0,C)24 i7·:·cells(0,C)
  
25 o7·=·{Cell·of·dimension·0·with·label·z,·Cell·of·dimension·0·with·label·x,25 o7·=·{Cell·of·dimension·0·with·label·x,·Cell·of·dimension·0·with·label·z,
26 ·····------------------------------------------------------------------------26 ·····------------------------------------------------------------------------
27 ·····Cell·of·dimension·0·with·label·y}27 ·····Cell·of·dimension·0·with·label·y}
  
28 o7·:·List28 o7·:·List
29 i8·:·cells(1,C)29 i8·:·cells(1,C)
  
30 o8·=·{Cell·of·dimension·1·with·label·x*y}30 o8·=·{Cell·of·dimension·1·with·label·x*y}
762 B
./usr/share/doc/Macaulay2/ChainComplexExtras/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=307 #:len=30
8 SG9tKENoYWluQ29tcGxleCxDaGFpbkNvbXBsZXgp8 SG9tKENoYWluQ29tcGxleCxDaGFpbkNvbXBsZXgp
9 #:len=14769 #:len=1476
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ3JlYXRlIHRoZSBob21vbW9ycGhpc20g10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ3JlYXRlIHRoZSBob21vbW9ycGhpc20g
11 Y29tcGxleCBvZiBhIHBhaXIgb2YgY2hhaW4gY29tcGxleGVzLiIsICJsaW5lbnVtIiA9PiA4MDYs11 Y29tcGxleCBvZiBhIHBhaXIgb2YgY2hhaW4gY29tcGxleGVzLiIsICJsaW5lbnVtIiA9PiA4MDYs
494 B
./usr/share/doc/Macaulay2/ChainComplexExtras/example-output/_minimize_lp__Chain__Complex_rp.out
    
Offset 63, 15 lines modifiedOffset 63, 15 lines modified
63 o11·:·ChainComplex63 o11·:·ChainComplex
  
64 i12·:·isMinimalChainComplex·E64 i12·:·isMinimalChainComplex·E
  
65 o12·=·false65 o12·=·false
  
66 i13·:·time·m·=·minimize·(E[1]);66 i13·:·time·m·=·minimize·(E[1]);
67 ·--·used·0.218774s·(cpu);·0.175811s·(thread);·0s·(gc)67 ·--·used·0.25252s·(cpu);·0.199081s·(thread);·0s·(gc)
  
68 i14·:·isQuasiIsomorphism·m68 i14·:·isQuasiIsomorphism·m
  
69 o14·=·true69 o14·=·true
  
70 i15·:·E[1]·==·source·m70 i15·:·E[1]·==·source·m
  
949 B
./usr/share/doc/Macaulay2/ChainComplexExtras/example-output/_resolution__Of__Chain__Complex.out
    
Offset 27, 18 lines modifiedOffset 27, 18 lines modified
27 i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5);27 i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5);
  
28 i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);28 i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);
  
29 i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S));29 i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S));
  
30 i8·:·time·m·=·resolutionOfChainComplex·C;30 i8·:·time·m·=·resolutionOfChainComplex·C;
31 ·--·used·0.0826138s·(cpu);·0.0836316s·(thread);·0s·(gc)31 ·--·used·0.106176s·(cpu);·0.106974s·(thread);·0s·(gc)
  
32 i9·:·time·n·=·cartanEilenbergResolution·C;32 i9·:·time·n·=·cartanEilenbergResolution·C;
33 ·--·used·0.165669s·(cpu);·0.125635s·(thread);·0s·(gc)33 ·--·used·0.195442s·(cpu);·0.137064s·(thread);·0s·(gc)
  
34 i10·:·betti·source·m34 i10·:·betti·source·m
  
35 ·············0··1··2···3···4···5···6···735 ·············0··1··2···3···4···5···6···7
36 o10·=·total:·1·19·80·181·312·484·447·15636 o10·=·total:·1·19·80·181·312·484·447·156
37 ··········0:·1··3··3···1···.···.···.···.37 ··········0:·1··3··3···1···.···.···.···.
38 ··········1:·.··.··1···3···3···.···.···.38 ··········1:·.··.··1···3···3···.···.···.
1.27 KB
./usr/share/doc/Macaulay2/ChainComplexExtras/html/_minimize_lp__Chain__Complex_rp.html
    
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181 ········<div>181 ········<div>
182 ··········<p>Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero,·and·thus·is·part·of·the·minimization.</p>182 ··········<p>Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero,·and·thus·is·part·of·the·minimization.</p>
183 ········</div>183 ········</div>
184 ········<table·class="examples">184 ········<table·class="examples">
185 ··········<tr>185 ··········<tr>
186 ············<td>186 ············<td>
187 ··············<pre><code·class="language-macaulay2">i13·:·time·m·=·minimize·(E[1]);187 ··············<pre><code·class="language-macaulay2">i13·:·time·m·=·minimize·(E[1]);
188 ·--·used·0.218774s·(cpu);·0.175811s·(thread);·0s·(gc)</code></pre>188 ·--·used·0.25252s·(cpu);·0.199081s·(thread);·0s·(gc)</code></pre>
189 ············</td>189 ············</td>
190 ··········</tr>190 ··········</tr>
191 ··········<tr>191 ··········<tr>
192 ············<td>192 ············<td>
193 ··············<pre><code·class="language-macaulay2">i14·:·isQuasiIsomorphism·m193 ··············<pre><code·class="language-macaulay2">i14·:·isQuasiIsomorphism·m
  
194 o14·=·true</code></pre>194 o14·=·true</code></pre>
472 B
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81 o11·:·ChainComplex81 o11·:·ChainComplex
82 i12·:·isMinimalChainComplex·E82 i12·:·isMinimalChainComplex·E
  
83 o12·=·false83 o12·=·false
84 Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero,84 Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero,
85 and·thus·is·part·of·the·minimization.85 and·thus·is·part·of·the·minimization.
86 i13·:·time·m·=·minimize·(E[1]);86 i13·:·time·m·=·minimize·(E[1]);
87 ·--·used·0.218774s·(cpu);·0.175811s·(thread);·0s·(gc)87 ·--·used·0.25252s·(cpu);·0.199081s·(thread);·0s·(gc)
88 i14·:·isQuasiIsomorphism·m88 i14·:·isQuasiIsomorphism·m
  
89 o14·=·true89 o14·=·true
90 i15·:·E[1]·==·source·m90 i15·:·E[1]·==·source·m
  
91 o15·=·true91 o15·=·true
92 i16·:·E'·=·target·m92 i16·:·E'·=·target·m
1.97 KB
./usr/share/doc/Macaulay2/ChainComplexExtras/html/_resolution__Of__Chain__Complex.html
    
Offset 129, 21 lines modifiedOffset 129, 21 lines modified
129 ············<td>129 ············<td>
130 ··············<pre><code·class="language-macaulay2">i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S));</code></pre>130 ··············<pre><code·class="language-macaulay2">i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S));</code></pre>
131 ············</td>131 ············</td>
132 ··········</tr>132 ··········</tr>
133 ··········<tr>133 ··········<tr>
134 ············<td>134 ············<td>
135 ··············<pre><code·class="language-macaulay2">i8·:·time·m·=·resolutionOfChainComplex·C;135 ··············<pre><code·class="language-macaulay2">i8·:·time·m·=·resolutionOfChainComplex·C;
136 ·--·used·0.0826138s·(cpu);·0.0836316s·(thread);·0s·(gc)</code></pre>136 ·--·used·0.106176s·(cpu);·0.106974s·(thread);·0s·(gc)</code></pre>
137 ············</td>137 ············</td>
138 ··········</tr>138 ··········</tr>
139 ··········<tr>139 ··········<tr>
140 ············<td>140 ············<td>
141 ··············<pre><code·class="language-macaulay2">i9·:·time·n·=·cartanEilenbergResolution·C;141 ··············<pre><code·class="language-macaulay2">i9·:·time·n·=·cartanEilenbergResolution·C;
142 ·--·used·0.165669s·(cpu);·0.125635s·(thread);·0s·(gc)</code></pre>142 ·--·used·0.195442s·(cpu);·0.137064s·(thread);·0s·(gc)</code></pre>
143 ············</td>143 ············</td>
144 ··········</tr>144 ··········</tr>
145 ··········<tr>145 ··········<tr>
146 ············<td>146 ············<td>
147 ··············<pre><code·class="language-macaulay2">i10·:·betti·source·m147 ··············<pre><code·class="language-macaulay2">i10·:·betti·source·m
  
148 ·············0··1··2···3···4···5···6···7148 ·············0··1··2···3···4···5···6···7
841 B
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49 o4·:·RingMap·R·<--·S49 o4·:·RingMap·R·<--·S
50 i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5);50 i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5);
51 i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);51 i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);
52 i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-52 i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-
53 1),mods_i,substitute(matrix·C.dd_i,S));53 1),mods_i,substitute(matrix·C.dd_i,S));
54 i8·:·time·m·=·resolutionOfChainComplex·C;54 i8·:·time·m·=·resolutionOfChainComplex·C;
55 ·--·used·0.0826138s·(cpu);·0.0836316s·(thread);·0s·(gc)55 ·--·used·0.106176s·(cpu);·0.106974s·(thread);·0s·(gc)
56 i9·:·time·n·=·cartanEilenbergResolution·C;56 i9·:·time·n·=·cartanEilenbergResolution·C;
57 ·--·used·0.165669s·(cpu);·0.125635s·(thread);·0s·(gc)57 ·--·used·0.195442s·(cpu);·0.137064s·(thread);·0s·(gc)
58 i10·:·betti·source·m58 i10·:·betti·source·m
  
59 ·············0··1··2···3···4···5···6···759 ·············0··1··2···3···4···5···6···7
60 o10·=·total:·1·19·80·181·312·484·447·15660 o10·=·total:·1·19·80·181·312·484·447·156
61 ··········0:·1··3··3···1···.···.···.···.61 ··········0:·1··3··3···1···.···.···.···.
62 ··········1:·.··.··1···3···3···.···.···.62 ··········1:·.··.··1···3···3···.···.···.
63 ··········2:·.··1··3···3···2···.···.···.63 ··········2:·.··1··3···3···2···.···.···.
785 B
./usr/share/doc/Macaulay2/ChainComplexOperations/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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7 #:len=417 #:len=41
8 cmV2ZXJzZUZhY3RvcnMoQ2hhaW5Db21wbGV4LENoYWluQ29tcGxleCk=8 cmV2ZXJzZUZhY3RvcnMoQ2hhaW5Db21wbGV4LENoYWluQ29tcGxleCk=
9 #:len=3359 #:len=335
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjE0LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjE0LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyZXZlcnNlRmFjdG9ycyxDaGFpbkNvbXBsZXgsQ2hh11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyZXZlcnNlRmFjdG9ycyxDaGFpbkNvbXBsZXgsQ2hh
752 B
./usr/share/doc/Macaulay2/CharacteristicClasses/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=187 #:len=18
8 TXVsdGlQcm9qQ29vcmRSaW5n8 TXVsdGlQcm9qQ29vcmRSaW5n
9 #:len=22069 #:len=2206
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQSBxdWljayB3YXkgdG8gYnVpbGQgdGhl10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQSBxdWljayB3YXkgdG8gYnVpbGQgdGhl
11 IGNvb3JkaW5hdGUgcmluZyBvZiBhIHByb2R1Y3Qgb2YgcHJvamVjdGl2ZSBzcGFjZXMiLCAibGlu11 IGNvb3JkaW5hdGUgcmluZyBvZiBhIHByb2R1Y3Qgb2YgcHJvamVjdGl2ZSBzcGFjZXMiLCAibGlu
1.05 KB
./usr/share/doc/Macaulay2/CharacteristicClasses/example-output/___C__S__M.out
    
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83 ··············2··············283 ··············2··············2
84 o14·=·ideal·(x·x··-·x·x·x·,·x·x·)84 o14·=·ideal·(x·x··-·x·x·x·,·x·x·)
85 ··············0·3····1·2·4···2·585 ··············0·3····1·2·4···2·5
  
86 o14·:·Ideal·of·R86 o14·:·Ideal·of·R
  
87 i15·:·time·csmK=CSM(A,K)87 i15·:·time·csmK=CSM(A,K)
88 ·--·used·1.38254s·(cpu);·0.374939s·(thread);·0s·(gc)88 ·--·used·2.3478s·(cpu);·0.4198s·(thread);·0s·(gc)
  
89 ········2·2·····2·········2····2············289 ········2·2·····2·········2····2············2
90 o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h90 o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h
91 ········1·2·····1·2·····1·2····1·····1·2····291 ········1·2·····1·2·····1·2····1·····1·2····2
  
92 o15·:·A92 o15·:·A
  
Offset 124, 15 lines modifiedOffset 124, 15 lines modified
124 ········2·2·····2·········2·····2·············2124 ········2·2·····2·········2·····2·············2
125 o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h125 o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h
126 ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2126 ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2
  
127 o21·:·A127 o21·:·A
  
128 i22·:·time·CSM(A,K,m)128 i22·:·time·CSM(A,K,m)
129 ·--·used·0.0478725s·(cpu);·0.0487251s·(thread);·0s·(gc)129 ·--·used·0.222445s·(cpu);·0.0515015s·(thread);·0s·(gc)
  
130 ········2·2·····2·········2····2············2130 ········2·2·····2·········2····2············2
131 o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h131 o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h
132 ········1·2·····1·2·····1·2····1·····1·2····2132 ········1·2·····1·2·····1·2····1·····1·2····2
  
133 o22·:·A133 o22·:·A
  
1.35 KB
./usr/share/doc/Macaulay2/CharacteristicClasses/example-output/___Check__Smooth.out
    
Offset 9, 28 lines modifiedOffset 9, 28 lines modified
9 i2·:·U·=·toricProjectiveSpace·79 i2·:·U·=·toricProjectiveSpace·7
  
10 o2·=·U10 o2·=·U
  
11 o2·:·NormalToricVariety11 o2·:·NormalToricVariety
  
12 i3·:·time·CSM·U12 i3·:·time·CSM·U
13 ·--·used·0.233576s·(cpu);·0.190751s·(thread);·0s·(gc)13 ·--·used·0.190961s·(cpu);·0.153353s·(thread);·0s·(gc)
  
14 ·······7······6······5······4······3······214 ·······7······6······5······4······3······2
15 o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·115 o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1
16 ·······7······7······7······7······7······7·····716 ·······7······7······7······7······7······7·····7
  
17 ················································ZZ[x·..x·]17 ················································ZZ[x·..x·]
18 ····················································0···718 ····················································0···7
19 o3·:·-----------------------------------------------------------------------------------------------19 o3·:·-----------------------------------------------------------------------------------------------
20 ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·)20 ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·)
21 ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····721 ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7
  
22 i4·:·time·CSM(U,CheckSmooth=>false)22 i4·:·time·CSM(U,CheckSmooth=>false)
23 ·--·used·0.288033s·(cpu);·0.240004s·(thread);·0s·(gc)23 ·--·used·0.326518s·(cpu);·0.263399s·(thread);·0s·(gc)
  
24 ·······7······6······5······4······3······224 ·······7······6······5······4······3······2
25 o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·125 o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1
26 ·······7······7······7······7······7······7·····726 ·······7······7······7······7······7······7·····7
  
27 ················································ZZ[x·..x·]27 ················································ZZ[x·..x·]
28 ····················································0···728 ····················································0···7
1.47 KB
./usr/share/doc/Macaulay2/CharacteristicClasses/example-output/___Comp__Method.out
    
Offset 18, 29 lines modifiedOffset 18, 29 lines modified
18 i3·:·R=ZZ/32749[v_0..v_5];18 i3·:·R=ZZ/32749[v_0..v_5];
  
19 i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3));19 i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3));
  
20 o4·:·Ideal·of·R20 o4·:·Ideal·of·R
  
21 i5·:·time·CSM(I,CompMethod=>ProjectiveDegree)21 i5·:·time·CSM(I,CompMethod=>ProjectiveDegree)
22 ·--·used·0.402516s·(cpu);·0.292617s·(thread);·0s·(gc)22 ·--·used·0.935282s·(cpu);·0.355954s·(thread);·0s·(gc)
  
23 ·······5······4······3······223 ·······5······4······3······2
24 o5·=·6h··+·14h··+·14h··+·10h24 o5·=·6h··+·14h··+·14h··+·10h
25 ·······1······1······1······125 ·······1······1······1······1
  
26 ·····ZZ[h·]26 ·····ZZ[h·]
27 ·········127 ·········1
28 o5·:·------28 o5·:·------
29 ········629 ········6
30 ·······h30 ·······h
31 ········131 ········1
  
32 i6·:·time·CSM(I,CompMethod=>PnResidual)32 i6·:·time·CSM(I,CompMethod=>PnResidual)
33 ·--·used·1.67976s·(cpu);·1.53053s·(thread);·0s·(gc)33 ·--·used·1.92486s·(cpu);·1.72281s·(thread);·0s·(gc)
  
34 ·······5······4······3······234 ·······5······4······3······2
35 o6·=·6H··+·14H··+·14H··+·10H35 o6·=·6H··+·14H··+·14H··+·10H
  
36 ·····ZZ[H]36 ·····ZZ[H]
37 o6·:·-----37 o6·:·-----
38 ········638 ········6
Offset 53, 29 lines modifiedOffset 53, 29 lines modified
53 i8·:·S=QQ[s_0..s_3];53 i8·:·S=QQ[s_0..s_3];
  
54 i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3));54 i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3));
  
55 o9·:·Ideal·of·S55 o9·:·Ideal·of·S
  
56 i10·:·time·CSM(K,CompMethod=>ProjectiveDegree)56 i10·:·time·CSM(K,CompMethod=>ProjectiveDegree)
57 ·--·used·0.125748s·(cpu);·0.126487s·(thread);·0s·(gc)57 ·--·used·0.165604s·(cpu);·0.164911s·(thread);·0s·(gc)
  
58 ········3·····258 ········3·····2
59 o10·=·3h··+·5h59 o10·=·3h··+·5h
60 ········1·····160 ········1·····1
  
61 ······ZZ[h·]61 ······ZZ[h·]
62 ··········162 ··········1
63 o10·:·------63 o10·:·------
64 ·········464 ·········4
65 ········h65 ········h
66 ·········166 ·········1
  
67 i11·:·time·CSM(K,CompMethod=>PnResidual)67 i11·:·time·CSM(K,CompMethod=>PnResidual)
68 ·--·used·0.15611s·(cpu);·0.103277s·(thread);·0s·(gc)68 ·--·used·0.167029s·(cpu);·0.105482s·(thread);·0s·(gc)
  
69 ········3·····269 ········3·····2
70 o11·=·3H··+·5H70 o11·=·3H··+·5H
  
71 ······ZZ[H]71 ······ZZ[H]
72 o11·:·-----72 o11·:·-----
73 ·········473 ·········4
1.32 KB
./usr/share/doc/Macaulay2/CharacteristicClasses/example-output/___Euler.out
    
Offset 21, 20 lines modifiedOffset 21, 20 lines modified
21 ·············2························································221 ·············2························································2
22 ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·)22 ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·)
23 ·············3·········0·4········1·4·········2·4·········3·4·········423 ·············3·········0·4········1·4·········2·4·········3·4·········4
  
24 o3·:·Ideal·of·R24 o3·:·Ideal·of·R
  
25 i4·:·time·Euler(I,InputIsSmooth=>true)25 i4·:·time·Euler(I,InputIsSmooth=>true)
26 ·--·used·0.0378974s·(cpu);·0.0347243s·(thread);·0s·(gc)26 ·--·used·0.0811438s·(cpu);·0.0402533s·(thread);·0s·(gc)
  
27 o4·=·427 o4·=·4
  
28 i5·:·time·Euler·I28 i5·:·time·Euler·I
29 ·--·used·0.172429s·(cpu);·0.119864s·(thread);·0s·(gc)29 ·--·used·0.448982s·(cpu);·0.147942s·(thread);·0s·(gc)
  
30 o5·=·430 o5·=·4
  
31 i6·:·EulerIHash=Euler(I,Output=>HashForm);31 i6·:·EulerIHash=Euler(I,Output=>HashForm);
  
32 i7·:·A=ring·EulerIHash#"CSM"32 i7·:·A=ring·EulerIHash#"CSM"
  
Offset 62, 20 lines modifiedOffset 62, 20 lines modified
62 ·····------------------------------------------------------------------------62 ·····------------------------------------------------------------------------
63 ·····-·x·x·)63 ·····-·x·x·)
64 ········0·364 ········0·3
  
65 o9·:·Ideal·of·R65 o9·:·Ideal·of·R
  
66 i10·:·time·Euler(J,Method=>DirectCompleteInt)66 i10·:·time·Euler(J,Method=>DirectCompleteInt)
67 ·--·used·0.0694855s·(cpu);·0.0623664s·(thread);·0s·(gc)67 ·--·used·0.443871s·(cpu);·0.0774841s·(thread);·0s·(gc)
  
68 o10·=·268 o10·=·2
  
69 i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1})69 i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1})
70 ·--·used·0.125296s·(cpu);·0.0731341s·(thread);·0s·(gc)70 ·--·used·0.301716s·(cpu);·0.0936436s·(thread);·0s·(gc)
  
71 o11·=·271 o11·=·2
  
72 i12·:·R=MultiProjCoordRing({2,2})72 i12·:·R=MultiProjCoordRing({2,2})
  
73 o12·=·R73 o12·=·R
  
926 B
./usr/share/doc/Macaulay2/CharacteristicClasses/example-output/___Inds__Of__Smooth.out
    
Offset 7, 29 lines modifiedOffset 7, 29 lines modified
7 o1·:·PolynomialRing7 o1·:·PolynomialRing
  
8 i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R));8 i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R));
  
9 o2·:·Ideal·of·R9 o2·:·Ideal·of·R
  
10 i3·:·time·CSM(I,Method=>DirectCompletInt)10 i3·:·time·CSM(I,Method=>DirectCompletInt)
11 ·--·used·2.95918s·(cpu);·1.06925s·(thread);·0s·(gc)11 ·--·used·4.9513s·(cpu);·1.19937s·(thread);·0s·(gc)
  
12 ·······2·2·····2·········212 ·······2·2·····2·········2
13 o3·=·2h·h··+·2h·h··+·5h·h13 o3·=·2h·h··+·2h·h··+·5h·h
14 ·······1·2·····1·2·····1·214 ·······1·2·····1·2·····1·2
  
15 ·····ZZ[h·..h·]15 ·····ZZ[h·..h·]
16 ·········1···216 ·········1···2
17 o3·:·----------17 o3·:·----------
18 ········3···318 ········3···3
19 ······(h·,·h·)19 ······(h·,·h·)
20 ········1···220 ········1···2
  
21 i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})21 i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})
22 ·--·used·2.75683s·(cpu);·1.04916s·(thread);·0s·(gc)22 ·--·used·5.24446s·(cpu);·1.20312s·(thread);·0s·(gc)
  
23 ·······2·2·····2·········223 ·······2·2·····2·········2
24 o4·=·2h·h··+·2h·h··+·5h·h24 o4·=·2h·h··+·2h·h··+·5h·h
25 ·······1·2·····1·2·····1·225 ·······1·2·····1·2·····1·2
  
26 ·····ZZ[h·..h·]26 ·····ZZ[h·..h·]
27 ·········1···227 ·········1···2
974 B
./usr/share/doc/Macaulay2/CharacteristicClasses/example-output/___Input__Is__Smooth.out
    
Offset 3, 43 lines modifiedOffset 3, 43 lines modified
3 i1·:·R·=·ZZ/32749[x_0..x_4];3 i1·:·R·=·ZZ/32749[x_0..x_4];
  
4 i2·:·I=ideal(random(2,R),random(2,R),random(1,R));4 i2·:·I=ideal(random(2,R),random(2,R),random(1,R));
  
5 o2·:·Ideal·of·R5 o2·:·Ideal·of·R
  
6 i3·:·time·CSM·I6 i3·:·time·CSM·I
7 ·--·used·0.580594s·(cpu);·0.367879s·(thread);·0s·(gc)7 ·--·used·1.05011s·(cpu);·0.416291s·(thread);·0s·(gc)
  
8 ·······38 ·······3
9 o3·=·4h9 o3·=·4h
10 ·······110 ·······1
  
11 ·····ZZ[h·]11 ·····ZZ[h·]
12 ·········112 ·········1
13 o3·:·------13 o3·:·------
14 ········514 ········5
15 ·······h15 ·······h
16 ········116 ········1
  
17 i4·:·time·CSM(I,InputIsSmooth=>true)17 i4·:·time·CSM(I,InputIsSmooth=>true)
18 ·--·used·0.025682s·(cpu);·0.0276377s·(thread);·0s·(gc)18 ·--·used·0.0842578s·(cpu);·0.0387837s·(thread);·0s·(gc)
  
19 ·······319 ·······3
20 o4·=·4h20 o4·=·4h
21 ·······121 ·······1
  
22 ·····ZZ[h·]22 ·····ZZ[h·]
23 ·········123 ·········1
24 o4·:·------24 o4·:·------
25 ········525 ········5
26 ·······h26 ·······h
27 ········127 ········1
  
28 i5·:·time·Chern·I28 i5·:·time·Chern·I
29 ·--·used·0.0330291s·(cpu);·0.0253647s·(thread);·0s·(gc)29 ·--·used·0.153931s·(cpu);·0.0365383s·(thread);·0s·(gc)
  
30 ·······330 ·······3
31 o5·=·4h31 o5·=·4h
32 ·······132 ·······1
  
33 ·····ZZ[h·]33 ·····ZZ[h·]
34 ·········134 ·········1
799 B
./usr/share/doc/Macaulay2/CharacteristicClasses/example-output/___Method.out
    
Offset 7, 29 lines modifiedOffset 7, 29 lines modified
7 o1·:·PolynomialRing7 o1·:·PolynomialRing
  
8 i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3);8 i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3);
  
9 o2·:·Ideal·of·R9 o2·:·Ideal·of·R
  
10 i3·:·time·CSM·I10 i3·:·time·CSM·I
11 ·--·used·0.989445s·(cpu);·0.786184s·(thread);·0s·(gc)11 ·--·used·2.35579s·(cpu);·0.873637s·(thread);·0s·(gc)
  
12 ········5······4·····312 ········5······4·····3
13 o3·=·12h··+·10h··+·6h13 o3·=·12h··+·10h··+·6h
14 ········1······1·····114 ········1······1·····1
  
15 ·····ZZ[h·]15 ·····ZZ[h·]
16 ·········116 ·········1
17 o3·:·------17 o3·:·------
18 ········718 ········7
19 ·······h19 ·······h
20 ········120 ········1
  
21 i4·:·time·CSM(I,Method=>DirectCompleteInt)21 i4·:·time·CSM(I,Method=>DirectCompleteInt)
22 ·--·used·0.357044s·(cpu);·0.196663s·(thread);·0s·(gc)22 ·--·used·0.914501s·(cpu);·0.210051s·(thread);·0s·(gc)
  
23 ········5······4·····323 ········5······4·····3
24 o4·=·12h··+·10h··+·6h24 o4·=·12h··+·10h··+·6h
25 ········1······1·····125 ········1······1·····1
  
26 ·····ZZ[h·]26 ·····ZZ[h·]
27 ·········127 ·········1
2.14 KB
./usr/share/doc/Macaulay2/CharacteristicClasses/html/___C__S__M.html
    
Offset 234, 15 lines modifiedOffset 234, 15 lines modified
  
234 o14·:·Ideal·of·R</code></pre>234 o14·:·Ideal·of·R</code></pre>
235 ············</td>235 ············</td>
236 ··········</tr>236 ··········</tr>
237 ··········<tr>237 ··········<tr>
238 ············<td>238 ············<td>
239 ··············<pre><code·class="language-macaulay2">i15·:·time·csmK=CSM(A,K)239 ··············<pre><code·class="language-macaulay2">i15·:·time·csmK=CSM(A,K)
240 ·--·used·1.38254s·(cpu);·0.374939s·(thread);·0s·(gc)240 ·--·used·2.3478s·(cpu);·0.4198s·(thread);·0s·(gc)
  
241 ········2·2·····2·········2····2············2241 ········2·2·····2·········2····2············2
242 o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h242 o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h
243 ········1·2·····1·2·····1·2····1·····1·2····2243 ········1·2·····1·2·····1·2····1·····1·2····2
  
244 o15·:·A</code></pre>244 o15·:·A</code></pre>
245 ············</td>245 ············</td>
Offset 301, 15 lines modifiedOffset 301, 15 lines modified
  
301 o21·:·A</code></pre>301 o21·:·A</code></pre>
302 ············</td>302 ············</td>
303 ··········</tr>303 ··········</tr>
304 ··········<tr>304 ··········<tr>
305 ············<td>305 ············<td>
306 ··············<pre><code·class="language-macaulay2">i22·:·time·CSM(A,K,m)306 ··············<pre><code·class="language-macaulay2">i22·:·time·CSM(A,K,m)
307 ·--·used·0.0478725s·(cpu);·0.0487251s·(thread);·0s·(gc)307 ·--·used·0.222445s·(cpu);·0.0515015s·(thread);·0s·(gc)
  
308 ········2·2·····2·········2····2············2308 ········2·2·····2·········2····2············2
309 o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h309 o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h
310 ········1·2·····1·2·····1·2····1·····1·2····2310 ········1·2·····1·2·····1·2····1·····1·2····2
  
311 o22·:·A</code></pre>311 o22·:·A</code></pre>
312 ············</td>312 ············</td>
1.04 KB
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160 ··············2··············2160 ··············2··············2
161 o14·=·ideal·(x·x··-·x·x·x·,·x·x·)161 o14·=·ideal·(x·x··-·x·x·x·,·x·x·)
162 ··············0·3····1·2·4···2·5162 ··············0·3····1·2·4···2·5
  
163 o14·:·Ideal·of·R163 o14·:·Ideal·of·R
164 i15·:·time·csmK=CSM(A,K)164 i15·:·time·csmK=CSM(A,K)
165 ·--·used·1.38254s·(cpu);·0.374939s·(thread);·0s·(gc)165 ·--·used·2.3478s·(cpu);·0.4198s·(thread);·0s·(gc)
  
166 ········2·2·····2·········2····2············2166 ········2·2·····2·········2····2············2
167 o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h167 o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h
168 ········1·2·····1·2·····1·2····1·····1·2····2168 ········1·2·····1·2·····1·2····1·····1·2····2
  
169 o15·:·A169 o15·:·A
170 i16·:·csmKHash=·CSM(A,K,Output=>HashForm)170 i16·:·csmKHash=·CSM(A,K,Output=>HashForm)
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199 ········2·2·····2·········2·····2·············2199 ········2·2·····2·········2·····2·············2
200 o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h200 o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h
201 ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2201 ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2
  
202 o21·:·A202 o21·:·A
203 i22·:·time·CSM(A,K,m)203 i22·:·time·CSM(A,K,m)
204 ·--·used·0.0478725s·(cpu);·0.0487251s·(thread);·0s·(gc)204 ·--·used·0.222445s·(cpu);·0.0515015s·(thread);·0s·(gc)
  
205 ········2·2·····2·········2····2············2205 ········2·2·····2·········2····2············2
206 o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h206 o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h
207 ········1·2·····1·2·····1·2····1·····1·2····2207 ········1·2·····1·2·····1·2····1·····1·2····2
  
208 o22·:·A208 o22·:·A
209 In·the·case·where·the·ambient·space·is·a·toric·variety·which·is·not·a·product209 In·the·case·where·the·ambient·space·is·a·toric·variety·which·is·not·a·product
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72 o2·:·NormalToricVariety</code></pre>72 o2·:·NormalToricVariety</code></pre>
73 ············</td>73 ············</td>
74 ··········</tr>74 ··········</tr>
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM·U77 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM·U
78 ·--·used·0.233576s·(cpu);·0.190751s·(thread);·0s·(gc)78 ·--·used·0.190961s·(cpu);·0.153353s·(thread);·0s·(gc)
  
79 ·······7······6······5······4······3······279 ·······7······6······5······4······3······2
80 o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·180 o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1
81 ·······7······7······7······7······7······7·····781 ·······7······7······7······7······7······7·····7
  
82 ················································ZZ[x·..x·]82 ················································ZZ[x·..x·]
83 ····················································0···783 ····················································0···7
Offset 88, 15 lines modifiedOffset 88, 15 lines modified
88 ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·)88 ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·)
89 ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7</code></pre>89 ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(U,CheckSmooth=>false)94 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(U,CheckSmooth=>false)
95 ·--·used·0.288033s·(cpu);·0.240004s·(thread);·0s·(gc)95 ·--·used·0.326518s·(cpu);·0.263399s·(thread);·0s·(gc)
  
96 ·······7······6······5······4······3······296 ·······7······6······5······4······3······2
97 o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·197 o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1
98 ·······7······7······7······7······7······7·····798 ·······7······7······7······7······7······7·····7
  
99 ················································ZZ[x·..x·]99 ················································ZZ[x·..x·]
100 ····················································0···7100 ····················································0···7
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16 o1·:·Package16 o1·:·Package
17 i2·:·U·=·toricProjectiveSpace·717 i2·:·U·=·toricProjectiveSpace·7
  
18 o2·=·U18 o2·=·U
  
19 o2·:·NormalToricVariety19 o2·:·NormalToricVariety
20 i3·:·time·CSM·U20 i3·:·time·CSM·U
21 ·--·used·0.233576s·(cpu);·0.190751s·(thread);·0s·(gc)21 ·--·used·0.190961s·(cpu);·0.153353s·(thread);·0s·(gc)
  
22 ·······7······6······5······4······3······222 ·······7······6······5······4······3······2
23 o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·123 o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1
24 ·······7······7······7······7······7······7·····724 ·······7······7······7······7······7······7·····7
  
25 ················································ZZ[x·..x·]25 ················································ZZ[x·..x·]
26 ····················································0···726 ····················································0···7
27 o3·:·--------------------------------------------------------------------------27 o3·:·--------------------------------------------------------------------------
28 ---------------------28 ---------------------
29 ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,29 ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,
30 -·x··+·x·,·-·x··+·x·)30 -·x··+·x·,·-·x··+·x·)
31 ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····531 ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5
32 0····6·····0····732 0····6·····0····7
33 i4·:·time·CSM(U,CheckSmooth=>false)33 i4·:·time·CSM(U,CheckSmooth=>false)
34 ·--·used·0.288033s·(cpu);·0.240004s·(thread);·0s·(gc)34 ·--·used·0.326518s·(cpu);·0.263399s·(thread);·0s·(gc)
  
35 ·······7······6······5······4······3······235 ·······7······6······5······4······3······2
36 o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·136 o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1
37 ·······7······7······7······7······7······7·····737 ·······7······7······7······7······7······7·····7
  
38 ················································ZZ[x·..x·]38 ················································ZZ[x·..x·]
39 ····················································0···739 ····················································0···7
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92 o4·:·Ideal·of·R</code></pre>92 o4·:·Ideal·of·R</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i5·:·time·CSM(I,CompMethod=>ProjectiveDegree)97 ··············<pre><code·class="language-macaulay2">i5·:·time·CSM(I,CompMethod=>ProjectiveDegree)
98 ·--·used·0.402516s·(cpu);·0.292617s·(thread);·0s·(gc)98 ·--·used·0.935282s·(cpu);·0.355954s·(thread);·0s·(gc)
  
99 ·······5······4······3······299 ·······5······4······3······2
100 o5·=·6h··+·14h··+·14h··+·10h100 o5·=·6h··+·14h··+·14h··+·10h
101 ·······1······1······1······1101 ·······1······1······1······1
  
102 ·····ZZ[h·]102 ·····ZZ[h·]
103 ·········1103 ·········1
Offset 109, 15 lines modifiedOffset 109, 15 lines modified
109 ·······h109 ·······h
110 ········1</code></pre>110 ········1</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i6·:·time·CSM(I,CompMethod=>PnResidual)115 ··············<pre><code·class="language-macaulay2">i6·:·time·CSM(I,CompMethod=>PnResidual)
116 ·--·used·1.67976s·(cpu);·1.53053s·(thread);·0s·(gc)116 ·--·used·1.92486s·(cpu);·1.72281s·(thread);·0s·(gc)
  
117 ·······5······4······3······2117 ·······5······4······3······2
118 o6·=·6H··+·14H··+·14H··+·10H118 o6·=·6H··+·14H··+·14H··+·10H
  
119 ·····ZZ[H]119 ·····ZZ[H]
120 o6·:·-----120 o6·:·-----
121 ········6121 ········6
Offset 142, 15 lines modifiedOffset 142, 15 lines modified
  
142 o9·:·Ideal·of·S</code></pre>142 o9·:·Ideal·of·S</code></pre>
143 ············</td>143 ············</td>
144 ··········</tr>144 ··········</tr>
145 ··········<tr>145 ··········<tr>
146 ············<td>146 ············<td>
147 ··············<pre><code·class="language-macaulay2">i10·:·time·CSM(K,CompMethod=>ProjectiveDegree)147 ··············<pre><code·class="language-macaulay2">i10·:·time·CSM(K,CompMethod=>ProjectiveDegree)
148 ·--·used·0.125748s·(cpu);·0.126487s·(thread);·0s·(gc)148 ·--·used·0.165604s·(cpu);·0.164911s·(thread);·0s·(gc)
  
149 ········3·····2149 ········3·····2
150 o10·=·3h··+·5h150 o10·=·3h··+·5h
151 ········1·····1151 ········1·····1
  
152 ······ZZ[h·]152 ······ZZ[h·]
153 ··········1153 ··········1
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159 ········h159 ········h
160 ·········1</code></pre>160 ·········1</code></pre>
161 ············</td>161 ············</td>
162 ··········</tr>162 ··········</tr>
163 ··········<tr>163 ··········<tr>
164 ············<td>164 ············<td>
165 ··············<pre><code·class="language-macaulay2">i11·:·time·CSM(K,CompMethod=>PnResidual)165 ··············<pre><code·class="language-macaulay2">i11·:·time·CSM(K,CompMethod=>PnResidual)
166 ·--·used·0.15611s·(cpu);·0.103277s·(thread);·0s·(gc)166 ·--·used·0.167029s·(cpu);·0.105482s·(thread);·0s·(gc)
  
167 ········3·····2167 ········3·····2
168 o11·=·3H··+·5H168 o11·=·3H··+·5H
  
169 ······ZZ[H]169 ······ZZ[H]
170 o11·:·-----170 o11·:·-----
171 ·········4171 ·········4
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32 using·the·regenerative·cascade·implemented·in·Bertini.·This·is·done·by·choosing32 using·the·regenerative·cascade·implemented·in·Bertini.·This·is·done·by·choosing
33 the·option·bertini,·provided·Bertini·is·_\x8i_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8e_\x8d_\x8·_\x8a_\x8n_\x8d_\x8·_\x8c_\x8o_\x8n_\x8f_\x8i_\x8g_\x8u_\x8r_\x8e_\x8d.33 the·option·bertini,·provided·Bertini·is·_\x8i_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8e_\x8d_\x8·_\x8a_\x8n_\x8d_\x8·_\x8c_\x8o_\x8n_\x8f_\x8i_\x8g_\x8u_\x8r_\x8e_\x8d.
34 i3·:·R=ZZ/32749[v_0..v_5];34 i3·:·R=ZZ/32749[v_0..v_5];
35 i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3));35 i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3));
  
36 o4·:·Ideal·of·R36 o4·:·Ideal·of·R
37 i5·:·time·CSM(I,CompMethod=>ProjectiveDegree)37 i5·:·time·CSM(I,CompMethod=>ProjectiveDegree)
38 ·--·used·0.402516s·(cpu);·0.292617s·(thread);·0s·(gc)38 ·--·used·0.935282s·(cpu);·0.355954s·(thread);·0s·(gc)
  
39 ·······5······4······3······239 ·······5······4······3······2
40 o5·=·6h··+·14h··+·14h··+·10h40 o5·=·6h··+·14h··+·14h··+·10h
41 ·······1······1······1······141 ·······1······1······1······1
  
42 ·····ZZ[h·]42 ·····ZZ[h·]
43 ·········143 ·········1
44 o5·:·------44 o5·:·------
45 ········645 ········6
46 ·······h46 ·······h
47 ········147 ········1
48 i6·:·time·CSM(I,CompMethod=>PnResidual)48 i6·:·time·CSM(I,CompMethod=>PnResidual)
49 ·--·used·1.67976s·(cpu);·1.53053s·(thread);·0s·(gc)49 ·--·used·1.92486s·(cpu);·1.72281s·(thread);·0s·(gc)
  
50 ·······5······4······3······250 ·······5······4······3······2
51 o6·=·6H··+·14H··+·14H··+·10H51 o6·=·6H··+·14H··+·14H··+·10H
  
52 ·····ZZ[H]52 ·····ZZ[H]
53 o6·:·-----53 o6·:·-----
54 ········654 ········6
Offset 62, 28 lines modifiedOffset 62, 28 lines modified
  
62 o7·=·262 o7·=·2
63 i8·:·S=QQ[s_0..s_3];63 i8·:·S=QQ[s_0..s_3];
64 i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3));64 i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3));
  
65 o9·:·Ideal·of·S65 o9·:·Ideal·of·S
66 i10·:·time·CSM(K,CompMethod=>ProjectiveDegree)66 i10·:·time·CSM(K,CompMethod=>ProjectiveDegree)
67 ·--·used·0.125748s·(cpu);·0.126487s·(thread);·0s·(gc)67 ·--·used·0.165604s·(cpu);·0.164911s·(thread);·0s·(gc)
  
68 ········3·····268 ········3·····2
69 o10·=·3h··+·5h69 o10·=·3h··+·5h
70 ········1·····170 ········1·····1
  
71 ······ZZ[h·]71 ······ZZ[h·]
72 ··········172 ··········1
73 o10·:·------73 o10·:·------
74 ·········474 ·········4
75 ········h75 ········h
76 ·········176 ·········1
77 i11·:·time·CSM(K,CompMethod=>PnResidual)77 i11·:·time·CSM(K,CompMethod=>PnResidual)
78 ·--·used·0.15611s·(cpu);·0.103277s·(thread);·0s·(gc)78 ·--·used·0.167029s·(cpu);·0.105482s·(thread);·0s·(gc)
  
79 ········3·····279 ········3·····2
80 o11·=·3H··+·5H80 o11·=·3H··+·5H
  
81 ······ZZ[H]81 ······ZZ[H]
82 o11·:·-----82 o11·:·-----
83 ·········483 ·········4
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125 o3·:·Ideal·of·R</code></pre>125 o3·:·Ideal·of·R</code></pre>
126 ············</td>126 ············</td>
127 ··········</tr>127 ··········</tr>
128 ··········<tr>128 ··········<tr>
129 ············<td>129 ············<td>
130 ··············<pre><code·class="language-macaulay2">i4·:·time·Euler(I,InputIsSmooth=>true)130 ··············<pre><code·class="language-macaulay2">i4·:·time·Euler(I,InputIsSmooth=>true)
131 ·--·used·0.0378974s·(cpu);·0.0347243s·(thread);·0s·(gc)131 ·--·used·0.0811438s·(cpu);·0.0402533s·(thread);·0s·(gc)
  
132 o4·=·4</code></pre>132 o4·=·4</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i5·:·time·Euler·I137 ··············<pre><code·class="language-macaulay2">i5·:·time·Euler·I
138 ·--·used·0.172429s·(cpu);·0.119864s·(thread);·0s·(gc)138 ·--·used·0.448982s·(cpu);·0.147942s·(thread);·0s·(gc)
  
139 o5·=·4</code></pre>139 o5·=·4</code></pre>
140 ············</td>140 ············</td>
141 ··········</tr>141 ··········</tr>
142 ··········<tr>142 ··········<tr>
143 ············<td>143 ············<td>
144 ··············<pre><code·class="language-macaulay2">i6·:·EulerIHash=Euler(I,Output=>HashForm);</code></pre>144 ··············<pre><code·class="language-macaulay2">i6·:·EulerIHash=Euler(I,Output=>HashForm);</code></pre>
Offset 189, 23 lines modifiedOffset 189, 23 lines modified
189 ········<div>189 ········<div>
190 ··········<p>Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the·method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that·the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and·input·this·information·into·the·method.·This·may·also·improve·computation·speed.</p>190 ··········<p>Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the·method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that·the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and·input·this·information·into·the·method.·This·may·also·improve·computation·speed.</p>
191 ········</div>191 ········</div>
192 ········<table·class="examples">192 ········<table·class="examples">
193 ··········<tr>193 ··········<tr>
194 ············<td>194 ············<td>
195 ··············<pre><code·class="language-macaulay2">i10·:·time·Euler(J,Method=>DirectCompleteInt)195 ··············<pre><code·class="language-macaulay2">i10·:·time·Euler(J,Method=>DirectCompleteInt)
196 ·--·used·0.0694855s·(cpu);·0.0623664s·(thread);·0s·(gc)196 ·--·used·0.443871s·(cpu);·0.0774841s·(thread);·0s·(gc)
  
197 o10·=·2</code></pre>197 o10·=·2</code></pre>
198 ············</td>198 ············</td>
199 ··········</tr>199 ··········</tr>
200 ··········<tr>200 ··········<tr>
201 ············<td>201 ············<td>
202 ··············<pre><code·class="language-macaulay2">i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1})202 ··············<pre><code·class="language-macaulay2">i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1})
203 ·--·used·0.125296s·(cpu);·0.0731341s·(thread);·0s·(gc)203 ·--·used·0.301716s·(cpu);·0.0936436s·(thread);·0s·(gc)
  
204 o11·=·2</code></pre>204 o11·=·2</code></pre>
205 ············</td>205 ············</td>
206 ··········</tr>206 ··········</tr>
207 ········</table>207 ········</table>
208 ········<div>208 ········<div>
209 ··········<p>Now·consider·an·example·in·\PP^2·\times·\PP^2.</p>209 ··········<p>Now·consider·an·example·in·\PP^2·\times·\PP^2.</p>
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Offset 74, 19 lines modifiedOffset 74, 19 lines modified
74 ·····------------------------------------------------------------------------74 ·····------------------------------------------------------------------------
75 ·············2························································275 ·············2························································2
76 ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·)76 ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·)
77 ·············3·········0·4········1·4·········2·4·········3·4·········477 ·············3·········0·4········1·4·········2·4·········3·4·········4
  
78 o3·:·Ideal·of·R78 o3·:·Ideal·of·R
79 i4·:·time·Euler(I,InputIsSmooth=>true)79 i4·:·time·Euler(I,InputIsSmooth=>true)
80 ·--·used·0.0378974s·(cpu);·0.0347243s·(thread);·0s·(gc)80 ·--·used·0.0811438s·(cpu);·0.0402533s·(thread);·0s·(gc)
  
81 o4·=·481 o4·=·4
82 i5·:·time·Euler·I82 i5·:·time·Euler·I
83 ·--·used·0.172429s·(cpu);·0.119864s·(thread);·0s·(gc)83 ·--·used·0.448982s·(cpu);·0.147942s·(thread);·0s·(gc)
  
84 o5·=·484 o5·=·4
85 i6·:·EulerIHash=Euler(I,Output=>HashForm);85 i6·:·EulerIHash=Euler(I,Output=>HashForm);
86 i7·:·A=ring·EulerIHash#"CSM"86 i7·:·A=ring·EulerIHash#"CSM"
  
87 o7·=·A87 o7·=·A
  
Offset 114, 19 lines modifiedOffset 114, 19 lines modified
114 o9·:·Ideal·of·R114 o9·:·Ideal·of·R
115 Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the115 Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the
116 method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that116 method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that
117 the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and117 the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and
118 input·this·information·into·the·method.·This·may·also·improve·computation118 input·this·information·into·the·method.·This·may·also·improve·computation
119 speed.119 speed.
120 i10·:·time·Euler(J,Method=>DirectCompleteInt)120 i10·:·time·Euler(J,Method=>DirectCompleteInt)
121 ·--·used·0.0694855s·(cpu);·0.0623664s·(thread);·0s·(gc)121 ·--·used·0.443871s·(cpu);·0.0774841s·(thread);·0s·(gc)
  
122 o10·=·2122 o10·=·2
123 i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1})123 i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1})
124 ·--·used·0.125296s·(cpu);·0.0731341s·(thread);·0s·(gc)124 ·--·used·0.301716s·(cpu);·0.0936436s·(thread);·0s·(gc)
  
125 o11·=·2125 o11·=·2
126 Now·consider·an·example·in·\PP^2·\times·\PP^2.126 Now·consider·an·example·in·\PP^2·\times·\PP^2.
127 i12·:·R=MultiProjCoordRing({2,2})127 i12·:·R=MultiProjCoordRing({2,2})
  
128 o12·=·R128 o12·=·R
  
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Offset 70, 15 lines modifiedOffset 70, 15 lines modified
  
70 o2·:·Ideal·of·R</code></pre>70 o2·:·Ideal·of·R</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ··········<tr>73 ··········<tr>
74 ············<td>74 ············<td>
75 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM(I,Method=>DirectCompletInt)75 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM(I,Method=>DirectCompletInt)
76 ·--·used·2.95918s·(cpu);·1.06925s·(thread);·0s·(gc)76 ·--·used·4.9513s·(cpu);·1.19937s·(thread);·0s·(gc)
  
77 ·······2·2·····2·········277 ·······2·2·····2·········2
78 o3·=·2h·h··+·2h·h··+·5h·h78 o3·=·2h·h··+·2h·h··+·5h·h
79 ·······1·2·····1·2·····1·279 ·······1·2·····1·2·····1·2
  
80 ·····ZZ[h·..h·]80 ·····ZZ[h·..h·]
81 ·········1···281 ·········1···2
Offset 87, 15 lines modifiedOffset 87, 15 lines modified
87 ······(h·,·h·)87 ······(h·,·h·)
88 ········1···2</code></pre>88 ········1···2</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})93 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})
94 ·--·used·2.75683s·(cpu);·1.04916s·(thread);·0s·(gc)94 ·--·used·5.24446s·(cpu);·1.20312s·(thread);·0s·(gc)
  
95 ·······2·2·····2·········295 ·······2·2·····2·········2
96 o4·=·2h·h··+·2h·h··+·5h·h96 o4·=·2h·h··+·2h·h··+·5h·h
97 ·······1·2·····1·2·····1·297 ·······1·2·····1·2·····1·2
  
98 ·····ZZ[h·..h·]98 ·····ZZ[h·..h·]
99 ·········1···299 ·········1···2
784 B
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Offset 16, 28 lines modifiedOffset 16, 28 lines modified
16 o1·=·R16 o1·=·R
  
17 o1·:·PolynomialRing17 o1·:·PolynomialRing
18 i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R));18 i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R));
  
19 o2·:·Ideal·of·R19 o2·:·Ideal·of·R
20 i3·:·time·CSM(I,Method=>DirectCompletInt)20 i3·:·time·CSM(I,Method=>DirectCompletInt)
21 ·--·used·2.95918s·(cpu);·1.06925s·(thread);·0s·(gc)21 ·--·used·4.9513s·(cpu);·1.19937s·(thread);·0s·(gc)
  
22 ·······2·2·····2·········222 ·······2·2·····2·········2
23 o3·=·2h·h··+·2h·h··+·5h·h23 o3·=·2h·h··+·2h·h··+·5h·h
24 ·······1·2·····1·2·····1·224 ·······1·2·····1·2·····1·2
  
25 ·····ZZ[h·..h·]25 ·····ZZ[h·..h·]
26 ·········1···226 ·········1···2
27 o3·:·----------27 o3·:·----------
28 ········3···328 ········3···3
29 ······(h·,·h·)29 ······(h·,·h·)
30 ········1···230 ········1···2
31 i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})31 i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2})
32 ·--·used·2.75683s·(cpu);·1.04916s·(thread);·0s·(gc)32 ·--·used·5.24446s·(cpu);·1.20312s·(thread);·0s·(gc)
  
33 ·······2·2·····2·········233 ·······2·2·····2·········2
34 o4·=·2h·h··+·2h·h··+·5h·h34 o4·=·2h·h··+·2h·h··+·5h·h
35 ·······1·2·····1·2·····1·235 ·······1·2·····1·2·····1·2
  
36 ·····ZZ[h·..h·]36 ·····ZZ[h·..h·]
37 ·········1···237 ·········1···2
2.4 KB
./usr/share/doc/Macaulay2/CharacteristicClasses/html/___Input__Is__Smooth.html
    
Offset 66, 15 lines modifiedOffset 66, 15 lines modified
  
66 o2·:·Ideal·of·R</code></pre>66 o2·:·Ideal·of·R</code></pre>
67 ············</td>67 ············</td>
68 ··········</tr>68 ··········</tr>
69 ··········<tr>69 ··········<tr>
70 ············<td>70 ············<td>
71 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I71 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I
72 ·--·used·0.580594s·(cpu);·0.367879s·(thread);·0s·(gc)72 ·--·used·1.05011s·(cpu);·0.416291s·(thread);·0s·(gc)
  
73 ·······373 ·······3
74 o3·=·4h74 o3·=·4h
75 ·······175 ·······1
  
76 ·····ZZ[h·]76 ·····ZZ[h·]
77 ·········177 ·········1
Offset 83, 15 lines modifiedOffset 83, 15 lines modified
83 ·······h83 ·······h
84 ········1</code></pre>84 ········1</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,InputIsSmooth=>true)89 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,InputIsSmooth=>true)
90 ·--·used·0.025682s·(cpu);·0.0276377s·(thread);·0s·(gc)90 ·--·used·0.0842578s·(cpu);·0.0387837s·(thread);·0s·(gc)
  
91 ·······391 ·······3
92 o4·=·4h92 o4·=·4h
93 ·······193 ·······1
  
94 ·····ZZ[h·]94 ·····ZZ[h·]
95 ·········195 ·········1
Offset 105, 15 lines modifiedOffset 105, 15 lines modified
105 ········<div>105 ········<div>
106 ··········<p>Note·that·one·could,·equivalently,·use·the·command·<a·title="The·Chern·class"·href="___Chern.html">Chern</a>·instead·in·this·case.</p>106 ··········<p>Note·that·one·could,·equivalently,·use·the·command·<a·title="The·Chern·class"·href="___Chern.html">Chern</a>·instead·in·this·case.</p>
107 ········</div>107 ········</div>
108 ········<table·class="examples">108 ········<table·class="examples">
109 ··········<tr>109 ··········<tr>
110 ············<td>110 ············<td>
111 ··············<pre><code·class="language-macaulay2">i5·:·time·Chern·I111 ··············<pre><code·class="language-macaulay2">i5·:·time·Chern·I
112 ·--·used·0.0330291s·(cpu);·0.0253647s·(thread);·0s·(gc)112 ·--·used·0.153931s·(cpu);·0.0365383s·(thread);·0s·(gc)
  
113 ·······3113 ·······3
114 o5·=·4h114 o5·=·4h
115 ·······1115 ·······1
  
116 ·····ZZ[h·]116 ·····ZZ[h·]
117 ·········1117 ·········1
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Offset 9, 42 lines modifiedOffset 9, 42 lines modified
9 input·ideal·is·known·to·define·a·smooth·subscheme·setting·this·option·to·true9 input·ideal·is·known·to·define·a·smooth·subscheme·setting·this·option·to·true
10 will·speed·up·computations·(it·is·set·to·false·by·default).10 will·speed·up·computations·(it·is·set·to·false·by·default).
11 i1·:·R·=·ZZ/32749[x_0..x_4];11 i1·:·R·=·ZZ/32749[x_0..x_4];
12 i2·:·I=ideal(random(2,R),random(2,R),random(1,R));12 i2·:·I=ideal(random(2,R),random(2,R),random(1,R));
  
13 o2·:·Ideal·of·R13 o2·:·Ideal·of·R
14 i3·:·time·CSM·I14 i3·:·time·CSM·I
15 ·--·used·0.580594s·(cpu);·0.367879s·(thread);·0s·(gc)15 ·--·used·1.05011s·(cpu);·0.416291s·(thread);·0s·(gc)
  
16 ·······316 ·······3
17 o3·=·4h17 o3·=·4h
18 ·······118 ·······1
  
19 ·····ZZ[h·]19 ·····ZZ[h·]
20 ·········120 ·········1
21 o3·:·------21 o3·:·------
22 ········522 ········5
23 ·······h23 ·······h
24 ········124 ········1
25 i4·:·time·CSM(I,InputIsSmooth=>true)25 i4·:·time·CSM(I,InputIsSmooth=>true)
26 ·--·used·0.025682s·(cpu);·0.0276377s·(thread);·0s·(gc)26 ·--·used·0.0842578s·(cpu);·0.0387837s·(thread);·0s·(gc)
  
27 ·······327 ·······3
28 o4·=·4h28 o4·=·4h
29 ·······129 ·······1
  
30 ·····ZZ[h·]30 ·····ZZ[h·]
31 ·········131 ·········1
32 o4·:·------32 o4·:·------
33 ········533 ········5
34 ·······h34 ·······h
35 ········135 ········1
36 Note·that·one·could,·equivalently,·use·the·command·_\x8C_\x8h_\x8e_\x8r_\x8n·instead·in·this·case.36 Note·that·one·could,·equivalently,·use·the·command·_\x8C_\x8h_\x8e_\x8r_\x8n·instead·in·this·case.
37 i5·:·time·Chern·I37 i5·:·time·Chern·I
38 ·--·used·0.0330291s·(cpu);·0.0253647s·(thread);·0s·(gc)38 ·--·used·0.153931s·(cpu);·0.0365383s·(thread);·0s·(gc)
  
39 ·······339 ·······3
40 o5·=·4h40 o5·=·4h
41 ·······141 ·······1
  
42 ·····ZZ[h·]42 ·····ZZ[h·]
43 ·········143 ·········1
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Offset 70, 15 lines modifiedOffset 70, 15 lines modified
  
70 o2·:·Ideal·of·R</code></pre>70 o2·:·Ideal·of·R</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ··········<tr>73 ··········<tr>
74 ············<td>74 ············<td>
75 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I75 ··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I
76 ·--·used·0.989445s·(cpu);·0.786184s·(thread);·0s·(gc)76 ·--·used·2.35579s·(cpu);·0.873637s·(thread);·0s·(gc)
  
77 ········5······4·····377 ········5······4·····3
78 o3·=·12h··+·10h··+·6h78 o3·=·12h··+·10h··+·6h
79 ········1······1·····179 ········1······1·····1
  
80 ·····ZZ[h·]80 ·····ZZ[h·]
81 ·········181 ·········1
Offset 87, 15 lines modifiedOffset 87, 15 lines modified
87 ·······h87 ·······h
88 ········1</code></pre>88 ········1</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompleteInt)93 ··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompleteInt)
94 ·--·used·0.357044s·(cpu);·0.196663s·(thread);·0s·(gc)94 ·--·used·0.914501s·(cpu);·0.210051s·(thread);·0s·(gc)
  
95 ········5······4·····395 ········5······4·····3
96 o4·=·12h··+·10h··+·6h96 o4·=·12h··+·10h··+·6h
97 ········1······1·····197 ········1······1·····1
  
98 ·····ZZ[h·]98 ·····ZZ[h·]
99 ·········199 ·········1
677 B
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Offset 18, 28 lines modifiedOffset 18, 28 lines modified
18 o1·=·R18 o1·=·R
  
19 o1·:·PolynomialRing19 o1·:·PolynomialRing
20 i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3);20 i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3);
  
21 o2·:·Ideal·of·R21 o2·:·Ideal·of·R
22 i3·:·time·CSM·I22 i3·:·time·CSM·I
23 ·--·used·0.989445s·(cpu);·0.786184s·(thread);·0s·(gc)23 ·--·used·2.35579s·(cpu);·0.873637s·(thread);·0s·(gc)
  
24 ········5······4·····324 ········5······4·····3
25 o3·=·12h··+·10h··+·6h25 o3·=·12h··+·10h··+·6h
26 ········1······1·····126 ········1······1·····1
  
27 ·····ZZ[h·]27 ·····ZZ[h·]
28 ·········128 ·········1
29 o3·:·------29 o3·:·------
30 ········730 ········7
31 ·······h31 ·······h
32 ········132 ········1
33 i4·:·time·CSM(I,Method=>DirectCompleteInt)33 i4·:·time·CSM(I,Method=>DirectCompleteInt)
34 ·--·used·0.357044s·(cpu);·0.196663s·(thread);·0s·(gc)34 ·--·used·0.914501s·(cpu);·0.210051s·(thread);·0s·(gc)
  
35 ········5······4·····335 ········5······4·····3
36 o4·=·12h··+·10h··+·6h36 o4·=·12h··+·10h··+·6h
37 ········1······1·····137 ········1······1·····1
  
38 ·····ZZ[h·]38 ·····ZZ[h·]
39 ·········139 ·········1
724 B
./usr/share/doc/Macaulay2/Chordal/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/Classic/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/CodingTheory/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/CodingTheory/example-output/_cartesian__Code.out
    
Offset 45, 108 lines modifiedOffset 45, 108 lines modified
  
45 i2·:·F=GF(4);45 i2·:·F=GF(4);
  
46 i3·:·R=F[x,y];46 i3·:·R=F[x,y];
  
47 i4·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y})47 i4·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y})
  
48 o4·=·EvaluationCode{cache·=>·CacheTable{}···················································································································································································································································}48 o4·=·EvaluationCode{cache·=>·CacheTable{}···············································································································································································································································}
49 ·······························································949 ·······························································9
50 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F····························································································································································································································}50 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F························································································································································································································}
51 ·············································BaseField·=>·F51 ·············································BaseField·=>·F
52 ·············································cache·=>·CacheTable{}52 ·············································cache·=>·CacheTable{}
53 ·············································Code·=>·image·|·1···0···|53 ·············································Code·=>·image·|·a+1·0···|
54 ···························································|·0···0···|54 ···························································|·1···a+1·|
55 ···························································|·0···0···| 
56 ···························································|·a+1·0···| 
57 ···························································|·a+1·0···|55 ···························································|·a+1·0···|
58 ···························································|·1···1···|56 ···························································|·1···0···|
 57 ···························································|·0···0···|
59 ···························································|·a···a···|58 ···························································|·a···a···|
 59 ···························································|·0···0···|
60 ···························································|·a···a···|60 ···························································|·a···a···|
61 ···························································|·1···a+1·|61 ···························································|·1···1···|
62 ·············································GeneratorMatrix·=>·|·1·0·0·a+1·a+1·1·a·a·1···|62 ·············································GeneratorMatrix·=>·|·a+1·1···a+1·1·0·a·0·a·1·|
63 ································································|·0·0·0·0···0···1·a·a·a+1·|63 ································································|·0···a+1·0···0·0·a·0·a·1·|
64 ·············································Generators·=>·{{1,·0,·0,·a·+·1,·a·+·1,·1,·a,·a,·1},·{0,·0,·0,·0,·0,·1,·a,·a,·a·+·1}}64 ·············································Generators·=>·{{a·+·1,·1,·a·+·1,·1,·0,·a,·0,·a,·1},·{0,·a·+·1,·0,·0,·0,·a,·0,·a,·1}}
65 ·············································ParityCheckMatrix·=>·|·1·0·0·0·0·0·1···0·a+1·|65 ·············································ParityCheckMatrix·=>·|·1·0·0·a+1·0·0·0·0·0···|
 66 ··································································|·0·1·0·a···0·0·0·0·a+1·|
66 ··································································|·0·1·0·0·0·0·0···0·0···|67 ··································································|·0·0·1·a+1·0·0·0·0·0···|
67 ··································································|·0·0·1·0·0·0·0···0·0···| 
68 ··································································|·0·0·0·1·0·0·a+1·0·a···| 
69 ··································································|·0·0·0·0·1·0·a+1·0·a···|68 ··································································|·0·0·0·0···1·0·0·0·0···|
 69 ··································································|·0·0·0·0···0·1·0·0·a···|
70 ··································································|·0·0·0·0·0·1·a+1·0·0···|70 ··································································|·0·0·0·0···0·0·1·0·0···|
71 ··································································|·0·0·0·0·0·0·1···1·0···|71 ··································································|·0·0·0·0···0·0·0·1·a···|
72 ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·0,·0,·1,·0,·a·+·1},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·1,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·0,·1,·a·+·1,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·1,·0}} 
73 ····················Points·=>·{{0,·0},·{1,·0},·{0,·1},·{a,·0},·{0,·a},·{1,·1},·{1,·a},·{a,·1},·{a,·a}}72 ·············································ParityCheckRows·=>·{{1,·0,·0,·a·+·1,·0,·0,·0,·0,·0},·{0,·1,·0,·a,·0,·0,·0,·0,·a·+·1},·{0,·0,·1,·a·+·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·1,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·a},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·a}}
 73 ····················Points·=>·{{0,·a},·{a,·a},·{a,·0},·{0,·0},·{0,·1},·{a,·1},·{1,·0},·{1,·a},·{1,·1}}
74 ····················PolynomialSet·=>·{x·+·y·+·1,·x*y}74 ····················PolynomialSet·=>·{x·+·y·+·1,·x*y}
75 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}75 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}
76 ··············································3···········2·········3···········276 ··············································3···········2·········3···········2
77 ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y)77 ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y)
  
78 o4·:·EvaluationCode78 o4·:·EvaluationCode
  
79 i5·:·C.LinearCode79 i5·:·C.LinearCode
  
80 ··································980 ··································9
81 o5·=·LinearCode{AmbientModule·=>·F····························································································································································································································}81 o5·=·LinearCode{AmbientModule·=>·F························································································································································································································}
82 ················BaseField·=>·F82 ················BaseField·=>·F
83 ················cache·=>·CacheTable{}83 ················cache·=>·CacheTable{}
84 ················Code·=>·image·|·1···0···|84 ················Code·=>·image·|·a+1·0···|
85 ······························|·0···0···|85 ······························|·1···a+1·|
86 ······························|·0···0···| 
87 ······························|·a+1·0···| 
88 ······························|·a+1·0···|86 ······························|·a+1·0···|
89 ······························|·1···1···|87 ······························|·1···0···|
 88 ······························|·0···0···|
90 ······························|·a···a···|89 ······························|·a···a···|
 90 ······························|·0···0···|
91 ······························|·a···a···|91 ······························|·a···a···|
92 ······························|·1···a+1·|92 ······························|·1···1···|
93 ················GeneratorMatrix·=>·|·1·0·0·a+1·a+1·1·a·a·1···|93 ················GeneratorMatrix·=>·|·a+1·1···a+1·1·0·a·0·a·1·|
94 ···································|·0·0·0·0···0···1·a·a·a+1·|94 ···································|·0···a+1·0···0·0·a·0·a·1·|
95 ················Generators·=>·{{1,·0,·0,·a·+·1,·a·+·1,·1,·a,·a,·1},·{0,·0,·0,·0,·0,·1,·a,·a,·a·+·1}}95 ················Generators·=>·{{a·+·1,·1,·a·+·1,·1,·0,·a,·0,·a,·1},·{0,·a·+·1,·0,·0,·0,·a,·0,·a,·1}}
96 ················ParityCheckMatrix·=>·|·1·0·0·0·0·0·1···0·a+1·|96 ················ParityCheckMatrix·=>·|·1·0·0·a+1·0·0·0·0·0···|
 97 ·····································|·0·1·0·a···0·0·0·0·a+1·|
97 ·····································|·0·1·0·0·0·0·0···0·0···|98 ·····································|·0·0·1·a+1·0·0·0·0·0···|
98 ·····································|·0·0·1·0·0·0·0···0·0···| 
99 ·····································|·0·0·0·1·0·0·a+1·0·a···| 
100 ·····································|·0·0·0·0·1·0·a+1·0·a···|99 ·····································|·0·0·0·0···1·0·0·0·0···|
 100 ·····································|·0·0·0·0···0·1·0·0·a···|
101 ·····································|·0·0·0·0·0·1·a+1·0·0···|101 ·····································|·0·0·0·0···0·0·1·0·0···|
102 ·····································|·0·0·0·0·0·0·1···1·0···|102 ·····································|·0·0·0·0···0·0·0·1·a···|
103 ················ParityCheckRows·=>·{{1,·0,·0,·0,·0,·0,·1,·0,·a·+·1},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·1,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·0,·1,·a·+·1,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·1,·0}}103 ················ParityCheckRows·=>·{{1,·0,·0,·a·+·1,·0,·0,·0,·0,·0},·{0,·1,·0,·a,·0,·0,·0,·0,·a·+·1},·{0,·0,·1,·a·+·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·1,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·a},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·a}}
  
104 o5·:·LinearCode104 o5·:·LinearCode
  
105 i6·:·F=GF(4);105 i6·:·F=GF(4);
  
106 i7·:·R=F[x,y];106 i7·:·R=F[x,y];
  
107 i8·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},matrix{{1,2},{2,3}})107 i8·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},matrix{{1,2},{2,3}})
  
108 o8·=·EvaluationCode{cache·=>·CacheTable{}·······································································································································································································································}108 o8·=·EvaluationCode{cache·=>·CacheTable{}···································································································································································································································}
109 ·······························································9109 ·······························································9
110 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F················································································································································································································}110 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F············································································································································································································}
111 ·············································BaseField·=>·F111 ·············································BaseField·=>·F
112 ·············································cache·=>·CacheTable{}112 ·············································cache·=>·CacheTable{}
113 ·············································Code·=>·image·|·1···a+1·|113 ·············································Code·=>·image·|·1···a+1·|
114 ···························································|·0···0···|114 ···························································|·0···0···|
115 ···························································|·0···0···|115 ···························································|·0···0···|
 116 ···························································|·a+1·1···|
 117 ···························································|·a···a+1·|
116 ···························································|·0···0···|118 ···························································|·0···0···|
117 ···························································|·1···1···| 
118 ···························································|·0···0···|119 ···························································|·0···0···|
119 ···························································|·0···0···|120 ···························································|·0···0···|
120 ···························································|·a···a+1·| 
121 ···························································|·a+1·1···|121 ···························································|·1···1···|
122 ·············································GeneratorMatrix·=>·|·1···0·0·0·1·0·0·a···a+1·|122 ·············································GeneratorMatrix·=>·|·1···0·0·a+1·a···0·0·0·1·|
123 ································································|·a+1·0·0·0·1·0·0·a+1·1···|123 ································································|·a+1·0·0·1···a+1·0·0·0·1·|
124 ·············································Generators·=>·{{1,·0,·0,·0,·1,·0,·0,·a,·a·+·1},·{a·+·1,·0,·0,·0,·1,·0,·0,·a·+·1,·1}}124 ·············································Generators·=>·{{1,·0,·0,·a·+·1,·a,·0,·0,·0,·1},·{a·+·1,·0,·0,·1,·a·+·1,·0,·0,·0,·1}}
125 ·············································ParityCheckMatrix·=>·|·1·0·0·0·a·0·0·0·1···|125 ·············································ParityCheckMatrix·=>·|·1·0·0·0·a·0·0·0·a·|
126 ··································································|·0·1·0·0·0·0·0·0·0···|126 ··································································|·0·1·0·0·0·0·0·0·0·|
127 ··································································|·0·0·1·0·0·0·0·0·0···|127 ··································································|·0·0·1·0·0·0·0·0·0·|
128 ··································································|·0·0·0·1·0·0·0·0·0···|128 ··································································|·0·0·0·1·a·0·0·0·0·|
129 ··································································|·0·0·0·0·0·1·0·0·0···|129 ··································································|·0·0·0·0·0·1·0·0·0·|
130 ··································································|·0·0·0·0·0·0·1·0·0···|130 ··································································|·0·0·0·0·0·0·1·0·0·|
131 ··································································|·0·0·0·0·0·0·0·1·a+1·|131 ··································································|·0·0·0·0·0·0·0·1·0·|
132 ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·a,·0,·0,·0,·1},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·a·+·1}}132 ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·a,·0,·0,·0,·a},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·a,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·0}}
133 ····················Points·=>·{{a,·a},·{0,·0},·{1,·0},·{0,·1},·{1,·1},·{0,·a},·{a,·0},·{a,·1},·{1,·a}}133 ····················Points·=>·{{a,·a},·{0,·a},·{a,·0},·{1,·a},·{a,·1},·{0,·0},·{0,·1},·{1,·0},·{1,·1}}
134 ·········································2···2·3134 ·········································2···2·3
135 ····················PolynomialSet·=>·{t·t·,·t·t·}135 ····················PolynomialSet·=>·{t·t·,·t·t·}
136 ·······································0·1···0·1136 ·······································0·1···0·1
137 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}137 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}
138 ··············································3···········2··········3···········2138 ··············································3···········2··········3···········2
139 ····················VanishingIdeal·=>·ideal·(t··+·(a·+·1)t··+·a*t·,·t··+·(a·+·1)t··+·a*t·)139 ····················VanishingIdeal·=>·ideal·(t··+·(a·+·1)t··+·a*t·,·t··+·(a·+·1)t··+·a*t·)
140 ··············································0···········0······0···1···········1······1140 ··············································0···········0······0···1···········1······1
1.85 KB
./usr/share/doc/Macaulay2/CodingTheory/example-output/_dim_lp__Linear__Code_rp.out
    
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8 i3·:·H·=·hammingCode(2,3)8 i3·:·H·=·hammingCode(2,3)
  
9 ·······································79 ·······································7
10 o3·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}10 o3·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}
11 ················BaseField·=>·GF·211 ················BaseField·=>·GF·2
12 ················cache·=>·CacheTable{}12 ················cache·=>·CacheTable{}
13 ················Code·=>·image·|·1·1·0·1·|13 ················Code·=>·image·|·1·1·1·0·|
14 ······························|·1·0·1·1·|14 ······························|·1·0·1·1·|
15 ······························|·1·1·1·0·|15 ······························|·1·1·0·1·|
16 ······························|·1·0·0·0·|16 ······························|·1·0·0·0·|
17 ······························|·0·1·0·0·|17 ······························|·0·1·0·0·|
18 ······························|·0·0·1·0·|18 ······························|·0·0·1·0·|
19 ······························|·0·0·0·1·|19 ······························|·0·0·0·1·|
20 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|20 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|
21 ···································|·1·0·1·0·1·0·0·|21 ···································|·1·0·1·0·1·0·0·|
22 ···································|·0·1·1·0·0·1·0·|22 ···································|·1·1·0·0·0·1·0·|
23 ···································|·1·1·0·0·0·0·1·|23 ···································|·0·1·1·0·0·0·1·|
24 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{0,·1,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}24 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{1,·1,·0,·0,·0,·1,·0},·{0,·1,·1,·0,·0,·0,·1}}
25 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|25 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|
26 ·····································|·0·0·1·1·1·1·0·|26 ·····································|·0·1·1·0·1·1·0·|
27 ·····································|·0·1·0·1·0·1·1·|27 ·····································|·0·1·0·1·0·1·1·|
28 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}}28 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}}
  
29 o3·:·LinearCode29 o3·:·LinearCode
  
30 i4·:·dim·H30 i4·:·dim·H
  
31 o4·=·431 o4·=·4
  
396 B
./usr/share/doc/Macaulay2/CodingTheory/example-output/_hamming__Code.out
    
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2 i1·:·C1·=·hammingCode(2,3);2 i1·:·C1·=·hammingCode(2,3);
  
3 i2·:·C1.ParityCheckMatrix3 i2·:·C1.ParityCheckMatrix
  
4 o2·=·|·1·1·1·1·0·0·0·|4 o2·=·|·1·1·1·1·0·0·0·|
5 ·····|·0·1·0·1·1·1·0·|5 ·····|·0·1·0·1·1·1·0·|
6 ·····|·1·0·0·1·1·0·1·|6 ·····|·0·1·1·0·0·1·1·|
  
7 ··················3···········77 ··················3···········7
8 o2·:·Matrix·(GF·2)··<--·(GF·2)8 o2·:·Matrix·(GF·2)··<--·(GF·2)
  
9 i3·:·9 i3·:·
3.52 KB
./usr/share/doc/Macaulay2/CodingTheory/example-output/_order__Code.out
    
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59 o10·=·EvaluationCode{cache·=>·CacheTable{}·····································································································································}59 o10·=·EvaluationCode{cache·=>·CacheTable{}·····································································································································}
60 ·····················Points·=>·{{0,·0},·{a,·a},·{a·+·1,·a},·{1,·a}}60 ·····················Points·=>·{{0,·0},·{a,·a},·{a·+·1,·a},·{1,·a}}
61 ································································461 ································································4
62 ·····················LinearCode·=>·LinearCode{AmbientModule·=>·F··············································································································}62 ·····················LinearCode·=>·LinearCode{AmbientModule·=>·F··············································································································}
63 ··············································BaseField·=>·F63 ··············································BaseField·=>·F
64 ··············································cache·=>·CacheTable{}64 ··············································cache·=>·CacheTable{}
65 ··············································Code·=>·image·|·0···0···1·0·0···0·0···|65 ··············································Code·=>·image·|·0···0·0···0···0···1·0·|
66 ····························································|·a+1·a···1·1·1···a·a+1·| 
67 ····························································|·a···a+1·1·1·a+1·a·1···|66 ····························································|·1···a·a+1·a+1·a···1·1·|
68 ····························································|·1···1···1·1·a···a·a···|67 ····························································|·a+1·a·1···a···a+1·1·1·|
 68 ····························································|·a···a·a···1···1···1·1·|
69 ··············································GeneratorMatrix·=>·|·0·a+1·a···1·|69 ··············································GeneratorMatrix·=>·|·0·1···a+1·a·|
 70 ·································································|·0·a···a···a·|
 71 ·································································|·0·a+1·1···a·|
 72 ·································································|·0·a+1·a···1·|
70 ·································································|·0·a···a+1·1·|73 ·································································|·0·a···a+1·1·|
71 ·································································|·1·1···1···1·|74 ·································································|·1·1···1···1·|
72 ·································································|·0·1···1···1·|75 ·································································|·0·1···1···1·|
 76 ··············································Generators·=>·{{0,·1,·a·+·1,·a},·{0,·a,·a,·a},·{0,·a·+·1,·1,·a},·{0,·a·+·1,·a,·1},·{0,·a,·a·+·1,·1},·{1,·1,·1,·1},·{0,·1,·1,·1}}
73 ·································································|·0·1···a+1·a·| 
74 ·································································|·0·a···a···a·| 
75 ·································································|·0·a+1·1···a·| 
76 ··············································Generators·=>·{{0,·a·+·1,·a,·1},·{0,·a,·a·+·1,·1},·{1,·1,·1,·1},·{0,·1,·1,·1},·{0,·1,·a·+·1,·a},·{0,·a,·a,·a},·{0,·a·+·1,·1,·a}} 
77 ··············································ParityCheckMatrix·=>·077 ··············································ParityCheckMatrix·=>·0
78 ··············································ParityCheckRows·=>·{}78 ··············································ParityCheckRows·=>·{}
79 ···············································2·······················379 ···············································2·······················3
80 ·····················VanishingIdeal·=>·ideal·(t··+·a*t·,·t·t··+·a*t·,·t··+·(a·+·1)t·)80 ·····················VanishingIdeal·=>·ideal·(t··+·a*t·,·t·t··+·a*t·,·t··+·(a·+·1)t·)
81 ···············································1······1···0·1······0···0···········181 ···············································1······1···0·1······0···0···········1
82 ········································2··········3···282 ········································2···············2··········3
83 ·····················PolynomialSet·=>·{t·,·t·,·1,·t·,·t·t·,·t·,·t·t·}83 ·····················PolynomialSet·=>·{t·t·,·t·,·t·t·,·t·,·t·,·1,·t·}
84 ········································0···0······0···0·1···1···0·184 ········································0·1···1···0·1···0···0······0
  
85 i11·:·F·=·GF(4);85 i11·:·F·=·GF(4);
  
86 i12·:·R·=·F[x,y];86 i12·:·R·=·F[x,y];
  
87 i13·:·I·=·ideal(x^3+y^2+y);87 i13·:·I·=·ideal(x^3+y^2+y);
  
1.86 KB
./usr/share/doc/Macaulay2/CodingTheory/example-output/_ring_lp__Linear__Code_rp.out
    
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2 i1·:·C·=·hammingCode(2,·3)2 i1·:·C·=·hammingCode(2,·3)
  
3 ·······································73 ·······································7
4 o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}4 o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}
5 ················BaseField·=>·GF·25 ················BaseField·=>·GF·2
6 ················cache·=>·CacheTable{}6 ················cache·=>·CacheTable{}
7 ················Code·=>·image·|·1·0·1·1·|7 ················Code·=>·image·|·1·1·0·1·|
8 ······························|·1·1·0·1·|8 ······························|·1·0·1·1·|
9 ······························|·1·1·1·0·|9 ······························|·1·1·1·0·|
10 ······························|·1·0·0·0·|10 ······························|·1·0·0·0·|
11 ······························|·0·1·0·0·|11 ······························|·0·1·0·0·|
12 ······························|·0·0·1·0·|12 ······························|·0·0·1·0·|
13 ······························|·0·0·0·1·|13 ······························|·0·0·0·1·|
14 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|14 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|
15 ···································|·0·1·1·0·1·0·0·|15 ···································|·1·0·1·0·1·0·0·|
16 ···································|·1·0·1·0·0·1·0·|16 ···································|·0·1·1·0·0·1·0·|
17 ···································|·1·1·0·0·0·0·1·|17 ···································|·1·1·0·0·0·0·1·|
18 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·0,·0},·{1,·0,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}18 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{0,·1,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}
19 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|19 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|
20 ·····································|·0·0·1·1·1·1·0·|20 ·····································|·0·0·1·1·1·1·0·|
21 ·····································|·0·1·0·1·1·0·1·|21 ·····································|·0·1·0·1·0·1·1·|
22 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·1,·0,·1}}22 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}}
  
23 o1·:·LinearCode23 o1·:·LinearCode
  
24 i2·:·ring(C)24 i2·:·ring(C)
  
25 o2·=·GF·225 o2·=·GF·2
  
1.8 KB
./usr/share/doc/Macaulay2/CodingTheory/example-output/_syndrome__Decode.out
    
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37 ························|·0·|37 ························|·0·|
38 ························|·0·|38 ························|·0·|
39 ························|·1·|39 ························|·1·|
40 ···············|·0·|·=>·|·0·|40 ···············|·0·|·=>·|·0·|
41 ···············|·1·|····|·0·|41 ···············|·1·|····|·0·|
42 ···············|·0·|····|·0·|42 ···············|·0·|····|·0·|
43 ························|·0·|43 ························|·0·|
44 ························|·1·| 
45 ························|·0·|44 ························|·0·|
 45 ························|·1·|
46 ························|·0·|46 ························|·0·|
47 ···············|·0·|·=>·|·0·|47 ···············|·0·|·=>·|·0·|
48 ···············|·1·|····|·0·|48 ···············|·1·|····|·0·|
49 ···············|·1·|····|·0·|49 ···············|·1·|····|·0·|
50 ························|·0·|50 ························|·0·|
51 ························|·0·| 
52 ························|·1·|51 ························|·1·|
53 ························|·0·|52 ························|·0·|
 53 ························|·0·|
54 ···············|·1·|·=>·|·1·|54 ···············|·1·|·=>·|·1·|
55 ···············|·0·|····|·0·|55 ···············|·0·|····|·0·|
56 ···············|·0·|····|·0·|56 ···············|·0·|····|·0·|
57 ························|·0·|57 ························|·0·|
58 ························|·0·|58 ························|·0·|
59 ························|·0·|59 ························|·0·|
60 ························|·0·|60 ························|·0·|
61 ···············|·1·|·=>·|·0·|61 ···············|·1·|·=>·|·0·|
62 ···············|·0·|····|·0·|62 ···············|·0·|····|·1·|
63 ···············|·1·|····|·1·|63 ···············|·1·|····|·0·|
64 ························|·0·|64 ························|·0·|
65 ························|·0·|65 ························|·0·|
66 ························|·0·|66 ························|·0·|
67 ························|·0·|67 ························|·0·|
68 ···············|·1·|·=>·|·0·|68 ···············|·1·|·=>·|·0·|
69 ···············|·1·|····|·0·|69 ···············|·1·|····|·0·|
70 ···············|·0·|····|·0·|70 ···············|·0·|····|·1·|
71 ························|·1·|71 ························|·0·|
72 ························|·0·|72 ························|·0·|
73 ························|·0·|73 ························|·0·|
74 ························|·0·|74 ························|·0·|
75 ···············|·1·|·=>·|·0·|75 ···············|·1·|·=>·|·0·|
76 ···············|·1·|····|·1·| 
77 ···············|·1·|····|·0·|76 ···············|·1·|····|·0·|
 77 ···············|·1·|····|·0·|
78 ························|·0·|78 ························|·1·|
79 ························|·0·|79 ························|·0·|
80 ························|·0·|80 ························|·0·|
81 ························|·0·|81 ························|·0·|
  
82 o7·:·HashTable82 o7·:·HashTable
  
83 i8·:·83 i8·:·
25.2 KB
./usr/share/doc/Macaulay2/CodingTheory/html/_cartesian__Code.html
    
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182 ················<pre><code·class="language-macaulay2">i3·:·R=F[x,y];</code></pre>182 ················<pre><code·class="language-macaulay2">i3·:·R=F[x,y];</code></pre>
183 ··············</td>183 ··············</td>
184 ············</tr>184 ············</tr>
185 ············<tr>185 ············<tr>
186 ··············<td>186 ··············<td>
187 ················<pre><code·class="language-macaulay2">i4·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y})187 ················<pre><code·class="language-macaulay2">i4·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y})
  
188 o4·=·EvaluationCode{cache·=>·CacheTable{}···················································································································································································································································}188 o4·=·EvaluationCode{cache·=>·CacheTable{}···············································································································································································································································}
189 ·······························································9189 ·······························································9
190 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F····························································································································································································································}190 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F························································································································································································································}
191 ·············································BaseField·=>·F191 ·············································BaseField·=>·F
192 ·············································cache·=>·CacheTable{}192 ·············································cache·=>·CacheTable{}
193 ·············································Code·=>·image·|·1···0···|193 ·············································Code·=>·image·|·a+1·0···|
194 ···························································|·0···0···|194 ···························································|·1···a+1·|
195 ···························································|·0···0···| 
196 ···························································|·a+1·0···| 
197 ···························································|·a+1·0···|195 ···························································|·a+1·0···|
198 ···························································|·1···1···|196 ···························································|·1···0···|
 197 ···························································|·0···0···|
199 ···························································|·a···a···|198 ···························································|·a···a···|
 199 ···························································|·0···0···|
200 ···························································|·a···a···|200 ···························································|·a···a···|
201 ···························································|·1···a+1·|201 ···························································|·1···1···|
202 ·············································GeneratorMatrix·=>·|·1·0·0·a+1·a+1·1·a·a·1···|202 ·············································GeneratorMatrix·=>·|·a+1·1···a+1·1·0·a·0·a·1·|
203 ································································|·0·0·0·0···0···1·a·a·a+1·|203 ································································|·0···a+1·0···0·0·a·0·a·1·|
204 ·············································Generators·=>·{{1,·0,·0,·a·+·1,·a·+·1,·1,·a,·a,·1},·{0,·0,·0,·0,·0,·1,·a,·a,·a·+·1}}204 ·············································Generators·=>·{{a·+·1,·1,·a·+·1,·1,·0,·a,·0,·a,·1},·{0,·a·+·1,·0,·0,·0,·a,·0,·a,·1}}
205 ·············································ParityCheckMatrix·=>·|·1·0·0·0·0·0·1···0·a+1·|205 ·············································ParityCheckMatrix·=>·|·1·0·0·a+1·0·0·0·0·0···|
 206 ··································································|·0·1·0·a···0·0·0·0·a+1·|
206 ··································································|·0·1·0·0·0·0·0···0·0···|207 ··································································|·0·0·1·a+1·0·0·0·0·0···|
207 ··································································|·0·0·1·0·0·0·0···0·0···| 
208 ··································································|·0·0·0·1·0·0·a+1·0·a···| 
209 ··································································|·0·0·0·0·1·0·a+1·0·a···|208 ··································································|·0·0·0·0···1·0·0·0·0···|
 209 ··································································|·0·0·0·0···0·1·0·0·a···|
210 ··································································|·0·0·0·0·0·1·a+1·0·0···|210 ··································································|·0·0·0·0···0·0·1·0·0···|
211 ··································································|·0·0·0·0·0·0·1···1·0···|211 ··································································|·0·0·0·0···0·0·0·1·a···|
212 ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·0,·0,·1,·0,·a·+·1},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·1,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·0,·1,·a·+·1,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·1,·0}} 
213 ····················Points·=>·{{0,·0},·{1,·0},·{0,·1},·{a,·0},·{0,·a},·{1,·1},·{1,·a},·{a,·1},·{a,·a}}212 ·············································ParityCheckRows·=>·{{1,·0,·0,·a·+·1,·0,·0,·0,·0,·0},·{0,·1,·0,·a,·0,·0,·0,·0,·a·+·1},·{0,·0,·1,·a·+·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·1,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·a},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·a}}
 213 ····················Points·=>·{{0,·a},·{a,·a},·{a,·0},·{0,·0},·{0,·1},·{a,·1},·{1,·0},·{1,·a},·{1,·1}}
214 ····················PolynomialSet·=>·{x·+·y·+·1,·x*y}214 ····················PolynomialSet·=>·{x·+·y·+·1,·x*y}
215 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}215 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}
216 ··············································3···········2·········3···········2216 ··············································3···········2·········3···········2
217 ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y)217 ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y)
  
218 o4·:·EvaluationCode</code></pre>218 o4·:·EvaluationCode</code></pre>
219 ··············</td>219 ··············</td>
220 ············</tr>220 ············</tr>
221 ············<tr>221 ············<tr>
222 ··············<td>222 ··············<td>
223 ················<pre><code·class="language-macaulay2">i5·:·C.LinearCode223 ················<pre><code·class="language-macaulay2">i5·:·C.LinearCode
  
224 ··································9224 ··································9
225 o5·=·LinearCode{AmbientModule·=>·F····························································································································································································································}225 o5·=·LinearCode{AmbientModule·=>·F························································································································································································································}
226 ················BaseField·=>·F226 ················BaseField·=>·F
227 ················cache·=>·CacheTable{}227 ················cache·=>·CacheTable{}
228 ················Code·=>·image·|·1···0···|228 ················Code·=>·image·|·a+1·0···|
229 ······························|·0···0···|229 ······························|·1···a+1·|
230 ······························|·0···0···| 
231 ······························|·a+1·0···| 
232 ······························|·a+1·0···|230 ······························|·a+1·0···|
233 ······························|·1···1···|231 ······························|·1···0···|
 232 ······························|·0···0···|
234 ······························|·a···a···|233 ······························|·a···a···|
 234 ······························|·0···0···|
235 ······························|·a···a···|235 ······························|·a···a···|
236 ······························|·1···a+1·|236 ······························|·1···1···|
237 ················GeneratorMatrix·=>·|·1·0·0·a+1·a+1·1·a·a·1···|237 ················GeneratorMatrix·=>·|·a+1·1···a+1·1·0·a·0·a·1·|
238 ···································|·0·0·0·0···0···1·a·a·a+1·|238 ···································|·0···a+1·0···0·0·a·0·a·1·|
239 ················Generators·=>·{{1,·0,·0,·a·+·1,·a·+·1,·1,·a,·a,·1},·{0,·0,·0,·0,·0,·1,·a,·a,·a·+·1}}239 ················Generators·=>·{{a·+·1,·1,·a·+·1,·1,·0,·a,·0,·a,·1},·{0,·a·+·1,·0,·0,·0,·a,·0,·a,·1}}
240 ················ParityCheckMatrix·=>·|·1·0·0·0·0·0·1···0·a+1·|240 ················ParityCheckMatrix·=>·|·1·0·0·a+1·0·0·0·0·0···|
 241 ·····································|·0·1·0·a···0·0·0·0·a+1·|
241 ·····································|·0·1·0·0·0·0·0···0·0···|242 ·····································|·0·0·1·a+1·0·0·0·0·0···|
242 ·····································|·0·0·1·0·0·0·0···0·0···| 
243 ·····································|·0·0·0·1·0·0·a+1·0·a···| 
244 ·····································|·0·0·0·0·1·0·a+1·0·a···|243 ·····································|·0·0·0·0···1·0·0·0·0···|
 244 ·····································|·0·0·0·0···0·1·0·0·a···|
245 ·····································|·0·0·0·0·0·1·a+1·0·0···|245 ·····································|·0·0·0·0···0·0·1·0·0···|
246 ·····································|·0·0·0·0·0·0·1···1·0···|246 ·····································|·0·0·0·0···0·0·0·1·a···|
247 ················ParityCheckRows·=>·{{1,·0,·0,·0,·0,·0,·1,·0,·a·+·1},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·1,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·0,·1,·a·+·1,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·1,·0}}247 ················ParityCheckRows·=>·{{1,·0,·0,·a·+·1,·0,·0,·0,·0,·0},·{0,·1,·0,·a,·0,·0,·0,·0,·a·+·1},·{0,·0,·1,·a·+·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·1,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·a},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·a}}
  
248 o5·:·LinearCode</code></pre>248 o5·:·LinearCode</code></pre>
249 ··············</td>249 ··············</td>
250 ············</tr>250 ············</tr>
251 ··········</table>251 ··········</table>
252 ········</div>252 ········</div>
253 ········<div>253 ········<div>
Offset 288, 40 lines modifiedOffset 288, 40 lines modified
288 ················<pre><code·class="language-macaulay2">i7·:·R=F[x,y];</code></pre>288 ················<pre><code·class="language-macaulay2">i7·:·R=F[x,y];</code></pre>
289 ··············</td>289 ··············</td>
290 ············</tr>290 ············</tr>
291 ············<tr>291 ············<tr>
292 ··············<td>292 ··············<td>
293 ················<pre><code·class="language-macaulay2">i8·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},matrix{{1,2},{2,3}})293 ················<pre><code·class="language-macaulay2">i8·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},matrix{{1,2},{2,3}})
  
294 o8·=·EvaluationCode{cache·=>·CacheTable{}·······································································································································································································································}294 o8·=·EvaluationCode{cache·=>·CacheTable{}···································································································································································································································}
295 ·······························································9295 ·······························································9
296 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F················································································································································································································}296 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F············································································································································································································}
297 ·············································BaseField·=>·F297 ·············································BaseField·=>·F
298 ·············································cache·=>·CacheTable{}298 ·············································cache·=>·CacheTable{}
299 ·············································Code·=>·image·|·1···a+1·|299 ·············································Code·=>·image·|·1···a+1·|
300 ···························································|·0···0···|300 ···························································|·0···0···|
301 ···························································|·0···0···|301 ···························································|·0···0···|
 302 ···························································|·a+1·1···|
 303 ···························································|·a···a+1·|
302 ···························································|·0···0···|304 ···························································|·0···0···|
303 ···························································|·1···1···| 
304 ···························································|·0···0···|305 ···························································|·0···0···|
305 ···························································|·0···0···|306 ···························································|·0···0···|
306 ···························································|·a···a+1·| 
307 ···························································|·a+1·1···|307 ···························································|·1···1···|
308 ·············································GeneratorMatrix·=>·|·1···0·0·0·1·0·0·a···a+1·|308 ·············································GeneratorMatrix·=>·|·1···0·0·a+1·a···0·0·0·1·|
309 ································································|·a+1·0·0·0·1·0·0·a+1·1···|309 ································································|·a+1·0·0·1···a+1·0·0·0·1·|
310 ·············································Generators·=>·{{1,·0,·0,·0,·1,·0,·0,·a,·a·+·1},·{a·+·1,·0,·0,·0,·1,·0,·0,·a·+·1,·1}}310 ·············································Generators·=>·{{1,·0,·0,·a·+·1,·a,·0,·0,·0,·1},·{a·+·1,·0,·0,·1,·a·+·1,·0,·0,·0,·1}}
311 ·············································ParityCheckMatrix·=>·|·1·0·0·0·a·0·0·0·1···|311 ·············································ParityCheckMatrix·=>·|·1·0·0·0·a·0·0·0·a·|
312 ··································································|·0·1·0·0·0·0·0·0·0···|312 ··································································|·0·1·0·0·0·0·0·0·0·|
313 ··································································|·0·0·1·0·0·0·0·0·0···|313 ··································································|·0·0·1·0·0·0·0·0·0·|
314 ··································································|·0·0·0·1·0·0·0·0·0···|314 ··································································|·0·0·0·1·a·0·0·0·0·|
315 ··································································|·0·0·0·0·0·1·0·0·0···|315 ··································································|·0·0·0·0·0·1·0·0·0·|
316 ··································································|·0·0·0·0·0·0·1·0·0···|316 ··································································|·0·0·0·0·0·0·1·0·0·|
317 ··································································|·0·0·0·0·0·0·0·1·a+1·|317 ··································································|·0·0·0·0·0·0·0·1·0·|
318 ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·a,·0,·0,·0,·1},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·a·+·1}}318 ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·a,·0,·0,·0,·a},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·a,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·0}}
319 ····················Points·=>·{{a,·a},·{0,·0},·{1,·0},·{0,·1},·{1,·1},·{0,·a},·{a,·0},·{a,·1},·{1,·a}}319 ····················Points·=>·{{a,·a},·{0,·a},·{a,·0},·{1,·a},·{a,·1},·{0,·0},·{0,·1},·{1,·0},·{1,·1}}
320 ·········································2···2·3320 ·········································2···2·3
321 ····················PolynomialSet·=>·{t·t·,·t·t·}321 ····················PolynomialSet·=>·{t·t·,·t·t·}
322 ·······································0·1···0·1322 ·······································0·1···0·1
323 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}323 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}
324 ··············································3···········2··········3···········2324 ··············································3···········2··········3···········2
325 ····················VanishingIdeal·=>·ideal·(t··+·(a·+·1)t··+·a*t·,·t··+·(a·+·1)t··+·a*t·)325 ····················VanishingIdeal·=>·ideal·(t··+·(a·+·1)t··+·a*t·,·t··+·(a·+·1)t··+·a*t·)
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Offset 123, 49 lines modifiedOffset 123, 49 lines modified
123 o4·=·EvaluationCode{cache·=>·CacheTable{}123 o4·=·EvaluationCode{cache·=>·CacheTable{}
124 }124 }
125 ·······························································9125 ·······························································9
126 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F126 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F
127 }127 }
128 ·············································BaseField·=>·F128 ·············································BaseField·=>·F
129 ·············································cache·=>·CacheTable{}129 ·············································cache·=>·CacheTable{}
130 ·············································Code·=>·image·|·1···0···|130 ·············································Code·=>·image·|·a+1·0···|
131 ···························································|·0···0···|131 ···························································|·1···a+1·|
132 ···························································|·0···0···| 
133 ···························································|·a+1·0···| 
134 ···························································|·a+1·0···|132 ···························································|·a+1·0···|
135 ···························································|·1···1···|133 ···························································|·1···0···|
 134 ···························································|·0···0···|
136 ···························································|·a···a···|135 ···························································|·a···a···|
 136 ···························································|·0···0···|
137 ···························································|·a···a···|137 ···························································|·a···a···|
138 ···························································|·1···a+1·|138 ···························································|·1···1···|
139 ·············································GeneratorMatrix·=>·|·1·0·0·a+1·a+1139 ·············································GeneratorMatrix·=>·|·a+1·1···a+1·1
140 1·a·a·1···|140 0·a·0·a·1·|
141 ································································|·0·0·0·0···0141 ································································|·0···a+1·0···0
142 1·a·a·a+1·|142 0·a·0·a·1·|
143 ·············································Generators·=>·{{1,·0,·0,·a·+·1,·a143 ·············································Generators·=>·{{a·+·1,·1,·a·+·1,
144 +·1,·1,·a,·a,·1},·{0,·0,·0,·0,·0,·1,·a,·a,·a·+·1}}144 1,·0,·a,·0,·a,·1},·{0,·a·+·1,·0,·0,·0,·a,·0,·a,·1}}
145 ·············································ParityCheckMatrix·=>·|·1·0·0·0·0·0145 ·············································ParityCheckMatrix·=>·|·1·0·0·a+1·0
146 1···0·a+1·|146 0·0·0·0···|
147 ··································································|·0·1·0·0·0·0147 ··································································|·0·1·0·a···0
148 0···0·0···|148 0·0·0·a+1·|
149 ··································································|·0·0·1·0·0·0149 ··································································|·0·0·1·a+1·0
150 0···0·0···|150 0·0·0·0···|
151 ··································································|·0·0·0·1·0·0 
152 a+1·0·a···| 
153 ··································································|·0·0·0·0·1·0 
154 a+1·0·a···| 
155 ··································································|·0·0·0·0·0·1151 ··································································|·0·0·0·0···1
156 a+1·0·0···|152 0·0·0·0···|
157 ··································································|·0·0·0·0·0·0153 ··································································|·0·0·0·0···0
158 1···1·0···|154 1·0·0·a···|
 155 ··································································|·0·0·0·0···0
 156 0·1·0·0···|
 157 ··································································|·0·0·0·0···0
 158 0·0·1·a···|
159 ·············································ParityCheckRows·=>·{{1,·0,·0,·0,159 ·············································ParityCheckRows·=>·{{1,·0,·0,·a·+
160 0,·0,·1,·0,·a·+·1},·{0,·1,·0,·0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0}, 
161 {0,·0,·0,·1,·0,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·1,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,160 1,·0,·0,·0,·0,·0},·{0,·1,·0,·a,·0,·0,·0,·0,·a·+·1},·{0,·0,·1,·a·+·1,·0,·0,·0,
 161 0,·0},·{0,·0,·0,·0,·1,·0,·0,·0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·a},·{0,·0,·0,·0,
162 0,·1,·a·+·1,·0,·0},·{0,·0,·0,·0,·0,·0,·1,·1,·0}}162 0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·a}}
163 ····················Points·=>·{{0,·0},·{1,·0},·{0,·1},·{a,·0},·{0,·a},·{1,·1},163 ····················Points·=>·{{0,·a},·{a,·a},·{a,·0},·{0,·0},·{0,·1},·{a,·1},
164 {1,·a},·{a,·1},·{a,·a}}164 {1,·0},·{1,·a},·{1,·1}}
165 ····················PolynomialSet·=>·{x·+·y·+·1,·x*y}165 ····················PolynomialSet·=>·{x·+·y·+·1,·x*y}
166 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}166 ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}}
167 ··············································3···········2·········3167 ··············································3···········2·········3
168 2168 2
169 ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+169 ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+
170 1)y··+·a*y)170 1)y··+·a*y)
  
Offset 173, 38 lines modifiedOffset 173, 38 lines modified
173 i5·:·C.LinearCode173 i5·:·C.LinearCode
  
174 ··································9174 ··································9
175 o5·=·LinearCode{AmbientModule·=>·F175 o5·=·LinearCode{AmbientModule·=>·F
176 }176 }
177 ················BaseField·=>·F177 ················BaseField·=>·F
178 ················cache·=>·CacheTable{}178 ················cache·=>·CacheTable{}
179 ················Code·=>·image·|·1···0···|179 ················Code·=>·image·|·a+1·0···|
180 ······························|·0···0···|180 ······························|·1···a+1·|
181 ······························|·0···0···| 
182 ······························|·a+1·0···| 
183 ······························|·a+1·0···|181 ······························|·a+1·0···|
184 ······························|·1···1···|182 ······························|·1···0···|
 183 ······························|·0···0···|
185 ······························|·a···a···|184 ······························|·a···a···|
 185 ······························|·0···0···|
186 ······························|·a···a···|186 ······························|·a···a···|
187 ······························|·1···a+1·|187 ······························|·1···1···|
188 ················GeneratorMatrix·=>·|·1·0·0·a+1·a+1·1·a·a·1···|188 ················GeneratorMatrix·=>·|·a+1·1···a+1·1·0·a·0·a·1·|
189 ···································|·0·0·0·0···0···1·a·a·a+1·|189 ···································|·0···a+1·0···0·0·a·0·a·1·|
190 ················Generators·=>·{{1,·0,·0,·a·+·1,·a·+·1,·1,·a,·a,·1},·{0,·0,·0,190 ················Generators·=>·{{a·+·1,·1,·a·+·1,·1,·0,·a,·0,·a,·1},·{0,·a·+·1,
191 0,·0,·1,·a,·a,·a·+·1}}191 0,·0,·0,·a,·0,·a,·1}}
192 ················ParityCheckMatrix·=>·|·1·0·0·0·0·0·1···0·a+1·|192 ················ParityCheckMatrix·=>·|·1·0·0·a+1·0·0·0·0·0···|
 193 ·····································|·0·1·0·a···0·0·0·0·a+1·|
193 ·····································|·0·1·0·0·0·0·0···0·0···|194 ·····································|·0·0·1·a+1·0·0·0·0·0···|
194 ·····································|·0·0·1·0·0·0·0···0·0···| 
195 ·····································|·0·0·0·1·0·0·a+1·0·a···| 
196 ·····································|·0·0·0·0·1·0·a+1·0·a···|195 ·····································|·0·0·0·0···1·0·0·0·0···|
 196 ·····································|·0·0·0·0···0·1·0·0·a···|
197 ·····································|·0·0·0·0·0·1·a+1·0·0···|197 ·····································|·0·0·0·0···0·0·1·0·0···|
198 ·····································|·0·0·0·0·0·0·1···1·0···|198 ·····································|·0·0·0·0···0·0·0·1·a···|
199 ················ParityCheckRows·=>·{{1,·0,·0,·0,·0,·0,·1,·0,·a·+·1},·{0,·1,·0,199 ················ParityCheckRows·=>·{{1,·0,·0,·a·+·1,·0,·0,·0,·0,·0},·{0,·1,·0,
200 0,·0,·0,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·a·+·1,·0,200 a,·0,·0,·0,·0,·a·+·1},·{0,·0,·1,·a·+·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·1,·0,·0,
201 a},·{0,·0,·0,·0,·1,·0,·a·+·1,·0,·a},·{0,·0,·0,·0,·0,·1,·a·+·1,·0,·0},·{0,·0,·0,201 0,·0},·{0,·0,·0,·0,·0,·1,·0,·0,·a},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,
202 0,·0,·0,·1,·1,·0}}202 0,·0,·0,·1,·a}}
  
203 o5·:·LinearCode203 o5·:·LinearCode
204 *\x8**\x8**\x8**\x8**\x8*·a\x8a·r\x8ri\x8in\x8ng\x8g,\x8,·a\x8a·l\x8li\x8is\x8st\x8t·a\x8an\x8nd\x8d·a\x8a·M\x8Ma\x8at\x8tr\x8ri\x8ix\x8x·a\x8ar\x8re\x8e·g\x8gi\x8iv\x8ve\x8en\x8n·*\x8**\x8**\x8**\x8**\x8*204 *\x8**\x8**\x8**\x8**\x8*·a\x8a·r\x8ri\x8in\x8ng\x8g,\x8,·a\x8a·l\x8li\x8is\x8st\x8t·a\x8an\x8nd\x8d·a\x8a·M\x8Ma\x8at\x8tr\x8ri\x8ix\x8x·a\x8ar\x8re\x8e·g\x8gi\x8iv\x8ve\x8en\x8n·*\x8**\x8**\x8**\x8**\x8*
205 ····*···Usage:205 ····*···Usage:
206 ············cartesianCode(F,·L,·M)206 ············cartesianCode(F,·L,·M)
207 ····*·Inputs:207 ····*·Inputs:
208 ··········o·F,·a·_\x8r_\x8i_\x8n_\x8g,208 ··········o·F,·a·_\x8r_\x8i_\x8n_\x8g,
Offset 226, 46 lines modifiedOffset 226, 46 lines modified
226 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F226 ····················LinearCode·=>·LinearCode{AmbientModule·=>·F
227 }227 }
228 ·············································BaseField·=>·F228 ·············································BaseField·=>·F
229 ·············································cache·=>·CacheTable{}229 ·············································cache·=>·CacheTable{}
230 ·············································Code·=>·image·|·1···a+1·|230 ·············································Code·=>·image·|·1···a+1·|
231 ···························································|·0···0···|231 ···························································|·0···0···|
232 ···························································|·0···0···|232 ···························································|·0···0···|
 233 ···························································|·a+1·1···|
 234 ···························································|·a···a+1·|
233 ···························································|·0···0···|235 ···························································|·0···0···|
234 ···························································|·1···1···| 
235 ···························································|·0···0···|236 ···························································|·0···0···|
236 ···························································|·0···0···|237 ···························································|·0···0···|
237 ···························································|·a···a+1·| 
238 ···························································|·a+1·1···|238 ···························································|·1···1···|
239 ·············································GeneratorMatrix·=>·|·1···0·0·0·1·0239 ·············································GeneratorMatrix·=>·|·1···0·0·a+1·a
240 0·a···a+1·|240 0·0·0·1·|
241 ································································|·a+1·0·0·0·1·0241 ································································|·a+1·0·0·1
242 0·a+1·1···|242 a+1·0·0·0·1·|
243 ·············································Generators·=>·{{1,·0,·0,·0,·1,·0,243 ·············································Generators·=>·{{1,·0,·0,·a·+·1,·a,
244 0,·a,·a·+·1},·{a·+·1,·0,·0,·0,·1,·0,·0,·a·+·1,·1}}244 0,·0,·0,·1},·{a·+·1,·0,·0,·1,·a·+·1,·0,·0,·0,·1}}
245 ·············································ParityCheckMatrix·=>·|·1·0·0·0·a·0245 ·············································ParityCheckMatrix·=>·|·1·0·0·0·a·0
246 0·0·1···|246 0·0·a·|
247 ··································································|·0·1·0·0·0·0247 ··································································|·0·1·0·0·0·0
248 0·0·0···|248 0·0·0·|
249 ··································································|·0·0·1·0·0·0249 ··································································|·0·0·1·0·0·0
250 0·0·0···|250 0·0·0·|
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./usr/share/doc/Macaulay2/CodingTheory/html/_dim_lp__Linear__Code_rp.html
    
Offset 88, 30 lines modifiedOffset 88, 30 lines modified
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i3·:·H·=·hammingCode(2,3)89 ··············<pre><code·class="language-macaulay2">i3·:·H·=·hammingCode(2,3)
  
90 ·······································790 ·······································7
91 o3·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}91 o3·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}
92 ················BaseField·=>·GF·292 ················BaseField·=>·GF·2
93 ················cache·=>·CacheTable{}93 ················cache·=>·CacheTable{}
94 ················Code·=>·image·|·1·1·0·1·|94 ················Code·=>·image·|·1·1·1·0·|
95 ······························|·1·0·1·1·|95 ······························|·1·0·1·1·|
96 ······························|·1·1·1·0·|96 ······························|·1·1·0·1·|
97 ······························|·1·0·0·0·|97 ······························|·1·0·0·0·|
98 ······························|·0·1·0·0·|98 ······························|·0·1·0·0·|
99 ······························|·0·0·1·0·|99 ······························|·0·0·1·0·|
100 ······························|·0·0·0·1·|100 ······························|·0·0·0·1·|
101 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|101 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|
102 ···································|·1·0·1·0·1·0·0·|102 ···································|·1·0·1·0·1·0·0·|
103 ···································|·0·1·1·0·0·1·0·|103 ···································|·1·1·0·0·0·1·0·|
104 ···································|·1·1·0·0·0·0·1·|104 ···································|·0·1·1·0·0·0·1·|
105 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{0,·1,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}105 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{1,·1,·0,·0,·0,·1,·0},·{0,·1,·1,·0,·0,·0,·1}}
106 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|106 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|
107 ·····································|·0·0·1·1·1·1·0·|107 ·····································|·0·1·1·0·1·1·0·|
108 ·····································|·0·1·0·1·0·1·1·|108 ·····································|·0·1·0·1·0·1·1·|
109 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}}109 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}}
  
110 o3·:·LinearCode</code></pre>110 o3·:·LinearCode</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i4·:·dim·H115 ··············<pre><code·class="language-macaulay2">i4·:·dim·H
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21 i3·:·H·=·hammingCode(2,3)21 i3·:·H·=·hammingCode(2,3)
  
22 ·······································722 ·······································7
23 o3·=·LinearCode{AmbientModule·=>·(GF·2)23 o3·=·LinearCode{AmbientModule·=>·(GF·2)
24 }24 }
25 ················BaseField·=>·GF·225 ················BaseField·=>·GF·2
26 ················cache·=>·CacheTable{}26 ················cache·=>·CacheTable{}
27 ················Code·=>·image·|·1·1·0·1·|27 ················Code·=>·image·|·1·1·1·0·|
28 ······························|·1·0·1·1·|28 ······························|·1·0·1·1·|
29 ······························|·1·1·1·0·|29 ······························|·1·1·0·1·|
30 ······························|·1·0·0·0·|30 ······························|·1·0·0·0·|
31 ······························|·0·1·0·0·|31 ······························|·0·1·0·0·|
32 ······························|·0·0·1·0·|32 ······························|·0·0·1·0·|
33 ······························|·0·0·0·1·|33 ······························|·0·0·0·1·|
34 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|34 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|
35 ···································|·1·0·1·0·1·0·0·|35 ···································|·1·0·1·0·1·0·0·|
36 ···································|·0·1·1·0·0·1·0·|36 ···································|·1·1·0·0·0·1·0·|
37 ···································|·1·1·0·0·0·0·1·|37 ···································|·0·1·1·0·0·0·1·|
38 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},38 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},
39 {0,·1,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}39 {1,·1,·0,·0,·0,·1,·0},·{0,·1,·1,·0,·0,·0,·1}}
40 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|40 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|
41 ·····································|·0·0·1·1·1·1·0·|41 ·····································|·0·1·1·0·1·1·0·|
42 ·····································|·0·1·0·1·0·1·1·|42 ·····································|·0·1·0·1·0·1·1·|
43 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,43 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·1,
44 0},·{0,·1,·0,·1,·0,·1,·1}}44 0},·{0,·1,·0,·1,·0,·1,·1}}
  
45 o3·:·LinearCode45 o3·:·LinearCode
46 i4·:·dim·H46 i4·:·dim·H
  
47 o4·=·447 o4·=·4
48 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*48 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
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79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·C1.ParityCheckMatrix82 ··············<pre><code·class="language-macaulay2">i2·:·C1.ParityCheckMatrix
  
83 o2·=·|·1·1·1·1·0·0·0·|83 o2·=·|·1·1·1·1·0·0·0·|
84 ·····|·0·1·0·1·1·1·0·|84 ·····|·0·1·0·1·1·1·0·|
85 ·····|·1·0·0·1·1·0·1·|85 ·····|·0·1·1·0·0·1·1·|
  
86 ··················3···········786 ··················3···········7
87 o2·:·Matrix·(GF·2)··&lt;--·(GF·2)</code></pre>87 o2·:·Matrix·(GF·2)··&lt;--·(GF·2)</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ········</table>90 ········</table>
91 ······</div>91 ······</div>
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14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 Returns·the·Hamming·code·$C$·over·GF(q)·whose·dual·has·dimension·s.15 Returns·the·Hamming·code·$C$·over·GF(q)·whose·dual·has·dimension·s.
16 i1·:·C1·=·hammingCode(2,3);16 i1·:·C1·=·hammingCode(2,3);
17 i2·:·C1.ParityCheckMatrix17 i2·:·C1.ParityCheckMatrix
  
18 o2·=·|·1·1·1·1·0·0·0·|18 o2·=·|·1·1·1·1·0·0·0·|
19 ·····|·0·1·0·1·1·1·0·|19 ·····|·0·1·0·1·1·1·0·|
20 ·····|·1·0·0·1·1·0·1·|20 ·····|·0·1·1·0·0·1·1·|
  
21 ··················3···········721 ··················3···········7
22 o2·:·Matrix·(GF·2)··<--·(GF·2)22 o2·:·Matrix·(GF·2)··<--·(GF·2)
23 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ha\x8am\x8mm\x8mi\x8in\x8ng\x8gC\x8Co\x8od\x8de\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ha\x8am\x8mm\x8mi\x8in\x8ng\x8gC\x8Co\x8od\x8de\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*
24 ····*·hammingCode(ZZ,ZZ)24 ····*·hammingCode(ZZ,ZZ)
25 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*25 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
26 The·object·_\x8h_\x8a_\x8m_\x8m_\x8i_\x8n_\x8g_\x8C_\x8o_\x8d_\x8e·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.26 The·object·_\x8h_\x8a_\x8m_\x8m_\x8i_\x8n_\x8g_\x8C_\x8o_\x8d_\x8e·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
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216 o10·=·EvaluationCode{cache·=>·CacheTable{}·····································································································································}216 o10·=·EvaluationCode{cache·=>·CacheTable{}·····································································································································}
217 ·····················Points·=>·{{0,·0},·{a,·a},·{a·+·1,·a},·{1,·a}}217 ·····················Points·=>·{{0,·0},·{a,·a},·{a·+·1,·a},·{1,·a}}
218 ································································4218 ································································4
219 ·····················LinearCode·=>·LinearCode{AmbientModule·=>·F··············································································································}219 ·····················LinearCode·=>·LinearCode{AmbientModule·=>·F··············································································································}
220 ··············································BaseField·=>·F220 ··············································BaseField·=>·F
221 ··············································cache·=>·CacheTable{}221 ··············································cache·=>·CacheTable{}
222 ··············································Code·=>·image·|·0···0···1·0·0···0·0···|222 ··············································Code·=>·image·|·0···0·0···0···0···1·0·|
223 ····························································|·a+1·a···1·1·1···a·a+1·| 
224 ····························································|·a···a+1·1·1·a+1·a·1···|223 ····························································|·1···a·a+1·a+1·a···1·1·|
225 ····························································|·1···1···1·1·a···a·a···|224 ····························································|·a+1·a·1···a···a+1·1·1·|
 225 ····························································|·a···a·a···1···1···1·1·|
226 ··············································GeneratorMatrix·=>·|·0·a+1·a···1·|226 ··············································GeneratorMatrix·=>·|·0·1···a+1·a·|
 227 ·································································|·0·a···a···a·|
 228 ·································································|·0·a+1·1···a·|
 229 ·································································|·0·a+1·a···1·|
227 ·································································|·0·a···a+1·1·|230 ·································································|·0·a···a+1·1·|
228 ·································································|·1·1···1···1·|231 ·································································|·1·1···1···1·|
229 ·································································|·0·1···1···1·|232 ·································································|·0·1···1···1·|
 233 ··············································Generators·=>·{{0,·1,·a·+·1,·a},·{0,·a,·a,·a},·{0,·a·+·1,·1,·a},·{0,·a·+·1,·a,·1},·{0,·a,·a·+·1,·1},·{1,·1,·1,·1},·{0,·1,·1,·1}}
230 ·································································|·0·1···a+1·a·| 
231 ·································································|·0·a···a···a·| 
232 ·································································|·0·a+1·1···a·| 
233 ··············································Generators·=>·{{0,·a·+·1,·a,·1},·{0,·a,·a·+·1,·1},·{1,·1,·1,·1},·{0,·1,·1,·1},·{0,·1,·a·+·1,·a},·{0,·a,·a,·a},·{0,·a·+·1,·1,·a}} 
234 ··············································ParityCheckMatrix·=>·0234 ··············································ParityCheckMatrix·=>·0
235 ··············································ParityCheckRows·=>·{}235 ··············································ParityCheckRows·=>·{}
236 ···············································2·······················3236 ···············································2·······················3
237 ·····················VanishingIdeal·=>·ideal·(t··+·a*t·,·t·t··+·a*t·,·t··+·(a·+·1)t·)237 ·····················VanishingIdeal·=>·ideal·(t··+·a*t·,·t·t··+·a*t·,·t··+·(a·+·1)t·)
238 ···············································1······1···0·1······0···0···········1238 ···············································1······1···0·1······0···0···········1
239 ········································2··········3···2239 ········································2···············2··········3
240 ·····················PolynomialSet·=>·{t·,·t·,·1,·t·,·t·t·,·t·,·t·t·}240 ·····················PolynomialSet·=>·{t·t·,·t·,·t·t·,·t·,·t·,·1,·t·}
241 ········································0···0······0···0·1···1···0·1</code></pre>241 ········································0·1···1···0·1···0···0······0</code></pre>
242 ··············</td>242 ··············</td>
243 ············</tr>243 ············</tr>
244 ··········</table>244 ··········</table>
245 ········</div>245 ········</div>
246 ········<div>246 ········<div>
247 ··········<h2>given·just·an·ideal·and·the·weight·vector</h2>247 ··········<h2>given·just·an·ideal·and·the·weight·vector</h2>
248 ··········<ul>248 ··········<ul>
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126 }126 }
127 ·····················Points·=>·{{0,·0},·{a,·a},·{a·+·1,·a},·{1,·a}}127 ·····················Points·=>·{{0,·0},·{a,·a},·{a·+·1,·a},·{1,·a}}
128 ································································4128 ································································4
129 ·····················LinearCode·=>·LinearCode{AmbientModule·=>·F129 ·····················LinearCode·=>·LinearCode{AmbientModule·=>·F
130 }130 }
131 ··············································BaseField·=>·F131 ··············································BaseField·=>·F
132 ··············································cache·=>·CacheTable{}132 ··············································cache·=>·CacheTable{}
133 ··············································Code·=>·image·|·0···0···1·0·0···0133 ··············································Code·=>·image·|·0···0·0···0···0
 134 1·0·|
134 0···| 
135 ····························································|·a+1·a···1·1·1···a 
136 a+1·| 
137 ····························································|·a···a+1·1·1·a+1·a135 ····························································|·1···a·a+1·a+1·a
138 1···|136 1·1·|
139 ····························································|·1···1···1·1·a···a137 ····························································|·a+1·a·1···a···a+1
140 a···|138 1·1·|
 139 ····························································|·a···a·a···1···1
 140 1·1·|
141 ··············································GeneratorMatrix·=>·|·0·a+1·a···1141 ··············································GeneratorMatrix·=>·|·0·1···a+1·a
142 |142 |
143 ·································································|·0·a···a+1·1143 ·································································|·0·a···a···a
144 |144 |
145 ·································································|·1·1···1···1145 ·································································|·0·a+1·1···a
146 |146 |
147 ·································································|·0·1···1···1147 ·································································|·0·a+1·a···1
148 |148 |
149 ·································································|·0·1···a+1·a149 ·································································|·0·a···a+1·1
150 |150 |
151 ·································································|·0·a···a···a151 ·································································|·1·1···1···1
152 |152 |
153 ·································································|·0·a+1·1···a153 ·································································|·0·1···1···1
154 |154 |
155 ··············································Generators·=>·{{0,·a·+·1,·a,·1},155 ··············································Generators·=>·{{0,·1,·a·+·1,·a},
156 {0,·a,·a·+·1,·1},·{1,·1,·1,·1},·{0,·1,·1,·1},·{0,·1,·a·+·1,·a},·{0,·a,·a,·a}, 
157 {0,·a·+·1,·1,·a}}156 {0,·a,·a,·a},·{0,·a·+·1,·1,·a},·{0,·a·+·1,·a,·1},·{0,·a,·a·+·1,·1},·{1,·1,·1,
 157 1},·{0,·1,·1,·1}}
158 ··············································ParityCheckMatrix·=>·0158 ··············································ParityCheckMatrix·=>·0
159 ··············································ParityCheckRows·=>·{}159 ··············································ParityCheckRows·=>·{}
160 ···············································2·······················3160 ···············································2·······················3
161 ·····················VanishingIdeal·=>·ideal·(t··+·a*t·,·t·t··+·a*t·,·t··+·(a·+161 ·····················VanishingIdeal·=>·ideal·(t··+·a*t·,·t·t··+·a*t·,·t··+·(a·+
162 1)t·)162 1)t·)
163 ···············································1······1···0·1······0···0163 ···············································1······1···0·1······0···0
164 1164 1
165 ········································2··········3···2165 ········································2···············2··········3
166 ·····················PolynomialSet·=>·{t·,·t·,·1,·t·,·t·t·,·t·,·t·t·}166 ·····················PolynomialSet·=>·{t·t·,·t·,·t·t·,·t·,·t·,·1,·t·}
167 ········································0···0······0···0·1···1···0·1167 ········································0·1···1···0·1···0···0······0
168 *\x8**\x8**\x8**\x8**\x8*·g\x8gi\x8iv\x8ve\x8en\x8n·j\x8ju\x8us\x8st\x8t·a\x8an\x8n·i\x8id\x8de\x8ea\x8al\x8l·a\x8an\x8nd\x8d·t\x8th\x8he\x8e·w\x8we\x8ei\x8ig\x8gh\x8ht\x8t·v\x8ve\x8ec\x8ct\x8to\x8or\x8r·*\x8**\x8**\x8**\x8**\x8*168 *\x8**\x8**\x8**\x8**\x8*·g\x8gi\x8iv\x8ve\x8en\x8n·j\x8ju\x8us\x8st\x8t·a\x8an\x8n·i\x8id\x8de\x8ea\x8al\x8l·a\x8an\x8nd\x8d·t\x8th\x8he\x8e·w\x8we\x8ei\x8ig\x8gh\x8ht\x8t·v\x8ve\x8ec\x8ct\x8to\x8or\x8r·*\x8**\x8**\x8**\x8**\x8*
169 ····*···Usage:169 ····*···Usage:
170 ············orderCode(I,v,d)170 ············orderCode(I,v,d)
171 ····*·Inputs:171 ····*·Inputs:
172 ··········o·I,·an·_\x8i_\x8d_\x8e_\x8a_\x8l,172 ··········o·I,·an·_\x8i_\x8d_\x8e_\x8a_\x8l,
173 ··········o·v,·a·_\x8l_\x8i_\x8s_\x8t,173 ··········o·v,·a·_\x8l_\x8i_\x8s_\x8t,
174 ··········o·d,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,174 ··········o·d,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,
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76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i1·:·C·=·hammingCode(2,·3)77 ··············<pre><code·class="language-macaulay2">i1·:·C·=·hammingCode(2,·3)
  
78 ·······································778 ·······································7
79 o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}79 o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································}
80 ················BaseField·=>·GF·280 ················BaseField·=>·GF·2
81 ················cache·=>·CacheTable{}81 ················cache·=>·CacheTable{}
82 ················Code·=>·image·|·1·0·1·1·|82 ················Code·=>·image·|·1·1·0·1·|
83 ······························|·1·1·0·1·|83 ······························|·1·0·1·1·|
84 ······························|·1·1·1·0·|84 ······························|·1·1·1·0·|
85 ······························|·1·0·0·0·|85 ······························|·1·0·0·0·|
86 ······························|·0·1·0·0·|86 ······························|·0·1·0·0·|
87 ······························|·0·0·1·0·|87 ······························|·0·0·1·0·|
88 ······························|·0·0·0·1·|88 ······························|·0·0·0·1·|
89 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|89 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|
90 ···································|·0·1·1·0·1·0·0·|90 ···································|·1·0·1·0·1·0·0·|
91 ···································|·1·0·1·0·0·1·0·|91 ···································|·0·1·1·0·0·1·0·|
92 ···································|·1·1·0·0·0·0·1·|92 ···································|·1·1·0·0·0·0·1·|
93 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·0,·0},·{1,·0,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}93 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{0,·1,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}
94 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|94 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|
95 ·····································|·0·0·1·1·1·1·0·|95 ·····································|·0·0·1·1·1·1·0·|
96 ·····································|·0·1·0·1·1·0·1·|96 ·····································|·0·1·0·1·0·1·1·|
97 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·1,·0,·1}}97 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}}
  
98 o1·:·LinearCode</code></pre>98 o1·:·LinearCode</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i2·:·ring(C)103 ··············<pre><code·class="language-macaulay2">i2·:·ring(C)
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17 i1·:·C·=·hammingCode(2,·3)17 i1·:·C·=·hammingCode(2,·3)
  
18 ·······································718 ·······································7
19 o1·=·LinearCode{AmbientModule·=>·(GF·2)19 o1·=·LinearCode{AmbientModule·=>·(GF·2)
20 }20 }
21 ················BaseField·=>·GF·221 ················BaseField·=>·GF·2
22 ················cache·=>·CacheTable{}22 ················cache·=>·CacheTable{}
23 ················Code·=>·image·|·1·0·1·1·|23 ················Code·=>·image·|·1·1·0·1·|
24 ······························|·1·1·0·1·|24 ······························|·1·0·1·1·|
25 ······························|·1·1·1·0·|25 ······························|·1·1·1·0·|
26 ······························|·1·0·0·0·|26 ······························|·1·0·0·0·|
27 ······························|·0·1·0·0·|27 ······························|·0·1·0·0·|
28 ······························|·0·0·1·0·|28 ······························|·0·0·1·0·|
29 ······························|·0·0·0·1·|29 ······························|·0·0·0·1·|
30 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|30 ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·|
31 ···································|·0·1·1·0·1·0·0·|31 ···································|·1·0·1·0·1·0·0·|
32 ···································|·1·0·1·0·0·1·0·|32 ···································|·0·1·1·0·0·1·0·|
33 ···································|·1·1·0·0·0·0·1·|33 ···································|·1·1·0·0·0·0·1·|
34 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·0,·0},34 ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},
35 {1,·0,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}35 {0,·1,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}}
36 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|36 ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·|
37 ·····································|·0·0·1·1·1·1·0·|37 ·····································|·0·0·1·1·1·1·0·|
38 ·····································|·0·1·0·1·1·0·1·|38 ·····································|·0·1·0·1·0·1·1·|
39 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,39 ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,
40 0},·{0,·1,·0,·1,·1,·0,·1}}40 0},·{0,·1,·0,·1,·0,·1,·1}}
  
41 o1·:·LinearCode41 o1·:·LinearCode
42 i2·:·ring(C)42 i2·:·ring(C)
  
43 o2·=·GF·243 o2·=·GF·2
  
44 o2·:·GaloisField44 o2·:·GaloisField
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165 ························|·0·|165 ························|·0·|
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167 ························|·0·|167 ························|·0·|
168 ···············|·1·|·=>·|·0·|168 ···············|·1·|·=>·|·0·|
169 ···············|·1·|····|·1·| 
170 ···············|·1·|····|·0·|169 ···············|·1·|····|·0·|
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171 ························|·0·|171 ························|·1·|
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174 ························|·0·|174 ························|·0·|
  
175 o7·:·HashTable</code></pre>175 o7·:·HashTable</code></pre>
176 ············</td>176 ············</td>
177 ··········</tr>177 ··········</tr>
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79 ························|·0·|79 ························|·0·|
80 ························|·0·|80 ························|·0·|
81 ························|·0·|81 ························|·0·|
82 ···············|·1·|·=>·|·0·|82 ···············|·1·|·=>·|·0·|
83 ···············|·1·|····|·0·|83 ···············|·1·|····|·0·|
84 ···············|·0·|····|·0·|84 ···············|·0·|····|·1·|
85 ························|·1·|85 ························|·0·|
86 ························|·0·|86 ························|·0·|
87 ························|·0·|87 ························|·0·|
88 ························|·0·|88 ························|·0·|
89 ···············|·1·|·=>·|·0·|89 ···············|·1·|·=>·|·0·|
90 ···············|·1·|····|·1·| 
91 ···············|·1·|····|·0·|90 ···············|·1·|····|·0·|
 91 ···············|·1·|····|·0·|
92 ························|·0·|92 ························|·1·|
93 ························|·0·|93 ························|·0·|
94 ························|·0·|94 ························|·0·|
95 ························|·0·|95 ························|·0·|
  
96 o7·:·HashTable96 o7·:·HashTable
97 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8yn\x8nd\x8dr\x8ro\x8om\x8me\x8eD\x8De\x8ec\x8co\x8od\x8de\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*97 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8yn\x8nd\x8dr\x8ro\x8om\x8me\x8eD\x8De\x8ec\x8co\x8od\x8de\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*
98 ····*·syndromeDecode(LinearCode,Matrix,ZZ)98 ····*·syndromeDecode(LinearCode,Matrix,ZZ)
744 B
./usr/share/doc/Macaulay2/CohomCalg/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
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11 Z3kgdmVjdG9ycyBmcm9tIENvaG9tQ2FsZyIsICJsaW5lbnVtIiA9PiAyODIsIElucHV0cyA9PiB711 Z3kgdmVjdG9ycyBmcm9tIENvaG9tQ2FsZyIsICJsaW5lbnVtIiA9PiAyODIsIElucHV0cyA9PiB7
1.82 KB
./usr/share/doc/Macaulay2/CohomCalg/example-output/___Cohom__Calg.out
    
Offset 184, 15 lines modifiedOffset 184, 15 lines modified
184 ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0,184 ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0,
185 ······-----------------------------------------------------------------------185 ······-----------------------------------------------------------------------
186 ······0,·0,·0,·-1,·-1}}186 ······0,·0,·0,·-1,·-1}}
  
187 o19·:·List187 o19·:·List
  
188 i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2)188 i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2)
189 ·--·2.80223s·elapsed189 ·--·7.14958s·elapsed
  
190 o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},190 o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},
191 ······-----------------------------------------------------------------------191 ······-----------------------------------------------------------------------
192 ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,192 ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,
193 ······-----------------------------------------------------------------------193 ······-----------------------------------------------------------------------
194 ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,194 ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,
195 ······-----------------------------------------------------------------------195 ······-----------------------------------------------------------------------
Offset 265, 45 lines modifiedOffset 265, 45 lines modified
265 i22·:·degree(X_3·+·X_7·+·X_8)265 i22·:·degree(X_3·+·X_7·+·X_8)
  
266 o22·=·{0,·0,·1,·2,·0,·-1}266 o22·=·{0,·0,·1,·2,·0,·-1}
  
267 o22·:·List267 o22·:·List
  
268 i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8)268 i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8)
269 ·--·.368525s·elapsed269 ·--·1.144s·elapsed
  
270 o23·=·{1,·0,·0,·0,·0}270 o23·=·{1,·0,·0,·0,·0}
  
271 o23·:·List271 o23·:·List
  
272 i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1))272 i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1))
273 ·--·93.8192s·elapsed273 ·--·227.883s·elapsed
  
274 o24·=·{1,·0,·0,·0,·0}274 o24·=·{1,·0,·0,·0,·0}
  
275 o24·:·List275 o24·:·List
  
276 i25·:·assert(cohomvec1·==·cohomvec2)276 i25·:·assert(cohomvec1·==·cohomvec2)
  
277 i26·:·degree(X_3·+·X_7·-·X_8)277 i26·:·degree(X_3·+·X_7·-·X_8)
  
278 o26·=·{0,·0,·1,·2,·-2,·-1}278 o26·=·{0,·0,·1,·2,·-2,·-1}
  
279 o26·:·List279 o26·:·List
  
280 i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8)280 i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8)
281 ·--·.330447s·elapsed281 ·--·1.32405s·elapsed
  
282 o27·=·{0,·0,·0,·0,·0}282 o27·=·{0,·0,·0,·0,·0}
  
283 o27·:·List283 o27·:·List
  
284 i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1))284 i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1))
285 ·--·.455957s·elapsed285 ·--·.829249s·elapsed
286 ·--·.456001s·elapsed286 ·--·.829293s·elapsed
  
287 o28·=·{0,·0,·0,·0,·0}287 o28·=·{0,·0,·0,·0,·0}
  
288 o28·:·List288 o28·:·List
  
289 i29·:·assert(cohomvec1·==·cohomvec2)289 i29·:·assert(cohomvec1·==·cohomvec2)
  
4.23 KB
./usr/share/doc/Macaulay2/CohomCalg/html/index.html
    
Offset 309, 15 lines modifiedOffset 309, 15 lines modified
  
309 o19·:·List</code></pre>309 o19·:·List</code></pre>
310 ············</td>310 ············</td>
311 ··········</tr>311 ··········</tr>
312 ··········<tr>312 ··········<tr>
313 ············<td>313 ············<td>
314 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2)314 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2)
315 ·--·2.80223s·elapsed315 ·--·7.14958s·elapsed
  
316 o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},316 o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},
317 ······-----------------------------------------------------------------------317 ······-----------------------------------------------------------------------
318 ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,318 ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,
319 ······-----------------------------------------------------------------------319 ······-----------------------------------------------------------------------
320 ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,320 ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,
321 ······-----------------------------------------------------------------------321 ······-----------------------------------------------------------------------
Offset 399, 25 lines modifiedOffset 399, 25 lines modified
  
399 o22·:·List</code></pre>399 o22·:·List</code></pre>
400 ············</td>400 ············</td>
401 ··········</tr>401 ··········</tr>
402 ··········<tr>402 ··········<tr>
403 ············<td>403 ············<td>
404 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8)404 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8)
405 ·--·.368525s·elapsed405 ·--·1.144s·elapsed
  
406 o23·=·{1,·0,·0,·0,·0}406 o23·=·{1,·0,·0,·0,·0}
  
407 o23·:·List</code></pre>407 o23·:·List</code></pre>
408 ············</td>408 ············</td>
409 ··········</tr>409 ··········</tr>
410 ··········<tr>410 ··········<tr>
411 ············<td>411 ············<td>
412 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1))412 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1))
413 ·--·93.8192s·elapsed413 ·--·227.883s·elapsed
  
414 o24·=·{1,·0,·0,·0,·0}414 o24·=·{1,·0,·0,·0,·0}
  
415 o24·:·List</code></pre>415 o24·:·List</code></pre>
416 ············</td>416 ············</td>
417 ··········</tr>417 ··········</tr>
418 ··········<tr>418 ··········<tr>
Offset 433, 26 lines modifiedOffset 433, 26 lines modified
  
433 o26·:·List</code></pre>433 o26·:·List</code></pre>
434 ············</td>434 ············</td>
435 ··········</tr>435 ··········</tr>
436 ··········<tr>436 ··········<tr>
437 ············<td>437 ············<td>
438 ··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8)438 ··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8)
439 ·--·.330447s·elapsed439 ·--·1.32405s·elapsed
  
440 o27·=·{0,·0,·0,·0,·0}440 o27·=·{0,·0,·0,·0,·0}
  
441 o27·:·List</code></pre>441 o27·:·List</code></pre>
442 ············</td>442 ············</td>
443 ··········</tr>443 ··········</tr>
444 ··········<tr>444 ··········<tr>
445 ············<td>445 ············<td>
446 ··············<pre><code·class="language-macaulay2">i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1))446 ··············<pre><code·class="language-macaulay2">i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1))
447 ·--·.455957s·elapsed447 ·--·.829249s·elapsed
448 ·--·.456001s·elapsed448 ·--·.829293s·elapsed
  
449 o28·=·{0,·0,·0,·0,·0}449 o28·=·{0,·0,·0,·0,·0}
  
450 o28·:·List</code></pre>450 o28·:·List</code></pre>
451 ············</td>451 ············</td>
452 ··········</tr>452 ··········</tr>
453 ··········<tr>453 ··········<tr>
2.02 KB
html2text {}
    
Offset 182, 15 lines modifiedOffset 182, 15 lines modified
182 ······-----------------------------------------------------------------------182 ······-----------------------------------------------------------------------
183 ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0,183 ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0,
184 ······-----------------------------------------------------------------------184 ······-----------------------------------------------------------------------
185 ······0,·0,·0,·-1,·-1}}185 ······0,·0,·0,·-1,·-1}}
  
186 o19·:·List186 o19·:·List
187 i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2)187 i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2)
188 ·--·2.80223s·elapsed188 ·--·7.14958s·elapsed
  
189 o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},189 o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},
190 ······-----------------------------------------------------------------------190 ······-----------------------------------------------------------------------
191 ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,191 ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,
192 ······-----------------------------------------------------------------------192 ······-----------------------------------------------------------------------
193 ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,193 ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,
194 ······-----------------------------------------------------------------------194 ······-----------------------------------------------------------------------
Offset 262, 42 lines modifiedOffset 262, 42 lines modified
262 ·······················{2,·2,·3,·1,·-4,·-6}·=>·{{0,·1,·0,·0,·0},·{{1,·1x1*x2}}}262 ·······················{2,·2,·3,·1,·-4,·-6}·=>·{{0,·1,·0,·0,·0},·{{1,·1x1*x2}}}
263 i22·:·degree(X_3·+·X_7·+·X_8)263 i22·:·degree(X_3·+·X_7·+·X_8)
  
264 o22·=·{0,·0,·1,·2,·0,·-1}264 o22·=·{0,·0,·1,·2,·0,·-1}
  
265 o22·:·List265 o22·:·List
266 i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8)266 i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8)
267 ·--·.368525s·elapsed267 ·--·1.144s·elapsed
  
268 o23·=·{1,·0,·0,·0,·0}268 o23·=·{1,·0,·0,·0,·0}
  
269 o23·:·List269 o23·:·List
270 i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X270 i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X
271 (0,0,1,2,0,-1))271 (0,0,1,2,0,-1))
272 ·--·93.8192s·elapsed272 ·--·227.883s·elapsed
  
273 o24·=·{1,·0,·0,·0,·0}273 o24·=·{1,·0,·0,·0,·0}
  
274 o24·:·List274 o24·:·List
275 i25·:·assert(cohomvec1·==·cohomvec2)275 i25·:·assert(cohomvec1·==·cohomvec2)
276 i26·:·degree(X_3·+·X_7·-·X_8)276 i26·:·degree(X_3·+·X_7·-·X_8)
  
277 o26·=·{0,·0,·1,·2,·-2,·-1}277 o26·=·{0,·0,·1,·2,·-2,·-1}
  
278 o26·:·List278 o26·:·List
279 i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8)279 i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8)
280 ·--·.330447s·elapsed280 ·--·1.32405s·elapsed
  
281 o27·=·{0,·0,·0,·0,·0}281 o27·=·{0,·0,·0,·0,·0}
  
282 o27·:·List282 o27·:·List
283 i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j283 i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j
284 (X,·OO_X(0,0,1,2,-2,-1))284 (X,·OO_X(0,0,1,2,-2,-1))
285 ·--·.455957s·elapsed285 ·--·.829249s·elapsed
286 ·--·.456001s·elapsed286 ·--·.829293s·elapsed
  
287 o28·=·{0,·0,·0,·0,·0}287 o28·=·{0,·0,·0,·0,·0}
  
288 o28·:·List288 o28·:·List
289 i29·:·assert(cohomvec1·==·cohomvec2)289 i29·:·assert(cohomvec1·==·cohomvec2)
290 _\x8c_\x8o_\x8h_\x8o_\x8m_\x8C_\x8a_\x8l_\x8g·computes·cohomology·vectors·by·calling·CohomCalg.·It·also·stashes290 _\x8c_\x8o_\x8h_\x8o_\x8m_\x8C_\x8a_\x8l_\x8g·computes·cohomology·vectors·by·calling·CohomCalg.·It·also·stashes
291 it's·results·in·the·toric·variety's·cache·table,·so·computations·need·not·be291 it's·results·in·the·toric·variety's·cache·table,·so·computations·need·not·be
753 B
./usr/share/doc/Macaulay2/CoincidentRootLoci/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=247 #:len=24
8 Y29tcGxleHJhbmsoUmluZ0VsZW1lbnQp8 Y29tcGxleHJhbmsoUmluZ0VsZW1lbnQp
9 #:len=2979 #:len=297
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgxLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgxLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV4cmFuayxSaW5nRWxlbWVudCksImNvbXBs11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV4cmFuayxSaW5nRWxlbWVudCksImNvbXBs
787 B
./usr/share/doc/Macaulay2/CompleteIntersectionResolutions/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=287 #:len=28
8 RWlzZW5idWRTaGFtYXNoVG90YWwoTW9kdWxlKQ==8 RWlzZW5idWRTaGFtYXNoVG90YWwoTW9kdWxlKQ==
9 #:len=3499 #:len=349
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTE2OSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTE2OSwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoRWlzZW5idWRTaGFtYXNoVG90YWwsTW9kdWxlKSwi11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoRWlzZW5idWRTaGFtYXNoVG90YWwsTW9kdWxlKSwi
2.71 KB
./usr/share/doc/Macaulay2/CompleteIntersectionResolutions/example-output/___Eisenbud__Shamash.out
    
Offset 35, 15 lines modifiedOffset 35, 15 lines modified
35 o5·:·QuotientRing35 o5·:·QuotientRing
  
36 i6·:·len·=·1036 i6·:·len·=·10
  
37 o6·=·1037 o6·=·10
  
38 i7·:·time·G·=·EisenbudShamash(ff,F,len)38 i7·:·time·G·=·EisenbudShamash(ff,F,len)
39 ·--·used·5.60964s·(cpu);·4.36897s·(thread);·0s·(gc)39 ·--·used·6.84607s·(cpu);·5.16829s·(thread);·0s·(gc)
  
40 ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\7640 ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76
41 o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|41 o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|
42 ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|42 ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|
43 ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|43 ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|
44 ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/44 ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/
45 ··············································································································································································45 ··············································································································································································
Offset 140, 37 lines modifiedOffset 140, 37 lines modified
140 i19·:·R1·=·R/ideal·ff140 i19·:·R1·=·R/ideal·ff
  
141 o19·=·R1141 o19·=·R1
  
142 o19·:·QuotientRing142 o19·:·QuotientRing
  
143 i20·:·FF·=·time·Shamash(R1,F,4)143 i20·:·FF·=·time·Shamash(R1,F,4)
144 ·--·used·0.0676725s·(cpu);·0.067763s·(thread);·0s·(gc)144 ·--·used·0.0743259s·(cpu);·0.0757134s·(thread);·0s·(gc)
  
145 ········1·······6·······18·······38·······66145 ········1·······6·······18·······38·······66
146 o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1146 o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1
147 ·········································147 ·········································
148 ······0·······1·······2········3········4148 ······0·······1·······2········3········4
  
149 o20·:·Complex149 o20·:·Complex
  
150 i21·:·GG·=·time·EisenbudShamash(ff,F,4)150 i21·:·GG·=·time·EisenbudShamash(ff,F,4)
151 ·--·used·0.789405s·(cpu);·0.657486s·(thread);·0s·(gc)151 ·--·used·0.946978s·(cpu);·0.759093s·(thread);·0s·(gc)
  
152 ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66152 ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66
153 o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--|153 o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--|
154 ······|·3|······|·3|······|·3|·······|·3|·······|·3|154 ······|·3|······|·3|······|·3|·······|·3|·······|·3|
155 ······\c·/······\c·/······\c·/·······\c·/·······\c·/155 ······\c·/······\c·/······\c·/·······\c·/·······\c·/
156 ·················································156 ·················································
157 ······0·········1·········2··········3··········4157 ······0·········1·········2··········3··········4
  
158 o21·:·Complex158 o21·:·Complex
  
159 i22·:·GG·=·time·EisenbudShamash(R1,F[2],4)159 i22·:·GG·=·time·EisenbudShamash(R1,F[2],4)
160 ·--·used·0.840325s·(cpu);·0.668034s·(thread);·0s·(gc)160 ·--·used·1.05671s·(cpu);·0.784398s·(thread);·0s·(gc)
  
161 ········1·······6·······18·······38·······66161 ········1·······6·······18·······38·······66
162 o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1162 o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1
163 ·········································163 ·········································
164 ······-2······-1······0········1········2164 ······-2······-1······0········1········2
  
165 o22·:·Complex165 o22·:·Complex
712 B
./usr/share/doc/Macaulay2/CompleteIntersectionResolutions/example-output/_sum__Two__Monomials.out
    
Offset 2, 17 lines modifiedOffset 2, 17 lines modified
  
2 i1·:·setRandomSeed·02 i1·:·setRandomSeed·0
3 ·--·setting·random·seed·to·03 ·--·setting·random·seed·to·0
  
4 o1·=·04 o1·=·0
  
5 i2·:·sumTwoMonomials(2,3)5 i2·:·sumTwoMonomials(2,3)
6 ·--·used·1.22862s·(cpu);·0.439429s·(thread);·0s·(gc)6 ·--·used·1.20589s·(cpu);·0.433414s·(thread);·0s·(gc)
7 ·--·used·0.436461s·(cpu);·0.16151s·(thread);·0s·(gc)7 ·--·used·0.387189s·(cpu);·0.147588s·(thread);·0s·(gc)
8 ·--·used·0.000144247s·(cpu);·1.162e-06s·(thread);·0s·(gc)8 ·--·used·0.00019196s·(cpu);·2.214e-06s·(thread);·0s·(gc)
9 29 2
10 Tally{{{2,·2},·{1,·2}}·=>·3}10 Tally{{{2,·2},·{1,·2}}·=>·3}
  
11 311 3
12 Tally{{{2,·2},·{1,·2}}·=>·1}12 Tally{{{2,·2},·{1,·2}}·=>·1}
  
13 413 4
786 B
./usr/share/doc/Macaulay2/CompleteIntersectionResolutions/example-output/_two__Monomials.out
    
Offset 2, 23 lines modifiedOffset 2, 23 lines modified
  
2 i1·:·setRandomSeed·02 i1·:·setRandomSeed·0
3 ·--·setting·random·seed·to·03 ·--·setting·random·seed·to·0
  
4 o1·=·04 o1·=·0
  
5 i2·:·twoMonomials(2,3)5 i2·:·twoMonomials(2,3)
6 ·--·used·2.35914s·(cpu);·0.74026s·(thread);·0s·(gc)6 ·--·used·2.3078s·(cpu);·0.754976s·(thread);·0s·(gc)
7 27 2
8 Tally{{{1,·1}}·=>·2········}8 Tally{{{1,·1}}·=>·2········}
9 ······{{2,·2},·{1,·2}}·=>·49 ······{{2,·2},·{1,·2}}·=>·4
  
10 ·--·used·1.09259s·(cpu);·0.364393s·(thread);·0s·(gc)10 ·--·used·1.07901s·(cpu);·0.392715s·(thread);·0s·(gc)
11 311 3
12 Tally{{{2,·2},·{1,·2}}·=>·2}12 Tally{{{2,·2},·{1,·2}}·=>·2}
13 ······{{3,·3},·{2,·3}}·=>·113 ······{{3,·3},·{2,·3}}·=>·1
  
14 ·--·used·0.442286s·(cpu);·0.14144s·(thread);·0s·(gc)14 ·--·used·0.44846s·(cpu);·0.179148s·(thread);·0s·(gc)
15 415 4
16 Tally{{{2,·2},·{1,·2}}·=>·1}16 Tally{{{2,·2},·{1,·2}}·=>·1}
  
  
17 i3·:·17 i3·:·
5.14 KB
./usr/share/doc/Macaulay2/CompleteIntersectionResolutions/html/___Eisenbud__Shamash.html
    
Offset 131, 15 lines modifiedOffset 131, 15 lines modified
  
131 o6·=·10</code></pre>131 o6·=·10</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i7·:·time·G·=·EisenbudShamash(ff,F,len)136 ··············<pre><code·class="language-macaulay2">i7·:·time·G·=·EisenbudShamash(ff,F,len)
137 ·--·used·5.60964s·(cpu);·4.36897s·(thread);·0s·(gc)137 ·--·used·6.84607s·(cpu);·5.16829s·(thread);·0s·(gc)
  
138 ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76138 ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76
139 o7·=·|--------|··&lt;--·|--------|··&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|139 o7·=·|--------|··&lt;--·|--------|··&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|···&lt;--·|--------|
140 ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|140 ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|
141 ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|141 ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|
142 ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/142 ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/
143 ··············································································································································································143 ··············································································································································································
Offset 295, 28 lines modifiedOffset 295, 28 lines modified
  
295 o19·:·QuotientRing</code></pre>295 o19·:·QuotientRing</code></pre>
296 ············</td>296 ············</td>
297 ··········</tr>297 ··········</tr>
298 ··········<tr>298 ··········<tr>
299 ············<td>299 ············<td>
300 ··············<pre><code·class="language-macaulay2">i20·:·FF·=·time·Shamash(R1,F,4)300 ··············<pre><code·class="language-macaulay2">i20·:·FF·=·time·Shamash(R1,F,4)
301 ·--·used·0.0676725s·(cpu);·0.067763s·(thread);·0s·(gc)301 ·--·used·0.0743259s·(cpu);·0.0757134s·(thread);·0s·(gc)
  
302 ········1·······6·······18·······38·······66302 ········1·······6·······18·······38·······66
303 o20·=·R1··&lt;--·R1··&lt;--·R1···&lt;--·R1···&lt;--·R1303 o20·=·R1··&lt;--·R1··&lt;--·R1···&lt;--·R1···&lt;--·R1
304 ·········································304 ·········································
305 ······0·······1·······2········3········4305 ······0·······1·······2········3········4
  
306 o20·:·Complex</code></pre>306 o20·:·Complex</code></pre>
307 ············</td>307 ············</td>
308 ··········</tr>308 ··········</tr>
309 ··········<tr>309 ··········<tr>
310 ············<td>310 ············<td>
311 ··············<pre><code·class="language-macaulay2">i21·:·GG·=·time·EisenbudShamash(ff,F,4)311 ··············<pre><code·class="language-macaulay2">i21·:·GG·=·time·EisenbudShamash(ff,F,4)
312 ·--·used·0.789405s·(cpu);·0.657486s·(thread);·0s·(gc)312 ·--·used·0.946978s·(cpu);·0.759093s·(thread);·0s·(gc)
  
313 ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66313 ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66
314 o21·=·|--|··&lt;--·|--|··&lt;--·|--|···&lt;--·|--|···&lt;--·|--|314 o21·=·|--|··&lt;--·|--|··&lt;--·|--|···&lt;--·|--|···&lt;--·|--|
315 ······|·3|······|·3|······|·3|·······|·3|·······|·3|315 ······|·3|······|·3|······|·3|·······|·3|·······|·3|
316 ······\c·/······\c·/······\c·/·······\c·/·······\c·/316 ······\c·/······\c·/······\c·/·······\c·/·······\c·/
317 ·················································317 ·················································
318 ······0·········1·········2··········3··········4318 ······0·········1·········2··········3··········4
Offset 328, 15 lines modifiedOffset 328, 15 lines modified
328 ········<div>328 ········<div>
329 ··········<p>The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:</p>329 ··········<p>The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:</p>
330 ········</div>330 ········</div>
331 ········<table·class="examples">331 ········<table·class="examples">
332 ··········<tr>332 ··········<tr>
333 ············<td>333 ············<td>
334 ··············<pre><code·class="language-macaulay2">i22·:·GG·=·time·EisenbudShamash(R1,F[2],4)334 ··············<pre><code·class="language-macaulay2">i22·:·GG·=·time·EisenbudShamash(R1,F[2],4)
335 ·--·used·0.840325s·(cpu);·0.668034s·(thread);·0s·(gc)335 ·--·used·1.05671s·(cpu);·0.784398s·(thread);·0s·(gc)
  
336 ········1·······6·······18·······38·······66336 ········1·······6·······18·······38·······66
337 o22·=·R1··&lt;--·R1··&lt;--·R1···&lt;--·R1···&lt;--·R1337 o22·=·R1··&lt;--·R1··&lt;--·R1···&lt;--·R1···&lt;--·R1
338 ·········································338 ·········································
339 ······-2······-1······0········1········2339 ······-2······-1······0········1········2
  
340 o22·:·Complex</code></pre>340 o22·:·Complex</code></pre>
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Offset 49, 15 lines modifiedOffset 49, 15 lines modified
49 o5·=·R49 o5·=·R
  
50 o5·:·QuotientRing50 o5·:·QuotientRing
51 i6·:·len·=·1051 i6·:·len·=·10
  
52 o6·=·1052 o6·=·10
53 i7·:·time·G·=·EisenbudShamash(ff,F,len)53 i7·:·time·G·=·EisenbudShamash(ff,F,len)
54 ·--·used·5.60964s·(cpu);·4.36897s·(thread);·0s·(gc)54 ·--·used·6.84607s·(cpu);·5.16829s·(thread);·0s·(gc)
  
55 ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S55 ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S
56 \28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/56 \28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/
57 S···\68·····/····S···\7657 S···\68·····/····S···\76
58 o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|-------58 o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|-------
59 -|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|-59 -|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|-
60 -------|···<--·|--------|60 -------|···<--·|--------|
Offset 165, 36 lines modifiedOffset 165, 36 lines modified
165 o18·:·Matrix·R··<--·R165 o18·:·Matrix·R··<--·R
166 i19·:·R1·=·R/ideal·ff166 i19·:·R1·=·R/ideal·ff
  
167 o19·=·R1167 o19·=·R1
  
168 o19·:·QuotientRing168 o19·:·QuotientRing
169 i20·:·FF·=·time·Shamash(R1,F,4)169 i20·:·FF·=·time·Shamash(R1,F,4)
170 ·--·used·0.0676725s·(cpu);·0.067763s·(thread);·0s·(gc)170 ·--·used·0.0743259s·(cpu);·0.0757134s·(thread);·0s·(gc)
  
171 ········1·······6·······18·······38·······66171 ········1·······6·······18·······38·······66
172 o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1172 o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1
  
173 ······0·······1·······2········3········4173 ······0·······1·······2········3········4
  
174 o20·:·Complex174 o20·:·Complex
175 i21·:·GG·=·time·EisenbudShamash(ff,F,4)175 i21·:·GG·=·time·EisenbudShamash(ff,F,4)
176 ·--·used·0.789405s·(cpu);·0.657486s·(thread);·0s·(gc)176 ·--·used·0.946978s·(cpu);·0.759093s·(thread);·0s·(gc)
  
177 ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66177 ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66
178 o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--|178 o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--|
179 ······|·3|······|·3|······|·3|·······|·3|·······|·3|179 ······|·3|······|·3|······|·3|·······|·3|·······|·3|
180 ······\c·/······\c·/······\c·/·······\c·/·······\c·/180 ······\c·/······\c·/······\c·/·······\c·/·······\c·/
  
181 ······0·········1·········2··········3··········4181 ······0·········1·········2··········3··········4
  
182 o21·:·Complex182 o21·:·Complex
183 The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:183 The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:
184 i22·:·GG·=·time·EisenbudShamash(R1,F[2],4)184 i22·:·GG·=·time·EisenbudShamash(R1,F[2],4)
185 ·--·used·0.840325s·(cpu);·0.668034s·(thread);·0s·(gc)185 ·--·used·1.05671s·(cpu);·0.784398s·(thread);·0s·(gc)
  
186 ········1·······6·······18·······38·······66186 ········1·······6·······18·······38·······66
187 o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1187 o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1
  
188 ······-2······-1······0········1········2188 ······-2······-1······0········1········2
  
189 o22·:·Complex189 o22·:·Complex
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./usr/share/doc/Macaulay2/CompleteIntersectionResolutions/html/_sum__Two__Monomials.html
    
Offset 79, 17 lines modifiedOffset 79, 17 lines modified
  
79 o1·=·0</code></pre>79 o1·=·0</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i2·:·sumTwoMonomials(2,3)84 ··············<pre><code·class="language-macaulay2">i2·:·sumTwoMonomials(2,3)
85 ·--·used·1.22862s·(cpu);·0.439429s·(thread);·0s·(gc)85 ·--·used·1.20589s·(cpu);·0.433414s·(thread);·0s·(gc)
86 ·--·used·0.436461s·(cpu);·0.16151s·(thread);·0s·(gc)86 ·--·used·0.387189s·(cpu);·0.147588s·(thread);·0s·(gc)
87 ·--·used·0.000144247s·(cpu);·1.162e-06s·(thread);·0s·(gc)87 ·--·used·0.00019196s·(cpu);·2.214e-06s·(thread);·0s·(gc)
88 288 2
89 Tally{{{2,·2},·{1,·2}}·=>·3}89 Tally{{{2,·2},·{1,·2}}·=>·3}
  
90 390 3
91 Tally{{{2,·2},·{1,·2}}·=>·1}91 Tally{{{2,·2},·{1,·2}}·=>·1}
  
92 492 4
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18 appropriate·syzygy·M·of·M0·=·R/(m1+m2)·where·m1·and·m2·are·monomials·of·the18 appropriate·syzygy·M·of·M0·=·R/(m1+m2)·where·m1·and·m2·are·monomials·of·the
19 same·degree.19 same·degree.
20 i1·:·setRandomSeed·020 i1·:·setRandomSeed·0
21 ·--·setting·random·seed·to·021 ·--·setting·random·seed·to·0
  
22 o1·=·022 o1·=·0
23 i2·:·sumTwoMonomials(2,3)23 i2·:·sumTwoMonomials(2,3)
24 ·--·used·1.22862s·(cpu);·0.439429s·(thread);·0s·(gc)24 ·--·used·1.20589s·(cpu);·0.433414s·(thread);·0s·(gc)
25 ·--·used·0.436461s·(cpu);·0.16151s·(thread);·0s·(gc)25 ·--·used·0.387189s·(cpu);·0.147588s·(thread);·0s·(gc)
26 ·--·used·0.000144247s·(cpu);·1.162e-06s·(thread);·0s·(gc)26 ·--·used·0.00019196s·(cpu);·2.214e-06s·(thread);·0s·(gc)
27 227 2
28 Tally{{{2,·2},·{1,·2}}·=>·3}28 Tally{{{2,·2},·{1,·2}}·=>·3}
  
29 329 3
30 Tally{{{2,·2},·{1,·2}}·=>·1}30 Tally{{{2,·2},·{1,·2}}·=>·1}
  
31 431 4
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./usr/share/doc/Macaulay2/CompleteIntersectionResolutions/html/_two__Monomials.html
    
Offset 83, 25 lines modifiedOffset 83, 25 lines modified
  
83 o1·=·0</code></pre>83 o1·=·0</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i2·:·twoMonomials(2,3)88 ··············<pre><code·class="language-macaulay2">i2·:·twoMonomials(2,3)
89 ·--·used·2.35914s·(cpu);·0.74026s·(thread);·0s·(gc)89 ·--·used·2.3078s·(cpu);·0.754976s·(thread);·0s·(gc)
90 290 2
91 Tally{{{1,·1}}·=>·2········}91 Tally{{{1,·1}}·=>·2········}
92 ······{{2,·2},·{1,·2}}·=>·492 ······{{2,·2},·{1,·2}}·=>·4
  
93 ·--·used·1.09259s·(cpu);·0.364393s·(thread);·0s·(gc)93 ·--·used·1.07901s·(cpu);·0.392715s·(thread);·0s·(gc)
94 394 3
95 Tally{{{2,·2},·{1,·2}}·=>·2}95 Tally{{{2,·2},·{1,·2}}·=>·2}
96 ······{{3,·3},·{2,·3}}·=>·196 ······{{3,·3},·{2,·3}}·=>·1
  
97 ·--·used·0.442286s·(cpu);·0.14144s·(thread);·0s·(gc)97 ·--·used·0.44846s·(cpu);·0.179148s·(thread);·0s·(gc)
98 498 4
99 Tally{{{2,·2},·{1,·2}}·=>·1}</code></pre>99 Tally{{{2,·2},·{1,·2}}·=>·1}</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ········</table>102 ········</table>
103 ······</div>103 ······</div>
104 ······<div>104 ······<div>
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20 that·is,·for·an·appropriate·syzygy·M·of·M0·=·R/(m1,·m2)·where·m1·and·m2·are20 that·is,·for·an·appropriate·syzygy·M·of·M0·=·R/(m1,·m2)·where·m1·and·m2·are
21 monomials·of·the·same·degree.21 monomials·of·the·same·degree.
22 i1·:·setRandomSeed·022 i1·:·setRandomSeed·0
23 ·--·setting·random·seed·to·023 ·--·setting·random·seed·to·0
  
24 o1·=·024 o1·=·0
25 i2·:·twoMonomials(2,3)25 i2·:·twoMonomials(2,3)
26 ·--·used·2.35914s·(cpu);·0.74026s·(thread);·0s·(gc)26 ·--·used·2.3078s·(cpu);·0.754976s·(thread);·0s·(gc)
27 227 2
28 Tally{{{1,·1}}·=>·2········}28 Tally{{{1,·1}}·=>·2········}
29 ······{{2,·2},·{1,·2}}·=>·429 ······{{2,·2},·{1,·2}}·=>·4
  
30 ·--·used·1.09259s·(cpu);·0.364393s·(thread);·0s·(gc)30 ·--·used·1.07901s·(cpu);·0.392715s·(thread);·0s·(gc)
31 331 3
32 Tally{{{2,·2},·{1,·2}}·=>·2}32 Tally{{{2,·2},·{1,·2}}·=>·2}
33 ······{{3,·3},·{2,·3}}·=>·133 ······{{3,·3},·{2,·3}}·=>·1
  
34 ·--·used·0.442286s·(cpu);·0.14144s·(thread);·0s·(gc)34 ·--·used·0.44846s·(cpu);·0.179148s·(thread);·0s·(gc)
35 435 4
36 Tally{{{2,·2},·{1,·2}}·=>·1}36 Tally{{{2,·2},·{1,·2}}·=>·1}
37 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*37 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
38 ····*·_\x8t_\x8w_\x8o_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·tally·the·sequences·of·BRanks·for·certain·examples38 ····*·_\x8t_\x8w_\x8o_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·tally·the·sequences·of·BRanks·for·certain·examples
39 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8tw\x8wo\x8oM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8ls\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8tw\x8wo\x8oM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8ls\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
40 ····*·twoMonomials(ZZ,ZZ)40 ····*·twoMonomials(ZZ,ZZ)
41 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*41 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
731 B
./usr/share/doc/Macaulay2/Complexes/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/ConformalBlocks/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/ConnectionMatrices/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/ConnectionMatrices/example-output/___Cosmological_spcorrelator_spfor_spthe_sp2-site_spchain.out
    
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27 ·····-·ϵ*z*dy·+···-·ϵ,·x*dx·+·y*dy·+·z*dz·-·2ϵ)27 ·····-·ϵ*z*dy·+···-·ϵ,·x*dx·+·y*dy·+·z*dz·-·2ϵ)
  
28 o7·:·Ideal·of·D28 o7·:·Ideal·of·D
  
29 i8·:·assert(holonomicRank·I·==·4)29 i8·:·assert(holonomicRank·I·==·4)
  
30 i9·:·elapsedTime·A·=·connectionMatrices·I;30 i9·:·elapsedTime·A·=·connectionMatrices·I;
31 ·--·2.07985s·elapsed31 ·--·4.78861s·elapsed
  
32 i10·:·elapsedTime·assert·isIntegrable·A32 i10·:·elapsedTime·assert·isIntegrable·A
33 ·--·3.7658s·elapsed33 ·--·8.81575s·elapsed
  
34 i11·:·netList·A34 i11·:·netList·A
  
35 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+35 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
36 o11·=·||·2ϵ/x····································································································································································································································································································································································································································(-y)/x·································································································································································································································································································································································································································································(-z)/x················································································································································································································································································································································································································································0·····························································································································|·····································································································································································································································································································································|36 o11·=·||·2ϵ/x····································································································································································································································································································································································································································(-y)/x·································································································································································································································································································································································································································································(-z)/x················································································································································································································································································································································································································································0·····························································································································|·····································································································································································································································································································································|
37 ······||·(4x2y2ϵ^2+4xy2zϵ^2-2x2z2ϵ^2-2y2z2ϵ^2-4xz3ϵ^2+x3zϵ-3xy2zϵ+2xz3ϵ)/(2x4y2+2x3y3+x4yz+2x3y2z+x2y3z-x4z2-x3yz2-x2y2z2-xy3z2-x3z3-2x2yz3-xy2z3)·······························································································································································································································································································(2x3y2ϵ-2x2y3ϵ+2x3yzϵ-2xy3zϵ-x3z2ϵ+x2yz2ϵ-xy2z2ϵ+y3z2ϵ-2x3yz+2xy3z)/(2x4y2+2x3y3+x4yz+2x3y2z+x2y3z-x4z2-x3yz2-x2y2z2-xy3z2-x3z3-2x2yz3-xy2z3)··························································································································································································································································································································(-2x2y2zϵ-x3z2ϵ-3xy2z2ϵ+x2z3ϵ+y2z3ϵ+4xz4ϵ+2xy2z2-2xz4)/(2x4y2+2x3y3+x4yz+2x3y2z+x2y3z-x4z2-x3yz2-x2y2z2-xy3z2-x3z3-2x2yz3-xy2z3)······················································································································································································································································································································(-xyz+xz2+yz2-z3)/(2x2y+2xy2-x2z-2xyz-y2z)····················································································|·····································································································································································································································································································································|37 ······||·(4x2y2ϵ^2+4xy2zϵ^2-2x2z2ϵ^2-2y2z2ϵ^2-4xz3ϵ^2+x3zϵ-3xy2zϵ+2xz3ϵ)/(2x4y2+2x3y3+x4yz+2x3y2z+x2y3z-x4z2-x3yz2-x2y2z2-xy3z2-x3z3-2x2yz3-xy2z3)·······························································································································································································································································································(2x3y2ϵ-2x2y3ϵ+2x3yzϵ-2xy3zϵ-x3z2ϵ+x2yz2ϵ-xy2z2ϵ+y3z2ϵ-2x3yz+2xy3z)/(2x4y2+2x3y3+x4yz+2x3y2z+x2y3z-x4z2-x3yz2-x2y2z2-xy3z2-x3z3-2x2yz3-xy2z3)··························································································································································································································································································································(-2x2y2zϵ-x3z2ϵ-3xy2z2ϵ+x2z3ϵ+y2z3ϵ+4xz4ϵ+2xy2z2-2xz4)/(2x4y2+2x3y3+x4yz+2x3y2z+x2y3z-x4z2-x3yz2-x2y2z2-xy3z2-x3z3-2x2yz3-xy2z3)······················································································································································································································································································································(-xyz+xz2+yz2-z3)/(2x2y+2xy2-x2z-2xyz-y2z)····················································································|·····································································································································································································································································································································|
38 ······||·(-2xyz2ϵ^2-2y2z2ϵ^2-4yz3ϵ^2+2x2y2ϵ+x2yzϵ+xy2zϵ+2y2z2ϵ+2yz3ϵ)/(2x3y2z+x3yz2+x2y2z2-x3z3-xy2z3-x2z4-xyz4)·································································································································································································································································································································(x2yz2ϵ+2xy2z2ϵ+y3z2ϵ+2xyz3ϵ+2y2z3ϵ-2x2y3-x2y2z-xy3z-x2yz2-y3z2-xyz3-y2z3)/(2x3y2z+x3yz2+x2y2z2-x3z3-xy2z3-x2z4-xyz4)··················································································································································································································································································································································(2x2y2ϵ+x2yzϵ+xy2zϵ-2x2z2ϵ+xyz2ϵ+y2z2ϵ-2xz3ϵ+2yz3ϵ-2x2y2-x2yz-xy2z+x2z2-y2z2+xz3-yz3)/(2x3y2+x3yz+x2y2z-x3z2-xy2z2-x2z3-xyz3)·························································································································································································································································································································(-yz+z2)/(2xy-xz-yz)··········································································································|·····································································································································································································································································································································|38 ······||·(-2xyz2ϵ^2-2y2z2ϵ^2-4yz3ϵ^2+2x2y2ϵ+x2yzϵ+xy2zϵ+2y2z2ϵ+2yz3ϵ)/(2x3y2z+x3yz2+x2y2z2-x3z3-xy2z3-x2z4-xyz4)·································································································································································································································································································································(x2yz2ϵ+2xy2z2ϵ+y3z2ϵ+2xyz3ϵ+2y2z3ϵ-2x2y3-x2y2z-xy3z-x2yz2-y3z2-xyz3-y2z3)/(2x3y2z+x3yz2+x2y2z2-x3z3-xy2z3-x2z4-xyz4)··················································································································································································································································································································································(2x2y2ϵ+x2yzϵ+xy2zϵ-2x2z2ϵ+xyz2ϵ+y2z2ϵ-2xz3ϵ+2yz3ϵ-2x2y2-x2yz-xy2z+x2z2-y2z2+xz3-yz3)/(2x3y2+x3yz+x2y2z-x3z2-xy2z2-x2z3-xyz3)·························································································································································································································································································································(-yz+z2)/(2xy-xz-yz)··········································································································|·····································································································································································································································································································································|
Offset 56, 24 lines modifiedOffset 56, 24 lines modified
56 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+56 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
  
57 i12·:·F·=·baseFractionField·D;57 i12·:·F·=·baseFractionField·D;
  
58 i13·:·B·=·{1_D,dx,dy,dx*dy};58 i13·:·B·=·{1_D,dx,dy,dx*dy};
  
59 i14·:·elapsedTime·g·=·gaugeMatrix(I,·B);59 i14·:·elapsedTime·g·=·gaugeMatrix(I,·B);
60 ·--·.416818s·elapsed60 ·--·1.40347s·elapsed
  
61 ··············4······461 ··············4······4
62 o14·:·Matrix·F··<--·F62 o14·:·Matrix·F··<--·F
  
63 i15·:·elapsedTime·A1·=·gaugeTransform(g,·A);63 i15·:·elapsedTime·A1·=·gaugeTransform(g,·A);
64 ·--·1.05211s·elapsed64 ·--·2.41785s·elapsed
  
65 i16·:·elapsedTime·assert·isIntegrable·A165 i16·:·elapsedTime·assert·isIntegrable·A1
66 ·--·.784278s·elapsed66 ·--·1.94159s·elapsed
  
67 i17·:·netList·A167 i17·:·netList·A1
  
68 ······+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+68 ······+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
69 o17·=·||·0····························1······················0·········································0······················································|·········································································|69 o17·=·||·0····························1······················0·········································0······················································|·········································································|
70 ······||·(-2ϵ^2+ϵ)/(x2-z2)············(3xϵ+zϵ-2x)/(x2-z2)····(yϵ+zϵ)/(x2-z2)···························(-y-z)/(x-z)···········································|·········································································|70 ······||·(-2ϵ^2+ϵ)/(x2-z2)············(3xϵ+zϵ-2x)/(x2-z2)····(yϵ+zϵ)/(x2-z2)···························(-y-z)/(x-z)···········································|·········································································|
71 ······||·0····························0······················0·········································1······················································|·········································································|71 ······||·0····························0······················0·········································1······················································|·········································································|
Offset 96, 18 lines modifiedOffset 96, 18 lines modified
96 ··············{0,·0,·ϵ*(y^2-z^2),·ϵ*(x+y)*(y+z)},96 ··············{0,·0,·ϵ*(y^2-z^2),·ϵ*(x+y)*(y+z)},
97 ··············{0,·0,·0,·-(x+y)*(x+z)*(y+z)}});97 ··············{0,·0,·0,·-(x+y)*(x+z)*(y+z)}});
  
98 ··············4······498 ··············4······4
99 o18·:·Matrix·F··<--·F99 o18·:·Matrix·F··<--·F
  
100 i19·:·elapsedTime·A2·=·gaugeTransform(changeEps,·A1);100 i19·:·elapsedTime·A2·=·gaugeTransform(changeEps,·A1);
101 ·--·.281172s·elapsed101 ·--·.615959s·elapsed
  
102 i20·:·elapsedTime·assert·isIntegrable·A2102 i20·:·elapsedTime·assert·isIntegrable·A2
103 ·--·.570019s·elapsed103 ·--·1.40761s·elapsed
  
104 i21·:·netList·A2104 i21·:·netList·A2
  
105 ······+---------------------------------------------------------------------------------------------+105 ······+---------------------------------------------------------------------------------------------+
106 o21·=·||·ϵ/(x+z)·2zϵ/(x2-z2)·0·······0······················|·······································|106 o21·=·||·ϵ/(x+z)·2zϵ/(x2-z2)·0·······0······················|·······································|
107 ······||·0·······ϵ/(x-z)·····0·······ϵ/(x+y)················|·······································|107 ······||·0·······ϵ/(x-z)·····0·······ϵ/(x+y)················|·······································|
108 ······||·0·······0···········ϵ/(x+z)·(-yϵ+zϵ)/(x2+xy+xz+yz)·|·······································|108 ······||·0·······0···········ϵ/(x+z)·(-yϵ+zϵ)/(x2+xy+xz+yz)·|·······································|
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16 ···················216 ···················2
17 o6·=·{1,·dx,·dy,·dy·}17 o6·=·{1,·dx,·dy,·dy·}
  
18 o6·:·List18 o6·:·List
  
19 i7·:·elapsedTime·A·=·connectionMatrices·I;19 i7·:·elapsedTime·A·=·connectionMatrices·I;
20 ·--·.182538s·elapsed20 ·--·.423517s·elapsed
  
21 i8·:·elapsedTime·assert·isIntegrable·A21 i8·:·elapsedTime·assert·isIntegrable·A
22 ·--·.200166s·elapsed22 ·--·.573295s·elapsed
  
23 i9·:·netList·A23 i9·:·netList·A
  
24 ·····+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+24 ·····+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
25 o9·=·||·0·······················································1···············································0·····································································0······································································||25 o9·=·||·0·······················································1···············································0·····································································0······································································||
26 ·····||·0·······················································(-1)/x··········································1/x···································································y/x····································································||26 ·····||·0·······················································(-1)/x··········································1/x···································································y/x····································································||
27 ·····||·(-1)/2xy················································(-1)/y··········································(-x-3y+1)/2xy·························································(-x-y+1)/2x····························································||27 ·····||·(-1)/2xy················································(-1)/y··········································(-x-3y+1)/2xy·························································(-x-y+1)/2x····························································||
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118 ········<div>118 ········<div>
119 ··········<p>Then,·we·compute·the·system·in·connection·form·and·verify·that·it·meets·the·integrability·conditions.</p>119 ··········<p>Then,·we·compute·the·system·in·connection·form·and·verify·that·it·meets·the·integrability·conditions.</p>
120 ········</div>120 ········</div>
121 ········<table·class="examples">121 ········<table·class="examples">
122 ··········<tr>122 ··········<tr>
123 ············<td>123 ············<td>
124 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·A·=·connectionMatrices·I;124 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·A·=·connectionMatrices·I;
125 ·--·2.07985s·elapsed</code></pre>125 ·--·4.78861s·elapsed</code></pre>
126 ············</td>126 ············</td>
127 ··········</tr>127 ··········</tr>
128 ··········<tr>128 ··········<tr>
129 ············<td>129 ············<td>
130 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·assert·isIntegrable·A130 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·assert·isIntegrable·A
131 ·--·3.7658s·elapsed</code></pre>131 ·--·8.81575s·elapsed</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i11·:·netList·A136 ··············<pre><code·class="language-macaulay2">i11·:·netList·A
  
137 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+137 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
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167 ············<td>167 ············<td>
168 ··············<pre><code·class="language-macaulay2">i13·:·B·=·{1_D,dx,dy,dx*dy};</code></pre>168 ··············<pre><code·class="language-macaulay2">i13·:·B·=·{1_D,dx,dy,dx*dy};</code></pre>
169 ············</td>169 ············</td>
170 ··········</tr>170 ··········</tr>
171 ··········<tr>171 ··········<tr>
172 ············<td>172 ············<td>
173 ··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·g·=·gaugeMatrix(I,·B);173 ··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·g·=·gaugeMatrix(I,·B);
174 ·--·.416818s·elapsed174 ·--·1.40347s·elapsed
  
175 ··············4······4175 ··············4······4
176 o14·:·Matrix·F··&lt;--·F</code></pre>176 o14·:·Matrix·F··&lt;--·F</code></pre>
177 ············</td>177 ············</td>
178 ··········</tr>178 ··········</tr>
179 ··········<tr>179 ··········<tr>
180 ············<td>180 ············<td>
181 ··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·A1·=·gaugeTransform(g,·A);181 ··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·A1·=·gaugeTransform(g,·A);
182 ·--·1.05211s·elapsed</code></pre>182 ·--·2.41785s·elapsed</code></pre>
183 ············</td>183 ············</td>
184 ··········</tr>184 ··········</tr>
185 ··········<tr>185 ··········<tr>
186 ············<td>186 ············<td>
187 ··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·assert·isIntegrable·A1187 ··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·assert·isIntegrable·A1
188 ·--·.784278s·elapsed</code></pre>188 ·--·1.94159s·elapsed</code></pre>
189 ············</td>189 ············</td>
190 ··········</tr>190 ··········</tr>
191 ··········<tr>191 ··········<tr>
192 ············<td>192 ············<td>
193 ··············<pre><code·class="language-macaulay2">i17·:·netList·A1193 ··············<pre><code·class="language-macaulay2">i17·:·netList·A1
  
194 ······+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+194 ······+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
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227 ··············4······4227 ··············4······4
228 o18·:·Matrix·F··&lt;--·F</code></pre>228 o18·:·Matrix·F··&lt;--·F</code></pre>
229 ············</td>229 ············</td>
230 ··········</tr>230 ··········</tr>
231 ··········<tr>231 ··········<tr>
232 ············<td>232 ············<td>
233 ··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·A2·=·gaugeTransform(changeEps,·A1);233 ··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·A2·=·gaugeTransform(changeEps,·A1);
234 ·--·.281172s·elapsed</code></pre>234 ·--·.615959s·elapsed</code></pre>
235 ············</td>235 ············</td>
236 ··········</tr>236 ··········</tr>
237 ··········<tr>237 ··········<tr>
238 ············<td>238 ············<td>
239 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·assert·isIntegrable·A2239 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·assert·isIntegrable·A2
240 ·--·.570019s·elapsed</code></pre>240 ·--·1.40761s·elapsed</code></pre>
241 ············</td>241 ············</td>
242 ··········</tr>242 ··········</tr>
243 ··········<tr>243 ··········<tr>
244 ············<td>244 ············<td>
245 ··············<pre><code·class="language-macaulay2">i21·:·netList·A2245 ··············<pre><code·class="language-macaulay2">i21·:·netList·A2
  
246 ······+---------------------------------------------------------------------------------------------+246 ······+---------------------------------------------------------------------------------------------+
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41 o7·:·Ideal·of·D41 o7·:·Ideal·of·D
42 First,·we·check·that·the·system·has·finite·holonomic·rank·using·_\x8h_\x8o_\x8l_\x8o_\x8n_\x8o_\x8m_\x8i_\x8c_\x8R_\x8a_\x8n_\x8k.42 First,·we·check·that·the·system·has·finite·holonomic·rank·using·_\x8h_\x8o_\x8l_\x8o_\x8n_\x8o_\x8m_\x8i_\x8c_\x8R_\x8a_\x8n_\x8k.
43 i8·:·assert(holonomicRank·I·==·4)43 i8·:·assert(holonomicRank·I·==·4)
44 Then,·we·compute·the·system·in·connection·form·and·verify·that·it·meets·the44 Then,·we·compute·the·system·in·connection·form·and·verify·that·it·meets·the
45 integrability·conditions.45 integrability·conditions.
46 i9·:·elapsedTime·A·=·connectionMatrices·I;46 i9·:·elapsedTime·A·=·connectionMatrices·I;
47 ·--·2.07985s·elapsed47 ·--·4.78861s·elapsed
48 i10·:·elapsedTime·assert·isIntegrable·A48 i10·:·elapsedTime·assert·isIntegrable·A
49 ·--·3.7658s·elapsed49 ·--·8.81575s·elapsed
50 i11·:·netList·A50 i11·:·netList·A
  
51 ······+----------------------------------------------------------------------------------------------------------51 ······+----------------------------------------------------------------------------------------------------------
52 -----------------------------------------------------------------------------------------------------------------52 -----------------------------------------------------------------------------------------------------------------
53 -----------------------------------------------------------------------------------------------------------------53 -----------------------------------------------------------------------------------------------------------------
54 -----------------------------------------------------------------------------------------------------------------54 -----------------------------------------------------------------------------------------------------------------
55 -----------------------------------------------------------------------------------------------------------------55 -----------------------------------------------------------------------------------------------------------------
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227 -----------------------------------------------------------------------------------+227 -----------------------------------------------------------------------------------+
228 Next,·we·use·_\x8g_\x8a_\x8u_\x8g_\x8e_\x8·_\x8m_\x8a_\x8t_\x8r_\x8i_\x8x·for·changing·base·to·a·base·given·by·suitable·set·of228 Next,·we·use·_\x8g_\x8a_\x8u_\x8g_\x8e_\x8·_\x8m_\x8a_\x8t_\x8r_\x8i_\x8x·for·changing·base·to·a·base·given·by·suitable·set·of
229 standard·monomials,·and·compute·the·_\x8g_\x8a_\x8u_\x8g_\x8e_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m·with·respect·to·this·gauge229 standard·monomials,·and·compute·the·_\x8g_\x8a_\x8u_\x8g_\x8e_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m·with·respect·to·this·gauge
230 matrix.230 matrix.
231 i12·:·F·=·baseFractionField·D;231 i12·:·F·=·baseFractionField·D;
232 i13·:·B·=·{1_D,dx,dy,dx*dy};232 i13·:·B·=·{1_D,dx,dy,dx*dy};
233 i14·:·elapsedTime·g·=·gaugeMatrix(I,·B);233 i14·:·elapsedTime·g·=·gaugeMatrix(I,·B);
234 ·--·.416818s·elapsed234 ·--·1.40347s·elapsed
  
235 ··············4······4235 ··············4······4
236 o14·:·Matrix·F··<--·F236 o14·:·Matrix·F··<--·F
237 i15·:·elapsedTime·A1·=·gaugeTransform(g,·A);237 i15·:·elapsedTime·A1·=·gaugeTransform(g,·A);
238 ·--·1.05211s·elapsed238 ·--·2.41785s·elapsed
239 i16·:·elapsedTime·assert·isIntegrable·A1239 i16·:·elapsedTime·assert·isIntegrable·A1
240 ·--·.784278s·elapsed240 ·--·1.94159s·elapsed
241 i17·:·netList·A1241 i17·:·netList·A1
  
242 ······+------------------------------------------------------------------------242 ······+------------------------------------------------------------------------
243 -------------------------------------------------------------------------------243 -------------------------------------------------------------------------------
244 --------------------------------------------------------------------------+244 --------------------------------------------------------------------------+
245 o17·=·||·0····························1······················0245 o17·=·||·0····························1······················0
246 0······················································|246 0······················································|
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300 ··············{0,·Ïµ*(x^2-z^2),·0,·Ïµ*(x+y)*(x+z)},300 ··············{0,·Ïµ*(x^2-z^2),·0,·Ïµ*(x+y)*(x+z)},
301 ··············{0,·0,·Ïµ*(y^2-z^2),·Ïµ*(x+y)*(y+z)},301 ··············{0,·0,·Ïµ*(y^2-z^2),·Ïµ*(x+y)*(y+z)},
302 ··············{0,·0,·0,·-(x+y)*(x+z)*(y+z)}});302 ··············{0,·0,·0,·-(x+y)*(x+z)*(y+z)}});
  
303 ··············4······4303 ··············4······4
304 o18·:·Matrix·F··<--·F304 o18·:·Matrix·F··<--·F
305 i19·:·elapsedTime·A2·=·gaugeTransform(changeEps,·A1);305 i19·:·elapsedTime·A2·=·gaugeTransform(changeEps,·A1);
306 ·--·.281172s·elapsed306 ·--·.615959s·elapsed
307 i20·:·elapsedTime·assert·isIntegrable·A2307 i20·:·elapsedTime·assert·isIntegrable·A2
308 ·--·.570019s·elapsed308 ·--·1.40761s·elapsed
309 i21·:·netList·A2309 i21·:·netList·A2
  
310 ······+------------------------------------------------------------------------310 ······+------------------------------------------------------------------------
311 ---------------------+311 ---------------------+
312 o21·=·||·Ïµ/(x+z)·2zϵ/(x2-z2)·0·······0······················|312 o21·=·||·Ïµ/(x+z)·2zϵ/(x2-z2)·0·······0······················|
313 |313 |
314 ······||·0·······Ïµ/(x-z)·····0·······Ïµ/(x+y)················|314 ······||·0·······Ïµ/(x-z)·····0·······Ïµ/(x+y)················|
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100 ········<div>100 ········<div>
101 ··········<p>Finally,·we·can·compute·the·connection·matrices.</p>101 ··········<p>Finally,·we·can·compute·the·connection·matrices.</p>
102 ········</div>102 ········</div>
103 ········<table·class="examples">103 ········<table·class="examples">
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·A·=·connectionMatrices·I;106 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·A·=·connectionMatrices·I;
107 ·--·.182538s·elapsed</code></pre>107 ·--·.423517s·elapsed</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·isIntegrable·A112 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·isIntegrable·A
113 ·--·.200166s·elapsed</code></pre>113 ·--·.573295s·elapsed</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ··········<tr>116 ··········<tr>
117 ············<td>117 ············<td>
118 ··············<pre><code·class="language-macaulay2">i9·:·netList·A118 ··············<pre><code·class="language-macaulay2">i9·:·netList·A
  
119 ·····+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+119 ·····+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
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20 ···················220 ···················2
21 o6·=·{1,·dx,·dy,·dy·}21 o6·=·{1,·dx,·dy,·dy·}
  
22 o6·:·List22 o6·:·List
23 Finally,·we·can·compute·the·connection·matrices.23 Finally,·we·can·compute·the·connection·matrices.
24 i7·:·elapsedTime·A·=·connectionMatrices·I;24 i7·:·elapsedTime·A·=·connectionMatrices·I;
25 ·--·.182538s·elapsed25 ·--·.423517s·elapsed
26 i8·:·elapsedTime·assert·isIntegrable·A26 i8·:·elapsedTime·assert·isIntegrable·A
27 ·--·.200166s·elapsed27 ·--·.573295s·elapsed
28 i9·:·netList·A28 i9·:·netList·A
  
29 ·····+-------------------------------------------------------------------------29 ·····+-------------------------------------------------------------------------
30 -------------------------------------------------------------------------------30 -------------------------------------------------------------------------------
31 -------------------------------------------------------------------------------31 -------------------------------------------------------------------------------
32 -----------------+32 -----------------+
33 o9·=·||·0·······················································133 o9·=·||·0·······················································1
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./usr/share/doc/Macaulay2/CorrespondenceScrolls/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=527 #:len=52
8 cHJvZHVjdE9mUHJvamVjdGl2ZVNwYWNlcyguLi4sQ29lZmZpY2llbnRGaWVsZD0+Li4uKQ==8 cHJvZHVjdE9mUHJvamVjdGl2ZVNwYWNlcyguLi4sQ29lZmZpY2llbnRGaWVsZD0+Li4uKQ==
9 #:len=3679 #:len=367
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzcwLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzcwLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1twcm9kdWN0T2ZQcm9qZWN0aXZlU3BhY2VzLENvZWZm11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1twcm9kdWN0T2ZQcm9qZWN0aXZlU3BhY2VzLENvZWZm
726 B
./usr/share/doc/Macaulay2/CotangentSchubert/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=67 #:len=6
8 TGFiZWxz8 TGFiZWxz
9 #:len=1839 #:len=183
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA2LCAidW5kb2N1bWVudGVkIiA9PiB010 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA2LCAidW5kb2N1bWVudGVkIiA9PiB0
11 cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJMYWJlbHMi11 cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJMYWJlbHMi
728 B
./usr/share/doc/Macaulay2/Cremona/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=217 #:len=21
8 ZGVzY3JpYmUoUmF0aW9uYWxNYXAp8 ZGVzY3JpYmUoUmF0aW9uYWxNYXAp
9 #:len=10969 #:len=1096
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGVzY3JpYmUgYSByYXRpb25hbCBtYXAi10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGVzY3JpYmUgYSByYXRpb25hbCBtYXAi
11 LCAibGluZW51bSIgPT4gOTgzLCBJbnB1dHMgPT4ge1NQQU57VFR7InBoaSJ9LCIsICIsU1BBTnsi11 LCAibGluZW51bSIgPT4gOTgzLCBJbnB1dHMgPT4ge1NQQU57VFR7InBoaSJ9LCIsICIsU1BBTnsi
1.66 KB
./usr/share/doc/Macaulay2/Cremona/example-output/___Chern__Schwartz__Mac__Pherson.out
    
Offset 13, 26 lines modifiedOffset 13, 26 lines modified
13 o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·)13 o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·)
14 ···············1····0·2·····1·2····0·3·····2····1·314 ···············1····0·2·····1·2····0·3·····2····1·3
  
15 o2·:·Ideal·of·GF·78125[x·..x·]15 o2·:·Ideal·of·GF·78125[x·..x·]
16 ························0···416 ························0···4
  
17 i3·:·time·ChernSchwartzMacPherson·C17 i3·:·time·ChernSchwartzMacPherson·C
18 ·--·used·1.15281s·(cpu);·0.776751s·(thread);·0s·(gc)18 ·--·used·1.4464s·(cpu);·0.930233s·(thread);·0s·(gc)
  
19 ·······4·····3·····219 ·······4·····3·····2
20 o3·=·3H··+·5H··+·3H20 o3·=·3H··+·5H··+·3H
  
21 ·····ZZ[H]21 ·····ZZ[H]
22 o3·:·-----22 o3·:·-----
23 ········523 ········5
24 ·······H24 ·······H
  
25 i4·:·time·ChernSchwartzMacPherson(C,Certify=>true)25 i4·:·time·ChernSchwartzMacPherson(C,Certify=>true)
26 ·--·used·2.44728s·(cpu);·0.862882s·(thread);·0s·(gc)26 ·--·used·2.46997s·(cpu);·0.928831s·(thread);·0s·(gc)
27 Certify:·output·certified!27 Certify:·output·certified!
  
28 ·······4·····3·····228 ·······4·····3·····2
29 o4·=·3H··+·5H··+·3H29 o4·=·3H··+·5H··+·3H
  
30 ·····ZZ[H]30 ·····ZZ[H]
31 o4·:·-----31 o4·:·-----
Offset 62, 26 lines modifiedOffset 62, 26 lines modified
62 ········0,2·1,3····0,1·2,362 ········0,2·1,3····0,1·2,3
  
63 ················ZZ63 ················ZZ
64 o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]64 o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]
65 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,465 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4
  
66 i9·:·time·ChernClass·G66 i9·:·time·ChernClass·G
67 ·--·used·0.165292s·(cpu);·0.135278s·(thread);·0s·(gc)67 ·--·used·0.184597s·(cpu);·0.13865s·(thread);·0s·(gc)
  
68 ········9······8······7······6······5······4·····368 ········9······8······7······6······5······4·····3
69 o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H69 o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H
  
70 ·····ZZ[H]70 ·····ZZ[H]
71 o9·:·-----71 o9·:·-----
72 ·······1072 ·······10
73 ······H73 ······H
  
74 i10·:·time·ChernClass(G,Certify=>true)74 i10·:·time·ChernClass(G,Certify=>true)
75 ·--·used·0.295023s·(cpu);·0.0656588s·(thread);·0s·(gc)75 ·--·used·0.276832s·(cpu);·0.0541502s·(thread);·0s·(gc)
76 Certify:·output·certified!76 Certify:·output·certified!
  
77 ·········9······8······7······6······5······4·····377 ·········9······8······7······6······5······4·····3
78 o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H78 o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H
  
79 ······ZZ[H]79 ······ZZ[H]
80 o10·:·-----80 o10·:·-----
14.0 KB
./usr/share/doc/Macaulay2/Cremona/example-output/___Cremona.out
    
Offset 1, 56 lines modifiedOffset 1, 56 lines modified
1 --·-*-·M2-comint·-*-·hash:·104334092679444218251 --·-*-·M2-comint·-*-·hash:·10433409267944421825
  
2 i1·:·ZZ/300007[t_0..t_6];2 i1·:·ZZ/300007[t_0..t_6];
  
3 i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})3 i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})
4 ·--·used·0.00401246s·(cpu);·0.00395623s·(thread);·0s·(gc)4 ·--·used·0.00394461s·(cpu);·0.00417509s·(thread);·0s·(gc)
  
5 ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····25 ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2
6 o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})6 o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})
7 ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·67 ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6
  
8 ···············ZZ·················ZZ8 ···············ZZ·················ZZ
9 o2·:·RingMap·------[t·..t·]·<--·------[x·..x·]9 o2·:·RingMap·------[t·..t·]·<--·------[x·..x·]
10 ·············300007··0···6······300007··0···910 ·············300007··0···6······300007··0···9
  
11 i3·:·time·J·=·kernel(phi,2)11 i3·:·time·J·=·kernel(phi,2)
12 ·--·used·0.0410654s·(cpu);·0.0419253s·(thread);·0s·(gc)12 ·--·used·0.0349428s·(cpu);·0.0380202s·(thread);·0s·(gc)
  
13 o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x·13 o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x·
14 ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·414 ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4
15 ·····------------------------------------------------------------------------15 ·····------------------------------------------------------------------------
16 ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)16 ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)
17 ········1·6····0·8···2·4····1·5····0·717 ········1·6····0·8···2·4····1·5····0·7
  
18 ················ZZ18 ················ZZ
19 o3·:·Ideal·of·------[x·..x·]19 o3·:·Ideal·of·------[x·..x·]
20 ··············300007··0···920 ··············300007··0···9
  
21 i4·:·time·degreeMap·phi21 i4·:·time·degreeMap·phi
22 ·--·used·0.0255553s·(cpu);·0.0256617s·(thread);·0s·(gc)22 ·--·used·0.0231091s·(cpu);·0.0258764s·(thread);·0s·(gc)
  
23 o4·=·123 o4·=·1
  
24 i5·:·time·projectiveDegrees·phi24 i5·:·time·projectiveDegrees·phi
25 ·--·used·0.402417s·(cpu);·0.331126s·(thread);·0s·(gc)25 ·--·used·0.487287s·(cpu);·0.358582s·(thread);·0s·(gc)
  
26 o5·=·{1,·3,·9,·17,·21,·15,·5}26 o5·=·{1,·3,·9,·17,·21,·15,·5}
  
27 o5·:·List27 o5·:·List
  
28 i6·:·time·projectiveDegrees(phi,NumDegrees=>0)28 i6·:·time·projectiveDegrees(phi,NumDegrees=>0)
29 ·--·used·0.117123s·(cpu);·0.0754688s·(thread);·0s·(gc)29 ·--·used·0.116466s·(cpu);·0.0642495s·(thread);·0s·(gc)
  
30 o6·=·{5}30 o6·=·{5}
  
31 o6·:·List31 o6·:·List
  
32 i7·:·time·phi·=·toMap(phi,Dominant=>J)32 i7·:·time·phi·=·toMap(phi,Dominant=>J)
33 ·--·used·0.000157788s·(cpu);·0.00186622s·(thread);·0s·(gc)33 ·--·used·0.00083198s·(cpu);·0.00232522s·(thread);·0s·(gc)
  
34 ·······································································ZZ34 ·······································································ZZ
35 ·····································································------[x·..x·]35 ·····································································------[x·..x·]
36 ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····236 ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2
37 o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})37 o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})
38 ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·638 ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6
39 ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·739 ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7
Offset 59, 15 lines modifiedOffset 59, 15 lines modified
59 ···········································································------[x·..x·]59 ···········································································------[x·..x·]
60 ···············ZZ··························································300007··0···960 ···············ZZ··························································300007··0···9
61 o7·:·RingMap·------[t·..t·]·<--·----------------------------------------------------------------------------------------------------61 o7·:·RingMap·------[t·..t·]·<--·----------------------------------------------------------------------------------------------------
62 ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)62 ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)
63 ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·763 ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7
  
64 i8·:·time·psi·=·inverseMap·phi64 i8·:·time·psi·=·inverseMap·phi
65 ·--·used·0.456109s·(cpu);·0.412271s·(thread);·0s·(gc)65 ·--·used·0.417561s·(cpu);·0.367241s·(thread);·0s·(gc)
  
66 ·······················································ZZ66 ·······················································ZZ
67 ·····················································------[x·..x·]67 ·····················································------[x·..x·]
68 ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································268 ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································2
69 o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·})69 o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·})
70 ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·970 ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·9
71 ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·771 ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7
Offset 76, 32 lines modifiedOffset 76, 32 lines modified
76 ························································------[x·..x·]76 ························································------[x·..x·]
77 ························································300007··0···9···················································ZZ77 ························································300007··0···9···················································ZZ
78 o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·]78 o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·]
79 ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···679 ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6
80 ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·780 ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7
  
81 i9·:·time·isInverseMap(phi,psi)81 i9·:·time·isInverseMap(phi,psi)
82 ·--·used·0.00480108s·(cpu);·0.00772231s·(thread);·0s·(gc)82 ·--·used·0.00847325s·(cpu);·0.00769845s·(thread);·0s·(gc)
  
83 o9·=·true83 o9·=·true
  
84 i10·:·time·degreeMap·psi84 i10·:·time·degreeMap·psi
85 ·--·used·0.192915s·(cpu);·0.149974s·(thread);·0s·(gc)85 ·--·used·0.2006s·(cpu);·0.160561s·(thread);·0s·(gc)
  
86 o10·=·186 o10·=·1
  
87 i11·:·time·projectiveDegrees·psi87 i11·:·time·projectiveDegrees·psi
88 ·--·used·4.3311s·(cpu);·4.01164s·(thread);·0s·(gc)88 ·--·used·4.93938s·(cpu);·4.57918s·(thread);·0s·(gc)
  
89 o11·=·{5,·15,·21,·17,·9,·3,·1}89 o11·=·{5,·15,·21,·17,·9,·3,·1}
  
90 o11·:·List90 o11·:·List
  
91 i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})91 i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})
92 ·--·used·0.000879674s·(cpu);·0.00189829s·(thread);·0s·(gc)92 ·--·used·0.000183784s·(cpu);·0.00200697s·(thread);·0s·(gc)
  
93 o12·=·--·rational·map·--93 o12·=·--·rational·map·--
94 ·····················ZZ94 ·····················ZZ
95 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])95 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])
96 ···················300007··0···1···2···3···4···5···696 ···················300007··0···1···2···3···4···5···6
97 ·····················ZZ97 ·····················ZZ
98 ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])98 ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
Offset 147, 15 lines modifiedOffset 147, 15 lines modified
147 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t147 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t
148 ··························4·····3·4·5····2·5····3·6····2·4·6148 ··························4·····3·4·5····2·5····3·6····2·4·6
149 ······················}149 ······················}
  
150 o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)150 o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)
  
151 i13·:·time·phi·=·rationalMap(phi,Dominant=>2)151 i13·:·time·phi·=·rationalMap(phi,Dominant=>2)
152 ·--·used·0.12219s·(cpu);·0.080011s·(thread);·0s·(gc)152 ·--·used·0.130066s·(cpu);·0.0698304s·(thread);·0s·(gc)
  
153 o13·=·--·rational·map·--153 o13·=·--·rational·map·--
154 ·····················ZZ154 ·····················ZZ
155 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])155 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])
156 ···················300007··0···1···2···3···4···5···6156 ···················300007··0···1···2···3···4···5···6
157 ···································ZZ157 ···································ZZ
158 ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])·defined·by158 ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])·defined·by
Offset 217, 15 lines modifiedOffset 217, 15 lines modified
217 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t217 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t
218 ··························4·····3·4·5····2·5····3·6····2·4·6218 ··························4·····3·4·5····2·5····3·6····2·4·6
219 ······················}219 ······················}
  
220 o13·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)220 o13·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)
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778 B
./usr/share/doc/Macaulay2/Cremona/example-output/___Euler__Characteristic.out
    
Offset 3, 18 lines modifiedOffset 3, 18 lines modified
3 i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181);3 i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181);
  
4 ················ZZ4 ················ZZ
5 o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]5 o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]
6 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,46 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4
  
7 i2·:·time·EulerCharacteristic·I7 i2·:·time·EulerCharacteristic·I
8 ·--·used·0.21929s·(cpu);·0.129003s·(thread);·0s·(gc)8 ·--·used·0.256095s·(cpu);·0.158894s·(thread);·0s·(gc)
  
9 o2·=·109 o2·=·10
  
10 i3·:·time·EulerCharacteristic(I,Certify=>true)10 i3·:·time·EulerCharacteristic(I,Certify=>true)
11 ·--·used·0.322006s·(cpu);·0.0459866s·(thread);·0s·(gc)11 ·--·used·0.191015s·(cpu);·0.0306611s·(thread);·0s·(gc)
12 Certify:·output·certified!12 Certify:·output·certified!
  
13 o3·=·1013 o3·=·10
  
14 i4·:·14 i4·:·
1.01 KB
./usr/share/doc/Macaulay2/Cremona/example-output/___Rational__Map_sp!.out
    
Offset 8, 15 lines modifiedOffset 8, 15 lines modified
  
8 o3·=·rational·map·defined·by·forms·of·degree·28 o3·=·rational·map·defined·by·forms·of·degree·2
9 ·····source·variety:·PP^59 ·····source·variety:·PP^5
10 ·····target·variety:·PP^510 ·····target·variety:·PP^5
11 ·····coefficient·ring:·QQ11 ·····coefficient·ring:·QQ
  
12 i4·:·time·phi!·;12 i4·:·time·phi!·;
13 ·--·used·0.360888s·(cpu);·0.110237s·(thread);·0s·(gc)13 ·--·used·0.306406s·(cpu);·0.0872304s·(thread);·0s·(gc)
  
14 o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))14 o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))
  
15 i5·:·describe·phi15 i5·:·describe·phi
  
16 o5·=·rational·map·defined·by·forms·of·degree·216 o5·=·rational·map·defined·by·forms·of·degree·2
17 ·····source·variety:·PP^517 ·····source·variety:·PP^5
Offset 37, 15 lines modifiedOffset 37, 15 lines modified
  
37 o8·=·rational·map·defined·by·forms·of·degree·237 o8·=·rational·map·defined·by·forms·of·degree·2
38 ·····source·variety:·PP^438 ·····source·variety:·PP^4
39 ·····target·variety:·PP^539 ·····target·variety:·PP^5
40 ·····coefficient·ring:·QQ40 ·····coefficient·ring:·QQ
  
41 i9·:·time·phi!·;41 i9·:·time·phi!·;
42 ·--·used·0.369233s·(cpu);·0.0678051s·(thread);·0s·(gc)42 ·--·used·0.314867s·(cpu);·0.0792633s·(thread);·0s·(gc)
  
43 o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)43 o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)
  
44 i10·:·describe·phi44 i10·:·describe·phi
  
45 o10·=·rational·map·defined·by·forms·of·degree·245 o10·=·rational·map·defined·by·forms·of·degree·2
46 ······source·variety:·PP^446 ······source·variety:·PP^4
724 B
./usr/share/doc/Macaulay2/Cremona/example-output/___Rational__Map_sp^_st_st_sp__Ideal.out
    
Offset 67, 15 lines modifiedOffset 67, 15 lines modified
67 ·····-·a*c·+·e·········-·b*c·+·f67 ·····-·a*c·+·e·········-·b*c·+·f
68 ·····----------*v,·x·+·----------*v)68 ·····----------*v,·x·+·----------*v)
69 ······d*e·-·a*f·········d*e·-·a*f69 ······d*e·-·a*f·········d*e·-·a*f
  
70 o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]70 o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]
  
71 i6·:·time·phi^**·q71 i6·:·time·phi^**·q
72 ·--·used·0.195335s·(cpu);·0.145455s·(thread);·0s·(gc)72 ·--·used·0.270708s·(cpu);·0.191903s·(thread);·0s·(gc)
  
73 ················-e········-d········-c········-b········-a73 ················-e········-d········-c········-b········-a
74 o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v)74 o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v)
75 ·················f·········f·········f·········f·········f75 ·················f·········f·········f·········f·········f
  
76 o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]76 o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]
  
5.0 KB
./usr/share/doc/Macaulay2/Cremona/example-output/___Segre__Class.out
    
Offset 47, 49 lines modifiedOffset 47, 49 lines modified
47 ··········································································P747 ··········································································P7
48 o3·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------48 o3·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------
49 ···············2·2················2·2········································2·2····················································2·249 ···············2·2················2·2········································2·2····················································2·2
50 ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x50 ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x
51 ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·751 ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7
  
52 i4·:·time·SegreClass·X52 i4·:·time·SegreClass·X
53 ·--·used·0.380436s·(cpu);·0.351659s·(thread);·0s·(gc)53 ·--·used·0.429616s·(cpu);·0.382741s·(thread);·0s·(gc)
  
54 ··········7········6·······5·······4······354 ··········7········6·······5·······4······3
55 o4·=·3240H··-·1188H··+·396H··-·114H··+·24H55 o4·=·3240H··-·1188H··+·396H··-·114H··+·24H
  
56 ·····ZZ[H]56 ·····ZZ[H]
57 o4·:·-----57 o4·:·-----
58 ········858 ········8
59 ·······H59 ·······H
  
60 i5·:·time·SegreClass·lift(X,P7)60 i5·:·time·SegreClass·lift(X,P7)
61 ·--·used·0.332568s·(cpu);·0.260207s·(thread);·0s·(gc)61 ·--·used·0.38557s·(cpu);·0.284851s·(thread);·0s·(gc)
  
62 ··········7········6·······5······4······362 ··········7········6·······5······4······3
63 o5·=·2816H··-·1056H··+·324H··-·78H··+·12H63 o5·=·2816H··-·1056H··+·324H··-·78H··+·12H
  
64 ·····ZZ[H]64 ·····ZZ[H]
65 o5·:·-----65 o5·:·-----
66 ········866 ········8
67 ·······H67 ·······H
  
68 i6·:·time·SegreClass(X,Certify=>true)68 i6·:·time·SegreClass(X,Certify=>true)
69 ·--·used·0.318387s·(cpu);·0.0489743s·(thread);·0s·(gc)69 ·--·used·0.247191s·(cpu);·0.0462595s·(thread);·0s·(gc)
70 Certify:·output·certified!70 Certify:·output·certified!
  
71 ··········7········6·······5·······4······371 ··········7········6·······5·······4······3
72 o6·=·3240H··-·1188H··+·396H··-·114H··+·24H72 o6·=·3240H··-·1188H··+·396H··-·114H··+·24H
  
73 ·····ZZ[H]73 ·····ZZ[H]
74 o6·:·-----74 o6·:·-----
75 ········875 ········8
76 ·······H76 ·······H
  
77 i7·:·time·SegreClass(lift(X,P7),Certify=>true)77 i7·:·time·SegreClass(lift(X,P7),Certify=>true)
78 ·--·used·0.373743s·(cpu);·0.119007s·(thread);·0s·(gc)78 ·--·used·0.382237s·(cpu);·0.14173s·(thread);·0s·(gc)
79 Certify:·output·certified!79 Certify:·output·certified!
  
80 ··········7········6·······5······4······380 ··········7········6·······5······4······3
81 o7·=·2816H··-·1056H··+·324H··-·78H··+·12H81 o7·=·2816H··-·1056H··+·324H··-·78H··+·12H
  
82 ·····ZZ[H]82 ·····ZZ[H]
83 o7·:·-----83 o7·:·-----
Offset 105, 15 lines modifiedOffset 105, 15 lines modified
105 ·······ZZ105 ·······ZZ
106 o9·=·------[x·..x·]106 o9·=·------[x·..x·]
107 ·····100003··0···6107 ·····100003··0···6
  
108 o9·:·PolynomialRing108 o9·:·PolynomialRing
  
109 i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2)109 i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2)
110 ·--·used·0.111315s·(cpu);·0.0726621s·(thread);·0s·(gc)110 ·--·used·0.0557109s·(cpu);·0.0553453s·(thread);·0s·(gc)
  
111 ························································ZZ111 ························································ZZ
112 ······················································------[y·..y·]112 ······················································------[y·..y·]
113 ······················································100003··0···9················································ZZ··············2······························2113 ······················································100003··0···9················································ZZ··············2······························2
114 o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·})114 o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·})
115 ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9115 ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9
116 ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5116 ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5
Offset 122, 15 lines modifiedOffset 122, 15 lines modified
122 ·························································------[y·..y·]122 ·························································------[y·..y·]
123 ·························································100003··0···9···················································ZZ123 ·························································100003··0···9···················································ZZ
124 o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·]124 o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·]
125 ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6125 ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6
126 ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5126 ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5
  
127 i11·:·time·SegreClass·phi127 i11·:·time·SegreClass·phi
128 ·--·used·0.269797s·(cpu);·0.198307s·(thread);·0s·(gc)128 ·--·used·0.317858s·(cpu);·0.2022s·(thread);·0s·(gc)
  
129 ·········9······8······7······6·····5129 ·········9······8······7······6·····5
130 o11·=·23H··-·42H··+·36H··-·22H··+·9H130 o11·=·23H··-·42H··+·36H··-·22H··+·9H
  
131 ······ZZ[H]131 ······ZZ[H]
132 o11·:·-----132 o11·:·-----
133 ········10133 ········10
Offset 150, 27 lines modifiedOffset 150, 27 lines modified
150 ··························································100003··0···9150 ··························································100003··0···9
151 o12·:·Ideal·of·----------------------------------------------------------------------------------------------------151 o12·:·Ideal·of·----------------------------------------------------------------------------------------------------
152 ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)152 ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)
153 ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5153 ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5
  
154 i13·:·--·Segre·class·of·B·in·G(1,4)154 i13·:·--·Segre·class·of·B·in·G(1,4)
155 ······time·SegreClass·B155 ······time·SegreClass·B
156 ·--·used·0.247629s·(cpu);·0.213747s·(thread);·0s·(gc)156 ·--·used·0.325561s·(cpu);·0.231201s·(thread);·0s·(gc)
  
157 ·········9······8······7······6·····5157 ·········9······8······7······6·····5
158 o13·=·23H··-·42H··+·36H··-·22H··+·9H158 o13·=·23H··-·42H··+·36H··-·22H··+·9H
  
159 ······ZZ[H]159 ······ZZ[H]
160 o13·:·-----160 o13·:·-----
161 ········10161 ········10
162 ·······H162 ·······H
  
163 i14·:·--·Segre·class·of·B·in·P^9163 i14·:·--·Segre·class·of·B·in·P^9
164 ······time·SegreClass·lift(B,ambient·ring·B)164 ······time·SegreClass·lift(B,ambient·ring·B)
165 ·--·used·0.801144s·(cpu);·0.643097s·(thread);·0s·(gc)165 ·--·used·0.884823s·(cpu);·0.685533s·(thread);·0s·(gc)
  
166 ···········9·······8·······7······6·····5166 ···········9·······8·······7······6·····5
167 o14·=·2764H··-·984H··+·294H··-·67H··+·9H167 o14·=·2764H··-·984H··+·294H··-·67H··+·9H
  
168 ······ZZ[H]168 ······ZZ[H]
169 o14·:·-----169 o14·:·-----
170 ········10170 ········10
3.14 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_abstract__Rational__Map.out
    
Offset 17, 32 lines modifiedOffset 17, 32 lines modified
  
17 o3·=·QQ[u·..u·]17 o3·=·QQ[u·..u·]
18 ·········0···518 ·········0···5
  
19 o3·:·PolynomialRing19 o3·:·PolynomialRing
  
20 i4·:·time·psi·=·abstractRationalMap(P4,P5,f)20 i4·:·time·psi·=·abstractRationalMap(P4,P5,f)
21 ·--·used·6.9485e-05s·(cpu);·0.000326031s·(thread);·0s·(gc)21 ·--·used·0.000760977s·(cpu);·0.000441147s·(thread);·0s·(gc)
  
22 o4·=·--·rational·map·--22 o4·=·--·rational·map·--
23 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])23 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])
24 ······················0···1···2···3···424 ······················0···1···2···3···4
25 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])25 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])
26 ······················0···1···2···3···4···526 ······················0···1···2···3···4···5
27 ·····defining·forms:·given·by·a·function27 ·····defining·forms:·given·by·a·function
  
28 o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)28 o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)
  
29 i5·:·time·projectiveDegrees(psi,3)29 i5·:·time·projectiveDegrees(psi,3)
30 ·--·used·0.160461s·(cpu);·0.116645s·(thread);·0s·(gc)30 ·--·used·0.202836s·(cpu);·0.14785s·(thread);·0s·(gc)
  
31 o5·=·231 o5·=·2
  
32 i6·:·time·rationalMap·psi32 i6·:·time·rationalMap·psi
33 ·--·used·0.320145s·(cpu);·0.277596s·(thread);·0s·(gc)33 ·--·used·0.351476s·(cpu);·0.304661s·(thread);·0s·(gc)
  
34 o6·=·--·rational·map·--34 o6·=·--·rational·map·--
35 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])35 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])
36 ······················0···1···2···3···436 ······················0···1···2···3···4
37 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])37 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])
38 ······················0···1···2···3···4···538 ······················0···1···2···3···4···5
39 ·····defining·forms:·{39 ·····defining·forms:·{
Offset 113, 48 lines modifiedOffset 113, 48 lines modified
113 ················1····0·2·····1·2····0·3·····2····1·3113 ················1····0·2·····1·2····0·3·····2····1·3
  
114 ·················ZZ114 ·················ZZ
115 o13·:·Ideal·of·-----[x·..x·]115 o13·:·Ideal·of·-----[x·..x·]
116 ···············65521··0···3116 ···············65521··0···3
  
117 i14·:·time·T·=·abstractRationalMap(I,"OADP")117 i14·:·time·T·=·abstractRationalMap(I,"OADP")
118 ·--·used·0.108609s·(cpu);·0.066128s·(thread);·0s·(gc)118 ·--·used·0.117609s·(cpu);·0.067279s·(thread);·0s·(gc)
  
119 o14·=·--·rational·map·--119 o14·=·--·rational·map·--
120 ·····················ZZ120 ·····················ZZ
121 ······source:·Proj(-----[x·,·x·,·x·,·x·])121 ······source:·Proj(-----[x·,·x·,·x·,·x·])
122 ···················65521··0···1···2···3122 ···················65521··0···1···2···3
123 ·····················ZZ123 ·····················ZZ
124 ······target:·Proj(-----[x·,·x·,·x·,·x·])124 ······target:·Proj(-----[x·,·x·,·x·,·x·])
125 ···················65521··0···1···2···3125 ···················65521··0···1···2···3
126 ······defining·forms:·given·by·a·function126 ······defining·forms:·given·by·a·function
  
127 o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)127 o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)
  
128 i15·:·time·projectiveDegrees(T,2)128 i15·:·time·projectiveDegrees(T,2)
129 ·--·used·2.49477s·(cpu);·1.62007s·(thread);·0s·(gc)129 ·--·used·2.79982s·(cpu);·1.68088s·(thread);·0s·(gc)
  
130 o15·=·3130 o15·=·3
  
131 i16·:·time·T2·=·T·*·T131 i16·:·time·T2·=·T·*·T
132 ·--·used·0.000155904s·(cpu);·2.2584e-05s·(thread);·0s·(gc)132 ·--·used·0.000154119s·(cpu);·2.6349e-05s·(thread);·0s·(gc)
  
133 o16·=·--·rational·map·--133 o16·=·--·rational·map·--
134 ·····················ZZ134 ·····················ZZ
135 ······source:·Proj(-----[x·,·x·,·x·,·x·])135 ······source:·Proj(-----[x·,·x·,·x·,·x·])
136 ···················65521··0···1···2···3136 ···················65521··0···1···2···3
137 ·····················ZZ137 ·····················ZZ
138 ······target:·Proj(-----[x·,·x·,·x·,·x·])138 ······target:·Proj(-----[x·,·x·,·x·,·x·])
139 ···················65521··0···1···2···3139 ···················65521··0···1···2···3
140 ······defining·forms:·given·by·a·function140 ······defining·forms:·given·by·a·function
  
141 o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)141 o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)
  
142 i17·:·time·projectiveDegrees(T2,2)142 i17·:·time·projectiveDegrees(T2,2)
143 ·--·used·4.07831s·(cpu);·2.61383s·(thread);·0s·(gc)143 ·--·used·4.61879s·(cpu);·2.69855s·(thread);·0s·(gc)
  
144 o17·=·1144 o17·=·1
  
145 i18·:·p·=·apply(3,i->random(ZZ/65521))|{1}145 i18·:·p·=·apply(3,i->random(ZZ/65521))|{1}
  
146 o18·=·{-6648,·-23396,·-12311,·1}146 o18·=·{-6648,·-23396,·-12311,·1}
  
Offset 169, 15 lines modifiedOffset 169, 15 lines modified
169 i20·:·T·q169 i20·:·T·q
  
170 o20·=·{-6648,·-23396,·-12311,·1}170 o20·=·{-6648,·-23396,·-12311,·1}
  
171 o20·:·List171 o20·:·List
  
172 i21·:·time·f·=·rationalMap·T172 i21·:·time·f·=·rationalMap·T
173 ·--·used·3.30752s·(cpu);·2.20322s·(thread);·0s·(gc)173 ·--·used·3.69916s·(cpu);·2.33673s·(thread);·0s·(gc)
  
174 o21·=·--·rational·map·--174 o21·=·--·rational·map·--
175 ·····················ZZ175 ·····················ZZ
176 ······source:·Proj(-----[x·,·x·,·x·,·x·])176 ······source:·Proj(-----[x·,·x·,·x·,·x·])
177 ···················65521··0···1···2···3177 ···················65521··0···1···2···3
178 ·····················ZZ178 ·····················ZZ
179 ······target:·Proj(-----[x·,·x·,·x·,·x·])179 ······target:·Proj(-----[x·,·x·,·x·,·x·])
2.73 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_approximate__Inverse__Map.out
    
Offset 44, 15 lines modifiedOffset 44, 15 lines modified
44 ······················x·x··-·x·x44 ······················x·x··-·x·x
45 ·······················1·2····0·445 ·······················1·2····0·4
46 ·····················}46 ·····················}
  
47 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)47 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)
  
48 i3·:·time·psi·=·approximateInverseMap·phi48 i3·:·time·psi·=·approximateInverseMap·phi
49 ·--·used·0.278895s·(cpu);·0.192424s·(thread);·0s·(gc)49 ·--·used·0.337968s·(cpu);·0.224819s·(thread);·0s·(gc)
50 --·approximateInverseMap:·step·1·of·1050 --·approximateInverseMap:·step·1·of·10
51 --·approximateInverseMap:·step·2·of·1051 --·approximateInverseMap:·step·2·of·10
52 --·approximateInverseMap:·step·3·of·1052 --·approximateInverseMap:·step·3·of·10
53 --·approximateInverseMap:·step·4·of·1053 --·approximateInverseMap:·step·4·of·10
54 --·approximateInverseMap:·step·5·of·1054 --·approximateInverseMap:·step·5·of·10
55 --·approximateInverseMap:·step·6·of·1055 --·approximateInverseMap:·step·6·of·10
56 --·approximateInverseMap:·step·7·of·1056 --·approximateInverseMap:·step·7·of·10
Offset 106, 15 lines modifiedOffset 106, 15 lines modified
106 ·····················}106 ·····················}
  
107 o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)107 o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)
  
108 i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)108 i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)
  
109 i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5);109 i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5);
110 ·--·used·0.179434s·(cpu);·0.137873s·(thread);·0s·(gc)110 ·--·used·0.188136s·(cpu);·0.146222s·(thread);·0s·(gc)
111 --·approximateInverseMap:·step·1·of·3111 --·approximateInverseMap:·step·1·of·3
112 --·approximateInverseMap:·step·2·of·3112 --·approximateInverseMap:·step·2·of·3
113 --·approximateInverseMap:·step·3·of·3113 --·approximateInverseMap:·step·3·of·3
  
114 o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)114 o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)
  
115 i6·:·assert(psi·==·psi')115 i6·:·assert(psi·==·psi')
Offset 189, 15 lines modifiedOffset 189, 15 lines modified
189 ·······················0······1·4······0·5······1·5·····2·5······3·5······4·5······5······0·6······1·6······2·6······4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8······5·8······6·8·····7·8189 ·······················0······1·4······0·5······1·5·····2·5······3·5······4·5······5······0·6······1·6······2·6······4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8······5·8······6·8·····7·8
190 ·····················}190 ·····················}
  
191 o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)191 o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)
  
192 i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time·192 i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time·
193 ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4)193 ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4)
194 ·--·used·1.66994s·(cpu);·1.39425s·(thread);·0s·(gc)194 ·--·used·2.08092s·(cpu);·1.75381s·(thread);·0s·(gc)
195 --·approximateInverseMap:·step·1·of·3195 --·approximateInverseMap:·step·1·of·3
196 --·approximateInverseMap:·step·2·of·3196 --·approximateInverseMap:·step·2·of·3
197 --·approximateInverseMap:·step·3·of·3197 --·approximateInverseMap:·step·3·of·3
  
198 o8·=·--·rational·map·--198 o8·=·--·rational·map·--
199 ································ZZ199 ································ZZ
200 ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by200 ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by
Offset 254, 15 lines modifiedOffset 254, 15 lines modified
254 i9·:·--·but...254 i9·:·--·but...
255 ·····phi·*·psi·==·1255 ·····phi·*·psi·==·1
  
256 o9·=·false256 o9·=·false
  
257 i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify257 i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify
258 ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true)258 ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true)
259 ·--·used·2.37868s·(cpu);·2.07197s·(thread);·0s·(gc)259 ·--·used·2.9864s·(cpu);·2.59223s·(thread);·0s·(gc)
260 --·approximateInverseMap:·step·1·of·3260 --·approximateInverseMap:·step·1·of·3
261 --·approximateInverseMap:·step·2·of·3261 --·approximateInverseMap:·step·2·of·3
262 --·approximateInverseMap:·step·3·of·3262 --·approximateInverseMap:·step·3·of·3
263 Certify:·output·certified!263 Certify:·output·certified!
  
264 o10·=·--·rational·map·--264 o10·=·--·rational·map·--
265 ·································ZZ265 ·································ZZ
32.4 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_degree__Map.out
    
Offset 9, 27 lines modifiedOffset 9, 27 lines modified
9 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10 o4·=·map·(ringP8,·ringP14,·{-·95x··+·181x·x··+·1028x··-·1384x·x··-·1455x·x··+·559x··-·502x·x··+·1264x·x··-·162x·x··+·1209x··-·180x·x··-·504x·x··-·1168x·x··-·676x·x··+·501x··+·73x·x··+·1263x·x··+·1035x·x··+·844x·x··+·1593x·x··+·785x··+·982x·x··-·412x·x··+·1335x·x··+·1136x·x··+·826x·x··+·1078x·x··+·1158x··+·335x·x··-·982x·x··-·1479x·x··-·15x·x··+·1363x·x··+·1397x·x··-·575x·x··-·71x··+·1255x·x··-·1138x·x··-·1590x·x··+·604x·x··+·1182x·x··-·63x·x··-·1382x·x··-·1255x·x··-·613x·,·-·1444x··+·575x·x··+·767x··-·1495x·x··+·1631x·x··-·217x··-·294x·x··-·1511x·x··-·504x·x··-·1284x··-·1459x·x··+·152x·x··+·141x·x··-·10x·x··-·95x··+·1056x·x··+·654x·x··+·1397x·x··-·930x·x··+·578x·x··-·696x··+·759x·x··+·733x·x··+·505x·x··-·609x·x··+·526x·x··-·659x·x··+·846x··+·1253x·x··-·1519x·x··+·635x·x··+·576x·x··+·54x·x··-·1261x·x··-·822x·x··-·257x··-·986x·x··+·356x·x··-·1488x·x··-·1561x·x··-·850x·x··-·85x·x··-·1350x·x··-·783x·x··-·1335x·,·-·871x··+·1006x·x··-·1399x··-·1636x·x··-·699x·x··-·769x··-·307x·x··-·1645x·x··-·502x·x··-·719x··+·1405x·x··+·870x·x··-·1133x·x··+·425x·x··-·1203x··-·1601x·x··+·117x·x··-·382x·x··+·318x·x··-·117x·x··-·560x··+·1135x·x··+·1468x·x··+·869x·x··-·943x·x··-·335x·x··-·1218x·x··+·201x··-·11x·x··+·540x·x··-·710x·x··-·489x·x··+·1605x·x··+·1663x·x··-·423x·x··+·1246x··+·97x·x··-·644x·x··+·1655x·x··+·1219x·x··+·1476x·x··+·1355x·x··+·1594x·x··+·893x·x··+·1150x·,·-·143x··+·1240x·x··-·1042x··+·1649x·x··+·1024x·x··+·794x··+·1442x·x··-·1263x·x··+·537x·x··-·82x··-·734x·x··-·1569x·x··-·798x·x··-·366x·x··+·1289x··-·569x·x··-·254x·x··+·237x·x··-·1234x·x··-·807x·x··+·264x··-·202x·x··-·616x·x··+·44x·x··+·1465x·x··+·685x·x··+·1630x·x··-·406x··-·123x·x··-·4x·x··+·1583x·x··+·1235x·x··+·162x·x··+·1034x·x··-·1035x·x··+·737x··+·660x·x··+·1459x·x··-·359x·x··-·1291x·x··+·1638x·x··-·325x·x··-·631x·x··+·73x·x··-·1471x·,·-·1340x··+·31x·x··-·994x··-·880x·x··-·89x·x··+·574x··+·760x·x··-·1054x·x··+·772x·x··-·239x··-·443x·x··+·1240x·x··+·637x·x··-·1423x·x··+·320x··-·1363x·x··-·1139x·x··-·158x·x··-·325x·x··-·1578x·x··+·32x··+·695x·x··+·305x·x··+·1012x·x··+·1492x·x··+·1290x·x··+·1579x·x··-·342x··-·83x·x··-·104x·x··+·998x·x··-·92x·x··+·1554x·x··+·201x·x··-·237x·x··+·160x··-·228x·x··-·543x·x··-·1147x·x··-·376x·x··+·1313x·x··+·603x·x··+·106x·x··-·1361x·x··+·699x·,·-·228x··-·1510x·x··+·277x··-·4x·x··-·22x·x··-·1526x··+·234x·x··+·969x·x··+·1253x·x··-·1426x··-·1474x·x··+·947x·x··+·194x·x··-·316x·x··-·988x··-·1211x·x··+·1087x·x··+·536x·x··-·491x·x··+·870x·x··-·659x··+·1490x·x··-·469x·x··+·1190x·x··+·807x·x··+·650x·x··+·448x·x··-·1353x··-·218x·x··+·759x·x··-·253x·x··+·830x·x··-·1080x·x··-·143x·x··-·1313x·x··-·374x··-·180x·x··+·741x·x··+·742x·x··-·1254x·x··+·458x·x··-·345x·x··+·597x·x··+·1567x·x··-·31x·,·1120x··+·709x·x··-·1538x··-·1048x·x··-·162x·x··-·1518x··-·73x·x··+·380x·x··+·533x·x··-·286x··+·1374x·x··-·74x·x··-·22x·x··+·1535x·x··-·1071x··-·839x·x··-·560x·x··+·928x·x··+·335x·x··-·1008x·x··+·810x··-·448x·x··-·357x·x··-·107x·x··+·40x·x··+·784x·x··-·1423x·x··+·1276x··+·147x·x··+·443x·x··-·598x·x··-·1077x·x··-·1214x·x··+·322x·x··-·1408x·x··+·72x··-·63x·x··-·1513x·x··-·791x·x··+·11x·x··+·77x·x··+·836x·x··-·1100x·x··+·1637x·x··-·788x·,·1331x··+·318x·x··-·704x··+·51x·x··+·275x·x··+·1149x··+·1526x·x··+·768x·x··+·414x·x··-·782x··-·262x·x··+·686x·x··-·380x·x··+·1377x·x··+·1077x··+·1650x·x··-·1129x·x··-·508x·x··+·846x·x··+·1513x·x··+·460x··-·1626x·x··-·1024x·x··+·862x·x··+·1352x·x··-·188x·x··-·1382x·x··-·650x··+·55x·x··-·326x·x··+·1037x·x··+·705x·x··-·667x·x··+·1483x·x··+·1661x·x··-·1652x··-·1052x·x··-·692x·x··-·542x·x··+·162x·x··+·582x·x··-·1369x·x··+·934x·x··+·1392x·x··+·1227x·,·-·346x··+·1408x·x··-·1225x··-·1536x·x··-·1028x·x··-·985x··-·210x·x··-·1312x·x··+·915x·x··+·1633x··-·202x·x··-·1636x·x··-·1653x·x··-·480x·x··-·1260x··-·813x·x··-·1623x·x··-·1429x·x··+·1094x·x··-·747x·x··+·955x··+·898x·x··-·795x·x··-·35x·x··-·566x·x··+·1631x·x··-·324x·x··+·926x··-·132x·x··-·9x·x··-·1290x·x··-·543x·x··+·902x·x··+·735x·x··-·342x·x··-·400x··+·900x·x··-·463x·x··+·694x·x··-·1262x·x··-·1449x·x··-·448x·x··-·1402x·x··-·731x·x··-·996x·,·301x··+·166x·x··-·955x··-·739x·x··-·1199x·x··-·319x··+·1047x·x··-·532x·x··+·902x·x··+·1195x··-·663x·x··+·1215x·x··-·534x·x··-·332x·x··-·973x··+·772x·x··-·308x·x··+·315x·x··-·454x·x··-·483x·x··-·239x··-·1313x·x··-·419x·x··-·1340x·x··-·1388x·x··-·1340x·x··-·1665x·x··-·333x··-·465x·x··-·1084x·x··+·676x·x··-·1612x·x··-·288x·x··+·11x·x··-·1170x·x··-·189x··+·498x·x··-·889x·x··+·693x·x··+·1460x·x··-·473x·x··-·414x·x··-·122x·x··-·1659x·x··-·1421x·,·14x··-·1049x·x··+·1506x··+·1235x·x··+·642x·x··-·1034x··+·460x·x··+·150x·x··+·760x·x··-·1246x··-·1407x·x··+·1570x·x··+·1403x·x··-·1610x·x··-·431x··+·574x·x··+·893x·x··-·657x·x··+·417x·x··+·1362x·x··+·224x··+·268x·x··+·1097x·x··+·1132x·x··+·148x·x··+·1331x·x··-·77x·x··-·756x··+·228x·x··+·136x·x··-·1484x·x··-·1478x·x··-·13x·x··+·1620x·x··-·701x·x··-·769x··-·760x·x··-·492x·x··-·1077x·x··-·1249x·x··-·834x·x··-·395x·x··-·1358x·x··-·988x·x··+·113x·,·-·1634x··-·13x·x··+·805x··-·21x·x··-·1655x·x··+·1479x··-·1510x·x··-·646x·x··+·225x·x··-·1411x··+·1227x·x··-·1108x·x··+·1291x·x··-·59x·x··-·142x··+·586x·x··-·676x·x··+·655x·x··-·1476x·x··+·453x·x··-·1076x··-·1152x·x··+·1373x·x··-·1191x·x··-·416x·x··+·699x·x··+·317x·x··+·825x··-·1560x·x··-·488x·x··-·1035x·x··-·1561x·x··-·644x·x··-·1178x·x··-·1320x·x··+·158x··+·889x·x··+·1444x·x··-·1486x·x··-·1211x·x··+·1269x·x··-·1228x·x··+·568x·x··+·1591x·x··+·1207x·,·105x··-·538x·x··-·1222x··-·277x·x··+·716x·x··-·1067x··-·428x·x··+·154x·x··-·469x·x··+·77x··+·538x·x··-·179x·x··+·921x·x··-·223x·x··+·1093x··-·262x·x··+·1299x·x··+·631x·x··+·1486x·x··-·1280x·x··-·121x··-·50x·x··-·978x·x··-·694x·x··-·531x·x··+·505x·x··+·1412x·x··-·1061x··+·1202x·x··+·448x·x··-·187x·x··+·1276x·x··-·121x·x··+·1361x·x··+·697x·x··+·682x··+·1592x·x··+·705x·x··-·227x·x··-·7x·x··-·1423x·x··-·1446x·x··-·1578x·x··+·1511x·x··+·917x·,·1270x··-·391x·x··-·1116x··-·287x·x··+·653x·x··+·1643x··+·1623x·x··+·514x·x··-·14x·x··-·90x··+·1232x·x··-·1434x·x··+·1296x·x··+·1522x·x··+·136x··-·623x·x··-·607x·x··+·18x·x··+·896x·x··-·29x·x··+·1059x··-·1053x·x··+·1643x·x··+·1652x·x··-·1190x·x··-·1073x·x··+·1470x·x··-·944x··-·93x·x··-·187x·x··-·994x·x··-·1415x·x··-·229x·x··-·796x·x··+·1642x·x··+·1600x··-·344x·x··+·905x·x··+·1032x·x··-·538x·x··-·891x·x··+·1243x·x··+·1290x·x··+·490x·x··-·1148x·,·1613x··+·175x·x··-·1346x··-·1000x·x··-·1217x·x··-·729x··-·1296x·x··+·1456x·x··+·745x·x··+·539x··+·525x·x··-·811x·x··+·753x·x··+·1362x·x··+·1629x··-·840x·x··+·513x·x··+·429x·x··+·842x·x··+·1414x·x··-·308x··+·1415x·x··-·1461x·x··-·1135x·x··+·701x·x··+·766x·x··+·785x·x··+·1503x··+·147x·x··+·929x·x··-·1220x·x··-·853x·x··+·493x·x··+·226x·x··+·1416x·x··+·280x··-·7x·x··+·1632x·x··+·520x·x··+·1259x·x··+·157x·x··+·1596x·x··+·655x·x··-·42x·x··-·586x·})10 o4·=·map·(ringP8,·ringP14,·{-·95x··+·181x·x··+·1028x··-·1384x·x··-·1455x·x··+·559x··-·502x·x··+·1264x·x··-·162x·x··+·1209x··-·180x·x··-·504x·x··-·1168x·x··-·676x·x··+·501x··+·73x·x··+·1263x·x··+·1035x·x··+·844x·x··+·1593x·x··+·785x··+·982x·x··-·412x·x··+·1335x·x··+·1136x·x··+·826x·x··+·1078x·x··+·1158x··+·335x·x··-·982x·x··-·1479x·x··-·15x·x··+·1363x·x··+·1397x·x··-·575x·x··-·71x··+·1255x·x··-·1138x·x··-·1590x·x··+·604x·x··+·1182x·x··-·63x·x··-·1382x·x··-·1255x·x··-·613x·,·-·1444x··+·575x·x··+·767x··-·1495x·x··+·1631x·x··-·217x··-·294x·x··-·1511x·x··-·504x·x··-·1284x··-·1459x·x··+·152x·x··+·141x·x··-·10x·x··-·95x··+·1056x·x··+·654x·x··+·1397x·x··-·930x·x··+·578x·x··-·696x··+·759x·x··+·733x·x··+·505x·x··-·609x·x··+·526x·x··-·659x·x··+·846x··+·1253x·x··-·1519x·x··+·635x·x··+·576x·x··+·54x·x··-·1261x·x··-·822x·x··-·257x··-·986x·x··+·356x·x··-·1488x·x··-·1561x·x··-·850x·x··-·85x·x··-·1350x·x··-·783x·x··-·1335x·,·-·871x··+·1006x·x··-·1399x··-·1636x·x··-·699x·x··-·769x··-·307x·x··-·1645x·x··-·502x·x··-·719x··+·1405x·x··+·870x·x··-·1133x·x··+·425x·x··-·1203x··-·1601x·x··+·117x·x··-·382x·x··+·318x·x··-·117x·x··-·560x··+·1135x·x··+·1468x·x··+·869x·x··-·943x·x··-·335x·x··-·1218x·x··+·201x··-·11x·x··+·540x·x··-·710x·x··-·489x·x··+·1605x·x··+·1663x·x··-·423x·x··+·1246x··+·97x·x··-·644x·x··+·1655x·x··+·1219x·x··+·1476x·x··+·1355x·x··+·1594x·x··+·893x·x··+·1150x·,·-·143x··+·1240x·x··-·1042x··+·1649x·x··+·1024x·x··+·794x··+·1442x·x··-·1263x·x··+·537x·x··-·82x··-·734x·x··-·1569x·x··-·798x·x··-·366x·x··+·1289x··-·569x·x··-·254x·x··+·237x·x··-·1234x·x··-·807x·x··+·264x··-·202x·x··-·616x·x··+·44x·x··+·1465x·x··+·685x·x··+·1630x·x··-·406x··-·123x·x··-·4x·x··+·1583x·x··+·1235x·x··+·162x·x··+·1034x·x··-·1035x·x··+·737x··+·660x·x··+·1459x·x··-·359x·x··-·1291x·x··+·1638x·x··-·325x·x··-·631x·x··+·73x·x··-·1471x·,·-·1340x··+·31x·x··-·994x··-·880x·x··-·89x·x··+·574x··+·760x·x··-·1054x·x··+·772x·x··-·239x··-·443x·x··+·1240x·x··+·637x·x··-·1423x·x··+·320x··-·1363x·x··-·1139x·x··-·158x·x··-·325x·x··-·1578x·x··+·32x··+·695x·x··+·305x·x··+·1012x·x··+·1492x·x··+·1290x·x··+·1579x·x··-·342x··-·83x·x··-·104x·x··+·998x·x··-·92x·x··+·1554x·x··+·201x·x··-·237x·x··+·160x··-·228x·x··-·543x·x··-·1147x·x··-·376x·x··+·1313x·x··+·603x·x··+·106x·x··-·1361x·x··+·699x·,·-·228x··-·1510x·x··+·277x··-·4x·x··-·22x·x··-·1526x··+·234x·x··+·969x·x··+·1253x·x··-·1426x··-·1474x·x··+·947x·x··+·194x·x··-·316x·x··-·988x··-·1211x·x··+·1087x·x··+·536x·x··-·491x·x··+·870x·x··-·659x··+·1490x·x··-·469x·x··+·1190x·x··+·807x·x··+·650x·x··+·448x·x··-·1353x··-·218x·x··+·759x·x··-·253x·x··+·830x·x··-·1080x·x··-·143x·x··-·1313x·x··-·374x··-·180x·x··+·741x·x··+·742x·x··-·1254x·x··+·458x·x··-·345x·x··+·597x·x··+·1567x·x··-·31x·,·1120x··+·709x·x··-·1538x··-·1048x·x··-·162x·x··-·1518x··-·73x·x··+·380x·x··+·533x·x··-·286x··+·1374x·x··-·74x·x··-·22x·x··+·1535x·x··-·1071x··-·839x·x··-·560x·x··+·928x·x··+·335x·x··-·1008x·x··+·810x··-·448x·x··-·357x·x··-·107x·x··+·40x·x··+·784x·x··-·1423x·x··+·1276x··+·147x·x··+·443x·x··-·598x·x··-·1077x·x··-·1214x·x··+·322x·x··-·1408x·x··+·72x··-·63x·x··-·1513x·x··-·791x·x··+·11x·x··+·77x·x··+·836x·x··-·1100x·x··+·1637x·x··-·788x·,·1331x··+·318x·x··-·704x··+·51x·x··+·275x·x··+·1149x··+·1526x·x··+·768x·x··+·414x·x··-·782x··-·262x·x··+·686x·x··-·380x·x··+·1377x·x··+·1077x··+·1650x·x··-·1129x·x··-·508x·x··+·846x·x··+·1513x·x··+·460x··-·1626x·x··-·1024x·x··+·862x·x··+·1352x·x··-·188x·x··-·1382x·x··-·650x··+·55x·x··-·326x·x··+·1037x·x··+·705x·x··-·667x·x··+·1483x·x··+·1661x·x··-·1652x··-·1052x·x··-·692x·x··-·542x·x··+·162x·x··+·582x·x··-·1369x·x··+·934x·x··+·1392x·x··+·1227x·,·-·346x··+·1408x·x··-·1225x··-·1536x·x··-·1028x·x··-·985x··-·210x·x··-·1312x·x··+·915x·x··+·1633x··-·202x·x··-·1636x·x··-·1653x·x··-·480x·x··-·1260x··-·813x·x··-·1623x·x··-·1429x·x··+·1094x·x··-·747x·x··+·955x··+·898x·x··-·795x·x··-·35x·x··-·566x·x··+·1631x·x··-·324x·x··+·926x··-·132x·x··-·9x·x··-·1290x·x··-·543x·x··+·902x·x··+·735x·x··-·342x·x··-·400x··+·900x·x··-·463x·x··+·694x·x··-·1262x·x··-·1449x·x··-·448x·x··-·1402x·x··-·731x·x··-·996x·,·301x··+·166x·x··-·955x··-·739x·x··-·1199x·x··-·319x··+·1047x·x··-·532x·x··+·902x·x··+·1195x··-·663x·x··+·1215x·x··-·534x·x··-·332x·x··-·973x··+·772x·x··-·308x·x··+·315x·x··-·454x·x··-·483x·x··-·239x··-·1313x·x··-·419x·x··-·1340x·x··-·1388x·x··-·1340x·x··-·1665x·x··-·333x··-·465x·x··-·1084x·x··+·676x·x··-·1612x·x··-·288x·x··+·11x·x··-·1170x·x··-·189x··+·498x·x··-·889x·x··+·693x·x··+·1460x·x··-·473x·x··-·414x·x··-·122x·x··-·1659x·x··-·1421x·,·14x··-·1049x·x··+·1506x··+·1235x·x··+·642x·x··-·1034x··+·460x·x··+·150x·x··+·760x·x··-·1246x··-·1407x·x··+·1570x·x··+·1403x·x··-·1610x·x··-·431x··+·574x·x··+·893x·x··-·657x·x··+·417x·x··+·1362x·x··+·224x··+·268x·x··+·1097x·x··+·1132x·x··+·148x·x··+·1331x·x··-·77x·x··-·756x··+·228x·x··+·136x·x··-·1484x·x··-·1478x·x··-·13x·x··+·1620x·x··-·701x·x··-·769x··-·760x·x··-·492x·x··-·1077x·x··-·1249x·x··-·834x·x··-·395x·x··-·1358x·x··-·988x·x··+·113x·,·-·1634x··-·13x·x··+·805x··-·21x·x··-·1655x·x··+·1479x··-·1510x·x··-·646x·x··+·225x·x··-·1411x··+·1227x·x··-·1108x·x··+·1291x·x··-·59x·x··-·142x··+·586x·x··-·676x·x··+·655x·x··-·1476x·x··+·453x·x··-·1076x··-·1152x·x··+·1373x·x··-·1191x·x··-·416x·x··+·699x·x··+·317x·x··+·825x··-·1560x·x··-·488x·x··-·1035x·x··-·1561x·x··-·644x·x··-·1178x·x··-·1320x·x··+·158x··+·889x·x··+·1444x·x··-·1486x·x··-·1211x·x··+·1269x·x··-·1228x·x··+·568x·x··+·1591x·x··+·1207x·,·105x··-·538x·x··-·1222x··-·277x·x··+·716x·x··-·1067x··-·428x·x··+·154x·x··-·469x·x··+·77x··+·538x·x··-·179x·x··+·921x·x··-·223x·x··+·1093x··-·262x·x··+·1299x·x··+·631x·x··+·1486x·x··-·1280x·x··-·121x··-·50x·x··-·978x·x··-·694x·x··-·531x·x··+·505x·x··+·1412x·x··-·1061x··+·1202x·x··+·448x·x··-·187x·x··+·1276x·x··-·121x·x··+·1361x·x··+·697x·x··+·682x··+·1592x·x··+·705x·x··-·227x·x··-·7x·x··-·1423x·x··-·1446x·x··-·1578x·x··+·1511x·x··+·917x·,·1270x··-·391x·x··-·1116x··-·287x·x··+·653x·x··+·1643x··+·1623x·x··+·514x·x··-·14x·x··-·90x··+·1232x·x··-·1434x·x··+·1296x·x··+·1522x·x··+·136x··-·623x·x··-·607x·x··+·18x·x··+·896x·x··-·29x·x··+·1059x··-·1053x·x··+·1643x·x··+·1652x·x··-·1190x·x··-·1073x·x··+·1470x·x··-·944x··-·93x·x··-·187x·x··-·994x·x··-·1415x·x··-·229x·x··-·796x·x··+·1642x·x··+·1600x··-·344x·x··+·905x·x··+·1032x·x··-·538x·x··-·891x·x··+·1243x·x··+·1290x·x··+·490x·x··-·1148x·,·1613x··+·175x·x··-·1346x··-·1000x·x··-·1217x·x··-·729x··-·1296x·x··+·1456x·x··+·745x·x··+·539x··+·525x·x··-·811x·x··+·753x·x··+·1362x·x··+·1629x··-·840x·x··+·513x·x··+·429x·x··+·842x·x··+·1414x·x··-·308x··+·1415x·x··-·1461x·x··-·1135x·x··+·701x·x··+·766x·x··+·785x·x··+·1503x··+·147x·x··+·929x·x··-·1220x·x··-·853x·x··+·493x·x··+·226x·x··+·1416x·x··+·280x··-·7x·x··+·1632x·x··+·520x·x··+·1259x·x··+·157x·x··+·1596x·x··+·655x·x··-·42x·x··-·586x·})
11 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·····1·3·······2·3········3········0·4········1·4········2·4······3·4·······4·······0·5·······1·5·······2·5········3·5·······4·5········5········0·6········1·6········2·6·······3·6·······4·6·······5·6·······6········0·7·······1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8········2·8········3·8········4·8········5·8·······6·8········7·8········8······0·······0·1········1·······0·2·······1·2········2·······0·3·······1·3·······2·3······3·······0·4·······1·4·······2·4·······3·4········4·······0·5········1·5·······2·5········3·5········4·5·······5······0·6·······1·6·······2·6·······3·6·······4·6········5·6········6········0·7·······1·7·······2·7········3·7·······4·7········5·7·······6·7·······7········0·8·······1·8·······2·8·····3·8········4·8········5·8········6·8········7·8·······8·······0·······0·1········1·······0·2·······1·2········2········0·3·······1·3······2·3······3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5······2·5·······3·5······4·5········5········0·6········1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7········3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8·······4·8········5·8········6·8·······7·8········8·······0·······0·1········1········0·2········1·2·······2········0·3········1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6········1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7········2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2·8········3·8·······4·8········5·8·······6·8······7·8·······811 ·································0·······0·1········1········0·2········1·2·······2·······0·3········1·3·······2·3········3·······0·4·······1·4········2·4·······3·4·······4······0·5········1·5········2·5·······3·5········4·5·······5·······0·6·······1·6········2·6········3·6·······4·6········5·6········6·······0·7·······1·7········2·7······3·7········4·7········5·7·······6·7······7········0·8········1·8········2·8·······3·8········4·8······5·8········6·8········7·8·······8·········0·······0·1·······1········0·2········1·2·······2·······0·3········1·3·······2·3········3········0·4·······1·4·······2·4······3·4······4········0·5·······1·5········2·5·······3·5·······4·5·······5·······0·6·······1·6·······2·6·······3·6·······4·6·······5·6·······6········0·7········1·7·······2·7·······3·7······4·7········5·7·······6·7·······7·······0·8·······1·8········2·8········3·8·······4·8······5·8········6·8·······7·8········8········0········0·1········1········0·2·······1·2·······2·······0·3········1·3·······2·3·······3········0·4·······1·4········2·4·······3·4········4········0·5·······1·5·······2·5·······3·5·······4·5·······5········0·6········1·6·······2·6·······3·6·······4·6········5·6·······6······0·7·······1·7·······2·7·······3·7········4·7········5·7·······6·7········7······0·8·······1·8········2·8········3·8········4·8········5·8········6·8·······7·8········8········0········0·1········1········0·2········1·2·······2········0·3········1·3·······2·3······3·······0·4········1·4·······2·4·······3·4········4·······0·5·······1·5·······2·5········3·5·······4·5·······5·······0·6·······1·6······2·6········3·6·······4·6········5·6·······6·······0·7·····1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8·······2·8········3·8········4·8·······5·8·······6·8······7·8········8·········0······0·1·······1·······0·2······1·2·······2·······0·3········1·3·······2·3·······3·······0·4········1·4·······2·4········3·4·······4········0·5········1·5·······2·5·······3·5········4·5······5·······0·6·······1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7······3·7········4·7·······5·7·······6·7·······7·······0·8·······1·8········2·8·······3·8········4·8·······5·8·······6·8········7·8·······8········0········0·1·······1·····0·2······1·2········2·······0·3·······1·3········2·3········3········0·4·······1·4·······2·4·······3·4·······4········0·5········1·5·······2·5·······3·5·······4·5·······5········0·6·······1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7·······2·7·······3·7········4·7·······5·7········6·7·······7·······0·8·······1·8·······2·8········3·8·······4·8·······5·8·······6·8········7·8······8·······0·······0·1········1········0·2·······1·2········2······0·3·······1·3·······2·3·······3········0·4······1·4······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5·······0·6·······1·6·······2·6······3·6·······4·6········5·6········6·······0·7·······1·7·······2·7········3·7········4·7·······5·7········6·7······7······0·8········1·8·······2·8······3·8······4·8·······5·8········6·8········7·8·······8·······0·······0·1·······1······0·2·······1·2········2········0·3·······1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4········0·5········1·5·······2·5·······3·5········4·5·······5········0·6········1·6·······2·6········3·6·······4·6········5·6·······6······0·7·······1·7········2·7·······3·7·······4·7········5·7········6·7········7········0·8·······1·8·······2·8·······3·8·······4·8········5·8·······6·8········7·8········8········0········0·1········1········0·2········1·2·······2·······0·3········1·3·······2·3········3·······0·4········1·4········2·4·······3·4········4·······0·5········1·5········2·5········3·5·······4·5·······5·······0·6·······1·6······2·6·······3·6········4·6·······5·6·······6·······0·7·····1·7········2·7·······3·7·······4·7·······5·7·······6·7·······7·······0·8·······1·8·······2·8········3·8········4·8·······5·8········6·8·······7·8·······8······0·······0·1·······1·······0·2········1·2·······2········0·3·······1·3·······2·3········3·······0·4········1·4·······2·4·······3·4·······4·······0·5·······1·5·······2·5·······3·5·······4·5·······5········0·6·······1·6········2·6········3·6········4·6········5·6·······6·······0·7········1·7·······2·7········3·7·······4·7······5·7········6·7·······7·······0·8·······1·8·······2·8········3·8·······4·8·······5·8·······6·8········7·8········8·····0········0·1········1········0·2·······1·2········2·······0·3·······1·3·······2·3········3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5·······2·5·······3·5········4·5·······5·······0·6········1·6········2·6·······3·6········4·6······5·6·······6·······0·7·······1·7········2·7········3·7······4·7········5·7·······6·7·······7·······0·8·······1·8········2·8········3·8·······4·8·······5·8········6·8·······7·8·······8·········0······0·1·······1······0·2········1·2········2········0·3·······1·3·······2·3········3········0·4········1·4········2·4······3·4·······4·······0·5·······1·5·······2·5········3·5·······4·5········5········0·6········1·6········2·6·······3·6·······4·6·······5·6·······6········0·7·······1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8········2·8········3·8········4·8········5·8·······6·8········7·8········8······0·······0·1········1·······0·2·······1·2········2·······0·3·······1·3·······2·3······3·······0·4·······1·4·······2·4·······3·4········4·······0·5········1·5·······2·5········3·5········4·5·······5······0·6·······1·6·······2·6·······3·6·······4·6········5·6········6········0·7·······1·7·······2·7········3·7·······4·7········5·7·······6·7·······7········0·8·······1·8·······2·8·····3·8········4·8········5·8········6·8········7·8·······8·······0·······0·1········1·······0·2·······1·2········2········0·3·······1·3······2·3······3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5······2·5·······3·5······4·5········5········0·6········1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7········3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8·······4·8········5·8········6·8·······7·8········8·······0·······0·1········1········0·2········1·2·······2········0·3········1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6········1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7········2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2·8········3·8·······4·8········5·8·······6·8······7·8·······8
  
12 o4·:·RingMap·ringP8·<--·ringP1412 o4·:·RingMap·ringP8·<--·ringP14
  
13 i5·:·time·degreeMap·phi13 i5·:·time·degreeMap·phi
14 ·--·used·0.036535s·(cpu);·0.038007s·(thread);·0s·(gc)14 ·--·used·0.0470279s·(cpu);·0.0467061s·(thread);·0s·(gc)
  
15 o5·=·115 o5·=·1
  
16 i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14·16 i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14·
17 ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14)17 ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14)
18 ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14))18 ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14))
  
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·································2··················2···························2······································2·················································2···························································2···································································2··············································································2··························································································2········2··················2······························2·······································2················································2·····························································2··································································2··············································································2····························································································2········2··················2·····························2·······································2················································2···························································2······································································2··············································································2·························································································2·········2·················2····························2·······································2··················································2·····························································2····································································2················································································2·····························································································2·······2···················2····························2·····································2················································2··························································2··································································2···················································································2····························································································2········2················2···························2······································2··················································2····························································2······································································2·················································································2··························································································2···2···················2···························2·····································2··················································2···························································2····································································2··············································································2·························································································2······2··················2···························2······································2··················································2·····························································2·······································································2··············································································2··························································································2·········2··················2····························2·····································2·················································2······························································2····································································2···············································································2························································································219 ·································2··················2···························2······································2·················································2···························································2···································································2··············································································2··························································································2········2··················2······························2·······································2················································2·····························································2··································································2··············································································2····························································································2········2··················2·····························2·······································2················································2···························································2······································································2··············································································2·························································································2·········2·················2····························2·······································2··················································2·····························································2····································································2················································································2·····························································································2·······2···················2····························2·····································2················································2··························································2··································································2···················································································2····························································································2········2················2···························2······································2··················································2····························································2······································································2·················································································2··························································································2···2···················2···························2·····································2··················································2···························································2····································································2··············································································2·························································································2······2··················2···························2······································2··················································2·····························································2·······································································2··············································································2··························································································2·········2··················2····························2·····································2·················································2······························································2····································································2···············································································2························································································2
20 o6·=·map·(ringP8,·ringP8,·{-·780x··-·506x·x··+·1537x··-·132x·x··-·928x·x··+·386x··-·102x·x··+·422x·x··+·725x·x··-·1073x··-·905x·x··-·830x·x··+·1500x·x··+·276x·x··+·1533x··-·653x·x··+·1558x·x··+·939x·x··-·1432x·x··+·462x·x··-·329x··-·92x·x··+·661x·x··-·1298x·x··-·684x·x··+·70x·x··-·715x·x··+·1093x··+·581x·x··+·329x·x··+·454x·x··-·911x·x··-·84x·x··-·1452x·x··-·809x·x··+·1202x··+·1353x·x··+·1503x·x··+·482x·x··+·893x·x··-·643x·x··+·598x·x··+·110x·x··+·1064x·x··-·472x·,·-·522x··-·583x·x··+·1339x··+·1535x·x··-·1317x·x··+·1113x··-·169x·x··+·1440x·x··-·1657x·x··+·721x··+·40x·x··-·1576x·x··-·367x·x··+·257x·x··-·1454x··+·1612x·x··+·1529x·x··-·1068x·x··+·560x·x··-·1441x·x··+·608x··-·92x·x··-·1006x·x··+·285x·x··+·102x·x··-·397x·x··+·66x·x··-·643x··-·38x·x··+·1380x·x··+·1069x·x··-·426x·x··+·1147x·x··+·982x·x··+·10x·x··-·662x··+·16x·x··+·1561x·x··+·1597x·x··+·512x·x··+·1288x·x··-·1253x·x··+·1317x·x··+·1481x·x··-·354x·,·-·640x··-·1551x·x··+·469x··+·1482x·x··-·1593x·x··-·986x··+·471x·x··+·612x·x··+·1228x·x··+·1156x··-·731x·x··+·1503x·x··-·628x·x··+·674x·x··-·799x··+·1137x·x··+·844x·x··+·589x·x··-·666x·x··+·829x·x··-·1024x··-·170x·x··+·450x·x··+·1497x·x··+·1204x·x··-·907x·x··+·1621x·x··-·417x··+·1297x·x··+·1444x·x··+·4x·x··+·398x·x··+·996x·x··-·1031x·x··+·239x·x··+·303x··+·1215x·x··-·83x·x··+·1571x·x··-·1543x·x··-·925x·x··-·694x·x··+·151x·x··-·520x·x··+·880x·,·-·1210x··-·222x·x··+·185x··+·245x·x··+·1059x·x··-·322x··+·238x·x··+·962x·x··+·1260x·x··-·1581x··+·50x·x··+·1352x·x··-·1465x·x··+·1555x·x··+·1333x··+·1362x·x··+·1365x·x··+·1168x·x··-·1401x·x··+·149x·x··-·652x··+·1378x·x··-·557x·x··-·112x·x··+·26x·x··+·315x·x··+·111x·x··+·1592x··-·283x·x··-·1454x·x··+·907x·x··+·212x·x··+·400x·x··+·1049x·x··-·882x·x··-·1429x··-·183x·x··+·1571x·x··-·1286x·x··-·1179x·x··+·1319x·x··+·240x·x··-·1100x·x··+·1500x·x··-·348x·,·1051x··-·1325x·x··+·1354x··-·346x·x··-·1532x·x··-·466x··+·163x·x··-·659x·x··-·291x·x··+·966x··+·789x·x··+·393x·x··+·403x·x··-·1199x·x··-·570x··-·93x·x··-·492x·x··-·418x·x··+·713x·x··-·1323x·x··-·1384x··-·830x·x··-·54x·x··-·306x·x··+·709x·x··+·421x·x··-·954x·x··-·299x··+·1053x·x··-·1080x·x··+·686x·x··+·170x·x··-·1272x·x··-·1661x·x··+·1235x·x··+·1553x··-·1454x·x··-·1411x·x··-·1195x·x··-·962x·x··+·737x·x··-·390x·x··+·957x·x··+·1538x·x··+·1234x·,·-·509x··+·9x·x··-·1563x··-·710x·x··-·642x·x··+·541x··+·220x·x··-·1214x·x··-·16x·x··+·1008x··-·1088x·x··+·755x·x··-·886x·x··-·1433x·x··+·1154x··+·1627x·x··-·1547x·x··-·951x·x··+·866x·x··+·163x·x··-·1142x··-·668x·x··+·1361x·x··+·1324x·x··-·490x·x··+·282x·x··-·1133x·x··-·612x··+·805x·x··-·126x·x··+·1296x·x··-·973x·x··+·1271x·x··-·1646x·x··+·844x·x··+·1073x··-·1452x·x··-·1112x·x··-·141x·x··+·176x·x··-·1579x·x··-·78x·x··+·848x·x··-·1365x·x··+·711x·,·x··+·1543x·x··-·1076x··+·493x·x··-·526x·x··+·868x··-·582x·x··-·996x·x··+·206x·x··-·419x··+·1258x·x··-·391x·x··+·1002x·x··-·1539x·x··+·931x··-·1504x·x··+·810x·x··+·324x·x··+·1356x·x··+·313x·x··+·772x··+·299x·x··+·1186x·x··+·718x·x··+·407x·x··-·64x·x··-·828x·x··-·1393x··+·94x·x··-·290x·x··-·766x·x··+·950x·x··-·640x·x··+·265x·x··-·1640x·x··-·1403x··-·126x·x··+·891x·x··-·1519x·x··-·927x·x··-·1335x·x··-·1448x·x··-·x·x··-·1103x·x··-·1152x·,·821x··+·558x·x··-·1174x··-·168x·x··+·986x·x··+·790x··+·549x·x··+·817x·x··+·1396x·x··+·695x··+·1211x·x··+·878x·x··-·1061x·x··-·1244x·x··-·880x··+·1409x·x··-·567x·x··+·1240x·x··+·1126x·x··-·1262x·x··+·490x··+·1553x·x··+·1276x·x··+·805x·x··+·576x·x··-·1076x·x··+·1617x·x··-·495x··-·750x·x··-·277x·x··+·544x·x··+·1479x·x··-·784x·x··-·64x·x··-·1203x·x··+·405x··+·1013x·x··+·604x·x··+·1301x·x··+·1003x·x··+·235x·x··+·696x·x··+·939x·x··-·714x·x··-·879x·,·-·1452x··+·727x·x··-·1159x··+·449x·x··-·1169x·x··+·732x··+·575x·x··-·600x·x··+·924x·x··-·837x··+·1298x·x··-·860x·x··+·1010x·x··+·774x·x··+·319x··+·1087x·x··-·1120x·x··+·1439x·x··+·1175x·x··-·1648x·x··+·985x··-·1317x·x··-·878x·x··+·399x·x··-·1339x·x··+·70x·x··-·463x·x··+·470x··-·628x·x··-·907x·x··+·748x·x··+·98x·x··+·1150x·x··+·1140x·x··+·1308x·x··+·621x··+·369x·x··-·991x·x··-·1186x·x··+·61x·x··-·907x·x··-·681x·x··-·1528x·x··+·717x·x··+·854x·})20 o6·=·map·(ringP8,·ringP8,·{-·780x··-·506x·x··+·1537x··-·132x·x··-·928x·x··+·386x··-·102x·x··+·422x·x··+·725x·x··-·1073x··-·905x·x··-·830x·x··+·1500x·x··+·276x·x··+·1533x··-·653x·x··+·1558x·x··+·939x·x··-·1432x·x··+·462x·x··-·329x··-·92x·x··+·661x·x··-·1298x·x··-·684x·x··+·70x·x··-·715x·x··+·1093x··+·581x·x··+·329x·x··+·454x·x··-·911x·x··-·84x·x··-·1452x·x··-·809x·x··+·1202x··+·1353x·x··+·1503x·x··+·482x·x··+·893x·x··-·643x·x··+·598x·x··+·110x·x··+·1064x·x··-·472x·,·-·522x··-·583x·x··+·1339x··+·1535x·x··-·1317x·x··+·1113x··-·169x·x··+·1440x·x··-·1657x·x··+·721x··+·40x·x··-·1576x·x··-·367x·x··+·257x·x··-·1454x··+·1612x·x··+·1529x·x··-·1068x·x··+·560x·x··-·1441x·x··+·608x··-·92x·x··-·1006x·x··+·285x·x··+·102x·x··-·397x·x··+·66x·x··-·643x··-·38x·x··+·1380x·x··+·1069x·x··-·426x·x··+·1147x·x··+·982x·x··+·10x·x··-·662x··+·16x·x··+·1561x·x··+·1597x·x··+·512x·x··+·1288x·x··-·1253x·x··+·1317x·x··+·1481x·x··-·354x·,·-·640x··-·1551x·x··+·469x··+·1482x·x··-·1593x·x··-·986x··+·471x·x··+·612x·x··+·1228x·x··+·1156x··-·731x·x··+·1503x·x··-·628x·x··+·674x·x··-·799x··+·1137x·x··+·844x·x··+·589x·x··-·666x·x··+·829x·x··-·1024x··-·170x·x··+·450x·x··+·1497x·x··+·1204x·x··-·907x·x··+·1621x·x··-·417x··+·1297x·x··+·1444x·x··+·4x·x··+·398x·x··+·996x·x··-·1031x·x··+·239x·x··+·303x··+·1215x·x··-·83x·x··+·1571x·x··-·1543x·x··-·925x·x··-·694x·x··+·151x·x··-·520x·x··+·880x·,·-·1210x··-·222x·x··+·185x··+·245x·x··+·1059x·x··-·322x··+·238x·x··+·962x·x··+·1260x·x··-·1581x··+·50x·x··+·1352x·x··-·1465x·x··+·1555x·x··+·1333x··+·1362x·x··+·1365x·x··+·1168x·x··-·1401x·x··+·149x·x··-·652x··+·1378x·x··-·557x·x··-·112x·x··+·26x·x··+·315x·x··+·111x·x··+·1592x··-·283x·x··-·1454x·x··+·907x·x··+·212x·x··+·400x·x··+·1049x·x··-·882x·x··-·1429x··-·183x·x··+·1571x·x··-·1286x·x··-·1179x·x··+·1319x·x··+·240x·x··-·1100x·x··+·1500x·x··-·348x·,·1051x··-·1325x·x··+·1354x··-·346x·x··-·1532x·x··-·466x··+·163x·x··-·659x·x··-·291x·x··+·966x··+·789x·x··+·393x·x··+·403x·x··-·1199x·x··-·570x··-·93x·x··-·492x·x··-·418x·x··+·713x·x··-·1323x·x··-·1384x··-·830x·x··-·54x·x··-·306x·x··+·709x·x··+·421x·x··-·954x·x··-·299x··+·1053x·x··-·1080x·x··+·686x·x··+·170x·x··-·1272x·x··-·1661x·x··+·1235x·x··+·1553x··-·1454x·x··-·1411x·x··-·1195x·x··-·962x·x··+·737x·x··-·390x·x··+·957x·x··+·1538x·x··+·1234x·,·-·509x··+·9x·x··-·1563x··-·710x·x··-·642x·x··+·541x··+·220x·x··-·1214x·x··-·16x·x··+·1008x··-·1088x·x··+·755x·x··-·886x·x··-·1433x·x··+·1154x··+·1627x·x··-·1547x·x··-·951x·x··+·866x·x··+·163x·x··-·1142x··-·668x·x··+·1361x·x··+·1324x·x··-·490x·x··+·282x·x··-·1133x·x··-·612x··+·805x·x··-·126x·x··+·1296x·x··-·973x·x··+·1271x·x··-·1646x·x··+·844x·x··+·1073x··-·1452x·x··-·1112x·x··-·141x·x··+·176x·x··-·1579x·x··-·78x·x··+·848x·x··-·1365x·x··+·711x·,·x··+·1543x·x··-·1076x··+·493x·x··-·526x·x··+·868x··-·582x·x··-·996x·x··+·206x·x··-·419x··+·1258x·x··-·391x·x··+·1002x·x··-·1539x·x··+·931x··-·1504x·x··+·810x·x··+·324x·x··+·1356x·x··+·313x·x··+·772x··+·299x·x··+·1186x·x··+·718x·x··+·407x·x··-·64x·x··-·828x·x··-·1393x··+·94x·x··-·290x·x··-·766x·x··+·950x·x··-·640x·x··+·265x·x··-·1640x·x··-·1403x··-·126x·x··+·891x·x··-·1519x·x··-·927x·x··-·1335x·x··-·1448x·x··-·x·x··-·1103x·x··-·1152x·,·821x··+·558x·x··-·1174x··-·168x·x··+·986x·x··+·790x··+·549x·x··+·817x·x··+·1396x·x··+·695x··+·1211x·x··+·878x·x··-·1061x·x··-·1244x·x··-·880x··+·1409x·x··-·567x·x··+·1240x·x··+·1126x·x··-·1262x·x··+·490x··+·1553x·x··+·1276x·x··+·805x·x··+·576x·x··-·1076x·x··+·1617x·x··-·495x··-·750x·x··-·277x·x··+·544x·x··+·1479x·x··-·784x·x··-·64x·x··-·1203x·x··+·405x··+·1013x·x··+·604x·x··+·1301x·x··+·1003x·x··+·235x·x··+·696x·x··+·939x·x··-·714x·x··-·879x·,·-·1452x··+·727x·x··-·1159x··+·449x·x··-·1169x·x··+·732x··+·575x·x··-·600x·x··+·924x·x··-·837x··+·1298x·x··-·860x·x··+·1010x·x··+·774x·x··+·319x··+·1087x·x··-·1120x·x··+·1439x·x··+·1175x·x··-·1648x·x··+·985x··-·1317x·x··-·878x·x··+·399x·x··-·1339x·x··+·70x·x··-·463x·x··+·470x··-·628x·x··-·907x·x··+·748x·x··+·98x·x··+·1150x·x··+·1140x·x··+·1308x·x··+·621x··+·369x·x··-·991x·x··-·1186x·x··+·61x·x··-·907x·x··-·681x·x··-·1528x·x··+·717x·x··+·854x·})
21 ·································0·······0·1········1·······0·2·······1·2·······2·······0·3·······1·3·······2·3········3·······0·4·······1·4········2·4·······3·4········4·······0·5········1·5·······2·5········3·5·······4·5·······5······0·6·······1·6········2·6·······3·6······4·6·······5·6········6·······0·7·······1·7·······2·7·······3·7······4·7········5·7·······6·7········7········0·8········1·8·······2·8·······3·8·······4·8·······5·8·······6·8········7·8·······8········0·······0·1········1········0·2········1·2········2·······0·3········1·3········2·3·······3······0·4········1·4·······2·4·······3·4········4········0·5········1·5········2·5·······3·5········4·5·······5······0·6········1·6·······2·6·······3·6·······4·6······5·6·······6······0·7········1·7········2·7·······3·7········4·7·······5·7······6·7·······7······0·8········1·8········2·8·······3·8········4·8········5·8········6·8········7·8·······8········0········0·1·······1········0·2········1·2·······2·······0·3·······1·3········2·3········3·······0·4········1·4·······2·4·······3·4·······4········0·5·······1·5·······2·5·······3·5·······4·5········5·······0·6·······1·6········2·6········3·6·······4·6········5·6·······6········0·7········1·7·····2·7·······3·7·······4·7········5·7·······6·7·······7········0·8······1·8········2·8········3·8·······4·8·······5·8·······6·8·······7·8·······8·········0·······0·1·······1·······0·2········1·2·······2·······0·3·······1·3········2·3········3······0·4········1·4········2·4········3·4········4········0·5········1·5········2·5········3·5·······4·5·······5········0·6·······1·6·······2·6······3·6·······4·6·······5·6········6·······0·7········1·7·······2·7·······3·7·······4·7········5·7·······6·7········7·······0·8········1·8········2·8········3·8········4·8·······5·8········6·8········7·8·······8·······0········0·1········1·······0·2········1·2·······2·······0·3·······1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4·······4······0·5·······1·5·······2·5·······3·5········4·5········5·······0·6······1·6·······2·6·······3·6·······4·6·······5·6·······6········0·7········1·7·······2·7·······3·7········4·7········5·7········6·7········7········0·8········1·8········2·8·······3·8·······4·8·······5·8·······6·8········7·8········8········0·····0·1········1·······0·2·······1·2·······2·······0·3········1·3······2·3········3········0·4·······1·4·······2·4········3·4········4········0·5········1·5·······2·5·······3·5·······4·5········5·······0·6········1·6········2·6·······3·6·······4·6········5·6·······6·······0·7·······1·7········2·7·······3·7········4·7········5·7·······6·7········7········0·8········1·8·······2·8·······3·8········4·8······5·8·······6·8········7·8·······8···0········0·1········1·······0·2·······1·2·······2·······0·3·······1·3·······2·3·······3········0·4·······1·4········2·4········3·4·······4········0·5·······1·5·······2·5········3·5·······4·5·······5·······0·6········1·6·······2·6·······3·6······4·6·······5·6········6······0·7·······1·7·······2·7·······3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8········4·8········5·8····6·8········7·8········8······0·······0·1········1·······0·2·······1·2·······2·······0·3·······1·3········2·3·······3········0·4·······1·4········2·4········3·4·······4········0·5·······1·5········2·5········3·5········4·5·······5········0·6········1·6·······2·6·······3·6········4·6········5·6·······6·······0·7·······1·7·······2·7········3·7·······4·7······5·7········6·7·······7········0·8·······1·8········2·8········3·8·······4·8·······5·8·······6·8·······7·8·······8·········0·······0·1········1·······0·2········1·2·······2·······0·3·······1·3·······2·3·······3········0·4·······1·4········2·4·······3·4·······4········0·5········1·5········2·5········3·5········4·5·······5········0·6·······1·6·······2·6········3·6······4·6·······5·6·······6·······0·7·······1·7·······2·7······3·7········4·7········5·7········6·7·······7·······0·8·······1·8········2·8······3·8·······4·8·······5·8········6·8·······7·8·······821 ·································0·······0·1········1·······0·2·······1·2·······2·······0·3·······1·3·······2·3········3·······0·4·······1·4········2·4·······3·4········4·······0·5········1·5·······2·5········3·5·······4·5·······5······0·6·······1·6········2·6·······3·6······4·6·······5·6········6·······0·7·······1·7·······2·7·······3·7······4·7········5·7·······6·7········7········0·8········1·8·······2·8·······3·8·······4·8·······5·8·······6·8········7·8·······8········0·······0·1········1········0·2········1·2········2·······0·3········1·3········2·3·······3······0·4········1·4·······2·4·······3·4········4········0·5········1·5········2·5·······3·5········4·5·······5······0·6········1·6·······2·6·······3·6·······4·6······5·6·······6······0·7········1·7········2·7·······3·7········4·7·······5·7······6·7·······7······0·8········1·8········2·8·······3·8········4·8········5·8········6·8········7·8·······8········0········0·1·······1········0·2········1·2·······2·······0·3·······1·3········2·3········3·······0·4········1·4·······2·4·······3·4·······4········0·5·······1·5·······2·5·······3·5·······4·5········5·······0·6·······1·6········2·6········3·6·······4·6········5·6·······6········0·7········1·7·····2·7·······3·7·······4·7········5·7·······6·7·······7········0·8······1·8········2·8········3·8·······4·8·······5·8·······6·8·······7·8·······8·········0·······0·1·······1·······0·2········1·2·······2·······0·3·······1·3········2·3········3······0·4········1·4········2·4········3·4········4········0·5········1·5········2·5········3·5·······4·5·······5········0·6·······1·6·······2·6······3·6·······4·6·······5·6········6·······0·7········1·7·······2·7·······3·7·······4·7········5·7·······6·7········7·······0·8········1·8········2·8········3·8········4·8·······5·8········6·8········7·8·······8·······0········0·1········1·······0·2········1·2·······2·······0·3·······1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4·······4······0·5·······1·5·······2·5·······3·5········4·5········5·······0·6······1·6·······2·6·······3·6·······4·6·······5·6·······6········0·7········1·7·······2·7·······3·7········4·7········5·7········6·7········7········0·8········1·8········2·8·······3·8·······4·8·······5·8·······6·8········7·8········8········0·····0·1········1·······0·2·······1·2·······2·······0·3········1·3······2·3········3········0·4·······1·4·······2·4········3·4········4········0·5········1·5·······2·5·······3·5·······4·5········5·······0·6········1·6········2·6·······3·6·······4·6········5·6·······6·······0·7·······1·7········2·7·······3·7········4·7········5·7·······6·7········7········0·8········1·8·······2·8·······3·8········4·8······5·8·······6·8········7·8·······8···0········0·1········1·······0·2·······1·2·······2·······0·3·······1·3·······2·3·······3········0·4·······1·4········2·4········3·4·······4········0·5·······1·5·······2·5········3·5·······4·5·······5·······0·6········1·6·······2·6·······3·6······4·6·······5·6········6······0·7·······1·7·······2·7·······3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8········4·8········5·8····6·8········7·8········8······0·······0·1········1·······0·2·······1·2·······2·······0·3·······1·3········2·3·······3········0·4·······1·4········2·4········3·4·······4········0·5·······1·5········2·5········3·5········4·5·······5········0·6········1·6·······2·6·······3·6········4·6········5·6·······6·······0·7·······1·7·······2·7········3·7·······4·7······5·7········6·7·······7········0·8·······1·8········2·8········3·8·······4·8·······5·8·······6·8·······7·8·······8·········0·······0·1········1·······0·2········1·2·······2·······0·3·······1·3·······2·3·······3········0·4·······1·4········2·4·······3·4·······4········0·5········1·5········2·5········3·5········4·5·······5········0·6·······1·6·······2·6········3·6······4·6·······5·6·······6·······0·7·······1·7·······2·7······3·7········4·7········5·7········6·7·······7·······0·8·······1·8········2·8······3·8·······4·8·······5·8········6·8·······7·8·······8
  
22 o6·:·RingMap·ringP8·<--·ringP822 o6·:·RingMap·ringP8·<--·ringP8
  
23 i7·:·time·degreeMap·phi'23 i7·:·time·degreeMap·phi'
24 ·--·used·0.506456s·(cpu);·0.421357s·(thread);·0s·(gc)24 ·--·used·0.604075s·(cpu);·0.468586s·(thread);·0s·(gc)
  
25 o7·=·1425 o7·=·14
  
26 i8·:·26 i8·:·
586 B
./usr/share/doc/Macaulay2/Cremona/example-output/_force__Image.out
    
Offset 5, 14 lines modifiedOffset 5, 14 lines modified
5 o2·:·Ideal·of·P65 o2·:·Ideal·of·P6
  
6 i3·:·Phi·=·rationalMap(X,Dominant=>2);6 i3·:·Phi·=·rationalMap(X,Dominant=>2);
  
7 o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)7 o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)
  
8 i4·:·time·forceImage(Phi,ideal·0_(target·Phi))8 i4·:·time·forceImage(Phi,ideal·0_(target·Phi))
9 ·--·used·0.00123435s·(cpu);·0.000594134s·(thread);·0s·(gc)9 ·--·used·0.000161323s·(cpu);·0.000847168s·(thread);·0s·(gc)
  
10 i5·:·Phi;10 i5·:·Phi;
  
11 o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)11 o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)
  
12 i6·:·12 i6·:·
1.13 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_graph.out
    
Offset 35, 15 lines modifiedOffset 35, 15 lines modified
35 ······················-·x··+·x·x35 ······················-·x··+·x·x
36 ·························3····2·436 ·························3····2·4
37 ·····················}37 ·····················}
  
38 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)38 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)
  
39 i3·:·time·(p1,p2)·=·graph·phi;39 i3·:·time·(p1,p2)·=·graph·phi;
40 ·--·used·0.277032s·(cpu);·0.0546614s·(thread);·0s·(gc)40 ·--·used·0.199719s·(cpu);·0.0343623s·(thread);·0s·(gc)
  
41 i4·:·p141 i4·:·p1
  
42 o4·=·--·rational·map·--42 o4·=·--·rational·map·--
43 ··································ZZ·································ZZ43 ··································ZZ·································ZZ
44 ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by44 ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by
45 ································190181··0···1···2···3···4··········190181··0···1···2···3···4···545 ································190181··0···1···2···3···4··········190181··0···1···2···3···4···5
Offset 173, 15 lines modifiedOffset 173, 15 lines modified
173 i8·:·projectiveDegrees·p2173 i8·:·projectiveDegrees·p2
  
174 o8·=·{51,·28,·14,·6,·2}174 o8·=·{51,·28,·14,·6,·2}
  
175 o8·:·List175 o8·:·List
  
176 i9·:·time·g·=·graph·p2;176 i9·:·time·g·=·graph·p2;
177 ·--·used·0.287131s·(cpu);·0.0433417s·(thread);·0s·(gc)177 ·--·used·0.242029s·(cpu);·0.0407132s·(thread);·0s·(gc)
  
178 i10·:·g_0;178 i10·:·g_0;
  
179 o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)179 o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)
  
180 i11·:·g_1;180 i11·:·g_1;
  
1.82 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_ideal_lp__Rational__Map_rp.out
    
Offset 33, 15 lines modifiedOffset 33, 15 lines modified
33 ······················x··-·x·x33 ······················x··-·x·x
34 ·······················1····0·334 ·······················1····0·3
35 ·····················}35 ·····················}
  
36 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)36 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)
  
37 i3·:·time·ideal·phi37 i3·:·time·ideal·phi
38 ·--·used·0.00623863s·(cpu);·0.00277868s·(thread);·0s·(gc)38 ·--·used·0.000283682s·(cpu);·0.00326776s·(thread);·0s·(gc)
  
39 ·············2·····································2······················39 ·············2·····································2······················
40 o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+40 o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+
41 ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3··41 ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3··
42 ·····------------------------------------------------------------------------42 ·····------------------------------------------------------------------------
43 ············243 ············2
44 ·····x·x·,·x··-·x·x·)44 ·····x·x·,·x··-·x·x·)
Offset 108, 15 lines modifiedOffset 108, 15 lines modified
108 ······················y108 ······················y
109 ·······················4109 ·······················4
110 ·····················}110 ·····················}
  
111 o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)111 o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)
  
112 i6·:·time·ideal·phi'112 i6·:·time·ideal·phi'
113 ·--·used·0.161454s·(cpu);·0.0943583s·(thread);·0s·(gc)113 ·--·used·0.180122s·(cpu);·0.106703s·(thread);·0s·(gc)
  
114 o6·=·ideal·1114 o6·=·ideal·1
  
115 ············································································································QQ[x·..x·,·y·..y·]115 ············································································································QQ[x·..x·,·y·..y·]
116 ················································································································0···5···0···4116 ················································································································0···5···0···4
117 o6·:·Ideal·of·--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------117 o6·:·Ideal·of·--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
118 ·····································································································································································································2118 ·····································································································································································································2
5.75 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_inverse__Map.out
    
Offset 72, 15 lines modifiedOffset 72, 15 lines modified
72 ······················w·w··-·w·w··+·w·w72 ······················w·w··-·w·w··+·w·w
73 ·······················2·4····1·5····0·673 ·······················2·4····1·5····0·6
74 ·····················}74 ·····················}
  
75 o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)75 o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)
  
76 i2·:·time·psi·=·inverseMap·phi76 i2·:·time·psi·=·inverseMap·phi
77 ·--·used·0.123862s·(cpu);·0.0827311s·(thread);·0s·(gc)77 ·--·used·0.136945s·(cpu);·0.0833575s·(thread);·0s·(gc)
  
78 o2·=·--·rational·map·--78 o2·=·--·rational·map·--
79 ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])79 ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])
80 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···2080 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20
81 ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])81 ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])
82 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···2082 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20
83 ·····defining·forms:·{83 ·····defining·forms:·{
Offset 158, 15 lines modifiedOffset 158, 15 lines modified
158 o4·=·map·(QQ[w·..w··],·QQ[w·..w··],·{w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w··-·w·w··-·w·w··+·w·w··-·w·w·})158 o4·=·map·(QQ[w·..w··],·QQ[w·..w··],·{w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w··-·w·w··-·w·w··+·w·w··-·w·w·})
159 ··············0···26·······0···26·····21·22····20·23····15·24····10·25····0·26···19·22····18·23····16·24····11·25····1·26···19·20····18·21····17·24····12·25····2·26···15·19····16·21····17·23····13·25····3·26···10·19····11·21····12·23····13·24····4·26···0·19····1·21····2·23····3·24····4·25···15·18····16·20····17·22····14·25····5·26···10·18····11·20····12·22····14·24····6·26···0·18····1·20····2·22····5·24····6·25···12·16····11·17····13·18····14·19····7·26···2·16····1·17····3·18····5·19····7·25···12·15····10·17····13·20····14·21····8·26···11·15····10·16····13·22····14·23····9·26···2·15····0·17····3·20····5·21····8·25···1·15····0·16····3·22····5·23····9·25···5·13····3·14····7·15····8·16····9·17···5·12····2·14····6·17····8·18····7·20···3·12····2·13····4·17····8·19····7·21···5·11····1·14····6·16····9·18····7·22···3·11····1·13····4·16····9·19····7·23···2·11····1·12····4·18····6·19····7·24···7·10····8·11····9·12····6·13····4·14···5·10····0·14····6·15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4·20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7····1·8····2·9159 ··············0···26·······0···26·····21·22····20·23····15·24····10·25····0·26···19·22····18·23····16·24····11·25····1·26···19·20····18·21····17·24····12·25····2·26···15·19····16·21····17·23····13·25····3·26···10·19····11·21····12·23····13·24····4·26···0·19····1·21····2·23····3·24····4·25···15·18····16·20····17·22····14·25····5·26···10·18····11·20····12·22····14·24····6·26···0·18····1·20····2·22····5·24····6·25···12·16····11·17····13·18····14·19····7·26···2·16····1·17····3·18····5·19····7·25···12·15····10·17····13·20····14·21····8·26···11·15····10·16····13·22····14·23····9·26···2·15····0·17····3·20····5·21····8·25···1·15····0·16····3·22····5·23····9·25···5·13····3·14····7·15····8·16····9·17···5·12····2·14····6·17····8·18····7·20···3·12····2·13····4·17····8·19····7·21···5·11····1·14····6·16····9·18····7·22···3·11····1·13····4·16····9·19····7·23···2·11····1·12····4·18····6·19····7·24···7·10····8·11····9·12····6·13····4·14···5·10····0·14····6·15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4·20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7····1·8····2·9
  
160 o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··]160 o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··]
161 ·················0···26··········0···26161 ·················0···26··········0···26
  
162 i5·:·time·psi·=·inverseMap·phi162 i5·:·time·psi·=·inverseMap·phi
163 ·--·used·0.235622s·(cpu);·0.164023s·(thread);·0s·(gc)163 ·--·used·0.26766s·(cpu);·0.159342s·(thread);·0s·(gc)
  
164 o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··})164 o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··})
165 ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12165 ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12
  
166 o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··]166 o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··]
167 ·················0···26··········0···26167 ·················0···26··········0···26
  
3.17 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_inverse_lp__Rational__Map_rp.out
    
Offset 28, 15 lines modifiedOffset 28, 15 lines modified
28 ······················-·-------x··+·---------x·x··+·------------x·x··-·----------x·x··-·-----x··-·-----------x·x··+·-------------x·x·x··+·-------------x·x·x··-·--------x·x··-·----------x·x··+·-------------x·x·x··-·----------x·x··-·-----------x·x··+·----------x·x··+·------x··+·-----------x·x··+·----------x·x·x··-·-----------x·x·x··-·-------x·x··+·-------------x·x·x··+·------------x·x·x·x··-·-----------x·x·x··+·-----------x·x·x··-·------------x·x·x··+·----------x·x··-·-----------x·x··-·------------x·x·x··-·---------x·x··-·------------x·x·x··-·-----------x·x·x··+·-----------x·x··-·----------x·x··+·-------x·x··+·--------x·x··+·------x··+·---------x·x··-·------------x·x·x··-·-------------x·x·x··-·----------x·x··+·--------------x·x·x··+·-------------x·x·x·x··-·------------x·x·x··+·-------------x·x·x··+·------------x·x·x··+·----------x·x··+·-----------x·x·x··-·-------------x·x·x·x··-·----------x·x·x··+·--------------x·x·x·x··-·-------------x·x·x·x··+·-------------x·x·x··-·------------x·x·x··+·---------x·x·x··-·------------x·x·x··+·---------x·x··-·---------x·x··-·-----------x·x·x··-·----------x·x··+·-----------x·x·x··+·-----------x·x·x··+·----------x·x··-·-----------x·x·x··-·-----------x·x·x··-·------------x·x·x··-·----------x·x··+·---------x·x··-·------x·x··-·--------x·x··-·----------x·x··-·-----x28 ······················-·-------x··+·---------x·x··+·------------x·x··-·----------x·x··-·-----x··-·-----------x·x··+·-------------x·x·x··+·-------------x·x·x··-·--------x·x··-·----------x·x··+·-------------x·x·x··-·----------x·x··-·-----------x·x··+·----------x·x··+·------x··+·-----------x·x··+·----------x·x·x··-·-----------x·x·x··-·-------x·x··+·-------------x·x·x··+·------------x·x·x·x··-·-----------x·x·x··+·-----------x·x·x··-·------------x·x·x··+·----------x·x··-·-----------x·x··-·------------x·x·x··-·---------x·x··-·------------x·x·x··-·-----------x·x·x··+·-----------x·x··-·----------x·x··+·-------x·x··+·--------x·x··+·------x··+·---------x·x··-·------------x·x·x··-·-------------x·x·x··-·----------x·x··+·--------------x·x·x··+·-------------x·x·x·x··-·------------x·x·x··+·-------------x·x·x··+·------------x·x·x··+·----------x·x··+·-----------x·x·x··-·-------------x·x·x·x··-·----------x·x·x··+·--------------x·x·x·x··-·-------------x·x·x·x··+·-------------x·x·x··-·------------x·x·x··+·---------x·x·x··-·------------x·x·x··+·---------x·x··-·---------x·x··-·-----------x·x·x··-·----------x·x··+·-----------x·x·x··+·-----------x·x·x··+·----------x·x··-·-----------x·x·x··-·-----------x·x·x··-·------------x·x·x··-·----------x·x··+·---------x·x··-·------x·x··-·--------x·x··-·----------x·x··-·-----x
29 ·························290304·0····3888000··0·1····2939328000··0·1····163296000·0·1···20250·1····228614400··0·2····41150592000··0·1·2····41150592000··0·1·2····3888000·1·2·····3572100··0·2····10287648000··0·1·2····342921600·1·2····114307200··0·2····63504000··1·2····25200·2·····76204800··0·3····42336000··0·1·3····428652000··0·1·3····212625·1·3·····5334336000··0·2·3····9601804800··0·1·2·3····489888000··1·2·3····222264000··0·2·3····12002256000·1·2·3····66679200··2·3····666792000··0·3·····666792000··0·1·3····47628000·1·3····1333584000··0·2·3····444528000··1·2·3····777924000··2·3····55566000··0·3····105840·1·3····3472875·2·3····11025·3····4665600··0·4····2939328000··0·1·4·····4898880000··0·1·4····29160000··1·4·····41150592000··0·2·4····20575296000··0·1·2·4····4898880000··1·2·4····20575296000··0·2·4····1371686400··1·2·4····95256000··2·4·····40824000··0·3·4·····8573040000··0·1·3·4····11664000··1·3·4·····24004512000··0·2·3·4····34292160000··1·2·3·4····12002256000··2·3·4·····333396000··0·3·4····5292000··1·3·4····1333584000··2·3·4····3969000··3·4····6804000··0·4····272160000··0·1·4····58320000··1·4····190512000··0·2·4····4898880000·1·2·4····190512000·2·4····476280000··0·3·4····204120000··1·3·4····2857680000··2·3·4····23814000··3·4····30618000·0·4····46656·1·4···12757500·2·4····51030000··3·4···30375·429 ·························290304·0····3888000··0·1····2939328000··0·1····163296000·0·1···20250·1····228614400··0·2····41150592000··0·1·2····41150592000··0·1·2····3888000·1·2·····3572100··0·2····10287648000··0·1·2····342921600·1·2····114307200··0·2····63504000··1·2····25200·2·····76204800··0·3····42336000··0·1·3····428652000··0·1·3····212625·1·3·····5334336000··0·2·3····9601804800··0·1·2·3····489888000··1·2·3····222264000··0·2·3····12002256000·1·2·3····66679200··2·3····666792000··0·3·····666792000··0·1·3····47628000·1·3····1333584000··0·2·3····444528000··1·2·3····777924000··2·3····55566000··0·3····105840·1·3····3472875·2·3····11025·3····4665600··0·4····2939328000··0·1·4·····4898880000··0·1·4····29160000··1·4·····41150592000··0·2·4····20575296000··0·1·2·4····4898880000··1·2·4····20575296000··0·2·4····1371686400··1·2·4····95256000··2·4·····40824000··0·3·4·····8573040000··0·1·3·4····11664000··1·3·4·····24004512000··0·2·3·4····34292160000··1·2·3·4····12002256000··2·3·4·····333396000··0·3·4····5292000··1·3·4····1333584000··2·3·4····3969000··3·4····6804000··0·4····272160000··0·1·4····58320000··1·4····190512000··0·2·4····4898880000·1·2·4····190512000·2·4····476280000··0·3·4····204120000··1·3·4····2857680000··2·3·4····23814000··3·4····30618000·0·4····46656·1·4···12757500·2·4····51030000··3·4···30375·4
30 ·····················}30 ·····················}
  
31 o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)31 o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)
  
32 i3·:·time·inverse·phi32 i3·:·time·inverse·phi
33 ·--·used·0.0711021s·(cpu);·0.0683487s·(thread);·0s·(gc)33 ·--·used·0.0503565s·(cpu);·0.0535115s·(thread);·0s·(gc)
  
34 o3·=·--·rational·map·--34 o3·=·--·rational·map·--
35 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·])35 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·])
36 ······················0···1···2···3···436 ······················0···1···2···3···4
37 ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·])37 ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·])
38 ······················0···1···2···3···438 ······················0···1···2···3···4
39 ·····defining·forms:·{39 ·····defining·forms:·{
700 B
./usr/share/doc/Macaulay2/Cremona/example-output/_is__Birational.out
    
Offset 40, 18 lines modifiedOffset 40, 18 lines modified
40 ······················-·t··+·t·t40 ······················-·t··+·t·t
41 ·························3····2·441 ·························3····2·4
42 ·····················}42 ·····················}
  
43 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)43 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)
  
44 i3·:·time·isBirational·phi44 i3·:·time·isBirational·phi
45 ·--·used·0.0160016s·(cpu);·0.0154305s·(thread);·0s·(gc)45 ·--·used·0.0159539s·(cpu);·0.0177911s·(thread);·0s·(gc)
  
46 o3·=·true46 o3·=·true
  
47 i4·:·time·isBirational(phi,Certify=>true)47 i4·:·time·isBirational(phi,Certify=>true)
48 ·--·used·0.261018s·(cpu);·0.049664s·(thread);·0s·(gc)48 ·--·used·0.252217s·(cpu);·0.0329917s·(thread);·0s·(gc)
49 Certify:·output·certified!49 Certify:·output·certified!
  
50 o4·=·true50 o4·=·true
  
51 i5·:·51 i5·:·
941 B
./usr/share/doc/Macaulay2/Cremona/example-output/_is__Dominant.out
    
Offset 3, 15 lines modifiedOffset 3, 15 lines modified
3 i1·:·P8·=·ZZ/101[x_0..x_8];3 i1·:·P8·=·ZZ/101[x_0..x_8];
  
4 i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},{x_4..x_8}};4 i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},{x_4..x_8}};
  
5 o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)5 o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)
  
6 i3·:·time·isDominant(phi,Certify=>true)6 i3·:·time·isDominant(phi,Certify=>true)
7 ·--·used·1.64884s·(cpu);·1.51236s·(thread);·0s·(gc)7 ·--·used·1.93851s·(cpu);·1.76759s·(thread);·0s·(gc)
8 Certify:·output·certified!8 Certify:·output·certified!
  
9 o3·=·true9 o3·=·true
  
10 i4·:·P7·=·ZZ/101[x_0..x_7];10 i4·:·P7·=·ZZ/101[x_0..x_7];
  
11 i5·:·--·hyperelliptic·curve·of·genus·311 i5·:·--·hyperelliptic·curve·of·genus·3
Offset 20, 13 lines modifiedOffset 20, 13 lines modified
20 o5·:·Ideal·of·P720 o5·:·Ideal·of·P7
  
21 i6·:·phi·=·rationalMap(C,3,2);21 i6·:·phi·=·rationalMap(C,3,2);
  
22 o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)22 o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)
  
23 i7·:·time·isDominant(phi,Certify=>true)23 i7·:·time·isDominant(phi,Certify=>true)
24 ·--·used·2.33087s·(cpu);·1.82168s·(thread);·0s·(gc)24 ·--·used·2.87427s·(cpu);·2.20425s·(thread);·0s·(gc)
25 Certify:·output·certified!25 Certify:·output·certified!
  
26 o7·=·false26 o7·=·false
  
27 i8·:·27 i8·:·
3.66 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_kernel_lp__Ring__Map_cm__Z__Z_rp.out
    
Offset 6, 23 lines modifiedOffset 6, 23 lines modified
6 o1·=·map·(QQ[x·..x·],·QQ[y·..y··],·{-·5x·x··+·x·x··+·x·x··+·35x·x··-·7x·x··+·x·x··-·x·x··-·49x··-·5x·x··+·2x·x··-·x·x··+·27x·x··-·4x··+·x·x··-·7x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x·,·-·x·x··-·6x·x··-·5x·x··+·2x·x··+·x·x··+·x·x··-·5x·x··-·x·x··+·2x·x··+·7x·x··-·2x·x··+·2x·x··-·3x·x·,·-·25x··+·9x·x··+·10x·x··-·2x·x··-·x··+·29x·x··-·x·x··-·7x·x··-·13x·x··+·3x·x··+·x·x··-·x·x··+·2x·x··-·x·x··+·7x·x··-·2x·x··-·8x·x··+·2x·x··-·3x·x·,·x·x··+·x·x··+·x··+·7x·x··-·9x·x··+·12x·x··-·4x··+·2x·x··+·2x·x··-·14x·x··+·4x·x··+·x·x··-·x·x··-·14x·x··+·x·x·,·-·5x·x··+·x·x··-·7x·x··+·8x·x··-·5x·x··+·2x·x··-·x·x··+·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·x·x··+·x··-·7x·x··-·8x·x··+·x·x··+·x·x··+·2x·x··-·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··+·x··-·8x·x··+·x·x··+·6x·x··-·2x··+·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··-·7x·x··+·x·x··+·x·x··-·7x·x··+·2x··-·x·x·,·-·4x·x··+·x·x··-·x··-·7x·x··+·8x·x··+·x·x··-·x·x··-·6x·x··+·2x··-·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·-·5x·x··+·2x··+·x·x··-·x··-·x·x··+·8x·x··-·10x·x··+·2x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x··+·5x·x··-·3x·x··-·2x·x··+·7x·x··-·2x·x··-·3x·x·,·-·5x·x··+·x·x··+·x·x··-·4x·x··-·x·x··+·x·x··+·x·x·,·x·x··-·x·x··+·5x·x··+·x·x··-·14x·x··-·x·x··-·8x·x··-·8x·x··+·2x·x··+·4x·x··+·2x·x··+·4x·x··+·3x·x··-·7x·x··+·2x·x··-·3x·x·})6 o1·=·map·(QQ[x·..x·],·QQ[y·..y··],·{-·5x·x··+·x·x··+·x·x··+·35x·x··-·7x·x··+·x·x··-·x·x··-·49x··-·5x·x··+·2x·x··-·x·x··+·27x·x··-·4x··+·x·x··-·7x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x·,·-·x·x··-·6x·x··-·5x·x··+·2x·x··+·x·x··+·x·x··-·5x·x··-·x·x··+·2x·x··+·7x·x··-·2x·x··+·2x·x··-·3x·x·,·-·25x··+·9x·x··+·10x·x··-·2x·x··-·x··+·29x·x··-·x·x··-·7x·x··-·13x·x··+·3x·x··+·x·x··-·x·x··+·2x·x··-·x·x··+·7x·x··-·2x·x··-·8x·x··+·2x·x··-·3x·x·,·x·x··+·x·x··+·x··+·7x·x··-·9x·x··+·12x·x··-·4x··+·2x·x··+·2x·x··-·14x·x··+·4x·x··+·x·x··-·x·x··-·14x·x··+·x·x·,·-·5x·x··+·x·x··-·7x·x··+·8x·x··-·5x·x··+·2x·x··-·x·x··+·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·x·x··+·x··-·7x·x··-·8x·x··+·x·x··+·x·x··+·2x·x··-·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··+·x··-·8x·x··+·x·x··+·6x·x··-·2x··+·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··-·7x·x··+·x·x··+·x·x··-·7x·x··+·2x··-·x·x·,·-·4x·x··+·x·x··-·x··-·7x·x··+·8x·x··+·x·x··-·x·x··-·6x·x··+·2x··-·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·-·5x·x··+·2x··+·x·x··-·x··-·x·x··+·8x·x··-·10x·x··+·2x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x··+·5x·x··-·3x·x··-·2x·x··+·7x·x··-·2x·x··-·3x·x·,·-·5x·x··+·x·x··+·x·x··-·4x·x··-·x·x··+·x·x··+·x·x·,·x·x··-·x·x··+·5x·x··+·x·x··-·14x·x··-·x·x··-·8x·x··-·8x·x··+·2x·x··+·4x·x··+·2x·x··+·4x·x··+·3x·x··-·7x·x··+·2x·x··-·3x·x·})
7 ··············0···8·······0···11········0·3····2·4····3·4······0·5·····2·5····3·5····4·5······5·····0·6·····2·6····4·6······5·6·····6····4·7·····5·7·····6·7·····4·8······5·8·····6·8·····1·2·····1·5·····0·6·····1·6····4·6····5·6·····0·7····1·7·····2·7·····5·7·····6·7·····1·8·····7·8·······0·····0·2······0·4·····2·4····4······0·5····2·5·····4·5······0·6·····4·6····5·6····0·7·····2·7····4·7·····5·7·····6·7·····0·8·····4·8·····7·8···2·4····3·4····4·····2·5·····4·5······5·6·····6·····3·7·····4·7······5·7·····6·7····3·8····4·8······5·8····6·8······0·4····2·4·····2·5·····4·5·····0·6·····2·6····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···0·4····4·····1·5·····4·5····0·6····1·6·····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···2·3····4·····4·5····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8···1·3·····1·5····1·6····4·6·····5·6·····6····3·7······0·3····3·4····4·····0·5·····4·5····0·6····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8······0·2·····2····2·4····4····2·5·····4·5······0·6·····5·6·····2·7·····4·7······5·7·····6·7·····0·8·····2·8·····4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7···0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2·7·····0·8·····1·8·····5·8·····6·8·····7·87 ··············0···8·······0···11········0·3····2·4····3·4······0·5·····2·5····3·5····4·5······5·····0·6·····2·6····4·6······5·6·····6····4·7·····5·7·····6·7·····4·8······5·8·····6·8·····1·2·····1·5·····0·6·····1·6····4·6····5·6·····0·7····1·7·····2·7·····5·7·····6·7·····1·8·····7·8·······0·····0·2······0·4·····2·4····4······0·5····2·5·····4·5······0·6·····4·6····5·6····0·7·····2·7····4·7·····5·7·····6·7·····0·8·····4·8·····7·8···2·4····3·4····4·····2·5·····4·5······5·6·····6·····3·7·····4·7······5·7·····6·7····3·8····4·8······5·8····6·8······0·4····2·4·····2·5·····4·5·····0·6·····2·6····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···0·4····4·····1·5·····4·5····0·6····1·6·····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···2·3····4·····4·5····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8···1·3·····1·5····1·6····4·6·····5·6·····6····3·7······0·3····3·4····4·····0·5·····4·5····0·6····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8······0·2·····2····2·4····4····2·5·····4·5······0·6·····5·6·····2·7·····4·7······5·7·····6·7·····0·8·····2·8·····4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7···0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2·7·····0·8·····1·8·····5·8·····6·8·····7·8
  
8 o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··]8 o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··]
9 ·················0···8··········0···119 ·················0···8··········0···11
  
10 i2·:·time·kernel(phi,1)10 i2·:·time·kernel(phi,1)
11 ·--·used·0.0140069s·(cpu);·0.0162045s·(thread);·0s·(gc)11 ·--·used·0.0160174s·(cpu);·0.018429s·(thread);·0s·(gc)
  
12 o2·=·ideal·()12 o2·=·ideal·()
  
13 o2·:·Ideal·of·QQ[y·..y··]13 o2·:·Ideal·of·QQ[y·..y··]
14 ··················0···1114 ··················0···11
  
15 i3·:·time·kernel(phi,2)15 i3·:·time·kernel(phi,2)
16 ·--·used·0.340745s·(cpu);·0.25179s·(thread);·0s·(gc)16 ·--·used·0.408882s·(cpu);·0.301061s·(thread);·0s·(gc)
  
17 ···························2················································17 ···························2················································
18 o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··-18 o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··-
19 ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6··19 ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6··
20 ·····------------------------------------------------------------------------20 ·····------------------------------------------------------------------------
21 ···········································································21 ···········································································
22 ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···-22 ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···-
1.23 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_parametrize_lp__Ideal_rp.out
    
Offset 26, 15 lines modifiedOffset 26, 15 lines modified
26 ··············8···········926 ··············8···········9
  
27 ·················ZZ27 ·················ZZ
28 o2·:·Ideal·of·--------[x·..x·]28 o2·:·Ideal·of·--------[x·..x·]
29 ··············10000019··0···929 ··············10000019··0···9
  
30 i3·:·time·parametrize·L30 i3·:·time·parametrize·L
31 ·--·used·0.00400165s·(cpu);·0.00411878s·(thread);·0s·(gc)31 ·--·used·0.00799083s·(cpu);·0.00675167s·(thread);·0s·(gc)
  
32 o3·=·--·rational·map·--32 o3·=·--·rational·map·--
33 ·····················ZZ33 ·····················ZZ
34 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·])34 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·])
35 ··················10000019··0···1···2···3···4···535 ··················10000019··0···1···2···3···4···5
36 ·····················ZZ36 ·····················ZZ
37 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])37 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
Offset 116, 15 lines modifiedOffset 116, 15 lines modified
116 ·············5·9···········6·9···········7·9···········8·9···········9116 ·············5·9···········6·9···········7·9···········8·9···········9
  
117 ·················ZZ117 ·················ZZ
118 o4·:·Ideal·of·--------[x·..x·]118 o4·:·Ideal·of·--------[x·..x·]
119 ··············10000019··0···9119 ··············10000019··0···9
  
120 i5·:·time·parametrize·Q120 i5·:·time·parametrize·Q
121 ·--·used·0.738276s·(cpu);·0.373795s·(thread);·0s·(gc)121 ·--·used·0.831027s·(cpu);·0.421444s·(thread);·0s·(gc)
  
122 o5·=·--·rational·map·--122 o5·=·--·rational·map·--
123 ·····················ZZ123 ·····················ZZ
124 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·])124 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·])
125 ··················10000019··0···1···2···3···4···5···6125 ··················10000019··0···1···2···3···4···5···6
126 ·····················ZZ126 ·····················ZZ
127 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])127 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
1.63 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_point_lp__Quotient__Ring_rp.out
    
Offset 1, 15 lines modifiedOffset 1, 15 lines modified
1 --·-*-·M2-comint·-*-·hash:·35605838294899886901 --·-*-·M2-comint·-*-·hash:·3560583829489988690
  
2 i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331);2 i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331);
  
3 o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)3 o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)
  
4 i2·:·time·p·=·point·source·f4 i2·:·time·p·=·point·source·f
5 ·--·used·0.214883s·(cpu);·0.134364s·(thread);·0s·(gc)5 ·--·used·0.252287s·(cpu);·0.15139s·(thread);·0s·(gc)
  
6 o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+6 o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+
7 ·············10········11···9·········11···8········11···7········11···6··7 ·············10········11···9·········11···8········11···7········11···6··
8 ·····------------------------------------------------------------------------8 ·····------------------------------------------------------------------------
9 ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··-9 ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··-
10 ···········11···5········11···4········11···3·········11···2········11···1··10 ···········11···5········11···4········11···3·········11···2········11···1··
11 ·····------------------------------------------------------------------------11 ·····------------------------------------------------------------------------
Offset 20, 12 lines modifiedOffset 20, 12 lines modified
20 ···························································-----[y·..y··]20 ···························································-----[y·..y··]
21 ···························································33331··0···1121 ···························································33331··0···11
22 o2·:·Ideal·of·-------------------------------------------------------------------------------------------------------22 o2·:·Ideal·of·-------------------------------------------------------------------------------------------------------
23 ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)23 ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)
24 ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·724 ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·7
  
25 i3·:·time·p·==·f^*·f·p25 i3·:·time·p·==·f^*·f·p
26 ·--·used·0.140675s·(cpu);·0.10235s·(thread);·0s·(gc)26 ·--·used·0.15602s·(cpu);·0.106898s·(thread);·0s·(gc)
  
27 o3·=·true27 o3·=·true
  
28 i4·:·28 i4·:·
2.71 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_projective__Degrees.out
    
Offset 7, 15 lines modifiedOffset 7, 15 lines modified
7 o2·=·map·(GF·109561[t·..t·],·GF·109561[x·..x·],·{-·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a})7 o2·=·map·(GF·109561[t·..t·],·GF·109561[x·..x·],·{-·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a})
8 ·····················0···4··············0···5·······1····0·2·····1·2····0·3·····2····1·3·····1·3····0·4·····2·3····1·4·····3····2·48 ·····················0···4··············0···5·······1····0·2·····1·2····0·3·····2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4
  
9 o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·]9 o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·]
10 ························0···4·················0···510 ························0···4·················0···5
  
11 i3·:·time·projectiveDegrees(phi,Certify=>true)11 i3·:·time·projectiveDegrees(phi,Certify=>true)
12 ·--·used·0.307085s·(cpu);·0.0428959s·(thread);·0s·(gc)12 ·--·used·0.282541s·(cpu);·0.0385457s·(thread);·0s·(gc)
13 Certify:·output·certified!13 Certify:·output·certified!
  
14 o3·=·{1,·2,·4,·4,·2}14 o3·=·{1,·2,·4,·4,·2}
  
15 o3·:·List15 o3·:·List
  
16 i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity))16 i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity))
Offset 29, 15 lines modifiedOffset 29, 15 lines modified
29 ··············GF·109561[x·..x·]29 ··············GF·109561[x·..x·]
30 ·························0···530 ·························0···5
31 o4·:·RingMap·------------------·<--·GF·109561[t·..t·]31 o4·:·RingMap·------------------·<--·GF·109561[t·..t·]
32 ·············x·x··-·x·x··+·x·x·················0···432 ·············x·x··-·x·x··+·x·x·················0···4
33 ··············2·3····1·4····0·533 ··············2·3····1·4····0·5
  
34 i5·:·time·projectiveDegrees(psi,Certify=>true)34 i5·:·time·projectiveDegrees(psi,Certify=>true)
35 ·--·used·0.309183s·(cpu);·0.0603617s·(thread);·0s·(gc)35 ·--·used·0.268221s·(cpu);·0.0424187s·(thread);·0s·(gc)
36 Certify:·output·certified!36 Certify:·output·certified!
  
37 o5·=·{2,·4,·4,·2,·1}37 o5·=·{2,·4,·4,·2,·1}
  
38 o5·:·List38 o5·:·List
  
39 i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a·rational·octic·surface39 i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a·rational·octic·surface
Offset 48, 21 lines modifiedOffset 48, 21 lines modified
48 ··········300007··0···6···300007··0···6·····2·4····1·5··········0·4··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6···2·3····0·5··········1·3··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6········0·3·········1·4·········3·4·········4··········0·5·········1·5·········2·5··········3·5··········4·5·········5·········3·6··········4·6·········5·6··········0·1··········1·········0·2··········1·2·········2··········1·4··········1·5·········2·5··········0·6·········1·6·········2·6·········0··········1·········0·2·········1·2·········2·········1·4··········4·········0·5·········1·5··········2·5··········4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6·········5·648 ··········300007··0···6···300007··0···6·····2·4····1·5··········0·4··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6···2·3····0·5··········1·3··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6········0·3·········1·4·········3·4·········4··········0·5·········1·5·········2·5··········3·5··········4·5·········5·········3·6··········4·6·········5·6··········0·1··········1·········0·2··········1·2·········2··········1·4··········1·5·········2·5··········0·6·········1·6·········2·6·········0··········1·········0·2·········1·2·········2·········1·4··········4·········0·5·········1·5··········2·5··········4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6·········5·6
  
49 ···············ZZ·················ZZ49 ···············ZZ·················ZZ
50 o6·:·RingMap·------[x·..x·]·<--·------[x·..x·]50 o6·:·RingMap·------[x·..x·]·<--·------[x·..x·]
51 ·············300007··0···6······300007··0···651 ·············300007··0···6······300007··0···6
  
52 i7·:·time·projectiveDegrees·phi52 i7·:·time·projectiveDegrees·phi
53 ·--·used·0.00356087s·(cpu);·4.2574e-05s·(thread);·0s·(gc)53 ·--·used·0.000972072s·(cpu);·5.7969e-05s·(thread);·0s·(gc)
  
54 o7·=·{1,·2,·4,·8,·8,·4,·1}54 o7·=·{1,·2,·4,·8,·8,·4,·1}
  
55 o7·:·List55 o7·:·List
  
56 i8·:·time·projectiveDegrees(phi,NumDegrees=>1)56 i8·:·time·projectiveDegrees(phi,NumDegrees=>1)
57 ·--·used·0.000198159s·(cpu);·4.8382e-05s·(thread);·0s·(gc)57 ·--·used·0.000102683s·(cpu);·2.0338e-05s·(thread);·0s·(gc)
  
58 o8·=·{4,·1}58 o8·=·{4,·1}
  
59 o8·:·List59 o8·:·List
  
60 i9·:·60 i9·:·
840 B
./usr/share/doc/Macaulay2/Cremona/example-output/_rational__Map_lp__Ideal_cm__Z__Z_cm__Z__Z_rp.out
    
Offset 3, 15 lines modifiedOffset 3, 15 lines modified
3 i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6);3 i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6);
  
4 ················ZZ4 ················ZZ
5 o2·:·Ideal·of·-----[x·..x·]5 o2·:·Ideal·of·-----[x·..x·]
6 ··············33331··0···66 ··············33331··0···6
  
7 i3·:·time·phi·=·rationalMap(V,3,2)7 i3·:·time·phi·=·rationalMap(V,3,2)
8 ·--·used·0.151455s·(cpu);·0.102289s·(thread);·0s·(gc)8 ·--·used·0.161635s·(cpu);·0.111425s·(thread);·0s·(gc)
  
9 o3·=·--·rational·map·--9 o3·=·--·rational·map·--
10 ····················ZZ10 ····················ZZ
11 ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·])11 ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·])
12 ··················33331··0···1···2···3···4···5···612 ··················33331··0···1···2···3···4···5···6
13 ····················ZZ13 ····················ZZ
14 ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··])14 ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··])
1.24 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_rational__Map_lp__Ring_cm__Tally_rp.out
    
Offset 18, 15 lines modifiedOffset 18, 15 lines modified
18 ···················0·········1·········2·········3········4·········518 ···················0·········1·········2·········3········4·········5
  
19 o4·:·Ideal·of·X19 o4·:·Ideal·of·X
  
20 i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};20 i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};
  
21 i6·:·time·phi·=·rationalMap·D21 i6·:·time·phi·=·rationalMap·D
22 ·--·used·0.0239993s·(cpu);·0.0243652s·(thread);·0s·(gc)22 ·--·used·0.026571s·(cpu);·0.027013s·(thread);·0s·(gc)
  
23 o6·=·--·rational·map·--23 o6·=·--·rational·map·--
24 ··································ZZ24 ··································ZZ
25 ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by25 ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by
26 ································65521··0···1···2···3···4···526 ································65521··0···1···2···3···4···5
27 ·············{27 ·············{
28 ·················2··················228 ·················2··················2
Offset 123, 13 lines modifiedOffset 123, 13 lines modified
123 ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x123 ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x
124 ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5124 ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5
125 ·····················}125 ·····················}
  
126 o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)126 o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)
  
127 i7·:·time·?·image(phi,"F4")127 i7·:·time·?·image(phi,"F4")
128 ·--·used·0.877865s·(cpu);·0.518111s·(thread);·0s·(gc)128 ·--·used·1.02321s·(cpu);·0.516756s·(thread);·0s·(gc)
  
129 o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153129 o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153
130 ·····hypersurfaces·of·degree·2130 ·····hypersurfaces·of·degree·2
  
131 i8·:·131 i8·:·
723 B
./usr/share/doc/Macaulay2/Cremona/example-output/_special__Cremona__Transformation.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·13308466410811 --·-*-·M2-comint·-*-·hash:·1330846641081
  
2 i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331))2 i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331))
3 ·--·used·0.871333s·(cpu);·0.772123s·(thread);·0s·(gc)3 ·--·used·1.02517s·(cpu);·0.924576s·(thread);·0s·(gc)
  
4 o1·=·(rational·map·defined·by·forms·of·degree·3,4 o1·=·(rational·map·defined·by·forms·of·degree·3,
5 ······source·variety:·PP^3······················5 ······source·variety:·PP^3······················
6 ······target·variety:·PP^3······················6 ······target·variety:·PP^3······················
7 ······dominance:·true···························7 ······dominance:·true···························
8 ······birationality:·true·······················8 ······birationality:·true·······················
9 ······projective·degrees:·{1,·3,·3,·1}··········9 ······projective·degrees:·{1,·3,·3,·1}··········
2.68 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_special__Cubic__Transformation.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·17300189127154982881 --·-*-·M2-comint·-*-·hash:·1730018912715498288
  
2 i1·:·time·specialCubicTransformation·92 i1·:·time·specialCubicTransformation·9
3 ·--·used·0.0706292s·(cpu);·0.0728482s·(thread);·0s·(gc)3 ·--·used·0.0767241s·(cpu);·0.0775018s·(thread);·0s·(gc)
  
4 o1·=·--·rational·map·--4 o1·=·--·rational·map·--
5 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·])5 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·])
6 ······················0···1···2···3···4···5···66 ······················0···1···2···3···4···5···6
7 ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by7 ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by
8 ····································0···1···2···3···4···5···6···7···8···98 ····································0···1···2···3···4···5···6···7···8···9
9 ·············{9 ·············{
Offset 62, 15 lines modifiedOffset 62, 15 lines modified
62 ······················8x·x··-·12x·x··+·24x··-·11x·x··+·17x·x·x··-·24x·x··-·10x·x··+·11x·x··-·3x··-·6x·x··+·28x·x·x··-·70x·x··-·21x·x·x··+·47x·x·x··-·13x·x··-·14x·x··+·66x·x··-·22x·x··-·20x··+·2x·x··-·2x·x·x··-·10x·x··-·11x·x·x··+·8x·x·x··-·5x·x··+·3x·x·x··+·23x·x·x··-·11x·x·x··-·12x·x··+·3x·x··-·3x·x··-·2x·x··+·3x·x··+·x··-·11x·x··+·14x·x·x··+·34x·x··-·6x·x·x··-·16x·x·x··+·3x·x··-·15x·x·x··-·66x·x·x··+·12x·x·x··+·30x·x··-·19x·x·x··+·2x·x·x··-·5x·x·x··-·2x·x·x··-·7x·x··+·6x·x··+·21x·x··-·3x·x··-·21x·x··+·x·x··+·5x··-·8x·x··+·7x·x·x··-·32x·x··-·13x·x·x··+·28x·x·x··-·9x·x··+·70x·x·x··-·27x·x·x··-·36x·x··+·x·x·x··+·4x·x·x··-·7x·x·x··-·2x·x·x··+·3x·x··-·25x·x·x··-·23x·x·x··+·4x·x·x··+·27x·x·x··-·14x·x·x··-·9x·x··-·2x·x··+·10x·x··-·6x·x··-·10x·x··+·3x·x··-·2x·x62 ······················8x·x··-·12x·x··+·24x··-·11x·x··+·17x·x·x··-·24x·x··-·10x·x··+·11x·x··-·3x··-·6x·x··+·28x·x·x··-·70x·x··-·21x·x·x··+·47x·x·x··-·13x·x··-·14x·x··+·66x·x··-·22x·x··-·20x··+·2x·x··-·2x·x·x··-·10x·x··-·11x·x·x··+·8x·x·x··-·5x·x··+·3x·x·x··+·23x·x·x··-·11x·x·x··-·12x·x··+·3x·x··-·3x·x··-·2x·x··+·3x·x··+·x··-·11x·x··+·14x·x·x··+·34x·x··-·6x·x·x··-·16x·x·x··+·3x·x··-·15x·x·x··-·66x·x·x··+·12x·x·x··+·30x·x··-·19x·x·x··+·2x·x·x··-·5x·x·x··-·2x·x·x··-·7x·x··+·6x·x··+·21x·x··-·3x·x··-·21x·x··+·x·x··+·5x··-·8x·x··+·7x·x·x··-·32x·x··-·13x·x·x··+·28x·x·x··-·9x·x··+·70x·x·x··-·27x·x·x··-·36x·x··+·x·x·x··+·4x·x·x··-·7x·x·x··-·2x·x·x··+·3x·x··-·25x·x·x··-·23x·x·x··+·4x·x·x··+·27x·x·x··-·14x·x·x··-·9x·x··-·2x·x··+·10x·x··-·6x·x··-·10x·x··+·3x·x··-·2x·x
63 ························0·1······0·1······1······0·2······0·1·2······1·2······0·2······1·2·····2·····0·3······0·1·3······1·3······0·2·3······1·2·3······2·3······0·3······1·3······2·3······3·····0·4·····0·1·4······1·4······0·2·4·····1·2·4·····2·4·····0·3·4······1·3·4······2·3·4······3·4·····0·4·····1·4·····2·4·····3·4····4······0·5······0·1·5······1·5·····0·2·5······1·2·5·····2·5······0·3·5······1·3·5······2·3·5······3·5······0·4·5·····1·4·5·····2·4·5·····3·4·5·····4·5·····0·5······1·5·····2·5······3·5····4·5·····5·····0·6·····0·1·6······1·6······0·2·6······1·2·6·····2·6······1·3·6······2·3·6······3·6····0·4·6·····1·4·6·····2·4·6·····3·4·6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6······1·6·····2·6······3·6·····4·6·····5·663 ························0·1······0·1······1······0·2······0·1·2······1·2······0·2······1·2·····2·····0·3······0·1·3······1·3······0·2·3······1·2·3······2·3······0·3······1·3······2·3······3·····0·4·····0·1·4······1·4······0·2·4·····1·2·4·····2·4·····0·3·4······1·3·4······2·3·4······3·4·····0·4·····1·4·····2·4·····3·4····4······0·5······0·1·5······1·5·····0·2·5······1·2·5·····2·5······0·3·5······1·3·5······2·3·5······3·5······0·4·5·····1·4·5·····2·4·5·····3·4·5·····4·5·····0·5······1·5·····2·5······3·5····4·5·····5·····0·6·····0·1·6······1·6······0·2·6······1·2·6·····2·6······1·3·6······2·3·6······3·6····0·4·6·····1·4·6·····2·4·6·····3·4·6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6······1·6·····2·6······3·6·····4·6·····5·6
64 ·····················}64 ·····················}
  
65 o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)65 o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)
  
66 i2·:·time·describe·oo66 i2·:·time·describe·oo
67 ·--·used·0.0159863s·(cpu);·0.0149846s·(thread);·0s·(gc)67 ·--·used·0.0153394s·(cpu);·0.0173588s·(thread);·0s·(gc)
  
68 o2·=·rational·map·defined·by·forms·of·degree·368 o2·=·rational·map·defined·by·forms·of·degree·3
69 ·····source·variety:·PP^669 ·····source·variety:·PP^6
70 ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^970 ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9
71 ·····dominance:·true71 ·····dominance:·true
72 ·····birationality:·true72 ·····birationality:·true
73 ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8}73 ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8}
1.32 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_special__Quadratic__Transformation.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·17292005823766787051 --·-*-·M2-comint·-*-·hash:·1729200582376678705
  
2 i1·:·time·specialQuadraticTransformation·42 i1·:·time·specialQuadraticTransformation·4
3 ·--·used·0.0533759s·(cpu);·0.0565336s·(thread);·0s·(gc)3 ·--·used·0.0699145s·(cpu);·0.0699369s·(thread);·0s·(gc)
  
4 o1·=·--·rational·map·--4 o1·=·--·rational·map·--
5 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])5 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
6 ······················0···1···2···3···4···5···6···7···86 ······················0···1···2···3···4···5···6···7···8
7 ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by7 ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by
8 ····································0···1···2···3···4···5···6···7···8···98 ····································0···1···2···3···4···5···6···7···8···9
9 ·············{9 ·············{
Offset 50, 15 lines modifiedOffset 50, 15 lines modified
50 ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x50 ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x
51 ·······················0·1····0·4····3·6····4·6····6····5·751 ·······················0·1····0·4····3·6····4·6····6····5·7
52 ·····················}52 ·····················}
  
53 o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)53 o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)
  
54 i2·:·time·describe·oo54 i2·:·time·describe·oo
55 ·--·used·0.00796617s·(cpu);·0.00563027s·(thread);·0s·(gc)55 ·--·used·0.00799664s·(cpu);·0.007039s·(thread);·0s·(gc)
  
56 o2·=·rational·map·defined·by·forms·of·degree·256 o2·=·rational·map·defined·by·forms·of·degree·2
57 ·····source·variety:·PP^857 ·····source·variety:·PP^8
58 ·····target·variety:·hypersurface·of·degree·3·in·PP^958 ·····target·variety:·hypersurface·of·degree·3·in·PP^9
59 ·····dominance:·true59 ·····dominance:·true
60 ·····birationality:·true60 ·····birationality:·true
61 ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3}61 ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3}
1.41 KB
./usr/share/doc/Macaulay2/Cremona/example-output/_to__External__String_lp__Rational__Map_rp.out
    
Offset 7, 34 lines modifiedOffset 7, 34 lines modified
7 i2·:·str·=·toExternalString·phi;7 i2·:·str·=·toExternalString·phi;
  
8 i3·:·#str8 i3·:·#str
  
9 o3·=·69279 o3·=·6927
  
10 i4·:·time·phi'·=·value·str;10 i4·:·time·phi'·=·value·str;
11 ·--·used·0.0199694s·(cpu);·0.0181479s·(thread);·0s·(gc)11 ·--·used·0.0239217s·(cpu);·0.0234164s·(thread);·0s·(gc)
  
12 o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)12 o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)
  
13 i5·:·time·describe·phi'13 i5·:·time·describe·phi'
14 ·--·used·0.00186898s·(cpu);·0.00405821s·(thread);·0s·(gc)14 ·--·used·0.00300101s·(cpu);·0.00592472s·(thread);·0s·(gc)
  
15 o5·=·rational·map·defined·by·forms·of·degree·315 o5·=·rational·map·defined·by·forms·of·degree·3
16 ·····source·variety:·PP^316 ·····source·variety:·PP^3
17 ·····target·variety:·smooth·quadric·hypersurface·in·PP^417 ·····target·variety:·smooth·quadric·hypersurface·in·PP^4
18 ·····dominance:·true18 ·····dominance:·true
19 ·····birationality:·true·(the·inverse·map·is·already·calculated)19 ·····birationality:·true·(the·inverse·map·is·already·calculated)
20 ·····projective·degrees:·{1,·3,·4,·2}20 ·····projective·degrees:·{1,·3,·4,·2}
21 ·····number·of·minimal·representatives:·121 ·····number·of·minimal·representatives:·1
22 ·····dimension·base·locus:·122 ·····dimension·base·locus:·1
23 ·····degree·base·locus:·523 ·····degree·base·locus:·5
24 ·····coefficient·ring:·ZZ/3333124 ·····coefficient·ring:·ZZ/33331
  
25 i6·:·time·describe·inverse·phi'25 i6·:·time·describe·inverse·phi'
26 ·--·used·0.00171302s·(cpu);·0.0034666s·(thread);·0s·(gc)26 ·--·used·0.00452781s·(cpu);·0.00454474s·(thread);·0s·(gc)
  
27 o6·=·rational·map·defined·by·forms·of·degree·227 o6·=·rational·map·defined·by·forms·of·degree·2
28 ·····source·variety:·smooth·quadric·hypersurface·in·PP^428 ·····source·variety:·smooth·quadric·hypersurface·in·PP^4
29 ·····target·variety:·PP^329 ·····target·variety:·PP^3
30 ·····dominance:·true30 ·····dominance:·true
31 ·····birationality:·true·(the·inverse·map·is·already·calculated)31 ·····birationality:·true·(the·inverse·map·is·already·calculated)
32 ·····projective·degrees:·{2,·4,·3,·1}32 ·····projective·degrees:·{2,·4,·3,·1}
3.56 KB
./usr/share/doc/Macaulay2/Cremona/html/___Chern__Schwartz__Mac__Pherson.html
    
Offset 97, 29 lines modifiedOffset 97, 29 lines modified
97 o2·:·Ideal·of·GF·78125[x·..x·]97 o2·:·Ideal·of·GF·78125[x·..x·]
98 ························0···4</code></pre>98 ························0···4</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i3·:·time·ChernSchwartzMacPherson·C103 ··············<pre><code·class="language-macaulay2">i3·:·time·ChernSchwartzMacPherson·C
104 ·--·used·1.15281s·(cpu);·0.776751s·(thread);·0s·(gc)104 ·--·used·1.4464s·(cpu);·0.930233s·(thread);·0s·(gc)
  
105 ·······4·····3·····2105 ·······4·····3·····2
106 o3·=·3H··+·5H··+·3H106 o3·=·3H··+·5H··+·3H
  
107 ·····ZZ[H]107 ·····ZZ[H]
108 o3·:·-----108 o3·:·-----
109 ········5109 ········5
110 ·······H</code></pre>110 ·······H</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i4·:·time·ChernSchwartzMacPherson(C,Certify=>true)115 ··············<pre><code·class="language-macaulay2">i4·:·time·ChernSchwartzMacPherson(C,Certify=>true)
116 ·--·used·2.44728s·(cpu);·0.862882s·(thread);·0s·(gc)116 ·--·used·2.46997s·(cpu);·0.928831s·(thread);·0s·(gc)
117 Certify:·output·certified!117 Certify:·output·certified!
  
118 ·······4·····3·····2118 ·······4·····3·····2
119 o4·=·3H··+·5H··+·3H119 o4·=·3H··+·5H··+·3H
  
120 ·····ZZ[H]120 ·····ZZ[H]
121 o4·:·-----121 o4·:·-----
Offset 167, 29 lines modifiedOffset 167, 29 lines modified
167 o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]167 o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]
168 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre>168 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre>
169 ············</td>169 ············</td>
170 ··········</tr>170 ··········</tr>
171 ··········<tr>171 ··········<tr>
172 ············<td>172 ············<td>
173 ··············<pre><code·class="language-macaulay2">i9·:·time·ChernClass·G173 ··············<pre><code·class="language-macaulay2">i9·:·time·ChernClass·G
174 ·--·used·0.165292s·(cpu);·0.135278s·(thread);·0s·(gc)174 ·--·used·0.184597s·(cpu);·0.13865s·(thread);·0s·(gc)
  
175 ········9······8······7······6······5······4·····3175 ········9······8······7······6······5······4·····3
176 o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H176 o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H
  
177 ·····ZZ[H]177 ·····ZZ[H]
178 o9·:·-----178 o9·:·-----
179 ·······10179 ·······10
180 ······H</code></pre>180 ······H</code></pre>
181 ············</td>181 ············</td>
182 ··········</tr>182 ··········</tr>
183 ··········<tr>183 ··········<tr>
184 ············<td>184 ············<td>
185 ··············<pre><code·class="language-macaulay2">i10·:·time·ChernClass(G,Certify=>true)185 ··············<pre><code·class="language-macaulay2">i10·:·time·ChernClass(G,Certify=>true)
186 ·--·used·0.295023s·(cpu);·0.0656588s·(thread);·0s·(gc)186 ·--·used·0.276832s·(cpu);·0.0541502s·(thread);·0s·(gc)
187 Certify:·output·certified!187 Certify:·output·certified!
  
188 ·········9······8······7······6······5······4·····3188 ·········9······8······7······6······5······4·····3
189 o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H189 o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H
  
190 ······ZZ[H]190 ······ZZ[H]
191 o10·:·-----191 o10·:·-----
1.55 KB
html2text {}
    
Offset 39, 25 lines modifiedOffset 39, 25 lines modified
39 ···············2···························239 ···············2···························2
40 o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·)40 o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·)
41 ···············1····0·2·····1·2····0·3·····2····1·341 ···············1····0·2·····1·2····0·3·····2····1·3
  
42 o2·:·Ideal·of·GF·78125[x·..x·]42 o2·:·Ideal·of·GF·78125[x·..x·]
43 ························0···443 ························0···4
44 i3·:·time·ChernSchwartzMacPherson·C44 i3·:·time·ChernSchwartzMacPherson·C
45 ·--·used·1.15281s·(cpu);·0.776751s·(thread);·0s·(gc)45 ·--·used·1.4464s·(cpu);·0.930233s·(thread);·0s·(gc)
  
46 ·······4·····3·····246 ·······4·····3·····2
47 o3·=·3H··+·5H··+·3H47 o3·=·3H··+·5H··+·3H
  
48 ·····ZZ[H]48 ·····ZZ[H]
49 o3·:·-----49 o3·:·-----
50 ········550 ········5
51 ·······H51 ·······H
52 i4·:·time·ChernSchwartzMacPherson(C,Certify=>true)52 i4·:·time·ChernSchwartzMacPherson(C,Certify=>true)
53 ·--·used·2.44728s·(cpu);·0.862882s·(thread);·0s·(gc)53 ·--·used·2.46997s·(cpu);·0.928831s·(thread);·0s·(gc)
54 Certify:·output·certified!54 Certify:·output·certified!
  
55 ·······4·····3·····255 ·······4·····3·····2
56 o4·=·3H··+·5H··+·3H56 o4·=·3H··+·5H··+·3H
  
57 ·····ZZ[H]57 ·····ZZ[H]
58 o4·:·-----58 o4·:·-----
Offset 88, 25 lines modifiedOffset 88, 25 lines modified
88 ········0,2·1,3····0,1·2,388 ········0,2·1,3····0,1·2,3
  
89 ················ZZ89 ················ZZ
90 o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p90 o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p
91 ]91 ]
92 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,492 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4
93 i9·:·time·ChernClass·G93 i9·:·time·ChernClass·G
94 ·--·used·0.165292s·(cpu);·0.135278s·(thread);·0s·(gc)94 ·--·used·0.184597s·(cpu);·0.13865s·(thread);·0s·(gc)
  
95 ········9······8······7······6······5······4·····395 ········9······8······7······6······5······4·····3
96 o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H96 o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H
  
97 ·····ZZ[H]97 ·····ZZ[H]
98 o9·:·-----98 o9·:·-----
99 ·······1099 ·······10
100 ······H100 ······H
101 i10·:·time·ChernClass(G,Certify=>true)101 i10·:·time·ChernClass(G,Certify=>true)
102 ·--·used·0.295023s·(cpu);·0.0656588s·(thread);·0s·(gc)102 ·--·used·0.276832s·(cpu);·0.0541502s·(thread);·0s·(gc)
103 Certify:·output·certified!103 Certify:·output·certified!
  
104 ·········9······8······7······6······5······4·····3104 ·········9······8······7······6······5······4·····3
105 o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H105 o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H
  
106 ······ZZ[H]106 ······ZZ[H]
107 o10·:·-----107 o10·:·-----
1.9 KB
./usr/share/doc/Macaulay2/Cremona/html/___Euler__Characteristic.html
    
Offset 85, 23 lines modifiedOffset 85, 23 lines modified
85 o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]85 o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···]
86 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre>86 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i2·:·time·EulerCharacteristic·I91 ··············<pre><code·class="language-macaulay2">i2·:·time·EulerCharacteristic·I
92 ·--·used·0.21929s·(cpu);·0.129003s·(thread);·0s·(gc)92 ·--·used·0.256095s·(cpu);·0.158894s·(thread);·0s·(gc)
  
93 o2·=·10</code></pre>93 o2·=·10</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i3·:·time·EulerCharacteristic(I,Certify=>true)98 ··············<pre><code·class="language-macaulay2">i3·:·time·EulerCharacteristic(I,Certify=>true)
99 ·--·used·0.322006s·(cpu);·0.0459866s·(thread);·0s·(gc)99 ·--·used·0.191015s·(cpu);·0.0306611s·(thread);·0s·(gc)
100 Certify:·output·certified!100 Certify:·output·certified!
  
101 o3·=·10</code></pre>101 o3·=·10</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ········</table>104 ········</table>
105 ······</div>105 ······</div>
926 B
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Offset 31, 19 lines modifiedOffset 31, 19 lines modified
31 i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181);31 i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181);
  
32 ················ZZ32 ················ZZ
33 o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p33 o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p
34 ]34 ]
35 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,435 ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4
36 i2·:·time·EulerCharacteristic·I36 i2·:·time·EulerCharacteristic·I
37 ·--·used·0.21929s·(cpu);·0.129003s·(thread);·0s·(gc)37 ·--·used·0.256095s·(cpu);·0.158894s·(thread);·0s·(gc)
  
38 o2·=·1038 o2·=·10
39 i3·:·time·EulerCharacteristic(I,Certify=>true)39 i3·:·time·EulerCharacteristic(I,Certify=>true)
40 ·--·used·0.322006s·(cpu);·0.0459866s·(thread);·0s·(gc)40 ·--·used·0.191015s·(cpu);·0.0306611s·(thread);·0s·(gc)
41 Certify:·output·certified!41 Certify:·output·certified!
  
42 o3·=·1042 o3·=·10
43 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*43 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
44 No·test·is·made·to·see·if·the·projective·variety·is·smooth.44 No·test·is·made·to·see·if·the·projective·variety·is·smooth.
45 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*45 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
46 ····*·_\x8e_\x8u_\x8l_\x8e_\x8r_\x8(_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·topological·Euler·characteristic·of·a46 ····*·_\x8e_\x8u_\x8l_\x8e_\x8r_\x8(_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·topological·Euler·characteristic·of·a
2.2 KB
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Offset 86, 15 lines modifiedOffset 86, 15 lines modified
86 ·····target·variety:·PP^586 ·····target·variety:·PP^5
87 ·····coefficient·ring:·QQ</code></pre>87 ·····coefficient·ring:·QQ</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i4·:·time·phi!·;92 ··············<pre><code·class="language-macaulay2">i4·:·time·phi!·;
93 ·--·used·0.360888s·(cpu);·0.110237s·(thread);·0s·(gc)93 ·--·used·0.306406s·(cpu);·0.0872304s·(thread);·0s·(gc)
  
94 o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))</code></pre>94 o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i5·:·describe·phi99 ··············<pre><code·class="language-macaulay2">i5·:·describe·phi
Offset 127, 15 lines modifiedOffset 127, 15 lines modified
127 ·····target·variety:·PP^5127 ·····target·variety:·PP^5
128 ·····coefficient·ring:·QQ</code></pre>128 ·····coefficient·ring:·QQ</code></pre>
129 ············</td>129 ············</td>
130 ··········</tr>130 ··········</tr>
131 ··········<tr>131 ··········<tr>
132 ············<td>132 ············<td>
133 ··············<pre><code·class="language-macaulay2">i9·:·time·phi!·;133 ··············<pre><code·class="language-macaulay2">i9·:·time·phi!·;
134 ·--·used·0.369233s·(cpu);·0.0678051s·(thread);·0s·(gc)134 ·--·used·0.314867s·(cpu);·0.0792633s·(thread);·0s·(gc)
  
135 o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)</code></pre>135 o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ··········<tr>138 ··········<tr>
139 ············<td>139 ············<td>
140 ··············<pre><code·class="language-macaulay2">i10·:·describe·phi140 ··············<pre><code·class="language-macaulay2">i10·:·describe·phi
1000 B
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Offset 21, 15 lines modifiedOffset 21, 15 lines modified
21 i3·:·describe·phi21 i3·:·describe·phi
  
22 o3·=·rational·map·defined·by·forms·of·degree·222 o3·=·rational·map·defined·by·forms·of·degree·2
23 ·····source·variety:·PP^523 ·····source·variety:·PP^5
24 ·····target·variety:·PP^524 ·····target·variety:·PP^5
25 ·····coefficient·ring:·QQ25 ·····coefficient·ring:·QQ
26 i4·:·time·phi!·;26 i4·:·time·phi!·;
27 ·--·used·0.360888s·(cpu);·0.110237s·(thread);·0s·(gc)27 ·--·used·0.306406s·(cpu);·0.0872304s·(thread);·0s·(gc)
  
28 o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))28 o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))
29 i5·:·describe·phi29 i5·:·describe·phi
  
30 o5·=·rational·map·defined·by·forms·of·degree·230 o5·=·rational·map·defined·by·forms·of·degree·2
31 ·····source·variety:·PP^531 ·····source·variety:·PP^5
32 ·····target·variety:·PP^532 ·····target·variety:·PP^5
Offset 47, 15 lines modifiedOffset 47, 15 lines modified
47 i8·:·describe·phi47 i8·:·describe·phi
  
48 o8·=·rational·map·defined·by·forms·of·degree·248 o8·=·rational·map·defined·by·forms·of·degree·2
49 ·····source·variety:·PP^449 ·····source·variety:·PP^4
50 ·····target·variety:·PP^550 ·····target·variety:·PP^5
51 ·····coefficient·ring:·QQ51 ·····coefficient·ring:·QQ
52 i9·:·time·phi!·;52 i9·:·time·phi!·;
53 ·--·used·0.369233s·(cpu);·0.0678051s·(thread);·0s·(gc)53 ·--·used·0.314867s·(cpu);·0.0792633s·(thread);·0s·(gc)
  
54 o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)54 o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)
55 i10·:·describe·phi55 i10·:·describe·phi
  
56 o10·=·rational·map·defined·by·forms·of·degree·256 o10·=·rational·map·defined·by·forms·of·degree·2
57 ······source·variety:·PP^457 ······source·variety:·PP^4
58 ······target·variety:·PP^558 ······target·variety:·PP^5
1.35 KB
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Offset 153, 15 lines modifiedOffset 153, 15 lines modified
  
153 o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre>153 o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre>
154 ············</td>154 ············</td>
155 ··········</tr>155 ··········</tr>
156 ··········<tr>156 ··········<tr>
157 ············<td>157 ············<td>
158 ··············<pre><code·class="language-macaulay2">i6·:·time·phi^**·q158 ··············<pre><code·class="language-macaulay2">i6·:·time·phi^**·q
159 ·--·used·0.195335s·(cpu);·0.145455s·(thread);·0s·(gc)159 ·--·used·0.270708s·(cpu);·0.191903s·(thread);·0s·(gc)
  
160 ················-e········-d········-c········-b········-a160 ················-e········-d········-c········-b········-a
161 o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v)161 o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v)
162 ·················f·········f·········f·········f·········f162 ·················f·········f·········f·········f·········f
  
163 o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre>163 o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre>
164 ············</td>164 ············</td>
615 B
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Offset 82, 15 lines modifiedOffset 82, 15 lines modified
82 ··············2·················282 ··············2·················2
83 ·····-·a*c·+·e·········-·b*c·+·f83 ·····-·a*c·+·e·········-·b*c·+·f
84 ·····----------*v,·x·+·----------*v)84 ·····----------*v,·x·+·----------*v)
85 ······d*e·-·a*f·········d*e·-·a*f85 ······d*e·-·a*f·········d*e·-·a*f
  
86 o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]86 o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]
87 i6·:·time·phi^**·q87 i6·:·time·phi^**·q
88 ·--·used·0.195335s·(cpu);·0.145455s·(thread);·0s·(gc)88 ·--·used·0.270708s·(cpu);·0.191903s·(thread);·0s·(gc)
  
89 ················-e········-d········-c········-b········-a89 ················-e········-d········-c········-b········-a
90 o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v)90 o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v)
91 ·················f·········f·········f·········f·········f91 ·················f·········f·········f·········f·········f
  
92 o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]92 o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]
93 i7·:·oo·==·p93 i7·:·oo·==·p
8.84 KB
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Offset 134, 58 lines modifiedOffset 134, 58 lines modified
134 ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x134 ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x
135 ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7</code></pre>135 ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ··········<tr>138 ··········<tr>
139 ············<td>139 ············<td>
140 ··············<pre><code·class="language-macaulay2">i4·:·time·SegreClass·X140 ··············<pre><code·class="language-macaulay2">i4·:·time·SegreClass·X
141 ·--·used·0.380436s·(cpu);·0.351659s·(thread);·0s·(gc)141 ·--·used·0.429616s·(cpu);·0.382741s·(thread);·0s·(gc)
  
142 ··········7········6·······5·······4······3142 ··········7········6·······5·······4······3
143 o4·=·3240H··-·1188H··+·396H··-·114H··+·24H143 o4·=·3240H··-·1188H··+·396H··-·114H··+·24H
  
144 ·····ZZ[H]144 ·····ZZ[H]
145 o4·:·-----145 o4·:·-----
146 ········8146 ········8
147 ·······H</code></pre>147 ·······H</code></pre>
148 ············</td>148 ············</td>
149 ··········</tr>149 ··········</tr>
150 ··········<tr>150 ··········<tr>
151 ············<td>151 ············<td>
152 ··············<pre><code·class="language-macaulay2">i5·:·time·SegreClass·lift(X,P7)152 ··············<pre><code·class="language-macaulay2">i5·:·time·SegreClass·lift(X,P7)
153 ·--·used·0.332568s·(cpu);·0.260207s·(thread);·0s·(gc)153 ·--·used·0.38557s·(cpu);·0.284851s·(thread);·0s·(gc)
  
154 ··········7········6·······5······4······3154 ··········7········6·······5······4······3
155 o5·=·2816H··-·1056H··+·324H··-·78H··+·12H155 o5·=·2816H··-·1056H··+·324H··-·78H··+·12H
  
156 ·····ZZ[H]156 ·····ZZ[H]
157 o5·:·-----157 o5·:·-----
158 ········8158 ········8
159 ·······H</code></pre>159 ·······H</code></pre>
160 ············</td>160 ············</td>
161 ··········</tr>161 ··········</tr>
162 ··········<tr>162 ··········<tr>
163 ············<td>163 ············<td>
164 ··············<pre><code·class="language-macaulay2">i6·:·time·SegreClass(X,Certify=>true)164 ··············<pre><code·class="language-macaulay2">i6·:·time·SegreClass(X,Certify=>true)
165 ·--·used·0.318387s·(cpu);·0.0489743s·(thread);·0s·(gc)165 ·--·used·0.247191s·(cpu);·0.0462595s·(thread);·0s·(gc)
166 Certify:·output·certified!166 Certify:·output·certified!
  
167 ··········7········6·······5·······4······3167 ··········7········6·······5·······4······3
168 o6·=·3240H··-·1188H··+·396H··-·114H··+·24H168 o6·=·3240H··-·1188H··+·396H··-·114H··+·24H
  
169 ·····ZZ[H]169 ·····ZZ[H]
170 o6·:·-----170 o6·:·-----
171 ········8171 ········8
172 ·······H</code></pre>172 ·······H</code></pre>
173 ············</td>173 ············</td>
174 ··········</tr>174 ··········</tr>
175 ··········<tr>175 ··········<tr>
176 ············<td>176 ············<td>
177 ··············<pre><code·class="language-macaulay2">i7·:·time·SegreClass(lift(X,P7),Certify=>true)177 ··············<pre><code·class="language-macaulay2">i7·:·time·SegreClass(lift(X,P7),Certify=>true)
178 ·--·used·0.373743s·(cpu);·0.119007s·(thread);·0s·(gc)178 ·--·used·0.382237s·(cpu);·0.14173s·(thread);·0s·(gc)
179 Certify:·output·certified!179 Certify:·output·certified!
  
180 ··········7········6·······5······4······3180 ··········7········6·······5······4······3
181 o7·=·2816H··-·1056H··+·324H··-·78H··+·12H181 o7·=·2816H··-·1056H··+·324H··-·78H··+·12H
  
182 ·····ZZ[H]182 ·····ZZ[H]
183 o7·:·-----183 o7·:·-----
Offset 213, 15 lines modifiedOffset 213, 15 lines modified
  
213 o9·:·PolynomialRing</code></pre>213 o9·:·PolynomialRing</code></pre>
214 ············</td>214 ············</td>
215 ··········</tr>215 ··········</tr>
216 ··········<tr>216 ··········<tr>
217 ············<td>217 ············<td>
218 ··············<pre><code·class="language-macaulay2">i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2)218 ··············<pre><code·class="language-macaulay2">i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2)
219 ·--·used·0.111315s·(cpu);·0.0726621s·(thread);·0s·(gc)219 ·--·used·0.0557109s·(cpu);·0.0553453s·(thread);·0s·(gc)
  
220 ························································ZZ220 ························································ZZ
221 ······················································------[y·..y·]221 ······················································------[y·..y·]
222 ······················································100003··0···9················································ZZ··············2······························2222 ······················································100003··0···9················································ZZ··············2······························2
223 o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·})223 o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·})
224 ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9224 ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9
225 ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5225 ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5
Offset 233, 15 lines modifiedOffset 233, 15 lines modified
233 ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6233 ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6
234 ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre>234 ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre>
235 ············</td>235 ············</td>
236 ··········</tr>236 ··········</tr>
237 ··········<tr>237 ··········<tr>
238 ············<td>238 ············<td>
239 ··············<pre><code·class="language-macaulay2">i11·:·time·SegreClass·phi239 ··············<pre><code·class="language-macaulay2">i11·:·time·SegreClass·phi
240 ·--·used·0.269797s·(cpu);·0.198307s·(thread);·0s·(gc)240 ·--·used·0.317858s·(cpu);·0.2022s·(thread);·0s·(gc)
  
241 ·········9······8······7······6·····5241 ·········9······8······7······6·····5
242 o11·=·23H··-·42H··+·36H··-·22H··+·9H242 o11·=·23H··-·42H··+·36H··-·22H··+·9H
  
243 ······ZZ[H]243 ······ZZ[H]
244 o11·:·-----244 o11·:·-----
245 ········10245 ········10
Offset 267, 30 lines modifiedOffset 267, 30 lines modified
267 ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre>267 ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre>
268 ············</td>268 ············</td>
269 ··········</tr>269 ··········</tr>
270 ··········<tr>270 ··········<tr>
271 ············<td>271 ············<td>
272 ··············<pre><code·class="language-macaulay2">i13·:·--·Segre·class·of·B·in·G(1,4)272 ··············<pre><code·class="language-macaulay2">i13·:·--·Segre·class·of·B·in·G(1,4)
273 ······time·SegreClass·B273 ······time·SegreClass·B
274 ·--·used·0.247629s·(cpu);·0.213747s·(thread);·0s·(gc)274 ·--·used·0.325561s·(cpu);·0.231201s·(thread);·0s·(gc)
  
275 ·········9······8······7······6·····5275 ·········9······8······7······6·····5
276 o13·=·23H··-·42H··+·36H··-·22H··+·9H276 o13·=·23H··-·42H··+·36H··-·22H··+·9H
  
277 ······ZZ[H]277 ······ZZ[H]
278 o13·:·-----278 o13·:·-----
279 ········10279 ········10
280 ·······H</code></pre>280 ·······H</code></pre>
281 ············</td>281 ············</td>
282 ··········</tr>282 ··········</tr>
283 ··········<tr>283 ··········<tr>
284 ············<td>284 ············<td>
285 ··············<pre><code·class="language-macaulay2">i14·:·--·Segre·class·of·B·in·P^9285 ··············<pre><code·class="language-macaulay2">i14·:·--·Segre·class·of·B·in·P^9
286 ······time·SegreClass·lift(B,ambient·ring·B)286 ······time·SegreClass·lift(B,ambient·ring·B)
287 ·--·used·0.801144s·(cpu);·0.643097s·(thread);·0s·(gc)287 ·--·used·0.884823s·(cpu);·0.685533s·(thread);·0s·(gc)
  
288 ···········9·······8·······7······6·····5288 ···········9·······8·······7······6·····5
289 o14·=·2764H··-·984H··+·294H··-·67H··+·9H289 o14·=·2764H··-·984H··+·294H··-·67H··+·9H
  
290 ······ZZ[H]290 ······ZZ[H]
291 o14·:·-----291 o14·:·-----
292 ········10292 ········10
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Offset 81, 46 lines modifiedOffset 81, 46 lines modified
81 ···············2·2················2·2········································281 ···············2·2················2·2········································2
82 2····················································2·282 2····················································2·2
83 ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x83 ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x
84 +·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x84 +·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x
85 ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····185 ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1
86 6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·786 6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7
87 i4·:·time·SegreClass·X87 i4·:·time·SegreClass·X
88 ·--·used·0.380436s·(cpu);·0.351659s·(thread);·0s·(gc)88 ·--·used·0.429616s·(cpu);·0.382741s·(thread);·0s·(gc)
  
89 ··········7········6·······5·······4······389 ··········7········6·······5·······4······3
90 o4·=·3240H··-·1188H··+·396H··-·114H··+·24H90 o4·=·3240H··-·1188H··+·396H··-·114H··+·24H
  
91 ·····ZZ[H]91 ·····ZZ[H]
92 o4·:·-----92 o4·:·-----
93 ········893 ········8
94 ·······H94 ·······H
95 i5·:·time·SegreClass·lift(X,P7)95 i5·:·time·SegreClass·lift(X,P7)
96 ·--·used·0.332568s·(cpu);·0.260207s·(thread);·0s·(gc)96 ·--·used·0.38557s·(cpu);·0.284851s·(thread);·0s·(gc)
  
97 ··········7········6·······5······4······397 ··········7········6·······5······4······3
98 o5·=·2816H··-·1056H··+·324H··-·78H··+·12H98 o5·=·2816H··-·1056H··+·324H··-·78H··+·12H
  
99 ·····ZZ[H]99 ·····ZZ[H]
100 o5·:·-----100 o5·:·-----
101 ········8101 ········8
102 ·······H102 ·······H
103 i6·:·time·SegreClass(X,Certify=>true)103 i6·:·time·SegreClass(X,Certify=>true)
104 ·--·used·0.318387s·(cpu);·0.0489743s·(thread);·0s·(gc)104 ·--·used·0.247191s·(cpu);·0.0462595s·(thread);·0s·(gc)
105 Certify:·output·certified!105 Certify:·output·certified!
  
106 ··········7········6·······5·······4······3106 ··········7········6·······5·······4······3
107 o6·=·3240H··-·1188H··+·396H··-·114H··+·24H107 o6·=·3240H··-·1188H··+·396H··-·114H··+·24H
  
108 ·····ZZ[H]108 ·····ZZ[H]
109 o6·:·-----109 o6·:·-----
110 ········8110 ········8
111 ·······H111 ·······H
112 i7·:·time·SegreClass(lift(X,P7),Certify=>true)112 i7·:·time·SegreClass(lift(X,P7),Certify=>true)
113 ·--·used·0.373743s·(cpu);·0.119007s·(thread);·0s·(gc)113 ·--·used·0.382237s·(cpu);·0.14173s·(thread);·0s·(gc)
114 Certify:·output·certified!114 Certify:·output·certified!
  
115 ··········7········6·······5······4······3115 ··········7········6·······5······4······3
116 o7·=·2816H··-·1056H··+·324H··-·78H··+·12H116 o7·=·2816H··-·1056H··+·324H··-·78H··+·12H
  
117 ·····ZZ[H]117 ·····ZZ[H]
118 o7·:·-----118 o7·:·-----
Offset 141, 15 lines modifiedOffset 141, 15 lines modified
141 ·······ZZ141 ·······ZZ
142 o9·=·------[x·..x·]142 o9·=·------[x·..x·]
143 ·····100003··0···6143 ·····100003··0···6
  
144 o9·:·PolynomialRing144 o9·:·PolynomialRing
145 i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},145 i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},
146 {x_1,x_2,x_4,x_5,x_6}}),Dominant=>2)146 {x_1,x_2,x_4,x_5,x_6}}),Dominant=>2)
147 ·--·used·0.111315s·(cpu);·0.0726621s·(thread);·0s·(gc)147 ·--·used·0.0557109s·(cpu);·0.0553453s·(thread);·0s·(gc)
  
148 ························································ZZ148 ························································ZZ
149 ······················································------[y·..y·]149 ······················································------[y·..y·]
150 ······················································100003··0···9150 ······················································100003··0···9
151 ZZ··············2······························2151 ZZ··············2······························2
152 o10·=·map·(--------------------------------------------------------------------152 o10·=·map·(--------------------------------------------------------------------
153 --------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y153 --------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y
Offset 169, 15 lines modifiedOffset 169, 15 lines modified
169 o10·:·RingMap·-----------------------------------------------------------------169 o10·:·RingMap·-----------------------------------------------------------------
170 -----------------------------------·<--·------[x·..x·]170 -----------------------------------·<--·------[x·..x·]
171 ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y171 ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y
172 -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6172 -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6
173 ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6173 ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6
174 1·7····0·8···2·3····1·4····0·5174 1·7····0·8···2·3····1·4····0·5
175 i11·:·time·SegreClass·phi175 i11·:·time·SegreClass·phi
176 ·--·used·0.269797s·(cpu);·0.198307s·(thread);·0s·(gc)176 ·--·used·0.317858s·(cpu);·0.2022s·(thread);·0s·(gc)
  
177 ·········9······8······7······6·····5177 ·········9······8······7······6·····5
178 o11·=·23H··-·42H··+·36H··-·22H··+·9H178 o11·=·23H··-·42H··+·36H··-·22H··+·9H
  
179 ······ZZ[H]179 ······ZZ[H]
180 o11·:·-----180 o11·:·-----
181 ········10181 ········10
Offset 198, 26 lines modifiedOffset 198, 26 lines modified
198 ------------------------------------198 ------------------------------------
199 ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y199 ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y
200 -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)200 -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)
201 ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2201 ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2
202 6····1·7····0·8···2·3····1·4····0·5202 6····1·7····0·8···2·3····1·4····0·5
203 i13·:·--·Segre·class·of·B·in·G(1,4)203 i13·:·--·Segre·class·of·B·in·G(1,4)
204 ······time·SegreClass·B204 ······time·SegreClass·B
205 ·--·used·0.247629s·(cpu);·0.213747s·(thread);·0s·(gc)205 ·--·used·0.325561s·(cpu);·0.231201s·(thread);·0s·(gc)
  
206 ·········9······8······7······6·····5206 ·········9······8······7······6·····5
207 o13·=·23H··-·42H··+·36H··-·22H··+·9H207 o13·=·23H··-·42H··+·36H··-·22H··+·9H
  
208 ······ZZ[H]208 ······ZZ[H]
209 o13·:·-----209 o13·:·-----
210 ········10210 ········10
211 ·······H211 ·······H
212 i14·:·--·Segre·class·of·B·in·P^9212 i14·:·--·Segre·class·of·B·in·P^9
213 ······time·SegreClass·lift(B,ambient·ring·B)213 ······time·SegreClass·lift(B,ambient·ring·B)
214 ·--·used·0.801144s·(cpu);·0.643097s·(thread);·0s·(gc)214 ·--·used·0.884823s·(cpu);·0.685533s·(thread);·0s·(gc)
  
215 ···········9·······8·······7······6·····5215 ···········9·······8·······7······6·····5
216 o14·=·2764H··-·984H··+·294H··-·67H··+·9H216 o14·=·2764H··-·984H··+·294H··-·67H··+·9H
  
217 ······ZZ[H]217 ······ZZ[H]
218 o14·:·-----218 o14·:·-----
219 ········10219 ········10
8.03 KB
./usr/share/doc/Macaulay2/Cremona/html/_abstract__Rational__Map.html
    
Offset 101, 15 lines modifiedOffset 101, 15 lines modified
  
101 o3·:·PolynomialRing</code></pre>101 o3·:·PolynomialRing</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i4·:·time·psi·=·abstractRationalMap(P4,P5,f)106 ··············<pre><code·class="language-macaulay2">i4·:·time·psi·=·abstractRationalMap(P4,P5,f)
107 ·--·used·6.9485e-05s·(cpu);·0.000326031s·(thread);·0s·(gc)107 ·--·used·0.000760977s·(cpu);·0.000441147s·(thread);·0s·(gc)
  
108 o4·=·--·rational·map·--108 o4·=·--·rational·map·--
109 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])109 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])
110 ······················0···1···2···3···4110 ······················0···1···2···3···4
111 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])111 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])
112 ······················0···1···2···3···4···5112 ······················0···1···2···3···4···5
113 ·····defining·forms:·given·by·a·function113 ·····defining·forms:·given·by·a·function
Offset 119, 23 lines modifiedOffset 119, 23 lines modified
119 ··········</tr>119 ··········</tr>
120 ········</table>120 ········</table>
121 ········<p>Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">psi</span>·and·then·the·corresponding·concrete·rational·map.</p>121 ········<p>Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">psi</span>·and·then·the·corresponding·concrete·rational·map.</p>
122 ········<table·class="examples">122 ········<table·class="examples">
123 ··········<tr>123 ··········<tr>
124 ············<td>124 ············<td>
125 ··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,3)125 ··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,3)
126 ·--·used·0.160461s·(cpu);·0.116645s·(thread);·0s·(gc)126 ·--·used·0.202836s·(cpu);·0.14785s·(thread);·0s·(gc)
  
127 o5·=·2</code></pre>127 o5·=·2</code></pre>
128 ············</td>128 ············</td>
129 ··········</tr>129 ··········</tr>
130 ··········<tr>130 ··········<tr>
131 ············<td>131 ············<td>
132 ··············<pre><code·class="language-macaulay2">i6·:·time·rationalMap·psi132 ··············<pre><code·class="language-macaulay2">i6·:·time·rationalMap·psi
133 ·--·used·0.320145s·(cpu);·0.277596s·(thread);·0s·(gc)133 ·--·used·0.351476s·(cpu);·0.304661s·(thread);·0s·(gc)
  
134 o6·=·--·rational·map·--134 o6·=·--·rational·map·--
135 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])135 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])
136 ······················0···1···2···3···4136 ······················0···1···2···3···4
137 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])137 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])
138 ······················0···1···2···3···4···5138 ······················0···1···2···3···4···5
139 ·····defining·forms:·{139 ·····defining·forms:·{
Offset 233, 15 lines modifiedOffset 233, 15 lines modified
233 o13·:·Ideal·of·-----[x·..x·]233 o13·:·Ideal·of·-----[x·..x·]
234 ···············65521··0···3</code></pre>234 ···············65521··0···3</code></pre>
235 ············</td>235 ············</td>
236 ··········</tr>236 ··········</tr>
237 ··········<tr>237 ··········<tr>
238 ············<td>238 ············<td>
239 ··············<pre><code·class="language-macaulay2">i14·:·time·T·=·abstractRationalMap(I,&quot;OADP&quot;)239 ··············<pre><code·class="language-macaulay2">i14·:·time·T·=·abstractRationalMap(I,&quot;OADP&quot;)
240 ·--·used·0.108609s·(cpu);·0.066128s·(thread);·0s·(gc)240 ·--·used·0.117609s·(cpu);·0.067279s·(thread);·0s·(gc)
  
241 o14·=·--·rational·map·--241 o14·=·--·rational·map·--
242 ·····················ZZ242 ·····················ZZ
243 ······source:·Proj(-----[x·,·x·,·x·,·x·])243 ······source:·Proj(-----[x·,·x·,·x·,·x·])
244 ···················65521··0···1···2···3244 ···················65521··0···1···2···3
245 ·····················ZZ245 ·····················ZZ
246 ······target:·Proj(-----[x·,·x·,·x·,·x·])246 ······target:·Proj(-----[x·,·x·,·x·,·x·])
Offset 253, 26 lines modifiedOffset 253, 26 lines modified
253 ··········</tr>253 ··········</tr>
254 ········</table>254 ········</table>
255 ········<p>The·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">T</span>·can·be·obtained·by·the·following·command:</p>255 ········<p>The·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">T</span>·can·be·obtained·by·the·following·command:</p>
256 ········<table·class="examples">256 ········<table·class="examples">
257 ··········<tr>257 ··········<tr>
258 ············<td>258 ············<td>
259 ··············<pre><code·class="language-macaulay2">i15·:·time·projectiveDegrees(T,2)259 ··············<pre><code·class="language-macaulay2">i15·:·time·projectiveDegrees(T,2)
260 ·--·used·2.49477s·(cpu);·1.62007s·(thread);·0s·(gc)260 ·--·used·2.79982s·(cpu);·1.68088s·(thread);·0s·(gc)
  
261 o15·=·3</code></pre>261 o15·=·3</code></pre>
262 ············</td>262 ············</td>
263 ··········</tr>263 ··········</tr>
264 ········</table>264 ········</table>
265 ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·is·defined·by·linear·forms:</p>265 ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·is·defined·by·linear·forms:</p>
266 ········<table·class="examples">266 ········<table·class="examples">
267 ··········<tr>267 ··········<tr>
268 ············<td>268 ············<td>
269 ··············<pre><code·class="language-macaulay2">i16·:·time·T2·=·T·*·T269 ··············<pre><code·class="language-macaulay2">i16·:·time·T2·=·T·*·T
270 ·--·used·0.000155904s·(cpu);·2.2584e-05s·(thread);·0s·(gc)270 ·--·used·0.000154119s·(cpu);·2.6349e-05s·(thread);·0s·(gc)
  
271 o16·=·--·rational·map·--271 o16·=·--·rational·map·--
272 ·····················ZZ272 ·····················ZZ
273 ······source:·Proj(-----[x·,·x·,·x·,·x·])273 ······source:·Proj(-----[x·,·x·,·x·,·x·])
274 ···················65521··0···1···2···3274 ···················65521··0···1···2···3
275 ·····················ZZ275 ·····················ZZ
276 ······target:·Proj(-----[x·,·x·,·x·,·x·])276 ······target:·Proj(-----[x·,·x·,·x·,·x·])
Offset 281, 15 lines modifiedOffset 281, 15 lines modified
  
281 o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre>281 o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre>
282 ············</td>282 ············</td>
283 ··········</tr>283 ··········</tr>
284 ··········<tr>284 ··········<tr>
285 ············<td>285 ············<td>
286 ··············<pre><code·class="language-macaulay2">i17·:·time·projectiveDegrees(T2,2)286 ··············<pre><code·class="language-macaulay2">i17·:·time·projectiveDegrees(T2,2)
287 ·--·used·4.07831s·(cpu);·2.61383s·(thread);·0s·(gc)287 ·--·used·4.61879s·(cpu);·2.69855s·(thread);·0s·(gc)
  
288 o17·=·1</code></pre>288 o17·=·1</code></pre>
289 ············</td>289 ············</td>
290 ··········</tr>290 ··········</tr>
291 ········</table>291 ········</table>
292 ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·leaves·a·random·point·fixed:</p>292 ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·leaves·a·random·point·fixed:</p>
293 ········<table·class="examples">293 ········<table·class="examples">
Offset 322, 15 lines modifiedOffset 322, 15 lines modified
322 ··········</tr>322 ··········</tr>
323 ········</table>323 ········</table>
324 ········<p>We·now·compute·the·concrete·rational·map·corresponding·to·<span·class="tt">T</span>:</p>324 ········<p>We·now·compute·the·concrete·rational·map·corresponding·to·<span·class="tt">T</span>:</p>
325 ········<table·class="examples">325 ········<table·class="examples">
326 ··········<tr>326 ··········<tr>
327 ············<td>327 ············<td>
328 ··············<pre><code·class="language-macaulay2">i21·:·time·f·=·rationalMap·T328 ··············<pre><code·class="language-macaulay2">i21·:·time·f·=·rationalMap·T
329 ·--·used·3.30752s·(cpu);·2.20322s·(thread);·0s·(gc)329 ·--·used·3.69916s·(cpu);·2.33673s·(thread);·0s·(gc)
  
330 o21·=·--·rational·map·--330 o21·=·--·rational·map·--
331 ·····················ZZ331 ·····················ZZ
332 ······source:·Proj(-----[x·,·x·,·x·,·x·])332 ······source:·Proj(-----[x·,·x·,·x·,·x·])
333 ···················65521··0···1···2···3333 ···················65521··0···1···2···3
334 ·····················ZZ334 ·····················ZZ
335 ······target:·Proj(-----[x·,·x·,·x·,·x·])335 ······target:·Proj(-----[x·,·x·,·x·,·x·])
3.5 KB
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Offset 35, 32 lines modifiedOffset 35, 32 lines modified
35 i3·:·P5·:=·QQ[u_0..u_5]35 i3·:·P5·:=·QQ[u_0..u_5]
  
36 o3·=·QQ[u·..u·]36 o3·=·QQ[u·..u·]
37 ·········0···537 ·········0···5
  
38 o3·:·PolynomialRing38 o3·:·PolynomialRing
39 i4·:·time·psi·=·abstractRationalMap(P4,P5,f)39 i4·:·time·psi·=·abstractRationalMap(P4,P5,f)
40 ·--·used·6.9485e-05s·(cpu);·0.000326031s·(thread);·0s·(gc)40 ·--·used·0.000760977s·(cpu);·0.000441147s·(thread);·0s·(gc)
  
41 o4·=·--·rational·map·--41 o4·=·--·rational·map·--
42 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])42 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])
43 ······················0···1···2···3···443 ······················0···1···2···3···4
44 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])44 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])
45 ······················0···1···2···3···4···545 ······················0···1···2···3···4···5
46 ·····defining·forms:·given·by·a·function46 ·····defining·forms:·given·by·a·function
  
47 o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)47 o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)
48 Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·psi·and48 Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·psi·and
49 then·the·corresponding·concrete·rational·map.49 then·the·corresponding·concrete·rational·map.
50 i5·:·time·projectiveDegrees(psi,3)50 i5·:·time·projectiveDegrees(psi,3)
51 ·--·used·0.160461s·(cpu);·0.116645s·(thread);·0s·(gc)51 ·--·used·0.202836s·(cpu);·0.14785s·(thread);·0s·(gc)
  
52 o5·=·252 o5·=·2
53 i6·:·time·rationalMap·psi53 i6·:·time·rationalMap·psi
54 ·--·used·0.320145s·(cpu);·0.277596s·(thread);·0s·(gc)54 ·--·used·0.351476s·(cpu);·0.304661s·(thread);·0s·(gc)
  
55 o6·=·--·rational·map·--55 o6·=·--·rational·map·--
56 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])56 ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·])
57 ······················0···1···2···3···457 ······················0···1···2···3···4
58 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])58 ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·])
59 ······················0···1···2···3···4···559 ······················0···1···2···3···4···5
60 ·····defining·forms:·{60 ·····defining·forms:·{
Offset 139, 48 lines modifiedOffset 139, 48 lines modified
139 o13·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·)139 o13·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·)
140 ················1····0·2·····1·2····0·3·····2····1·3140 ················1····0·2·····1·2····0·3·····2····1·3
  
141 ·················ZZ141 ·················ZZ
142 o13·:·Ideal·of·-----[x·..x·]142 o13·:·Ideal·of·-----[x·..x·]
143 ···············65521··0···3143 ···············65521··0···3
144 i14·:·time·T·=·abstractRationalMap(I,"OADP")144 i14·:·time·T·=·abstractRationalMap(I,"OADP")
145 ·--·used·0.108609s·(cpu);·0.066128s·(thread);·0s·(gc)145 ·--·used·0.117609s·(cpu);·0.067279s·(thread);·0s·(gc)
  
146 o14·=·--·rational·map·--146 o14·=·--·rational·map·--
147 ·····················ZZ147 ·····················ZZ
148 ······source:·Proj(-----[x·,·x·,·x·,·x·])148 ······source:·Proj(-----[x·,·x·,·x·,·x·])
149 ···················65521··0···1···2···3149 ···················65521··0···1···2···3
150 ·····················ZZ150 ·····················ZZ
151 ······target:·Proj(-----[x·,·x·,·x·,·x·])151 ······target:·Proj(-----[x·,·x·,·x·,·x·])
152 ···················65521··0···1···2···3152 ···················65521··0···1···2···3
153 ······defining·forms:·given·by·a·function153 ······defining·forms:·given·by·a·function
  
154 o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)154 o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)
155 The·degree·of·the·forms·defining·the·abstract·map·T·can·be·obtained·by·the155 The·degree·of·the·forms·defining·the·abstract·map·T·can·be·obtained·by·the
156 following·command:156 following·command:
157 i15·:·time·projectiveDegrees(T,2)157 i15·:·time·projectiveDegrees(T,2)
158 ·--·used·2.49477s·(cpu);·1.62007s·(thread);·0s·(gc)158 ·--·used·2.79982s·(cpu);·1.68088s·(thread);·0s·(gc)
  
159 o15·=·3159 o15·=·3
160 We·verify·that·the·composition·of·T·with·itself·is·defined·by·linear·forms:160 We·verify·that·the·composition·of·T·with·itself·is·defined·by·linear·forms:
161 i16·:·time·T2·=·T·*·T161 i16·:·time·T2·=·T·*·T
162 ·--·used·0.000155904s·(cpu);·2.2584e-05s·(thread);·0s·(gc)162 ·--·used·0.000154119s·(cpu);·2.6349e-05s·(thread);·0s·(gc)
  
163 o16·=·--·rational·map·--163 o16·=·--·rational·map·--
164 ·····················ZZ164 ·····················ZZ
165 ······source:·Proj(-----[x·,·x·,·x·,·x·])165 ······source:·Proj(-----[x·,·x·,·x·,·x·])
166 ···················65521··0···1···2···3166 ···················65521··0···1···2···3
167 ·····················ZZ167 ·····················ZZ
168 ······target:·Proj(-----[x·,·x·,·x·,·x·])168 ······target:·Proj(-----[x·,·x·,·x·,·x·])
169 ···················65521··0···1···2···3169 ···················65521··0···1···2···3
170 ······defining·forms:·given·by·a·function170 ······defining·forms:·given·by·a·function
  
171 o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)171 o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)
172 i17·:·time·projectiveDegrees(T2,2)172 i17·:·time·projectiveDegrees(T2,2)
173 ·--·used·4.07831s·(cpu);·2.61383s·(thread);·0s·(gc)173 ·--·used·4.61879s·(cpu);·2.69855s·(thread);·0s·(gc)
  
174 o17·=·1174 o17·=·1
175 We·verify·that·the·composition·of·T·with·itself·leaves·a·random·point·fixed:175 We·verify·that·the·composition·of·T·with·itself·leaves·a·random·point·fixed:
176 i18·:·p·=·apply(3,i->random(ZZ/65521))|{1}176 i18·:·p·=·apply(3,i->random(ZZ/65521))|{1}
  
177 o18·=·{-6648,·-23396,·-12311,·1}177 o18·=·{-6648,·-23396,·-12311,·1}
  
Offset 193, 15 lines modifiedOffset 193, 15 lines modified
193 i20·:·T·q193 i20·:·T·q
  
194 o20·=·{-6648,·-23396,·-12311,·1}194 o20·=·{-6648,·-23396,·-12311,·1}
  
195 o20·:·List195 o20·:·List
196 We·now·compute·the·concrete·rational·map·corresponding·to·T:196 We·now·compute·the·concrete·rational·map·corresponding·to·T:
197 i21·:·time·f·=·rationalMap·T197 i21·:·time·f·=·rationalMap·T
198 ·--·used·3.30752s·(cpu);·2.20322s·(thread);·0s·(gc)198 ·--·used·3.69916s·(cpu);·2.33673s·(thread);·0s·(gc)
  
199 o21·=·--·rational·map·--199 o21·=·--·rational·map·--
200 ·····················ZZ200 ·····················ZZ
201 ······source:·Proj(-----[x·,·x·,·x·,·x·])201 ······source:·Proj(-----[x·,·x·,·x·,·x·])
202 ···················65521··0···1···2···3202 ···················65521··0···1···2···3
203 ·····················ZZ203 ·····················ZZ
204 ······target:·Proj(-----[x·,·x·,·x·,·x·])204 ······target:·Proj(-----[x·,·x·,·x·,·x·])
5.61 KB
./usr/share/doc/Macaulay2/Cremona/html/_approximate__Inverse__Map.html
    
Offset 129, 15 lines modifiedOffset 129, 15 lines modified
  
129 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)</code></pre>129 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)</code></pre>
130 ············</td>130 ············</td>
131 ··········</tr>131 ··········</tr>
132 ··········<tr>132 ··········<tr>
133 ············<td>133 ············<td>
134 ··············<pre><code·class="language-macaulay2">i3·:·time·psi·=·approximateInverseMap·phi134 ··············<pre><code·class="language-macaulay2">i3·:·time·psi·=·approximateInverseMap·phi
135 ·--·used·0.278895s·(cpu);·0.192424s·(thread);·0s·(gc)135 ·--·used·0.337968s·(cpu);·0.224819s·(thread);·0s·(gc)
136 --·approximateInverseMap:·step·1·of·10136 --·approximateInverseMap:·step·1·of·10
137 --·approximateInverseMap:·step·2·of·10137 --·approximateInverseMap:·step·2·of·10
138 --·approximateInverseMap:·step·3·of·10138 --·approximateInverseMap:·step·3·of·10
139 --·approximateInverseMap:·step·4·of·10139 --·approximateInverseMap:·step·4·of·10
140 --·approximateInverseMap:·step·5·of·10140 --·approximateInverseMap:·step·5·of·10
141 --·approximateInverseMap:·step·6·of·10141 --·approximateInverseMap:·step·6·of·10
142 --·approximateInverseMap:·step·7·of·10142 --·approximateInverseMap:·step·7·of·10
Offset 197, 15 lines modifiedOffset 197, 15 lines modified
197 ············<td>197 ············<td>
198 ··············<pre><code·class="language-macaulay2">i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)</code></pre>198 ··············<pre><code·class="language-macaulay2">i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)</code></pre>
199 ············</td>199 ············</td>
200 ··········</tr>200 ··········</tr>
201 ··········<tr>201 ··········<tr>
202 ············<td>202 ············<td>
203 ··············<pre><code·class="language-macaulay2">i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5);203 ··············<pre><code·class="language-macaulay2">i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5);
204 ·--·used·0.179434s·(cpu);·0.137873s·(thread);·0s·(gc)204 ·--·used·0.188136s·(cpu);·0.146222s·(thread);·0s·(gc)
205 --·approximateInverseMap:·step·1·of·3205 --·approximateInverseMap:·step·1·of·3
206 --·approximateInverseMap:·step·2·of·3206 --·approximateInverseMap:·step·2·of·3
207 --·approximateInverseMap:·step·3·of·3207 --·approximateInverseMap:·step·3·of·3
  
208 o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre>208 o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre>
209 ············</td>209 ············</td>
210 ··········</tr>210 ··········</tr>
Offset 292, 15 lines modifiedOffset 292, 15 lines modified
292 o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)</code></pre>292 o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)</code></pre>
293 ············</td>293 ············</td>
294 ··········</tr>294 ··········</tr>
295 ··········<tr>295 ··········<tr>
296 ············<td>296 ············<td>
297 ··············<pre><code·class="language-macaulay2">i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time·297 ··············<pre><code·class="language-macaulay2">i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time·
298 ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4)298 ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4)
299 ·--·used·1.66994s·(cpu);·1.39425s·(thread);·0s·(gc)299 ·--·used·2.08092s·(cpu);·1.75381s·(thread);·0s·(gc)
300 --·approximateInverseMap:·step·1·of·3300 --·approximateInverseMap:·step·1·of·3
301 --·approximateInverseMap:·step·2·of·3301 --·approximateInverseMap:·step·2·of·3
302 --·approximateInverseMap:·step·3·of·3302 --·approximateInverseMap:·step·3·of·3
  
303 o8·=·--·rational·map·--303 o8·=·--·rational·map·--
304 ································ZZ304 ································ZZ
305 ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by305 ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by
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363 o9·=·false</code></pre>363 o9·=·false</code></pre>
364 ············</td>364 ············</td>
365 ··········</tr>365 ··········</tr>
366 ··········<tr>366 ··········<tr>
367 ············<td>367 ············<td>
368 ··············<pre><code·class="language-macaulay2">i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify368 ··············<pre><code·class="language-macaulay2">i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify
369 ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true)369 ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true)
370 ·--·used·2.37868s·(cpu);·2.07197s·(thread);·0s·(gc)370 ·--·used·2.9864s·(cpu);·2.59223s·(thread);·0s·(gc)
371 --·approximateInverseMap:·step·1·of·3371 --·approximateInverseMap:·step·1·of·3
372 --·approximateInverseMap:·step·2·of·3372 --·approximateInverseMap:·step·2·of·3
373 --·approximateInverseMap:·step·3·of·3373 --·approximateInverseMap:·step·3·of·3
374 Certify:·output·certified!374 Certify:·output·certified!
  
375 o10·=·--·rational·map·--375 o10·=·--·rational·map·--
376 ·································ZZ376 ·································ZZ
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125 ······················x·x··-·x·x125 ······················x·x··-·x·x
126 ·······················1·2····0·4126 ·······················1·2····0·4
127 ·····················}127 ·····················}
  
128 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)128 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)
129 i3·:·time·psi·=·approximateInverseMap·phi129 i3·:·time·psi·=·approximateInverseMap·phi
130 ·--·used·0.278895s·(cpu);·0.192424s·(thread);·0s·(gc)130 ·--·used·0.337968s·(cpu);·0.224819s·(thread);·0s·(gc)
131 --·approximateInverseMap:·step·1·of·10131 --·approximateInverseMap:·step·1·of·10
132 --·approximateInverseMap:·step·2·of·10132 --·approximateInverseMap:·step·2·of·10
133 --·approximateInverseMap:·step·3·of·10133 --·approximateInverseMap:·step·3·of·10
134 --·approximateInverseMap:·step·4·of·10134 --·approximateInverseMap:·step·4·of·10
135 --·approximateInverseMap:·step·5·of·10135 --·approximateInverseMap:·step·5·of·10
136 --·approximateInverseMap:·step·6·of·10136 --·approximateInverseMap:·step·6·of·10
137 --·approximateInverseMap:·step·7·of·10137 --·approximateInverseMap:·step·7·of·10
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249 0·6·····3·6······6······0·7······1·7······3·7······4·7······6·7······7······0·8249 0·6·····3·6······6······0·7······1·7······3·7······4·7······6·7······7······0·8
250 1·8······2·8······3·8······4·8······5·8······6·8······7·8·····8250 1·8······2·8······3·8······4·8······5·8······6·8······7·8·····8
251 ·····················}251 ·····················}
  
252 o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)252 o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)
253 i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)253 i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)
254 i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5);254 i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5);
255 ·--·used·0.179434s·(cpu);·0.137873s·(thread);·0s·(gc)255 ·--·used·0.188136s·(cpu);·0.146222s·(thread);·0s·(gc)
256 --·approximateInverseMap:·step·1·of·3256 --·approximateInverseMap:·step·1·of·3
257 --·approximateInverseMap:·step·2·of·3257 --·approximateInverseMap:·step·2·of·3
258 --·approximateInverseMap:·step·3·of·3258 --·approximateInverseMap:·step·3·of·3
  
259 o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)259 o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)
260 i6·:·assert(psi·==·psi')260 i6·:·assert(psi·==·psi')
261 A·more·complicated·example·is·the·following·(here·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8M_\x8a_\x8p·takes·a·lot·of261 A·more·complicated·example·is·the·following·(here·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8M_\x8a_\x8p·takes·a·lot·of
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415 4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8415 4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8
416 5·8······6·8·····7·8416 5·8······6·8·····7·8
417 ·····················}417 ·····················}
  
418 o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)418 o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)
419 i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time419 i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time
420 ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4)420 ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4)
421 ·--·used·1.66994s·(cpu);·1.39425s·(thread);·0s·(gc)421 ·--·used·2.08092s·(cpu);·1.75381s·(thread);·0s·(gc)
422 --·approximateInverseMap:·step·1·of·3422 --·approximateInverseMap:·step·1·of·3
423 --·approximateInverseMap:·step·2·of·3423 --·approximateInverseMap:·step·2·of·3
424 --·approximateInverseMap:·step·3·of·3424 --·approximateInverseMap:·step·3·of·3
  
425 o8·=·--·rational·map·--425 o8·=·--·rational·map·--
426 ································ZZ426 ································ZZ
427 ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by427 ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by
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522 o8·:·RationalMap·(quadratic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)522 o8·:·RationalMap·(quadratic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)
523 i9·:·--·but...523 i9·:·--·but...
524 ·····phi·*·psi·==·1524 ·····phi·*·psi·==·1
  
525 o9·=·false525 o9·=·false
526 i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify526 i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify
527 ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true)527 ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true)
528 ·--·used·2.37868s·(cpu);·2.07197s·(thread);·0s·(gc)528 ·--·used·2.9864s·(cpu);·2.59223s·(thread);·0s·(gc)
529 --·approximateInverseMap:·step·1·of·3529 --·approximateInverseMap:·step·1·of·3
530 --·approximateInverseMap:·step·2·of·3530 --·approximateInverseMap:·step·2·of·3
531 --·approximateInverseMap:·step·3·of·3531 --·approximateInverseMap:·step·3·of·3
532 Certify:·output·certified!532 Certify:·output·certified!
  
533 o10·=·--·rational·map·--533 o10·=·--·rational·map·--
534 ·································ZZ534 ·································ZZ
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92 o4·:·RingMap·ringP8·&lt;--·ringP14</code></pre>92 o4·:·RingMap·ringP8·&lt;--·ringP14</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i5·:·time·degreeMap·phi97 ··············<pre><code·class="language-macaulay2">i5·:·time·degreeMap·phi
98 ·--·used·0.036535s·(cpu);·0.038007s·(thread);·0s·(gc)98 ·--·used·0.0470279s·(cpu);·0.0467061s·(thread);·0s·(gc)
  
99 o5·=·1</code></pre>99 o5·=·1</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14·104 ··············<pre><code·class="language-macaulay2">i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14·
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113 o6·:·RingMap·ringP8·&lt;--·ringP8</code></pre>113 o6·:·RingMap·ringP8·&lt;--·ringP8</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ··········<tr>116 ··········<tr>
117 ············<td>117 ············<td>
118 ··············<pre><code·class="language-macaulay2">i7·:·time·degreeMap·phi'118 ··············<pre><code·class="language-macaulay2">i7·:·time·degreeMap·phi'
119 ·--·used·0.506456s·(cpu);·0.421357s·(thread);·0s·(gc)119 ·--·used·0.604075s·(cpu);·0.468586s·(thread);·0s·(gc)
  
120 o7·=·14</code></pre>120 o7·=·14</code></pre>
121 ············</td>121 ············</td>
122 ··········</tr>122 ··········</tr>
123 ········</table>123 ········</table>
124 ······</div>124 ······</div>
125 ······<div>125 ······<div>
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266 4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6266 4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6
267 1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7267 1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7
268 2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2268 2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2
269 8········3·8·······4·8········5·8·······6·8······7·8·······8269 8········3·8·······4·8········5·8·······6·8······7·8·······8
  
270 o4·:·RingMap·ringP8·<--·ringP14270 o4·:·RingMap·ringP8·<--·ringP14
271 i5·:·time·degreeMap·phi271 i5·:·time·degreeMap·phi
272 ·--·used·0.036535s·(cpu);·0.038007s·(thread);·0s·(gc)272 ·--·used·0.0470279s·(cpu);·0.0467061s·(thread);·0s·(gc)
  
273 o5·=·1273 o5·=·1
274 i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a274 i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a
275 general·subspace·of·P^14275 general·subspace·of·P^14
276 ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have276 ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have
277 degree·equal·to·deg(G(1,5))=14)277 degree·equal·to·deg(G(1,5))=14)
278 ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14))278 ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14))
Offset 418, 15 lines modifiedOffset 418, 15 lines modified
418 0·5········1·5········2·5········3·5········4·5·······5········0·6·······1·6418 0·5········1·5········2·5········3·5········4·5·······5········0·6·······1·6
419 2·6········3·6······4·6·······5·6·······6·······0·7·······1·7·······2·7······3419 2·6········3·6······4·6·······5·6·······6·······0·7·······1·7·······2·7······3
420 7········4·7········5·7········6·7·······7·······0·8·······1·8········2·8420 7········4·7········5·7········6·7·······7·······0·8·······1·8········2·8
421 3·8·······4·8·······5·8········6·8·······7·8·······8421 3·8·······4·8·······5·8········6·8·······7·8·······8
  
422 o6·:·RingMap·ringP8·<--·ringP8422 o6·:·RingMap·ringP8·<--·ringP8
423 i7·:·time·degreeMap·phi'423 i7·:·time·degreeMap·phi'
424 ·--·used·0.506456s·(cpu);·0.421357s·(thread);·0s·(gc)424 ·--·used·0.604075s·(cpu);·0.468586s·(thread);·0s·(gc)
  
425 o7·=·14425 o7·=·14
426 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*426 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
427 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map427 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map
428 ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·projective·degrees·of·a·rational·map·between428 ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·projective·degrees·of·a·rational·map·between
429 ······projective·varieties429 ······projective·varieties
430 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·d\x8de\x8eg\x8gr\x8re\x8ee\x8eM\x8Ma\x8ap\x8p:\x8:·*\x8**\x8**\x8**\x8**\x8*430 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·d\x8de\x8eg\x8gr\x8re\x8ee\x8eM\x8Ma\x8ap\x8p:\x8:·*\x8**\x8**\x8**\x8**\x8*
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83 o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre>83 o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i4·:·time·forceImage(Phi,ideal·0_(target·Phi))88 ··············<pre><code·class="language-macaulay2">i4·:·time·forceImage(Phi,ideal·0_(target·Phi))
89 ·--·used·0.00123435s·(cpu);·0.000594134s·(thread);·0s·(gc)</code></pre>89 ·--·used·0.000161323s·(cpu);·0.000847168s·(thread);·0s·(gc)</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i5·:·Phi;94 ··············<pre><code·class="language-macaulay2">i5·:·Phi;
  
95 o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre>95 o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre>
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19 o2·:·Ideal·of·P619 o2·:·Ideal·of·P6
20 i3·:·Phi·=·rationalMap(X,Dominant=>2);20 i3·:·Phi·=·rationalMap(X,Dominant=>2);
  
21 o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of21 o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of
22 PP^9)22 PP^9)
23 i4·:·time·forceImage(Phi,ideal·0_(target·Phi))23 i4·:·time·forceImage(Phi,ideal·0_(target·Phi))
24 ·--·used·0.00123435s·(cpu);·0.000594134s·(thread);·0s·(gc)24 ·--·used·0.000161323s·(cpu);·0.000847168s·(thread);·0s·(gc)
25 i5·:·Phi;25 i5·:·Phi;
  
26 o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional26 o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional
27 subvariety·of·PP^9)27 subvariety·of·PP^9)
28 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
29 If·the·declaration·is·false,·nonsensical·answers·may·result.29 If·the·declaration·is·false,·nonsensical·answers·may·result.
30 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*30 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
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113 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>113 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ··········<tr>116 ··········<tr>
117 ············<td>117 ············<td>
118 ··············<pre><code·class="language-macaulay2">i3·:·time·(p1,p2)·=·graph·phi;118 ··············<pre><code·class="language-macaulay2">i3·:·time·(p1,p2)·=·graph·phi;
119 ·--·used·0.277032s·(cpu);·0.0546614s·(thread);·0s·(gc)</code></pre>119 ·--·used·0.199719s·(cpu);·0.0343623s·(thread);·0s·(gc)</code></pre>
120 ············</td>120 ············</td>
121 ··········</tr>121 ··········</tr>
122 ··········<tr>122 ··········<tr>
123 ············<td>123 ············<td>
124 ··············<pre><code·class="language-macaulay2">i4·:·p1124 ··············<pre><code·class="language-macaulay2">i4·:·p1
  
125 o4·=·--·rational·map·--125 o4·=·--·rational·map·--
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272 ··········</tr>272 ··········</tr>
273 ········</table>273 ········</table>
274 ········<p>When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method·returns·all·the·projections.</p>274 ········<p>When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method·returns·all·the·projections.</p>
275 ········<table·class="examples">275 ········<table·class="examples">
276 ··········<tr>276 ··········<tr>
277 ············<td>277 ············<td>
278 ··············<pre><code·class="language-macaulay2">i9·:·time·g·=·graph·p2;278 ··············<pre><code·class="language-macaulay2">i9·:·time·g·=·graph·p2;
279 ·--·used·0.287131s·(cpu);·0.0433417s·(thread);·0s·(gc)</code></pre>279 ·--·used·0.242029s·(cpu);·0.0407132s·(thread);·0s·(gc)</code></pre>
280 ············</td>280 ············</td>
281 ··········</tr>281 ··········</tr>
282 ··········<tr>282 ··········<tr>
283 ············<td>283 ············<td>
284 ··············<pre><code·class="language-macaulay2">i10·:·g_0;284 ··············<pre><code·class="language-macaulay2">i10·:·g_0;
  
285 o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)</code></pre>285 o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)</code></pre>
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50 ······················-·x··+·x·x50 ······················-·x··+·x·x
51 ·························3····2·451 ·························3····2·4
52 ·····················}52 ·····················}
  
53 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in53 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in
54 PP^5)54 PP^5)
55 i3·:·time·(p1,p2)·=·graph·phi;55 i3·:·time·(p1,p2)·=·graph·phi;
56 ·--·used·0.277032s·(cpu);·0.0546614s·(thread);·0s·(gc)56 ·--·used·0.199719s·(cpu);·0.0343623s·(thread);·0s·(gc)
57 i4·:·p157 i4·:·p1
  
58 o4·=·--·rational·map·--58 o4·=·--·rational·map·--
59 ··································ZZ·································ZZ59 ··································ZZ·································ZZ
60 ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y60 ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y
61 ,·y·,·y·,·y·,·y·])·defined·by61 ,·y·,·y·,·y·,·y·])·defined·by
62 ································190181··0···1···2···3···4··········190181··062 ································190181··0···1···2···3···4··········190181··0
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192 o8·=·{51,·28,·14,·6,·2}192 o8·=·{51,·28,·14,·6,·2}
  
193 o8·:·List193 o8·:·List
194 When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method194 When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method
195 returns·all·the·projections.195 returns·all·the·projections.
196 i9·:·time·g·=·graph·p2;196 i9·:·time·g·=·graph·p2;
197 ·--·used·0.287131s·(cpu);·0.0433417s·(thread);·0s·(gc)197 ·--·used·0.242029s·(cpu);·0.0407132s·(thread);·0s·(gc)
198 i10·:·g_0;198 i10·:·g_0;
  
199 o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety199 o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety
200 of·PP^4·x·PP^5·x·PP^5·to·PP^4)200 of·PP^4·x·PP^5·x·PP^5·to·PP^4)
201 i11·:·g_1;201 i11·:·g_1;
  
202 o11·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety202 o11·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety
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111 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre>111 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre>
112 ············</td>112 ············</td>
113 ··········</tr>113 ··········</tr>
114 ··········<tr>114 ··········<tr>
115 ············<td>115 ············<td>
116 ··············<pre><code·class="language-macaulay2">i3·:·time·ideal·phi116 ··············<pre><code·class="language-macaulay2">i3·:·time·ideal·phi
117 ·--·used·0.00623863s·(cpu);·0.00277868s·(thread);·0s·(gc)117 ·--·used·0.000283682s·(cpu);·0.00326776s·(thread);·0s·(gc)
  
118 ·············2·····································2······················118 ·············2·····································2······················
119 o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+119 o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+
120 ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3··120 ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3··
121 ·····------------------------------------------------------------------------121 ·····------------------------------------------------------------------------
122 ············2122 ············2
123 ·····x·x·,·x··-·x·x·)123 ·····x·x·,·x··-·x·x·)
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195 o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)</code></pre>195 o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)</code></pre>
196 ············</td>196 ············</td>
197 ··········</tr>197 ··········</tr>
198 ··········<tr>198 ··········<tr>
199 ············<td>199 ············<td>
200 ··············<pre><code·class="language-macaulay2">i6·:·time·ideal·phi'200 ··············<pre><code·class="language-macaulay2">i6·:·time·ideal·phi'
201 ·--·used·0.161454s·(cpu);·0.0943583s·(thread);·0s·(gc)201 ·--·used·0.180122s·(cpu);·0.106703s·(thread);·0s·(gc)
  
202 o6·=·ideal·1202 o6·=·ideal·1
  
203 ············································································································QQ[x·..x·,·y·..y·]203 ············································································································QQ[x·..x·,·y·..y·]
204 ················································································································0···5···0···4204 ················································································································0···5···0···4
205 o6·:·Ideal·of·--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------205 o6·:·Ideal·of·--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
206 ·····································································································································································································2206 ·····································································································································································································2
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46 ·······················246 ·······················2
47 ······················x··-·x·x47 ······················x··-·x·x
48 ·······················1····0·348 ·······················1····0·3
49 ·····················}49 ·····················}
  
50 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)50 o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)
51 i3·:·time·ideal·phi51 i3·:·time·ideal·phi
52 ·--·used·0.00623863s·(cpu);·0.00277868s·(thread);·0s·(gc)52 ·--·used·0.000283682s·(cpu);·0.00326776s·(thread);·0s·(gc)
  
53 ·············2·····································253 ·············2·····································2
54 o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+54 o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+
55 ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·355 ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3
56 ·····------------------------------------------------------------------------56 ·····------------------------------------------------------------------------
57 ············257 ············2
58 ·····x·x·,·x··-·x·x·)58 ·····x·x·,·x··-·x·x·)
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121 ······················y121 ······················y
122 ·······················4122 ·······················4
123 ·····················}123 ·····················}
  
124 o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of124 o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of
125 PP^5·x·PP^4·to·PP^4)125 PP^5·x·PP^4·to·PP^4)
126 i6·:·time·ideal·phi'126 i6·:·time·ideal·phi'
127 ·--·used·0.161454s·(cpu);·0.0943583s·(thread);·0s·(gc)127 ·--·used·0.180122s·(cpu);·0.106703s·(thread);·0s·(gc)
  
128 o6·=·ideal·1128 o6·=·ideal·1
  
  
129 QQ[x·..x·,·y·..y·]129 QQ[x·..x·,·y·..y·]
  
130 0···5···0···4130 0···5···0···4
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153 o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)</code></pre>153 o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)</code></pre>
154 ············</td>154 ············</td>
155 ··········</tr>155 ··········</tr>
156 ··········<tr>156 ··········<tr>
157 ············<td>157 ············<td>
158 ··············<pre><code·class="language-macaulay2">i2·:·time·psi·=·inverseMap·phi158 ··············<pre><code·class="language-macaulay2">i2·:·time·psi·=·inverseMap·phi
159 ·--·used·0.123862s·(cpu);·0.0827311s·(thread);·0s·(gc)159 ·--·used·0.136945s·(cpu);·0.0833575s·(thread);·0s·(gc)
  
160 o2·=·--·rational·map·--160 o2·=·--·rational·map·--
161 ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])161 ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])
162 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20162 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20
163 ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])163 ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··])
164 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20164 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20
165 ·····defining·forms:·{165 ·····defining·forms:·{
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251 o4·:·RingMap·QQ[w·..w··]·&lt;--·QQ[w·..w··]251 o4·:·RingMap·QQ[w·..w··]·&lt;--·QQ[w·..w··]
252 ·················0···26··········0···26</code></pre>252 ·················0···26··········0···26</code></pre>
253 ············</td>253 ············</td>
254 ··········</tr>254 ··········</tr>
255 ··········<tr>255 ··········<tr>
256 ············<td>256 ············<td>
257 ··············<pre><code·class="language-macaulay2">i5·:·time·psi·=·inverseMap·phi257 ··············<pre><code·class="language-macaulay2">i5·:·time·psi·=·inverseMap·phi
258 ·--·used·0.235622s·(cpu);·0.164023s·(thread);·0s·(gc)258 ·--·used·0.26766s·(cpu);·0.159342s·(thread);·0s·(gc)
  
259 o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··})259 o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··})
260 ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12260 ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12
  
261 o5·:·RingMap·QQ[w·..w··]·&lt;--·QQ[w·..w··]261 o5·:·RingMap·QQ[w·..w··]·&lt;--·QQ[w·..w··]
262 ·················0···26··········0···26</code></pre>262 ·················0···26··········0···26</code></pre>
263 ············</td>263 ············</td>
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98 ······················w·w··-·w·w··+·w·w98 ······················w·w··-·w·w··+·w·w
99 ·······················2·4····1·5····0·699 ·······················2·4····1·5····0·6
100 ·····················}100 ·····················}
  
101 o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)101 o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)
102 i2·:·time·psi·=·inverseMap·phi102 i2·:·time·psi·=·inverseMap·phi
103 ·--·used·0.123862s·(cpu);·0.0827311s·(thread);·0s·(gc)103 ·--·used·0.136945s·(cpu);·0.0833575s·(thread);·0s·(gc)
  
104 o2·=·--·rational·map·--104 o2·=·--·rational·map·--
105 ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w105 ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w
106 ,·w··,·w··,·w··,·w··,·w··,·w··,·w··])106 ,·w··,·w··,·w··,·w··,·w··,·w··,·w··])
107 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13107 ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13
108 14···15···16···17···18···19···20108 14···15···16···17···18···19···20
109 ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w109 ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w
Offset 216, 15 lines modifiedOffset 216, 15 lines modified
216 15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4216 15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4
217 20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7217 20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7
218 1·8····2·9218 1·8····2·9
  
219 o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··]219 o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··]
220 ·················0···26··········0···26220 ·················0···26··········0···26
221 i5·:·time·psi·=·inverseMap·phi221 i5·:·time·psi·=·inverseMap·phi
222 ·--·used·0.235622s·(cpu);·0.164023s·(thread);·0s·(gc)222 ·--·used·0.26766s·(cpu);·0.159342s·(thread);·0s·(gc)
  
223 o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,223 o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,
224 -·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-224 -·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-
225 w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-225 w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-
226 w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+226 w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+
227 w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+227 w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+
228 w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w228 w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w
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104 o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)</code></pre>104 o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i3·:·time·inverse·phi109 ··············<pre><code·class="language-macaulay2">i3·:·time·inverse·phi
110 ·--·used·0.0711021s·(cpu);·0.0683487s·(thread);·0s·(gc)110 ·--·used·0.0503565s·(cpu);·0.0535115s·(thread);·0s·(gc)
  
111 o3·=·--·rational·map·--111 o3·=·--·rational·map·--
112 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·])112 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·])
113 ······················0···1···2···3···4113 ······················0···1···2···3···4
114 ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·])114 ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·])
115 ······················0···1···2···3···4115 ······················0···1···2···3···4
116 ·····defining·forms:·{116 ·····defining·forms:·{
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290 58320000··1·4····190512000··0·2·4····4898880000·1·2·4····190512000·2·4290 58320000··1·4····190512000··0·2·4····4898880000·1·2·4····190512000·2·4
291 476280000··0·3·4····204120000··1·3·4····2857680000··2·3·4····23814000··3·4291 476280000··0·3·4····204120000··1·3·4····2857680000··2·3·4····23814000··3·4
292 30618000·0·4····46656·1·4···12757500·2·4····51030000··3·4···30375·4292 30618000·0·4····46656·1·4···12757500·2·4····51030000··3·4···30375·4
293 ·····················}293 ·····················}
  
294 o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)294 o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)
295 i3·:·time·inverse·phi295 i3·:·time·inverse·phi
296 ·--·used·0.0711021s·(cpu);·0.0683487s·(thread);·0s·(gc)296 ·--·used·0.0503565s·(cpu);·0.0535115s·(thread);·0s·(gc)
  
297 o3·=·--·rational·map·--297 o3·=·--·rational·map·--
298 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·])298 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·])
299 ······················0···1···2···3···4299 ······················0···1···2···3···4
300 ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·])300 ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·])
301 ······················0···1···2···3···4301 ······················0···1···2···3···4
302 ·····defining·forms:·{302 ·····defining·forms:·{
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123 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>123 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i3·:·time·isBirational·phi128 ··············<pre><code·class="language-macaulay2">i3·:·time·isBirational·phi
129 ·--·used·0.0160016s·(cpu);·0.0154305s·(thread);·0s·(gc)129 ·--·used·0.0159539s·(cpu);·0.0177911s·(thread);·0s·(gc)
  
130 o3·=·true</code></pre>130 o3·=·true</code></pre>
131 ············</td>131 ············</td>
132 ··········</tr>132 ··········</tr>
133 ··········<tr>133 ··········<tr>
134 ············<td>134 ············<td>
135 ··············<pre><code·class="language-macaulay2">i4·:·time·isBirational(phi,Certify=>true)135 ··············<pre><code·class="language-macaulay2">i4·:·time·isBirational(phi,Certify=>true)
136 ·--·used·0.261018s·(cpu);·0.049664s·(thread);·0s·(gc)136 ·--·used·0.252217s·(cpu);·0.0329917s·(thread);·0s·(gc)
137 Certify:·output·certified!137 Certify:·output·certified!
  
138 o4·=·true</code></pre>138 o4·=·true</code></pre>
139 ············</td>139 ············</td>
140 ··········</tr>140 ··········</tr>
141 ········</table>141 ········</table>
142 ······</div>142 ······</div>
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58 ······················-·t··+·t·t58 ······················-·t··+·t·t
59 ·························3····2·459 ·························3····2·4
60 ·····················}60 ·····················}
  
61 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in61 o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in
62 PP^5)62 PP^5)
63 i3·:·time·isBirational·phi63 i3·:·time·isBirational·phi
64 ·--·used·0.0160016s·(cpu);·0.0154305s·(thread);·0s·(gc)64 ·--·used·0.0159539s·(cpu);·0.0177911s·(thread);·0s·(gc)
  
65 o3·=·true65 o3·=·true
66 i4·:·time·isBirational(phi,Certify=>true)66 i4·:·time·isBirational(phi,Certify=>true)
67 ·--·used·0.261018s·(cpu);·0.049664s·(thread);·0s·(gc)67 ·--·used·0.252217s·(cpu);·0.0329917s·(thread);·0s·(gc)
68 Certify:·output·certified!68 Certify:·output·certified!
  
69 o4·=·true69 o4·=·true
70 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*70 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
71 ····*·_\x8i_\x8s_\x8D_\x8o_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·whether·a·rational·map·is·dominant71 ····*·_\x8i_\x8s_\x8D_\x8o_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·whether·a·rational·map·is·dominant
72 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sB\x8Bi\x8ir\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*72 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sB\x8Bi\x8ir\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*
73 ····*·isBirational(RationalMap)73 ····*·isBirational(RationalMap)
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Offset 85, 15 lines modifiedOffset 85, 15 lines modified
  
85 o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)</code></pre>85 o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ··········<tr>88 ··········<tr>
89 ············<td>89 ············<td>
90 ··············<pre><code·class="language-macaulay2">i3·:·time·isDominant(phi,Certify=>true)90 ··············<pre><code·class="language-macaulay2">i3·:·time·isDominant(phi,Certify=>true)
91 ·--·used·1.64884s·(cpu);·1.51236s·(thread);·0s·(gc)91 ·--·used·1.93851s·(cpu);·1.76759s·(thread);·0s·(gc)
92 Certify:·output·certified!92 Certify:·output·certified!
  
93 o3·=·true</code></pre>93 o3·=·true</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
Offset 114, 15 lines modifiedOffset 114, 15 lines modified
  
114 o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)</code></pre>114 o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i7·:·time·isDominant(phi,Certify=>true)119 ··············<pre><code·class="language-macaulay2">i7·:·time·isDominant(phi,Certify=>true)
120 ·--·used·2.33087s·(cpu);·1.82168s·(thread);·0s·(gc)120 ·--·used·2.87427s·(cpu);·2.20425s·(thread);·0s·(gc)
121 Certify:·output·certified!121 Certify:·output·certified!
  
122 o7·=·false</code></pre>122 o7·=·false</code></pre>
123 ············</td>123 ············</td>
124 ··········</tr>124 ··········</tr>
125 ········</table>125 ········</table>
126 ······</div>126 ······</div>
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Offset 19, 15 lines modifiedOffset 19, 15 lines modified
19 be·to·perform·the·command·kernel·map·phi·==·0.19 be·to·perform·the·command·kernel·map·phi·==·0.
20 i1·:·P8·=·ZZ/101[x_0..x_8];20 i1·:·P8·=·ZZ/101[x_0..x_8];
21 i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},21 i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},
22 {x_4..x_8}};22 {x_4..x_8}};
  
23 o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)23 o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)
24 i3·:·time·isDominant(phi,Certify=>true)24 i3·:·time·isDominant(phi,Certify=>true)
25 ·--·used·1.64884s·(cpu);·1.51236s·(thread);·0s·(gc)25 ·--·used·1.93851s·(cpu);·1.76759s·(thread);·0s·(gc)
26 Certify:·output·certified!26 Certify:·output·certified!
  
27 o3·=·true27 o3·=·true
28 i4·:·P7·=·ZZ/101[x_0..x_7];28 i4·:·P7·=·ZZ/101[x_0..x_7];
29 i5·:·--·hyperelliptic·curve·of·genus·329 i5·:·--·hyperelliptic·curve·of·genus·3
30 ·····C·=·ideal(x_4*x_5+23*x_5^2-23*x_0*x_6-18*x_1*x_6+6*x_2*x_6+37*x_3*x_6+23*x_4*x_6-30 ·····C·=·ideal(x_4*x_5+23*x_5^2-23*x_0*x_6-18*x_1*x_6+6*x_2*x_6+37*x_3*x_6+23*x_4*x_6-
31 26*x_5*x_6+2*x_6^2-25*x_0*x_7+45*x_1*x_7+30*x_2*x_7-49*x_3*x_7-49*x_4*x_7+50*x_5*x_7,x_3*x_5-31 26*x_5*x_6+2*x_6^2-25*x_0*x_7+45*x_1*x_7+30*x_2*x_7-49*x_3*x_7-49*x_4*x_7+50*x_5*x_7,x_3*x_5-
Offset 64, 15 lines modifiedOffset 64, 15 lines modified
64 47*x_1*x_7-19*x_2*x_7+25*x_3*x_7+28*x_4*x_7+34*x_5*x_7);64 47*x_1*x_7-19*x_2*x_7+25*x_3*x_7+28*x_4*x_7+34*x_5*x_7);
  
65 o5·:·Ideal·of·P765 o5·:·Ideal·of·P7
66 i6·:·phi·=·rationalMap(C,3,2);66 i6·:·phi·=·rationalMap(C,3,2);
  
67 o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)67 o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)
68 i7·:·time·isDominant(phi,Certify=>true)68 i7·:·time·isDominant(phi,Certify=>true)
69 ·--·used·2.33087s·(cpu);·1.82168s·(thread);·0s·(gc)69 ·--·used·2.87427s·(cpu);·2.20425s·(thread);·0s·(gc)
70 Certify:·output·certified!70 Certify:·output·certified!
  
71 o7·=·false71 o7·=·false
72 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*72 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
73 ····*·_\x8i_\x8s_\x8B_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·rational·map·is·birational73 ····*·_\x8i_\x8s_\x8B_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·rational·map·is·birational
74 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sD\x8Do\x8om\x8mi\x8in\x8na\x8an\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*74 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sD\x8Do\x8om\x8mi\x8in\x8na\x8an\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*
75 ····*·isDominant(RationalMap)75 ····*·isDominant(RationalMap)
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./usr/share/doc/Macaulay2/Cremona/html/_kernel_lp__Ring__Map_cm__Z__Z_rp.html
    
Offset 90, 26 lines modifiedOffset 90, 26 lines modified
90 o1·:·RingMap·QQ[x·..x·]·&lt;--·QQ[y·..y··]90 o1·:·RingMap·QQ[x·..x·]·&lt;--·QQ[y·..y··]
91 ·················0···8··········0···11</code></pre>91 ·················0···8··········0···11</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i2·:·time·kernel(phi,1)96 ··············<pre><code·class="language-macaulay2">i2·:·time·kernel(phi,1)
97 ·--·used·0.0140069s·(cpu);·0.0162045s·(thread);·0s·(gc)97 ·--·used·0.0160174s·(cpu);·0.018429s·(thread);·0s·(gc)
  
98 o2·=·ideal·()98 o2·=·ideal·()
  
99 o2·:·Ideal·of·QQ[y·..y··]99 o2·:·Ideal·of·QQ[y·..y··]
100 ··················0···11</code></pre>100 ··················0···11</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i3·:·time·kernel(phi,2)105 ··············<pre><code·class="language-macaulay2">i3·:·time·kernel(phi,2)
106 ·--·used·0.340745s·(cpu);·0.25179s·(thread);·0s·(gc)106 ·--·used·0.408882s·(cpu);·0.301061s·(thread);·0s·(gc)
  
107 ···························2················································107 ···························2················································
108 o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··-108 o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··-
109 ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6··109 ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6··
110 ·····------------------------------------------------------------------------110 ·····------------------------------------------------------------------------
111 ···········································································111 ···········································································
112 ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···-112 ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···-
1020 B
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Offset 69, 22 lines modifiedOffset 69, 22 lines modified
69 4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·769 4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7
70 0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····270 0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2
71 7·····0·8·····1·8·····5·8·····6·8·····7·871 7·····0·8·····1·8·····5·8·····6·8·····7·8
  
72 o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··]72 o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··]
73 ·················0···8··········0···1173 ·················0···8··········0···11
74 i2·:·time·kernel(phi,1)74 i2·:·time·kernel(phi,1)
75 ·--·used·0.0140069s·(cpu);·0.0162045s·(thread);·0s·(gc)75 ·--·used·0.0160174s·(cpu);·0.018429s·(thread);·0s·(gc)
  
76 o2·=·ideal·()76 o2·=·ideal·()
  
77 o2·:·Ideal·of·QQ[y·..y··]77 o2·:·Ideal·of·QQ[y·..y··]
78 ··················0···1178 ··················0···11
79 i3·:·time·kernel(phi,2)79 i3·:·time·kernel(phi,2)
80 ·--·used·0.340745s·(cpu);·0.25179s·(thread);·0s·(gc)80 ·--·used·0.408882s·(cpu);·0.301061s·(thread);·0s·(gc)
  
81 ···························281 ···························2
82 o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··-82 o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··-
83 ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·683 ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6
84 ·····------------------------------------------------------------------------84 ·····------------------------------------------------------------------------
  
85 ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···-85 ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···-
2.53 KB
./usr/share/doc/Macaulay2/Cremona/html/_parametrize_lp__Ideal_rp.html
    
Offset 105, 15 lines modifiedOffset 105, 15 lines modified
105 o2·:·Ideal·of·--------[x·..x·]105 o2·:·Ideal·of·--------[x·..x·]
106 ··············10000019··0···9</code></pre>106 ··············10000019··0···9</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ··········<tr>109 ··········<tr>
110 ············<td>110 ············<td>
111 ··············<pre><code·class="language-macaulay2">i3·:·time·parametrize·L111 ··············<pre><code·class="language-macaulay2">i3·:·time·parametrize·L
112 ·--·used·0.00400165s·(cpu);·0.00411878s·(thread);·0s·(gc)112 ·--·used·0.00799083s·(cpu);·0.00675167s·(thread);·0s·(gc)
  
113 o3·=·--·rational·map·--113 o3·=·--·rational·map·--
114 ·····················ZZ114 ·····················ZZ
115 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·])115 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·])
116 ··················10000019··0···1···2···3···4···5116 ··················10000019··0···1···2···3···4···5
117 ·····················ZZ117 ·····················ZZ
118 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])118 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
Offset 201, 15 lines modifiedOffset 201, 15 lines modified
201 o4·:·Ideal·of·--------[x·..x·]201 o4·:·Ideal·of·--------[x·..x·]
202 ··············10000019··0···9</code></pre>202 ··············10000019··0···9</code></pre>
203 ············</td>203 ············</td>
204 ··········</tr>204 ··········</tr>
205 ··········<tr>205 ··········<tr>
206 ············<td>206 ············<td>
207 ··············<pre><code·class="language-macaulay2">i5·:·time·parametrize·Q207 ··············<pre><code·class="language-macaulay2">i5·:·time·parametrize·Q
208 ·--·used·0.738276s·(cpu);·0.373795s·(thread);·0s·(gc)208 ·--·used·0.831027s·(cpu);·0.421444s·(thread);·0s·(gc)
  
209 o5·=·--·rational·map·--209 o5·=·--·rational·map·--
210 ·····················ZZ210 ·····················ZZ
211 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·])211 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·])
212 ··················10000019··0···1···2···3···4···5···6212 ··················10000019··0···1···2···3···4···5···6
213 ·····················ZZ213 ·····················ZZ
214 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])214 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
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Offset 40, 15 lines modifiedOffset 40, 15 lines modified
40 ·····-·849671x··+·3034137x·)40 ·····-·849671x··+·3034137x·)
41 ··············8···········941 ··············8···········9
  
42 ·················ZZ42 ·················ZZ
43 o2·:·Ideal·of·--------[x·..x·]43 o2·:·Ideal·of·--------[x·..x·]
44 ··············10000019··0···944 ··············10000019··0···9
45 i3·:·time·parametrize·L45 i3·:·time·parametrize·L
46 ·--·used·0.00400165s·(cpu);·0.00411878s·(thread);·0s·(gc)46 ·--·used·0.00799083s·(cpu);·0.00675167s·(thread);·0s·(gc)
  
47 o3·=·--·rational·map·--47 o3·=·--·rational·map·--
48 ·····················ZZ48 ·····················ZZ
49 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·])49 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·])
50 ··················10000019··0···1···2···3···4···550 ··················10000019··0···1···2···3···4···5
51 ·····················ZZ51 ·····················ZZ
52 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])52 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
Offset 136, 15 lines modifiedOffset 136, 15 lines modified
136 ·····1211601x·x··-·2168594x·x··-·1801762x·x··+·3022242x·x··+·3618789x·)136 ·····1211601x·x··-·2168594x·x··-·1801762x·x··+·3022242x·x··+·3618789x·)
137 ·············5·9···········6·9···········7·9···········8·9···········9137 ·············5·9···········6·9···········7·9···········8·9···········9
  
138 ·················ZZ138 ·················ZZ
139 o4·:·Ideal·of·--------[x·..x·]139 o4·:·Ideal·of·--------[x·..x·]
140 ··············10000019··0···9140 ··············10000019··0···9
141 i5·:·time·parametrize·Q141 i5·:·time·parametrize·Q
142 ·--·used·0.738276s·(cpu);·0.373795s·(thread);·0s·(gc)142 ·--·used·0.831027s·(cpu);·0.421444s·(thread);·0s·(gc)
  
143 o5·=·--·rational·map·--143 o5·=·--·rational·map·--
144 ·····················ZZ144 ·····················ZZ
145 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·])145 ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·])
146 ··················10000019··0···1···2···3···4···5···6146 ··················10000019··0···1···2···3···4···5···6
147 ·····················ZZ147 ·····················ZZ
148 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])148 ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
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Offset 78, 15 lines modifiedOffset 78, 15 lines modified
  
78 o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)</code></pre>78 o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i2·:·time·p·=·point·source·f83 ··············<pre><code·class="language-macaulay2">i2·:·time·p·=·point·source·f
84 ·--·used·0.214883s·(cpu);·0.134364s·(thread);·0s·(gc)84 ·--·used·0.252287s·(cpu);·0.15139s·(thread);·0s·(gc)
  
85 o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+85 o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+
86 ·············10········11···9·········11···8········11···7········11···6··86 ·············10········11···9·········11···8········11···7········11···6··
87 ·····------------------------------------------------------------------------87 ·····------------------------------------------------------------------------
88 ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··-88 ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··-
89 ···········11···5········11···4········11···3·········11···2········11···1··89 ···········11···5········11···4········11···3·········11···2········11···1··
90 ·····------------------------------------------------------------------------90 ·····------------------------------------------------------------------------
Offset 100, 15 lines modifiedOffset 100, 15 lines modified
100 ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)100 ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)
101 ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·7</code></pre>101 ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·7</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i3·:·time·p·==·f^*·f·p106 ··············<pre><code·class="language-macaulay2">i3·:·time·p·==·f^*·f·p
107 ·--·used·0.140675s·(cpu);·0.10235s·(thread);·0s·(gc)107 ·--·used·0.15602s·(cpu);·0.106898s·(thread);·0s·(gc)
  
108 o3·=·true</code></pre>108 o3·=·true</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ········</table>111 ········</table>
112 ······</div>112 ······</div>
113 ······<div>113 ······<div>
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19 documentation)·,·see·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8).19 documentation)·,·see·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8).
20 Below·we·verify·the·birationality·of·a·rational·map.20 Below·we·verify·the·birationality·of·a·rational·map.
21 i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331);21 i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331);
  
22 o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to22 o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to
23 PP^8)23 PP^8)
24 i2·:·time·p·=·point·source·f24 i2·:·time·p·=·point·source·f
25 ·--·used·0.214883s·(cpu);·0.134364s·(thread);·0s·(gc)25 ·--·used·0.252287s·(cpu);·0.15139s·(thread);·0s·(gc)
  
26 o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+26 o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+
27 ·············10········11···9·········11···8········11···7········11···627 ·············10········11···9·········11···8········11···7········11···6
28 ·····------------------------------------------------------------------------28 ·····------------------------------------------------------------------------
29 ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··-29 ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··-
30 ···········11···5········11···4········11···3·········11···2········11···130 ···········11···5········11···4········11···3·········11···2········11···1
31 ·····------------------------------------------------------------------------31 ·····------------------------------------------------------------------------
Offset 40, 15 lines modifiedOffset 40, 15 lines modified
40 o2·:·Ideal·of·-----------------------------------------------------------------40 o2·:·Ideal·of·-----------------------------------------------------------------
41 --------------------------------------41 --------------------------------------
42 ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y42 ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y
43 y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)43 y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)
44 ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·1144 ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11
45 3·4····1·6····0·8···2·4····1·5····0·745 3·4····1·6····0·8···2·4····1·5····0·7
46 i3·:·time·p·==·f^*·f·p46 i3·:·time·p·==·f^*·f·p
47 ·--·used·0.140675s·(cpu);·0.10235s·(thread);·0s·(gc)47 ·--·used·0.15602s·(cpu);·0.106898s·(thread);·0s·(gc)
  
48 o3·=·true48 o3·=·true
49 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*49 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
50 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·--·pick·a·random·K·rational·point·on·the·scheme·X50 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·--·pick·a·random·K·rational·point·on·the·scheme·X
51 ······defined·by·I51 ······defined·by·I
52 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*52 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
53 ····*·point(PolynomialRing)53 ····*·point(PolynomialRing)
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Offset 88, 15 lines modifiedOffset 88, 15 lines modified
88 o2·:·RingMap·GF·109561[t·..t·]·&lt;--·GF·109561[x·..x·]88 o2·:·RingMap·GF·109561[t·..t·]·&lt;--·GF·109561[x·..x·]
89 ························0···4·················0···5</code></pre>89 ························0···4·················0···5</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·time·projectiveDegrees(phi,Certify=>true)94 ··············<pre><code·class="language-macaulay2">i3·:·time·projectiveDegrees(phi,Certify=>true)
95 ·--·used·0.307085s·(cpu);·0.0428959s·(thread);·0s·(gc)95 ·--·used·0.282541s·(cpu);·0.0385457s·(thread);·0s·(gc)
96 Certify:·output·certified!96 Certify:·output·certified!
  
97 o3·=·{1,·2,·4,·4,·2}97 o3·=·{1,·2,·4,·4,·2}
  
98 o3·:·List</code></pre>98 o3·:·List</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
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116 ·············x·x··-·x·x··+·x·x·················0···4116 ·············x·x··-·x·x··+·x·x·················0···4
117 ··············2·3····1·4····0·5</code></pre>117 ··············2·3····1·4····0·5</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,Certify=>true)122 ··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,Certify=>true)
123 ·--·used·0.309183s·(cpu);·0.0603617s·(thread);·0s·(gc)123 ·--·used·0.268221s·(cpu);·0.0424187s·(thread);·0s·(gc)
124 Certify:·output·certified!124 Certify:·output·certified!
  
125 o5·=·{2,·4,·4,·2,·1}125 o5·=·{2,·4,·4,·2,·1}
  
126 o5·:·List</code></pre>126 o5·:·List</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
Offset 143, 25 lines modifiedOffset 143, 25 lines modified
143 o6·:·RingMap·------[x·..x·]·&lt;--·------[x·..x·]143 o6·:·RingMap·------[x·..x·]·&lt;--·------[x·..x·]
144 ·············300007··0···6······300007··0···6</code></pre>144 ·············300007··0···6······300007··0···6</code></pre>
145 ············</td>145 ············</td>
146 ··········</tr>146 ··········</tr>
147 ··········<tr>147 ··········<tr>
148 ············<td>148 ············<td>
149 ··············<pre><code·class="language-macaulay2">i7·:·time·projectiveDegrees·phi149 ··············<pre><code·class="language-macaulay2">i7·:·time·projectiveDegrees·phi
150 ·--·used·0.00356087s·(cpu);·4.2574e-05s·(thread);·0s·(gc)150 ·--·used·0.000972072s·(cpu);·5.7969e-05s·(thread);·0s·(gc)
  
151 o7·=·{1,·2,·4,·8,·8,·4,·1}151 o7·=·{1,·2,·4,·8,·8,·4,·1}
  
152 o7·:·List</code></pre>152 o7·:·List</code></pre>
153 ············</td>153 ············</td>
154 ··········</tr>154 ··········</tr>
155 ··········<tr>155 ··········<tr>
156 ············<td>156 ············<td>
157 ··············<pre><code·class="language-macaulay2">i8·:·time·projectiveDegrees(phi,NumDegrees=>1)157 ··············<pre><code·class="language-macaulay2">i8·:·time·projectiveDegrees(phi,NumDegrees=>1)
158 ·--·used·0.000198159s·(cpu);·4.8382e-05s·(thread);·0s·(gc)158 ·--·used·0.000102683s·(cpu);·2.0338e-05s·(thread);·0s·(gc)
  
159 o8·=·{4,·1}159 o8·=·{4,·1}
  
160 o8·:·List</code></pre>160 o8·:·List</code></pre>
161 ············</td>161 ············</td>
162 ··········</tr>162 ··········</tr>
163 ········</table>163 ········</table>
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52 t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a})52 t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a})
53 ·····················0···4··············0···5·······1····0·2·····1·2····0·353 ·····················0···4··············0···5·······1····0·2·····1·2····0·3
54 2····1·3·····1·3····0·4·····2·3····1·4·····3····2·454 2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4
  
55 o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·]55 o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·]
56 ························0···4·················0···556 ························0···4·················0···5
57 i3·:·time·projectiveDegrees(phi,Certify=>true)57 i3·:·time·projectiveDegrees(phi,Certify=>true)
58 ·--·used·0.307085s·(cpu);·0.0428959s·(thread);·0s·(gc)58 ·--·used·0.282541s·(cpu);·0.0385457s·(thread);·0s·(gc)
59 Certify:·output·certified!59 Certify:·output·certified!
  
60 o3·=·{1,·2,·4,·4,·2}60 o3·=·{1,·2,·4,·4,·2}
  
61 o3·:·List61 o3·:·List
62 i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity))62 i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity))
  
Offset 75, 15 lines modifiedOffset 75, 15 lines modified
  
75 ··············GF·109561[x·..x·]75 ··············GF·109561[x·..x·]
76 ·························0···576 ·························0···5
77 o4·:·RingMap·------------------·<--·GF·109561[t·..t·]77 o4·:·RingMap·------------------·<--·GF·109561[t·..t·]
78 ·············x·x··-·x·x··+·x·x·················0···478 ·············x·x··-·x·x··+·x·x·················0···4
79 ··············2·3····1·4····0·579 ··············2·3····1·4····0·5
80 i5·:·time·projectiveDegrees(psi,Certify=>true)80 i5·:·time·projectiveDegrees(psi,Certify=>true)
81 ·--·used·0.309183s·(cpu);·0.0603617s·(thread);·0s·(gc)81 ·--·used·0.268221s·(cpu);·0.0424187s·(thread);·0s·(gc)
82 Certify:·output·certified!82 Certify:·output·certified!
  
83 o5·=·{2,·4,·4,·2,·1}83 o5·=·{2,·4,·4,·2,·1}
  
84 o5·:·List84 o5·:·List
85 i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a85 i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a
86 rational·octic·surface86 rational·octic·surface
Offset 119, 21 lines modifiedOffset 119, 21 lines modified
119 4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6119 4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6
120 5·6120 5·6
  
121 ···············ZZ·················ZZ121 ···············ZZ·················ZZ
122 o6·:·RingMap·------[x·..x·]·<--·------[x·..x·]122 o6·:·RingMap·------[x·..x·]·<--·------[x·..x·]
123 ·············300007··0···6······300007··0···6123 ·············300007··0···6······300007··0···6
124 i7·:·time·projectiveDegrees·phi124 i7·:·time·projectiveDegrees·phi
125 ·--·used·0.00356087s·(cpu);·4.2574e-05s·(thread);·0s·(gc)125 ·--·used·0.000972072s·(cpu);·5.7969e-05s·(thread);·0s·(gc)
  
126 o7·=·{1,·2,·4,·8,·8,·4,·1}126 o7·=·{1,·2,·4,·8,·8,·4,·1}
  
127 o7·:·List127 o7·:·List
128 i8·:·time·projectiveDegrees(phi,NumDegrees=>1)128 i8·:·time·projectiveDegrees(phi,NumDegrees=>1)
129 ·--·used·0.000198159s·(cpu);·4.8382e-05s·(thread);·0s·(gc)129 ·--·used·0.000102683s·(cpu);·2.0338e-05s·(thread);·0s·(gc)
  
130 o8·=·{4,·1}130 o8·=·{4,·1}
  
131 o8·:·List131 o8·:·List
132 Another·way·to·use·this·method·is·by·passing·an·integer·i·as·second·argument.132 Another·way·to·use·this·method·is·by·passing·an·integer·i·as·second·argument.
133 However,·this·is·equivalent·to·first·projectiveDegrees(phi,NumDegrees=>i)·and133 However,·this·is·equivalent·to·first·projectiveDegrees(phi,NumDegrees=>i)·and
134 generally·it·is·not·faster.134 generally·it·is·not·faster.
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Offset 88, 15 lines modifiedOffset 88, 15 lines modified
88 o2·:·Ideal·of·-----[x·..x·]88 o2·:·Ideal·of·-----[x·..x·]
89 ··············33331··0···6</code></pre>89 ··············33331··0···6</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·time·phi·=·rationalMap(V,3,2)94 ··············<pre><code·class="language-macaulay2">i3·:·time·phi·=·rationalMap(V,3,2)
95 ·--·used·0.151455s·(cpu);·0.102289s·(thread);·0s·(gc)95 ·--·used·0.161635s·(cpu);·0.111425s·(thread);·0s·(gc)
  
96 o3·=·--·rational·map·--96 o3·=·--·rational·map·--
97 ····················ZZ97 ····················ZZ
98 ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·])98 ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·])
99 ··················33331··0···1···2···3···4···5···699 ··················33331··0···1···2···3···4···5···6
100 ····················ZZ100 ····················ZZ
101 ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··])101 ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··])
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34 i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-34 i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-
35 x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6);35 x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6);
  
36 ················ZZ36 ················ZZ
37 o2·:·Ideal·of·-----[x·..x·]37 o2·:·Ideal·of·-----[x·..x·]
38 ··············33331··0···638 ··············33331··0···6
39 i3·:·time·phi·=·rationalMap(V,3,2)39 i3·:·time·phi·=·rationalMap(V,3,2)
40 ·--·used·0.151455s·(cpu);·0.102289s·(thread);·0s·(gc)40 ·--·used·0.161635s·(cpu);·0.111425s·(thread);·0s·(gc)
  
41 o3·=·--·rational·map·--41 o3·=·--·rational·map·--
42 ····················ZZ42 ····················ZZ
43 ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·])43 ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·])
44 ··················33331··0···1···2···3···4···5···644 ··················33331··0···1···2···3···4···5···6
45 ····················ZZ45 ····················ZZ
46 ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,46 ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,
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111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};</code></pre>112 ··············<pre><code·class="language-macaulay2">i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i6·:·time·phi·=·rationalMap·D117 ··············<pre><code·class="language-macaulay2">i6·:·time·phi·=·rationalMap·D
118 ·--·used·0.0239993s·(cpu);·0.0243652s·(thread);·0s·(gc)118 ·--·used·0.026571s·(cpu);·0.027013s·(thread);·0s·(gc)
  
119 o6·=·--·rational·map·--119 o6·=·--·rational·map·--
120 ··································ZZ120 ··································ZZ
121 ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by121 ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by
122 ································65521··0···1···2···3···4···5122 ································65521··0···1···2···3···4···5
123 ·············{123 ·············{
124 ·················2··················2124 ·················2··················2
Offset 219, 15 lines modifiedOffset 219, 15 lines modified
  
219 o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)</code></pre>219 o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)</code></pre>
220 ············</td>220 ············</td>
221 ··········</tr>221 ··········</tr>
222 ··········<tr>222 ··········<tr>
223 ············<td>223 ············<td>
224 ··············<pre><code·class="language-macaulay2">i7·:·time·?·image(phi,&quot;F4&quot;)224 ··············<pre><code·class="language-macaulay2">i7·:·time·?·image(phi,&quot;F4&quot;)
225 ·--·used·0.877865s·(cpu);·0.518111s·(thread);·0s·(gc)225 ·--·used·1.02321s·(cpu);·0.516756s·(thread);·0s·(gc)
  
226 o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153226 o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153
227 ·····hypersurfaces·of·degree·2</code></pre>227 ·····hypersurfaces·of·degree·2</code></pre>
228 ············</td>228 ············</td>
229 ··········</tr>229 ··········</tr>
230 ········</table>230 ········</table>
231 ········<p>See·also·the·package·<a·href="http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.16/share/doc/Macaulay2/Divisor/html/index.html">Divisor</a>,·which·provides·general·tools·for·working·with·divisors.</p>231 ········<p>See·also·the·package·<a·href="http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.16/share/doc/Macaulay2/Divisor/html/index.html">Divisor</a>,·which·provides·general·tools·for·working·with·divisors.</p>
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40 o4·=·ideal(-·32646x··-·28377x··+·26433x··-·29566x··+·3783x··+·26696x·)40 o4·=·ideal(-·32646x··-·28377x··+·26433x··-·29566x··+·3783x··+·26696x·)
41 ···················0·········1·········2·········3········4·········541 ···················0·········1·········2·········3········4·········5
  
42 o4·:·Ideal·of·X42 o4·:·Ideal·of·X
43 i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};43 i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};
44 i6·:·time·phi·=·rationalMap·D44 i6·:·time·phi·=·rationalMap·D
45 ·--·used·0.0239993s·(cpu);·0.0243652s·(thread);·0s·(gc)45 ·--·used·0.026571s·(cpu);·0.027013s·(thread);·0s·(gc)
  
46 o6·=·--·rational·map·--46 o6·=·--·rational·map·--
47 ··································ZZ47 ··································ZZ
48 ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by48 ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by
49 ································65521··0···1···2···3···4···549 ································65521··0···1···2···3···4···5
50 ·············{50 ·············{
51 ·················2··················251 ·················2··················2
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169 ··················································2·························2169 ··················································2·························2
170 ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x170 ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x
171 ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5171 ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5
172 ·····················}172 ·····················}
  
173 o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)173 o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)
174 i7·:·time·?·image(phi,"F4")174 i7·:·time·?·image(phi,"F4")
175 ·--·used·0.877865s·(cpu);·0.518111s·(thread);·0s·(gc)175 ·--·used·1.02321s·(cpu);·0.516756s·(thread);·0s·(gc)
  
176 o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153176 o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153
177 ·····hypersurfaces·of·degree·2177 ·····hypersurfaces·of·degree·2
178 See·also·the·package·_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r,·which·provides·general·tools·for·working·with178 See·also·the·package·_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r,·which·provides·general·tools·for·working·with
179 divisors.179 divisors.
180 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*180 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
181 ····*·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·makes·a·rational·map181 ····*·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·makes·a·rational·map
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70 ······<div>70 ······<div>
71 ········<h2>Description</h2>71 ········<h2>Description</h2>
72 ········<p>A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is·smooth·and·irreducible.·To·ensure·this·condition,·the·field·<span·class="tt">K</span>·must·be·large·enough·but·no·check·is·made.</p>72 ········<p>A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is·smooth·and·irreducible.·To·ensure·this·condition,·the·field·<span·class="tt">K</span>·must·be·large·enough·but·no·check·is·made.</p>
73 ········<table·class="examples">73 ········<table·class="examples">
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331))76 ··············<pre><code·class="language-macaulay2">i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331))
77 ·--·used·0.871333s·(cpu);·0.772123s·(thread);·0s·(gc)77 ·--·used·1.02517s·(cpu);·0.924576s·(thread);·0s·(gc)
  
78 o1·=·(rational·map·defined·by·forms·of·degree·3,78 o1·=·(rational·map·defined·by·forms·of·degree·3,
79 ······source·variety:·PP^3······················79 ······source·variety:·PP^3······················
80 ······target·variety:·PP^3······················80 ······target·variety:·PP^3······················
81 ······dominance:·true···························81 ······dominance:·true···························
82 ······birationality:·true·······················82 ······birationality:·true·······················
83 ······projective·degrees:·{1,·3,·3,·1}··········83 ······projective·degrees:·{1,·3,·3,·1}··········
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16 ············K,·according·to·the·classification·given·in·Table·1·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l16 ············K,·according·to·the·classification·given·in·Table·1·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l
17 ············_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8C_\x8r_\x8e_\x8m_\x8o_\x8n_\x8a_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8P_\x86_\x8·_\x8a_\x8n_\x8d_\x8·_\x8P_\x87.17 ············_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8C_\x8r_\x8e_\x8m_\x8o_\x8n_\x8a_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8P_\x86_\x8·_\x8a_\x8n_\x8d_\x8·_\x8P_\x87.
18 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*18 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
19 A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is19 A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is
20 smooth·and·irreducible.·To·ensure·this·condition,·the·field·K·must·be·large20 smooth·and·irreducible.·To·ensure·this·condition,·the·field·K·must·be·large
21 enough·but·no·check·is·made.21 enough·but·no·check·is·made.
22 i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331))22 i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331))
23 ·--·used·0.871333s·(cpu);·0.772123s·(thread);·0s·(gc)23 ·--·used·1.02517s·(cpu);·0.924576s·(thread);·0s·(gc)
  
24 o1·=·(rational·map·defined·by·forms·of·degree·3,24 o1·=·(rational·map·defined·by·forms·of·degree·3,
25 ······source·variety:·PP^325 ······source·variety:·PP^3
26 ······target·variety:·PP^326 ······target·variety:·PP^3
27 ······dominance:·true27 ······dominance:·true
28 ······birationality:·true28 ······birationality:·true
29 ······projective·degrees:·{1,·3,·3,·1}29 ······projective·degrees:·{1,·3,·3,·1}
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70 ······<div>70 ······<div>
71 ········<h2>Description</h2>71 ········<h2>Description</h2>
72 ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p>72 ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p>
73 ········<table·class="examples">73 ········<table·class="examples">
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i1·:·time·specialCubicTransformation·976 ··············<pre><code·class="language-macaulay2">i1·:·time·specialCubicTransformation·9
77 ·--·used·0.0706292s·(cpu);·0.0728482s·(thread);·0s·(gc)77 ·--·used·0.0767241s·(cpu);·0.0775018s·(thread);·0s·(gc)
  
78 o1·=·--·rational·map·--78 o1·=·--·rational·map·--
79 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·])79 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·])
80 ······················0···1···2···3···4···5···680 ······················0···1···2···3···4···5···6
81 ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by81 ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by
82 ····································0···1···2···3···4···5···6···7···8···982 ····································0···1···2···3···4···5···6···7···8···9
83 ·············{83 ·············{
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138 o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre>138 o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre>
139 ············</td>139 ············</td>
140 ··········</tr>140 ··········</tr>
141 ··········<tr>141 ··········<tr>
142 ············<td>142 ············<td>
143 ··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo143 ··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo
144 ·--·used·0.0159863s·(cpu);·0.0149846s·(thread);·0s·(gc)144 ·--·used·0.0153394s·(cpu);·0.0173588s·(thread);·0s·(gc)
  
145 o2·=·rational·map·defined·by·forms·of·degree·3145 o2·=·rational·map·defined·by·forms·of·degree·3
146 ·····source·variety:·PP^6146 ·····source·variety:·PP^6
147 ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9147 ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9
148 ·····dominance:·true148 ·····dominance:·true
149 ·····birationality:·true149 ·····birationality:·true
150 ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8}150 ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8}
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15 ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·cubic·birational15 ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·cubic·birational
16 ············transformation·over·K,·according·to·the·classification·given·in16 ············transformation·over·K,·according·to·the·classification·given·in
17 ············Table·2·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e17 ············Table·2·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e
18 ············_\x8s_\x8p_\x8a_\x8c_\x8e_\x8s.18 ············_\x8s_\x8p_\x8a_\x8c_\x8e_\x8s.
19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
20 The·field·K·is·required·to·be·large·enough.20 The·field·K·is·required·to·be·large·enough.
21 i1·:·time·specialCubicTransformation·921 i1·:·time·specialCubicTransformation·9
22 ·--·used·0.0706292s·(cpu);·0.0728482s·(thread);·0s·(gc)22 ·--·used·0.0767241s·(cpu);·0.0775018s·(thread);·0s·(gc)
  
23 o1·=·--·rational·map·--23 o1·=·--·rational·map·--
24 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·])24 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·])
25 ······················0···1···2···3···4···5···625 ······················0···1···2···3···4···5···6
26 ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])26 ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])
27 defined·by27 defined·by
28 ····································0···1···2···3···4···5···6···7···8···928 ····································0···1···2···3···4···5···6···7···8···9
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323 6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6323 6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6
324 1·6·····2·6······3·6·····4·6·····5·6324 1·6·····2·6······3·6·····4·6·····5·6
325 ·····················}325 ·····················}
  
326 o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of326 o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of
327 PP^9)327 PP^9)
328 i2·:·time·describe·oo328 i2·:·time·describe·oo
329 ·--·used·0.0159863s·(cpu);·0.0149846s·(thread);·0s·(gc)329 ·--·used·0.0153394s·(cpu);·0.0173588s·(thread);·0s·(gc)
  
330 o2·=·rational·map·defined·by·forms·of·degree·3330 o2·=·rational·map·defined·by·forms·of·degree·3
331 ·····source·variety:·PP^6331 ·····source·variety:·PP^6
332 ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9332 ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9
333 ·····dominance:·true333 ·····dominance:·true
334 ·····birationality:·true334 ·····birationality:·true
335 ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8}335 ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8}
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70 ······<div>70 ······<div>
71 ········<h2>Description</h2>71 ········<h2>Description</h2>
72 ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p>72 ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p>
73 ········<table·class="examples">73 ········<table·class="examples">
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i1·:·time·specialQuadraticTransformation·476 ··············<pre><code·class="language-macaulay2">i1·:·time·specialQuadraticTransformation·4
77 ·--·used·0.0533759s·(cpu);·0.0565336s·(thread);·0s·(gc)77 ·--·used·0.0699145s·(cpu);·0.0699369s·(thread);·0s·(gc)
  
78 o1·=·--·rational·map·--78 o1·=·--·rational·map·--
79 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])79 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
80 ······················0···1···2···3···4···5···6···7···880 ······················0···1···2···3···4···5···6···7···8
81 ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by81 ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by
82 ····································0···1···2···3···4···5···6···7···8···982 ····································0···1···2···3···4···5···6···7···8···9
83 ·············{83 ·············{
Offset 126, 15 lines modifiedOffset 126, 15 lines modified
  
126 o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre>126 o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo131 ··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo
132 ·--·used·0.00796617s·(cpu);·0.00563027s·(thread);·0s·(gc)132 ·--·used·0.00799664s·(cpu);·0.007039s·(thread);·0s·(gc)
  
133 o2·=·rational·map·defined·by·forms·of·degree·2133 o2·=·rational·map·defined·by·forms·of·degree·2
134 ·····source·variety:·PP^8134 ·····source·variety:·PP^8
135 ·····target·variety:·hypersurface·of·degree·3·in·PP^9135 ·····target·variety:·hypersurface·of·degree·3·in·PP^9
136 ·····dominance:·true136 ·····dominance:·true
137 ·····birationality:·true137 ·····birationality:·true
138 ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3}138 ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3}
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15 ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·quadratic·birational15 ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·quadratic·birational
16 ············transformation·over·K,·according·to·the·classification·given·in16 ············transformation·over·K,·according·to·the·classification·given·in
17 ············Table·1·of·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s_\x8·_\x8o_\x8f_\x8·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8a_\x8t_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s17 ············Table·1·of·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s_\x8·_\x8o_\x8f_\x8·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8a_\x8t_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s
18 ············_\x8i_\x8n_\x8t_\x8o_\x8·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8t_\x8e_\x8·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8i_\x8c_\x8s.18 ············_\x8i_\x8n_\x8t_\x8o_\x8·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8t_\x8e_\x8·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8i_\x8c_\x8s.
19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
20 The·field·K·is·required·to·be·large·enough.20 The·field·K·is·required·to·be·large·enough.
21 i1·:·time·specialQuadraticTransformation·421 i1·:·time·specialQuadraticTransformation·4
22 ·--·used·0.0533759s·(cpu);·0.0565336s·(thread);·0s·(gc)22 ·--·used·0.0699145s·(cpu);·0.0699369s·(thread);·0s·(gc)
  
23 o1·=·--·rational·map·--23 o1·=·--·rational·map·--
24 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])24 ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
25 ······················0···1···2···3···4···5···6···7···825 ······················0···1···2···3···4···5···6···7···8
26 ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])26 ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])
27 defined·by27 defined·by
28 ····································0···1···2···3···4···5···6···7···8···928 ····································0···1···2···3···4···5···6···7···8···9
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78 ···················································278 ···················································2
79 ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x79 ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x
80 ·······················0·1····0·4····3·6····4·6····6····5·780 ·······················0·1····0·4····3·6····4·6····6····5·7
81 ·····················}81 ·····················}
  
82 o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)82 o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)
83 i2·:·time·describe·oo83 i2·:·time·describe·oo
84 ·--·used·0.00796617s·(cpu);·0.00563027s·(thread);·0s·(gc)84 ·--·used·0.00799664s·(cpu);·0.007039s·(thread);·0s·(gc)
  
85 o2·=·rational·map·defined·by·forms·of·degree·285 o2·=·rational·map·defined·by·forms·of·degree·2
86 ·····source·variety:·PP^886 ·····source·variety:·PP^8
87 ·····target·variety:·hypersurface·of·degree·3·in·PP^987 ·····target·variety:·hypersurface·of·degree·3·in·PP^9
88 ·····dominance:·true88 ·····dominance:·true
89 ·····birationality:·true89 ·····birationality:·true
90 ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3}90 ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3}
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88 o3·=·6927</code></pre>88 o3·=·6927</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·time·phi'·=·value·str;93 ··············<pre><code·class="language-macaulay2">i4·:·time·phi'·=·value·str;
94 ·--·used·0.0199694s·(cpu);·0.0181479s·(thread);·0s·(gc)94 ·--·used·0.0239217s·(cpu);·0.0234164s·(thread);·0s·(gc)
  
95 o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)</code></pre>95 o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i5·:·time·describe·phi'100 ··············<pre><code·class="language-macaulay2">i5·:·time·describe·phi'
101 ·--·used·0.00186898s·(cpu);·0.00405821s·(thread);·0s·(gc)101 ·--·used·0.00300101s·(cpu);·0.00592472s·(thread);·0s·(gc)
  
102 o5·=·rational·map·defined·by·forms·of·degree·3102 o5·=·rational·map·defined·by·forms·of·degree·3
103 ·····source·variety:·PP^3103 ·····source·variety:·PP^3
104 ·····target·variety:·smooth·quadric·hypersurface·in·PP^4104 ·····target·variety:·smooth·quadric·hypersurface·in·PP^4
105 ·····dominance:·true105 ·····dominance:·true
106 ·····birationality:·true·(the·inverse·map·is·already·calculated)106 ·····birationality:·true·(the·inverse·map·is·already·calculated)
107 ·····projective·degrees:·{1,·3,·4,·2}107 ·····projective·degrees:·{1,·3,·4,·2}
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113 ·····degree·base·locus:·5113 ·····degree·base·locus:·5
114 ·····coefficient·ring:·ZZ/33331</code></pre>114 ·····coefficient·ring:·ZZ/33331</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i6·:·time·describe·inverse·phi'119 ··············<pre><code·class="language-macaulay2">i6·:·time·describe·inverse·phi'
120 ·--·used·0.00171302s·(cpu);·0.0034666s·(thread);·0s·(gc)120 ·--·used·0.00452781s·(cpu);·0.00454474s·(thread);·0s·(gc)
  
121 o6·=·rational·map·defined·by·forms·of·degree·2121 o6·=·rational·map·defined·by·forms·of·degree·2
122 ·····source·variety:·smooth·quadric·hypersurface·in·PP^4122 ·····source·variety:·smooth·quadric·hypersurface·in·PP^4
123 ·····target·variety:·PP^3123 ·····target·variety:·PP^3
124 ·····dominance:·true124 ·····dominance:·true
125 ·····birationality:·true·(the·inverse·map·is·already·calculated)125 ·····birationality:·true·(the·inverse·map·is·already·calculated)
126 ·····projective·degrees:·{2,·4,·3,·1}126 ·····projective·degrees:·{2,·4,·3,·1}
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19 o1·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)19 o1·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)
20 i2·:·str·=·toExternalString·phi;20 i2·:·str·=·toExternalString·phi;
21 i3·:·#str21 i3·:·#str
  
22 o3·=·692722 o3·=·6927
23 i4·:·time·phi'·=·value·str;23 i4·:·time·phi'·=·value·str;
24 ·--·used·0.0199694s·(cpu);·0.0181479s·(thread);·0s·(gc)24 ·--·used·0.0239217s·(cpu);·0.0234164s·(thread);·0s·(gc)
  
25 o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)25 o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)
26 i5·:·time·describe·phi'26 i5·:·time·describe·phi'
27 ·--·used·0.00186898s·(cpu);·0.00405821s·(thread);·0s·(gc)27 ·--·used·0.00300101s·(cpu);·0.00592472s·(thread);·0s·(gc)
  
28 o5·=·rational·map·defined·by·forms·of·degree·328 o5·=·rational·map·defined·by·forms·of·degree·3
29 ·····source·variety:·PP^329 ·····source·variety:·PP^3
30 ·····target·variety:·smooth·quadric·hypersurface·in·PP^430 ·····target·variety:·smooth·quadric·hypersurface·in·PP^4
31 ·····dominance:·true31 ·····dominance:·true
32 ·····birationality:·true·(the·inverse·map·is·already·calculated)32 ·····birationality:·true·(the·inverse·map·is·already·calculated)
33 ·····projective·degrees:·{1,·3,·4,·2}33 ·····projective·degrees:·{1,·3,·4,·2}
34 ·····number·of·minimal·representatives:·134 ·····number·of·minimal·representatives:·1
35 ·····dimension·base·locus:·135 ·····dimension·base·locus:·1
36 ·····degree·base·locus:·536 ·····degree·base·locus:·5
37 ·····coefficient·ring:·ZZ/3333137 ·····coefficient·ring:·ZZ/33331
38 i6·:·time·describe·inverse·phi'38 i6·:·time·describe·inverse·phi'
39 ·--·used·0.00171302s·(cpu);·0.0034666s·(thread);·0s·(gc)39 ·--·used·0.00452781s·(cpu);·0.00454474s·(thread);·0s·(gc)
  
40 o6·=·rational·map·defined·by·forms·of·degree·240 o6·=·rational·map·defined·by·forms·of·degree·2
41 ·····source·variety:·smooth·quadric·hypersurface·in·PP^441 ·····source·variety:·smooth·quadric·hypersurface·in·PP^4
42 ·····target·variety:·PP^342 ·····target·variety:·PP^3
43 ·····dominance:·true43 ·····dominance:·true
44 ·····birationality:·true·(the·inverse·map·is·already·calculated)44 ·····birationality:·true·(the·inverse·map·is·already·calculated)
45 ·····projective·degrees:·{2,·4,·3,·1}45 ·····projective·degrees:·{2,·4,·3,·1}
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./usr/share/doc/Macaulay2/Cremona/html/index.html
    
Offset 58, 29 lines modifiedOffset 58, 29 lines modified
58 ············<td>58 ············<td>
59 ··············<pre><code·class="language-macaulay2">i1·:·ZZ/300007[t_0..t_6];</code></pre>59 ··············<pre><code·class="language-macaulay2">i1·:·ZZ/300007[t_0..t_6];</code></pre>
60 ············</td>60 ············</td>
61 ··········</tr>61 ··········</tr>
62 ··········<tr>62 ··········<tr>
63 ············<td>63 ············<td>
64 ··············<pre><code·class="language-macaulay2">i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})64 ··············<pre><code·class="language-macaulay2">i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})
65 ·--·used·0.00401246s·(cpu);·0.00395623s·(thread);·0s·(gc)65 ·--·used·0.00394461s·(cpu);·0.00417509s·(thread);·0s·(gc)
  
66 ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····266 ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2
67 o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})67 o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})
68 ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·668 ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6
  
69 ···············ZZ·················ZZ69 ···············ZZ·················ZZ
70 o2·:·RingMap·------[t·..t·]·&lt;--·------[x·..x·]70 o2·:·RingMap·------[t·..t·]·&lt;--·------[x·..x·]
71 ·············300007··0···6······300007··0···9</code></pre>71 ·············300007··0···6······300007··0···9</code></pre>
72 ············</td>72 ············</td>
73 ··········</tr>73 ··········</tr>
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i3·:·time·J·=·kernel(phi,2)76 ··············<pre><code·class="language-macaulay2">i3·:·time·J·=·kernel(phi,2)
77 ·--·used·0.0410654s·(cpu);·0.0419253s·(thread);·0s·(gc)77 ·--·used·0.0349428s·(cpu);·0.0380202s·(thread);·0s·(gc)
  
78 o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x·78 o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x·
79 ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·479 ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4
80 ·····------------------------------------------------------------------------80 ·····------------------------------------------------------------------------
81 ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)81 ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)
82 ········1·6····0·8···2·4····1·5····0·782 ········1·6····0·8···2·4····1·5····0·7
  
Offset 88, 43 lines modifiedOffset 88, 43 lines modified
88 o3·:·Ideal·of·------[x·..x·]88 o3·:·Ideal·of·------[x·..x·]
89 ··············300007··0···9</code></pre>89 ··············300007··0···9</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i4·:·time·degreeMap·phi94 ··············<pre><code·class="language-macaulay2">i4·:·time·degreeMap·phi
95 ·--·used·0.0255553s·(cpu);·0.0256617s·(thread);·0s·(gc)95 ·--·used·0.0231091s·(cpu);·0.0258764s·(thread);·0s·(gc)
  
96 o4·=·1</code></pre>96 o4·=·1</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees·phi101 ··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees·phi
102 ·--·used·0.402417s·(cpu);·0.331126s·(thread);·0s·(gc)102 ·--·used·0.487287s·(cpu);·0.358582s·(thread);·0s·(gc)
  
103 o5·=·{1,·3,·9,·17,·21,·15,·5}103 o5·=·{1,·3,·9,·17,·21,·15,·5}
  
104 o5·:·List</code></pre>104 o5·:·List</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i6·:·time·projectiveDegrees(phi,NumDegrees=>0)109 ··············<pre><code·class="language-macaulay2">i6·:·time·projectiveDegrees(phi,NumDegrees=>0)
110 ·--·used·0.117123s·(cpu);·0.0754688s·(thread);·0s·(gc)110 ·--·used·0.116466s·(cpu);·0.0642495s·(thread);·0s·(gc)
  
111 o6·=·{5}111 o6·=·{5}
  
112 o6·:·List</code></pre>112 o6·:·List</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i7·:·time·phi·=·toMap(phi,Dominant=>J)117 ··············<pre><code·class="language-macaulay2">i7·:·time·phi·=·toMap(phi,Dominant=>J)
118 ·--·used·0.000157788s·(cpu);·0.00186622s·(thread);·0s·(gc)118 ·--·used·0.00083198s·(cpu);·0.00232522s·(thread);·0s·(gc)
  
119 ·······································································ZZ119 ·······································································ZZ
120 ·····································································------[x·..x·]120 ·····································································------[x·..x·]
121 ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2121 ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2
122 o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})122 o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·})
123 ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6123 ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6
124 ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7124 ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7
Offset 136, 15 lines modifiedOffset 136, 15 lines modified
136 ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)136 ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)
137 ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre>137 ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre>
138 ············</td>138 ············</td>
139 ··········</tr>139 ··········</tr>
140 ··········<tr>140 ··········<tr>
141 ············<td>141 ············<td>
142 ··············<pre><code·class="language-macaulay2">i8·:·time·psi·=·inverseMap·phi142 ··············<pre><code·class="language-macaulay2">i8·:·time·psi·=·inverseMap·phi
143 ·--·used·0.456109s·(cpu);·0.412271s·(thread);·0s·(gc)143 ·--·used·0.417561s·(cpu);·0.367241s·(thread);·0s·(gc)
  
144 ·······················································ZZ144 ·······················································ZZ
145 ·····················································------[x·..x·]145 ·····················································------[x·..x·]
146 ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································2146 ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································2
147 o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·})147 o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·})
148 ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·9148 ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·9
149 ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7149 ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7
Offset 156, 44 lines modifiedOffset 156, 44 lines modified
156 ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6156 ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6
157 ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre>157 ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre>
158 ············</td>158 ············</td>
159 ··········</tr>159 ··········</tr>
160 ··········<tr>160 ··········<tr>
161 ············<td>161 ············<td>
162 ··············<pre><code·class="language-macaulay2">i9·:·time·isInverseMap(phi,psi)162 ··············<pre><code·class="language-macaulay2">i9·:·time·isInverseMap(phi,psi)
163 ·--·used·0.00480108s·(cpu);·0.00772231s·(thread);·0s·(gc)163 ·--·used·0.00847325s·(cpu);·0.00769845s·(thread);·0s·(gc)
  
164 o9·=·true</code></pre>164 o9·=·true</code></pre>
165 ············</td>165 ············</td>
166 ··········</tr>166 ··········</tr>
167 ··········<tr>167 ··········<tr>
168 ············<td>168 ············<td>
169 ··············<pre><code·class="language-macaulay2">i10·:·time·degreeMap·psi169 ··············<pre><code·class="language-macaulay2">i10·:·time·degreeMap·psi
170 ·--·used·0.192915s·(cpu);·0.149974s·(thread);·0s·(gc)170 ·--·used·0.2006s·(cpu);·0.160561s·(thread);·0s·(gc)
  
171 o10·=·1</code></pre>171 o10·=·1</code></pre>
172 ············</td>172 ············</td>
173 ··········</tr>173 ··········</tr>
174 ··········<tr>174 ··········<tr>
175 ············<td>175 ············<td>
176 ··············<pre><code·class="language-macaulay2">i11·:·time·projectiveDegrees·psi176 ··············<pre><code·class="language-macaulay2">i11·:·time·projectiveDegrees·psi
177 ·--·used·4.3311s·(cpu);·4.01164s·(thread);·0s·(gc)177 ·--·used·4.93938s·(cpu);·4.57918s·(thread);·0s·(gc)
  
178 o11·=·{5,·15,·21,·17,·9,·3,·1}178 o11·=·{5,·15,·21,·17,·9,·3,·1}
  
179 o11·:·List</code></pre>179 o11·:·List</code></pre>
180 ············</td>180 ············</td>
181 ··········</tr>181 ··········</tr>
182 ········</table>182 ········</table>
183 ········<p>We·repeat·the·example·using·the·type·<a·title="the·class·of·all·rational·maps·between·absolutely·irreducible·projective·varieties·over·a·field"·href="___Rational__Map.html">RationalMap</a>·and·using·deterministic·methods.</p>183 ········<p>We·repeat·the·example·using·the·type·<a·title="the·class·of·all·rational·maps·between·absolutely·irreducible·projective·varieties·over·a·field"·href="___Rational__Map.html">RationalMap</a>·and·using·deterministic·methods.</p>
184 ········<table·class="examples">184 ········<table·class="examples">
185 ··········<tr>185 ··········<tr>
186 ············<td>186 ············<td>
187 ··············<pre><code·class="language-macaulay2">i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})187 ··············<pre><code·class="language-macaulay2">i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})
188 ·--·used·0.000879674s·(cpu);·0.00189829s·(thread);·0s·(gc)188 ·--·used·0.000183784s·(cpu);·0.00200697s·(thread);·0s·(gc)
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Offset 25, 15 lines modifiedOffset 25, 15 lines modified
25 map)·from·a·list·of·$m+1$·homogeneous·elements·of·the·same·degree·in·$K25 map)·from·a·list·of·$m+1$·homogeneous·elements·of·the·same·degree·in·$K
26 [x_0,...,x_n]/I$.26 [x_0,...,x_n]/I$.
27 Below·is·an·example·using·the·methods·provided·by·this·package,·dealing·with·a27 Below·is·an·example·using·the·methods·provided·by·this·package,·dealing·with·a
28 birational·transformation·$\Phi:\mathbb{P}^6·\dashrightarrow·\mathbb{G}28 birational·transformation·$\Phi:\mathbb{P}^6·\dashrightarrow·\mathbb{G}
29 (2,4)\subset\mathbb{P}^9$·of·bidegree·$(3,3)$.29 (2,4)\subset\mathbb{P}^9$·of·bidegree·$(3,3)$.
30 i1·:·ZZ/300007[t_0..t_6];30 i1·:·ZZ/300007[t_0..t_6];
31 i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})31 i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})
32 ·--·used·0.00401246s·(cpu);·0.00395623s·(thread);·0s·(gc)32 ·--·used·0.00394461s·(cpu);·0.00417509s·(thread);·0s·(gc)
  
33 ············ZZ··············ZZ················3················2····233 ············ZZ··············ZZ················3················2····2
34 2········2······················2··················2····2·················234 2········2······················2··················2····2·················2
35 3················2····2················2·································235 3················2····2················2·································2
36 2····2··································2········2······················236 2····2··································2········2······················2
37 2························2·························2····2·················237 2························2·························2····2·················2
38 3················2····238 3················2····2
Offset 52, 43 lines modifiedOffset 52, 43 lines modified
52 0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····452 0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4
53 3·4·5····2·5····3·6····2·4·653 3·4·5····2·5····3·6····2·4·6
  
54 ···············ZZ·················ZZ54 ···············ZZ·················ZZ
55 o2·:·RingMap·------[t·..t·]·<--·------[x·..x·]55 o2·:·RingMap·------[t·..t·]·<--·------[x·..x·]
56 ·············300007··0···6······300007··0···956 ·············300007··0···6······300007··0···9
57 i3·:·time·J·=·kernel(phi,2)57 i3·:·time·J·=·kernel(phi,2)
58 ·--·used·0.0410654s·(cpu);·0.0419253s·(thread);·0s·(gc)58 ·--·used·0.0349428s·(cpu);·0.0380202s·(thread);·0s·(gc)
  
59 o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x59 o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x
60 ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·460 ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4
61 ·····------------------------------------------------------------------------61 ·····------------------------------------------------------------------------
62 ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)62 ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)
63 ········1·6····0·8···2·4····1·5····0·763 ········1·6····0·8···2·4····1·5····0·7
  
64 ················ZZ64 ················ZZ
65 o3·:·Ideal·of·------[x·..x·]65 o3·:·Ideal·of·------[x·..x·]
66 ··············300007··0···966 ··············300007··0···9
67 i4·:·time·degreeMap·phi67 i4·:·time·degreeMap·phi
68 ·--·used·0.0255553s·(cpu);·0.0256617s·(thread);·0s·(gc)68 ·--·used·0.0231091s·(cpu);·0.0258764s·(thread);·0s·(gc)
  
69 o4·=·169 o4·=·1
70 i5·:·time·projectiveDegrees·phi70 i5·:·time·projectiveDegrees·phi
71 ·--·used·0.402417s·(cpu);·0.331126s·(thread);·0s·(gc)71 ·--·used·0.487287s·(cpu);·0.358582s·(thread);·0s·(gc)
  
72 o5·=·{1,·3,·9,·17,·21,·15,·5}72 o5·=·{1,·3,·9,·17,·21,·15,·5}
  
73 o5·:·List73 o5·:·List
74 i6·:·time·projectiveDegrees(phi,NumDegrees=>0)74 i6·:·time·projectiveDegrees(phi,NumDegrees=>0)
75 ·--·used·0.117123s·(cpu);·0.0754688s·(thread);·0s·(gc)75 ·--·used·0.116466s·(cpu);·0.0642495s·(thread);·0s·(gc)
  
76 o6·=·{5}76 o6·=·{5}
  
77 o6·:·List77 o6·:·List
78 i7·:·time·phi·=·toMap(phi,Dominant=>J)78 i7·:·time·phi·=·toMap(phi,Dominant=>J)
79 ·--·used·0.000157788s·(cpu);·0.00186622s·(thread);·0s·(gc)79 ·--·used·0.00083198s·(cpu);·0.00232522s·(thread);·0s·(gc)
  
80 ·······································································ZZ80 ·······································································ZZ
81 ·····································································------[x81 ·····································································------[x
82 ..x·]82 ..x·]
83 ············ZZ·······················································300007··083 ············ZZ·······················································300007··0
84 9··················································3················2····284 9··················································3················2····2
85 2········2······················2··················2····2·················285 2········2······················2··················2····2·················2
Offset 123, 15 lines modifiedOffset 123, 15 lines modified
123 o7·:·RingMap·------[t·..t·]·<--·-----------------------------------------------123 o7·:·RingMap·------[t·..t·]·<--·-----------------------------------------------
124 -----------------------------------------------------124 -----------------------------------------------------
125 ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-125 ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-
126 x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)126 x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)
127 ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5127 ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5
128 2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7128 2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7
129 i8·:·time·psi·=·inverseMap·phi129 i8·:·time·psi·=·inverseMap·phi
130 ·--·used·0.456109s·(cpu);·0.412271s·(thread);·0s·(gc)130 ·--·used·0.417561s·(cpu);·0.367241s·(thread);·0s·(gc)
  
131 ·······················································ZZ131 ·······················································ZZ
132 ·····················································------[x·..x·]132 ·····················································------[x·..x·]
133 ·····················································300007··0···9133 ·····················································300007··0···9
134 ZZ··············3················2···············2····2134 ZZ··············3················2···············2····2
135 2··························2·····2········2·······························2135 2··························2·····2········2·······························2
136 2···············2·············2·······················3136 2···············2·············2·······················3
Offset 164, 31 lines modifiedOffset 164, 31 lines modified
164 o8·:·RingMap·------------------------------------------------------------------164 o8·:·RingMap·------------------------------------------------------------------
165 ----------------------------------·<--·------[t·..t·]165 ----------------------------------·<--·------[t·..t·]
166 ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x166 ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x
167 -·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6167 -·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6
168 ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4168 ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4
169 1·6····0·8···2·4····1·5····0·7169 1·6····0·8···2·4····1·5····0·7
170 i9·:·time·isInverseMap(phi,psi)170 i9·:·time·isInverseMap(phi,psi)
171 ·--·used·0.00480108s·(cpu);·0.00772231s·(thread);·0s·(gc)171 ·--·used·0.00847325s·(cpu);·0.00769845s·(thread);·0s·(gc)
  
172 o9·=·true172 o9·=·true
173 i10·:·time·degreeMap·psi173 i10·:·time·degreeMap·psi
174 ·--·used·0.192915s·(cpu);·0.149974s·(thread);·0s·(gc)174 ·--·used·0.2006s·(cpu);·0.160561s·(thread);·0s·(gc)
  
175 o10·=·1175 o10·=·1
176 i11·:·time·projectiveDegrees·psi176 i11·:·time·projectiveDegrees·psi
177 ·--·used·4.3311s·(cpu);·4.01164s·(thread);·0s·(gc)177 ·--·used·4.93938s·(cpu);·4.57918s·(thread);·0s·(gc)
  
178 o11·=·{5,·15,·21,·17,·9,·3,·1}178 o11·=·{5,·15,·21,·17,·9,·3,·1}
  
179 o11·:·List179 o11·:·List
180 We·repeat·the·example·using·the·type·_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·and·using·deterministic180 We·repeat·the·example·using·the·type·_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·and·using·deterministic
181 methods.181 methods.
182 i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})182 i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}})
183 ·--·used·0.000879674s·(cpu);·0.00189829s·(thread);·0s·(gc)183 ·--·used·0.000183784s·(cpu);·0.00200697s·(thread);·0s·(gc)
  
184 o12·=·--·rational·map·--184 o12·=·--·rational·map·--
185 ·····················ZZ185 ·····················ZZ
186 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])186 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])
187 ···················300007··0···1···2···3···4···5···6187 ···················300007··0···1···2···3···4···5···6
188 ·····················ZZ188 ·····················ZZ
189 ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])189 ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])
Offset 233, 15 lines modifiedOffset 233, 15 lines modified
233 ··························3················2····2233 ··························3················2····2
234 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t234 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t
235 ··························4·····3·4·5····2·5····3·6····2·4·6235 ··························4·····3·4·5····2·5····3·6····2·4·6
236 ······················}236 ······················}
  
237 o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)237 o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)
238 i13·:·time·phi·=·rationalMap(phi,Dominant=>2)238 i13·:·time·phi·=·rationalMap(phi,Dominant=>2)
239 ·--·used·0.12219s·(cpu);·0.080011s·(thread);·0s·(gc)239 ·--·used·0.130066s·(cpu);·0.0698304s·(thread);·0s·(gc)
  
240 o13·=·--·rational·map·--240 o13·=·--·rational·map·--
241 ·····················ZZ241 ·····················ZZ
242 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])242 ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·])
243 ···················300007··0···1···2···3···4···5···6243 ···················300007··0···1···2···3···4···5···6
244 ···································ZZ244 ···································ZZ
245 ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x245 ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x
Offset 304, 15 lines modifiedOffset 304, 15 lines modified
304 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t304 ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t
305 ··························4·····3·4·5····2·5····3·6····2·4·6305 ··························4·····3·4·5····2·5····3·6····2·4·6
306 ······················}306 ······················}
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721 B
./usr/share/doc/Macaulay2/Cyclotomic/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=107 #:len=10
8 Q3ljbG90b21pYw==8 Q3ljbG90b21pYw==
9 #:len=4789 #:len=478
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY3ljbG90b21pYyBmaWVsZHMiLCBEZXNj10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY3ljbG90b21pYyBmaWVsZHMiLCBEZXNj
11 cmlwdGlvbiA9PiAoRU17IkN5Y2xvdG9taWMifSwiIGlzIGEgcGFja2FnZSBmb3IgY3ljbG90b21p11 cmlwdGlvbiA9PiAoRU17IkN5Y2xvdG9taWMifSwiIGlzIGEgcGFja2FnZSBmb3IgY3ljbG90b21p
733 B
./usr/share/doc/Macaulay2/DGAlgebras/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=207 #:len=20
8 c291cmNlKERHQWxnZWJyYU1hcCk=8 c291cmNlKERHQWxnZWJyYU1hcCk=
9 #:len=6599 #:len=659
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3V0cHV0cyB0aGUgc291cmNlIG9mIGEg10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3V0cHV0cyB0aGUgc291cmNlIG9mIGEg
11 REdBbGdlYnJhTWFwIiwgImxpbmVudW0iID0+IDMxMDgsIElucHV0cyA9PiB7U1BBTntUVHsicGhp11 REdBbGdlYnJhTWFwIiwgImxpbmVudW0iID0+IDMxMDgsIElucHV0cyA9PiB7U1BBTntUVHsicGhp
1.07 KB
./usr/share/doc/Macaulay2/DGAlgebras/example-output/___Basic_spoperations_spon_sp__D__G_sp__Algebra_sp__Maps.out
    
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155 ··································2·····2·····2·······2·2·····2·2······2·2······2·2·····2·2········2·2·······2·2········2·······2·······2155 ··································2·····2·····2·······2·2·····2·2······2·2······2·2·····2·2········2·2·······2·2········2·······2·······2
156 ·······Differential·=>·{a,·b,·c,·a·T·,·b·T·,·c·T·,·a*b·c·T·,·b·c·T·,·-a·b·T·,·-a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·}156 ·······Differential·=>·{a,·b,·c,·a·T·,·b·T·,·c·T·,·a*b·c·T·,·b·c·T·,·-a·b·T·,·-a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·}
157 ····································1·····2·····3·········1·······4········6········5·······3·4········3·5·······2·4······1·7·····3·7·····2·7157 ····································1·····2·····3·········1·······4········6········5·······3·4········3·5·······2·4······1·7·····3·7·····2·7
  
158 o16·:·DGAlgebra158 o16·:·DGAlgebra
  
159 i17·:·HHg·=·HH·g159 i17·:·HHg·=·HH·g
160 ·--·used·0.646693s·(cpu);·0.10954s·(thread);·0s·(gc)160 ·--·used·0.559673s·(cpu);·0.0826428s·(thread);·0s·(gc)
161 Finding·easy·relations···········:·161 Finding·easy·relations···········:·
162 ··························ZZ162 ··························ZZ
163 ·························---[a..c]163 ·························---[a..c]
164 ············ZZ···········101164 ············ZZ···········101
165 o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})165 o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})
166 ···········101··1···2···········3···1·····1166 ···········101··1···2···········3···1·····1
167 ························(c,·b,·a·)167 ························(c,·b,·a·)
1.06 KB
./usr/share/doc/Macaulay2/DGAlgebras/example-output/___Basic_spoperations_spon_sp__D__G_sp__Algebras.out
    
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30 ······Underlying·algebra·=>·R[S·..S·]30 ······Underlying·algebra·=>·R[S·..S·]
31 ·······························1···431 ·······························1···4
32 ······Differential·=>·{a,·b,·c,·d}32 ······Differential·=>·{a,·b,·c,·d}
  
33 o4·:·DGAlgebra33 o4·:·DGAlgebra
  
34 i5·:·HB·=·HH·B34 i5·:·HB·=·HH·B
35 ·--·used·0.66153s·(cpu);·0.0767972s·(thread);·0s·(gc)35 ·--·used·0.578537s·(cpu);·0.09041s·(thread);·0s·(gc)
36 Finding·easy·relations···········:·36 Finding·easy·relations···········:·
37 o5·=·HB37 o5·=·HB
  
38 o5·:·PolynomialRing,·4·skew·commutative·variable(s)38 o5·:·PolynomialRing,·4·skew·commutative·variable(s)
  
39 i6·:·describe·HB39 i6·:·describe·HB
  
Offset 68, 15 lines modifiedOffset 68, 15 lines modified
68 ····································268 ····································2
69 ······Differential·=>·{a,·b,·c,·d,·a·T·}69 ······Differential·=>·{a,·b,·c,·d,·a·T·}
70 ······································170 ······································1
  
71 o9·:·DGAlgebra71 o9·:·DGAlgebra
  
72 i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4)72 i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4)
73 ·--·used·1.15043s·(cpu);·0.125478s·(thread);·0s·(gc)73 ·--·used·1.17211s·(cpu);·0.170466s·(thread);·0s·(gc)
74 Finding·easy·relations···········:·74 Finding·easy·relations···········:·
75 ·······ZZ75 ·······ZZ
76 o10·=·---[X·..X·]76 o10·=·---[X·..X·]
77 ······101··1···377 ······101··1···3
  
78 o10·:·PolynomialRing,·3·skew·commutative·variable(s)78 o10·:·PolynomialRing,·3·skew·commutative·variable(s)
  
684 B
./usr/share/doc/Macaulay2/DGAlgebras/example-output/___H__H_sp__D__G__Algebra__Map.out
    
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55 ···············{2}·|·0·|55 ···············{2}·|·0·|
56 ···············{2}·|·0·|56 ···············{2}·|·0·|
57 ···············{2}·|·1·|57 ···············{2}·|·1·|
  
58 o6·:·ComplexMap58 o6·:·ComplexMap
  
59 i7·:·HHg·=·HH·g59 i7·:·HHg·=·HH·g
60 ·--·used·0.478531s·(cpu);·0.0677541s·(thread);·0s·(gc)60 ·--·used·0.545475s·(cpu);·0.0757035s·(thread);·0s·(gc)
61 Finding·easy·relations···········:·61 Finding·easy·relations···········:·
62 ·························ZZ62 ·························ZZ
63 ························---[a..c]63 ························---[a..c]
64 ···········ZZ···········10164 ···········ZZ···········101
65 o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})65 o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})
66 ··········101··1···2···········3···1·····166 ··········101··1···2···········3···1·····1
67 ·······················(c,·b,·a·)67 ·······················(c,·b,·a·)
1.19 KB
./usr/share/doc/Macaulay2/DGAlgebras/example-output/___The_sp__Koszul_spcomplex_spas_spa_sp__D__G_sp__Algebra.out
    
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49 ······························1·····························································{6}·|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·d·c·b·a·|·····349 ······························1·····························································{6}·|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·d·c·b·a·|·····3
50 ····················································································50 ····················································································
51 ···················································································251 ···················································································2
  
52 o6·:·Complex52 o6·:·Complex
  
53 i7·:·HKR·=·HH·KR53 i7·:·HKR·=·HH·KR
54 ·--·used·0.697355s·(cpu);·0.0756314s·(thread);·0s·(gc)54 ·--·used·0.53925s·(cpu);·0.0766079s·(thread);·0s·(gc)
55 Finding·easy·relations···········:·55 Finding·easy·relations···········:·
56 o7·=·HKR56 o7·=·HKR
  
57 o7·:·PolynomialRing,·4·skew·commutative·variable(s)57 o7·:·PolynomialRing,·4·skew·commutative·variable(s)
  
58 i8·:·ideal·HKR58 i8·:·ideal·HKR
  
Offset 68, 15 lines modifiedOffset 68, 15 lines modified
68 i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2-c^2*d^2}68 i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2-c^2*d^2}
  
69 o9·=·R'69 o9·=·R'
  
70 o9·:·QuotientRing70 o9·:·QuotientRing
  
71 i10·:·HKR'·=·HH·koszulComplexDGA·R'71 i10·:·HKR'·=·HH·koszulComplexDGA·R'
72 ·--·used·2.5175s·(cpu);·0.813839s·(thread);·0s·(gc)72 ·--·used·2.50507s·(cpu);·0.803209s·(thread);·0s·(gc)
73 Finding·easy·relations···········:·73 Finding·easy·relations···········:·
74 o10·=·HKR'74 o10·=·HKR'
  
75 o10·:·QuotientRing75 o10·:·QuotientRing
  
76 i11·:·numgens·HKR'76 i11·:·numgens·HKR'
  
508 B
./usr/share/doc/Macaulay2/DGAlgebras/example-output/_cycles.out
    
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18 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))18 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
19 o3·=·{1,·4,·6,·4,·1}19 o3·=·{1,·4,·6,·4,·1}
  
20 o3·:·List20 o3·:·List
  
21 i4·:·HA·=·homologyAlgebra(A)21 i4·:·HA·=·homologyAlgebra(A)
22 ·--·used·1.89945s·(cpu);·0.326972s·(thread);·0s·(gc)22 ·--·used·1.54595s·(cpu);·0.197557s·(thread);·0s·(gc)
23 Finding·easy·relations···········:·23 Finding·easy·relations···········:·
24 o4·=·HA24 o4·=·HA
  
25 o4·:·PolynomialRing,·4·skew·commutative·variable(s)25 o4·:·PolynomialRing,·4·skew·commutative·variable(s)
  
26 i5·:·numgens·HA26 i5·:·numgens·HA
  
1.7 KB
./usr/share/doc/Macaulay2/DGAlgebras/example-output/_homology__Algebra.out
    
Offset 18, 15 lines modifiedOffset 18, 15 lines modified
18 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))18 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
19 o3·=·{1,·4,·6,·4,·1}19 o3·=·{1,·4,·6,·4,·1}
  
20 o3·:·List20 o3·:·List
  
21 i4·:·HA·=·homologyAlgebra(A)21 i4·:·HA·=·homologyAlgebra(A)
22 ·--·used·0.65759s·(cpu);·0.0920584s·(thread);·0s·(gc)22 ·--·used·0.531874s·(cpu);·0.0919985s·(thread);·0s·(gc)
23 Finding·easy·relations···········:·23 Finding·easy·relations···········:·
24 o4·=·HA24 o4·=·HA
  
25 o4·:·PolynomialRing,·4·skew·commutative·variable(s)25 o4·:·PolynomialRing,·4·skew·commutative·variable(s)
  
26 i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3}26 i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3}
  
Offset 46, 15 lines modifiedOffset 46, 15 lines modified
46 i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))46 i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
47 o7·=·{1,·5,·10,·10,·4}47 o7·=·{1,·5,·10,·10,·4}
  
48 o7·:·List48 o7·:·List
  
49 i8·:·HA·=·homologyAlgebra(A)49 i8·:·HA·=·homologyAlgebra(A)
50 ·--·used·2.08481s·(cpu);·0.359835s·(thread);·0s·(gc)50 ·--·used·1.69612s·(cpu);·0.274983s·(thread);·0s·(gc)
51 Finding·easy·relations···········:·51 Finding·easy·relations···········:·
52 o8·=·HA52 o8·=·HA
  
53 o8·:·QuotientRing53 o8·:·QuotientRing
  
54 i9·:·numgens·HA54 i9·:·numgens·HA
  
Offset 114, 15 lines modifiedOffset 114, 15 lines modified
114 i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))114 i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
115 o15·=·{1,·7,·7,·1}115 o15·=·{1,·7,·7,·1}
  
116 o15·:·List116 o15·:·List
  
117 i16·:·HA·=·homologyAlgebra(A)117 i16·:·HA·=·homologyAlgebra(A)
118 ·--·used·1.14669s·(cpu);·0.187573s·(thread);·0s·(gc)118 ·--·used·0.816507s·(cpu);·0.137409s·(thread);·0s·(gc)
119 Finding·easy·relations···········:·119 Finding·easy·relations···········:·
120 o16·=·HA120 o16·=·HA
  
121 o16·:·QuotientRing121 o16·:·QuotientRing
  
122 i17·:·R·=·ZZ/101[a,b,c,d]122 i17·:·R·=·ZZ/101[a,b,c,d]
  
Offset 151, 14 lines modifiedOffset 151, 14 lines modified
151 ·······Underlying·algebra·=>·S[T·..T·]151 ·······Underlying·algebra·=>·S[T·..T·]
152 ································1···4152 ································1···4
153 ·······Differential·=>·{a,·b,·c,·d}153 ·······Differential·=>·{a,·b,·c,·d}
  
154 o20·:·DGAlgebra154 o20·:·DGAlgebra
  
155 i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14)155 i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14)
156 ·--·used·0.70203s·(cpu);·0.144184s·(thread);·0s·(gc)156 ·--·used·0.547253s·(cpu);·0.0778176s·(thread);·0s·(gc)
157 Finding·easy·relations···········:·157 Finding·easy·relations···········:·
158 o21·=·HB158 o21·=·HB
  
159 o21·:·PolynomialRing,·4·skew·commutative·variable(s)159 o21·:·PolynomialRing,·4·skew·commutative·variable(s)
  
160 i22·:·160 i22·:·
482 B
./usr/share/doc/Macaulay2/DGAlgebras/example-output/_homology__Class.out
    
Offset 43, 15 lines modifiedOffset 43, 15 lines modified
43 o6·=·y·T43 o6·=·y·T
44 ········244 ········2
  
45 o6·:·R[T·..T·]45 o6·:·R[T·..T·]
46 ········1···346 ········1···3
  
47 i7·:·H·=·HH(KR)47 i7·:·H·=·HH(KR)
48 ·--·used·0.633698s·(cpu);·0.084598s·(thread);·0s·(gc)48 ·--·used·0.556701s·(cpu);·0.0736723s·(thread);·0s·(gc)
49 Finding·easy·relations···········:·49 Finding·easy·relations···········:·
50 o7·=·H50 o7·=·H
  
51 o7·:·PolynomialRing,·3·skew·commutative·variable(s)51 o7·:·PolynomialRing,·3·skew·commutative·variable(s)
  
52 i8·:·homologyClass(KR,z1*z2)52 i8·:·homologyClass(KR,z1*z2)
  
545 B
./usr/share/doc/Macaulay2/DGAlgebras/example-output/_homology__Module.out
    
Offset 34, 15 lines modifiedOffset 34, 15 lines modified
34 o5·=·R··<--·R··<--·R··<--·R··<--·R34 o5·=·R··<--·R··<--·R··<--·R··<--·R
35 ··································35 ··································
36 ·····0······1······2······3······436 ·····0······1······2······3······4
  
37 o5·:·Complex37 o5·:·Complex
  
38 i6·:·HKR·=·HH(KR)38 i6·:·HKR·=·HH(KR)
39 ·--·used·1.45727s·(cpu);·0.244941s·(thread);·0s·(gc)39 ·--·used·1.31079s·(cpu);·0.246631s·(thread);·0s·(gc)
40 Finding·easy·relations···········:·40 Finding·easy·relations···········:·
41 o6·=·HKR41 o6·=·HKR
  
42 o6·:·QuotientRing42 o6·:·QuotientRing
  
43 i7·:·degList·=·first·entries·vars·Q·/·degree·/·first43 i7·:·degList·=·first·entries·vars·Q·/·degree·/·first
  
585 B
./usr/share/doc/Macaulay2/DGAlgebras/example-output/_massey__Triple__Product.out
    
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68 ···············268 ···············2
69 o9·=·(true,·x·y·T·T·T··-·x·x·y·T·T·T·)69 o9·=·(true,·x·y·T·T·T··-·x·x·y·T·T·T·)
70 ·············2·2·1·2·3····1·2·2·2·3·470 ·············2·2·1·2·3····1·2·2·2·3·4
  
71 o9·:·Sequence71 o9·:·Sequence
  
72 i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3)72 i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3)
73 ·--·used·3.06855s·(cpu);·0.756243s·(thread);·0s·(gc)73 ·--·used·2.6074s·(cpu);·0.754577s·(thread);·0s·(gc)
74 Finding·easy·relations···········:·74 Finding·easy·relations···········:·
75 ·············275 ·············2
76 o10·=·x·x·y·z·T·T·T·T76 o10·=·x·x·y·z·T·T·T·T
77 ·······1·2·2···2·3·4·577 ·······1·2·2···2·3·4·5
  
78 o10·:·R[T·..T·]78 o10·:·R[T·..T·]
79 ·········1···579 ·········1···5
655 B
./usr/share/doc/Macaulay2/DGAlgebras/example-output/_massey__Triple__Product_lp__D__G__Algebra_cm__Z__Z_cm__Z__Z_cm__Z__Z_rp.out
    
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27 ·······························1···427 ·······························1···4
28 ······Differential·=>·{t·,·t·,·t·,·t·}28 ······Differential·=>·{t·,·t·,·t·,·t·}
29 ························1···2···3···429 ························1···2···3···4
  
30 o4·:·DGAlgebra30 o4·:·DGAlgebra
  
31 i5·:·H·=·HH(KR)31 i5·:·H·=·HH(KR)
32 ·--·used·2.14024s·(cpu);·0.357025s·(thread);·0s·(gc)32 ·--·used·1.88136s·(cpu);·0.405927s·(thread);·0s·(gc)
33 Finding·easy·relations···········:·33 Finding·easy·relations···········:·
34 o5·=·H34 o5·=·H
  
35 o5·:·QuotientRing35 o5·:·QuotientRing
  
36 i6·:·masseys·=·masseyTripleProduct(KR,1,1,1);36 i6·:·masseys·=·masseyTripleProduct(KR,1,1,1);
  
527 B
./usr/share/doc/Macaulay2/DGAlgebras/example-output/_tor__Algebra_lp__Ring_cm__Ring_rp.out
    
Offset 11, 15 lines modifiedOffset 11, 15 lines modified
11 i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3}11 i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3}
  
12 o3·=·S12 o3·=·S
  
13 o3·:·QuotientRing13 o3·:·QuotientRing
  
14 i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8)14 i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8)
15 ·--·used·3.19211s·(cpu);·0.709337s·(thread);·0s·(gc)15 ·--·used·2.75995s·(cpu);·0.721281s·(thread);·0s·(gc)
16 Finding·easy·relations···········:·16 Finding·easy·relations···········:·
17 o4·=·HB17 o4·=·HB
  
18 o4·:·QuotientRing18 o4·:·QuotientRing
  
19 i5·:·numgens·HB19 i5·:·numgens·HB
  
1.56 KB
./usr/share/doc/Macaulay2/DGAlgebras/html/___Basic_spoperations_spon_sp__D__G_sp__Algebra_sp__Maps.html
    
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289 ········<div>289 ········<div>
290 ··········<p>One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.</p>290 ··········<p>One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.</p>
291 ········</div>291 ········</div>
292 ········<table·class="examples">292 ········<table·class="examples">
293 ··········<tr>293 ··········<tr>
294 ············<td>294 ············<td>
295 ··············<pre><code·class="language-macaulay2">i17·:·HHg·=·HH·g295 ··············<pre><code·class="language-macaulay2">i17·:·HHg·=·HH·g
296 ·--·used·0.646693s·(cpu);·0.10954s·(thread);·0s·(gc)296 ·--·used·0.559673s·(cpu);·0.0826428s·(thread);·0s·(gc)
297 Finding·easy·relations···········:·297 Finding·easy·relations···········:·
298 ··························ZZ298 ··························ZZ
299 ·························---[a..c]299 ·························---[a..c]
300 ············ZZ···········101300 ············ZZ···········101
301 o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})301 o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})
302 ···········101··1···2···········3···1·····1302 ···········101··1···2···········3···1·····1
303 ························(c,·b,·a·)303 ························(c,·b,·a·)
733 B
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210 a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·}210 a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·}
211 ····································1·····2·····3·········1·······4········6211 ····································1·····2·····3·········1·······4········6
212 5·······3·4········3·5·······2·4······1·7·····3·7·····2·7212 5·······3·4········3·5·······2·4······1·7·····3·7·····2·7
  
213 o16·:·DGAlgebra213 o16·:·DGAlgebra
214 One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.214 One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.
215 i17·:·HHg·=·HH·g215 i17·:·HHg·=·HH·g
216 ·--·used·0.646693s·(cpu);·0.10954s·(thread);·0s·(gc)216 ·--·used·0.559673s·(cpu);·0.0826428s·(thread);·0s·(gc)
217 Finding·easy·relations···········:217 Finding·easy·relations···········:
218 ··························ZZ218 ··························ZZ
219 ·························---[a..c]219 ·························---[a..c]
220 ············ZZ···········101220 ············ZZ···········101
221 o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})221 o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})
222 ···········101··1···2···········3···1·····1222 ···········101··1···2···········3···1·····1
223 ························(c,·b,·a·)223 ························(c,·b,·a·)
2.24 KB
./usr/share/doc/Macaulay2/DGAlgebras/html/___Basic_spoperations_spon_sp__D__G_sp__Algebras.html
    
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113 ········<div>113 ········<div>
114 ··········<p>One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)·command.</p>114 ··········<p>One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)·command.</p>
115 ········</div>115 ········</div>
116 ········<table·class="examples">116 ········<table·class="examples">
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i5·:·HB·=·HH·B119 ··············<pre><code·class="language-macaulay2">i5·:·HB·=·HH·B
120 ·--·used·0.66153s·(cpu);·0.0767972s·(thread);·0s·(gc)120 ·--·used·0.578537s·(cpu);·0.09041s·(thread);·0s·(gc)
121 Finding·easy·relations···········:·121 Finding·easy·relations···········:·
122 o5·=·HB122 o5·=·HB
  
123 o5·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>123 o5·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
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174 o9·:·DGAlgebra</code></pre>174 o9·:·DGAlgebra</code></pre>
175 ············</td>175 ············</td>
176 ··········</tr>176 ··········</tr>
177 ··········<tr>177 ··········<tr>
178 ············<td>178 ············<td>
179 ··············<pre><code·class="language-macaulay2">i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4)179 ··············<pre><code·class="language-macaulay2">i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4)
180 ·--·used·1.15043s·(cpu);·0.125478s·(thread);·0s·(gc)180 ·--·used·1.17211s·(cpu);·0.170466s·(thread);·0s·(gc)
181 Finding·easy·relations···········:·181 Finding·easy·relations···········:·
182 ·······ZZ182 ·······ZZ
183 o10·=·---[X·..X·]183 o10·=·---[X·..X·]
184 ······101··1···3184 ······101··1···3
  
185 o10·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre>185 o10·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre>
186 ············</td>186 ············</td>
1010 B
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42 ·······························1···442 ·······························1···4
43 ······Differential·=>·{a,·b,·c,·d}43 ······Differential·=>·{a,·b,·c,·d}
  
44 o4·:·DGAlgebra44 o4·:·DGAlgebra
45 One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)45 One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)
46 command.46 command.
47 i5·:·HB·=·HH·B47 i5·:·HB·=·HH·B
48 ·--·used·0.66153s·(cpu);·0.0767972s·(thread);·0s·(gc)48 ·--·used·0.578537s·(cpu);·0.09041s·(thread);·0s·(gc)
49 Finding·easy·relations···········:49 Finding·easy·relations···········:
50 o5·=·HB50 o5·=·HB
  
51 o5·:·PolynomialRing,·4·skew·commutative·variable(s)51 o5·:·PolynomialRing,·4·skew·commutative·variable(s)
52 i6·:·describe·HB52 i6·:·describe·HB
  
53 ······ZZ53 ······ZZ
Offset 86, 15 lines modifiedOffset 86, 15 lines modified
86 ·······························1···586 ·······························1···5
87 ····································287 ····································2
88 ······Differential·=>·{a,·b,·c,·d,·a·T·}88 ······Differential·=>·{a,·b,·c,·d,·a·T·}
89 ······································189 ······································1
  
90 o9·:·DGAlgebra90 o9·:·DGAlgebra
91 i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4)91 i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4)
92 ·--·used·1.15043s·(cpu);·0.125478s·(thread);·0s·(gc)92 ·--·used·1.17211s·(cpu);·0.170466s·(thread);·0s·(gc)
93 Finding·easy·relations···········:93 Finding·easy·relations···········:
94 ·······ZZ94 ·······ZZ
95 o10·=·---[X·..X·]95 o10·=·---[X·..X·]
96 ······101··1···396 ······101··1···3
  
97 o10·:·PolynomialRing,·3·skew·commutative·variable(s)97 o10·:·PolynomialRing,·3·skew·commutative·variable(s)
98 i11·:·C·=·killCycles(B)98 i11·:·C·=·killCycles(B)
1.26 KB
./usr/share/doc/Macaulay2/DGAlgebras/html/___H__H_sp__D__G__Algebra__Map.html
    
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144 o6·:·ComplexMap</code></pre>144 o6·:·ComplexMap</code></pre>
145 ············</td>145 ············</td>
146 ··········</tr>146 ··········</tr>
147 ··········<tr>147 ··········<tr>
148 ············<td>148 ············<td>
149 ··············<pre><code·class="language-macaulay2">i7·:·HHg·=·HH·g149 ··············<pre><code·class="language-macaulay2">i7·:·HHg·=·HH·g
150 ·--·used·0.478531s·(cpu);·0.0677541s·(thread);·0s·(gc)150 ·--·used·0.545475s·(cpu);·0.0757035s·(thread);·0s·(gc)
151 Finding·easy·relations···········:·151 Finding·easy·relations···········:·
152 ·························ZZ152 ·························ZZ
153 ························---[a..c]153 ························---[a..c]
154 ···········ZZ···········101154 ···········ZZ···········101
155 o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})155 o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})
156 ··········101··1···2···········3···1·····1156 ··········101··1···2···········3···1·····1
157 ·······················(c,·b,·a·)157 ·······················(c,·b,·a·)
568 B
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62 ·····2·:·R··<-------------·R··:·262 ·····2·:·R··<-------------·R··:·2
63 ···············{2}·|·0·|63 ···············{2}·|·0·|
64 ···············{2}·|·0·|64 ···············{2}·|·0·|
65 ···············{2}·|·1·|65 ···············{2}·|·1·|
  
66 o6·:·ComplexMap66 o6·:·ComplexMap
67 i7·:·HHg·=·HH·g67 i7·:·HHg·=·HH·g
68 ·--·used·0.478531s·(cpu);·0.0677541s·(thread);·0s·(gc)68 ·--·used·0.545475s·(cpu);·0.0757035s·(thread);·0s·(gc)
69 Finding·easy·relations···········:69 Finding·easy·relations···········:
70 ·························ZZ70 ·························ZZ
71 ························---[a..c]71 ························---[a..c]
72 ···········ZZ···········10172 ···········ZZ···········101
73 o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})73 o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0})
74 ··········101··1···2···········3···1·····174 ··········101··1···2···········3···1·····1
75 ·······················(c,·b,·a·)75 ·······················(c,·b,·a·)
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138 ········<div>138 ········<div>
139 ··········<p>Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra.··One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH·(all·commands·work).··This·algebra·structure·can·detect·whether·or·not·the·ring·is·a·complete·intersection·or·Gorenstein.</p>139 ··········<p>Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra.··One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH·(all·commands·work).··This·algebra·structure·can·detect·whether·or·not·the·ring·is·a·complete·intersection·or·Gorenstein.</p>
140 ········</div>140 ········</div>
141 ········<table·class="examples">141 ········<table·class="examples">
142 ··········<tr>142 ··········<tr>
143 ············<td>143 ············<td>
144 ··············<pre><code·class="language-macaulay2">i7·:·HKR·=·HH·KR144 ··············<pre><code·class="language-macaulay2">i7·:·HKR·=·HH·KR
145 ·--·used·0.697355s·(cpu);·0.0756314s·(thread);·0s·(gc)145 ·--·used·0.53925s·(cpu);·0.0766079s·(thread);·0s·(gc)
146 Finding·easy·relations···········:·146 Finding·easy·relations···········:·
147 o7·=·HKR147 o7·=·HKR
  
148 o7·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>148 o7·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
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166 o9·:·QuotientRing</code></pre>166 o9·:·QuotientRing</code></pre>
167 ············</td>167 ············</td>
168 ··········</tr>168 ··········</tr>
169 ··········<tr>169 ··········<tr>
170 ············<td>170 ············<td>
171 ··············<pre><code·class="language-macaulay2">i10·:·HKR'·=·HH·koszulComplexDGA·R'171 ··············<pre><code·class="language-macaulay2">i10·:·HKR'·=·HH·koszulComplexDGA·R'
172 ·--·used·2.5175s·(cpu);·0.813839s·(thread);·0s·(gc)172 ·--·used·2.50507s·(cpu);·0.803209s·(thread);·0s·(gc)
173 Finding·easy·relations···········:·173 Finding·easy·relations···········:·
174 o10·=·HKR'174 o10·=·HKR'
  
175 o10·:·QuotientRing</code></pre>175 o10·:·QuotientRing</code></pre>
176 ············</td>176 ············</td>
177 ··········</tr>177 ··········</tr>
178 ··········<tr>178 ··········<tr>
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76 o6·:·Complex76 o6·:·Complex
77 Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra.77 Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra.
78 One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH78 One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH
79 (all·commands·work).·This·algebra·structure·can·detect·whether·or·not·the·ring79 (all·commands·work).·This·algebra·structure·can·detect·whether·or·not·the·ring
80 is·a·complete·intersection·or·Gorenstein.80 is·a·complete·intersection·or·Gorenstein.
81 i7·:·HKR·=·HH·KR81 i7·:·HKR·=·HH·KR
82 ·--·used·0.697355s·(cpu);·0.0756314s·(thread);·0s·(gc)82 ·--·used·0.53925s·(cpu);·0.0766079s·(thread);·0s·(gc)
83 Finding·easy·relations···········:83 Finding·easy·relations···········:
84 o7·=·HKR84 o7·=·HKR
  
85 o7·:·PolynomialRing,·4·skew·commutative·variable(s)85 o7·:·PolynomialRing,·4·skew·commutative·variable(s)
86 i8·:·ideal·HKR86 i8·:·ideal·HKR
  
87 o8·=·ideal·()87 o8·=·ideal·()
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93 i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2-93 i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2-
94 c^2*d^2}94 c^2*d^2}
  
95 o9·=·R'95 o9·=·R'
  
96 o9·:·QuotientRing96 o9·:·QuotientRing
97 i10·:·HKR'·=·HH·koszulComplexDGA·R'97 i10·:·HKR'·=·HH·koszulComplexDGA·R'
98 ·--·used·2.5175s·(cpu);·0.813839s·(thread);·0s·(gc)98 ·--·used·2.50507s·(cpu);·0.803209s·(thread);·0s·(gc)
99 Finding·easy·relations···········:99 Finding·easy·relations···········:
100 o10·=·HKR'100 o10·=·HKR'
  
101 o10·:·QuotientRing101 o10·:·QuotientRing
102 i11·:·numgens·HKR'102 i11·:·numgens·HKR'
  
103 o11·=·34103 o11·=·34
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89 o3·:·List</code></pre>89 o3·:·List</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A)94 ··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A)
95 ·--·used·1.89945s·(cpu);·0.326972s·(thread);·0s·(gc)95 ·--·used·1.54595s·(cpu);·0.197557s·(thread);·0s·(gc)
96 Finding·easy·relations···········:·96 Finding·easy·relations···········:·
97 o4·=·HA97 o4·=·HA
  
98 o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>98 o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
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23 o2·:·DGAlgebra23 o2·:·DGAlgebra
24 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))24 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
25 o3·=·{1,·4,·6,·4,·1}25 o3·=·{1,·4,·6,·4,·1}
  
26 o3·:·List26 o3·:·List
27 i4·:·HA·=·homologyAlgebra(A)27 i4·:·HA·=·homologyAlgebra(A)
28 ·--·used·1.89945s·(cpu);·0.326972s·(thread);·0s·(gc)28 ·--·used·1.54595s·(cpu);·0.197557s·(thread);·0s·(gc)
29 Finding·easy·relations···········:29 Finding·easy·relations···········:
30 o4·=·HA30 o4·=·HA
  
31 o4·:·PolynomialRing,·4·skew·commutative·variable(s)31 o4·:·PolynomialRing,·4·skew·commutative·variable(s)
32 i5·:·numgens·HA32 i5·:·numgens·HA
  
33 o5·=·433 o5·=·4
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103 o3·:·List</code></pre>103 o3·:·List</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A)108 ··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A)
109 ·--·used·0.65759s·(cpu);·0.0920584s·(thread);·0s·(gc)109 ·--·used·0.531874s·(cpu);·0.0919985s·(thread);·0s·(gc)
110 Finding·easy·relations···········:·110 Finding·easy·relations···········:·
111 o4·=·HA111 o4·=·HA
  
112 o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>112 o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ········</table>115 ········</table>
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148 o7·:·List</code></pre>148 o7·:·List</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
152 ············<td>152 ············<td>
153 ··············<pre><code·class="language-macaulay2">i8·:·HA·=·homologyAlgebra(A)153 ··············<pre><code·class="language-macaulay2">i8·:·HA·=·homologyAlgebra(A)
154 ·--·used·2.08481s·(cpu);·0.359835s·(thread);·0s·(gc)154 ·--·used·1.69612s·(cpu);·0.274983s·(thread);·0s·(gc)
155 Finding·easy·relations···········:·155 Finding·easy·relations···········:·
156 o8·=·HA156 o8·=·HA
  
157 o8·:·QuotientRing</code></pre>157 o8·:·QuotientRing</code></pre>
158 ············</td>158 ············</td>
159 ··········</tr>159 ··········</tr>
160 ··········<tr>160 ··········<tr>
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242 o15·:·List</code></pre>242 o15·:·List</code></pre>
243 ············</td>243 ············</td>
244 ··········</tr>244 ··········</tr>
245 ··········<tr>245 ··········<tr>
246 ············<td>246 ············<td>
247 ··············<pre><code·class="language-macaulay2">i16·:·HA·=·homologyAlgebra(A)247 ··············<pre><code·class="language-macaulay2">i16·:·HA·=·homologyAlgebra(A)
248 ·--·used·1.14669s·(cpu);·0.187573s·(thread);·0s·(gc)248 ·--·used·0.816507s·(cpu);·0.137409s·(thread);·0s·(gc)
249 Finding·easy·relations···········:·249 Finding·easy·relations···········:·
250 o16·=·HA250 o16·=·HA
  
251 o16·:·QuotientRing</code></pre>251 o16·:·QuotientRing</code></pre>
252 ············</td>252 ············</td>
253 ··········</tr>253 ··········</tr>
254 ········</table>254 ········</table>
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302 o20·:·DGAlgebra</code></pre>302 o20·:·DGAlgebra</code></pre>
303 ············</td>303 ············</td>
304 ··········</tr>304 ··········</tr>
305 ··········<tr>305 ··········<tr>
306 ············<td>306 ············<td>
307 ··············<pre><code·class="language-macaulay2">i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14)307 ··············<pre><code·class="language-macaulay2">i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14)
308 ·--·used·0.70203s·(cpu);·0.144184s·(thread);·0s·(gc)308 ·--·used·0.547253s·(cpu);·0.0778176s·(thread);·0s·(gc)
309 Finding·easy·relations···········:·309 Finding·easy·relations···········:·
310 o21·=·HB310 o21·=·HB
  
311 o21·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>311 o21·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre>
312 ············</td>312 ············</td>
313 ··········</tr>313 ··········</tr>
314 ········</table>314 ········</table>
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33 o2·:·DGAlgebra33 o2·:·DGAlgebra
34 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))34 i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
35 o3·=·{1,·4,·6,·4,·1}35 o3·=·{1,·4,·6,·4,·1}
  
36 o3·:·List36 o3·:·List
37 i4·:·HA·=·homologyAlgebra(A)37 i4·:·HA·=·homologyAlgebra(A)
38 ·--·used·0.65759s·(cpu);·0.0920584s·(thread);·0s·(gc)38 ·--·used·0.531874s·(cpu);·0.0919985s·(thread);·0s·(gc)
39 Finding·easy·relations···········:39 Finding·easy·relations···········:
40 o4·=·HA40 o4·=·HA
  
41 o4·:·PolynomialRing,·4·skew·commutative·variable(s)41 o4·:·PolynomialRing,·4·skew·commutative·variable(s)
42 Note·that·HA·is·a·graded·commutative·polynomial·ring·(i.e.·an·exterior·algebra)42 Note·that·HA·is·a·graded·commutative·polynomial·ring·(i.e.·an·exterior·algebra)
43 since·R·is·a·complete·intersection.43 since·R·is·a·complete·intersection.
44 i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3}44 i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3}
Offset 59, 15 lines modifiedOffset 59, 15 lines modified
59 o6·:·DGAlgebra59 o6·:·DGAlgebra
60 i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))60 i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
61 o7·=·{1,·5,·10,·10,·4}61 o7·=·{1,·5,·10,·10,·4}
  
62 o7·:·List62 o7·:·List
63 i8·:·HA·=·homologyAlgebra(A)63 i8·:·HA·=·homologyAlgebra(A)
64 ·--·used·2.08481s·(cpu);·0.359835s·(thread);·0s·(gc)64 ·--·used·1.69612s·(cpu);·0.274983s·(thread);·0s·(gc)
65 Finding·easy·relations···········:65 Finding·easy·relations···········:
66 o8·=·HA66 o8·=·HA
  
67 o8·:·QuotientRing67 o8·:·QuotientRing
68 i9·:·numgens·HA68 i9·:·numgens·HA
  
69 o9·=·1969 o9·=·19
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120 o14·:·DGAlgebra120 o14·:·DGAlgebra
121 i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))121 i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A))
  
122 o15·=·{1,·7,·7,·1}122 o15·=·{1,·7,·7,·1}
  
123 o15·:·List123 o15·:·List
124 i16·:·HA·=·homologyAlgebra(A)124 i16·:·HA·=·homologyAlgebra(A)
125 ·--·used·1.14669s·(cpu);·0.187573s·(thread);·0s·(gc)125 ·--·used·0.816507s·(cpu);·0.137409s·(thread);·0s·(gc)
126 Finding·easy·relations···········:126 Finding·easy·relations···········:
127 o16·=·HA127 o16·=·HA
  
128 o16·:·QuotientRing128 o16·:·QuotientRing
129 One·can·check·that·HA·has·Poincare·duality·since·R·is·Gorenstein.129 One·can·check·that·HA·has·Poincare·duality·since·R·is·Gorenstein.
130 If·your·DGAlgebra·has·generators·in·even·degrees,·then·one·must·specify·the130 If·your·DGAlgebra·has·generators·in·even·degrees,·then·one·must·specify·the
131 options·GenDegreeLimit·and·RelDegreeLimit.131 options·GenDegreeLimit·and·RelDegreeLimit.
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155 o20·=·{Ring·=>·S······················}155 o20·=·{Ring·=>·S······················}
156 ·······Underlying·algebra·=>·S[T·..T·]156 ·······Underlying·algebra·=>·S[T·..T·]
157 ································1···4157 ································1···4
158 ·······Differential·=>·{a,·b,·c,·d}158 ·······Differential·=>·{a,·b,·c,·d}
  
159 o20·:·DGAlgebra159 o20·:·DGAlgebra
160 i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14)160 i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14)
161 ·--·used·0.70203s·(cpu);·0.144184s·(thread);·0s·(gc)161 ·--·used·0.547253s·(cpu);·0.0778176s·(thread);·0s·(gc)
162 Finding·easy·relations···········:162 Finding·easy·relations···········:
163 o21·=·HB163 o21·=·HB
  
164 o21·:·PolynomialRing,·4·skew·commutative·variable(s)164 o21·:·PolynomialRing,·4·skew·commutative·variable(s)
165 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ho\x8om\x8mo\x8ol\x8lo\x8og\x8gy\x8yA\x8Al\x8lg\x8ge\x8eb\x8br\x8ra\x8a:\x8:·*\x8**\x8**\x8**\x8**\x8*165 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ho\x8om\x8mo\x8ol\x8lo\x8og\x8gy\x8yA\x8Al\x8lg\x8ge\x8eb\x8br\x8ra\x8a:\x8:·*\x8**\x8**\x8**\x8**\x8*
166 ····*·homologyAlgebra(DGAlgebra)166 ····*·homologyAlgebra(DGAlgebra)
167 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*167 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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135 o6·:·R[T·..T·]135 o6·:·R[T·..T·]
136 ········1···3</code></pre>136 ········1···3</code></pre>
137 ············</td>137 ············</td>
138 ··········</tr>138 ··········</tr>
139 ··········<tr>139 ··········<tr>
140 ············<td>140 ············<td>
141 ··············<pre><code·class="language-macaulay2">i7·:·H·=·HH(KR)141 ··············<pre><code·class="language-macaulay2">i7·:·H·=·HH(KR)
142 ·--·used·0.633698s·(cpu);·0.084598s·(thread);·0s·(gc)142 ·--·used·0.556701s·(cpu);·0.0736723s·(thread);·0s·(gc)
143 Finding·easy·relations···········:·143 Finding·easy·relations···········:·
144 o7·=·H144 o7·=·H
  
145 o7·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre>145 o7·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre>
146 ············</td>146 ············</td>
147 ··········</tr>147 ··········</tr>
148 ··········<tr>148 ··········<tr>
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53 ······253 ······2
54 o6·=·y·T54 o6·=·y·T
55 ········255 ········2
  
56 o6·:·R[T·..T·]56 o6·:·R[T·..T·]
57 ········1···357 ········1···3
58 i7·:·H·=·HH(KR)58 i7·:·H·=·HH(KR)
59 ·--·used·0.633698s·(cpu);·0.084598s·(thread);·0s·(gc)59 ·--·used·0.556701s·(cpu);·0.0736723s·(thread);·0s·(gc)
60 Finding·easy·relations···········:60 Finding·easy·relations···········:
61 o7·=·H61 o7·=·H
  
62 o7·:·PolynomialRing,·3·skew·commutative·variable(s)62 o7·:·PolynomialRing,·3·skew·commutative·variable(s)
63 i8·:·homologyClass(KR,z1*z2)63 i8·:·homologyClass(KR,z1*z2)
  
64 o8·=·X·X64 o8·=·X·X
1.01 KB
./usr/share/doc/Macaulay2/DGAlgebras/html/_homology__Module.html
    
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129 o5·:·Complex</code></pre>129 o5·:·Complex</code></pre>
130 ············</td>130 ············</td>
131 ··········</tr>131 ··········</tr>
132 ··········<tr>132 ··········<tr>
133 ············<td>133 ············<td>
134 ··············<pre><code·class="language-macaulay2">i6·:·HKR·=·HH(KR)134 ··············<pre><code·class="language-macaulay2">i6·:·HKR·=·HH(KR)
135 ·--·used·1.45727s·(cpu);·0.244941s·(thread);·0s·(gc)135 ·--·used·1.31079s·(cpu);·0.246631s·(thread);·0s·(gc)
136 Finding·easy·relations···········:·136 Finding·easy·relations···········:·
137 o6·=·HKR137 o6·=·HKR
  
138 o6·:·QuotientRing</code></pre>138 o6·:·QuotientRing</code></pre>
139 ············</td>139 ············</td>
140 ··········</tr>140 ··········</tr>
141 ········</table>141 ········</table>
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54 ······1······4······6······4······154 ······1······4······6······4······1
55 o5·=·R··<--·R··<--·R··<--·R··<--·R55 o5·=·R··<--·R··<--·R··<--·R··<--·R
  
56 ·····0······1······2······3······456 ·····0······1······2······3······4
  
57 o5·:·Complex57 o5·:·Complex
58 i6·:·HKR·=·HH(KR)58 i6·:·HKR·=·HH(KR)
59 ·--·used·1.45727s·(cpu);·0.244941s·(thread);·0s·(gc)59 ·--·used·1.31079s·(cpu);·0.246631s·(thread);·0s·(gc)
60 Finding·easy·relations···········:60 Finding·easy·relations···········:
61 o6·=·HKR61 o6·=·HKR
  
62 o6·:·QuotientRing62 o6·:·QuotientRing
63 The·following·is·the·graded·canonical·module·of·R:63 The·following·is·the·graded·canonical·module·of·R:
64 i7·:·degList·=·first·entries·vars·Q·/·degree·/·first64 i7·:·degList·=·first·entries·vars·Q·/·degree·/·first
  
1.6 KB
./usr/share/doc/Macaulay2/DGAlgebras/html/_massey__Triple__Product.html
    
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192 ········<div>192 ········<div>
193 ··········<p>Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey·triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the·homology·class·of·lift12*z3·+·z1*lift23.··To·see·this,·we·compute·and·check:</p>193 ··········<p>Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey·triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the·homology·class·of·lift12*z3·+·z1*lift23.··To·see·this,·we·compute·and·check:</p>
194 ········</div>194 ········</div>
195 ········<table·class="examples">195 ········<table·class="examples">
196 ··········<tr>196 ··········<tr>
197 ············<td>197 ············<td>
198 ··············<pre><code·class="language-macaulay2">i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3)198 ··············<pre><code·class="language-macaulay2">i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3)
199 ·--·used·3.06855s·(cpu);·0.756243s·(thread);·0s·(gc)199 ·--·used·2.6074s·(cpu);·0.754577s·(thread);·0s·(gc)
200 Finding·easy·relations···········:·200 Finding·easy·relations···········:·
201 ·············2201 ·············2
202 o10·=·x·x·y·z·T·T·T·T202 o10·=·x·x·y·z·T·T·T·T
203 ·······1·2·2···2·3·4·5203 ·······1·2·2···2·3·4·5
  
204 o10·:·R[T·..T·]204 o10·:·R[T·..T·]
205 ·········1···5</code></pre>205 ·········1···5</code></pre>
779 B
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90 Note·that·the·first·return·value·of·_\x8g_\x8e_\x8t_\x8B_\x8o_\x8u_\x8n_\x8d_\x8a_\x8r_\x8y_\x8P_\x8r_\x8e_\x8i_\x8m_\x8a_\x8g_\x8e·indicates·that·the90 Note·that·the·first·return·value·of·_\x8g_\x8e_\x8t_\x8B_\x8o_\x8u_\x8n_\x8d_\x8a_\x8r_\x8y_\x8P_\x8r_\x8e_\x8i_\x8m_\x8a_\x8g_\x8e·indicates·that·the
91 inputs·are·indeed·boundaries,·and·the·second·value·is·the·lift·of·the·boundary91 inputs·are·indeed·boundaries,·and·the·second·value·is·the·lift·of·the·boundary
92 along·the·differential.92 along·the·differential.
93 Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey93 Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey
94 triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the94 triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the
95 homology·class·of·lift12*z3·+·z1*lift23.·To·see·this,·we·compute·and·check:95 homology·class·of·lift12*z3·+·z1*lift23.·To·see·this,·we·compute·and·check:
96 i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3)96 i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3)
97 ·--·used·3.06855s·(cpu);·0.756243s·(thread);·0s·(gc)97 ·--·used·2.6074s·(cpu);·0.754577s·(thread);·0s·(gc)
98 Finding·easy·relations···········:98 Finding·easy·relations···········:
99 ·············299 ·············2
100 o10·=·x·x·y·z·T·T·T·T100 o10·=·x·x·y·z·T·T·T·T
101 ·······1·2·2···2·3·4·5101 ·······1·2·2···2·3·4·5
  
102 o10·:·R[T·..T·]102 o10·:·R[T·..T·]
103 ·········1···5103 ·········1···5
1.13 KB
./usr/share/doc/Macaulay2/DGAlgebras/html/_massey__Triple__Product_lp__D__G__Algebra_cm__Z__Z_cm__Z__Z_cm__Z__Z_rp.html
    
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119 o4·:·DGAlgebra</code></pre>119 o4·:·DGAlgebra</code></pre>
120 ············</td>120 ············</td>
121 ··········</tr>121 ··········</tr>
122 ··········<tr>122 ··········<tr>
123 ············<td>123 ············<td>
124 ··············<pre><code·class="language-macaulay2">i5·:·H·=·HH(KR)124 ··············<pre><code·class="language-macaulay2">i5·:·H·=·HH(KR)
125 ·--·used·2.14024s·(cpu);·0.357025s·(thread);·0s·(gc)125 ·--·used·1.88136s·(cpu);·0.405927s·(thread);·0s·(gc)
126 Finding·easy·relations···········:·126 Finding·easy·relations···········:·
127 o5·=·H127 o5·=·H
  
128 o5·:·QuotientRing</code></pre>128 o5·:·QuotientRing</code></pre>
129 ············</td>129 ············</td>
130 ··········</tr>130 ··········</tr>
131 ··········<tr>131 ··········<tr>
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49 ······Underlying·algebra·=>·R[T·..T·]49 ······Underlying·algebra·=>·R[T·..T·]
50 ·······························1···450 ·······························1···4
51 ······Differential·=>·{t·,·t·,·t·,·t·}51 ······Differential·=>·{t·,·t·,·t·,·t·}
52 ························1···2···3···452 ························1···2···3···4
  
53 o4·:·DGAlgebra53 o4·:·DGAlgebra
54 i5·:·H·=·HH(KR)54 i5·:·H·=·HH(KR)
55 ·--·used·2.14024s·(cpu);·0.357025s·(thread);·0s·(gc)55 ·--·used·1.88136s·(cpu);·0.405927s·(thread);·0s·(gc)
56 Finding·easy·relations···········:56 Finding·easy·relations···········:
57 o5·=·H57 o5·=·H
  
58 o5·:·QuotientRing58 o5·:·QuotientRing
59 i6·:·masseys·=·masseyTripleProduct(KR,1,1,1);59 i6·:·masseys·=·masseyTripleProduct(KR,1,1,1);
  
60 ··············5·······34360 ··············5·······343
1.04 KB
./usr/share/doc/Macaulay2/DGAlgebras/html/_tor__Algebra_lp__Ring_cm__Ring_rp.html
    
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97 o3·:·QuotientRing</code></pre>97 o3·:·QuotientRing</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8)102 ··············<pre><code·class="language-macaulay2">i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8)
103 ·--·used·3.19211s·(cpu);·0.709337s·(thread);·0s·(gc)103 ·--·used·2.75995s·(cpu);·0.721281s·(thread);·0s·(gc)
104 Finding·easy·relations···········:·104 Finding·easy·relations···········:·
105 o4·=·HB105 o4·=·HB
  
106 o4·:·QuotientRing</code></pre>106 o4·:·QuotientRing</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ··········<tr>109 ··········<tr>
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27 i2·:·M·=·coker·matrix·{{a^3*b^3*c^3*d^3}};27 i2·:·M·=·coker·matrix·{{a^3*b^3*c^3*d^3}};
28 i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3}28 i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3}
  
29 o3·=·S29 o3·=·S
  
30 o3·:·QuotientRing30 o3·:·QuotientRing
31 i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8)31 i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8)
32 ·--·used·3.19211s·(cpu);·0.709337s·(thread);·0s·(gc)32 ·--·used·2.75995s·(cpu);·0.721281s·(thread);·0s·(gc)
33 Finding·easy·relations···········:33 Finding·easy·relations···········:
34 o4·=·HB34 o4·=·HB
  
35 o4·:·QuotientRing35 o4·:·QuotientRing
36 i5·:·numgens·HB36 i5·:·numgens·HB
  
37 o5·=·3537 o5·=·35
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./usr/share/doc/Macaulay2/Divisor/example-output/___Basic__Divisor.out
    
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1 --·-*-·M2-comint·-*-·hash:·183802960661610432891 --·-*-·M2-comint·-*-·hash:·18380296066161043289
  
2 i1·:·R·=·QQ[x,y,z];2 i1·:·R·=·QQ[x,y,z];
  
3 i2·:·D·=·divisor(x*y^2*z^3)3 i2·:·D·=·divisor(x*y^2*z^3)
  
4 o2·=·2*Div(y)·+·3*Div(z)·+·Div(x)4 o2·=·Div(x)·+·2*Div(y)·+·3*Div(z)
  
5 o2·:·WeilDivisor·on·R5 o2·:·WeilDivisor·on·R
  
6 i3·:·H·=·new·HashTable·from·D6 i3·:·H·=·new·HashTable·from·D
  
7 o3·=·HashTable{{x}·=>·{1}··················}7 o3·=·HashTable{{x}·=>·{1}··················}
8 ···············{y}·=>·{2}8 ···············{y}·=>·{2}
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16 ···············cache·=>·CacheTable{...1...}16 ···············cache·=>·CacheTable{...1...}
17 ···············ring·=>·R17 ···············ring·=>·R
  
18 o3·:·HashTable18 o3·:·HashTable
  
19 i4·:·(2/3)*D19 i4·:·(2/3)*D
  
20 o4·=·2*Div(z)·+·4/3*Div(y)·+·2/3*Div(x)20 o4·=·2/3*Div(x)·+·2*Div(z)·+·4/3*Div(y)
  
21 o4·:·QWeilDivisor·on·R21 o4·:·QWeilDivisor·on·R
  
22 i5·:·0.6*D22 i5·:·0.6*D
  
23 o5·=·1.8*Div(z)·+·1.2*Div(y)·+·.6*Div(x)23 o5·=·.6*Div(x)·+·1.8*Div(z)·+·1.2*Div(y)
  
24 o5·:·RWeilDivisor·on·R24 o5·:·RWeilDivisor·on·R
  
25 i6·:·25 i6·:·
886 B
./usr/share/doc/Macaulay2/Divisor/example-output/___Basic__Divisor_sp_pl_sp__Basic__Divisor.out
    
Offset 64, 30 lines modifiedOffset 64, 30 lines modified
  
64 o12·:·RWeilDivisor·on·R64 o12·:·RWeilDivisor·on·R
  
65 i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);65 i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);
  
66 i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)})66 i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)})
  
67 o14·=·3*Div(x,·z)·+·0*Div(y,·z)·+·-Div(x-y,·x-z)67 o14·=·0*Div(y,·z)·+·-Div(x-y,·x-z)·+·3*Div(x,·z)
  
68 o14·:·WeilDivisor·on·R68 o14·:·WeilDivisor·on·R
  
69 i15·:·-D69 i15·:·-D
  
70 o15·=·-3*Div(x,·z)·+·Div(x-y,·x-z)70 o15·=·Div(x-y,·x-z)·+·-3*Div(x,·z)
  
71 o15·:·WeilDivisor·on·R71 o15·:·WeilDivisor·on·R
  
72 i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)})72 i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)})
  
73 o16·=·3/2*Div(x,·z)·+·-2/3*Div(y,·z)73 o16·=·-2/3*Div(y,·z)·+·3/2*Div(x,·z)
  
74 o16·:·WeilDivisor·on·R74 o16·:·WeilDivisor·on·R
  
75 i17·:·-E75 i17·:·-E
  
76 o17·=·-3/2*Div(x,·z)·+·2/3*Div(y,·z)76 o17·=·2/3*Div(y,·z)·+·-3/2*Div(x,·z)
  
77 o17·:·WeilDivisor·on·R77 o17·:·WeilDivisor·on·R
  
78 i18·:·78 i18·:·
523 B
./usr/share/doc/Macaulay2/Divisor/example-output/_apply__To__Coefficients.out
    
Offset 1, 17 lines modifiedOffset 1, 17 lines modified
1 --·-*-·M2-comint·-*-·hash:·149379346520408128891 --·-*-·M2-comint·-*-·hash:·14937934652040812889
  
2 i1·:·R·=·QQ[x,·y,·z];2 i1·:·R·=·QQ[x,·y,·z];
  
3 i2·:·D·=·divisor(x*y^2/z)3 i2·:·D·=·divisor(x*y^2/z)
  
4 o2·=·-Div(z)·+·2*Div(y)·+·Div(x)4 o2·=·Div(x)·+·-Div(z)·+·2*Div(y)
  
5 o2·:·WeilDivisor·on·R5 o2·:·WeilDivisor·on·R
  
6 i3·:·applyToCoefficients(D,·u->5*u)6 i3·:·applyToCoefficients(D,·u->5*u)
  
7 o3·=·10*Div(y)·+·-5*Div(z)·+·5*Div(x)7 o3·=·5*Div(x)·+·10*Div(y)·+·-5*Div(z)
  
8 o3·:·WeilDivisor·on·R8 o3·:·WeilDivisor·on·R
  
9 i4·:·9 i4·:·
1.62 KB
./usr/share/doc/Macaulay2/Divisor/example-output/_dualize.out
    
Offset 44, 51 lines modifiedOffset 44, 51 lines modified
44 i10·:·J·=·m^9;44 i10·:·J·=·m^9;
  
45 o10·:·Ideal·of·R45 o10·:·Ideal·of·R
  
46 i11·:·M·=·J*R^1;46 i11·:·M·=·J*R^1;
  
47 i12·:·time·dualize(J,·Strategy=>IdealStrategy);47 i12·:·time·dualize(J,·Strategy=>IdealStrategy);
48 ·--·used·0.037363s·(cpu);·0.0382174s·(thread);·0s·(gc)48 ·--·used·0.0424712s·(cpu);·0.0433159s·(thread);·0s·(gc)
  
49 o12·:·Ideal·of·R49 o12·:·Ideal·of·R
  
50 i13·:·time·dualize(J,·Strategy=>ModuleStrategy);50 i13·:·time·dualize(J,·Strategy=>ModuleStrategy);
51 ·--·used·0.36289s·(cpu);·0.365145s·(thread);·0s·(gc)51 ·--·used·0.47362s·(cpu);·0.475712s·(thread);·0s·(gc)
  
52 o13·:·Ideal·of·R52 o13·:·Ideal·of·R
  
53 i14·:·time·dualize(M,·Strategy=>IdealStrategy);53 i14·:·time·dualize(M,·Strategy=>IdealStrategy);
54 ·--·used·0.476484s·(cpu);·0.439445s·(thread);·0s·(gc)54 ·--·used·0.556623s·(cpu);·0.511528s·(thread);·0s·(gc)
  
55 i15·:·time·dualize(M,·Strategy=>ModuleStrategy);55 i15·:·time·dualize(M,·Strategy=>ModuleStrategy);
56 ·--·used·9.5073e-05s·(cpu);·0.00244451s·(thread);·0s·(gc)56 ·--·used·0.000108062s·(cpu);·0.00264498s·(thread);·0s·(gc)
  
57 i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy);57 i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy);
58 ·--·used·0.000268374s·(cpu);·0.00200294s·(thread);·0s·(gc)58 ·--·used·0.000566071s·(cpu);·0.00231002s·(thread);·0s·(gc)
  
59 o16·:·Ideal·of·R59 o16·:·Ideal·of·R
  
60 i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v);60 i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v);
  
61 i18·:·I·=·ideal(x,u);61 i18·:·I·=·ideal(x,u);
  
62 o18·:·Ideal·of·R62 o18·:·Ideal·of·R
  
63 i19·:·J·=·I^15;63 i19·:·J·=·I^15;
  
64 o19·:·Ideal·of·R64 o19·:·Ideal·of·R
  
65 i20·:·time·dualize(J,·Strategy=>IdealStrategy);65 i20·:·time·dualize(J,·Strategy=>IdealStrategy);
66 ·--·used·0.187316s·(cpu);·0.106764s·(thread);·0s·(gc)66 ·--·used·0.242469s·(cpu);·0.112348s·(thread);·0s·(gc)
  
67 o20·:·Ideal·of·R67 o20·:·Ideal·of·R
  
68 i21·:·time·dualize(J,·Strategy=>ModuleStrategy);68 i21·:·time·dualize(J,·Strategy=>ModuleStrategy);
69 ·--·used·0.00265352s·(cpu);·0.00495863s·(thread);·0s·(gc)69 ·--·used·0.00320012s·(cpu);·0.00585463s·(thread);·0s·(gc)
  
70 o21·:·Ideal·of·R70 o21·:·Ideal·of·R
  
71 i22·:·R·=·QQ[x,y]/ideal(x*y);71 i22·:·R·=·QQ[x,y]/ideal(x*y);
  
72 i23·:·J·=·ideal(x,y);72 i23·:·J·=·ideal(x,y);
  
1010 B
./usr/share/doc/Macaulay2/Divisor/example-output/_is__Linear__Equivalent.out
    
Offset 1, 38 lines modifiedOffset 1, 38 lines modified
1 --·-*-·M2-comint·-*-·hash:·60191193470828113961 --·-*-·M2-comint·-*-·hash:·6019119347082811396
  
2 i1·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);2 i1·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);
  
3 i2·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})3 i2·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})
  
4 o2·=·8*Div(y,·z)·+·3*Div(x,·z)4 o2·=·3*Div(x,·z)·+·8*Div(y,·z)
  
5 o2·:·WeilDivisor·on·R5 o2·:·WeilDivisor·on·R
  
6 i3·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})6 i3·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})
  
7 o3·=·8*Div(y,·z)·+·Div(x,·z)7 o3·=·Div(x,·z)·+·8*Div(y,·z)
  
8 o3·:·WeilDivisor·on·R8 o3·:·WeilDivisor·on·R
  
9 i4·:·isLinearEquivalent(D1,·D2)9 i4·:·isLinearEquivalent(D1,·D2)
  
10 o4·=·true10 o4·=·true
  
11 i5·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);11 i5·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);
  
12 i6·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})12 i6·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})
  
13 o6·=·3*Div(x,·z)·+·8*Div(y,·z)13 o6·=·8*Div(y,·z)·+·3*Div(x,·z)
  
14 o6·:·WeilDivisor·on·R14 o6·:·WeilDivisor·on·R
  
15 i7·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})15 i7·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})
  
16 o7·=·Div(x,·z)·+·8*Div(y,·z)16 o7·=·8*Div(y,·z)·+·Div(x,·z)
  
17 o7·:·WeilDivisor·on·R17 o7·:·WeilDivisor·on·R
  
18 i8·:·isLinearEquivalent(D1,·D2,·IsGraded·=>·true)18 i8·:·isLinearEquivalent(D1,·D2,·IsGraded·=>·true)
  
19 o8·=·false19 o8·=·false
  
1.19 KB
./usr/share/doc/Macaulay2/Divisor/example-output/_is__Q__Linear__Equivalent.out
    
Offset 1, 20 lines modifiedOffset 1, 20 lines modified
1 --·-*-·M2-comint·-*-·hash:·139209593881088032161 --·-*-·M2-comint·-*-·hash:·13920959388108803216
  
2 i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);2 i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);
  
3 i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)3 i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)
  
4 o2·=·3/4*Div(y,·z)·+·1/2*Div(x,·z)4 o2·=·1/2*Div(x,·z)·+·3/4*Div(y,·z)
  
5 o2·:·QWeilDivisor·on·R5 o2·:·QWeilDivisor·on·R
  
6 i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)6 i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)
  
7 o3·=·3/4*Div(y,·z)·+·5/2*Div(x,·z)7 o3·=·5/2*Div(x,·z)·+·3/4*Div(y,·z)
  
8 o3·:·QWeilDivisor·on·R8 o3·:·QWeilDivisor·on·R
  
9 i4·:·isQLinearEquivalent(10,·D,·E)9 i4·:·isQLinearEquivalent(10,·D,·E)
  
10 o4·=·true10 o4·=·true
  
Offset 36, 21 lines modifiedOffset 36, 21 lines modified
  
36 o9·=·true36 o9·=·true
  
37 i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);37 i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);
  
38 i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)38 i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)
  
39 o11·=·1/2*Div(x,·z)·+·3/4*Div(y,·z)39 o11·=·3/4*Div(y,·z)·+·1/2*Div(x,·z)
  
40 o11·:·QWeilDivisor·on·R40 o11·:·QWeilDivisor·on·R
  
41 i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)41 i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)
  
42 o12·=·-1/4*Div(x,·z)·+·3/2*Div(y,·z)42 o12·=·3/2*Div(y,·z)·+·-1/4*Div(x,·z)
  
43 o12·:·QWeilDivisor·on·R43 o12·:·QWeilDivisor·on·R
  
44 i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true)44 i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true)
  
45 o13·=·true45 o13·=·true
  
515 B
./usr/share/doc/Macaulay2/Divisor/example-output/_is__Reduced.out
    
Offset 1, 20 lines modifiedOffset 1, 20 lines modified
1 --·-*-·M2-comint·-*-·hash:·62633715804780901721 --·-*-·M2-comint·-*-·hash:·6263371580478090172
  
2 i1·:·R·=·QQ[x,·y,·z];2 i1·:·R·=·QQ[x,·y,·z];
  
3 i2·:·D1·=·divisor(x^2·*·y^3·*·z)3 i2·:·D1·=·divisor(x^2·*·y^3·*·z)
  
4 o2·=·3*Div(y)·+·Div(z)·+·2*Div(x)4 o2·=·2*Div(x)·+·3*Div(y)·+·Div(z)
  
5 o2·:·WeilDivisor·on·R5 o2·:·WeilDivisor·on·R
  
6 i3·:·D2·=·divisor(x·*·y·*·z)6 i3·:·D2·=·divisor(x·*·y·*·z)
  
7 o3·=·Div(y)·+·Div(z)·+·Div(x)7 o3·=·Div(x)·+·Div(y)·+·Div(z)
  
8 o3·:·WeilDivisor·on·R8 o3·:·WeilDivisor·on·R
  
9 i4·:·isReduced(·D1·)9 i4·:·isReduced(·D1·)
  
10 o4·=·false10 o4·=·false
  
669 B
./usr/share/doc/Macaulay2/Divisor/example-output/_is__Weil__Divisor.out
    
Offset 1, 20 lines modifiedOffset 1, 20 lines modified
1 --·-*-·M2-comint·-*-·hash:·90883278571461956641 --·-*-·M2-comint·-*-·hash:·9088327857146195664
  
2 i1·:·R·=·QQ[x,·y,·z];2 i1·:·R·=·QQ[x,·y,·z];
  
3 i2·:·D1·=·divisor({1/1,·2/2,·-6/3},·{ideal(x),·ideal(y),·ideal(z)},·CoefficientType=>QQ)3 i2·:·D1·=·divisor({1/1,·2/2,·-6/3},·{ideal(x),·ideal(y),·ideal(z)},·CoefficientType=>QQ)
  
4 o2·=·Div(x)·+·Div(y)·+·-2*Div(z)4 o2·=·Div(y)·+·-2*Div(z)·+·Div(x)
  
5 o2·:·QWeilDivisor·on·R5 o2·:·QWeilDivisor·on·R
  
6 i3·:·D2·=·divisor({1/2,·3/4,·5/6},·{ideal(y),·ideal(z),·ideal(x)},·CoefficientType=>QQ)6 i3·:·D2·=·divisor({1/2,·3/4,·5/6},·{ideal(y),·ideal(z),·ideal(x)},·CoefficientType=>QQ)
  
7 o3·=·5/6*Div(x)·+·1/2*Div(y)·+·3/4*Div(z)7 o3·=·1/2*Div(y)·+·3/4*Div(z)·+·5/6*Div(x)
  
8 o3·:·QWeilDivisor·on·R8 o3·:·QWeilDivisor·on·R
  
9 i4·:·isWeilDivisor(·D1·)9 i4·:·isWeilDivisor(·D1·)
  
10 o4·=·true10 o4·=·true
  
533 B
./usr/share/doc/Macaulay2/Divisor/example-output/_pullback_lp__Ring__Map_cm__R__Weil__Divisor_rp.out
    
Offset 36, 18 lines modifiedOffset 36, 18 lines modified
  
36 i10·:·D·=·divisor(x*y*(x+y));36 i10·:·D·=·divisor(x*y*(x+y));
  
37 o10·:·WeilDivisor·on·R37 o10·:·WeilDivisor·on·R
  
38 i11·:·D1·=·pullback(f,·D)38 i11·:·D1·=·pullback(f,·D)
  
39 o11·=·Div(a+1)·+·3*Div(b)·+·Div(a)39 o11·=·Div(a)·+·3*Div(b)·+·Div(a+1)
  
40 o11·:·WeilDivisor·on·S40 o11·:·WeilDivisor·on·S
  
41 i12·:·f^*·D41 i12·:·f^*·D
  
42 o12·=·Div(a+1)·+·3*Div(b)·+·Div(a)42 o12·=·Div(a)·+·3*Div(b)·+·Div(a+1)
  
43 o12·:·WeilDivisor·on·S43 o12·:·WeilDivisor·on·S
  
44 i13·:·44 i13·:·
3.47 KB
./usr/share/doc/Macaulay2/Divisor/example-output/_reflexify.out
    
Offset 103, 104 lines modifiedOffset 103, 104 lines modified
103 o21·:·Ideal·of·R103 o21·:·Ideal·of·R
  
104 i22·:·J·=·I^21;104 i22·:·J·=·I^21;
  
105 o22·:·Ideal·of·R105 o22·:·Ideal·of·R
  
106 i23·:·time·reflexify(J);106 i23·:·time·reflexify(J);
107 ·--·used·0.193733s·(cpu);·0.153478s·(thread);·0s·(gc)107 ·--·used·0.231862s·(cpu);·0.188752s·(thread);·0s·(gc)
  
108 o23·:·Ideal·of·R108 o23·:·Ideal·of·R
  
109 i24·:·time·reflexify(J*R^1);109 i24·:·time·reflexify(J*R^1);
110 ·--·used·0.302365s·(cpu);·0.26108s·(thread);·0s·(gc)110 ·--·used·0.368034s·(cpu);·0.326261s·(thread);·0s·(gc)
  
111 i25·:·R·=·ZZ/13[x,y,z]/ideal(x^3·+·y^3-z^11*x*y);111 i25·:·R·=·ZZ/13[x,y,z]/ideal(x^3·+·y^3-z^11*x*y);
  
112 i26·:·I·=·ideal(x-4*y,·z);112 i26·:·I·=·ideal(x-4*y,·z);
  
113 o26·:·Ideal·of·R113 o26·:·Ideal·of·R
  
114 i27·:·J·=·I^20;114 i27·:·J·=·I^20;
  
115 o27·:·Ideal·of·R115 o27·:·Ideal·of·R
  
116 i28·:·M·=·J*R^1;116 i28·:·M·=·J*R^1;
  
117 i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·)117 i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·)
118 ·--·used·0.198576s·(cpu);·0.114034s·(thread);·0s·(gc)118 ·--·used·0.212751s·(cpu);·0.116713s·(thread);·0s·(gc)
  
119 ··············2············2·····9·······9···11119 ··············2············2·····9·······9···11
120 o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)120 o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)
  
121 o29·:·Ideal·of·R121 o29·:·Ideal·of·R
  
122 i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·)122 i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·)
123 ·--·used·4.61899s·(cpu);·3.56006s·(thread);·0s·(gc)123 ·--·used·4.8383s·(cpu);·3.78425s·(thread);·0s·(gc)
  
124 ··············2············2·····9·······9···11124 ··············2············2·····9·······9···11
125 o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)125 o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)
  
126 o30·:·Ideal·of·R126 o30·:·Ideal·of·R
  
127 i31·:·J1·==·J2127 i31·:·J1·==·J2
  
128 o31·=·true128 o31·=·true
  
129 i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·);129 i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·);
130 ·--·used·4.7491s·(cpu);·3.75787s·(thread);·0s·(gc)130 ·--·used·5.38506s·(cpu);·4.2357s·(thread);·0s·(gc)
  
131 i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);131 i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);
132 ·--·used·0.424617s·(cpu);·0.307849s·(thread);·0s·(gc)132 ·--·used·0.442613s·(cpu);·0.3133s·(thread);·0s·(gc)
  
133 i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v);133 i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v);
  
134 i35·:·I·=·ideal(x,u);134 i35·:·I·=·ideal(x,u);
  
135 o35·:·Ideal·of·R135 o35·:·Ideal·of·R
  
136 i36·:·J·=·I^20;136 i36·:·J·=·I^20;
  
137 o36·:·Ideal·of·R137 o36·:·Ideal·of·R
  
138 i37·:·M·=·I^20*R^1;138 i37·:·M·=·I^20*R^1;
  
139 i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·)139 i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·)
140 ·--·used·0.809782s·(cpu);·0.30444s·(thread);·0s·(gc)140 ·--·used·0.807535s·(cpu);·0.301082s·(thread);·0s·(gc)
  
141 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·141 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·
142 o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,142 o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,
143 ······-----------------------------------------------------------------------143 ······-----------------------------------------------------------------------
144 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·144 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·
145 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,145 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,
146 ······-----------------------------------------------------------------------146 ······-----------------------------------------------------------------------
147 ·······19····20147 ·······19····20
148 ······x··u,·x··)148 ······x··u,·x··)
  
149 o38·:·Ideal·of·R149 o38·:·Ideal·of·R
  
150 i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·)150 i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·)
151 ·--·used·0.174601s·(cpu);·0.0531627s·(thread);·0s·(gc)151 ·--·used·0.157457s·(cpu);·0.0366832s·(thread);·0s·(gc)
  
152 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·152 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·
153 o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,153 o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,
154 ······-----------------------------------------------------------------------154 ······-----------------------------------------------------------------------
155 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·155 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·
156 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,156 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,
157 ······-----------------------------------------------------------------------157 ······-----------------------------------------------------------------------
158 ·······19····20158 ·······19····20
159 ······x··u,·x··)159 ······x··u,·x··)
  
160 o39·:·Ideal·of·R160 o39·:·Ideal·of·R
  
161 i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·);161 i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·);
162 ·--·used·0.0324022s·(cpu);·0.033304s·(thread);·0s·(gc)162 ·--·used·0.0380324s·(cpu);·0.037759s·(thread);·0s·(gc)
  
163 i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);163 i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);
164 ·--·used·0.00272989s·(cpu);·0.00538526s·(thread);·0s·(gc)164 ·--·used·0.00485728s·(cpu);·0.00613396s·(thread);·0s·(gc)
  
165 i42·:·R·=·QQ[x,y]/ideal(x*y);165 i42·:·R·=·QQ[x,y]/ideal(x*y);
  
166 i43·:·I·=·ideal(x,y);166 i43·:·I·=·ideal(x,y);
  
167 o43·:·Ideal·of·R167 o43·:·Ideal·of·R
  
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Offset 23, 44 lines modifiedOffset 23, 44 lines modified
23 i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);23 i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);
  
24 i6·:·I·=·ideal(x-z,y-2*z);24 i6·:·I·=·ideal(x-z,y-2*z);
  
25 o6·:·Ideal·of·R25 o6·:·Ideal·of·R
  
26 i7·:·time·J20a·=·reflexivePower(20,·I);26 i7·:·time·J20a·=·reflexivePower(20,·I);
27 ·--·used·0.0751719s·(cpu);·0.043511s·(thread);·0s·(gc)27 ·--·used·0.0809171s·(cpu);·0.0398099s·(thread);·0s·(gc)
  
28 o7·:·Ideal·of·R28 o7·:·Ideal·of·R
  
29 i8·:·I20·=·I^20;29 i8·:·I20·=·I^20;
  
30 o8·:·Ideal·of·R30 o8·:·Ideal·of·R
  
31 i9·:·time·J20b·=·reflexify(I20);31 i9·:·time·J20b·=·reflexify(I20);
32 ·--·used·0.0946508s·(cpu);·0.0959172s·(thread);·0s·(gc)32 ·--·used·0.139705s·(cpu);·0.136087s·(thread);·0s·(gc)
  
33 o9·:·Ideal·of·R33 o9·:·Ideal·of·R
  
34 i10·:·J20a·==·J20b34 i10·:·J20a·==·J20b
  
35 o10·=·true35 o10·=·true
  
36 i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);36 i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);
  
37 i12·:·I·=·ideal(x-z,y-2*z);37 i12·:·I·=·ideal(x-z,y-2*z);
  
38 o12·:·Ideal·of·R38 o12·:·Ideal·of·R
  
39 i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy);39 i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy);
40 ·--·used·0.0777736s·(cpu);·0.0459113s·(thread);·0s·(gc)40 ·--·used·0.105248s·(cpu);·0.0493528s·(thread);·0s·(gc)
  
41 o13·:·Ideal·of·R41 o13·:·Ideal·of·R
  
42 i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy);42 i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy);
43 ·--·used·0.0465363s·(cpu);·0.0478035s·(thread);·0s·(gc)43 ·--·used·0.056438s·(cpu);·0.0566698s·(thread);·0s·(gc)
  
44 o14·:·Ideal·of·R44 o14·:·Ideal·of·R
  
45 i15·:·J1·==·J245 i15·:·J1·==·J2
  
46 o15·=·true46 o15·=·true
  
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Offset 72, 15 lines modifiedOffset 72, 15 lines modified
72 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre>72 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre>
73 ············</td>73 ············</td>
74 ··········</tr>74 ··········</tr>
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor(x*y^2*z^3)77 ··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor(x*y^2*z^3)
  
78 o2·=·2*Div(y)·+·3*Div(z)·+·Div(x)78 o2·=·Div(x)·+·2*Div(y)·+·3*Div(z)
  
79 o2·:·WeilDivisor·on·R</code></pre>79 o2·:·WeilDivisor·on·R</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i3·:·H·=·new·HashTable·from·D84 ··············<pre><code·class="language-macaulay2">i3·:·H·=·new·HashTable·from·D
Offset 94, 24 lines modifiedOffset 94, 24 lines modified
94 o3·:·HashTable</code></pre>94 o3·:·HashTable</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i4·:·(2/3)*D99 ··············<pre><code·class="language-macaulay2">i4·:·(2/3)*D
  
100 o4·=·2*Div(z)·+·4/3*Div(y)·+·2/3*Div(x)100 o4·=·2/3*Div(x)·+·2*Div(z)·+·4/3*Div(y)
  
101 o4·:·QWeilDivisor·on·R</code></pre>101 o4·:·QWeilDivisor·on·R</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i5·:·0.6*D106 ··············<pre><code·class="language-macaulay2">i5·:·0.6*D
  
107 o5·=·1.8*Div(z)·+·1.2*Div(y)·+·.6*Div(x)107 o5·=·.6*Div(x)·+·1.8*Div(z)·+·1.2*Div(y)
  
108 o5·:·RWeilDivisor·on·R</code></pre>108 o5·:·RWeilDivisor·on·R</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ········</table>111 ········</table>
112 ······</div>112 ······</div>
113 ······<div>113 ······<div>
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Offset 15, 34 lines modifiedOffset 15, 34 lines modified
15 specifies·the·ambient·ring.·Another·key·is·cache·which·points·to·a·CacheTable.15 specifies·the·ambient·ring.·Another·key·is·cache·which·points·to·a·CacheTable.
16 The·remaining·keys·are·a·Groebner·basis·$L$·for·each·prime·ideal·$P$·in·the16 The·remaining·keys·are·a·Groebner·basis·$L$·for·each·prime·ideal·$P$·in·the
17 support·with·corresponding·value·a·list·with·one·entry·{$n$}·where·$n$·is·the17 support·with·corresponding·value·a·list·with·one·entry·{$n$}·where·$n$·is·the
18 coefficient·of·the·height·one·prime.18 coefficient·of·the·height·one·prime.
19 i1·:·R·=·QQ[x,y,z];19 i1·:·R·=·QQ[x,y,z];
20 i2·:·D·=·divisor(x*y^2*z^3)20 i2·:·D·=·divisor(x*y^2*z^3)
  
21 o2·=·2*Div(y)·+·3*Div(z)·+·Div(x)21 o2·=·Div(x)·+·2*Div(y)·+·3*Div(z)
  
22 o2·:·WeilDivisor·on·R22 o2·:·WeilDivisor·on·R
23 i3·:·H·=·new·HashTable·from·D23 i3·:·H·=·new·HashTable·from·D
  
24 o3·=·HashTable{{x}·=>·{1}··················}24 o3·=·HashTable{{x}·=>·{1}··················}
25 ···············{y}·=>·{2}25 ···············{y}·=>·{2}
26 ···············{z}·=>·{3}26 ···············{z}·=>·{3}
27 ···············cache·=>·CacheTable{...1...}27 ···············cache·=>·CacheTable{...1...}
28 ···············ring·=>·R28 ···············ring·=>·R
  
29 o3·:·HashTable29 o3·:·HashTable
30 i4·:·(2/3)*D30 i4·:·(2/3)*D
  
31 o4·=·2*Div(z)·+·4/3*Div(y)·+·2/3*Div(x)31 o4·=·2/3*Div(x)·+·2*Div(z)·+·4/3*Div(y)
  
32 o4·:·QWeilDivisor·on·R32 o4·:·QWeilDivisor·on·R
33 i5·:·0.6*D33 i5·:·0.6*D
  
34 o5·=·1.8*Div(z)·+·1.2*Div(y)·+·.6*Div(x)34 o5·=·.6*Div(x)·+·1.8*Div(z)·+·1.2*Div(y)
  
35 o5·:·RWeilDivisor·on·R35 o5·:·RWeilDivisor·on·R
36 *\x8**\x8**\x8**\x8**\x8*·T\x8Ty\x8yp\x8pe\x8es\x8s·o\x8of\x8f·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*36 *\x8**\x8**\x8**\x8**\x8*·T\x8Ty\x8yp\x8pe\x8es\x8s·o\x8of\x8f·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
37 ····*·RWeilDivisor37 ····*·RWeilDivisor
38 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8an\x8n·o\x8ob\x8bj\x8je\x8ec\x8ct\x8t·o\x8of\x8f·c\x8cl\x8la\x8as\x8ss\x8s·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*38 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8an\x8n·o\x8ob\x8bj\x8je\x8ec\x8ct\x8t·o\x8of\x8f·c\x8cl\x8la\x8as\x8ss\x8s·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
39 ····*·applyToCoefficients(BasicDivisor,Function)·--·see·_\x8a_\x8p_\x8p_\x8l_\x8y_\x8T_\x8o_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8s·-39 ····*·applyToCoefficients(BasicDivisor,Function)·--·see·_\x8a_\x8p_\x8p_\x8l_\x8y_\x8T_\x8o_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8s·-
40 ······-·apply·a·function·to·the·coefficients·of·a·divisor40 ······-·apply·a·function·to·the·coefficients·of·a·divisor
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190 ··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);</code></pre>190 ··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);</code></pre>
191 ············</td>191 ············</td>
192 ··········</tr>192 ··········</tr>
193 ··········<tr>193 ··········<tr>
194 ············<td>194 ············<td>
195 ··············<pre><code·class="language-macaulay2">i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)})195 ··············<pre><code·class="language-macaulay2">i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)})
  
196 o14·=·3*Div(x,·z)·+·0*Div(y,·z)·+·-Div(x-y,·x-z)196 o14·=·0*Div(y,·z)·+·-Div(x-y,·x-z)·+·3*Div(x,·z)
  
197 o14·:·WeilDivisor·on·R</code></pre>197 o14·:·WeilDivisor·on·R</code></pre>
198 ············</td>198 ············</td>
199 ··········</tr>199 ··········</tr>
200 ··········<tr>200 ··········<tr>
201 ············<td>201 ············<td>
202 ··············<pre><code·class="language-macaulay2">i15·:·-D202 ··············<pre><code·class="language-macaulay2">i15·:·-D
  
203 o15·=·-3*Div(x,·z)·+·Div(x-y,·x-z)203 o15·=·Div(x-y,·x-z)·+·-3*Div(x,·z)
  
204 o15·:·WeilDivisor·on·R</code></pre>204 o15·:·WeilDivisor·on·R</code></pre>
205 ············</td>205 ············</td>
206 ··········</tr>206 ··········</tr>
207 ··········<tr>207 ··········<tr>
208 ············<td>208 ············<td>
209 ··············<pre><code·class="language-macaulay2">i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)})209 ··············<pre><code·class="language-macaulay2">i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)})
  
210 o16·=·3/2*Div(x,·z)·+·-2/3*Div(y,·z)210 o16·=·-2/3*Div(y,·z)·+·3/2*Div(x,·z)
  
211 o16·:·WeilDivisor·on·R</code></pre>211 o16·:·WeilDivisor·on·R</code></pre>
212 ············</td>212 ············</td>
213 ··········</tr>213 ··········</tr>
214 ··········<tr>214 ··········<tr>
215 ············<td>215 ············<td>
216 ··············<pre><code·class="language-macaulay2">i17·:·-E216 ··············<pre><code·class="language-macaulay2">i17·:·-E
  
217 o17·=·-3/2*Div(x,·z)·+·2/3*Div(y,·z)217 o17·=·2/3*Div(y,·z)·+·-3/2*Div(x,·z)
  
218 o17·:·WeilDivisor·on·R</code></pre>218 o17·:·WeilDivisor·on·R</code></pre>
219 ············</td>219 ············</td>
220 ··········</tr>220 ··········</tr>
221 ········</table>221 ········</table>
222 ······</div>222 ······</div>
223 ······<div>223 ······<div>
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70 o12·=·-Div(y)·+·2.75*Div(x)70 o12·=·-Div(y)·+·2.75*Div(x)
  
71 o12·:·RWeilDivisor·on·R71 o12·:·RWeilDivisor·on·R
72 Finally,·we·can·negate·a·divisor.72 Finally,·we·can·negate·a·divisor.
73 i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);73 i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);
74 i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)})74 i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)})
  
75 o14·=·3*Div(x,·z)·+·0*Div(y,·z)·+·-Div(x-y,·x-z)75 o14·=·0*Div(y,·z)·+·-Div(x-y,·x-z)·+·3*Div(x,·z)
  
76 o14·:·WeilDivisor·on·R76 o14·:·WeilDivisor·on·R
77 i15·:·-D77 i15·:·-D
  
78 o15·=·-3*Div(x,·z)·+·Div(x-y,·x-z)78 o15·=·Div(x-y,·x-z)·+·-3*Div(x,·z)
  
79 o15·:·WeilDivisor·on·R79 o15·:·WeilDivisor·on·R
80 i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)})80 i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)})
  
81 o16·=·3/2*Div(x,·z)·+·-2/3*Div(y,·z)81 o16·=·-2/3*Div(y,·z)·+·3/2*Div(x,·z)
  
82 o16·:·WeilDivisor·on·R82 o16·:·WeilDivisor·on·R
83 i17·:·-E83 i17·:·-E
  
84 o17·=·-3/2*Div(x,·z)·+·2/3*Div(y,·z)84 o17·=·2/3*Div(y,·z)·+·-3/2*Div(x,·z)
  
85 o17·:·WeilDivisor·on·R85 o17·:·WeilDivisor·on·R
86 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*86 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
87 ····*·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8·_\x8+_\x8·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·add·or·subtract·two·divisors,·or·negate·a87 ····*·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8·_\x8+_\x8·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·add·or·subtract·two·divisors,·or·negate·a
88 ······divisor88 ······divisor
89 ===============================================================================89 ===============================================================================
90 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-90 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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Offset 82, 24 lines modifiedOffset 82, 24 lines modified
82 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre>82 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor(x*y^2/z)87 ··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor(x*y^2/z)
  
88 o2·=·-Div(z)·+·2*Div(y)·+·Div(x)88 o2·=·Div(x)·+·-Div(z)·+·2*Div(y)
  
89 o2·:·WeilDivisor·on·R</code></pre>89 o2·:·WeilDivisor·on·R</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·applyToCoefficients(D,·u->5*u)94 ··············<pre><code·class="language-macaulay2">i3·:·applyToCoefficients(D,·u->5*u)
  
95 o3·=·10*Div(y)·+·-5*Div(z)·+·5*Div(x)95 o3·=·5*Div(x)·+·10*Div(y)·+·-5*Div(z)
  
96 o3·:·WeilDivisor·on·R</code></pre>96 o3·:·WeilDivisor·on·R</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ········</table>99 ········</table>
100 ······</div>100 ······</div>
101 ······<div>101 ······<div>
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25 the·output·D·is·the·same·as·the·class·of·the·input·D1·(WeilDivisor,25 the·output·D·is·the·same·as·the·class·of·the·input·D1·(WeilDivisor,
26 QWeilDivisor,·RWeilDivisor,·BasicDivisor).·If·Safe·is·set·to·true·(the·default26 QWeilDivisor,·RWeilDivisor,·BasicDivisor).·If·Safe·is·set·to·true·(the·default
27 is·false),·then·the·function·will·check·to·make·sure·the·output·is·a·valid27 is·false),·then·the·function·will·check·to·make·sure·the·output·is·a·valid
28 divisor.28 divisor.
29 i1·:·R·=·QQ[x,·y,·z];29 i1·:·R·=·QQ[x,·y,·z];
30 i2·:·D·=·divisor(x*y^2/z)30 i2·:·D·=·divisor(x*y^2/z)
  
31 o2·=·-Div(z)·+·2*Div(y)·+·Div(x)31 o2·=·Div(x)·+·-Div(z)·+·2*Div(y)
  
32 o2·:·WeilDivisor·on·R32 o2·:·WeilDivisor·on·R
33 i3·:·applyToCoefficients(D,·u->5*u)33 i3·:·applyToCoefficients(D,·u->5*u)
  
34 o3·=·10*Div(y)·+·-5*Div(z)·+·5*Div(x)34 o3·=·5*Div(x)·+·10*Div(y)·+·-5*Div(z)
  
35 o3·:·WeilDivisor·on·R35 o3·:·WeilDivisor·on·R
36 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*36 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
37 ····*·_\x8f_\x8l_\x8o_\x8o_\x8r_\x8(_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8)·--·produce·a·WeilDivisor·whose·coefficients·are37 ····*·_\x8f_\x8l_\x8o_\x8o_\x8r_\x8(_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8)·--·produce·a·WeilDivisor·whose·coefficients·are
38 ······ceilings·or·floors·of·the·divisor38 ······ceilings·or·floors·of·the·divisor
39 ····*·_\x8c_\x8e_\x8i_\x8l_\x8i_\x8n_\x8g_\x8(_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8)·--·produce·a·WeilDivisor·whose·coefficients·are39 ····*·_\x8c_\x8e_\x8i_\x8l_\x8i_\x8n_\x8g_\x8(_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8)·--·produce·a·WeilDivisor·whose·coefficients·are
40 ······ceilings·or·floors·of·the·divisor40 ······ceilings·or·floors·of·the·divisor
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Offset 163, 43 lines modifiedOffset 163, 43 lines modified
163 ············<td>163 ············<td>
164 ··············<pre><code·class="language-macaulay2">i11·:·M·=·J*R^1;</code></pre>164 ··············<pre><code·class="language-macaulay2">i11·:·M·=·J*R^1;</code></pre>
165 ············</td>165 ············</td>
166 ··········</tr>166 ··········</tr>
167 ··········<tr>167 ··········<tr>
168 ············<td>168 ············<td>
169 ··············<pre><code·class="language-macaulay2">i12·:·time·dualize(J,·Strategy=>IdealStrategy);169 ··············<pre><code·class="language-macaulay2">i12·:·time·dualize(J,·Strategy=>IdealStrategy);
170 ·--·used·0.037363s·(cpu);·0.0382174s·(thread);·0s·(gc)170 ·--·used·0.0424712s·(cpu);·0.0433159s·(thread);·0s·(gc)
  
171 o12·:·Ideal·of·R</code></pre>171 o12·:·Ideal·of·R</code></pre>
172 ············</td>172 ············</td>
173 ··········</tr>173 ··········</tr>
174 ··········<tr>174 ··········<tr>
175 ············<td>175 ············<td>
176 ··············<pre><code·class="language-macaulay2">i13·:·time·dualize(J,·Strategy=>ModuleStrategy);176 ··············<pre><code·class="language-macaulay2">i13·:·time·dualize(J,·Strategy=>ModuleStrategy);
177 ·--·used·0.36289s·(cpu);·0.365145s·(thread);·0s·(gc)177 ·--·used·0.47362s·(cpu);·0.475712s·(thread);·0s·(gc)
  
178 o13·:·Ideal·of·R</code></pre>178 o13·:·Ideal·of·R</code></pre>
179 ············</td>179 ············</td>
180 ··········</tr>180 ··········</tr>
181 ··········<tr>181 ··········<tr>
182 ············<td>182 ············<td>
183 ··············<pre><code·class="language-macaulay2">i14·:·time·dualize(M,·Strategy=>IdealStrategy);183 ··············<pre><code·class="language-macaulay2">i14·:·time·dualize(M,·Strategy=>IdealStrategy);
184 ·--·used·0.476484s·(cpu);·0.439445s·(thread);·0s·(gc)</code></pre>184 ·--·used·0.556623s·(cpu);·0.511528s·(thread);·0s·(gc)</code></pre>
185 ············</td>185 ············</td>
186 ··········</tr>186 ··········</tr>
187 ··········<tr>187 ··········<tr>
188 ············<td>188 ············<td>
189 ··············<pre><code·class="language-macaulay2">i15·:·time·dualize(M,·Strategy=>ModuleStrategy);189 ··············<pre><code·class="language-macaulay2">i15·:·time·dualize(M,·Strategy=>ModuleStrategy);
190 ·--·used·9.5073e-05s·(cpu);·0.00244451s·(thread);·0s·(gc)</code></pre>190 ·--·used·0.000108062s·(cpu);·0.00264498s·(thread);·0s·(gc)</code></pre>
191 ············</td>191 ············</td>
192 ··········</tr>192 ··········</tr>
193 ··········<tr>193 ··········<tr>
194 ············<td>194 ············<td>
195 ··············<pre><code·class="language-macaulay2">i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy);195 ··············<pre><code·class="language-macaulay2">i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy);
196 ·--·used·0.000268374s·(cpu);·0.00200294s·(thread);·0s·(gc)196 ·--·used·0.000566071s·(cpu);·0.00231002s·(thread);·0s·(gc)
  
197 o16·:·Ideal·of·R</code></pre>197 o16·:·Ideal·of·R</code></pre>
198 ············</td>198 ············</td>
199 ··········</tr>199 ··········</tr>
200 ········</table>200 ········</table>
201 ········<div>201 ········<div>
202 ··········<p>For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.</p>202 ··········<p>For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.</p>
Offset 223, 23 lines modifiedOffset 223, 23 lines modified
  
223 o19·:·Ideal·of·R</code></pre>223 o19·:·Ideal·of·R</code></pre>
224 ············</td>224 ············</td>
225 ··········</tr>225 ··········</tr>
226 ··········<tr>226 ··········<tr>
227 ············<td>227 ············<td>
228 ··············<pre><code·class="language-macaulay2">i20·:·time·dualize(J,·Strategy=>IdealStrategy);228 ··············<pre><code·class="language-macaulay2">i20·:·time·dualize(J,·Strategy=>IdealStrategy);
229 ·--·used·0.187316s·(cpu);·0.106764s·(thread);·0s·(gc)229 ·--·used·0.242469s·(cpu);·0.112348s·(thread);·0s·(gc)
  
230 o20·:·Ideal·of·R</code></pre>230 o20·:·Ideal·of·R</code></pre>
231 ············</td>231 ············</td>
232 ··········</tr>232 ··········</tr>
233 ··········<tr>233 ··········<tr>
234 ············<td>234 ············<td>
235 ··············<pre><code·class="language-macaulay2">i21·:·time·dualize(J,·Strategy=>ModuleStrategy);235 ··············<pre><code·class="language-macaulay2">i21·:·time·dualize(J,·Strategy=>ModuleStrategy);
236 ·--·used·0.00265352s·(cpu);·0.00495863s·(thread);·0s·(gc)236 ·--·used·0.00320012s·(cpu);·0.00585463s·(thread);·0s·(gc)
  
237 o21·:·Ideal·of·R</code></pre>237 o21·:·Ideal·of·R</code></pre>
238 ············</td>238 ············</td>
239 ··········</tr>239 ··········</tr>
240 ········</table>240 ········</table>
241 ········<div>241 ········<div>
242 ··········<p><span·class="tt">KnownDomain</span>·is·an·option·for·<span·class="tt">dualize</span>.··If·it·is·<span·class="tt">false</span>·(default·is·<span·class="tt">true</span>),·then·the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then·it·will·revert·to·<span·class="tt">ModuleStrategy</span>.··If·<span·class="tt">KnownDomain</span>·is·set·to·<span·class="tt">true</span>·for·a·non-domain,·then·the·function·can·return·an·incorrect·answer.</p>242 ··········<p><span·class="tt">KnownDomain</span>·is·an·option·for·<span·class="tt">dualize</span>.··If·it·is·<span·class="tt">false</span>·(default·is·<span·class="tt">true</span>),·then·the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then·it·will·revert·to·<span·class="tt">ModuleStrategy</span>.··If·<span·class="tt">KnownDomain</span>·is·set·to·<span·class="tt">true</span>·for·a·non-domain,·then·the·function·can·return·an·incorrect·answer.</p>
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Offset 60, 43 lines modifiedOffset 60, 43 lines modified
  
60 o9·:·Ideal·of·R60 o9·:·Ideal·of·R
61 i10·:·J·=·m^9;61 i10·:·J·=·m^9;
  
62 o10·:·Ideal·of·R62 o10·:·Ideal·of·R
63 i11·:·M·=·J*R^1;63 i11·:·M·=·J*R^1;
64 i12·:·time·dualize(J,·Strategy=>IdealStrategy);64 i12·:·time·dualize(J,·Strategy=>IdealStrategy);
65 ·--·used·0.037363s·(cpu);·0.0382174s·(thread);·0s·(gc)65 ·--·used·0.0424712s·(cpu);·0.0433159s·(thread);·0s·(gc)
  
66 o12·:·Ideal·of·R66 o12·:·Ideal·of·R
67 i13·:·time·dualize(J,·Strategy=>ModuleStrategy);67 i13·:·time·dualize(J,·Strategy=>ModuleStrategy);
68 ·--·used·0.36289s·(cpu);·0.365145s·(thread);·0s·(gc)68 ·--·used·0.47362s·(cpu);·0.475712s·(thread);·0s·(gc)
  
69 o13·:·Ideal·of·R69 o13·:·Ideal·of·R
70 i14·:·time·dualize(M,·Strategy=>IdealStrategy);70 i14·:·time·dualize(M,·Strategy=>IdealStrategy);
71 ·--·used·0.476484s·(cpu);·0.439445s·(thread);·0s·(gc)71 ·--·used·0.556623s·(cpu);·0.511528s·(thread);·0s·(gc)
72 i15·:·time·dualize(M,·Strategy=>ModuleStrategy);72 i15·:·time·dualize(M,·Strategy=>ModuleStrategy);
73 ·--·used·9.5073e-05s·(cpu);·0.00244451s·(thread);·0s·(gc)73 ·--·used·0.000108062s·(cpu);·0.00264498s·(thread);·0s·(gc)
74 i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy);74 i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy);
75 ·--·used·0.000268374s·(cpu);·0.00200294s·(thread);·0s·(gc)75 ·--·used·0.000566071s·(cpu);·0.00231002s·(thread);·0s·(gc)
  
76 o16·:·Ideal·of·R76 o16·:·Ideal·of·R
77 For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.77 For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.
78 i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v);78 i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v);
79 i18·:·I·=·ideal(x,u);79 i18·:·I·=·ideal(x,u);
  
80 o18·:·Ideal·of·R80 o18·:·Ideal·of·R
81 i19·:·J·=·I^15;81 i19·:·J·=·I^15;
  
82 o19·:·Ideal·of·R82 o19·:·Ideal·of·R
83 i20·:·time·dualize(J,·Strategy=>IdealStrategy);83 i20·:·time·dualize(J,·Strategy=>IdealStrategy);
84 ·--·used·0.187316s·(cpu);·0.106764s·(thread);·0s·(gc)84 ·--·used·0.242469s·(cpu);·0.112348s·(thread);·0s·(gc)
  
85 o20·:·Ideal·of·R85 o20·:·Ideal·of·R
86 i21·:·time·dualize(J,·Strategy=>ModuleStrategy);86 i21·:·time·dualize(J,·Strategy=>ModuleStrategy);
87 ·--·used·0.00265352s·(cpu);·0.00495863s·(thread);·0s·(gc)87 ·--·used·0.00320012s·(cpu);·0.00585463s·(thread);·0s·(gc)
  
88 o21·:·Ideal·of·R88 o21·:·Ideal·of·R
89 KnownDomain·is·an·option·for·dualize.·If·it·is·false·(default·is·true),·then89 KnownDomain·is·an·option·for·dualize.·If·it·is·false·(default·is·true),·then
90 the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then90 the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then
91 it·will·revert·to·ModuleStrategy.·If·KnownDomain·is·set·to·true·for·a·non-91 it·will·revert·to·ModuleStrategy.·If·KnownDomain·is·set·to·true·for·a·non-
92 domain,·then·the·function·can·return·an·incorrect·answer.92 domain,·then·the·function·can·return·an·incorrect·answer.
93 i22·:·R·=·QQ[x,y]/ideal(x*y);93 i22·:·R·=·QQ[x,y]/ideal(x*y);
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Offset 81, 24 lines modifiedOffset 81, 24 lines modified
81 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);</code></pre>81 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})86 ··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})
  
87 o2·=·8*Div(y,·z)·+·3*Div(x,·z)87 o2·=·3*Div(x,·z)·+·8*Div(y,·z)
  
88 o2·:·WeilDivisor·on·R</code></pre>88 o2·:·WeilDivisor·on·R</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})93 ··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})
  
94 o3·=·8*Div(y,·z)·+·Div(x,·z)94 o3·=·Div(x,·z)·+·8*Div(y,·z)
  
95 o3·:·WeilDivisor·on·R</code></pre>95 o3·:·WeilDivisor·on·R</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i4·:·isLinearEquivalent(D1,·D2)100 ··············<pre><code·class="language-macaulay2">i4·:·isLinearEquivalent(D1,·D2)
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116 ··············<pre><code·class="language-macaulay2">i5·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);</code></pre>116 ··············<pre><code·class="language-macaulay2">i5·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);</code></pre>
117 ············</td>117 ············</td>
118 ··········</tr>118 ··········</tr>
119 ··········<tr>119 ··········<tr>
120 ············<td>120 ············<td>
121 ··············<pre><code·class="language-macaulay2">i6·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})121 ··············<pre><code·class="language-macaulay2">i6·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})
  
122 o6·=·3*Div(x,·z)·+·8*Div(y,·z)122 o6·=·8*Div(y,·z)·+·3*Div(x,·z)
  
123 o6·:·WeilDivisor·on·R</code></pre>123 o6·:·WeilDivisor·on·R</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i7·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})128 ··············<pre><code·class="language-macaulay2">i7·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})
  
129 o7·=·Div(x,·z)·+·8*Div(y,·z)129 o7·=·8*Div(y,·z)·+·Div(x,·z)
  
130 o7·:·WeilDivisor·on·R</code></pre>130 o7·:·WeilDivisor·on·R</code></pre>
131 ············</td>131 ············</td>
132 ··········</tr>132 ··········</tr>
133 ··········<tr>133 ··········<tr>
134 ············<td>134 ············<td>
135 ··············<pre><code·class="language-macaulay2">i8·:·isLinearEquivalent(D1,·D2,·IsGraded·=>·true)135 ··············<pre><code·class="language-macaulay2">i8·:·isLinearEquivalent(D1,·D2,·IsGraded·=>·true)
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17 ··········o·flag,·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,17 ··········o·flag,·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,
18 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*18 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
19 Given·two·Weil·divisors,·this·method·checks·whether·they·are·linearly19 Given·two·Weil·divisors,·this·method·checks·whether·they·are·linearly
20 equivalent.20 equivalent.
21 i1·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);21 i1·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);
22 i2·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})22 i2·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})
  
23 o2·=·8*Div(y,·z)·+·3*Div(x,·z)23 o2·=·3*Div(x,·z)·+·8*Div(y,·z)
  
24 o2·:·WeilDivisor·on·R24 o2·:·WeilDivisor·on·R
25 i3·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})25 i3·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})
  
26 o3·=·8*Div(y,·z)·+·Div(x,·z)26 o3·=·Div(x,·z)·+·8*Div(y,·z)
  
27 o3·:·WeilDivisor·on·R27 o3·:·WeilDivisor·on·R
28 i4·:·isLinearEquivalent(D1,·D2)28 i4·:·isLinearEquivalent(D1,·D2)
  
29 o4·=·true29 o4·=·true
30 If·IsGraded·is·set·to·true·(by·default·it·is·false),·then·it·treats·the30 If·IsGraded·is·set·to·true·(by·default·it·is·false),·then·it·treats·the
31 divisors·as·divisors·on·the·$Proj$·of·their·ambient·ring.31 divisors·as·divisors·on·the·$Proj$·of·their·ambient·ring.
32 i5·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);32 i5·:·R·=·QQ[x,·y,·z]/·ideal(x·*·y·-·z^2);
33 i6·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})33 i6·:·D1·=·divisor({3,·8},·{ideal(x,·z),·ideal(y,·z)})
  
34 o6·=·3*Div(x,·z)·+·8*Div(y,·z)34 o6·=·8*Div(y,·z)·+·3*Div(x,·z)
  
35 o6·:·WeilDivisor·on·R35 o6·:·WeilDivisor·on·R
36 i7·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})36 i7·:·D2·=·divisor({8,·1},·{ideal(y,·z),·ideal(x,·z)})
  
37 o7·=·Div(x,·z)·+·8*Div(y,·z)37 o7·=·8*Div(y,·z)·+·Div(x,·z)
  
38 o7·:·WeilDivisor·on·R38 o7·:·WeilDivisor·on·R
39 i8·:·isLinearEquivalent(D1,·D2,·IsGraded·=>·true)39 i8·:·isLinearEquivalent(D1,·D2,·IsGraded·=>·true)
  
40 o8·=·false40 o8·=·false
41 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*41 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
42 ····*·_\x8O_\x8O_\x8·_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r42 ····*·_\x8O_\x8O_\x8·_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r
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82 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre>82 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)87 ··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)
  
88 o2·=·3/4*Div(y,·z)·+·1/2*Div(x,·z)88 o2·=·1/2*Div(x,·z)·+·3/4*Div(y,·z)
  
89 o2·:·QWeilDivisor·on·R</code></pre>89 o2·:·QWeilDivisor·on·R</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)94 ··············<pre><code·class="language-macaulay2">i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)
  
95 o3·=·3/4*Div(y,·z)·+·5/2*Div(x,·z)95 o3·=·5/2*Div(x,·z)·+·3/4*Div(y,·z)
  
96 o3·:·QWeilDivisor·on·R</code></pre>96 o3·:·QWeilDivisor·on·R</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·isQLinearEquivalent(10,·D,·E)101 ··············<pre><code·class="language-macaulay2">i4·:·isQLinearEquivalent(10,·D,·E)
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155 ··············<pre><code·class="language-macaulay2">i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre>155 ··············<pre><code·class="language-macaulay2">i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre>
156 ············</td>156 ············</td>
157 ··········</tr>157 ··········</tr>
158 ··········<tr>158 ··········<tr>
159 ············<td>159 ············<td>
160 ··············<pre><code·class="language-macaulay2">i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)160 ··············<pre><code·class="language-macaulay2">i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)
  
161 o11·=·1/2*Div(x,·z)·+·3/4*Div(y,·z)161 o11·=·3/4*Div(y,·z)·+·1/2*Div(x,·z)
  
162 o11·:·QWeilDivisor·on·R</code></pre>162 o11·:·QWeilDivisor·on·R</code></pre>
163 ············</td>163 ············</td>
164 ··········</tr>164 ··········</tr>
165 ··········<tr>165 ··········<tr>
166 ············<td>166 ············<td>
167 ··············<pre><code·class="language-macaulay2">i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)167 ··············<pre><code·class="language-macaulay2">i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)
  
168 o12·=·-1/4*Div(x,·z)·+·3/2*Div(y,·z)168 o12·=·3/2*Div(y,·z)·+·-1/4*Div(x,·z)
  
169 o12·:·QWeilDivisor·on·R</code></pre>169 o12·:·QWeilDivisor·on·R</code></pre>
170 ············</td>170 ············</td>
171 ··········</tr>171 ··········</tr>
172 ··········<tr>172 ··········<tr>
173 ············<td>173 ············<td>
174 ··············<pre><code·class="language-macaulay2">i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true)174 ··············<pre><code·class="language-macaulay2">i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true)
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19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
20 Given·two·rational·divisors,·this·method·returns·true·if·they·linearly20 Given·two·rational·divisors,·this·method·returns·true·if·they·linearly
21 equivalent·after·clearing·denominators·or·if·some·further·multiple·up·to·n21 equivalent·after·clearing·denominators·or·if·some·further·multiple·up·to·n
22 makes·them·linearly·equivalent.·Otherwise·it·returns·false.22 makes·them·linearly·equivalent.·Otherwise·it·returns·false.
23 i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);23 i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);
24 i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)24 i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ)
  
25 o2·=·3/4*Div(y,·z)·+·1/2*Div(x,·z)25 o2·=·1/2*Div(x,·z)·+·3/4*Div(y,·z)
  
26 o2·:·QWeilDivisor·on·R26 o2·:·QWeilDivisor·on·R
27 i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)27 i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ)
  
28 o3·=·3/4*Div(y,·z)·+·5/2*Div(x,·z)28 o3·=·5/2*Div(x,·z)·+·3/4*Div(y,·z)
  
29 o3·:·QWeilDivisor·on·R29 o3·:·QWeilDivisor·on·R
30 i4·:·isQLinearEquivalent(10,·D,·E)30 i4·:·isQLinearEquivalent(10,·D,·E)
  
31 o4·=·true31 o4·=·true
32 In·the·above·ring,·every·pair·of·divisors·is·Q-linearly·equivalent·because·the32 In·the·above·ring,·every·pair·of·divisors·is·Q-linearly·equivalent·because·the
33 Weil·divisor·class·group·is·isomorphic·to·Z/2.·However,·if·we·don't·set·n·high33 Weil·divisor·class·group·is·isomorphic·to·Z/2.·However,·if·we·don't·set·n·high
Offset 52, 21 lines modifiedOffset 52, 21 lines modified
52 o9·=·true52 o9·=·true
53 If·IsGraded=>true·(the·default·is·false),·then·it·treats·the·divisors·as·if53 If·IsGraded=>true·(the·default·is·false),·then·it·treats·the·divisors·as·if
54 they·are·divisors·on·the·$Proj$·of·their·ambient·ring.54 they·are·divisors·on·the·$Proj$·of·their·ambient·ring.
55 i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);55 i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);
56 i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>56 i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>
57 QQ)57 QQ)
  
58 o11·=·1/2*Div(x,·z)·+·3/4*Div(y,·z)58 o11·=·3/4*Div(y,·z)·+·1/2*Div(x,·z)
  
59 o11·:·QWeilDivisor·on·R59 o11·:·QWeilDivisor·on·R
60 i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>60 i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>
61 QQ)61 QQ)
  
62 o12·=·-1/4*Div(x,·z)·+·3/2*Div(y,·z)62 o12·=·3/2*Div(y,·z)·+·-1/4*Div(x,·z)
  
63 o12·:·QWeilDivisor·on·R63 o12·:·QWeilDivisor·on·R
64 i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true)64 i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true)
  
65 o13·=·true65 o13·=·true
66 i14·:·isQLinearEquivalent(10,·3*D,·E,·IsGraded·=>·true)66 i14·:·isQLinearEquivalent(10,·3*D,·E,·IsGraded·=>·true)
  
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76 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre>76 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor(x^2·*·y^3·*·z)81 ··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor(x^2·*·y^3·*·z)
  
82 o2·=·3*Div(y)·+·Div(z)·+·2*Div(x)82 o2·=·2*Div(x)·+·3*Div(y)·+·Div(z)
  
83 o2·:·WeilDivisor·on·R</code></pre>83 o2·:·WeilDivisor·on·R</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor(x·*·y·*·z)88 ··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor(x·*·y·*·z)
  
89 o3·=·Div(y)·+·Div(z)·+·Div(x)89 o3·=·Div(x)·+·Div(y)·+·Div(z)
  
90 o3·:·WeilDivisor·on·R</code></pre>90 o3·:·WeilDivisor·on·R</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i4·:·isReduced(·D1·)95 ··············<pre><code·class="language-macaulay2">i4·:·isReduced(·D1·)
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12 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,12 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 This·function·returns·true·if·the·divisor·is·reduced·(all·coefficients·equal·to14 This·function·returns·true·if·the·divisor·is·reduced·(all·coefficients·equal·to
15 1),·otherwise·it·returns·false.15 1),·otherwise·it·returns·false.
16 i1·:·R·=·QQ[x,·y,·z];16 i1·:·R·=·QQ[x,·y,·z];
17 i2·:·D1·=·divisor(x^2·*·y^3·*·z)17 i2·:·D1·=·divisor(x^2·*·y^3·*·z)
  
18 o2·=·3*Div(y)·+·Div(z)·+·2*Div(x)18 o2·=·2*Div(x)·+·3*Div(y)·+·Div(z)
  
19 o2·:·WeilDivisor·on·R19 o2·:·WeilDivisor·on·R
20 i3·:·D2·=·divisor(x·*·y·*·z)20 i3·:·D2·=·divisor(x·*·y·*·z)
  
21 o3·=·Div(y)·+·Div(z)·+·Div(x)21 o3·=·Div(x)·+·Div(y)·+·Div(z)
  
22 o3·:·WeilDivisor·on·R22 o3·:·WeilDivisor·on·R
23 i4·:·isReduced(·D1·)23 i4·:·isReduced(·D1·)
  
24 o4·=·false24 o4·=·false
25 i5·:·isReduced(·D2·)25 i5·:·isReduced(·D2·)
  
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76 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre>76 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor({1/1,·2/2,·-6/3},·{ideal(x),·ideal(y),·ideal(z)},·CoefficientType=>QQ)81 ··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor({1/1,·2/2,·-6/3},·{ideal(x),·ideal(y),·ideal(z)},·CoefficientType=>QQ)
  
82 o2·=·Div(x)·+·Div(y)·+·-2*Div(z)82 o2·=·Div(y)·+·-2*Div(z)·+·Div(x)
  
83 o2·:·QWeilDivisor·on·R</code></pre>83 o2·:·QWeilDivisor·on·R</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor({1/2,·3/4,·5/6},·{ideal(y),·ideal(z),·ideal(x)},·CoefficientType=>QQ)88 ··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor({1/2,·3/4,·5/6},·{ideal(y),·ideal(z),·ideal(x)},·CoefficientType=>QQ)
  
89 o3·=·5/6*Div(x)·+·1/2*Div(y)·+·3/4*Div(z)89 o3·=·1/2*Div(y)·+·3/4*Div(z)·+·5/6*Div(x)
  
90 o3·:·QWeilDivisor·on·R</code></pre>90 o3·:·QWeilDivisor·on·R</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i4·:·isWeilDivisor(·D1·)95 ··············<pre><code·class="language-macaulay2">i4·:·isWeilDivisor(·D1·)
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13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 Check·if·a·rational/real·divisor·is·a·Weil·divisor15 Check·if·a·rational/real·divisor·is·a·Weil·divisor
16 i1·:·R·=·QQ[x,·y,·z];16 i1·:·R·=·QQ[x,·y,·z];
17 i2·:·D1·=·divisor({1/1,·2/2,·-6/3},·{ideal(x),·ideal(y),·ideal(z)},17 i2·:·D1·=·divisor({1/1,·2/2,·-6/3},·{ideal(x),·ideal(y),·ideal(z)},
18 CoefficientType=>QQ)18 CoefficientType=>QQ)
  
19 o2·=·Div(x)·+·Div(y)·+·-2*Div(z)19 o2·=·Div(y)·+·-2*Div(z)·+·Div(x)
  
20 o2·:·QWeilDivisor·on·R20 o2·:·QWeilDivisor·on·R
21 i3·:·D2·=·divisor({1/2,·3/4,·5/6},·{ideal(y),·ideal(z),·ideal(x)},21 i3·:·D2·=·divisor({1/2,·3/4,·5/6},·{ideal(y),·ideal(z),·ideal(x)},
22 CoefficientType=>QQ)22 CoefficientType=>QQ)
  
23 o3·=·5/6*Div(x)·+·1/2*Div(y)·+·3/4*Div(z)23 o3·=·1/2*Div(y)·+·3/4*Div(z)·+·5/6*Div(x)
  
24 o3·:·QWeilDivisor·on·R24 o3·:·QWeilDivisor·on·R
25 i4·:·isWeilDivisor(·D1·)25 i4·:·isWeilDivisor(·D1·)
  
26 o4·=·true26 o4·=·true
27 i5·:·isWeilDivisor(·D2·)27 i5·:·isWeilDivisor(·D2·)
  
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150 o10·:·WeilDivisor·on·R</code></pre>150 o10·:·WeilDivisor·on·R</code></pre>
151 ············</td>151 ············</td>
152 ··········</tr>152 ··········</tr>
153 ··········<tr>153 ··········<tr>
154 ············<td>154 ············<td>
155 ··············<pre><code·class="language-macaulay2">i11·:·D1·=·pullback(f,·D)155 ··············<pre><code·class="language-macaulay2">i11·:·D1·=·pullback(f,·D)
  
156 o11·=·Div(a+1)·+·3*Div(b)·+·Div(a)156 o11·=·Div(a)·+·3*Div(b)·+·Div(a+1)
  
157 o11·:·WeilDivisor·on·S</code></pre>157 o11·:·WeilDivisor·on·S</code></pre>
158 ············</td>158 ············</td>
159 ··········</tr>159 ··········</tr>
160 ··········<tr>160 ··········<tr>
161 ············<td>161 ············<td>
162 ··············<pre><code·class="language-macaulay2">i12·:·f^*·D162 ··············<pre><code·class="language-macaulay2">i12·:·f^*·D
  
163 o12·=·Div(a+1)·+·3*Div(b)·+·Div(a)163 o12·=·Div(a)·+·3*Div(b)·+·Div(a+1)
  
164 o12·:·WeilDivisor·on·S</code></pre>164 o12·:·WeilDivisor·on·S</code></pre>
165 ············</td>165 ············</td>
166 ··········</tr>166 ··········</tr>
167 ········</table>167 ········</table>
168 ········<div>168 ········<div>
169 ··········<p>As·illustrated·by·the·previous·example,·the·same·functionality·can·also·be·accomplished·by·<span·class="tt">f^*</span>·(which·creates·a·function·which·sends·a·divisor·$D$·to·$f^*·D$).</p>169 ··········<p>As·illustrated·by·the·previous·example,·the·same·functionality·can·also·be·accomplished·by·<span·class="tt">f^*</span>·(which·creates·a·function·which·sends·a·divisor·$D$·to·$f^*·D$).</p>
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Offset 53, 20 lines modifiedOffset 53, 20 lines modified
  
53 o9·:·RingMap·S·<--·R53 o9·:·RingMap·S·<--·R
54 i10·:·D·=·divisor(x*y*(x+y));54 i10·:·D·=·divisor(x*y*(x+y));
  
55 o10·:·WeilDivisor·on·R55 o10·:·WeilDivisor·on·R
56 i11·:·D1·=·pullback(f,·D)56 i11·:·D1·=·pullback(f,·D)
  
57 o11·=·Div(a+1)·+·3*Div(b)·+·Div(a)57 o11·=·Div(a)·+·3*Div(b)·+·Div(a+1)
  
58 o11·:·WeilDivisor·on·S58 o11·:·WeilDivisor·on·S
59 i12·:·f^*·D59 i12·:·f^*·D
  
60 o12·=·Div(a+1)·+·3*Div(b)·+·Div(a)60 o12·=·Div(a)·+·3*Div(b)·+·Div(a+1)
  
61 o12·:·WeilDivisor·on·S61 o12·:·WeilDivisor·on·S
62 As·illustrated·by·the·previous·example,·the·same·functionality·can·also·be62 As·illustrated·by·the·previous·example,·the·same·functionality·can·also·be
63 accomplished·by·f^*·(which·creates·a·function·which·sends·a·divisor·$D$·to·$f^*63 accomplished·by·f^*·(which·creates·a·function·which·sends·a·divisor·$D$·to·$f^*
64 D$).64 D$).
65 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*65 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
66 ····*·_\x8P_\x8r_\x8i_\x8m_\x8e_\x8s·--·a·value·for·the·option·Strategy·for·the·pullback·method66 ····*·_\x8P_\x8r_\x8i_\x8m_\x8e_\x8s·--·a·value·for·the·option·Strategy·for·the·pullback·method
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Offset 267, 23 lines modifiedOffset 267, 23 lines modified
  
267 o22·:·Ideal·of·R</code></pre>267 o22·:·Ideal·of·R</code></pre>
268 ············</td>268 ············</td>
269 ··········</tr>269 ··········</tr>
270 ··········<tr>270 ··········<tr>
271 ············<td>271 ············<td>
272 ··············<pre><code·class="language-macaulay2">i23·:·time·reflexify(J);272 ··············<pre><code·class="language-macaulay2">i23·:·time·reflexify(J);
273 ·--·used·0.193733s·(cpu);·0.153478s·(thread);·0s·(gc)273 ·--·used·0.231862s·(cpu);·0.188752s·(thread);·0s·(gc)
  
274 o23·:·Ideal·of·R</code></pre>274 o23·:·Ideal·of·R</code></pre>
275 ············</td>275 ············</td>
276 ··········</tr>276 ··········</tr>
277 ··········<tr>277 ··········<tr>
278 ············<td>278 ············<td>
279 ··············<pre><code·class="language-macaulay2">i24·:·time·reflexify(J*R^1);279 ··············<pre><code·class="language-macaulay2">i24·:·time·reflexify(J*R^1);
280 ·--·used·0.302365s·(cpu);·0.26108s·(thread);·0s·(gc)</code></pre>280 ·--·used·0.368034s·(cpu);·0.326261s·(thread);·0s·(gc)</code></pre>
281 ············</td>281 ············</td>
282 ··········</tr>282 ··········</tr>
283 ········</table>283 ········</table>
284 ········<div>284 ········<div>
285 ··········<p>Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at·least·if·the·module·embeds·as·an·ideal).</p>285 ··········<p>Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at·least·if·the·module·embeds·as·an·ideal).</p>
286 ········</div>286 ········</div>
287 ········<div>287 ········<div>
Offset 319, 26 lines modifiedOffset 319, 26 lines modified
319 ············<td>319 ············<td>
320 ··············<pre><code·class="language-macaulay2">i28·:·M·=·J*R^1;</code></pre>320 ··············<pre><code·class="language-macaulay2">i28·:·M·=·J*R^1;</code></pre>
321 ············</td>321 ············</td>
322 ··········</tr>322 ··········</tr>
323 ··········<tr>323 ··········<tr>
324 ············<td>324 ············<td>
325 ··············<pre><code·class="language-macaulay2">i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·)325 ··············<pre><code·class="language-macaulay2">i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·)
326 ·--·used·0.198576s·(cpu);·0.114034s·(thread);·0s·(gc)326 ·--·used·0.212751s·(cpu);·0.116713s·(thread);·0s·(gc)
  
327 ··············2············2·····9·······9···11327 ··············2············2·····9·······9···11
328 o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)328 o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)
  
329 o29·:·Ideal·of·R</code></pre>329 o29·:·Ideal·of·R</code></pre>
330 ············</td>330 ············</td>
331 ··········</tr>331 ··········</tr>
332 ··········<tr>332 ··········<tr>
333 ············<td>333 ············<td>
334 ··············<pre><code·class="language-macaulay2">i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·)334 ··············<pre><code·class="language-macaulay2">i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·)
335 ·--·used·4.61899s·(cpu);·3.56006s·(thread);·0s·(gc)335 ·--·used·4.8383s·(cpu);·3.78425s·(thread);·0s·(gc)
  
336 ··············2············2·····9·······9···11336 ··············2············2·····9·······9···11
337 o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)337 o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)
  
338 o30·:·Ideal·of·R</code></pre>338 o30·:·Ideal·of·R</code></pre>
339 ············</td>339 ············</td>
340 ··········</tr>340 ··········</tr>
Offset 348, 21 lines modifiedOffset 348, 21 lines modified
  
348 o31·=·true</code></pre>348 o31·=·true</code></pre>
349 ············</td>349 ············</td>
350 ··········</tr>350 ··········</tr>
351 ··········<tr>351 ··········<tr>
352 ············<td>352 ············<td>
353 ··············<pre><code·class="language-macaulay2">i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·);353 ··············<pre><code·class="language-macaulay2">i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·);
354 ·--·used·4.7491s·(cpu);·3.75787s·(thread);·0s·(gc)</code></pre>354 ·--·used·5.38506s·(cpu);·4.2357s·(thread);·0s·(gc)</code></pre>
355 ············</td>355 ············</td>
356 ··········</tr>356 ··········</tr>
357 ··········<tr>357 ··········<tr>
358 ············<td>358 ············<td>
359 ··············<pre><code·class="language-macaulay2">i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);359 ··············<pre><code·class="language-macaulay2">i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);
360 ·--·used·0.424617s·(cpu);·0.307849s·(thread);·0s·(gc)</code></pre>360 ·--·used·0.442613s·(cpu);·0.3133s·(thread);·0s·(gc)</code></pre>
361 ············</td>361 ············</td>
362 ··········</tr>362 ··········</tr>
363 ········</table>363 ········</table>
364 ········<div>364 ········<div>
365 ··········<p>However,·sometimes·<span·class="tt">ModuleStrategy</span>·is·faster,·especially·for·Monomial·ideals.</p>365 ··········<p>However,·sometimes·<span·class="tt">ModuleStrategy</span>·is·faster,·especially·for·Monomial·ideals.</p>
366 ········</div>366 ········</div>
367 ········<table·class="examples">367 ········<table·class="examples">
Offset 389, 15 lines modifiedOffset 389, 15 lines modified
389 ············<td>389 ············<td>
390 ··············<pre><code·class="language-macaulay2">i37·:·M·=·I^20*R^1;</code></pre>390 ··············<pre><code·class="language-macaulay2">i37·:·M·=·I^20*R^1;</code></pre>
391 ············</td>391 ············</td>
392 ··········</tr>392 ··········</tr>
393 ··········<tr>393 ··········<tr>
394 ············<td>394 ············<td>
395 ··············<pre><code·class="language-macaulay2">i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·)395 ··············<pre><code·class="language-macaulay2">i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·)
396 ·--·used·0.809782s·(cpu);·0.30444s·(thread);·0s·(gc)396 ·--·used·0.807535s·(cpu);·0.301082s·(thread);·0s·(gc)
  
397 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·397 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·
398 o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,398 o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,
399 ······-----------------------------------------------------------------------399 ······-----------------------------------------------------------------------
400 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·400 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·
401 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,401 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,
402 ······-----------------------------------------------------------------------402 ······-----------------------------------------------------------------------
Offset 406, 15 lines modifiedOffset 406, 15 lines modified
  
406 o38·:·Ideal·of·R</code></pre>406 o38·:·Ideal·of·R</code></pre>
407 ············</td>407 ············</td>
408 ··········</tr>408 ··········</tr>
409 ··········<tr>409 ··········<tr>
410 ············<td>410 ············<td>
411 ··············<pre><code·class="language-macaulay2">i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·)411 ··············<pre><code·class="language-macaulay2">i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·)
412 ·--·used·0.174601s·(cpu);·0.0531627s·(thread);·0s·(gc)412 ·--·used·0.157457s·(cpu);·0.0366832s·(thread);·0s·(gc)
  
413 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·413 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12·
414 o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,414 o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,
415 ······-----------------------------------------------------------------------415 ······-----------------------------------------------------------------------
416 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·416 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2·
417 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,417 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,
418 ······-----------------------------------------------------------------------418 ······-----------------------------------------------------------------------
Offset 423, 21 lines modifiedOffset 423, 21 lines modified
  
423 o39·:·Ideal·of·R</code></pre>423 o39·:·Ideal·of·R</code></pre>
424 ············</td>424 ············</td>
425 ··········</tr>425 ··········</tr>
426 ··········<tr>426 ··········<tr>
427 ············<td>427 ············<td>
428 ··············<pre><code·class="language-macaulay2">i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·);428 ··············<pre><code·class="language-macaulay2">i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·);
429 ·--·used·0.0324022s·(cpu);·0.033304s·(thread);·0s·(gc)</code></pre>429 ·--·used·0.0380324s·(cpu);·0.037759s·(thread);·0s·(gc)</code></pre>
430 ············</td>430 ············</td>
431 ··········</tr>431 ··········</tr>
432 ··········<tr>432 ··········<tr>
433 ············<td>433 ············<td>
434 ··············<pre><code·class="language-macaulay2">i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);434 ··············<pre><code·class="language-macaulay2">i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);
435 ·--·used·0.00272989s·(cpu);·0.00538526s·(thread);·0s·(gc)</code></pre>435 ·--·used·0.00485728s·(cpu);·0.00613396s·(thread);·0s·(gc)</code></pre>
436 ············</td>436 ············</td>
437 ··········</tr>437 ··········</tr>
438 ········</table>438 ········</table>
439 ········<div>439 ········<div>
440 ··········<p>For·ideals,·if·<span·class="tt">KnownDomain</span>·is·false·(default·value·is·<span·class="tt">true</span>),·then·the·function·will·check·whether·it·is·a·domain.··If·it·is·a·domain·(or·assumed·to·be·a·domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if·not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially·reflexifying·it·as·a·module.</p>440 ··········<p>For·ideals,·if·<span·class="tt">KnownDomain</span>·is·false·(default·value·is·<span·class="tt">true</span>),·then·the·function·will·check·whether·it·is·a·domain.··If·it·is·a·domain·(or·assumed·to·be·a·domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if·not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially·reflexifying·it·as·a·module.</p>
441 ········</div>441 ········</div>
442 ········<div>442 ········<div>
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Offset 114, 19 lines modifiedOffset 114, 19 lines modified
114 i21·:·I·=·ideal(x-z,y-2*z);114 i21·:·I·=·ideal(x-z,y-2*z);
  
115 o21·:·Ideal·of·R115 o21·:·Ideal·of·R
116 i22·:·J·=·I^21;116 i22·:·J·=·I^21;
  
117 o22·:·Ideal·of·R117 o22·:·Ideal·of·R
118 i23·:·time·reflexify(J);118 i23·:·time·reflexify(J);
119 ·--·used·0.193733s·(cpu);·0.153478s·(thread);·0s·(gc)119 ·--·used·0.231862s·(cpu);·0.188752s·(thread);·0s·(gc)
  
120 o23·:·Ideal·of·R120 o23·:·Ideal·of·R
121 i24·:·time·reflexify(J*R^1);121 i24·:·time·reflexify(J*R^1);
122 ·--·used·0.302365s·(cpu);·0.26108s·(thread);·0s·(gc)122 ·--·used·0.368034s·(cpu);·0.326261s·(thread);·0s·(gc)
123 Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at123 Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at
124 least·if·the·module·embeds·as·an·ideal).124 least·if·the·module·embeds·as·an·ideal).
125 IdealStrategy.·In·the·case·that·$R$·is·a·domain,·and·our·module·is·isomorphic125 IdealStrategy.·In·the·case·that·$R$·is·a·domain,·and·our·module·is·isomorphic
126 to·an·ideal·$I$,·then·one·can·compute·the·reflexification·by·computing·colons.126 to·an·ideal·$I$,·then·one·can·compute·the·reflexification·by·computing·colons.
127 ModuleStrategy.·This·computes·the·reflexification·simply·by·computing·$Hom$127 ModuleStrategy.·This·computes·the·reflexification·simply·by·computing·$Hom$
128 twice.128 twice.
129 ModuleStrategy·is·the·default·strategy·for·modules,·IdealStrategy·is·the129 ModuleStrategy·is·the·default·strategy·for·modules,·IdealStrategy·is·the
Offset 139, 73 lines modifiedOffset 139, 73 lines modified
  
139 o26·:·Ideal·of·R139 o26·:·Ideal·of·R
140 i27·:·J·=·I^20;140 i27·:·J·=·I^20;
  
141 o27·:·Ideal·of·R141 o27·:·Ideal·of·R
142 i28·:·M·=·J*R^1;142 i28·:·M·=·J*R^1;
143 i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·)143 i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·)
144 ·--·used·0.198576s·(cpu);·0.114034s·(thread);·0s·(gc)144 ·--·used·0.212751s·(cpu);·0.116713s·(thread);·0s·(gc)
  
145 ··············2············2·····9·······9···11145 ··············2············2·····9·······9···11
146 o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)146 o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)
  
147 o29·:·Ideal·of·R147 o29·:·Ideal·of·R
148 i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·)148 i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·)
149 ·--·used·4.61899s·(cpu);·3.56006s·(thread);·0s·(gc)149 ·--·used·4.8383s·(cpu);·3.78425s·(thread);·0s·(gc)
  
150 ··············2············2·····9·······9···11150 ··············2············2·····9·······9···11
151 o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)151 o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y)
  
152 o30·:·Ideal·of·R152 o30·:·Ideal·of·R
153 i31·:·J1·==·J2153 i31·:·J1·==·J2
  
154 o31·=·true154 o31·=·true
155 i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·);155 i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·);
156 ·--·used·4.7491s·(cpu);·3.75787s·(thread);·0s·(gc)156 ·--·used·5.38506s·(cpu);·4.2357s·(thread);·0s·(gc)
157 i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);157 i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);
158 ·--·used·0.424617s·(cpu);·0.307849s·(thread);·0s·(gc)158 ·--·used·0.442613s·(cpu);·0.3133s·(thread);·0s·(gc)
159 However,·sometimes·ModuleStrategy·is·faster,·especially·for·Monomial·ideals.159 However,·sometimes·ModuleStrategy·is·faster,·especially·for·Monomial·ideals.
160 i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v);160 i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v);
161 i35·:·I·=·ideal(x,u);161 i35·:·I·=·ideal(x,u);
  
162 o35·:·Ideal·of·R162 o35·:·Ideal·of·R
163 i36·:·J·=·I^20;163 i36·:·J·=·I^20;
  
164 o36·:·Ideal·of·R164 o36·:·Ideal·of·R
165 i37·:·M·=·I^20*R^1;165 i37·:·M·=·I^20*R^1;
166 i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·)166 i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·)
167 ·--·used·0.809782s·(cpu);·0.30444s·(thread);·0s·(gc)167 ·--·used·0.807535s·(cpu);·0.301082s·(thread);·0s·(gc)
  
168 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12168 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12
169 o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,169 o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,
170 ······-----------------------------------------------------------------------170 ······-----------------------------------------------------------------------
171 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2171 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2
172 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,172 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,
173 ······-----------------------------------------------------------------------173 ······-----------------------------------------------------------------------
174 ·······19····20174 ·······19····20
175 ······x··u,·x··)175 ······x··u,·x··)
  
176 o38·:·Ideal·of·R176 o38·:·Ideal·of·R
177 i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·)177 i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·)
178 ·--·used·0.174601s·(cpu);·0.0531627s·(thread);·0s·(gc)178 ·--·used·0.157457s·(cpu);·0.0366832s·(thread);·0s·(gc)
  
179 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12179 ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12
180 o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,180 o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,
181 ······-----------------------------------------------------------------------181 ······-----------------------------------------------------------------------
182 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2182 ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2
183 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,183 ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,
184 ······-----------------------------------------------------------------------184 ······-----------------------------------------------------------------------
185 ·······19····20185 ·······19····20
186 ······x··u,·x··)186 ······x··u,·x··)
  
187 o39·:·Ideal·of·R187 o39·:·Ideal·of·R
188 i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·);188 i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·);
189 ·--·used·0.0324022s·(cpu);·0.033304s·(thread);·0s·(gc)189 ·--·used·0.0380324s·(cpu);·0.037759s·(thread);·0s·(gc)
190 i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);190 i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·);
191 ·--·used·0.00272989s·(cpu);·0.00538526s·(thread);·0s·(gc)191 ·--·used·0.00485728s·(cpu);·0.00613396s·(thread);·0s·(gc)
192 For·ideals,·if·KnownDomain·is·false·(default·value·is·true),·then·the·function192 For·ideals,·if·KnownDomain·is·false·(default·value·is·true),·then·the·function
193 will·check·whether·it·is·a·domain.·If·it·is·a·domain·(or·assumed·to·be·a193 will·check·whether·it·is·a·domain.·If·it·is·a·domain·(or·assumed·to·be·a
194 domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if194 domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if
195 not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially195 not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially
196 reflexifying·it·as·a·module.196 reflexifying·it·as·a·module.
197 Consider·the·following·example·showing·the·importance·of·making·the·correct197 Consider·the·following·example·showing·the·importance·of·making·the·correct
198 assumption·about·the·ring·being·a·domain.198 assumption·about·the·ring·being·a·domain.
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124 o6·:·Ideal·of·R</code></pre>124 o6·:·Ideal·of·R</code></pre>
125 ············</td>125 ············</td>
126 ··········</tr>126 ··········</tr>
127 ··········<tr>127 ··········<tr>
128 ············<td>128 ············<td>
129 ··············<pre><code·class="language-macaulay2">i7·:·time·J20a·=·reflexivePower(20,·I);129 ··············<pre><code·class="language-macaulay2">i7·:·time·J20a·=·reflexivePower(20,·I);
130 ·--·used·0.0751719s·(cpu);·0.043511s·(thread);·0s·(gc)130 ·--·used·0.0809171s·(cpu);·0.0398099s·(thread);·0s·(gc)
  
131 o7·:·Ideal·of·R</code></pre>131 o7·:·Ideal·of·R</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i8·:·I20·=·I^20;136 ··············<pre><code·class="language-macaulay2">i8·:·I20·=·I^20;
  
137 o8·:·Ideal·of·R</code></pre>137 o8·:·Ideal·of·R</code></pre>
138 ············</td>138 ············</td>
139 ··········</tr>139 ··········</tr>
140 ··········<tr>140 ··········<tr>
141 ············<td>141 ············<td>
142 ··············<pre><code·class="language-macaulay2">i9·:·time·J20b·=·reflexify(I20);142 ··············<pre><code·class="language-macaulay2">i9·:·time·J20b·=·reflexify(I20);
143 ·--·used·0.0946508s·(cpu);·0.0959172s·(thread);·0s·(gc)143 ·--·used·0.139705s·(cpu);·0.136087s·(thread);·0s·(gc)
  
144 o9·:·Ideal·of·R</code></pre>144 o9·:·Ideal·of·R</code></pre>
145 ············</td>145 ············</td>
146 ··········</tr>146 ··········</tr>
147 ··········<tr>147 ··········<tr>
148 ············<td>148 ············<td>
149 ··············<pre><code·class="language-macaulay2">i10·:·J20a·==·J20b149 ··············<pre><code·class="language-macaulay2">i10·:·J20a·==·J20b
Offset 171, 23 lines modifiedOffset 171, 23 lines modified
  
171 o12·:·Ideal·of·R</code></pre>171 o12·:·Ideal·of·R</code></pre>
172 ············</td>172 ············</td>
173 ··········</tr>173 ··········</tr>
174 ··········<tr>174 ··········<tr>
175 ············<td>175 ············<td>
176 ··············<pre><code·class="language-macaulay2">i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy);176 ··············<pre><code·class="language-macaulay2">i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy);
177 ·--·used·0.0777736s·(cpu);·0.0459113s·(thread);·0s·(gc)177 ·--·used·0.105248s·(cpu);·0.0493528s·(thread);·0s·(gc)
  
178 o13·:·Ideal·of·R</code></pre>178 o13·:·Ideal·of·R</code></pre>
179 ············</td>179 ············</td>
180 ··········</tr>180 ··········</tr>
181 ··········<tr>181 ··········<tr>
182 ············<td>182 ············<td>
183 ··············<pre><code·class="language-macaulay2">i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy);183 ··············<pre><code·class="language-macaulay2">i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy);
184 ·--·used·0.0465363s·(cpu);·0.0478035s·(thread);·0s·(gc)184 ·--·used·0.056438s·(cpu);·0.0566698s·(thread);·0s·(gc)
  
185 o14·:·Ideal·of·R</code></pre>185 o14·:·Ideal·of·R</code></pre>
186 ············</td>186 ············</td>
187 ··········</tr>187 ··········</tr>
188 ··········<tr>188 ··········<tr>
189 ············<td>189 ············<td>
190 ··············<pre><code·class="language-macaulay2">i15·:·J1·==·J2190 ··············<pre><code·class="language-macaulay2">i15·:·J1·==·J2
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Offset 40, 39 lines modifiedOffset 40, 39 lines modified
40 of·the·generators·of·$I$.·Consider·the·example·of·a·cone·over·a·point·on·an40 of·the·generators·of·$I$.·Consider·the·example·of·a·cone·over·a·point·on·an
41 elliptic·curve.41 elliptic·curve.
42 i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);42 i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);
43 i6·:·I·=·ideal(x-z,y-2*z);43 i6·:·I·=·ideal(x-z,y-2*z);
  
44 o6·:·Ideal·of·R44 o6·:·Ideal·of·R
45 i7·:·time·J20a·=·reflexivePower(20,·I);45 i7·:·time·J20a·=·reflexivePower(20,·I);
46 ·--·used·0.0751719s·(cpu);·0.043511s·(thread);·0s·(gc)46 ·--·used·0.0809171s·(cpu);·0.0398099s·(thread);·0s·(gc)
  
47 o7·:·Ideal·of·R47 o7·:·Ideal·of·R
48 i8·:·I20·=·I^20;48 i8·:·I20·=·I^20;
  
49 o8·:·Ideal·of·R49 o8·:·Ideal·of·R
50 i9·:·time·J20b·=·reflexify(I20);50 i9·:·time·J20b·=·reflexify(I20);
51 ·--·used·0.0946508s·(cpu);·0.0959172s·(thread);·0s·(gc)51 ·--·used·0.139705s·(cpu);·0.136087s·(thread);·0s·(gc)
  
52 o9·:·Ideal·of·R52 o9·:·Ideal·of·R
53 i10·:·J20a·==·J20b53 i10·:·J20a·==·J20b
  
54 o10·=·true54 o10·=·true
55 This·passes·the·Strategy·option·to·a·reflexify·call.·Valid·options·are55 This·passes·the·Strategy·option·to·a·reflexify·call.·Valid·options·are
56 IdealStrategy·and·ModuleStrategy.56 IdealStrategy·and·ModuleStrategy.
57 i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);57 i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3);
58 i12·:·I·=·ideal(x-z,y-2*z);58 i12·:·I·=·ideal(x-z,y-2*z);
  
59 o12·:·Ideal·of·R59 o12·:·Ideal·of·R
60 i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy);60 i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy);
61 ·--·used·0.0777736s·(cpu);·0.0459113s·(thread);·0s·(gc)61 ·--·used·0.105248s·(cpu);·0.0493528s·(thread);·0s·(gc)
  
62 o13·:·Ideal·of·R62 o13·:·Ideal·of·R
63 i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy);63 i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy);
64 ·--·used·0.0465363s·(cpu);·0.0478035s·(thread);·0s·(gc)64 ·--·used·0.056438s·(cpu);·0.0566698s·(thread);·0s·(gc)
  
65 o14·:·Ideal·of·R65 o14·:·Ideal·of·R
66 i15·:·J1·==·J266 i15·:·J1·==·J2
  
67 o15·=·true67 o15·=·true
68 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*68 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
69 ····*·_\x8r_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8f_\x8y·--·calculate·the·double·dual·of·an·ideal·or·module·Hom(Hom(M,69 ····*·_\x8r_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8f_\x8y·--·calculate·the·double·dual·of·an·ideal·or·module·Hom(Hom(M,
712 B
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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619 B
./usr/share/doc/Macaulay2/EdgeIdeals/example-output/_complement__Graph.out
    
Offset 2, 15 lines modifiedOffset 2, 15 lines modified
  
2 i1·:·R·=·QQ[a,b,c,d,e];2 i1·:·R·=·QQ[a,b,c,d,e];
  
3 i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle3 i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle
  
4 i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle4 i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle
  
5 o3·=·Graph{"edges"·=>·{{a,·c},·{b,·e},·{b,·d},·{c,·e},·{a,·d}}}5 o3·=·Graph{"edges"·=>·{{a,·d},·{a,·c},·{b,·e},·{b,·d},·{c,·e}}}
6 ···········"ring"·=>·R6 ···········"ring"·=>·R
7 ···········"vertices"·=>·{a,·b,·c,·d,·e}7 ···········"vertices"·=>·{a,·b,·c,·d,·e}
  
8 o3·:·Graph8 o3·:·Graph
  
9 i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph9 i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph
  
481 B
./usr/share/doc/Macaulay2/EdgeIdeals/example-output/_delete__Edges.out
    
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14 o3·=·{{a,·b},·{d,·e}}14 o3·=·{{a,·b},·{d,·e}}
  
15 o3·:·List15 o3·:·List
  
16 i4·:·gprime·=·deleteEdges·(g,T)16 i4·:·gprime·=·deleteEdges·(g,T)
  
17 o4·=·HyperGraph{"edges"·=>·{{c,·d},·{b,·c},·{a,·e}}}17 o4·=·HyperGraph{"edges"·=>·{{b,·c},·{a,·e},·{c,·d}}}
18 ················"ring"·=>·S18 ················"ring"·=>·S
19 ················"vertices"·=>·{a,·b,·c,·d,·e}19 ················"vertices"·=>·{a,·b,·c,·d,·e}
  
20 o4·:·HyperGraph20 o4·:·HyperGraph
  
21 i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e}21 i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e}
  
900 B
./usr/share/doc/Macaulay2/EdgeIdeals/example-output/_random__Hyper__Graph.out
    
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2 i1·:·R·=·QQ[x_1..x_5];2 i1·:·R·=·QQ[x_1..x_5];
  
3 i2·:·randomHyperGraph(R,{3,2,4})3 i2·:·randomHyperGraph(R,{3,2,4})
  
4 i3·:·randomHyperGraph(R,{3,2,4})4 i3·:·randomHyperGraph(R,{3,2,4})
  
5 i4·:·randomHyperGraph(R,{3,2,4}) 
  
6 o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}}5 o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}}
7 ······························1···3···4·····2···4·····1···2···3···56 ······························2···3···5·····2···4·····1···3···4···5
8 ················"ring"·=>·R7 ················"ring"·=>·R
9 ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·}8 ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·}
10 ································1···2···3···4···59 ································1···2···3···4···5
  
11 o4·:·HyperGraph10 o3·:·HyperGraph
  
 11 i4·:·randomHyperGraph(R,{3,2,4})
  
12 i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached12 i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached
  
13 i6·:·13 i6·:·
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./usr/share/doc/Macaulay2/EdgeIdeals/html/_complement__Graph.html
    
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84 ··············<pre><code·class="language-macaulay2">i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle</code></pre>84 ··············<pre><code·class="language-macaulay2">i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle89 ··············<pre><code·class="language-macaulay2">i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle
  
90 o3·=·Graph{&quot;edges&quot;·=>·{{a,·c},·{b,·e},·{b,·d},·{c,·e},·{a,·d}}}90 o3·=·Graph{&quot;edges&quot;·=>·{{a,·d},·{a,·c},·{b,·e},·{b,·d},·{c,·e}}}
91 ···········&quot;ring&quot;·=>·R91 ···········&quot;ring&quot;·=>·R
92 ···········&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}92 ···········&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}
  
93 o3·:·Graph</code></pre>93 o3·:·Graph</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
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22 When·applied·to·a·graph,·complementGraph·returns·the·graph·whose·edge·set·is22 When·applied·to·a·graph,·complementGraph·returns·the·graph·whose·edge·set·is
23 the·set·of·edges·not·in·G.·When·applied·to·a·hypergraph,·the·edge·set·is·found23 the·set·of·edges·not·in·G.·When·applied·to·a·hypergraph,·the·edge·set·is·found
24 by·taking·the·complement·of·each·edge·of·H·in·the·vertex·set.24 by·taking·the·complement·of·each·edge·of·H·in·the·vertex·set.
25 i1·:·R·=·QQ[a,b,c,d,e];25 i1·:·R·=·QQ[a,b,c,d,e];
26 i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle26 i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle
27 i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle27 i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle
  
28 o3·=·Graph{"edges"·=>·{{a,·c},·{b,·e},·{b,·d},·{c,·e},·{a,·d}}}28 o3·=·Graph{"edges"·=>·{{a,·d},·{a,·c},·{b,·e},·{b,·d},·{c,·e}}}
29 ···········"ring"·=>·R29 ···········"ring"·=>·R
30 ···········"vertices"·=>·{a,·b,·c,·d,·e}30 ···········"vertices"·=>·{a,·b,·c,·d,·e}
  
31 o3·:·Graph31 o3·:·Graph
32 i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph32 i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph
  
33 o4·=·HyperGraph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}}33 o4·=·HyperGraph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}}
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97 o3·:·List</code></pre>97 o3·:·List</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i4·:·gprime·=·deleteEdges·(g,T)102 ··············<pre><code·class="language-macaulay2">i4·:·gprime·=·deleteEdges·(g,T)
  
103 o4·=·HyperGraph{&quot;edges&quot;·=>·{{c,·d},·{b,·c},·{a,·e}}}103 o4·=·HyperGraph{&quot;edges&quot;·=>·{{b,·c},·{a,·e},·{c,·d}}}
104 ················&quot;ring&quot;·=>·S104 ················&quot;ring&quot;·=>·S
105 ················&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}105 ················&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}
  
106 o4·:·HyperGraph</code></pre>106 o4·:·HyperGraph</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ··········<tr>109 ··········<tr>
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26 i3·:·T·=·{{a,b},{d,e}}26 i3·:·T·=·{{a,b},{d,e}}
  
27 o3·=·{{a,·b},·{d,·e}}27 o3·=·{{a,·b},·{d,·e}}
  
28 o3·:·List28 o3·:·List
29 i4·:·gprime·=·deleteEdges·(g,T)29 i4·:·gprime·=·deleteEdges·(g,T)
  
30 o4·=·HyperGraph{"edges"·=>·{{c,·d},·{b,·c},·{a,·e}}}30 o4·=·HyperGraph{"edges"·=>·{{b,·c},·{a,·e},·{c,·d}}}
31 ················"ring"·=>·S31 ················"ring"·=>·S
32 ················"vertices"·=>·{a,·b,·c,·d,·e}32 ················"vertices"·=>·{a,·b,·c,·d,·e}
  
33 o4·:·HyperGraph33 o4·:·HyperGraph
34 i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e}34 i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e}
  
35 o5·=·HyperGraph{"edges"·=>·{{a,·b,·c},·{a,·e},·{c,·d,·e}}}35 o5·=·HyperGraph{"edges"·=>·{{a,·b,·c},·{a,·e},·{c,·d,·e}}}
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85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i2·:·randomHyperGraph(R,{3,2,4})</code></pre>87 ··············<pre><code·class="language-macaulay2">i2·:·randomHyperGraph(R,{3,2,4})</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i3·:·randomHyperGraph(R,{3,2,4})</code></pre> 
93 ············</td> 
94 ··········</tr> 
95 ··········<tr> 
96 ············<td> 
97 ··············<pre><code·class="language-macaulay2">i4·:·randomHyperGraph(R,{3,2,4})92 ··············<pre><code·class="language-macaulay2">i3·:·randomHyperGraph(R,{3,2,4})
  
98 o4·=·HyperGraph{&quot;edges&quot;·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}}93 o3·=·HyperGraph{&quot;edges&quot;·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}}
99 ······························1···3···4·····2···4·····1···2···3···594 ······························2···3···5·····2···4·····1···3···4···5
100 ················&quot;ring&quot;·=>·R95 ················&quot;ring&quot;·=>·R
101 ················&quot;vertices&quot;·=>·{x·,·x·,·x·,·x·,·x·}96 ················&quot;vertices&quot;·=>·{x·,·x·,·x·,·x·,·x·}
102 ································1···2···3···4···597 ································1···2···3···4···5
  
103 o4·:·HyperGraph</code></pre>98 o3·:·HyperGraph</code></pre>
 99 ············</td>
 100 ··········</tr>
 101 ··········<tr>
 102 ············<td>
 103 ··············<pre><code·class="language-macaulay2">i4·:·randomHyperGraph(R,{3,2,4})</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached</code></pre>108 ··············<pre><code·class="language-macaulay2">i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
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23 sizes·using·a·random·recursive·algorithm.·Limits·can·be·placed·on·the·both23 sizes·using·a·random·recursive·algorithm.·Limits·can·be·placed·on·the·both
24 number·of·recursive·steps·taken·(see·_\x8B_\x8r_\x8a_\x8n_\x8c_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t)·and·on·the·time·taken·(see24 number·of·recursive·steps·taken·(see·_\x8B_\x8r_\x8a_\x8n_\x8c_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t)·and·on·the·time·taken·(see
25 _\x8T_\x8i_\x8m_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t).·The·method·will·return·null·if·it·cannot·find·a·hypergraph·within25 _\x8T_\x8i_\x8m_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t).·The·method·will·return·null·if·it·cannot·find·a·hypergraph·within
26 the·branch·and·time·limits.26 the·branch·and·time·limits.
27 i1·:·R·=·QQ[x_1..x_5];27 i1·:·R·=·QQ[x_1..x_5];
28 i2·:·randomHyperGraph(R,{3,2,4})28 i2·:·randomHyperGraph(R,{3,2,4})
29 i3·:·randomHyperGraph(R,{3,2,4})29 i3·:·randomHyperGraph(R,{3,2,4})
30 i4·:·randomHyperGraph(R,{3,2,4}) 
  
31 o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}}30 o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}}
32 ······························1···3···4·····2···4·····1···2···3···531 ······························2···3···5·····2···4·····1···3···4···5
33 ················"ring"·=>·R32 ················"ring"·=>·R
34 ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·}33 ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·}
35 ································1···2···3···4···534 ································1···2···3···4···5
  
36 o4·:·HyperGraph35 o3·:·HyperGraph
 36 i4·:·randomHyperGraph(R,{3,2,4})
37 i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch37 i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch
38 limit·reached38 limit·reached
39 The·randomHyperGraph·method·will·return·null·immediately·if·the·sizes·of·the39 The·randomHyperGraph·method·will·return·null·immediately·if·the·sizes·of·the
40 edges·fail·to·pass·the·LYM-inequality:·$1/(n·choose·D_1)·+·1/(n·choose·D_2)·+40 edges·fail·to·pass·the·LYM-inequality:·$1/(n·choose·D_1)·+·1/(n·choose·D_2)·+
41 ...·+·1/(n·choose·D_m)·\leq·1$·where·$n$·is·the·number·of·variables·in·R·and41 ...·+·1/(n·choose·D_m)·\leq·1$·where·$n$·is·the·number·of·variables·in·R·and
42 $m$·is·the·length·of·D.·Note·that·even·if·D·passes·this·inequality,·it·is·not42 $m$·is·the·length·of·D.·Note·that·even·if·D·passes·this·inequality,·it·is·not
43 necessarily·true·that·there·is·some·hypergraph·with·edge·sizes·given·by·D.·See43 necessarily·true·that·there·is·some·hypergraph·with·edge·sizes·given·by·D.·See
735 B
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15 ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+15 ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+
16 ·····------------------------------------------------------------------------16 ·····------------------------------------------------------------------------
17 ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1)17 ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1)
  
18 o2·:·Ideal·of·QQ[a..f]18 o2·:·Ideal·of·QQ[a..f]
  
19 i3·:·elapsedTime·sols·=·zeroDimSolve·I;19 i3·:·elapsedTime·sols·=·zeroDimSolve·I;
20 ·--·.354831s·elapsed20 ·--·.641689s·elapsed
  
21 i4·:·#sols·--·156·solutions21 i4·:·#sols·--·156·solutions
  
22 o4·=·15622 o4·=·156
  
23 i5·:·23 i5·:·
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./usr/share/doc/Macaulay2/EigenSolver/html/index.html
    
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80 o2·:·Ideal·of·QQ[a..f]</code></pre>80 o2·:·Ideal·of·QQ[a..f]</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·sols·=·zeroDimSolve·I;85 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·sols·=·zeroDimSolve·I;
86 ·--·.354831s·elapsed</code></pre>86 ·--·.641689s·elapsed</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i4·:·#sols·--·156·solutions91 ··············<pre><code·class="language-macaulay2">i4·:·#sols·--·156·solutions
  
92 o4·=·156</code></pre>92 o4·=·156</code></pre>
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29 ·····------------------------------------------------------------------------29 ·····------------------------------------------------------------------------
30 ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+30 ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+
31 ·····------------------------------------------------------------------------31 ·····------------------------------------------------------------------------
32 ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1)32 ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1)
  
33 o2·:·Ideal·of·QQ[a..f]33 o2·:·Ideal·of·QQ[a..f]
34 i3·:·elapsedTime·sols·=·zeroDimSolve·I;34 i3·:·elapsedTime·sols·=·zeroDimSolve·I;
35 ·--·.354831s·elapsed35 ·--·.641689s·elapsed
36 i4·:·#sols·--·156·solutions36 i4·:·#sols·--·156·solutions
  
37 o4·=·15637 o4·=·156
38 The·authors·would·like·to·acknowledge·the·June·2020·Macaulay2·workshop·held38 The·authors·would·like·to·acknowledge·the·June·2020·Macaulay2·workshop·held
39 virtually·at·Warwick,·where·this·package·was·first·developed.39 virtually·at·Warwick,·where·this·package·was·first·developed.
40 R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s:40 R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s:
41 ····*·[1]·Sturmfels,·Bernd.·Solving·systems·of·polynomial·equations.·No.·97.41 ····*·[1]·Sturmfels,·Bernd.·Solving·systems·of·polynomial·equations.·No.·97.
735 B
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17 ······217 ······2
18 o3·=·x··+·x*c·+·d18 o3·=·x··+·x*c·+·d
  
19 o3·:·R19 o3·:·R
  
20 i4·:·time·eliminate(x,ideal(f,g))20 i4·:·time·eliminate(x,ideal(f,g))
21 ·--·used·0.0620562s·(cpu);·0.0170493s·(thread);·0s·(gc)21 ·--·used·0.0815769s·(cpu);·0.0104577s·(thread);·0s·(gc)
  
22 ······················2····2·············2···········222 ······················2····2·············2···········2
23 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)23 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)
  
24 o4·:·Ideal·of·R24 o4·:·Ideal·of·R
  
25 i5·:·time·ideal·resultant(f,g,x)25 i5·:·time·ideal·resultant(f,g,x)
26 ·--·used·0.00148091s·(cpu);·0.00127812s·(thread);·0s·(gc)26 ·--·used·0.000423224s·(cpu);·0.00140019s·(thread);·0s·(gc)
  
27 ························2····2·············2···········227 ························2····2·············2···········2
28 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)28 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)
  
29 o5·:·Ideal·of·R29 o5·:·Ideal·of·R
  
30 i6·:·sylvesterMatrix(f,g,x)30 i6·:·sylvesterMatrix(f,g,x)
808 B
./usr/share/doc/Macaulay2/Elimination/example-output/_eliminate.out
    
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17 ······217 ······2
18 o3·=·x··+·x*c·+·d18 o3·=·x··+·x*c·+·d
  
19 o3·:·R19 o3·:·R
  
20 i4·:·time·eliminate(x,ideal(f,g))20 i4·:·time·eliminate(x,ideal(f,g))
21 ·--·used·0.00400724s·(cpu);·0.00238137s·(thread);·0s·(gc)21 ·--·used·0.000867206s·(cpu);·0.00257062s·(thread);·0s·(gc)
  
22 ······················2····2·············2···········222 ······················2····2·············2···········2
23 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)23 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)
  
24 o4·:·Ideal·of·R24 o4·:·Ideal·of·R
  
25 i5·:·time·ideal·resultant(f,g,x)25 i5·:·time·ideal·resultant(f,g,x)
26 ·--·used·0.000312831s·(cpu);·0.00137956s·(thread);·0s·(gc)26 ·--·used·0.000340359s·(cpu);·0.0015172s·(thread);·0s·(gc)
  
27 ························2····2·············2···········227 ························2····2·············2···········2
28 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)28 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)
  
29 o5·:·Ideal·of·R29 o5·:·Ideal·of·R
  
30 i6·:·sylvesterMatrix(f,g,x)30 i6·:·sylvesterMatrix(f,g,x)
1.7 KB
./usr/share/doc/Macaulay2/Elimination/example-output/_resultant_lp__Ring__Element_cm__Ring__Element_cm__Ring__Element_rp.out
    
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17 ······8····517 ······8····5
18 o3·=·x··+·x··+·x*c·+·d18 o3·=·x··+·x··+·x*c·+·d
  
19 o3·:·R19 o3·:·R
  
20 i4·:·time·eliminate(ideal(f,g),x)20 i4·:·time·eliminate(ideal(f,g),x)
21 ·--·used·1.22719s·(cpu);·1.09708s·(thread);·0s·(gc)21 ·--·used·1.40431s·(cpu);·1.24004s·(thread);·0s·(gc)
  
22 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··22 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
23 o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-23 o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-
24 ·····------------------------------------------------------------------------24 ·····------------------------------------------------------------------------
25 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··25 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
26 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+26 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+
27 ·····------------------------------------------------------------------------27 ·····------------------------------------------------------------------------
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73 ·····------------------------------------------------------------------------73 ·····------------------------------------------------------------------------
74 ···············3··········4········474 ···············3··········4········4
75 ·····-·216b*c*d··+·2052a*d··-·1944d·)75 ·····-·216b*c*d··+·2052a*d··-·1944d·)
  
76 o4·:·Ideal·of·R76 o4·:·Ideal·of·R
  
77 i5·:·time·ideal·resultant(f,g,x)77 i5·:·time·ideal·resultant(f,g,x)
78 ·--·used·0.012497s·(cpu);·0.0131271s·(thread);·0s·(gc)78 ·--·used·0.0160627s·(cpu);·0.0134545s·(thread);·0s·(gc)
  
79 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··79 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
80 o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+80 o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+
81 ·····------------------------------------------------------------------------81 ·····------------------------------------------------------------------------
82 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··82 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
83 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-83 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-
84 ·····------------------------------------------------------------------------84 ·····------------------------------------------------------------------------
1.72 KB
./usr/share/doc/Macaulay2/Elimination/example-output/_sylvester__Matrix_lp__Ring__Element_cm__Ring__Element_cm__Ring__Element_rp.out
    
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19 ······8····519 ······8····5
20 o4·=·x··+·x··+·x*c·+·d20 o4·=·x··+·x··+·x*c·+·d
  
21 o4·:·R21 o4·:·R
  
22 i5·:·time·eliminate(ideal(f,g),x)22 i5·:·time·eliminate(ideal(f,g),x)
23 ·--·used·1.25502s·(cpu);·1.11684s·(thread);·0s·(gc)23 ·--·used·1.42181s·(cpu);·1.26031s·(thread);·0s·(gc)
  
24 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··24 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
25 o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-25 o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-
26 ·····------------------------------------------------------------------------26 ·····------------------------------------------------------------------------
27 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··27 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
28 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+28 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+
29 ·····------------------------------------------------------------------------29 ·····------------------------------------------------------------------------
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75 ·····------------------------------------------------------------------------75 ·····------------------------------------------------------------------------
76 ···············3··········4········476 ···············3··········4········4
77 ·····-·216b*c*d··+·2052a*d··-·1944d·)77 ·····-·216b*c*d··+·2052a*d··-·1944d·)
  
78 o5·:·Ideal·of·R78 o5·:·Ideal·of·R
  
79 i6·:·time·ideal·resultant(f,g,x)79 i6·:·time·ideal·resultant(f,g,x)
80 ·--·used·0.0160836s·(cpu);·0.013396s·(thread);·0s·(gc)80 ·--·used·0.011975s·(cpu);·0.0134221s·(thread);·0s·(gc)
  
81 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··81 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
82 o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+82 o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+
83 ·····------------------------------------------------------------------------83 ·····------------------------------------------------------------------------
84 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··84 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
85 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-85 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-
86 ·····------------------------------------------------------------------------86 ·····------------------------------------------------------------------------
1.79 KB
./usr/share/doc/Macaulay2/Elimination/html/_discriminant_lp__Ring__Element_cm__Ring__Element_rp.html
    
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103 o3·:·R</code></pre>103 o3·:·R</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g))108 ··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g))
109 ·--·used·0.0620562s·(cpu);·0.0170493s·(thread);·0s·(gc)109 ·--·used·0.0815769s·(cpu);·0.0104577s·(thread);·0s·(gc)
  
110 ······················2····2·············2···········2110 ······················2····2·············2···········2
111 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)111 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)
  
112 o4·:·Ideal·of·R</code></pre>112 o4·:·Ideal·of·R</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x)117 ··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x)
118 ·--·used·0.00148091s·(cpu);·0.00127812s·(thread);·0s·(gc)118 ·--·used·0.000423224s·(cpu);·0.00140019s·(thread);·0s·(gc)
  
119 ························2····2·············2···········2119 ························2····2·············2···········2
120 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)120 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)
  
121 o5·:·Ideal·of·R</code></pre>121 o5·:·Ideal·of·R</code></pre>
122 ············</td>122 ············</td>
123 ··········</tr>123 ··········</tr>
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29 i3·:·g·=·x^2+c*x+d29 i3·:·g·=·x^2+c*x+d
  
30 ······230 ······2
31 o3·=·x··+·x*c·+·d31 o3·=·x··+·x*c·+·d
  
32 o3·:·R32 o3·:·R
33 i4·:·time·eliminate(x,ideal(f,g))33 i4·:·time·eliminate(x,ideal(f,g))
34 ·--·used·0.0620562s·(cpu);·0.0170493s·(thread);·0s·(gc)34 ·--·used·0.0815769s·(cpu);·0.0104577s·(thread);·0s·(gc)
  
35 ······················2····2·············2···········235 ······················2····2·············2···········2
36 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)36 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)
  
37 o4·:·Ideal·of·R37 o4·:·Ideal·of·R
38 i5·:·time·ideal·resultant(f,g,x)38 i5·:·time·ideal·resultant(f,g,x)
39 ·--·used·0.00148091s·(cpu);·0.00127812s·(thread);·0s·(gc)39 ·--·used·0.000423224s·(cpu);·0.00140019s·(thread);·0s·(gc)
  
40 ························2····2·············2···········240 ························2····2·············2···········2
41 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)41 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)
  
42 o5·:·Ideal·of·R42 o5·:·Ideal·of·R
43 i6·:·sylvesterMatrix(f,g,x)43 i6·:·sylvesterMatrix(f,g,x)
  
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97 o3·:·R</code></pre>97 o3·:·R</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g))102 ··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g))
103 ·--·used·0.00400724s·(cpu);·0.00238137s·(thread);·0s·(gc)103 ·--·used·0.000867206s·(cpu);·0.00257062s·(thread);·0s·(gc)
  
104 ······················2····2·············2···········2104 ······················2····2·············2···········2
105 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)105 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)
  
106 o4·:·Ideal·of·R</code></pre>106 o4·:·Ideal·of·R</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ··········<tr>109 ··········<tr>
110 ············<td>110 ············<td>
111 ··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x)111 ··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x)
112 ·--·used·0.000312831s·(cpu);·0.00137956s·(thread);·0s·(gc)112 ·--·used·0.000340359s·(cpu);·0.0015172s·(thread);·0s·(gc)
  
113 ························2····2·············2···········2113 ························2····2·············2···········2
114 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)114 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)
  
115 o5·:·Ideal·of·R</code></pre>115 o5·:·Ideal·of·R</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
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30 i3·:·g·=·x^2+c*x+d30 i3·:·g·=·x^2+c*x+d
  
31 ······231 ······2
32 o3·=·x··+·x*c·+·d32 o3·=·x··+·x*c·+·d
  
33 o3·:·R33 o3·:·R
34 i4·:·time·eliminate(x,ideal(f,g))34 i4·:·time·eliminate(x,ideal(f,g))
35 ·--·used·0.00400724s·(cpu);·0.00238137s·(thread);·0s·(gc)35 ·--·used·0.000867206s·(cpu);·0.00257062s·(thread);·0s·(gc)
  
36 ······················2····2·············2···········236 ······················2····2·············2···········2
37 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)37 o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·)
  
38 o4·:·Ideal·of·R38 o4·:·Ideal·of·R
39 i5·:·time·ideal·resultant(f,g,x)39 i5·:·time·ideal·resultant(f,g,x)
40 ·--·used·0.000312831s·(cpu);·0.00137956s·(thread);·0s·(gc)40 ·--·used·0.000340359s·(cpu);·0.0015172s·(thread);·0s·(gc)
  
41 ························2····2·············2···········241 ························2····2·············2···········2
42 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)42 o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·)
  
43 o5·:·Ideal·of·R43 o5·:·Ideal·of·R
44 i6·:·sylvesterMatrix(f,g,x)44 i6·:·sylvesterMatrix(f,g,x)
  
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105 o3·:·R</code></pre>105 o3·:·R</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ··········<tr>108 ··········<tr>
109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(ideal(f,g),x)110 ··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(ideal(f,g),x)
111 ·--·used·1.22719s·(cpu);·1.09708s·(thread);·0s·(gc)111 ·--·used·1.40431s·(cpu);·1.24004s·(thread);·0s·(gc)
  
112 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··112 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
113 o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-113 o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-
114 ·····------------------------------------------------------------------------114 ·····------------------------------------------------------------------------
115 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··115 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
116 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+116 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+
117 ·····------------------------------------------------------------------------117 ·····------------------------------------------------------------------------
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164 o4·:·Ideal·of·R</code></pre>164 o4·:·Ideal·of·R</code></pre>
165 ············</td>165 ············</td>
166 ··········</tr>166 ··········</tr>
167 ··········<tr>167 ··········<tr>
168 ············<td>168 ············<td>
169 ··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x)169 ··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x)
170 ·--·used·0.012497s·(cpu);·0.0131271s·(thread);·0s·(gc)170 ·--·used·0.0160627s·(cpu);·0.0134545s·(thread);·0s·(gc)
  
171 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··171 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
172 o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+172 o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+
173 ·····------------------------------------------------------------------------173 ·····------------------------------------------------------------------------
174 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··174 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
175 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-175 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-
176 ·····------------------------------------------------------------------------176 ·····------------------------------------------------------------------------
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35 i3·:·g·=·x^8+x^5+c*x+d35 i3·:·g·=·x^8+x^5+c*x+d
  
36 ······8····536 ······8····5
37 o3·=·x··+·x··+·x*c·+·d37 o3·=·x··+·x··+·x*c·+·d
  
38 o3·:·R38 o3·:·R
39 i4·:·time·eliminate(ideal(f,g),x)39 i4·:·time·eliminate(ideal(f,g),x)
40 ·--·used·1.22719s·(cpu);·1.09708s·(thread);·0s·(gc)40 ·--·used·1.40431s·(cpu);·1.24004s·(thread);·0s·(gc)
  
41 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·241 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2
42 o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-42 o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-
43 ·····------------------------------------------------------------------------43 ·····------------------------------------------------------------------------
44 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······744 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7
45 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+45 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+
46 ·····------------------------------------------------------------------------46 ·····------------------------------------------------------------------------
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90 ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d90 ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d
91 ·····------------------------------------------------------------------------91 ·····------------------------------------------------------------------------
92 ···············3··········4········492 ···············3··········4········4
93 ·····-·216b*c*d··+·2052a*d··-·1944d·)93 ·····-·216b*c*d··+·2052a*d··-·1944d·)
  
94 o4·:·Ideal·of·R94 o4·:·Ideal·of·R
95 i5·:·time·ideal·resultant(f,g,x)95 i5·:·time·ideal·resultant(f,g,x)
96 ·--·used·0.012497s·(cpu);·0.0131271s·(thread);·0s·(gc)96 ·--·used·0.0160627s·(cpu);·0.0134545s·(thread);·0s·(gc)
  
97 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·297 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2
98 o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+98 o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+
99 ·····------------------------------------------------------------------------99 ·····------------------------------------------------------------------------
100 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7100 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7
101 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-101 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-
102 ·····------------------------------------------------------------------------102 ·····------------------------------------------------------------------------
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104 o4·:·R</code></pre>104 o4·:·R</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i5·:·time·eliminate(ideal(f,g),x)109 ··············<pre><code·class="language-macaulay2">i5·:·time·eliminate(ideal(f,g),x)
110 ·--·used·1.25502s·(cpu);·1.11684s·(thread);·0s·(gc)110 ·--·used·1.42181s·(cpu);·1.26031s·(thread);·0s·(gc)
  
111 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··111 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
112 o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-112 o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-
113 ·····------------------------------------------------------------------------113 ·····------------------------------------------------------------------------
114 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··114 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
115 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+115 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+
116 ·····------------------------------------------------------------------------116 ·····------------------------------------------------------------------------
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163 o5·:·Ideal·of·R</code></pre>163 o5·:·Ideal·of·R</code></pre>
164 ············</td>164 ············</td>
165 ··········</tr>165 ··········</tr>
166 ··········<tr>166 ··········<tr>
167 ············<td>167 ············<td>
168 ··············<pre><code·class="language-macaulay2">i6·:·time·ideal·resultant(f,g,x)168 ··············<pre><code·class="language-macaulay2">i6·:·time·ideal·resultant(f,g,x)
169 ·--·used·0.0160836s·(cpu);·0.013396s·(thread);·0s·(gc)169 ·--·used·0.011975s·(cpu);·0.0134221s·(thread);·0s·(gc)
  
170 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··170 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2··
171 o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+171 o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+
172 ·····------------------------------------------------------------------------172 ·····------------------------------------------------------------------------
173 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··173 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7··
174 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-174 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-
175 ·····------------------------------------------------------------------------175 ·····------------------------------------------------------------------------
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30 i4·:·g·=·x^8+x^5+c*x+d30 i4·:·g·=·x^8+x^5+c*x+d
  
31 ······8····531 ······8····5
32 o4·=·x··+·x··+·x*c·+·d32 o4·=·x··+·x··+·x*c·+·d
  
33 o4·:·R33 o4·:·R
34 i5·:·time·eliminate(ideal(f,g),x)34 i5·:·time·eliminate(ideal(f,g),x)
35 ·--·used·1.25502s·(cpu);·1.11684s·(thread);·0s·(gc)35 ·--·used·1.42181s·(cpu);·1.26031s·(thread);·0s·(gc)
  
36 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·236 ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2
37 o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-37 o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··-
38 ·····------------------------------------------------------------------------38 ·····------------------------------------------------------------------------
39 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······739 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7
40 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+40 ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+
41 ·····------------------------------------------------------------------------41 ·····------------------------------------------------------------------------
Offset 85, 15 lines modifiedOffset 85, 15 lines modified
85 ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d85 ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d
86 ·····------------------------------------------------------------------------86 ·····------------------------------------------------------------------------
87 ···············3··········4········487 ···············3··········4········4
88 ·····-·216b*c*d··+·2052a*d··-·1944d·)88 ·····-·216b*c*d··+·2052a*d··-·1944d·)
  
89 o5·:·Ideal·of·R89 o5·:·Ideal·of·R
90 i6·:·time·ideal·resultant(f,g,x)90 i6·:·time·ideal·resultant(f,g,x)
91 ·--·used·0.0160836s·(cpu);·0.013396s·(thread);·0s·(gc)91 ·--·used·0.011975s·(cpu);·0.0134221s·(thread);·0s·(gc)
  
92 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·292 ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2
93 o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+93 o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+
94 ·····------------------------------------------------------------------------94 ·····------------------------------------------------------------------------
95 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······795 ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7
96 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-96 ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··-
97 ·····------------------------------------------------------------------------97 ·····------------------------------------------------------------------------
743 B
./usr/share/doc/Macaulay2/EliminationMatrices/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/EllipticIntegrals/dump/rawdocumentation.dump
    
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723 B
./usr/share/doc/Macaulay2/EngineTests/dump/rawdocumentation.dump
    
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743 B
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613 B
./usr/share/doc/Macaulay2/EnumerationCurves/example-output/_lines__Hypersurface.out
    
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1 --·-*-·M2-comint·-*-·hash:·13319756731771 --·-*-·M2-comint·-*-·hash:·1331975673177
  
2 i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n)2 i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n)
3 ·--·used·0.0225086s·(cpu);·0.0216525s·(thread);·0s·(gc)3 ·--·used·0.0291784s·(cpu);·0.0306535s·(thread);·0s·(gc)
  
4 o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,4 o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,
5 ·····------------------------------------------------------------------------5 ·····------------------------------------------------------------------------
6 ·····289139638632755625,·520764738758073845321}6 ·····289139638632755625,·520764738758073845321}
  
7 o1·:·List7 o1·:·List
  
2.4 KB
./usr/share/doc/Macaulay2/EnumerationCurves/example-output/_rational__Curve.out
    
Offset 37, 83 lines modifiedOffset 37, 83 lines modified
37 i6·:·rationalCurve(2)·-·rationalCurve(1)/837 i6·:·rationalCurve(2)·-·rationalCurve(1)/8
  
38 o6·=·60925038 o6·=·609250
  
39 o6·:·QQ39 o6·:·QQ
  
40 i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/840 i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8
41 ·--·used·0.245423s·(cpu);·0.216954s·(thread);·0s·(gc)41 ·--·used·0.284851s·(cpu);·0.248685s·(thread);·0s·(gc)
  
42 o7·=·{609250,·92288,·52812,·22428,·9728}42 o7·=·{609250,·92288,·52812,·22428,·9728}
  
43 o7·:·List43 o7·:·List
  
44 i8·:·time·rationalCurve(3)44 i8·:·time·rationalCurve(3)
45 ·--·used·0.101911s·(cpu);·0.105469s·(thread);·0s·(gc)45 ·--·used·0.115102s·(cpu);·0.114909s·(thread);·0s·(gc)
  
46 ·····856457500046 ·····8564575000
47 o8·=·----------47 o8·=·----------
48 ·········2748 ·········27
  
49 o8·:·QQ49 o8·:·QQ
  
50 i9·:·time·for·D·in·T·list·rationalCurve(3,D)50 i9·:·time·for·D·in·T·list·rationalCurve(3,D)
51 ·--·used·3.89344s·(cpu);·3.52595s·(thread);·0s·(gc)51 ·--·used·4.3803s·(cpu);·3.86187s·(thread);·0s·(gc)
  
52 ······8564575000··422690816···········4834592··1123942452 ······8564575000··422690816···········4834592··11239424
53 o9·=·{----------,·---------,·6424365,·-------,·--------}53 o9·=·{----------,·---------,·6424365,·-------,·--------}
54 ··········27··········27·················3········2754 ··········27··········27·················3········27
  
55 o9·:·List55 o9·:·List
  
56 i10·:·time·rationalCurve(3)·-·rationalCurve(1)/2756 i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27
57 ·--·used·0.107434s·(cpu);·0.111058s·(thread);·0s·(gc)57 ·--·used·0.115614s·(cpu);·0.117188s·(thread);·0s·(gc)
  
58 o10·=·31720637558 o10·=·317206375
  
59 o10·:·QQ59 o10·:·QQ
  
60 i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/2760 i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27
61 ·--·used·3.97082s·(cpu);·3.59872s·(thread);·0s·(gc)61 ·--·used·4.66565s·(cpu);·4.11823s·(thread);·0s·(gc)
  
62 o11·=·{317206375,·15655168,·6424326,·1611504,·416256}62 o11·=·{317206375,·15655168,·6424326,·1611504,·416256}
  
63 o11·:·List63 o11·:·List
  
64 i12·:·time·rationalCurve(4)64 i12·:·time·rationalCurve(4)
65 ·--·used·1.18382s·(cpu);·1.08465s·(thread);·0s·(gc)65 ·--·used·1.37816s·(cpu);·1.22752s·(thread);·0s·(gc)
  
66 ······1551792679687566 ······15517926796875
67 o12·=·--------------67 o12·=·--------------
68 ············6468 ············64
  
69 o12·:·QQ69 o12·:·QQ
  
70 i13·:·time·rationalCurve(4,{4,2})70 i13·:·time·rationalCurve(4,{4,2})
71 ·--·used·5.12713s·(cpu);·4.36832s·(thread);·0s·(gc)71 ·--·used·6.34843s·(cpu);·5.32982s·(thread);·0s·(gc)
  
72 o13·=·388391408472 o13·=·3883914084
  
73 o13·:·QQ73 o13·:·QQ
  
74 i14·:·time·rationalCurve(4)·-·rationalCurve(2)/874 i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8
75 ·--·used·1.26235s·(cpu);·1.12524s·(thread);·0s·(gc)75 ·--·used·1.41324s·(cpu);·1.23418s·(thread);·0s·(gc)
  
76 o14·=·24246753000076 o14·=·242467530000
  
77 o14·:·QQ77 o14·:·QQ
  
78 i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/878 i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8
79 ·--·used·5.2093s·(cpu);·4.41808s·(thread);·0s·(gc)79 ·--·used·6.02203s·(cpu);·4.98188s·(thread);·0s·(gc)
  
80 o15·=·388390252880 o15·=·3883902528
  
81 o15·:·QQ81 o15·:·QQ
  
82 i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/882 i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8
83 ·--·used·5.15891s·(cpu);·4.41947s·(thread);·0s·(gc)83 ·--·used·6.38593s·(cpu);·5.34924s·(thread);·0s·(gc)
  
84 o16·=·113944838484 o16·=·1139448384
  
85 o16·:·QQ85 o16·:·QQ
  
86 i17·:·86 i17·:·
1.65 KB
./usr/share/doc/Macaulay2/EnumerationCurves/html/_lines__Hypersurface.html
    
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71 ··········<p>Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in·\mathbb·P^n.</p>71 ··········<p>Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in·\mathbb·P^n.</p>
72 ··········<p></p>72 ··········<p></p>
73 ········</div>73 ········</div>
74 ········<table·class="examples">74 ········<table·class="examples">
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n)77 ··············<pre><code·class="language-macaulay2">i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n)
78 ·--·used·0.0225086s·(cpu);·0.0216525s·(thread);·0s·(gc)78 ·--·used·0.0291784s·(cpu);·0.0306535s·(thread);·0s·(gc)
  
79 o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,79 o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,
80 ·····------------------------------------------------------------------------80 ·····------------------------------------------------------------------------
81 ·····289139638632755625,·520764738758073845321}81 ·····289139638632755625,·520764738758073845321}
  
82 o1·:·List</code></pre>82 o1·:·List</code></pre>
83 ············</td>83 ············</td>
848 B
html2text {}
    
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11 ····*·Outputs:11 ····*·Outputs:
12 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·number·of·lines·on·a·general·hypersurface·of·degree12 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·number·of·lines·on·a·general·hypersurface·of·degree
13 ············2n·-·3·in·\mathbb·P^n13 ············2n·-·3·in·\mathbb·P^n
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in15 Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in
16 \mathbb·P^n.16 \mathbb·P^n.
17 i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n)17 i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n)
18 ·--·used·0.0225086s·(cpu);·0.0216525s·(thread);·0s·(gc)18 ·--·used·0.0291784s·(cpu);·0.0306535s·(thread);·0s·(gc)
  
19 o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,19 o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,
20 ·····------------------------------------------------------------------------20 ·····------------------------------------------------------------------------
21 ·····289139638632755625,·520764738758073845321}21 ·····289139638632755625,·520764738758073845321}
  
22 o1·:·List22 o1·:·List
23 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·l\x8li\x8in\x8ne\x8es\x8sH\x8Hy\x8yp\x8pe\x8er\x8rs\x8su\x8ur\x8rf\x8fa\x8ac\x8ce\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·l\x8li\x8in\x8ne\x8es\x8sH\x8Hy\x8yp\x8pe\x8er\x8rs\x8su\x8ur\x8rf\x8fa\x8ac\x8ce\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*
8.04 KB
./usr/share/doc/Macaulay2/EnumerationCurves/html/_rational__Curve.html
    
Offset 152, 15 lines modifiedOffset 152, 15 lines modified
152 ··········<p>The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p>152 ··········<p>The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p>
153 ··········<p></p>153 ··········<p></p>
154 ········</div>154 ········</div>
155 ········<table·class="examples">155 ········<table·class="examples">
156 ··········<tr>156 ··········<tr>
157 ············<td>157 ············<td>
158 ··············<pre><code·class="language-macaulay2">i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8158 ··············<pre><code·class="language-macaulay2">i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8
159 ·--·used·0.245423s·(cpu);·0.216954s·(thread);·0s·(gc)159 ·--·used·0.284851s·(cpu);·0.248685s·(thread);·0s·(gc)
  
160 o7·=·{609250,·92288,·52812,·22428,·9728}160 o7·=·{609250,·92288,·52812,·22428,·9728}
  
161 o7·:·List</code></pre>161 o7·:·List</code></pre>
162 ············</td>162 ············</td>
163 ··········</tr>163 ··········</tr>
164 ········</table>164 ········</table>
Offset 168, 27 lines modifiedOffset 168, 27 lines modified
168 ··········<p>For·rational·curves·of·degree·3:</p>168 ··········<p>For·rational·curves·of·degree·3:</p>
169 ··········<p></p>169 ··········<p></p>
170 ········</div>170 ········</div>
171 ········<table·class="examples">171 ········<table·class="examples">
172 ··········<tr>172 ··········<tr>
173 ············<td>173 ············<td>
174 ··············<pre><code·class="language-macaulay2">i8·:·time·rationalCurve(3)174 ··············<pre><code·class="language-macaulay2">i8·:·time·rationalCurve(3)
175 ·--·used·0.101911s·(cpu);·0.105469s·(thread);·0s·(gc)175 ·--·used·0.115102s·(cpu);·0.114909s·(thread);·0s·(gc)
  
176 ·····8564575000176 ·····8564575000
177 o8·=·----------177 o8·=·----------
178 ·········27178 ·········27
  
179 o8·:·QQ</code></pre>179 o8·:·QQ</code></pre>
180 ············</td>180 ············</td>
181 ··········</tr>181 ··········</tr>
182 ··········<tr>182 ··········<tr>
183 ············<td>183 ············<td>
184 ··············<pre><code·class="language-macaulay2">i9·:·time·for·D·in·T·list·rationalCurve(3,D)184 ··············<pre><code·class="language-macaulay2">i9·:·time·for·D·in·T·list·rationalCurve(3,D)
185 ·--·used·3.89344s·(cpu);·3.52595s·(thread);·0s·(gc)185 ·--·used·4.3803s·(cpu);·3.86187s·(thread);·0s·(gc)
  
186 ······8564575000··422690816···········4834592··11239424186 ······8564575000··422690816···········4834592··11239424
187 o9·=·{----------,·---------,·6424365,·-------,·--------}187 o9·=·{----------,·---------,·6424365,·-------,·--------}
188 ··········27··········27·················3········27188 ··········27··········27·················3········27
  
189 o9·:·List</code></pre>189 o9·:·List</code></pre>
190 ············</td>190 ············</td>
Offset 198, 15 lines modifiedOffset 198, 15 lines modified
198 ··········<p>The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be·computed·as·follows:</p>198 ··········<p>The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be·computed·as·follows:</p>
199 ··········<p></p>199 ··········<p></p>
200 ········</div>200 ········</div>
201 ········<table·class="examples">201 ········<table·class="examples">
202 ··········<tr>202 ··········<tr>
203 ············<td>203 ············<td>
204 ··············<pre><code·class="language-macaulay2">i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27204 ··············<pre><code·class="language-macaulay2">i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27
205 ·--·used·0.107434s·(cpu);·0.111058s·(thread);·0s·(gc)205 ·--·used·0.115614s·(cpu);·0.117188s·(thread);·0s·(gc)
  
206 o10·=·317206375206 o10·=·317206375
  
207 o10·:·QQ</code></pre>207 o10·:·QQ</code></pre>
208 ············</td>208 ············</td>
209 ··········</tr>209 ··········</tr>
210 ········</table>210 ········</table>
Offset 214, 15 lines modifiedOffset 214, 15 lines modified
214 ··········<p>The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p>214 ··········<p>The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p>
215 ··········<p></p>215 ··········<p></p>
216 ········</div>216 ········</div>
217 ········<table·class="examples">217 ········<table·class="examples">
218 ··········<tr>218 ··········<tr>
219 ············<td>219 ············<td>
220 ··············<pre><code·class="language-macaulay2">i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27220 ··············<pre><code·class="language-macaulay2">i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27
221 ·--·used·3.97082s·(cpu);·3.59872s·(thread);·0s·(gc)221 ·--·used·4.66565s·(cpu);·4.11823s·(thread);·0s·(gc)
  
222 o11·=·{317206375,·15655168,·6424326,·1611504,·416256}222 o11·=·{317206375,·15655168,·6424326,·1611504,·416256}
  
223 o11·:·List</code></pre>223 o11·:·List</code></pre>
224 ············</td>224 ············</td>
225 ··········</tr>225 ··········</tr>
226 ········</table>226 ········</table>
Offset 230, 27 lines modifiedOffset 230, 27 lines modified
230 ··········<p>For·rational·curves·of·degree·4:</p>230 ··········<p>For·rational·curves·of·degree·4:</p>
231 ··········<p></p>231 ··········<p></p>
232 ········</div>232 ········</div>
233 ········<table·class="examples">233 ········<table·class="examples">
234 ··········<tr>234 ··········<tr>
235 ············<td>235 ············<td>
236 ··············<pre><code·class="language-macaulay2">i12·:·time·rationalCurve(4)236 ··············<pre><code·class="language-macaulay2">i12·:·time·rationalCurve(4)
237 ·--·used·1.18382s·(cpu);·1.08465s·(thread);·0s·(gc)237 ·--·used·1.37816s·(cpu);·1.22752s·(thread);·0s·(gc)
  
238 ······15517926796875238 ······15517926796875
239 o12·=·--------------239 o12·=·--------------
240 ············64240 ············64
  
241 o12·:·QQ</code></pre>241 o12·:·QQ</code></pre>
242 ············</td>242 ············</td>
243 ··········</tr>243 ··········</tr>
244 ··········<tr>244 ··········<tr>
245 ············<td>245 ············<td>
246 ··············<pre><code·class="language-macaulay2">i13·:·time·rationalCurve(4,{4,2})246 ··············<pre><code·class="language-macaulay2">i13·:·time·rationalCurve(4,{4,2})
247 ·--·used·5.12713s·(cpu);·4.36832s·(thread);·0s·(gc)247 ·--·used·6.34843s·(cpu);·5.32982s·(thread);·0s·(gc)
  
248 o13·=·3883914084248 o13·=·3883914084
  
249 o13·:·QQ</code></pre>249 o13·:·QQ</code></pre>
250 ············</td>250 ············</td>
251 ··········</tr>251 ··········</tr>
252 ········</table>252 ········</table>
Offset 258, 15 lines modifiedOffset 258, 15 lines modified
258 ··········<p>The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be·computed·as·follows:</p>258 ··········<p>The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be·computed·as·follows:</p>
259 ··········<p></p>259 ··········<p></p>
260 ········</div>260 ········</div>
261 ········<table·class="examples">261 ········<table·class="examples">
262 ··········<tr>262 ··········<tr>
263 ············<td>263 ············<td>
264 ··············<pre><code·class="language-macaulay2">i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8264 ··············<pre><code·class="language-macaulay2">i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8
265 ·--·used·1.26235s·(cpu);·1.12524s·(thread);·0s·(gc)265 ·--·used·1.41324s·(cpu);·1.23418s·(thread);·0s·(gc)
  
266 o14·=·242467530000266 o14·=·242467530000
  
267 o14·:·QQ</code></pre>267 o14·:·QQ</code></pre>
268 ············</td>268 ············</td>
269 ··········</tr>269 ··········</tr>
270 ········</table>270 ········</table>
Offset 274, 25 lines modifiedOffset 274, 25 lines modified
274 ··········<p>The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of·types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows:</p>274 ··········<p>The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of·types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows:</p>
275 ··········<p></p>275 ··········<p></p>
276 ········</div>276 ········</div>
277 ········<table·class="examples">277 ········<table·class="examples">
278 ··········<tr>278 ··········<tr>
279 ············<td>279 ············<td>
280 ··············<pre><code·class="language-macaulay2">i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8280 ··············<pre><code·class="language-macaulay2">i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8
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Offset 59, 85 lines modifiedOffset 59, 85 lines modified
  
59 o6·=·60925059 o6·=·609250
  
60 o6·:·QQ60 o6·:·QQ
61 The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds61 The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds
62 can·be·computed·as·follows:62 can·be·computed·as·follows:
63 i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/863 i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8
64 ·--·used·0.245423s·(cpu);·0.216954s·(thread);·0s·(gc)64 ·--·used·0.284851s·(cpu);·0.248685s·(thread);·0s·(gc)
  
65 o7·=·{609250,·92288,·52812,·22428,·9728}65 o7·=·{609250,·92288,·52812,·22428,·9728}
  
66 o7·:·List66 o7·:·List
67 For·rational·curves·of·degree·3:67 For·rational·curves·of·degree·3:
68 i8·:·time·rationalCurve(3)68 i8·:·time·rationalCurve(3)
69 ·--·used·0.101911s·(cpu);·0.105469s·(thread);·0s·(gc)69 ·--·used·0.115102s·(cpu);·0.114909s·(thread);·0s·(gc)
  
70 ·····856457500070 ·····8564575000
71 o8·=·----------71 o8·=·----------
72 ·········2772 ·········27
  
73 o8·:·QQ73 o8·:·QQ
74 i9·:·time·for·D·in·T·list·rationalCurve(3,D)74 i9·:·time·for·D·in·T·list·rationalCurve(3,D)
75 ·--·used·3.89344s·(cpu);·3.52595s·(thread);·0s·(gc)75 ·--·used·4.3803s·(cpu);·3.86187s·(thread);·0s·(gc)
  
76 ······8564575000··422690816···········4834592··1123942476 ······8564575000··422690816···········4834592··11239424
77 o9·=·{----------,·---------,·6424365,·-------,·--------}77 o9·=·{----------,·---------,·6424365,·-------,·--------}
78 ··········27··········27·················3········2778 ··········27··········27·················3········27
  
79 o9·:·List79 o9·:·List
80 The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be80 The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be
81 computed·as·follows:81 computed·as·follows:
82 i10·:·time·rationalCurve(3)·-·rationalCurve(1)/2782 i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27
83 ·--·used·0.107434s·(cpu);·0.111058s·(thread);·0s·(gc)83 ·--·used·0.115614s·(cpu);·0.117188s·(thread);·0s·(gc)
  
84 o10·=·31720637584 o10·=·317206375
  
85 o10·:·QQ85 o10·:·QQ
86 The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection86 The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection
87 Calabi-Yau·threefolds·can·be·computed·as·follows:87 Calabi-Yau·threefolds·can·be·computed·as·follows:
88 i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/2788 i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27
89 ·--·used·3.97082s·(cpu);·3.59872s·(thread);·0s·(gc)89 ·--·used·4.66565s·(cpu);·4.11823s·(thread);·0s·(gc)
  
90 o11·=·{317206375,·15655168,·6424326,·1611504,·416256}90 o11·=·{317206375,·15655168,·6424326,·1611504,·416256}
  
91 o11·:·List91 o11·:·List
92 For·rational·curves·of·degree·4:92 For·rational·curves·of·degree·4:
93 i12·:·time·rationalCurve(4)93 i12·:·time·rationalCurve(4)
94 ·--·used·1.18382s·(cpu);·1.08465s·(thread);·0s·(gc)94 ·--·used·1.37816s·(cpu);·1.22752s·(thread);·0s·(gc)
  
95 ······1551792679687595 ······15517926796875
96 o12·=·--------------96 o12·=·--------------
97 ············6497 ············64
  
98 o12·:·QQ98 o12·:·QQ
99 i13·:·time·rationalCurve(4,{4,2})99 i13·:·time·rationalCurve(4,{4,2})
100 ·--·used·5.12713s·(cpu);·4.36832s·(thread);·0s·(gc)100 ·--·used·6.34843s·(cpu);·5.32982s·(thread);·0s·(gc)
  
101 o13·=·3883914084101 o13·=·3883914084
  
102 o13·:·QQ102 o13·:·QQ
103 The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be103 The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be
104 computed·as·follows:104 computed·as·follows:
105 i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8105 i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8
106 ·--·used·1.26235s·(cpu);·1.12524s·(thread);·0s·(gc)106 ·--·used·1.41324s·(cpu);·1.23418s·(thread);·0s·(gc)
  
107 o14·=·242467530000107 o14·=·242467530000
  
108 o14·:·QQ108 o14·:·QQ
109 The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of109 The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of
110 types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows:110 types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows:
111 i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8111 i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8
112 ·--·used·5.2093s·(cpu);·4.41808s·(thread);·0s·(gc)112 ·--·used·6.02203s·(cpu);·4.98188s·(thread);·0s·(gc)
  
113 o15·=·3883902528113 o15·=·3883902528
  
114 o15·:·QQ114 o15·:·QQ
115 i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8115 i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8
116 ·--·used·5.15891s·(cpu);·4.41947s·(thread);·0s·(gc)116 ·--·used·6.38593s·(cpu);·5.34924s·(thread);·0s·(gc)
  
117 o16·=·1139448384117 o16·=·1139448384
  
118 o16·:·QQ118 o16·:·QQ
119 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lC\x8Cu\x8ur\x8rv\x8ve\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*119 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lC\x8Cu\x8ur\x8rv\x8ve\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8*
120 ····*·rationalCurve(ZZ)120 ····*·rationalCurve(ZZ)
121 ····*·rationalCurve(ZZ,List)121 ····*·rationalCurve(ZZ,List)
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./usr/share/doc/Macaulay2/EquivariantGB/dump/rawdocumentation.dump
    
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4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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7 #:len=337 #:len=33
8 YnVpbGRFTW9ub21pYWxNYXAoUmluZyxSaW5nLExpc3Qp8 YnVpbGRFTW9ub21pYWxNYXAoUmluZyxSaW5nLExpc3Qp
9 #:len=2999 #:len=299
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIzNiwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIzNiwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYnVpbGRFTW9ub21pYWxNYXAsUmluZyxSaW5nLExp11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYnVpbGRFTW9ub21pYWxNYXAsUmluZyxSaW5nLExp
1.3 KB
./usr/share/doc/Macaulay2/EquivariantGB/example-output/_egb__Toric.out
    
Offset 10, 34 lines modifiedOffset 10, 34 lines modified
10 o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·})10 o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·})
11 ··················1···1·0···1·0···011 ··················1···1·0···1·0···0
  
12 o3·:·RingMap·R·<--·S12 o3·:·RingMap·R·<--·S
  
13 i4·:·G·=·egbToric(m,·OutFile=>stdio)13 i4·:·G·=·egbToric(m,·OutFile=>stdio)
14 314 3
15 ·····--·used·.00388616·seconds15 ·····--·used·.00449773·seconds
16 ·····--·used·0·seconds16 ·····--·used·0·seconds
17 (9,·9)17 (9,·9)
18 new·stuff·found18 new·stuff·found
19 419 4
20 ·····--·used·.00355512·seconds20 ·····--·used·.00322777·seconds
21 ·····--·used·.00516262·seconds21 ·····--·used·.00341904·seconds
22 (16,·26)22 (16,·26)
23 new·stuff·found23 new·stuff·found
24 524 5
25 ·····--·used·.0058094·seconds 
26 ·····--·used·.020001·seconds25 ·····--·used·.00600019·seconds
 26 ·····--·used·.0211907·seconds
27 (25,·60)27 (25,·60)
28 628 6
29 ·····--·used·.0155716·seconds29 ·····--·used·.0170837·seconds
30 ·····--·used·.15761·seconds30 ·····--·used·.16234·seconds
31 (36,·120)31 (36,·120)
32 732 7
 33 ·····--·used·.032711·seconds
33 ·····--·used·.0305949·seconds34 ·····--·used·.701341·seconds
34 ·····--·used·.652555·seconds 
35 (49,·217)35 (49,·217)
  
36 ···································236 ···································2
37 o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+37 o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+
38 ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0··38 ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0··
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
40 ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+40 ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+
2.55 KB
./usr/share/doc/Macaulay2/EquivariantGB/html/_egb__Toric.html
    
Offset 101, 34 lines modifiedOffset 101, 34 lines modified
101 o3·:·RingMap·R·&lt;--·S</code></pre>101 o3·:·RingMap·R·&lt;--·S</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i4·:·G·=·egbToric(m,·OutFile=>stdio)106 ··············<pre><code·class="language-macaulay2">i4·:·G·=·egbToric(m,·OutFile=>stdio)
107 3107 3
108 ·····--·used·.00388616·seconds108 ·····--·used·.00449773·seconds
109 ·····--·used·0·seconds109 ·····--·used·0·seconds
110 (9,·9)110 (9,·9)
111 new·stuff·found111 new·stuff·found
112 4112 4
113 ·····--·used·.00355512·seconds113 ·····--·used·.00322777·seconds
114 ·····--·used·.00516262·seconds114 ·····--·used·.00341904·seconds
115 (16,·26)115 (16,·26)
116 new·stuff·found116 new·stuff·found
117 5117 5
118 ·····--·used·.0058094·seconds 
119 ·····--·used·.020001·seconds118 ·····--·used·.00600019·seconds
 119 ·····--·used·.0211907·seconds
120 (25,·60)120 (25,·60)
121 6121 6
122 ·····--·used·.0155716·seconds122 ·····--·used·.0170837·seconds
123 ·····--·used·.15761·seconds123 ·····--·used·.16234·seconds
124 (36,·120)124 (36,·120)
125 7125 7
 126 ·····--·used·.032711·seconds
126 ·····--·used·.0305949·seconds127 ·····--·used·.701341·seconds
127 ·····--·used·.652555·seconds 
128 (49,·217)128 (49,·217)
  
129 ···································2129 ···································2
130 o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+130 o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+
131 ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0··131 ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0··
132 ·····------------------------------------------------------------------------132 ·····------------------------------------------------------------------------
133 ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+133 ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+
1.22 KB
html2text {}
    
Offset 33, 34 lines modifiedOffset 33, 34 lines modified
33 ··················2···············233 ··················2···············2
34 o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·})34 o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·})
35 ··················1···1·0···1·0···035 ··················1···1·0···1·0···0
  
36 o3·:·RingMap·R·<--·S36 o3·:·RingMap·R·<--·S
37 i4·:·G·=·egbToric(m,·OutFile=>stdio)37 i4·:·G·=·egbToric(m,·OutFile=>stdio)
38 338 3
39 ·····--·used·.00388616·seconds39 ·····--·used·.00449773·seconds
40 ·····--·used·0·seconds40 ·····--·used·0·seconds
41 (9,·9)41 (9,·9)
42 new·stuff·found42 new·stuff·found
43 443 4
44 ·····--·used·.00355512·seconds44 ·····--·used·.00322777·seconds
45 ·····--·used·.00516262·seconds45 ·····--·used·.00341904·seconds
46 (16,·26)46 (16,·26)
47 new·stuff·found47 new·stuff·found
48 548 5
49 ·····--·used·.0058094·seconds 
50 ·····--·used·.020001·seconds49 ·····--·used·.00600019·seconds
 50 ·····--·used·.0211907·seconds
51 (25,·60)51 (25,·60)
52 652 6
53 ·····--·used·.0155716·seconds53 ·····--·used·.0170837·seconds
54 ·····--·used·.15761·seconds54 ·····--·used·.16234·seconds
55 (36,·120)55 (36,·120)
56 756 7
 57 ·····--·used·.032711·seconds
57 ·····--·used·.0305949·seconds58 ·····--·used·.701341·seconds
58 ·····--·used·.652555·seconds 
59 (49,·217)59 (49,·217)
  
60 ···································260 ···································2
61 o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+61 o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+
62 ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,062 ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0
63 ·····------------------------------------------------------------------------63 ·····------------------------------------------------------------------------
64 ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+64 ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+
721 B
./usr/share/doc/Macaulay2/ExampleSystems/dump/rawdocumentation.dump
    
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753 B
./usr/share/doc/Macaulay2/ExteriorIdeals/dump/rawdocumentation.dump
    
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751 B
./usr/share/doc/Macaulay2/ExteriorModules/dump/rawdocumentation.dump
    
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717 B
./usr/share/doc/Macaulay2/FGLM/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=167 #:len=16
8 ZmdsbShJZGVhbCxSaW5nKQ==8 ZmdsbShJZGVhbCxSaW5nKQ==
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11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmZ2xtLElkZWFsLFJpbmcpLCJmZ2xtKElkZWFsLFJp11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmZ2xtLElkZWFsLFJpbmcpLCJmZ2xtKElkZWFsLFJp
741 B
./usr/share/doc/Macaulay2/FastMinors/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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5.36 KB
./usr/share/doc/Macaulay2/FastMinors/example-output/___Fast__Minors__Strategy__Tutorial.out
    
Offset 462, 50 lines modifiedOffset 462, 50 lines modified
462 ···············3·2·4·····3·6462 ···············3·2·4·····3·6
463 o27·=·ideal(12x·x·x··-·4x·x·)463 o27·=·ideal(12x·x·x··-·4x·x·)
464 ···············3·7·9·····3·9464 ···············3·7·9·····3·9
  
465 o27·:·Ideal·of·S465 o27·:·Ideal·of·S
  
466 i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random))466 i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random))
467 ·--·used·0.0993859s·(cpu);·0.0991248s·(thread);·0s·(gc)467 ·--·used·0.0959555s·(cpu);·0.0980818s·(thread);·0s·(gc)
  
468 o28·=·2468 o28·=·2
  
469 i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest))469 i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest))
470 ·--·used·0.292043s·(cpu);·0.20273s·(thread);·0s·(gc)470 ·--·used·0.325274s·(cpu);·0.207555s·(thread);·0s·(gc)
  
471 o29·=·3471 o29·=·3
  
472 i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm))472 i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm))
473 ·--·used·0.334715s·(cpu);·0.273734s·(thread);·0s·(gc)473 ·--·used·0.368378s·(cpu);·0.265984s·(thread);·0s·(gc)
  
474 o30·=·1474 o30·=·1
  
475 i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest))475 i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest))
476 ·--·used·0.24478s·(cpu);·0.185298s·(thread);·0s·(gc)476 ·--·used·0.264907s·(cpu);·0.184087s·(thread);·0s·(gc)
  
477 o31·=·2477 o31·=·2
  
478 i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest))478 i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest))
479 ·--·used·0.227128s·(cpu);·0.166293s·(thread);·0s·(gc)479 ·--·used·0.243843s·(cpu);·0.161003s·(thread);·0s·(gc)
  
480 o32·=·3480 o32·=·3
  
481 i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm))481 i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm))
482 ·--·used·0.263228s·(cpu);·0.194093s·(thread);·0s·(gc)482 ·--·used·0.25891s·(cpu);·0.188926s·(thread);·0s·(gc)
  
483 o33·=·3483 o33·=·3
  
484 i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest))484 i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest))
485 ·--·used·0.285217s·(cpu);·0.170356s·(thread);·0s·(gc)485 ·--·used·0.269115s·(cpu);·0.156876s·(thread);·0s·(gc)
  
486 o34·=·3486 o34·=·3
  
487 i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points))487 i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points))
488 ·--·used·10.5035s·(cpu);·7.37759s·(thread);·0s·(gc)488 ·--·used·11.9234s·(cpu);·7.63965s·(thread);·0s·(gc)
  
489 o35·=·1489 o35·=·1
  
490 i36·:·peek·StrategyDefault490 i36·:·peek·StrategyDefault
  
491 o36·=·OptionTable{GRevLexLargest·=>·0······}491 o36·=·OptionTable{GRevLexLargest·=>·0······}
492 ··················GRevLexSmallest·=>·16492 ··················GRevLexSmallest·=>·16
Offset 514, 15 lines modifiedOffset 514, 15 lines modified
514 ··················LexSmallest·=>·16514 ··················LexSmallest·=>·16
515 ··················LexSmallestTerm·=>·16515 ··················LexSmallestTerm·=>·16
516 ··················Points·=>·0516 ··················Points·=>·0
517 ··················Random·=>·16517 ··················Random·=>·16
518 ··················RandomNonzero·=>·16518 ··················RandomNonzero·=>·16
  
519 i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true);519 i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true);
520 ·--·used·0.419124s·(cpu);·0.320611s·(thread);·0s·(gc)520 ·--·used·0.556191s·(cpu);·0.369175s·(thread);·0s·(gc)
521 internalChooseMinor:·Choosing·Random521 internalChooseMinor:·Choosing·Random
522 internalChooseMinor:·Choosing·LexSmallest522 internalChooseMinor:·Choosing·LexSmallest
523 internalChooseMinor:·Choosing·Random523 internalChooseMinor:·Choosing·Random
524 internalChooseMinor:·Choosing·GRevLexSmallestTerm524 internalChooseMinor:·Choosing·GRevLexSmallestTerm
525 internalChooseMinor:·Choosing·RandomNonZero525 internalChooseMinor:·Choosing·RandomNonZero
526 internalChooseMinor:·Choosing·RandomNonZero526 internalChooseMinor:·Choosing·RandomNonZero
527 internalChooseMinor:·Choosing·LexSmallest527 internalChooseMinor:·Choosing·LexSmallest
Offset 582, 15 lines modifiedOffset 582, 15 lines modified
582 i41·:·ptsStratGeometric·=·new·OptionTable·from·(options·chooseGoodMinors)#PointOptions;582 i41·:·ptsStratGeometric·=·new·OptionTable·from·(options·chooseGoodMinors)#PointOptions;
  
583 i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value583 i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value
  
584 o42·=·true584 o42·=·true
  
585 i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric))585 i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric))
586 ·--·used·0.755017s·(cpu);·0.504897s·(thread);·0s·(gc)586 ·--·used·0.884813s·(cpu);·0.540329s·(thread);·0s·(gc)
  
587 o43·=·2587 o43·=·2
  
588 i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value588 i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value
  
589 o44·=·OptionTable{DecompositionStrategy·=>·Decompose}589 o44·=·OptionTable{DecompositionStrategy·=>·Decompose}
590 ··················DimensionFunction·=>·dim590 ··················DimensionFunction·=>·dim
Offset 605, 47 lines modifiedOffset 605, 47 lines modified
605 o44·:·OptionTable605 o44·:·OptionTable
  
606 i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value606 i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value
  
607 o45·=·false607 o45·=·false
  
608 i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational))608 i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational))
609 ·--·used·0.548111s·(cpu);·0.36733s·(thread);·0s·(gc)609 ·--·used·0.723851s·(cpu);·0.431427s·(thread);·0s·(gc)
  
610 o46·=·2610 o46·=·2
  
611 i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault)611 i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault)
612 ·--·used·3.92809s·(cpu);·3.13674s·(thread);·0s·(gc)612 ·--·used·4.42176s·(cpu);·3.35364s·(thread);·0s·(gc)
  
613 i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom)613 i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom)
614 ·--·used·0.908274s·(cpu);·0.663673s·(thread);·0s·(gc)614 ·--·used·1.02911s·(cpu);·0.706055s·(thread);·0s·(gc)
  
615 o48·=·true615 o48·=·true
  
616 i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random)616 i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random)
617 ·--·used·2.76875s·(cpu);·2.43256s·(thread);·0s·(gc)617 ·--·used·3.02898s·(cpu);·2.58176s·(thread);·0s·(gc)
  
618 i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest)618 i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest)
619 ·--·used·2.87747s·(cpu);·1.98809s·(thread);·0s·(gc)619 ·--·used·3.36402s·(cpu);·2.12401s·(thread);·0s·(gc)
  
620 i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallestTerm)620 i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallestTerm)
621 ·--·used·0.948699s·(cpu);·0.754966s·(thread);·0s·(gc)621 ·--·used·1.04338s·(cpu);·0.763271s·(thread);·0s·(gc)
  
622 o51·=·true622 o51·=·true
  
623 i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallest)623 i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallest)
624 ·--·used·3.18381s·(cpu);·2.20838s·(thread);·0s·(gc)624 ·--·used·3.61076s·(cpu);·2.34984s·(thread);·0s·(gc)
  
625 i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallestTerm)625 i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallestTerm)
626 ·--·used·3.69334s·(cpu);·2.69377s·(thread);·0s·(gc)626 ·--·used·4.04602s·(cpu);·2.83432s·(thread);·0s·(gc)
  
627 i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points)627 i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points)
628 ·--·used·11.3645s·(cpu);·7.68981s·(thread);·0s·(gc)628 ·--·used·13.9724s·(cpu);·8.86549s·(thread);·0s·(gc)
  
629 o54·=·true629 o54·=·true
  
630 i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultWithPoints)630 i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultWithPoints)
631 ·--·used·8.96232s·(cpu);·6.13858s·(thread);·0s·(gc)631 ·--·used·10.9127s·(cpu);·6.8424s·(thread);·0s·(gc)
  
Max diff block lines reached; 10/5304 bytes (0.19%) of diff not shown.
6.45 KB
./usr/share/doc/Macaulay2/FastMinors/example-output/___Regular__In__Codimension__Tutorial.out
    
Offset 7, 20 lines modifiedOffset 7, 20 lines modified
7 o2·:·Ideal·of·S7 o2·:·Ideal·of·S
  
8 i3·:·dim·(S/J)8 i3·:·dim·(S/J)
  
9 o3·=·49 o3·=·4
  
10 i4·:·time·regularInCodimension(1,·S/J)10 i4·:·time·regularInCodimension(1,·S/J)
11 ·--·used·0.759299s·(cpu);·0.560341s·(thread);·0s·(gc)11 ·--·used·0.913681s·(cpu);·0.60059s·(thread);·0s·(gc)
  
12 o4·=·true12 o4·=·true
  
13 i5·:·time·regularInCodimension(2,·S/J)13 i5·:·time·regularInCodimension(2,·S/J)
14 ·--·used·8.71094s·(cpu);·6.81449s·(thread);·0s·(gc)14 ·--·used·10.0084s·(cpu);·7.41796s·(thread);·0s·(gc)
  
15 i6·:·time·regularInCodimension(1,·S/J,·Verbose=>true)15 i6·:·time·regularInCodimension(1,·S/J,·Verbose=>true)
16 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·452.908·of·them.16 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·452.908·of·them.
17 regularInCodimension:·About·to·enter·loop17 regularInCodimension:·About·to·enter·loop
18 internalChooseMinor:·Choosing·LexSmallestTerm18 internalChooseMinor:·Choosing·LexSmallestTerm
19 internalChooseMinor:·Choosing·Random19 internalChooseMinor:·Choosing·Random
20 internalChooseMinor:·Choosing·GRevLexSmallest20 internalChooseMinor:·Choosing·GRevLexSmallest
Offset 87, 21 lines modifiedOffset 87, 21 lines modified
87 internalChooseMinor:·Choosing·LexSmallest87 internalChooseMinor:·Choosing·LexSmallest
88 internalChooseMinor:·Choosing·LexSmallestTerm88 internalChooseMinor:·Choosing·LexSmallestTerm
89 internalChooseMinor:·Choosing·LexSmallest89 internalChooseMinor:·Choosing·LexSmallest
90 internalChooseMinor:·Choosing·Random90 internalChooseMinor:·Choosing·Random
91 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·3991 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39
92 regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast92 regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast
93 regularInCodimension:··partial·singular·locus·dimension·computed,·=·293 regularInCodimension:··partial·singular·locus·dimension·computed,·=·2
94 regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.12782s·(cpu);·0.872279s·(thread);·0s·(gc)94 regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.36723s·(cpu);·0.972727s·(thread);·0s·(gc)
95 d·=·39.··singular·locus·dimension·appears·to·be·=·295 d·=·39.··singular·locus·dimension·appears·to·be·=·2
  
96 o6·=·true96 o6·=·true
  
97 i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true)97 i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true)
98 ·--·used·0.139209s·(cpu);·0.111392s·(thread);·0s·(gc)98 ·--·used·0.163394s·(cpu);·0.118384s·(thread);·0s·(gc)
99 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.99 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.
100 regularInCodimension:·About·to·enter·loop100 regularInCodimension:·About·to·enter·loop
101 internalChooseMinor:·Choosing·Random101 internalChooseMinor:·Choosing·Random
102 internalChooseMinor:·Choosing·RandomNonZero102 internalChooseMinor:·Choosing·RandomNonZero
103 internalChooseMinor:·Choosing·GRevLexSmallestTerm103 internalChooseMinor:·Choosing·GRevLexSmallestTerm
104 internalChooseMinor:·Choosing·Random104 internalChooseMinor:·Choosing·Random
105 internalChooseMinor:·Choosing·Random105 internalChooseMinor:·Choosing·Random
Offset 115, 15 lines modifiedOffset 115, 15 lines modified
115 internalChooseMinor:·Choosing·LexSmallest115 internalChooseMinor:·Choosing·LexSmallest
116 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10116 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10
117 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.117 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
118 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3118 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3
119 regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3119 regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3
  
120 i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true)120 i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true)
121 ·--·used·0.120353s·(cpu);·0.0894023s·(thread);·0s·(gc)121 ·--·used·0.160235s·(cpu);·0.119668s·(thread);·0s·(gc)
122 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.122 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.
123 regularInCodimension:·About·to·enter·loop123 regularInCodimension:·About·to·enter·loop
124 internalChooseMinor:·Choosing·Random124 internalChooseMinor:·Choosing·Random
125 internalChooseMinor:·Choosing·Random125 internalChooseMinor:·Choosing·Random
126 internalChooseMinor:·Choosing·Random126 internalChooseMinor:·Choosing·Random
127 internalChooseMinor:·Choosing·Random127 internalChooseMinor:·Choosing·Random
128 internalChooseMinor:·Choosing·Random128 internalChooseMinor:·Choosing·Random
Offset 137, 15 lines modifiedOffset 137, 15 lines modified
137 internalChooseMinor:·Choosing·Random137 internalChooseMinor:·Choosing·Random
138 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10138 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10
139 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.139 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
140 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3140 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3
141 regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3141 regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3
  
142 i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true)142 i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true)
143 ·--·used·0.494139s·(cpu);·0.394153s·(thread);·0s·(gc)143 ·--·used·0.642239s·(cpu);·0.517448s·(thread);·0s·(gc)
144 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.144 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.
145 regularInCodimension:·About·to·enter·loop145 regularInCodimension:·About·to·enter·loop
146 internalChooseMinor:·Choosing·RandomNonZero146 internalChooseMinor:·Choosing·RandomNonZero
147 internalChooseMinor:·Choosing·Random147 internalChooseMinor:·Choosing·Random
148 internalChooseMinor:·Choosing·LexSmallest148 internalChooseMinor:·Choosing·LexSmallest
149 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3149 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3
150 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.150 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
Offset 165, 15 lines modifiedOffset 165, 15 lines modified
165 internalChooseMinor:·Choosing·GRevLexSmallestTerm165 internalChooseMinor:·Choosing·GRevLexSmallestTerm
166 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10166 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10
167 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.167 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
168 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3168 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3
169 regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3169 regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3
  
170 i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true)170 i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true)
171 ·--·used·0.582528s·(cpu);·0.44772s·(thread);·0s·(gc)171 ·--·used·0.639978s·(cpu);·0.473535s·(thread);·0s·(gc)
172 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.172 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.
173 regularInCodimension:·About·to·enter·loop173 regularInCodimension:·About·to·enter·loop
174 internalChooseMinor:·Choosing·GRevLexSmallestTerm174 internalChooseMinor:·Choosing·GRevLexSmallestTerm
175 internalChooseMinor:·Choosing·GRevLexSmallestTerm175 internalChooseMinor:·Choosing·GRevLexSmallestTerm
176 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2176 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2
177 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.177 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
178 regularInCodimension:··partial·singular·locus·dimension·computed,·=·4178 regularInCodimension:··partial·singular·locus·dimension·computed,·=·4
Offset 214, 15 lines modifiedOffset 214, 15 lines modified
214 internalChooseMinor:·Choosing·GRevLexSmallestTerm214 internalChooseMinor:·Choosing·GRevLexSmallestTerm
215 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·25,·and·computed·=·23215 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·25,·and·computed·=·23
216 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.216 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
217 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3217 regularInCodimension:··partial·singular·locus·dimension·computed,·=·3
218 regularInCodimension:··Loop·completed,·submatrices·considered·=·25,·and·computed·=·23.··singular·locus·dimension·appears·to·be·=·3218 regularInCodimension:··Loop·completed,·submatrices·considered·=·25,·and·computed·=·23.··singular·locus·dimension·appears·to·be·=·3
  
219 i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true)219 i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true)
220 ·--·used·0.374613s·(cpu);·0.274104s·(thread);·0s·(gc)220 ·--·used·0.422149s·(cpu);·0.292662s·(thread);·0s·(gc)
221 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.221 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.
222 regularInCodimension:·About·to·enter·loop222 regularInCodimension:·About·to·enter·loop
223 internalChooseMinor:·Choosing·GRevLexSmallest223 internalChooseMinor:·Choosing·GRevLexSmallest
224 internalChooseMinor:·Choosing·LexSmallest224 internalChooseMinor:·Choosing·LexSmallest
225 internalChooseMinor:·Choosing·RandomNonZero225 internalChooseMinor:·Choosing·RandomNonZero
226 internalChooseMinor:·Choosing·RandomNonZero226 internalChooseMinor:·Choosing·RandomNonZero
227 internalChooseMinor:·Choosing·GRevLexSmallestTerm227 internalChooseMinor:·Choosing·GRevLexSmallestTerm
1.21 KB
./usr/share/doc/Macaulay2/FastMinors/example-output/___Strategy__Default.out
    
Offset 1, 13 lines modifiedOffset 1, 13 lines modified
1 --·-*-·M2-comint·-*-·hash:·55092798754059419991 --·-*-·M2-comint·-*-·hash:·5509279875405941999
  
2 i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);2 i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);
  
3 i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault)3 i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault)
4 ·--·2.06011s·elapsed4 ·--·6.31115s·elapsed
  
5 o2·=·true5 o2·=·true
  
6 i3·:·peek·StrategyDefault6 i3·:·peek·StrategyDefault
  
7 o3·=·OptionTable{GRevLexLargest·=>·0······}7 o3·=·OptionTable{GRevLexLargest·=>·0······}
8 ·················GRevLexSmallest·=>·168 ·················GRevLexSmallest·=>·16
Offset 16, 12 lines modifiedOffset 16, 12 lines modified
16 ·················LexSmallest·=>·1616 ·················LexSmallest·=>·16
17 ·················LexSmallestTerm·=>·1617 ·················LexSmallestTerm·=>·16
18 ·················Points·=>·018 ·················Points·=>·0
19 ·················Random·=>·1619 ·················Random·=>·16
20 ·················RandomNonzero·=>·1620 ·················RandomNonzero·=>·16
  
21 i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm)21 i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm)
22 ·--·.955001s·elapsed22 ·--·3.44089s·elapsed
  
23 o4·=·true23 o4·=·true
  
24 i5·:·24 i5·:·
1.88 KB
./usr/share/doc/Macaulay2/FastMinors/example-output/_is__Codim__At__Least.out
    
Offset 16, 29 lines modifiedOffset 16, 29 lines modified
16 i5·:·r·=·rank·myDiff;16 i5·:·r·=·rank·myDiff;
  
17 i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom);17 i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom);
  
18 o6·:·Ideal·of·R18 o6·:·Ideal·of·R
  
19 i7·:·time·isCodimAtLeast(3,·J)19 i7·:·time·isCodimAtLeast(3,·J)
20 ·--·used·0.00101147s·(cpu);·0.00220379s·(thread);·0s·(gc)20 ·--·used·0.00400048s·(cpu);·0.00234453s·(thread);·0s·(gc)
  
21 o7·=·true21 o7·=·true
  
22 i8·:·I·=·ideal(x_2^8*x_10^3-3*x_1*x_2^7*x_10^2*x_11+3*x_1^2*x_2^6*x_10*x_11^2-x_1^3*x_2^5*x_11^3,x_5^5*x_6^3*x_11^3-3*x_5^6*x_6^2*x_11^2*x_12+3*x_5^7*x_6*x_11*x_12^2-x_5^8*x_12^3,x_1^5*x_2^3*x_4^3-3*x_1^6*x_2^2*x_4^2*x_5+3*x_1^7*x_2*x_4*x_5^2-x_1^8*x_5^3,x_6^8*x_11^3-3*x_5*x_6^7*x_11^2*x_12+3*x_5^2*x_6^6*x_11*x_12^2-x_5^3*x_6^5*x_12^3,x_8^3*x_10^8-3*x_7*x_8^2*x_10^7*x_11+3*x_7^2*x_8*x_10^6*x_11^2-x_7^3*x_10^5*x_11^3,x_2^8*x_4^3-3*x_1*x_2^7*x_4^2*x_5+3*x_1^2*x_2^6*x_4*x_5^2-x_1^3*x_2^5*x_5^3,-x_6^3*x_11^8+3*x_5*x_6^2*x_11^7*x_12-3*x_5^2*x_6*x_11^6*x_12^2+x_5^3*x_11^5*x_12^3,-x_6^3*x_7^3*x_9^5+3*x_4*x_6^2*x_7^2*x_9^6-3*x_4^2*x_6*x_7*x_9^7+x_4^3*x_9^8,x_8^8*x_10^3-3*x_7*x_8^7*x_10^2*x_11+3*x_7^2*x_8^6*x_10*x_11^2-x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3-3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3);22 i8·:·I·=·ideal(x_2^8*x_10^3-3*x_1*x_2^7*x_10^2*x_11+3*x_1^2*x_2^6*x_10*x_11^2-x_1^3*x_2^5*x_11^3,x_5^5*x_6^3*x_11^3-3*x_5^6*x_6^2*x_11^2*x_12+3*x_5^7*x_6*x_11*x_12^2-x_5^8*x_12^3,x_1^5*x_2^3*x_4^3-3*x_1^6*x_2^2*x_4^2*x_5+3*x_1^7*x_2*x_4*x_5^2-x_1^8*x_5^3,x_6^8*x_11^3-3*x_5*x_6^7*x_11^2*x_12+3*x_5^2*x_6^6*x_11*x_12^2-x_5^3*x_6^5*x_12^3,x_8^3*x_10^8-3*x_7*x_8^2*x_10^7*x_11+3*x_7^2*x_8*x_10^6*x_11^2-x_7^3*x_10^5*x_11^3,x_2^8*x_4^3-3*x_1*x_2^7*x_4^2*x_5+3*x_1^2*x_2^6*x_4*x_5^2-x_1^3*x_2^5*x_5^3,-x_6^3*x_11^8+3*x_5*x_6^2*x_11^7*x_12-3*x_5^2*x_6*x_11^6*x_12^2+x_5^3*x_11^5*x_12^3,-x_6^3*x_7^3*x_9^5+3*x_4*x_6^2*x_7^2*x_9^6-3*x_4^2*x_6*x_7*x_9^7+x_4^3*x_9^8,x_8^8*x_10^3-3*x_7*x_8^7*x_10^2*x_11+3*x_7^2*x_8^6*x_10*x_11^2-x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3-3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3);
  
23 ···············ZZ23 ···············ZZ
24 o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·]24 o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·]
25 ··············127··11···8···1···9···12···6···5···10···2···4···3···725 ··············127··11···8···1···9···12···6···5···10···2···4···3···7
  
26 i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true)26 i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true)
27 ·--·used·0.000810169s·(cpu);·0.00215295s·(thread);·0s·(gc)27 ·--·used·0.00252033s·(cpu);·0.00228522s·(thread);·0s·(gc)
28 isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators.28 isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators.
  
29 o9·=·true29 o9·=·true
  
30 i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false)30 i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false)
31 ·--·used·0.00104278s·(cpu);·0.00202828s·(thread);·0s·(gc)31 ·--·used·0.00223226s·(cpu);·0.00221931s·(thread);·0s·(gc)
  
32 o10·=·true32 o10·=·true
  
33 i11·:·33 i11·:·
586 B
./usr/share/doc/Macaulay2/FastMinors/example-output/_proj__Dim.out
    
Offset 7, 17 lines modifiedOffset 7, 17 lines modified
7 o2·:·Ideal·of·R7 o2·:·Ideal·of·R
  
8 i3·:·pdim(module·I)8 i3·:·pdim(module·I)
  
9 o3·=·29 o3·=·2
  
10 i4·:·time·projDim(module·I,·Strategy=>StrategyRandom)10 i4·:·time·projDim(module·I,·Strategy=>StrategyRandom)
11 ·--·used·0.201626s·(cpu);·0.126339s·(thread);·0s·(gc)11 ·--·used·0.209477s·(cpu);·0.136841s·(thread);·0s·(gc)
  
12 o4·=·112 o4·=·1
  
13 i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1)13 i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1)
14 ·--·used·0.0100835s·(cpu);·0.0110378s·(thread);·0s·(gc)14 ·--·used·0.0120046s·(cpu);·0.0132135s·(thread);·0s·(gc)
  
15 o5·=·115 o5·=·1
  
16 i6·:·16 i6·:·
647 B
./usr/share/doc/Macaulay2/FastMinors/example-output/_recursive__Minors.out
    
Offset 4, 20 lines modifiedOffset 4, 20 lines modified
  
4 i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7);4 i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7);
  
5 ·············6······75 ·············6······7
6 o2·:·Matrix·R··<--·R6 o2·:·Matrix·R··<--·R
  
7 i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0);7 i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0);
8 ·--·used·0.379483s·(cpu);·0.341637s·(thread);·0s·(gc)8 ·--·used·0.509179s·(cpu);·0.455061s·(thread);·0s·(gc)
  
9 o3·:·Ideal·of·R9 o3·:·Ideal·of·R
  
10 i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor);10 i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor);
11 ·--·used·1.05608s·(cpu);·0.982554s·(thread);·0s·(gc)11 ·--·used·1.26156s·(cpu);·1.12484s·(thread);·0s·(gc)
  
12 o4·:·Ideal·of·R12 o4·:·Ideal·of·R
  
13 i5·:·I1·==·I213 i5·:·I1·==·I2
  
14 o5·=·true14 o5·=·true
  
5.71 KB
./usr/share/doc/Macaulay2/FastMinors/example-output/_regular__In__Codimension.out
    
Offset 17, 44 lines modifiedOffset 17, 44 lines modified
17 i6·:·S·=·T/I;17 i6·:·S·=·T/I;
  
18 i7·:·dim·S18 i7·:·dim·S
  
19 o7·=·319 o7·=·3
  
20 i8·:·time·regularInCodimension(1,·S)20 i8·:·time·regularInCodimension(1,·S)
21 ·--·used·0.560401s·(cpu);·0.457261s·(thread);·0s·(gc)21 ·--·used·0.670977s·(cpu);·0.534349s·(thread);·0s·(gc)
  
22 o8·=·true22 o8·=·true
  
23 i9·:·time·regularInCodimension(2,·S)23 i9·:·time·regularInCodimension(2,·S)
24 ·--·used·5.36049s·(cpu);·4.36718s·(thread);·0s·(gc)24 ·--·used·5.86324s·(cpu);·4.46668s·(thread);·0s·(gc)
  
25 i10·:·R·=·QQ[c,·f,·g,·h]/ideal(g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3-f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h-c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c);25 i10·:·R·=·QQ[c,·f,·g,·h]/ideal(g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3-f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h-c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c);
  
26 i11·:·dim(R)26 i11·:·dim(R)
  
27 o11·=·227 o11·=·2
  
28 i12·:·time·(dim·singularLocus·(R))28 i12·:·time·(dim·singularLocus·(R))
29 ·--·used·0.0199633s·(cpu);·0.017094s·(thread);·0s·(gc)29 ·--·used·0.0196447s·(cpu);·0.0207464s·(thread);·0s·(gc)
  
30 o12·=·-130 o12·=·-1
  
31 i13·:·time·regularInCodimension(2,·R)31 i13·:·time·regularInCodimension(2,·R)
32 ·--·used·0.206638s·(cpu);·0.145898s·(thread);·0s·(gc)32 ·--·used·0.211411s·(cpu);·0.152562s·(thread);·0s·(gc)
  
33 o13·=·true33 o13·=·true
  
34 i14·:·time·regularInCodimension(2,·R)34 i14·:·time·regularInCodimension(2,·R)
35 ·--·used·0.67702s·(cpu);·0.507263s·(thread);·0s·(gc)35 ·--·used·0.719451s·(cpu);·0.540277s·(thread);·0s·(gc)
  
36 o14·=·true36 o14·=·true
  
37 i15·:·time·regularInCodimension(2,·R)37 i15·:·time·regularInCodimension(2,·R)
38 ·--·used·1.09761s·(cpu);·0.834927s·(thread);·0s·(gc)38 ·--·used·1.1684s·(cpu);·0.877206s·(thread);·0s·(gc)
  
39 o15·=·true39 o15·=·true
  
40 i16·:·time·regularInCodimension(2,·S,·Verbose=>true)40 i16·:·time·regularInCodimension(2,·S,·Verbose=>true)
41 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·327.599·of·them.41 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·327.599·of·them.
42 regularInCodimension:·About·to·enter·loop42 regularInCodimension:·About·to·enter·loop
43 internalChooseMinor:·Choosing·GRevLexSmallestTerm43 internalChooseMinor:·Choosing·GRevLexSmallestTerm
Offset 386, 15 lines modifiedOffset 386, 15 lines modified
386 internalChooseMinor:·Choosing·RandomNonZero386 internalChooseMinor:·Choosing·RandomNonZero
387 internalChooseMinor:·Choosing·GRevLexSmallestTerm387 internalChooseMinor:·Choosing·GRevLexSmallestTerm
388 internalChooseMinor:·Choosing·LexSmallestTerm388 internalChooseMinor:·Choosing·LexSmallestTerm
389 internalChooseMinor:·Choosing·GRevLexSmallest389 internalChooseMinor:·Choosing·GRevLexSmallest
390 internalChooseMinor:·Choosing·LexSmallestTerm390 internalChooseMinor:·Choosing·LexSmallestTerm
391 internalChooseMinor:·Choosing·LexSmallestTerm391 internalChooseMinor:·Choosing·LexSmallestTerm
392 internalChooseMinor:·Choosing·LexSmallestTerm392 internalChooseMinor:·Choosing·LexSmallestTerm
393 internalChooseMinor:·Ch·--·used·5.86363s·(cpu);·4.73632s·(thread);·0s·(gc)393 internalChooseMinor:·Ch·--·used·6.16394s·(cpu);·4.74013s·(thread);·0s·(gc)
394 oosing·GRevLexSmallestTerm394 oosing·GRevLexSmallestTerm
395 internalChooseMinor:·Choosing·RandomNonZero395 internalChooseMinor:·Choosing·RandomNonZero
396 internalChooseMinor:·Choosing·LexSmallest396 internalChooseMinor:·Choosing·LexSmallest
397 internalChooseMinor:·Choosing·Random397 internalChooseMinor:·Choosing·Random
398 internalChooseMinor:·Choosing·Random398 internalChooseMinor:·Choosing·Random
399 internalChooseMinor:·Choosing·LexSmallestTerm399 internalChooseMinor:·Choosing·LexSmallestTerm
400 internalChooseMinor:·Choosing·GRevLexSmallestTerm400 internalChooseMinor:·Choosing·GRevLexSmallestTerm
Offset 430, 15 lines modifiedOffset 430, 15 lines modified
430 internalChooseMinor:·Choosing·Random430 internalChooseMinor:·Choosing·Random
431 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·328,·and·computed·=·180431 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·328,·and·computed·=·180
432 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.432 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
433 regularInCodimension:··partial·singular·locus·dimension·computed,·=·1433 regularInCodimension:··partial·singular·locus·dimension·computed,·=·1
434 regularInCodimension:··Loop·completed,·submatrices·considered·=·328,·and·computed·=·180.··singular·locus·dimension·appears·to·be·=·1434 regularInCodimension:··Loop·completed,·submatrices·considered·=·328,·and·computed·=·180.··singular·locus·dimension·appears·to·be·=·1
  
435 i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30)435 i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30)
436 ·--·used·1.04494s·(cpu);·0.871997s·(thread);·0s·(gc)436 ·--·used·1.14834s·(cpu);·0.936411s·(thread);·0s·(gc)
437 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them.437 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them.
438 regularInCodimension:·About·to·enter·loop438 regularInCodimension:·About·to·enter·loop
439 internalChooseMinor:·Choosing·LexSmallestTerm439 internalChooseMinor:·Choosing·LexSmallestTerm
440 internalChooseMinor:·Choosing·LexSmallestTerm440 internalChooseMinor:·Choosing·LexSmallestTerm
441 internalChooseMinor:·Choosing·GRevLexSmallest441 internalChooseMinor:·Choosing·GRevLexSmallest
442 internalChooseMinor:·Choosing·GRevLexSmallest442 internalChooseMinor:·Choosing·GRevLexSmallest
443 internalChooseMinor:·Choosing·LexSmallestTerm443 internalChooseMinor:·Choosing·LexSmallestTerm
Offset 490, 59 lines modifiedOffset 490, 59 lines modified
490 i18·:·StrategyCurrent#Random·=·0;490 i18·:·StrategyCurrent#Random·=·0;
  
491 i19·:·StrategyCurrent#LexSmallest·=·100;491 i19·:·StrategyCurrent#LexSmallest·=·100;
  
492 i20·:·StrategyCurrent#LexSmallestTerm·=·0;492 i20·:·StrategyCurrent#LexSmallestTerm·=·0;
  
493 i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)493 i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
494 ·--·used·0.301792s·(cpu);·0.215181s·(thread);·0s·(gc)494 ·--·used·0.286687s·(cpu);·0.210711s·(thread);·0s·(gc)
  
495 o21·=·true495 o21·=·true
  
496 i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)496 i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
497 ·--·used·0.0513809s·(cpu);·0.0533503s·(thread);·0s·(gc)497 ·--·used·0.104497s·(cpu);·0.0743239s·(thread);·0s·(gc)
  
498 o22·=·true498 o22·=·true
  
499 i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)499 i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
500 ·--·used·0.369614s·(cpu);·0.263567s·(thread);·0s·(gc)500 ·--·used·0.400751s·(cpu);·0.291657s·(thread);·0s·(gc)
  
501 o23·=·true501 o23·=·true
  
502 i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)502 i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
503 ·--·used·1.3687s·(cpu);·1.10557s·(thread);·0s·(gc)503 ·--·used·1.55547s·(cpu);·1.18638s·(thread);·0s·(gc)
  
504 o24·=·true504 o24·=·true
  
505 i25·:·StrategyCurrent#LexSmallest·=·0;505 i25·:·StrategyCurrent#LexSmallest·=·0;
  
506 i26·:·StrategyCurrent#LexSmallestTerm·=·100;506 i26·:·StrategyCurrent#LexSmallestTerm·=·100;
  
507 i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)507 i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
508 ·--·used·1.98781s·(cpu);·1.53708s·(thread);·0s·(gc)508 ·--·used·2.13142s·(cpu);·1.51813s·(thread);·0s·(gc)
  
509 i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)509 i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
510 ·--·used·1.9685s·(cpu);·1.48903s·(thread);·0s·(gc)510 ·--·used·2.12549s·(cpu);·1.49126s·(thread);·0s·(gc)
  
511 o28·=·true511 o28·=·true
  
512 i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)512 i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
513 ·--·used·0.361901s·(cpu);·0.299031s·(thread);·0s·(gc)513 ·--·used·0.362785s·(cpu);·0.280763s·(thread);·0s·(gc)
  
514 o29·=·true514 o29·=·true
  
515 i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)515 i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
516 ·--·used·0.618531s·(cpu);·0.516824s·(thread);·0s·(gc)516 ·--·used·0.621179s·(cpu);·0.507013s·(thread);·0s·(gc)
  
517 o30·=·true517 o30·=·true
  
518 i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom)518 i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom)
519 ·--·used·0.860727s·(cpu);·0.724494s·(thread);·0s·(gc)519 ·--·used·0.870384s·(cpu);·0.722456s·(thread);·0s·(gc)
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18.0 KB
./usr/share/doc/Macaulay2/FastMinors/html/___Fast__Minors__Strategy__Tutorial.html
    
Offset 620, 71 lines modifiedOffset 620, 71 lines modified
620 ········<div>620 ········<div>
621 ··········<p>Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.··For·instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that·was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.··In·other·words,·if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/J$·has·dimension·3).</p>621 ··········<p>Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.··For·instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that·was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.··In·other·words,·if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/J$·has·dimension·3).</p>
622 ········</div>622 ········</div>
623 ········<table·class="examples">623 ········<table·class="examples">
624 ··········<tr>624 ··········<tr>
625 ············<td>625 ············<td>
626 ··············<pre><code·class="language-macaulay2">i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random))626 ··············<pre><code·class="language-macaulay2">i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random))
627 ·--·used·0.0993859s·(cpu);·0.0991248s·(thread);·0s·(gc)627 ·--·used·0.0959555s·(cpu);·0.0980818s·(thread);·0s·(gc)
  
628 o28·=·2</code></pre>628 o28·=·2</code></pre>
629 ············</td>629 ············</td>
630 ··········</tr>630 ··········</tr>
631 ··········<tr>631 ··········<tr>
632 ············<td>632 ············<td>
633 ··············<pre><code·class="language-macaulay2">i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest))633 ··············<pre><code·class="language-macaulay2">i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest))
634 ·--·used·0.292043s·(cpu);·0.20273s·(thread);·0s·(gc)634 ·--·used·0.325274s·(cpu);·0.207555s·(thread);·0s·(gc)
  
635 o29·=·3</code></pre>635 o29·=·3</code></pre>
636 ············</td>636 ············</td>
637 ··········</tr>637 ··········</tr>
638 ··········<tr>638 ··········<tr>
639 ············<td>639 ············<td>
640 ··············<pre><code·class="language-macaulay2">i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm))640 ··············<pre><code·class="language-macaulay2">i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm))
641 ·--·used·0.334715s·(cpu);·0.273734s·(thread);·0s·(gc)641 ·--·used·0.368378s·(cpu);·0.265984s·(thread);·0s·(gc)
  
642 o30·=·1</code></pre>642 o30·=·1</code></pre>
643 ············</td>643 ············</td>
644 ··········</tr>644 ··········</tr>
645 ··········<tr>645 ··········<tr>
646 ············<td>646 ············<td>
647 ··············<pre><code·class="language-macaulay2">i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest))647 ··············<pre><code·class="language-macaulay2">i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest))
648 ·--·used·0.24478s·(cpu);·0.185298s·(thread);·0s·(gc)648 ·--·used·0.264907s·(cpu);·0.184087s·(thread);·0s·(gc)
  
649 o31·=·2</code></pre>649 o31·=·2</code></pre>
650 ············</td>650 ············</td>
651 ··········</tr>651 ··········</tr>
652 ··········<tr>652 ··········<tr>
653 ············<td>653 ············<td>
654 ··············<pre><code·class="language-macaulay2">i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest))654 ··············<pre><code·class="language-macaulay2">i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest))
655 ·--·used·0.227128s·(cpu);·0.166293s·(thread);·0s·(gc)655 ·--·used·0.243843s·(cpu);·0.161003s·(thread);·0s·(gc)
  
656 o32·=·3</code></pre>656 o32·=·3</code></pre>
657 ············</td>657 ············</td>
658 ··········</tr>658 ··········</tr>
659 ··········<tr>659 ··········<tr>
660 ············<td>660 ············<td>
661 ··············<pre><code·class="language-macaulay2">i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm))661 ··············<pre><code·class="language-macaulay2">i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm))
662 ·--·used·0.263228s·(cpu);·0.194093s·(thread);·0s·(gc)662 ·--·used·0.25891s·(cpu);·0.188926s·(thread);·0s·(gc)
  
663 o33·=·3</code></pre>663 o33·=·3</code></pre>
664 ············</td>664 ············</td>
665 ··········</tr>665 ··········</tr>
666 ··········<tr>666 ··········<tr>
667 ············<td>667 ············<td>
668 ··············<pre><code·class="language-macaulay2">i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest))668 ··············<pre><code·class="language-macaulay2">i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest))
669 ·--·used·0.285217s·(cpu);·0.170356s·(thread);·0s·(gc)669 ·--·used·0.269115s·(cpu);·0.156876s·(thread);·0s·(gc)
  
670 o34·=·3</code></pre>670 o34·=·3</code></pre>
671 ············</td>671 ············</td>
672 ··········</tr>672 ··········</tr>
673 ··········<tr>673 ··········<tr>
674 ············<td>674 ············<td>
675 ··············<pre><code·class="language-macaulay2">i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points))675 ··············<pre><code·class="language-macaulay2">i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points))
676 ·--·used·10.5035s·(cpu);·7.37759s·(thread);·0s·(gc)676 ·--·used·11.9234s·(cpu);·7.63965s·(thread);·0s·(gc)
  
677 o35·=·1</code></pre>677 o35·=·1</code></pre>
678 ············</td>678 ············</td>
679 ··········</tr>679 ··········</tr>
680 ········</table>680 ········</table>
681 ········<div>681 ········<div>
682 ··········<p>Indeed,·in·this·example,·even·computing·determinants·of·1,000·random·submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in·codimension·1.··On·the·other·hand,·<span·class="tt">Points</span>·is·almost·always·quite·effective·at·finding·valuable·submatrices,·but·can·be·quite·slow.··In·this·particular·example,·we·can·see·that·<span·class="tt">LexSmallestTerm</span>·also·performs·very·well·(and·does·it·quickly).·Since·different·strategies·work·better·or·worse·on·different·examples,·the·default·strategy·actually·mixes·and·matches·various·strategies.··The·default·strategy,·which·we·now·elucidate,</p>682 ··········<p>Indeed,·in·this·example,·even·computing·determinants·of·1,000·random·submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in·codimension·1.··On·the·other·hand,·<span·class="tt">Points</span>·is·almost·always·quite·effective·at·finding·valuable·submatrices,·but·can·be·quite·slow.··In·this·particular·example,·we·can·see·that·<span·class="tt">LexSmallestTerm</span>·also·performs·very·well·(and·does·it·quickly).·Since·different·strategies·work·better·or·worse·on·different·examples,·the·default·strategy·actually·mixes·and·matches·various·strategies.··The·default·strategy,·which·we·now·elucidate,</p>
Offset 709, 15 lines modifiedOffset 709, 15 lines modified
709 ········<div>709 ········<div>
710 ··········<p>says·that·we·should·use·<span·class="tt">GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest,·LexSmallestTerm,·Random,·RandomNonzero</span>·all·with·equal·probability·(note·<span·class="tt">RandomNonzero</span>,·which·we·have·not·yet·discussed·chooses·random·submatrices·where·no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).··For·instance,·if·we·run:</p>710 ··········<p>says·that·we·should·use·<span·class="tt">GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest,·LexSmallestTerm,·Random,·RandomNonzero</span>·all·with·equal·probability·(note·<span·class="tt">RandomNonzero</span>,·which·we·have·not·yet·discussed·chooses·random·submatrices·where·no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).··For·instance,·if·we·run:</p>
711 ········</div>711 ········</div>
712 ········<table·class="examples">712 ········<table·class="examples">
713 ··········<tr>713 ··········<tr>
714 ············<td>714 ············<td>
715 ··············<pre><code·class="language-macaulay2">i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true);715 ··············<pre><code·class="language-macaulay2">i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true);
716 ·--·used·0.419124s·(cpu);·0.320611s·(thread);·0s·(gc)716 ·--·used·0.556191s·(cpu);·0.369175s·(thread);·0s·(gc)
717 internalChooseMinor:·Choosing·Random717 internalChooseMinor:·Choosing·Random
718 internalChooseMinor:·Choosing·LexSmallest718 internalChooseMinor:·Choosing·LexSmallest
719 internalChooseMinor:·Choosing·Random719 internalChooseMinor:·Choosing·Random
720 internalChooseMinor:·Choosing·GRevLexSmallestTerm720 internalChooseMinor:·Choosing·GRevLexSmallestTerm
721 internalChooseMinor:·Choosing·RandomNonZero721 internalChooseMinor:·Choosing·RandomNonZero
722 internalChooseMinor:·Choosing·RandomNonZero722 internalChooseMinor:·Choosing·RandomNonZero
723 internalChooseMinor:·Choosing·LexSmallest723 internalChooseMinor:·Choosing·LexSmallest
Offset 820, 15 lines modifiedOffset 820, 15 lines modified
  
820 o42·=·true</code></pre>820 o42·=·true</code></pre>
821 ············</td>821 ············</td>
822 ··········</tr>822 ··········</tr>
823 ··········<tr>823 ··········<tr>
824 ············<td>824 ············<td>
825 ··············<pre><code·class="language-macaulay2">i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric))825 ··············<pre><code·class="language-macaulay2">i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric))
826 ·--·used·0.755017s·(cpu);·0.504897s·(thread);·0s·(gc)826 ·--·used·0.884813s·(cpu);·0.540329s·(thread);·0s·(gc)
  
827 o43·=·2</code></pre>827 o43·=·2</code></pre>
828 ············</td>828 ············</td>
829 ··········</tr>829 ··········</tr>
830 ··········<tr>830 ··········<tr>
831 ············<td>831 ············<td>
832 ··············<pre><code·class="language-macaulay2">i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value832 ··············<pre><code·class="language-macaulay2">i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value
Offset 852, 15 lines modifiedOffset 852, 15 lines modified
  
852 o45·=·false</code></pre>852 o45·=·false</code></pre>
853 ············</td>853 ············</td>
854 ··········</tr>854 ··········</tr>
855 ··········<tr>855 ··········<tr>
856 ············<td>856 ············<td>
857 ··············<pre><code·class="language-macaulay2">i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational))857 ··············<pre><code·class="language-macaulay2">i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational))
858 ·--·used·0.548111s·(cpu);·0.36733s·(thread);·0s·(gc)858 ·--·used·0.723851s·(cpu);·0.431427s·(thread);·0s·(gc)
  
859 o46·=·2</code></pre>859 o46·=·2</code></pre>
860 ············</td>860 ············</td>
861 ··········</tr>861 ··········</tr>
862 ········</table>862 ········</table>
863 ········<div>863 ········<div>
864 ··········<p>Other·options·may·also·be·passed·to·the·<a·title="Obtain·random·points·in·a·variety"·href="../../RandomPoints/html/index.html">RandomPoints</a>·package·via·the·<a·title="options·to·pass·to·functions·in·the·package·RandomPoints"·href="___Point__Options.html">PointOptions</a>·option.</p>864 ··········<p>Other·options·may·also·be·passed·to·the·<a·title="Obtain·random·points·in·a·variety"·href="../../RandomPoints/html/index.html">RandomPoints</a>·package·via·the·<a·title="options·to·pass·to·functions·in·the·package·RandomPoints"·href="___Point__Options.html">PointOptions</a>·option.</p>
Offset 868, 69 lines modifiedOffset 868, 69 lines modified
868 ········<div>868 ········<div>
869 ··········<p><b>regularInCodimension:</b>··It·is·reasonable·to·think·that·you·should·find·a·few·minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have·computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.··This·is·exactly·what·<span·class="tt">regularInCodimension</span>·does.··One·can·control·at·a·fine·level·how·frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we·have·computed·so·far·is·checked,·by·the·option·<span·class="tt">codimCheckFunction</span>.··For·more·on·that,·see·<a·title="A·tutorial·for·how·to·use·the·advanced·options·of·the·regularInCodimension·function"·href="___Regular__In__Codimension__Tutorial.html">RegularInCodimensionTutorial</a>·and·<a·title="attempts·to·show·that·the·ring·is·regular·in·codimension·n"·href="_regular__In__Codimension.html">regularInCodimension</a>.··Let·us·finish·running·<span·class="tt">regularInCodimension</span>·on·our·example·with·several·different·strategies.</p>869 ··········<p><b>regularInCodimension:</b>··It·is·reasonable·to·think·that·you·should·find·a·few·minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have·computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.··This·is·exactly·what·<span·class="tt">regularInCodimension</span>·does.··One·can·control·at·a·fine·level·how·frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we·have·computed·so·far·is·checked,·by·the·option·<span·class="tt">codimCheckFunction</span>.··For·more·on·that,·see·<a·title="A·tutorial·for·how·to·use·the·advanced·options·of·the·regularInCodimension·function"·href="___Regular__In__Codimension__Tutorial.html">RegularInCodimensionTutorial</a>·and·<a·title="attempts·to·show·that·the·ring·is·regular·in·codimension·n"·href="_regular__In__Codimension.html">regularInCodimension</a>.··Let·us·finish·running·<span·class="tt">regularInCodimension</span>·on·our·example·with·several·different·strategies.</p>
870 ········</div>870 ········</div>
871 ········<table·class="examples">871 ········<table·class="examples">
872 ··········<tr>872 ··········<tr>
873 ············<td>873 ············<td>
874 ··············<pre><code·class="language-macaulay2">i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault)874 ··············<pre><code·class="language-macaulay2">i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault)
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Offset 486, 44 lines modifiedOffset 486, 44 lines modified
486 o27·:·Ideal·of·S486 o27·:·Ideal·of·S
487 Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.·For487 Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.·For
488 instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that488 instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that
489 was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.·In·other·words,489 was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.·In·other·words,
490 if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/490 if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/
491 J$·has·dimension·3).491 J$·has·dimension·3).
492 i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random))492 i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random))
493 ·--·used·0.0993859s·(cpu);·0.0991248s·(thread);·0s·(gc)493 ·--·used·0.0959555s·(cpu);·0.0980818s·(thread);·0s·(gc)
  
494 o28·=·2494 o28·=·2
495 i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest))495 i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest))
496 ·--·used·0.292043s·(cpu);·0.20273s·(thread);·0s·(gc)496 ·--·used·0.325274s·(cpu);·0.207555s·(thread);·0s·(gc)
  
497 o29·=·3497 o29·=·3
498 i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm))498 i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm))
499 ·--·used·0.334715s·(cpu);·0.273734s·(thread);·0s·(gc)499 ·--·used·0.368378s·(cpu);·0.265984s·(thread);·0s·(gc)
  
500 o30·=·1500 o30·=·1
501 i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest))501 i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest))
502 ·--·used·0.24478s·(cpu);·0.185298s·(thread);·0s·(gc)502 ·--·used·0.264907s·(cpu);·0.184087s·(thread);·0s·(gc)
  
503 o31·=·2503 o31·=·2
504 i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest))504 i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest))
505 ·--·used·0.227128s·(cpu);·0.166293s·(thread);·0s·(gc)505 ·--·used·0.243843s·(cpu);·0.161003s·(thread);·0s·(gc)
  
506 o32·=·3506 o32·=·3
507 i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,507 i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,
508 Strategy=>GRevLexSmallestTerm))508 Strategy=>GRevLexSmallestTerm))
509 ·--·used·0.263228s·(cpu);·0.194093s·(thread);·0s·(gc)509 ·--·used·0.25891s·(cpu);·0.188926s·(thread);·0s·(gc)
  
510 o33·=·3510 o33·=·3
511 i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest))511 i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest))
512 ·--·used·0.285217s·(cpu);·0.170356s·(thread);·0s·(gc)512 ·--·used·0.269115s·(cpu);·0.156876s·(thread);·0s·(gc)
  
513 o34·=·3513 o34·=·3
514 i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points))514 i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points))
515 ·--·used·10.5035s·(cpu);·7.37759s·(thread);·0s·(gc)515 ·--·used·11.9234s·(cpu);·7.63965s·(thread);·0s·(gc)
  
516 o35·=·1516 o35·=·1
517 Indeed,·in·this·example,·even·computing·determinants·of·1,000·random517 Indeed,·in·this·example,·even·computing·determinants·of·1,000·random
518 submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in518 submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in
519 codimension·1.·On·the·other·hand,·Points·is·almost·always·quite·effective·at519 codimension·1.·On·the·other·hand,·Points·is·almost·always·quite·effective·at
520 finding·valuable·submatrices,·but·can·be·quite·slow.·In·this·particular520 finding·valuable·submatrices,·but·can·be·quite·slow.·In·this·particular
521 example,·we·can·see·that·LexSmallestTerm·also·performs·very·well·(and·does·it521 example,·we·can·see·that·LexSmallestTerm·also·performs·very·well·(and·does·it
Offset 544, 15 lines modifiedOffset 544, 15 lines modified
544 says·that·we·should·use·GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest,544 says·that·we·should·use·GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest,
545 LexSmallestTerm,·Random,·RandomNonzero·all·with·equal·probability·(note545 LexSmallestTerm,·Random,·RandomNonzero·all·with·equal·probability·(note
546 RandomNonzero,·which·we·have·not·yet·discussed·chooses·random·submatrices·where546 RandomNonzero,·which·we·have·not·yet·discussed·chooses·random·submatrices·where
547 no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).·For547 no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).·For
548 instance,·if·we·run:548 instance,·if·we·run:
549 i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,549 i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,
550 Verbose=>true);550 Verbose=>true);
551 ·--·used·0.419124s·(cpu);·0.320611s·(thread);·0s·(gc)551 ·--·used·0.556191s·(cpu);·0.369175s·(thread);·0s·(gc)
552 internalChooseMinor:·Choosing·Random552 internalChooseMinor:·Choosing·Random
553 internalChooseMinor:·Choosing·LexSmallest553 internalChooseMinor:·Choosing·LexSmallest
554 internalChooseMinor:·Choosing·Random554 internalChooseMinor:·Choosing·Random
555 internalChooseMinor:·Choosing·GRevLexSmallestTerm555 internalChooseMinor:·Choosing·GRevLexSmallestTerm
556 internalChooseMinor:·Choosing·RandomNonZero556 internalChooseMinor:·Choosing·RandomNonZero
557 internalChooseMinor:·Choosing·RandomNonZero557 internalChooseMinor:·Choosing·RandomNonZero
558 internalChooseMinor:·Choosing·LexSmallest558 internalChooseMinor:·Choosing·LexSmallest
Offset 633, 15 lines modifiedOffset 633, 15 lines modified
633 i41·:·ptsStratGeometric·=·new·OptionTable·from·(options633 i41·:·ptsStratGeometric·=·new·OptionTable·from·(options
634 chooseGoodMinors)#PointOptions;634 chooseGoodMinors)#PointOptions;
635 i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value635 i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value
  
636 o42·=·true636 o42·=·true
637 i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,637 i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,
638 PointOptions=>ptsStratGeometric))638 PointOptions=>ptsStratGeometric))
639 ·--·used·0.755017s·(cpu);·0.504897s·(thread);·0s·(gc)639 ·--·used·0.884813s·(cpu);·0.540329s·(thread);·0s·(gc)
  
640 o43·=·2640 o43·=·2
641 i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that641 i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that
642 value642 value
  
643 o44·=·OptionTable{DecompositionStrategy·=>·Decompose}643 o44·=·OptionTable{DecompositionStrategy·=>·Decompose}
644 ··················DimensionFunction·=>·dim644 ··················DimensionFunction·=>·dim
Offset 655, 58 lines modifiedOffset 655, 58 lines modified
  
655 o44·:·OptionTable655 o44·:·OptionTable
656 i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value656 i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value
  
657 o45·=·false657 o45·=·false
658 i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,658 i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,
659 PointOptions=>ptsStratRational))659 PointOptions=>ptsStratRational))
660 ·--·used·0.548111s·(cpu);·0.36733s·(thread);·0s·(gc)660 ·--·used·0.723851s·(cpu);·0.431427s·(thread);·0s·(gc)
  
661 o46·=·2661 o46·=·2
662 Other·options·may·also·be·passed·to·the·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s·package·via·the662 Other·options·may·also·be·passed·to·the·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s·package·via·the
663 _\x8P_\x8o_\x8i_\x8n_\x8t_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s·option.663 _\x8P_\x8o_\x8i_\x8n_\x8t_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s·option.
664 r\x8re\x8eg\x8gu\x8ul\x8la\x8ar\x8rI\x8In\x8nC\x8Co\x8od\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n:\x8:·It·is·reasonable·to·think·that·you·should·find·a·few664 r\x8re\x8eg\x8gu\x8ul\x8la\x8ar\x8rI\x8In\x8nC\x8Co\x8od\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n:\x8:·It·is·reasonable·to·think·that·you·should·find·a·few
665 minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have665 minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have
666 computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.·This666 computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.·This
667 is·exactly·what·regularInCodimension·does.·One·can·control·at·a·fine·level·how667 is·exactly·what·regularInCodimension·does.·One·can·control·at·a·fine·level·how
668 frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we668 frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we
669 have·computed·so·far·is·checked,·by·the·option·codimCheckFunction.·For·more·on669 have·computed·so·far·is·checked,·by·the·option·codimCheckFunction.·For·more·on
670 that,·see·_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8T_\x8u_\x8t_\x8o_\x8r_\x8i_\x8a_\x8l·and·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n.·Let·us·finish670 that,·see·_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8T_\x8u_\x8t_\x8o_\x8r_\x8i_\x8a_\x8l·and·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n.·Let·us·finish
671 running·regularInCodimension·on·our·example·with·several·different·strategies.671 running·regularInCodimension·on·our·example·with·several·different·strategies.
672 i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,672 i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,
673 Strategy=>StrategyDefault)673 Strategy=>StrategyDefault)
674 ·--·used·3.92809s·(cpu);·3.13674s·(thread);·0s·(gc)674 ·--·used·4.42176s·(cpu);·3.35364s·(thread);·0s·(gc)
675 i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,675 i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,
676 Strategy=>StrategyDefaultNonRandom)676 Strategy=>StrategyDefaultNonRandom)
677 ·--·used·0.908274s·(cpu);·0.663673s·(thread);·0s·(gc)677 ·--·used·1.02911s·(cpu);·0.706055s·(thread);·0s·(gc)
  
678 o48·=·true678 o48·=·true
679 i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random)679 i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random)
680 ·--·used·2.76875s·(cpu);·2.43256s·(thread);·0s·(gc)680 ·--·used·3.02898s·(cpu);·2.58176s·(thread);·0s·(gc)
681 i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,681 i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,
682 Strategy=>LexSmallest)682 Strategy=>LexSmallest)
683 ·--·used·2.87747s·(cpu);·1.98809s·(thread);·0s·(gc)683 ·--·used·3.36402s·(cpu);·2.12401s·(thread);·0s·(gc)
684 i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,684 i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,
685 Strategy=>LexSmallestTerm)685 Strategy=>LexSmallestTerm)
686 ·--·used·0.948699s·(cpu);·0.754966s·(thread);·0s·(gc)686 ·--·used·1.04338s·(cpu);·0.763271s·(thread);·0s·(gc)
  
687 o51·=·true687 o51·=·true
688 i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,688 i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,
689 Strategy=>GRevLexSmallest)689 Strategy=>GRevLexSmallest)
690 ·--·used·3.18381s·(cpu);·2.20838s·(thread);·0s·(gc)690 ·--·used·3.61076s·(cpu);·2.34984s·(thread);·0s·(gc)
691 i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,691 i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,
692 Strategy=>GRevLexSmallestTerm)692 Strategy=>GRevLexSmallestTerm)
693 ·--·used·3.69334s·(cpu);·2.69377s·(thread);·0s·(gc)693 ·--·used·4.04602s·(cpu);·2.83432s·(thread);·0s·(gc)
694 i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points)694 i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points)
695 ·--·used·11.3645s·(cpu);·7.68981s·(thread);·0s·(gc)695 ·--·used·13.9724s·(cpu);·8.86549s·(thread);·0s·(gc)
  
696 o54·=·true696 o54·=·true
697 i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,697 i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,
698 Strategy=>StrategyDefaultWithPoints)698 Strategy=>StrategyDefaultWithPoints)
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Offset 81, 23 lines modifiedOffset 81, 23 lines modified
81 ········<div>81 ········<div>
82 ··········<p>It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.··We·have·embedded·it·with·a·Segre·embedding·inside·$P^8$.··In·particular,·this·example·is·even·regular·in·codimension·3.</p>82 ··········<p>It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.··We·have·embedded·it·with·a·Segre·embedding·inside·$P^8$.··In·particular,·this·example·is·even·regular·in·codimension·3.</p>
83 ········</div>83 ········</div>
84 ········<table·class="examples">84 ········<table·class="examples">
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i4·:·time·regularInCodimension(1,·S/J)87 ··············<pre><code·class="language-macaulay2">i4·:·time·regularInCodimension(1,·S/J)
88 ·--·used·0.759299s·(cpu);·0.560341s·(thread);·0s·(gc)88 ·--·used·0.913681s·(cpu);·0.60059s·(thread);·0s·(gc)
  
89 o4·=·true</code></pre>89 o4·=·true</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i5·:·time·regularInCodimension(2,·S/J)94 ··············<pre><code·class="language-macaulay2">i5·:·time·regularInCodimension(2,·S/J)
95 ·--·used·8.71094s·(cpu);·6.81449s·(thread);·0s·(gc)</code></pre>95 ·--·used·10.0084s·(cpu);·7.41796s·(thread);·0s·(gc)</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ········</table>98 ········</table>
99 ········<div>99 ········<div>
100 ··········<p>We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the·ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this·example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the·singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they·generate,·we·instead·compute·a·few·of·them.··<span·class="tt">regularInCodimension</span>·returns·<span·class="tt">true</span>·if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·<span·class="tt">null</span>·if·not.··Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the·execution·time·can·actually·vary·quite·a·bit.···Let's·take·a·look·at·what·is·occurring·by·using·the·<span·class="tt">Verbose</span>·option.··We·go·through·the·output·and·explain·what·each·line·is·telling·us.</p>100 ··········<p>We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the·ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this·example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the·singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they·generate,·we·instead·compute·a·few·of·them.··<span·class="tt">regularInCodimension</span>·returns·<span·class="tt">true</span>·if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·<span·class="tt">null</span>·if·not.··Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the·execution·time·can·actually·vary·quite·a·bit.···Let's·take·a·look·at·what·is·occurring·by·using·the·<span·class="tt">Verbose</span>·option.··We·go·through·the·output·and·explain·what·each·line·is·telling·us.</p>
101 ········</div>101 ········</div>
102 ········<table·class="examples">102 ········<table·class="examples">
Offset 172, 29 lines modifiedOffset 172, 29 lines modified
172 internalChooseMinor:·Choosing·LexSmallest172 internalChooseMinor:·Choosing·LexSmallest
173 internalChooseMinor:·Choosing·LexSmallestTerm173 internalChooseMinor:·Choosing·LexSmallestTerm
174 internalChooseMinor:·Choosing·LexSmallest174 internalChooseMinor:·Choosing·LexSmallest
175 internalChooseMinor:·Choosing·Random175 internalChooseMinor:·Choosing·Random
176 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39176 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39
177 regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast177 regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast
178 regularInCodimension:··partial·singular·locus·dimension·computed,·=·2178 regularInCodimension:··partial·singular·locus·dimension·computed,·=·2
179 regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.12782s·(cpu);·0.872279s·(thread);·0s·(gc)179 regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.36723s·(cpu);·0.972727s·(thread);·0s·(gc)
180 d·=·39.··singular·locus·dimension·appears·to·be·=·2180 d·=·39.··singular·locus·dimension·appears·to·be·=·2
  
181 o6·=·true</code></pre>181 o6·=·true</code></pre>
182 ············</td>182 ············</td>
183 ··········</tr>183 ··········</tr>
184 ········</table>184 ········</table>
185 ········<div>185 ········<div>
186 ··········<p><b>MaxMinors.</b>··The·first·output·says·that·we·will·compute·up·to·452.9·minors·before·giving·up.··We·can·control·that·by·setting·the·option·<span·class="tt">MaxMinors</span>.</p>186 ··········<p><b>MaxMinors.</b>··The·first·output·says·that·we·will·compute·up·to·452.9·minors·before·giving·up.··We·can·control·that·by·setting·the·option·<span·class="tt">MaxMinors</span>.</p>
187 ········</div>187 ········</div>
188 ········<table·class="examples">188 ········<table·class="examples">
189 ··········<tr>189 ··········<tr>
190 ············<td>190 ············<td>
191 ··············<pre><code·class="language-macaulay2">i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true)191 ··············<pre><code·class="language-macaulay2">i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true)
192 ·--·used·0.139209s·(cpu);·0.111392s·(thread);·0s·(gc)192 ·--·used·0.163394s·(cpu);·0.118384s·(thread);·0s·(gc)
193 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.193 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.
194 regularInCodimension:·About·to·enter·loop194 regularInCodimension:·About·to·enter·loop
195 internalChooseMinor:·Choosing·Random195 internalChooseMinor:·Choosing·Random
196 internalChooseMinor:·Choosing·RandomNonZero196 internalChooseMinor:·Choosing·RandomNonZero
197 internalChooseMinor:·Choosing·GRevLexSmallestTerm197 internalChooseMinor:·Choosing·GRevLexSmallestTerm
198 internalChooseMinor:·Choosing·Random198 internalChooseMinor:·Choosing·Random
199 internalChooseMinor:·Choosing·Random199 internalChooseMinor:·Choosing·Random
Offset 219, 15 lines modifiedOffset 219, 15 lines modified
219 ········<div>219 ········<div>
220 ··········<p><b>Selecting·submatrices·of·the·Jacobian.</b>··We·also·see·output·like:·``Choosing·LexSmallest''·or·``Choosing·Random''.··This·is·saying·how·we·are·selecting·a·given·submatrix.··For·instance,·we·can·run:</p>220 ··········<p><b>Selecting·submatrices·of·the·Jacobian.</b>··We·also·see·output·like:·``Choosing·LexSmallest''·or·``Choosing·Random''.··This·is·saying·how·we·are·selecting·a·given·submatrix.··For·instance,·we·can·run:</p>
221 ········</div>221 ········</div>
222 ········<table·class="examples">222 ········<table·class="examples">
223 ··········<tr>223 ··········<tr>
224 ············<td>224 ············<td>
225 ··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true)225 ··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true)
226 ·--·used·0.120353s·(cpu);·0.0894023s·(thread);·0s·(gc)226 ·--·used·0.160235s·(cpu);·0.119668s·(thread);·0s·(gc)
227 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.227 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.
228 regularInCodimension:·About·to·enter·loop228 regularInCodimension:·About·to·enter·loop
229 internalChooseMinor:·Choosing·Random229 internalChooseMinor:·Choosing·Random
230 internalChooseMinor:·Choosing·Random230 internalChooseMinor:·Choosing·Random
231 internalChooseMinor:·Choosing·Random231 internalChooseMinor:·Choosing·Random
232 internalChooseMinor:·Choosing·Random232 internalChooseMinor:·Choosing·Random
233 internalChooseMinor:·Choosing·Random233 internalChooseMinor:·Choosing·Random
Offset 252, 15 lines modifiedOffset 252, 15 lines modified
252 ········<div>252 ········<div>
253 ··········<p><b>Computing·minors·vs·considering·the·dimension·of·what·has·been·computed.</b>··Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have·computed·so·far.··There·are·two·options·to·control·this.··First,·we·can·tell·the·function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of·minors.</p>253 ··········<p><b>Computing·minors·vs·considering·the·dimension·of·what·has·been·computed.</b>··Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have·computed·so·far.··There·are·two·options·to·control·this.··First,·we·can·tell·the·function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of·minors.</p>
254 ········</div>254 ········</div>
255 ········<table·class="examples">255 ········<table·class="examples">
256 ··········<tr>256 ··········<tr>
257 ············<td>257 ············<td>
258 ··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true)258 ··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true)
259 ·--·used·0.494139s·(cpu);·0.394153s·(thread);·0s·(gc)259 ·--·used·0.642239s·(cpu);·0.517448s·(thread);·0s·(gc)
260 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.260 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them.
261 regularInCodimension:·About·to·enter·loop261 regularInCodimension:·About·to·enter·loop
262 internalChooseMinor:·Choosing·RandomNonZero262 internalChooseMinor:·Choosing·RandomNonZero
263 internalChooseMinor:·Choosing·Random263 internalChooseMinor:·Choosing·Random
264 internalChooseMinor:·Choosing·LexSmallest264 internalChooseMinor:·Choosing·LexSmallest
265 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3265 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3
266 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.266 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
Offset 291, 15 lines modifiedOffset 291, 15 lines modified
291 ········<div>291 ········<div>
292 ··········<p><b>CodimCheckFunction.</b>·The·option·<span·class="tt">CodimCheckFunction</span>·controls·how·frequently·the·dimension·of·the·partial·ideal·of·minors·is·computed.··For·instance,·setting·<span·class="tt">CodimCheckFunction·=>·t·->·t/5</span>·will·say·it·should·compute·dimension·after·every·5·minors·are·examined.··In·general,·after·the·output·of·the·CodimCheckFunction·increases·by·an·integer·we·compute·the·codimension·again.··The·default·function·has·the·space·between·computations·grow·exponentially.</p>292 ··········<p><b>CodimCheckFunction.</b>·The·option·<span·class="tt">CodimCheckFunction</span>·controls·how·frequently·the·dimension·of·the·partial·ideal·of·minors·is·computed.··For·instance,·setting·<span·class="tt">CodimCheckFunction·=>·t·->·t/5</span>·will·say·it·should·compute·dimension·after·every·5·minors·are·examined.··In·general,·after·the·output·of·the·CodimCheckFunction·increases·by·an·integer·we·compute·the·codimension·again.··The·default·function·has·the·space·between·computations·grow·exponentially.</p>
293 ········</div>293 ········</div>
294 ········<table·class="examples">294 ········<table·class="examples">
295 ··········<tr>295 ··········<tr>
296 ············<td>296 ············<td>
297 ··············<pre><code·class="language-macaulay2">i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true)297 ··············<pre><code·class="language-macaulay2">i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true)
298 ·--·used·0.582528s·(cpu);·0.44772s·(thread);·0s·(gc)298 ·--·used·0.639978s·(cpu);·0.473535s·(thread);·0s·(gc)
299 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.299 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.
300 regularInCodimension:·About·to·enter·loop300 regularInCodimension:·About·to·enter·loop
301 internalChooseMinor:·Choosing·GRevLexSmallestTerm301 internalChooseMinor:·Choosing·GRevLexSmallestTerm
302 internalChooseMinor:·Choosing·GRevLexSmallestTerm302 internalChooseMinor:·Choosing·GRevLexSmallestTerm
303 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2303 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2
304 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.304 regularInCodimension:··isCodimAtLeast·failed,·computing·codim.
305 regularInCodimension:··partial·singular·locus·dimension·computed,·=·4305 regularInCodimension:··partial·singular·locus·dimension·computed,·=·4
Offset 348, 15 lines modifiedOffset 348, 15 lines modified
348 ········<div>348 ········<div>
349 ··········<p><b>isCodimAtLeast·and·dim</b>.··We·see·the·lines·about·the·``isCodimAtLeast·failed''.··This·means·that·<span·class="tt">isCodimAtLeast</span>·was·not·enough·on·its·own·to·verify·that·our·ring·is·regular·in·codimension·1.··After·this,·``partial·singular·locus·dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the·partial·ideal·defining·the·singular·locus.··How·<span·class="tt">isCodimAtLeast</span>·is·called·can·be·controlled·via·the·options·<span·class="tt">SPairsFunction</span>·and·<span·class="tt">PairLimit</span>,·which·are·simply·passed·to·<a·title="returns·true·if·we·can·quickly·see·whether·the·codim·is·at·least·a·given·number"·href="_is__Codim__At__Least.html">isCodimAtLeast</a>.··You·can·force·the·function·to·only·use·<span·class="tt">isCodimAtLeast</span>·and·not·call·dimension·by·setting·<span·class="tt">UseOnlyFastCodim·=>·true</span>.</p>349 ··········<p><b>isCodimAtLeast·and·dim</b>.··We·see·the·lines·about·the·``isCodimAtLeast·failed''.··This·means·that·<span·class="tt">isCodimAtLeast</span>·was·not·enough·on·its·own·to·verify·that·our·ring·is·regular·in·codimension·1.··After·this,·``partial·singular·locus·dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the·partial·ideal·defining·the·singular·locus.··How·<span·class="tt">isCodimAtLeast</span>·is·called·can·be·controlled·via·the·options·<span·class="tt">SPairsFunction</span>·and·<span·class="tt">PairLimit</span>,·which·are·simply·passed·to·<a·title="returns·true·if·we·can·quickly·see·whether·the·codim·is·at·least·a·given·number"·href="_is__Codim__At__Least.html">isCodimAtLeast</a>.··You·can·force·the·function·to·only·use·<span·class="tt">isCodimAtLeast</span>·and·not·call·dimension·by·setting·<span·class="tt">UseOnlyFastCodim·=>·true</span>.</p>
350 ········</div>350 ········</div>
351 ········<table·class="examples">351 ········<table·class="examples">
352 ··········<tr>352 ··········<tr>
353 ············<td>353 ············<td>
354 ··············<pre><code·class="language-macaulay2">i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true)354 ··············<pre><code·class="language-macaulay2">i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true)
355 ·--·used·0.374613s·(cpu);·0.274104s·(thread);·0s·(gc)355 ·--·used·0.422149s·(cpu);·0.292662s·(thread);·0s·(gc)
356 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.356 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them.
357 regularInCodimension:·About·to·enter·loop357 regularInCodimension:·About·to·enter·loop
358 internalChooseMinor:·Choosing·GRevLexSmallest358 internalChooseMinor:·Choosing·GRevLexSmallest
359 internalChooseMinor:·Choosing·LexSmallest359 internalChooseMinor:·Choosing·LexSmallest
360 internalChooseMinor:·Choosing·RandomNonZero360 internalChooseMinor:·Choosing·RandomNonZero
361 internalChooseMinor:·Choosing·RandomNonZero361 internalChooseMinor:·Choosing·RandomNonZero
362 internalChooseMinor:·Choosing·GRevLexSmallestTerm362 internalChooseMinor:·Choosing·GRevLexSmallestTerm
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Offset 24, 19 lines modifiedOffset 24, 19 lines modified
24 i3·:·dim·(S/J)24 i3·:·dim·(S/J)
  
25 o3·=·425 o3·=·4
26 It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.·We·have26 It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.·We·have
27 embedded·it·with·a·Segre·embedding·inside·$P^8$.·In·particular,·this·example·is27 embedded·it·with·a·Segre·embedding·inside·$P^8$.·In·particular,·this·example·is
28 even·regular·in·codimension·3.28 even·regular·in·codimension·3.
29 i4·:·time·regularInCodimension(1,·S/J)29 i4·:·time·regularInCodimension(1,·S/J)
30 ·--·used·0.759299s·(cpu);·0.560341s·(thread);·0s·(gc)30 ·--·used·0.913681s·(cpu);·0.60059s·(thread);·0s·(gc)
  
31 o4·=·true31 o4·=·true
32 i5·:·time·regularInCodimension(2,·S/J)32 i5·:·time·regularInCodimension(2,·S/J)
33 ·--·used·8.71094s·(cpu);·6.81449s·(thread);·0s·(gc)33 ·--·used·10.0084s·(cpu);·7.41796s·(thread);·0s·(gc)
34 We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the34 We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the
35 ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this35 ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this
36 example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the36 example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the
37 singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they37 singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they
38 generate,·we·instead·compute·a·few·of·them.·regularInCodimension·returns·true38 generate,·we·instead·compute·a·few·of·them.·regularInCodimension·returns·true
39 if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·null39 if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·null
40 if·not.·Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the40 if·not.·Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the
Offset 121, 22 lines modifiedOffset 121, 22 lines modified
121 internalChooseMinor:·Choosing·LexSmallest121 internalChooseMinor:·Choosing·LexSmallest
122 internalChooseMinor:·Choosing·Random122 internalChooseMinor:·Choosing·Random
123 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices123 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices
124 considered:·49,·and·computed·=·39124 considered:·49,·and·computed·=·39
125 regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast125 regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast
126 regularInCodimension:··partial·singular·locus·dimension·computed,·=·2126 regularInCodimension:··partial·singular·locus·dimension·computed,·=·2
127 regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute127 regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute
128 --·used·1.12782s·(cpu);·0.872279s·(thread);·0s·(gc)128 --·used·1.36723s·(cpu);·0.972727s·(thread);·0s·(gc)
129 d·=·39.··singular·locus·dimension·appears·to·be·=·2129 d·=·39.··singular·locus·dimension·appears·to·be·=·2
  
130 o6·=·true130 o6·=·true
131 M\x8Ma\x8ax\x8xM\x8Mi\x8in\x8no\x8or\x8rs\x8s.\x8.·The·first·output·says·that·we·will·compute·up·to·452.9·minors·before131 M\x8Ma\x8ax\x8xM\x8Mi\x8in\x8no\x8or\x8rs\x8s.\x8.·The·first·output·says·that·we·will·compute·up·to·452.9·minors·before
132 giving·up.·We·can·control·that·by·setting·the·option·MaxMinors.132 giving·up.·We·can·control·that·by·setting·the·option·MaxMinors.
133 i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true)133 i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true)
134 ·--·used·0.139209s·(cpu);·0.111392s·(thread);·0s·(gc)134 ·--·used·0.163394s·(cpu);·0.118384s·(thread);·0s·(gc)
135 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5135 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5
136 minors,·we·will·compute·up·to·10·of·them.136 minors,·we·will·compute·up·to·10·of·them.
137 regularInCodimension:·About·to·enter·loop137 regularInCodimension:·About·to·enter·loop
138 internalChooseMinor:·Choosing·Random138 internalChooseMinor:·Choosing·Random
139 internalChooseMinor:·Choosing·RandomNonZero139 internalChooseMinor:·Choosing·RandomNonZero
140 internalChooseMinor:·Choosing·GRevLexSmallestTerm140 internalChooseMinor:·Choosing·GRevLexSmallestTerm
141 internalChooseMinor:·Choosing·Random141 internalChooseMinor:·Choosing·Random
Offset 159, 15 lines modifiedOffset 159, 15 lines modified
159 There·are·other·finer·ways·to·control·the·MaxMinors·option,·but·they·will·not159 There·are·other·finer·ways·to·control·the·MaxMinors·option,·but·they·will·not
160 be·discussed·in·this·tutorial.·See·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n.160 be·discussed·in·this·tutorial.·See·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n.
161 S\x8Se\x8el\x8le\x8ec\x8ct\x8ti\x8in\x8ng\x8g·s\x8su\x8ub\x8bm\x8ma\x8at\x8tr\x8ri\x8ic\x8ce\x8es\x8s·o\x8of\x8f·t\x8th\x8he\x8e·J\x8Ja\x8ac\x8co\x8ob\x8bi\x8ia\x8an\x8n.\x8.·We·also·see·output·like:·``Choosing161 S\x8Se\x8el\x8le\x8ec\x8ct\x8ti\x8in\x8ng\x8g·s\x8su\x8ub\x8bm\x8ma\x8at\x8tr\x8ri\x8ic\x8ce\x8es\x8s·o\x8of\x8f·t\x8th\x8he\x8e·J\x8Ja\x8ac\x8co\x8ob\x8bi\x8ia\x8an\x8n.\x8.·We·also·see·output·like:·``Choosing
162 LexSmallest''·or·``Choosing·Random''.·This·is·saying·how·we·are·selecting·a162 LexSmallest''·or·``Choosing·Random''.·This·is·saying·how·we·are·selecting·a
163 given·submatrix.·For·instance,·we·can·run:163 given·submatrix.·For·instance,·we·can·run:
164 i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,164 i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,
165 Verbose=>true)165 Verbose=>true)
166 ·--·used·0.120353s·(cpu);·0.0894023s·(thread);·0s·(gc)166 ·--·used·0.160235s·(cpu);·0.119668s·(thread);·0s·(gc)
167 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5167 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5
168 minors,·we·will·compute·up·to·10·of·them.168 minors,·we·will·compute·up·to·10·of·them.
169 regularInCodimension:·About·to·enter·loop169 regularInCodimension:·About·to·enter·loop
170 internalChooseMinor:·Choosing·Random170 internalChooseMinor:·Choosing·Random
171 internalChooseMinor:·Choosing·Random171 internalChooseMinor:·Choosing·Random
172 internalChooseMinor:·Choosing·Random172 internalChooseMinor:·Choosing·Random
173 internalChooseMinor:·Choosing·Random173 internalChooseMinor:·Choosing·Random
Offset 197, 15 lines modifiedOffset 197, 15 lines modified
197 C\x8Co\x8om\x8mp\x8pu\x8ut\x8ti\x8in\x8ng\x8g·m\x8mi\x8in\x8no\x8or\x8rs\x8s·v\x8vs\x8s·c\x8co\x8on\x8ns\x8si\x8id\x8de\x8er\x8ri\x8in\x8ng\x8g·t\x8th\x8he\x8e·d\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n·o\x8of\x8f·w\x8wh\x8ha\x8at\x8t·h\x8ha\x8as\x8s·b\x8be\x8ee\x8en\x8n·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8ed\x8d.\x8.197 C\x8Co\x8om\x8mp\x8pu\x8ut\x8ti\x8in\x8ng\x8g·m\x8mi\x8in\x8no\x8or\x8rs\x8s·v\x8vs\x8s·c\x8co\x8on\x8ns\x8si\x8id\x8de\x8er\x8ri\x8in\x8ng\x8g·t\x8th\x8he\x8e·d\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n·o\x8of\x8f·w\x8wh\x8ha\x8at\x8t·h\x8ha\x8as\x8s·b\x8be\x8ee\x8en\x8n·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8ed\x8d.\x8.
198 Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have198 Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have
199 computed·so·far.·There·are·two·options·to·control·this.·First,·we·can·tell·the199 computed·so·far.·There·are·two·options·to·control·this.·First,·we·can·tell·the
200 function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of200 function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of
201 minors.201 minors.
202 i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t-202 i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t-
203 >3,·Verbose=>true)203 >3,·Verbose=>true)
204 ·--·used·0.494139s·(cpu);·0.394153s·(thread);·0s·(gc)204 ·--·used·0.642239s·(cpu);·0.517448s·(thread);·0s·(gc)
205 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5205 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5
206 minors,·we·will·compute·up·to·10·of·them.206 minors,·we·will·compute·up·to·10·of·them.
207 regularInCodimension:·About·to·enter·loop207 regularInCodimension:·About·to·enter·loop
208 internalChooseMinor:·Choosing·RandomNonZero208 internalChooseMinor:·Choosing·RandomNonZero
209 internalChooseMinor:·Choosing·Random209 internalChooseMinor:·Choosing·Random
210 internalChooseMinor:·Choosing·LexSmallest210 internalChooseMinor:·Choosing·LexSmallest
211 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices211 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices
Offset 243, 15 lines modifiedOffset 243, 15 lines modified
243 dimension·of·the·partial·ideal·of·minors·is·computed.·For·instance,·setting243 dimension·of·the·partial·ideal·of·minors·is·computed.·For·instance,·setting
244 CodimCheckFunction·=>·t·->·t/5·will·say·it·should·compute·dimension·after·every244 CodimCheckFunction·=>·t·->·t/5·will·say·it·should·compute·dimension·after·every
245 5·minors·are·examined.·In·general,·after·the·output·of·the·CodimCheckFunction245 5·minors·are·examined.·In·general,·after·the·output·of·the·CodimCheckFunction
246 increases·by·an·integer·we·compute·the·codimension·again.·The·default·function246 increases·by·an·integer·we·compute·the·codimension·again.·The·default·function
247 has·the·space·between·computations·grow·exponentially.247 has·the·space·between·computations·grow·exponentially.
248 i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t-248 i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t-
249 >t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true)249 >t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true)
250 ·--·used·0.582528s·(cpu);·0.44772s·(thread);·0s·(gc)250 ·--·used·0.639978s·(cpu);·0.473535s·(thread);·0s·(gc)
251 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5251 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5
252 minors,·we·will·compute·up·to·25·of·them.252 minors,·we·will·compute·up·to·25·of·them.
253 regularInCodimension:·About·to·enter·loop253 regularInCodimension:·About·to·enter·loop
254 internalChooseMinor:·Choosing·GRevLexSmallestTerm254 internalChooseMinor:·Choosing·GRevLexSmallestTerm
255 internalChooseMinor:·Choosing·GRevLexSmallestTerm255 internalChooseMinor:·Choosing·GRevLexSmallestTerm
256 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices256 regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices
257 considered:·2,·and·computed·=·2257 considered:·2,·and·computed·=·2
Offset 308, 15 lines modifiedOffset 308, 15 lines modified
308 dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the308 dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the
309 partial·ideal·defining·the·singular·locus.·How·isCodimAtLeast·is·called·can·be309 partial·ideal·defining·the·singular·locus.·How·isCodimAtLeast·is·called·can·be
310 controlled·via·the·options·SPairsFunction·and·PairLimit,·which·are·simply310 controlled·via·the·options·SPairsFunction·and·PairLimit,·which·are·simply
311 passed·to·_\x8i_\x8s_\x8C_\x8o_\x8d_\x8i_\x8m_\x8A_\x8t_\x8L_\x8e_\x8a_\x8s_\x8t.·You·can·force·the·function·to·only·use·isCodimAtLeast311 passed·to·_\x8i_\x8s_\x8C_\x8o_\x8d_\x8i_\x8m_\x8A_\x8t_\x8L_\x8e_\x8a_\x8s_\x8t.·You·can·force·the·function·to·only·use·isCodimAtLeast
312 and·not·call·dimension·by·setting·UseOnlyFastCodim·=>·true.312 and·not·call·dimension·by·setting·UseOnlyFastCodim·=>·true.
313 i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>313 i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>
314 true,·Verbose=>true)314 true,·Verbose=>true)
315 ·--·used·0.374613s·(cpu);·0.274104s·(thread);·0s·(gc)315 ·--·used·0.422149s·(cpu);·0.292662s·(thread);·0s·(gc)
316 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5316 regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5
317 minors,·we·will·compute·up·to·25·of·them.317 minors,·we·will·compute·up·to·25·of·them.
318 regularInCodimension:·About·to·enter·loop318 regularInCodimension:·About·to·enter·loop
319 internalChooseMinor:·Choosing·GRevLexSmallest319 internalChooseMinor:·Choosing·GRevLexSmallest
320 internalChooseMinor:·Choosing·LexSmallest320 internalChooseMinor:·Choosing·LexSmallest
321 internalChooseMinor:·Choosing·RandomNonZero321 internalChooseMinor:·Choosing·RandomNonZero
322 internalChooseMinor:·Choosing·RandomNonZero322 internalChooseMinor:·Choosing·RandomNonZero
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68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);</code></pre>69 ··············<pre><code·class="language-macaulay2">i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);</code></pre>
70 ············</td>70 ············</td>
71 ··········</tr>71 ··········</tr>
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault)74 ··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault)
75 ·--·2.06011s·elapsed75 ·--·6.31115s·elapsed
  
76 o2·=·true</code></pre>76 o2·=·true</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ········</table>79 ········</table>
80 In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion·of·each·of·the·above·strategies·after·100·runs.········<ul>80 In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion·of·each·of·the·above·strategies·after·100·runs.········<ul>
81 ··········<li><span·class="tt">StrategyDefault</span>:·1.65·seconds</li>81 ··········<li><span·class="tt">StrategyDefault</span>:·1.65·seconds</li>
Offset 122, 15 lines modifiedOffset 122, 15 lines modified
122 ··········<li><span·class="tt">StrategyPoints</span>:·choose·all·submatrices·via·Points.</li>122 ··········<li><span·class="tt">StrategyPoints</span>:·choose·all·submatrices·via·Points.</li>
123 ··········<li><span·class="tt">StrategyDefaultWithPoints</span>:·like·<span·class="tt">StrategyDefault</span>·but·replaces·the·<span·class="tt">Random</span>·and·RandomNonZero·submatrices·as·with·matrices·chosen·as·in·Points.</li>123 ··········<li><span·class="tt">StrategyDefaultWithPoints</span>:·like·<span·class="tt">StrategyDefault</span>·but·replaces·the·<span·class="tt">Random</span>·and·RandomNonZero·submatrices·as·with·matrices·chosen·as·in·Points.</li>
124 ········</ul>124 ········</ul>
125 Additionally,·a·<span·class="tt">MutableHashTable</span>·named·<span·class="tt">StrategyCurrent</span>·is·also·exported.··It·begins·as·the·default·strategy,·but·the·user·can·modify·it.<br><br><b>Using·a·single·heuristic··</b>Alternatively,·if·the·user·only·wants·to·use·say·<span·class="tt">LexSmallestTerm</span>·they·can·set,·<span·class="tt">Strategy</span>·to·point·to·that·symbol,·instead·of·a·creating·a·custom·strategy·HashTable.··For·example:·········<table·class="examples">125 Additionally,·a·<span·class="tt">MutableHashTable</span>·named·<span·class="tt">StrategyCurrent</span>·is·also·exported.··It·begins·as·the·default·strategy,·but·the·user·can·modify·it.<br><br><b>Using·a·single·heuristic··</b>Alternatively,·if·the·user·only·wants·to·use·say·<span·class="tt">LexSmallestTerm</span>·they·can·set,·<span·class="tt">Strategy</span>·to·point·to·that·symbol,·instead·of·a·creating·a·custom·strategy·HashTable.··For·example:·········<table·class="examples">
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm)128 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm)
129 ·--·.955001s·elapsed129 ·--·3.44089s·elapsed
  
130 o4·=·true</code></pre>130 o4·=·true</code></pre>
131 ············</td>131 ············</td>
132 ··········</tr>132 ··········</tr>
133 ········</table>133 ········</table>
134 ······</div>134 ······</div>
135 ······<div>135 ······<div>
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41 i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-41 i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-
42 b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-42 b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-
43 e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-43 e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-
44 a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-44 a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-
45 g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-45 g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-
46 h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);46 h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);
47 i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault)47 i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault)
48 ·--·2.06011s·elapsed48 ·--·6.31115s·elapsed
  
49 o2·=·true49 o2·=·true
50 In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion50 In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion
51 of·each·of·the·above·strategies·after·100·runs.51 of·each·of·the·above·strategies·after·100·runs.
52 ····*·StrategyDefault:·1.65·seconds52 ····*·StrategyDefault:·1.65·seconds
53 ····*·StrategyRandom:·8.32·seconds53 ····*·StrategyRandom:·8.32·seconds
54 ····*·StrategyDefaultNonRandom:·0.99·seconds54 ····*·StrategyDefaultNonRandom:·0.99·seconds
Offset 135, 15 lines modifiedOffset 135, 15 lines modified
135 Additionally,·a·MutableHashTable·named·StrategyCurrent·is·also·exported.·It135 Additionally,·a·MutableHashTable·named·StrategyCurrent·is·also·exported.·It
136 begins·as·the·default·strategy,·but·the·user·can·modify·it.136 begins·as·the·default·strategy,·but·the·user·can·modify·it.
  
137 U\x8Us\x8si\x8in\x8ng\x8g·a\x8a·s\x8si\x8in\x8ng\x8gl\x8le\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8c·Alternatively,·if·the·user·only·wants·to·use·say137 U\x8Us\x8si\x8in\x8ng\x8g·a\x8a·s\x8si\x8in\x8ng\x8gl\x8le\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8c·Alternatively,·if·the·user·only·wants·to·use·say
138 LexSmallestTerm·they·can·set,·Strategy·to·point·to·that·symbol,·instead·of·a138 LexSmallestTerm·they·can·set,·Strategy·to·point·to·that·symbol,·instead·of·a
139 creating·a·custom·strategy·HashTable.·For·example:139 creating·a·custom·strategy·HashTable.·For·example:
140 i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm)140 i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm)
141 ·--·.955001s·elapsed141 ·--·3.44089s·elapsed
  
142 o4·=·true142 o4·=·true
143 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*143 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
144 The·object·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8D_\x8e_\x8f_\x8a_\x8u_\x8l_\x8t·is·an·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8·_\x8t_\x8a_\x8b_\x8l_\x8e.144 The·object·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8D_\x8e_\x8f_\x8a_\x8u_\x8l_\x8t·is·an·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8·_\x8t_\x8a_\x8b_\x8l_\x8e.
145 ===============================================================================145 ===============================================================================
146 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-146 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
147 1.25.06+ds/M2/Macaulay2/packages/FastMinors.m2:1993:0.147 1.25.06+ds/M2/Macaulay2/packages/FastMinors.m2:1993:0.
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114 o6·:·Ideal·of·R</code></pre>114 o6·:·Ideal·of·R</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i7·:·time·isCodimAtLeast(3,·J)119 ··············<pre><code·class="language-macaulay2">i7·:·time·isCodimAtLeast(3,·J)
120 ·--·used·0.00101147s·(cpu);·0.00220379s·(thread);·0s·(gc)120 ·--·used·0.00400048s·(cpu);·0.00234453s·(thread);·0s·(gc)
  
121 o7·=·true</code></pre>121 o7·=·true</code></pre>
122 ············</td>122 ············</td>
123 ··········</tr>123 ··········</tr>
124 ········</table>124 ········</table>
125 ········<div>125 ········<div>
126 ··········<p>The·function·works·by·computing·<span·class="tt">gb(I,·PairLimit=>f(i))</span>·for·successive·values·of·<span·class="tt">i</span>.··Here·<span·class="tt">f(i)</span>·is·a·function·that·takes·<span·class="tt">t</span>,·some·approximation·of·the·base·degree·value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial·ring,·this·is·probably·expected·to·be·<span·class="tt">\{1\}</span>).··And·<span·class="tt">i</span>·is·a·counting·variable.·You·can·provide·your·own·function·by·calling·<span·class="tt">isCodimAtLeast(n,·I,·SPairsFunction=>(·(i)·->·f(i)·)</span>,·the·default·function·is·<span·class="tt">SPairsFunction=>i->ceiling(1.5^i)</span>···Perhaps·more·commonly·however,·the·user·may·want·to·instead·tell·the·function·to·compute·for·larger·values·of·<span·class="tt">i</span>.··This·is·done·via·the·option·<span·class="tt">PairLimit</span>.··This·is·the·max·value·of·<span·class="tt">i</span>·to·be·plugged·into·<span·class="tt">SPairsFunction</span>·before·the·function·gives·up.··In·other·words,·<span·class="tt">PairLimit=>5</span>·will·tell·the·function·to·check·codimension·5·times.</p>126 ··········<p>The·function·works·by·computing·<span·class="tt">gb(I,·PairLimit=>f(i))</span>·for·successive·values·of·<span·class="tt">i</span>.··Here·<span·class="tt">f(i)</span>·is·a·function·that·takes·<span·class="tt">t</span>,·some·approximation·of·the·base·degree·value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial·ring,·this·is·probably·expected·to·be·<span·class="tt">\{1\}</span>).··And·<span·class="tt">i</span>·is·a·counting·variable.·You·can·provide·your·own·function·by·calling·<span·class="tt">isCodimAtLeast(n,·I,·SPairsFunction=>(·(i)·->·f(i)·)</span>,·the·default·function·is·<span·class="tt">SPairsFunction=>i->ceiling(1.5^i)</span>···Perhaps·more·commonly·however,·the·user·may·want·to·instead·tell·the·function·to·compute·for·larger·values·of·<span·class="tt">i</span>.··This·is·done·via·the·option·<span·class="tt">PairLimit</span>.··This·is·the·max·value·of·<span·class="tt">i</span>·to·be·plugged·into·<span·class="tt">SPairsFunction</span>·before·the·function·gives·up.··In·other·words,·<span·class="tt">PairLimit=>5</span>·will·tell·the·function·to·check·codimension·5·times.</p>
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136 o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·]136 o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·]
137 ··············127··11···8···1···9···12···6···5···10···2···4···3···7</code></pre>137 ··············127··11···8···1···9···12···6···5···10···2···4···3···7</code></pre>
138 ············</td>138 ············</td>
139 ··········</tr>139 ··········</tr>
140 ··········<tr>140 ··········<tr>
141 ············<td>141 ············<td>
142 ··············<pre><code·class="language-macaulay2">i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true)142 ··············<pre><code·class="language-macaulay2">i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true)
143 ·--·used·0.000810169s·(cpu);·0.00215295s·(thread);·0s·(gc)143 ·--·used·0.00252033s·(cpu);·0.00228522s·(thread);·0s·(gc)
144 isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators.144 isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators.
  
145 o9·=·true</code></pre>145 o9·=·true</code></pre>
146 ············</td>146 ············</td>
147 ··········</tr>147 ··········</tr>
148 ··········<tr>148 ··········<tr>
149 ············<td>149 ············<td>
150 ··············<pre><code·class="language-macaulay2">i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false)150 ··············<pre><code·class="language-macaulay2">i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false)
151 ·--·used·0.00104278s·(cpu);·0.00202828s·(thread);·0s·(gc)151 ·--·used·0.00223226s·(cpu);·0.00221931s·(thread);·0s·(gc)
  
152 o10·=·true</code></pre>152 o10·=·true</code></pre>
153 ············</td>153 ············</td>
154 ··········</tr>154 ··········</tr>
155 ········</table>155 ········</table>
156 ········<div>156 ········<div>
157 ··········<p>Notice·in·the·first·case·the·function·returned·<span·class="tt">null</span>,·because·the·depth·of·search·was·not·high·enough.··It·only·computed·<span·class="tt">codim</span>·5·times.··The·second·returned·true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the·<span·class="tt">PairLimit</span>·limit).</p>157 ··········<p>Notice·in·the·first·case·the·function·returned·<span·class="tt">null</span>,·because·the·depth·of·search·was·not·high·enough.··It·only·computed·<span·class="tt">codim</span>·5·times.··The·second·returned·true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the·<span·class="tt">PairLimit</span>·limit).</p>
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Offset 38, 15 lines modifiedOffset 38, 15 lines modified
38 ·············30······1238 ·············30······12
39 o4·:·Matrix·R···<--·R39 o4·:·Matrix·R···<--·R
40 i5·:·r·=·rank·myDiff;40 i5·:·r·=·rank·myDiff;
41 i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom);41 i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom);
  
42 o6·:·Ideal·of·R42 o6·:·Ideal·of·R
43 i7·:·time·isCodimAtLeast(3,·J)43 i7·:·time·isCodimAtLeast(3,·J)
44 ·--·used·0.00101147s·(cpu);·0.00220379s·(thread);·0s·(gc)44 ·--·used·0.00400048s·(cpu);·0.00234453s·(thread);·0s·(gc)
  
45 o7·=·true45 o7·=·true
46 The·function·works·by·computing·gb(I,·PairLimit=>f(i))·for·successive·values·of46 The·function·works·by·computing·gb(I,·PairLimit=>f(i))·for·successive·values·of
47 i.·Here·f(i)·is·a·function·that·takes·t,·some·approximation·of·the·base·degree47 i.·Here·f(i)·is·a·function·that·takes·t,·some·approximation·of·the·base·degree
48 value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial48 value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial
49 ring,·this·is·probably·expected·to·be·\{1\}).·And·i·is·a·counting·variable.·You49 ring,·this·is·probably·expected·to·be·\{1\}).·And·i·is·a·counting·variable.·You
50 can·provide·your·own·function·by·calling·isCodimAtLeast(n,·I,·SPairsFunction=>50 can·provide·your·own·function·by·calling·isCodimAtLeast(n,·I,·SPairsFunction=>
Offset 72, 20 lines modifiedOffset 72, 20 lines modified
72 x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3-72 x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3-
73 3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3);73 3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3);
  
74 ···············ZZ74 ···············ZZ
75 o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·]75 o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·]
76 ··············127··11···8···1···9···12···6···5···10···2···4···3···776 ··············127··11···8···1···9···12···6···5···10···2···4···3···7
77 i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true)77 i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true)
78 ·--·used·0.000810169s·(cpu);·0.00215295s·(thread);·0s·(gc)78 ·--·used·0.00252033s·(cpu);·0.00228522s·(thread);·0s·(gc)
79 isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators.79 isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators.
  
80 o9·=·true80 o9·=·true
81 i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false)81 i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false)
82 ·--·used·0.00104278s·(cpu);·0.00202828s·(thread);·0s·(gc)82 ·--·used·0.00223226s·(cpu);·0.00221931s·(thread);·0s·(gc)
  
83 o10·=·true83 o10·=·true
84 Notice·in·the·first·case·the·function·returned·null,·because·the·depth·of84 Notice·in·the·first·case·the·function·returned·null,·because·the·depth·of
85 search·was·not·high·enough.·It·only·computed·codim·5·times.·The·second·returned85 search·was·not·high·enough.·It·only·computed·codim·5·times.·The·second·returned
86 true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the86 true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the
87 PairLimit·limit).87 PairLimit·limit).
88 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8od\x8di\x8im\x8mA\x8At\x8tL\x8Le\x8ea\x8as\x8st\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*88 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8od\x8di\x8im\x8mA\x8At\x8tL\x8Le\x8ea\x8as\x8st\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*
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Offset 99, 23 lines modifiedOffset 99, 23 lines modified
  
99 o3·=·2</code></pre>99 o3·=·2</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i4·:·time·projDim(module·I,·Strategy=>StrategyRandom)104 ··············<pre><code·class="language-macaulay2">i4·:·time·projDim(module·I,·Strategy=>StrategyRandom)
105 ·--·used·0.201626s·(cpu);·0.126339s·(thread);·0s·(gc)105 ·--·used·0.209477s·(cpu);·0.136841s·(thread);·0s·(gc)
  
106 o4·=·1</code></pre>106 o4·=·1</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ··········<tr>109 ··········<tr>
110 ············<td>110 ············<td>
111 ··············<pre><code·class="language-macaulay2">i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1)111 ··············<pre><code·class="language-macaulay2">i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1)
112 ·--·used·0.0100835s·(cpu);·0.0110378s·(thread);·0s·(gc)112 ·--·used·0.0120046s·(cpu);·0.0132135s·(thread);·0s·(gc)
  
113 o5·=·1</code></pre>113 o5·=·1</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ········</table>116 ········</table>
117 ········<div>117 ········<div>
118 ··········<p>The·option·<span·class="tt">MaxMinors</span>·can·be·used·to·control·how·many·minors·are·computed·at·each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically·it·is·<span·class="tt">10·*·d·+·2·*·log_1.3(c)</span>.·Otherwise·the·user·can·set·the·option·<span·class="tt">MaxMinors·=>·ZZ</span>·to·specify·that·a·fixed·integer·is·used·for·each·step.··Alternatively,·the·user·can·control·the·number·of·minors·computed·at·each·step·by·setting·the·option·<span·class="tt">MaxMinors·=>·List</span>.··In·this·case,·the·list·specifies·how·many·minors·to·be·computed·at·each·step,·(working·backwards).·Finally,·you·can·also·set·<span·class="tt">MaxMinors</span>·to·be·a·custom·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·maximum·number·of·minors.</p>118 ··········<p>The·option·<span·class="tt">MaxMinors</span>·can·be·used·to·control·how·many·minors·are·computed·at·each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically·it·is·<span·class="tt">10·*·d·+·2·*·log_1.3(c)</span>.·Otherwise·the·user·can·set·the·option·<span·class="tt">MaxMinors·=>·ZZ</span>·to·specify·that·a·fixed·integer·is·used·for·each·step.··Alternatively,·the·user·can·control·the·number·of·minors·computed·at·each·step·by·setting·the·option·<span·class="tt">MaxMinors·=>·List</span>.··In·this·case,·the·list·specifies·how·many·minors·to·be·computed·at·each·step,·(working·backwards).·Finally,·you·can·also·set·<span·class="tt">MaxMinors</span>·to·be·a·custom·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·maximum·number·of·minors.</p>
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Offset 44, 19 lines modifiedOffset 44, 19 lines modified
44 i2·:·I·=·ideal((x^3+y)^2,·(x^2+y^2)^2,·(x+y^3)^2,·(x*y)^2);44 i2·:·I·=·ideal((x^3+y)^2,·(x^2+y^2)^2,·(x+y^3)^2,·(x*y)^2);
  
45 o2·:·Ideal·of·R45 o2·:·Ideal·of·R
46 i3·:·pdim(module·I)46 i3·:·pdim(module·I)
  
47 o3·=·247 o3·=·2
48 i4·:·time·projDim(module·I,·Strategy=>StrategyRandom)48 i4·:·time·projDim(module·I,·Strategy=>StrategyRandom)
49 ·--·used·0.201626s·(cpu);·0.126339s·(thread);·0s·(gc)49 ·--·used·0.209477s·(cpu);·0.136841s·(thread);·0s·(gc)
  
50 o4·=·150 o4·=·1
51 i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1)51 i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1)
52 ·--·used·0.0100835s·(cpu);·0.0110378s·(thread);·0s·(gc)52 ·--·used·0.0120046s·(cpu);·0.0132135s·(thread);·0s·(gc)
  
53 o5·=·153 o5·=·1
54 The·option·MaxMinors·can·be·used·to·control·how·many·minors·are·computed·at54 The·option·MaxMinors·can·be·used·to·control·how·many·minors·are·computed·at
55 each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the55 each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the
56 dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically56 dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically
57 it·is·10·*·d·+·2·*·log_1.3(c).·Otherwise·the·user·can·set·the·option·MaxMinors57 it·is·10·*·d·+·2·*·log_1.3(c).·Otherwise·the·user·can·set·the·option·MaxMinors
58 =>·ZZ·to·specify·that·a·fixed·integer·is·used·for·each·step.·Alternatively,·the58 =>·ZZ·to·specify·that·a·fixed·integer·is·used·for·each·step.·Alternatively,·the
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Offset 92, 23 lines modifiedOffset 92, 23 lines modified
92 ·············6······792 ·············6······7
93 o2·:·Matrix·R··&lt;--·R</code></pre>93 o2·:·Matrix·R··&lt;--·R</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0);98 ··············<pre><code·class="language-macaulay2">i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0);
99 ·--·used·0.379483s·(cpu);·0.341637s·(thread);·0s·(gc)99 ·--·used·0.509179s·(cpu);·0.455061s·(thread);·0s·(gc)
  
100 o3·:·Ideal·of·R</code></pre>100 o3·:·Ideal·of·R</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor);105 ··············<pre><code·class="language-macaulay2">i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor);
106 ·--·used·1.05608s·(cpu);·0.982554s·(thread);·0s·(gc)106 ·--·used·1.26156s·(cpu);·1.12484s·(thread);·0s·(gc)
  
107 o4·:·Ideal·of·R</code></pre>107 o4·:·Ideal·of·R</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i5·:·I1·==·I2112 ··············<pre><code·class="language-macaulay2">i5·:·I1·==·I2
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Offset 27, 19 lines modifiedOffset 27, 19 lines modified
27 strategy·for·minors27 strategy·for·minors
28 i1·:·R·=·QQ[x,y];28 i1·:·R·=·QQ[x,y];
29 i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7);29 i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7);
  
30 ·············6······730 ·············6······7
31 o2·:·Matrix·R··<--·R31 o2·:·Matrix·R··<--·R
32 i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0);32 i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0);
33 ·--·used·0.379483s·(cpu);·0.341637s·(thread);·0s·(gc)33 ·--·used·0.509179s·(cpu);·0.455061s·(thread);·0s·(gc)
  
34 o3·:·Ideal·of·R34 o3·:·Ideal·of·R
35 i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor);35 i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor);
36 ·--·used·1.05608s·(cpu);·0.982554s·(thread);·0s·(gc)36 ·--·used·1.26156s·(cpu);·1.12484s·(thread);·0s·(gc)
  
37 o4·:·Ideal·of·R37 o4·:·Ideal·of·R
38 i5·:·I1·==·I238 i5·:·I1·==·I2
  
39 o5·=·true39 o5·=·true
40 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*40 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
41 ····*·_\x8m_\x8i_\x8n_\x8o_\x8r_\x8s·--·ideal·generated·by·minors41 ····*·_\x8m_\x8i_\x8n_\x8o_\x8r_\x8s·--·ideal·generated·by·minors
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Offset 131, 23 lines modifiedOffset 131, 23 lines modified
  
131 o7·=·3</code></pre>131 o7·=·3</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S)136 ··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S)
137 ·--·used·0.560401s·(cpu);·0.457261s·(thread);·0s·(gc)137 ·--·used·0.670977s·(cpu);·0.534349s·(thread);·0s·(gc)
  
138 o8·=·true</code></pre>138 o8·=·true</code></pre>
139 ············</td>139 ············</td>
140 ··········</tr>140 ··········</tr>
141 ··········<tr>141 ··········<tr>
142 ············<td>142 ············<td>
143 ··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(2,·S)143 ··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(2,·S)
144 ·--·used·5.36049s·(cpu);·4.36718s·(thread);·0s·(gc)</code></pre>144 ·--·used·5.86324s·(cpu);·4.46668s·(thread);·0s·(gc)</code></pre>
145 ············</td>145 ············</td>
146 ··········</tr>146 ··········</tr>
147 ········</table>147 ········</table>
148 ········<div>148 ········<div>
149 ··········<p>There·are·numerous·examples·where·<span·class="tt">regularInCodimension</span>·is·several·orders·of·magnitude·faster·that·calls·of·<span·class="tt">dim·singularLocus</span>.</p>149 ··········<p>There·are·numerous·examples·where·<span·class="tt">regularInCodimension</span>·is·several·orders·of·magnitude·faster·that·calls·of·<span·class="tt">dim·singularLocus</span>.</p>
150 ········</div>150 ········</div>
151 ········<div>151 ········<div>
Offset 165, 39 lines modifiedOffset 165, 39 lines modified
  
165 o11·=·2</code></pre>165 o11·=·2</code></pre>
166 ············</td>166 ············</td>
167 ··········</tr>167 ··········</tr>
168 ··········<tr>168 ··········<tr>
169 ············<td>169 ············<td>
170 ··············<pre><code·class="language-macaulay2">i12·:·time·(dim·singularLocus·(R))170 ··············<pre><code·class="language-macaulay2">i12·:·time·(dim·singularLocus·(R))
171 ·--·used·0.0199633s·(cpu);·0.017094s·(thread);·0s·(gc)171 ·--·used·0.0196447s·(cpu);·0.0207464s·(thread);·0s·(gc)
  
172 o12·=·-1</code></pre>172 o12·=·-1</code></pre>
173 ············</td>173 ············</td>
174 ··········</tr>174 ··········</tr>
175 ··········<tr>175 ··········<tr>
176 ············<td>176 ············<td>
177 ··············<pre><code·class="language-macaulay2">i13·:·time·regularInCodimension(2,·R)177 ··············<pre><code·class="language-macaulay2">i13·:·time·regularInCodimension(2,·R)
178 ·--·used·0.206638s·(cpu);·0.145898s·(thread);·0s·(gc)178 ·--·used·0.211411s·(cpu);·0.152562s·(thread);·0s·(gc)
  
179 o13·=·true</code></pre>179 o13·=·true</code></pre>
180 ············</td>180 ············</td>
181 ··········</tr>181 ··········</tr>
182 ··········<tr>182 ··········<tr>
183 ············<td>183 ············<td>
184 ··············<pre><code·class="language-macaulay2">i14·:·time·regularInCodimension(2,·R)184 ··············<pre><code·class="language-macaulay2">i14·:·time·regularInCodimension(2,·R)
185 ·--·used·0.67702s·(cpu);·0.507263s·(thread);·0s·(gc)185 ·--·used·0.719451s·(cpu);·0.540277s·(thread);·0s·(gc)
  
186 o14·=·true</code></pre>186 o14·=·true</code></pre>
187 ············</td>187 ············</td>
188 ··········</tr>188 ··········</tr>
189 ··········<tr>189 ··········<tr>
190 ············<td>190 ············<td>
191 ··············<pre><code·class="language-macaulay2">i15·:·time·regularInCodimension(2,·R)191 ··············<pre><code·class="language-macaulay2">i15·:·time·regularInCodimension(2,·R)
192 ·--·used·1.09761s·(cpu);·0.834927s·(thread);·0s·(gc)192 ·--·used·1.1684s·(cpu);·0.877206s·(thread);·0s·(gc)
  
193 o15·=·true</code></pre>193 o15·=·true</code></pre>
194 ············</td>194 ············</td>
195 ··········</tr>195 ··········</tr>
196 ········</table>196 ········</table>
197 ········<div>197 ········<div>
198 ··········<p>The·function·works·by·choosing·interesting·looking·submatrices,·computing·their·determinants,·and·periodically·(based·on·a·logarithmic·growth·setting),·computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·<span·class="tt">Verbose</span>·can·be·used·to·see·this·in·action.</p>198 ··········<p>The·function·works·by·choosing·interesting·looking·submatrices,·computing·their·determinants,·and·periodically·(based·on·a·logarithmic·growth·setting),·computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·<span·class="tt">Verbose</span>·can·be·used·to·see·this·in·action.</p>
Offset 537, 15 lines modifiedOffset 537, 15 lines modified
537 internalChooseMinor:·Choosing·RandomNonZero537 internalChooseMinor:·Choosing·RandomNonZero
538 internalChooseMinor:·Choosing·GRevLexSmallestTerm538 internalChooseMinor:·Choosing·GRevLexSmallestTerm
539 internalChooseMinor:·Choosing·LexSmallestTerm539 internalChooseMinor:·Choosing·LexSmallestTerm
540 internalChooseMinor:·Choosing·GRevLexSmallest540 internalChooseMinor:·Choosing·GRevLexSmallest
541 internalChooseMinor:·Choosing·LexSmallestTerm541 internalChooseMinor:·Choosing·LexSmallestTerm
542 internalChooseMinor:·Choosing·LexSmallestTerm542 internalChooseMinor:·Choosing·LexSmallestTerm
543 internalChooseMinor:·Choosing·LexSmallestTerm543 internalChooseMinor:·Choosing·LexSmallestTerm
544 internalChooseMinor:·Ch·--·used·5.86363s·(cpu);·4.73632s·(thread);·0s·(gc)544 internalChooseMinor:·Ch·--·used·6.16394s·(cpu);·4.74013s·(thread);·0s·(gc)
545 oosing·GRevLexSmallestTerm545 oosing·GRevLexSmallestTerm
546 internalChooseMinor:·Choosing·RandomNonZero546 internalChooseMinor:·Choosing·RandomNonZero
547 internalChooseMinor:·Choosing·LexSmallest547 internalChooseMinor:·Choosing·LexSmallest
548 internalChooseMinor:·Choosing·Random548 internalChooseMinor:·Choosing·Random
549 internalChooseMinor:·Choosing·Random549 internalChooseMinor:·Choosing·Random
550 internalChooseMinor:·Choosing·LexSmallestTerm550 internalChooseMinor:·Choosing·LexSmallestTerm
551 internalChooseMinor:·Choosing·GRevLexSmallestTerm551 internalChooseMinor:·Choosing·GRevLexSmallestTerm
Offset 589, 15 lines modifiedOffset 589, 15 lines modified
589 ········<div>589 ········<div>
590 ··········<p>The·maximum·number·of·minors·considered·can·be·controlled·by·the·option·<span·class="tt">MaxMinors</span>.··Alternatively,·it·can·be·controlled·in·a·more·precise·way·by·passing·a·function·to·the·option·<span·class="tt">MaxMinors</span>.··This·function·should·have·two·inputs;·the·first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is·regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors·available·in·the·Jacobian.·The·function·<span·class="tt">regularInCodimension</span>·does·not·recompute·determinants,·so·<span·class="tt">MaxMinors</span>·or·is·only·an·upper·bound·on·the·number·of·minors·computed.</p>590 ··········<p>The·maximum·number·of·minors·considered·can·be·controlled·by·the·option·<span·class="tt">MaxMinors</span>.··Alternatively,·it·can·be·controlled·in·a·more·precise·way·by·passing·a·function·to·the·option·<span·class="tt">MaxMinors</span>.··This·function·should·have·two·inputs;·the·first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is·regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors·available·in·the·Jacobian.·The·function·<span·class="tt">regularInCodimension</span>·does·not·recompute·determinants,·so·<span·class="tt">MaxMinors</span>·or·is·only·an·upper·bound·on·the·number·of·minors·computed.</p>
591 ········</div>591 ········</div>
592 ········<table·class="examples">592 ········<table·class="examples">
593 ··········<tr>593 ··········<tr>
594 ············<td>594 ············<td>
595 ··············<pre><code·class="language-macaulay2">i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30)595 ··············<pre><code·class="language-macaulay2">i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30)
596 ·--·used·1.04494s·(cpu);·0.871997s·(thread);·0s·(gc)596 ·--·used·1.14834s·(cpu);·0.936411s·(thread);·0s·(gc)
597 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them.597 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them.
598 regularInCodimension:·About·to·enter·loop598 regularInCodimension:·About·to·enter·loop
599 internalChooseMinor:·Choosing·LexSmallestTerm599 internalChooseMinor:·Choosing·LexSmallestTerm
600 internalChooseMinor:·Choosing·LexSmallestTerm600 internalChooseMinor:·Choosing·LexSmallestTerm
601 internalChooseMinor:·Choosing·GRevLexSmallest601 internalChooseMinor:·Choosing·GRevLexSmallest
602 internalChooseMinor:·Choosing·GRevLexSmallest602 internalChooseMinor:·Choosing·GRevLexSmallest
603 internalChooseMinor:·Choosing·LexSmallestTerm603 internalChooseMinor:·Choosing·LexSmallestTerm
Offset 666, 39 lines modifiedOffset 666, 39 lines modified
666 ············<td>666 ············<td>
667 ··············<pre><code·class="language-macaulay2">i20·:·StrategyCurrent#LexSmallestTerm·=·0;</code></pre>667 ··············<pre><code·class="language-macaulay2">i20·:·StrategyCurrent#LexSmallestTerm·=·0;</code></pre>
668 ············</td>668 ············</td>
669 ··········</tr>669 ··········</tr>
670 ··········<tr>670 ··········<tr>
671 ············<td>671 ············<td>
672 ··············<pre><code·class="language-macaulay2">i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)672 ··············<pre><code·class="language-macaulay2">i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
673 ·--·used·0.301792s·(cpu);·0.215181s·(thread);·0s·(gc)673 ·--·used·0.286687s·(cpu);·0.210711s·(thread);·0s·(gc)
  
674 o21·=·true</code></pre>674 o21·=·true</code></pre>
675 ············</td>675 ············</td>
676 ··········</tr>676 ··········</tr>
677 ··········<tr>677 ··········<tr>
678 ············<td>678 ············<td>
679 ··············<pre><code·class="language-macaulay2">i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)679 ··············<pre><code·class="language-macaulay2">i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
680 ·--·used·0.0513809s·(cpu);·0.0533503s·(thread);·0s·(gc)680 ·--·used·0.104497s·(cpu);·0.0743239s·(thread);·0s·(gc)
  
681 o22·=·true</code></pre>681 o22·=·true</code></pre>
682 ············</td>682 ············</td>
683 ··········</tr>683 ··········</tr>
684 ··········<tr>684 ··········<tr>
685 ············<td>685 ············<td>
686 ··············<pre><code·class="language-macaulay2">i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)686 ··············<pre><code·class="language-macaulay2">i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
687 ·--·used·0.369614s·(cpu);·0.263567s·(thread);·0s·(gc)687 ·--·used·0.400751s·(cpu);·0.291657s·(thread);·0s·(gc)
  
688 o23·=·true</code></pre>688 o23·=·true</code></pre>
689 ············</td>689 ············</td>
690 ··········</tr>690 ··········</tr>
691 ··········<tr>691 ··········<tr>
692 ············<td>692 ············<td>
693 ··············<pre><code·class="language-macaulay2">i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)693 ··············<pre><code·class="language-macaulay2">i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
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Offset 72, 19 lines modifiedOffset 72, 19 lines modified
  
72 o5·:·Ideal·of·T72 o5·:·Ideal·of·T
73 i6·:·S·=·T/I;73 i6·:·S·=·T/I;
74 i7·:·dim·S74 i7·:·dim·S
  
75 o7·=·375 o7·=·3
76 i8·:·time·regularInCodimension(1,·S)76 i8·:·time·regularInCodimension(1,·S)
77 ·--·used·0.560401s·(cpu);·0.457261s·(thread);·0s·(gc)77 ·--·used·0.670977s·(cpu);·0.534349s·(thread);·0s·(gc)
  
78 o8·=·true78 o8·=·true
79 i9·:·time·regularInCodimension(2,·S)79 i9·:·time·regularInCodimension(2,·S)
80 ·--·used·5.36049s·(cpu);·4.36718s·(thread);·0s·(gc)80 ·--·used·5.86324s·(cpu);·4.46668s·(thread);·0s·(gc)
81 There·are·numerous·examples·where·regularInCodimension·is·several·orders·of81 There·are·numerous·examples·where·regularInCodimension·is·several·orders·of
82 magnitude·faster·that·calls·of·dim·singularLocus.82 magnitude·faster·that·calls·of·dim·singularLocus.
83 The·following·is·a·(pruned)·affine·chart·on·an·Abelian·surface·obtained·as·a83 The·following·is·a·(pruned)·affine·chart·on·an·Abelian·surface·obtained·as·a
84 product·of·two·elliptic·curves.·It·is·nonsingular,·as·our·function·verifies.·If84 product·of·two·elliptic·curves.·It·is·nonsingular,·as·our·function·verifies.·If
85 one·does·not·prune·it,·then·the·dim·singularLocus·call·takes·an·enormous·amount85 one·does·not·prune·it,·then·the·dim·singularLocus·call·takes·an·enormous·amount
86 of·time,·otherwise·the·running·times·of·dim·singularLocus·and·our·function·are86 of·time,·otherwise·the·running·times·of·dim·singularLocus·and·our·function·are
87 frequently·about·the·same.87 frequently·about·the·same.
Offset 92, 27 lines modifiedOffset 92, 27 lines modified
92 (g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3-92 (g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3-
93 f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h-93 f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h-
94 c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c);94 c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c);
95 i11·:·dim(R)95 i11·:·dim(R)
  
96 o11·=·296 o11·=·2
97 i12·:·time·(dim·singularLocus·(R))97 i12·:·time·(dim·singularLocus·(R))
98 ·--·used·0.0199633s·(cpu);·0.017094s·(thread);·0s·(gc)98 ·--·used·0.0196447s·(cpu);·0.0207464s·(thread);·0s·(gc)
  
99 o12·=·-199 o12·=·-1
100 i13·:·time·regularInCodimension(2,·R)100 i13·:·time·regularInCodimension(2,·R)
101 ·--·used·0.206638s·(cpu);·0.145898s·(thread);·0s·(gc)101 ·--·used·0.211411s·(cpu);·0.152562s·(thread);·0s·(gc)
  
102 o13·=·true102 o13·=·true
103 i14·:·time·regularInCodimension(2,·R)103 i14·:·time·regularInCodimension(2,·R)
104 ·--·used·0.67702s·(cpu);·0.507263s·(thread);·0s·(gc)104 ·--·used·0.719451s·(cpu);·0.540277s·(thread);·0s·(gc)
  
105 o14·=·true105 o14·=·true
106 i15·:·time·regularInCodimension(2,·R)106 i15·:·time·regularInCodimension(2,·R)
107 ·--·used·1.09761s·(cpu);·0.834927s·(thread);·0s·(gc)107 ·--·used·1.1684s·(cpu);·0.877206s·(thread);·0s·(gc)
  
108 o15·=·true108 o15·=·true
109 The·function·works·by·choosing·interesting·looking·submatrices,·computing·their109 The·function·works·by·choosing·interesting·looking·submatrices,·computing·their
110 determinants,·and·periodically·(based·on·a·logarithmic·growth·setting),110 determinants,·and·periodically·(based·on·a·logarithmic·growth·setting),
111 computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·Verbose·can111 computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·Verbose·can
112 be·used·to·see·this·in·action.112 be·used·to·see·this·in·action.
113 i16·:·time·regularInCodimension(2,·S,·Verbose=>true)113 i16·:·time·regularInCodimension(2,·S,·Verbose=>true)
Offset 461, 15 lines modifiedOffset 461, 15 lines modified
461 internalChooseMinor:·Choosing·RandomNonZero461 internalChooseMinor:·Choosing·RandomNonZero
462 internalChooseMinor:·Choosing·GRevLexSmallestTerm462 internalChooseMinor:·Choosing·GRevLexSmallestTerm
463 internalChooseMinor:·Choosing·LexSmallestTerm463 internalChooseMinor:·Choosing·LexSmallestTerm
464 internalChooseMinor:·Choosing·GRevLexSmallest464 internalChooseMinor:·Choosing·GRevLexSmallest
465 internalChooseMinor:·Choosing·LexSmallestTerm465 internalChooseMinor:·Choosing·LexSmallestTerm
466 internalChooseMinor:·Choosing·LexSmallestTerm466 internalChooseMinor:·Choosing·LexSmallestTerm
467 internalChooseMinor:·Choosing·LexSmallestTerm467 internalChooseMinor:·Choosing·LexSmallestTerm
468 internalChooseMinor:·Ch·--·used·5.86363s·(cpu);·4.73632s·(thread);·0s·(gc)468 internalChooseMinor:·Ch·--·used·6.16394s·(cpu);·4.74013s·(thread);·0s·(gc)
469 oosing·GRevLexSmallestTerm469 oosing·GRevLexSmallestTerm
470 internalChooseMinor:·Choosing·RandomNonZero470 internalChooseMinor:·Choosing·RandomNonZero
471 internalChooseMinor:·Choosing·LexSmallest471 internalChooseMinor:·Choosing·LexSmallest
472 internalChooseMinor:·Choosing·Random472 internalChooseMinor:·Choosing·Random
473 internalChooseMinor:·Choosing·Random473 internalChooseMinor:·Choosing·Random
474 internalChooseMinor:·Choosing·LexSmallestTerm474 internalChooseMinor:·Choosing·LexSmallestTerm
475 internalChooseMinor:·Choosing·GRevLexSmallestTerm475 internalChooseMinor:·Choosing·GRevLexSmallestTerm
Offset 515, 15 lines modifiedOffset 515, 15 lines modified
515 a·function·to·the·option·MaxMinors.·This·function·should·have·two·inputs;·the515 a·function·to·the·option·MaxMinors.·This·function·should·have·two·inputs;·the
516 first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is516 first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is
517 regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors517 regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors
518 available·in·the·Jacobian.·The·function·regularInCodimension·does·not·recompute518 available·in·the·Jacobian.·The·function·regularInCodimension·does·not·recompute
519 determinants,·so·MaxMinors·or·is·only·an·upper·bound·on·the·number·of·minors519 determinants,·so·MaxMinors·or·is·only·an·upper·bound·on·the·number·of·minors
520 computed.520 computed.
521 i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30)521 i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30)
522 ·--·used·1.04494s·(cpu);·0.871997s·(thread);·0s·(gc)522 ·--·used·1.14834s·(cpu);·0.936411s·(thread);·0s·(gc)
523 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4523 regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4
524 minors,·we·will·compute·up·to·30·of·them.524 minors,·we·will·compute·up·to·30·of·them.
525 regularInCodimension:·About·to·enter·loop525 regularInCodimension:·About·to·enter·loop
526 internalChooseMinor:·Choosing·LexSmallestTerm526 internalChooseMinor:·Choosing·LexSmallestTerm
527 internalChooseMinor:·Choosing·LexSmallestTerm527 internalChooseMinor:·Choosing·LexSmallestTerm
528 internalChooseMinor:·Choosing·GRevLexSmallest528 internalChooseMinor:·Choosing·GRevLexSmallest
529 internalChooseMinor:·Choosing·GRevLexSmallest529 internalChooseMinor:·Choosing·GRevLexSmallest
Offset 590, 51 lines modifiedOffset 590, 51 lines modified
590 because·there·are·a·small·number·of·entries·with·nonzero·constant·terms,·which590 because·there·are·a·small·number·of·entries·with·nonzero·constant·terms,·which
591 are·selected·repeatedly).·However,·in·our·first·example,·the·LexSmallestTerm·is591 are·selected·repeatedly).·However,·in·our·first·example,·the·LexSmallestTerm·is
592 much·faster,·and·Random·does·not·perform·well·at·all.592 much·faster,·and·Random·does·not·perform·well·at·all.
593 i18·:·StrategyCurrent#Random·=·0;593 i18·:·StrategyCurrent#Random·=·0;
594 i19·:·StrategyCurrent#LexSmallest·=·100;594 i19·:·StrategyCurrent#LexSmallest·=·100;
595 i20·:·StrategyCurrent#LexSmallestTerm·=·0;595 i20·:·StrategyCurrent#LexSmallestTerm·=·0;
596 i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)596 i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
597 ·--·used·0.301792s·(cpu);·0.215181s·(thread);·0s·(gc)597 ·--·used·0.286687s·(cpu);·0.210711s·(thread);·0s·(gc)
  
598 o21·=·true598 o21·=·true
599 i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)599 i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
600 ·--·used·0.0513809s·(cpu);·0.0533503s·(thread);·0s·(gc)600 ·--·used·0.104497s·(cpu);·0.0743239s·(thread);·0s·(gc)
  
601 o22·=·true601 o22·=·true
602 i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)602 i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
603 ·--·used·0.369614s·(cpu);·0.263567s·(thread);·0s·(gc)603 ·--·used·0.400751s·(cpu);·0.291657s·(thread);·0s·(gc)
  
604 o23·=·true604 o23·=·true
605 i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)605 i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
606 ·--·used·1.3687s·(cpu);·1.10557s·(thread);·0s·(gc)606 ·--·used·1.55547s·(cpu);·1.18638s·(thread);·0s·(gc)
  
607 o24·=·true607 o24·=·true
608 i25·:·StrategyCurrent#LexSmallest·=·0;608 i25·:·StrategyCurrent#LexSmallest·=·0;
609 i26·:·StrategyCurrent#LexSmallestTerm·=·100;609 i26·:·StrategyCurrent#LexSmallestTerm·=·100;
610 i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)610 i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
611 ·--·used·1.98781s·(cpu);·1.53708s·(thread);·0s·(gc)611 ·--·used·2.13142s·(cpu);·1.51813s·(thread);·0s·(gc)
612 i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)612 i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent)
613 ·--·used·1.9685s·(cpu);·1.48903s·(thread);·0s·(gc)613 ·--·used·2.12549s·(cpu);·1.49126s·(thread);·0s·(gc)
  
614 o28·=·true614 o28·=·true
615 i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)615 i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
616 ·--·used·0.361901s·(cpu);·0.299031s·(thread);·0s·(gc)616 ·--·used·0.362785s·(cpu);·0.280763s·(thread);·0s·(gc)
  
617 o29·=·true617 o29·=·true
618 i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)618 i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent)
619 ·--·used·0.618531s·(cpu);·0.516824s·(thread);·0s·(gc)619 ·--·used·0.621179s·(cpu);·0.507013s·(thread);·0s·(gc)
  
620 o30·=·true620 o30·=·true
621 i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom)621 i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom)
622 ·--·used·0.860727s·(cpu);·0.724494s·(thread);·0s·(gc)622 ·--·used·0.870384s·(cpu);·0.722456s·(thread);·0s·(gc)
  
623 o31·=·true623 o31·=·true
624 i32·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom)624 i32·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom)
625 ·--·used·1.3568s·(cpu);·1.13332s·(thread);·0s·(gc)625 ·--·used·1.46029s·(cpu);·1.18869s·(thread);·0s·(gc)
  
626 o32·=·true626 o32·=·true
627 The·minimum·number·of·minors·computed·before·checking·the·codimension·can·also627 The·minimum·number·of·minors·computed·before·checking·the·codimension·can·also
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759 B
./usr/share/doc/Macaulay2/FiniteFittingIdeals/dump/rawdocumentation.dump
    
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzU1LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzU1LCBzeW1ib2wgRG9jdW1lbnRUYWcg
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856 B
./usr/share/doc/Macaulay2/FiniteFittingIdeals/example-output/___Fitting_spideals_spof_spfinite_spmodules.out
    
Offset 81, 23 lines modifiedOffset 81, 23 lines modified
  
81 i14·:·K3=nextDegree(gens·ker·Q2,2,S);81 i14·:·K3=nextDegree(gens·ker·Q2,2,S);
  
82 ··············8······882 ··············8······8
83 o14·:·Matrix·R··<--·R83 o14·:·Matrix·R··<--·R
  
84 i15·:·time·I=co1Fitting(K3)84 i15·:·time·I=co1Fitting(K3)
85 ·--·used·0.00300436s·(cpu);·0.00243402s·(thread);·0s·(gc)85 ·--·used·0.000697437s·(cpu);·0.00251296s·(thread);·0s·(gc)
  
86 o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·)86 o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·)
87 ··············9·11····5····12···3·11····6···9·10····4····11···3·10····587 ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5
  
88 o15·:·Ideal·of·R88 o15·:·Ideal·of·R
  
89 i16·:·time·J=fittingIdeal(2-1,coker·K3);89 i16·:·time·J=fittingIdeal(2-1,coker·K3);
90 ·--·used·0.00554985s·(cpu);·0.0056673s·(thread);·0s·(gc)90 ·--·used·0.00527787s·(cpu);·0.00548762s·(thread);·0s·(gc)
  
91 o16·:·Ideal·of·R91 o16·:·Ideal·of·R
  
92 i17·:·I==J92 i17·:·I==J
  
93 o17·=·true93 o17·=·true
  
1.98 KB
./usr/share/doc/Macaulay2/FiniteFittingIdeals/html/___Fitting_spideals_spof_spfinite_spmodules.html
    
Offset 202, 26 lines modifiedOffset 202, 26 lines modified
202 ··············8······8202 ··············8······8
203 o14·:·Matrix·R··&lt;--·R</code></pre>203 o14·:·Matrix·R··&lt;--·R</code></pre>
204 ············</td>204 ············</td>
205 ··········</tr>205 ··········</tr>
206 ··········<tr>206 ··········<tr>
207 ············<td>207 ············<td>
208 ··············<pre><code·class="language-macaulay2">i15·:·time·I=co1Fitting(K3)208 ··············<pre><code·class="language-macaulay2">i15·:·time·I=co1Fitting(K3)
209 ·--·used·0.00300436s·(cpu);·0.00243402s·(thread);·0s·(gc)209 ·--·used·0.000697437s·(cpu);·0.00251296s·(thread);·0s·(gc)
  
210 o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·)210 o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·)
211 ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5211 ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5
  
212 o15·:·Ideal·of·R</code></pre>212 o15·:·Ideal·of·R</code></pre>
213 ············</td>213 ············</td>
214 ··········</tr>214 ··········</tr>
215 ··········<tr>215 ··········<tr>
216 ············<td>216 ············<td>
217 ··············<pre><code·class="language-macaulay2">i16·:·time·J=fittingIdeal(2-1,coker·K3);217 ··············<pre><code·class="language-macaulay2">i16·:·time·J=fittingIdeal(2-1,coker·K3);
218 ·--·used·0.00554985s·(cpu);·0.0056673s·(thread);·0s·(gc)218 ·--·used·0.00527787s·(cpu);·0.00548762s·(thread);·0s·(gc)
  
219 o16·:·Ideal·of·R</code></pre>219 o16·:·Ideal·of·R</code></pre>
220 ············</td>220 ············</td>
221 ··········</tr>221 ··········</tr>
222 ··········<tr>222 ··········<tr>
223 ············<td>223 ············<td>
224 ··············<pre><code·class="language-macaulay2">i17·:·I==J224 ··············<pre><code·class="language-macaulay2">i17·:·I==J
846 B
html2text {}
    
Offset 95, 22 lines modifiedOffset 95, 22 lines modified
95 ··············2······695 ··············2······6
96 o13·:·Matrix·R··<--·R96 o13·:·Matrix·R··<--·R
97 i14·:·K3=nextDegree(gens·ker·Q2,2,S);97 i14·:·K3=nextDegree(gens·ker·Q2,2,S);
  
98 ··············8······898 ··············8······8
99 o14·:·Matrix·R··<--·R99 o14·:·Matrix·R··<--·R
100 i15·:·time·I=co1Fitting(K3)100 i15·:·time·I=co1Fitting(K3)
101 ·--·used·0.00300436s·(cpu);·0.00243402s·(thread);·0s·(gc)101 ·--·used·0.000697437s·(cpu);·0.00251296s·(thread);·0s·(gc)
  
102 o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·)102 o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·)
103 ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5103 ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5
  
104 o15·:·Ideal·of·R104 o15·:·Ideal·of·R
105 i16·:·time·J=fittingIdeal(2-1,coker·K3);105 i16·:·time·J=fittingIdeal(2-1,coker·K3);
106 ·--·used·0.00554985s·(cpu);·0.0056673s·(thread);·0s·(gc)106 ·--·used·0.00527787s·(cpu);·0.00548762s·(thread);·0s·(gc)
  
107 o16·:·Ideal·of·R107 o16·:·Ideal·of·R
108 i17·:·I==J108 i17·:·I==J
  
109 o17·=·true109 o17·=·true
110 Note·that·our·method·is·a·bit·faster·for·this·small·example,·and·for·rank·2110 Note·that·our·method·is·a·bit·faster·for·this·small·example,·and·for·rank·2
111 quotients·of·S^3=\mathbb{Z}[x,y]^3·the·time·difference·is·massive.111 quotients·of·S^3=\mathbb{Z}[x,y]^3·the·time·difference·is·massive.
725 B
./usr/share/doc/Macaulay2/FirstPackage/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=127 #:len=12
8 Rmlyc3RQYWNrYWdl8 Rmlyc3RQYWNrYWdl
9 #:len=5099 #:len=509
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZXhhbXBsZSBNYWNhdWxheTIgcGFj10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZXhhbXBsZSBNYWNhdWxheTIgcGFj
11 a2FnZSIsICJsaW5lbnVtIiA9PiA1MywgImZpbGVuYW1lIiA9PiAiRmlyc3RQYWNrYWdlLm0yIiwg11 a2FnZSIsICJsaW5lbnVtIiA9PiA1MywgImZpbGVuYW1lIiA9PiAiRmlyc3RQYWNrYWdlLm0yIiwg
737 B
./usr/share/doc/Macaulay2/ForeignFunctions/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=137 #:len=13
8 dmFsdWUodWludDE2KQ==8 dmFsdWUodWludDE2KQ==
9 #:len=2739 #:len=273
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTcwNywgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTcwNywgc3ltYm9sIERvY3VtZW50VGFn
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429 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Foreign__Object.out
    
Offset 4, 19 lines modifiedOffset 4, 19 lines modified
  
4 o1·=·54 o1·=·5
  
5 o1·:·ForeignObject·of·type·int325 o1·:·ForeignObject·of·type·int32
  
6 i2·:·peek·x6 i2·:·peek·x
  
7 o2·=·int32{Address·=>·0x7f3a17455360}7 o2·=·int32{Address·=>·0x7fc1ce448300}
  
8 i3·:·address·x8 i3·:·address·x
  
9 o3·=·0x7f3a174553609 o3·=·0x7fc1ce448300
  
10 o3·:·Pointer10 o3·:·Pointer
  
11 i4·:·class·x11 i4·:·class·x
  
12 o4·=·int3212 o4·=·int32
  
596 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Foreign__Pointer__Array__Type.out
    
Offset 11, 15 lines modifiedOffset 11, 15 lines modified
  
11 o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog}11 o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog}
  
12 o2·:·ForeignObject·of·type·char**12 o2·:·ForeignObject·of·type·char**
  
13 i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}13 i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}
  
14 o3·=·{0x7fe3d3ca8ab0,·0x7fe3d3ca8a90,·0x7fe3d3ca8a80}14 o3·=·{0x7fe0ab7d03b0,·0x7fe0ab7d03a0,·0x7fe0ab7d0390}
  
15 o3·:·ForeignObject·of·type·void**15 o3·:·ForeignObject·of·type·void**
  
16 i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"}16 i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"}
  
17 o4·=·{foo,·bar,·baz}17 o4·=·{foo,·bar,·baz}
  
586 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Foreign__Pointer__Array__Type_sp__Visible__List.out
    
Offset 4, 15 lines modifiedOffset 4, 15 lines modified
  
4 o1·=·{foo,·bar}4 o1·=·{foo,·bar}
  
5 o1·:·ForeignObject·of·type·char**5 o1·:·ForeignObject·of·type·char**
  
6 i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}6 i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}
  
7 o2·=·{0x7f20bc884970,·0x7f20bc884960,·0x7f20bc884950}7 o2·=·{0x7f487a0d5f10,·0x7f487a0d5f00,·0x7f487a0d5ef0}
  
8 o2·:·ForeignObject·of·type·void**8 o2·:·ForeignObject·of·type·void**
  
9 i3·:·int2star·=·foreignPointerArrayType(2·*·int)9 i3·:·int2star·=·foreignPointerArrayType(2·*·int)
  
10 o3·=·int32[2]*10 o3·=·int32[2]*
  
462 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Foreign__Pointer__Type_sp__Pointer.out
    
Offset 1, 15 lines modifiedOffset 1, 15 lines modified
1 --·-*-·M2-comint·-*-·hash:·17308351698883994501 --·-*-·M2-comint·-*-·hash:·1730835169888399450
  
2 i1·:·ptr·=·address·int·02 i1·:·ptr·=·address·int·0
  
3 o1·=·0x7f39cb8d0ed03 o1·=·0x7ff3dd18c070
  
4 o1·:·Pointer4 o1·:·Pointer
  
5 i2·:·voidstar·ptr5 i2·:·voidstar·ptr
  
6 o2·=·0x7f39cb8d0ed06 o2·=·0x7ff3dd18c070
  
7 o2·:·ForeignObject·of·type·void*7 o2·:·ForeignObject·of·type·void*
  
8 i3·:·8 i3·:·
356 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Foreign__Type_sp__Pointer.out
    
Offset 4, 15 lines modifiedOffset 4, 15 lines modified
  
4 o1·=·54 o1·=·5
  
5 o1·:·ForeignObject·of·type·int325 o1·:·ForeignObject·of·type·int32
  
6 i2·:·ptr·=·address·x6 i2·:·ptr·=·address·x
  
7 o2·=·0x7f16e0c0f9907 o2·=·0x7f80484025c0
  
8 o2·:·Pointer8 o2·:·Pointer
  
9 i3·:·int·ptr9 i3·:·int·ptr
  
10 o3·=·510 o3·=·5
  
403 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Foreign__Type_sp_st_spvoidstar.out
    
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1 --·-*-·M2-comint·-*-·hash:·17312308291836839301 --·-*-·M2-comint·-*-·hash:·1731230829183683930
  
2 i1·:·ptr·=·voidstar·address·int·52 i1·:·ptr·=·voidstar·address·int·5
  
3 o1·=·0x7fb46d4204203 o1·=·0x7f933a65adb0
  
4 o1·:·ForeignObject·of·type·void*4 o1·:·ForeignObject·of·type·void*
  
5 i2·:·int·*·ptr5 i2·:·int·*·ptr
  
6 o2·=·56 o2·=·5
  
472 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Foreign__Union__Type_sp__Thing.out
    
Offset 4, 15 lines modifiedOffset 4, 15 lines modified
  
4 o1·=·myunion4 o1·=·myunion
  
5 o1·:·ForeignUnionType5 o1·:·ForeignUnionType
  
6 i2·:·myunion·276 i2·:·myunion·27
  
7 o2·=·HashTable{"bar"·=>·6.94614e-310}7 o2·=·HashTable{"bar"·=>·6.92683e-310}
8 ···············"foo"·=>·278 ···············"foo"·=>·27
  
9 o2·:·ForeignObject·of·type·myunion9 o2·:·ForeignObject·of·type·myunion
  
10 i3·:·myunion·pi10 i3·:·myunion·pi
  
11 o3·=·HashTable{"bar"·=>·3.14159···}11 o3·=·HashTable{"bar"·=>·3.14159···}
549 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Pointer.out
    
Offset 4, 28 lines modifiedOffset 4, 28 lines modified
  
4 o1·=·204 o1·=·20
  
5 o1·:·ForeignObject·of·type·int325 o1·:·ForeignObject·of·type·int32
  
6 i2·:·peek·x6 i2·:·peek·x
  
7 o2·=·int32{Address·=>·0x7f2213081d90}7 o2·=·int32{Address·=>·0x7f477a7d0c80}
  
8 i3·:·ptr·=·address·x8 i3·:·ptr·=·address·x
  
9 o3·=·0x7f2213081d909 o3·=·0x7f477a7d0c80
  
10 o3·:·Pointer10 o3·:·Pointer
  
11 i4·:·ptr·+·511 i4·:·ptr·+·5
  
12 o4·=·0x7f2213081d9512 o4·=·0x7f477a7d0c85
  
13 o4·:·Pointer13 o4·:·Pointer
  
14 i5·:·ptr·-·314 i5·:·ptr·-·3
  
15 o5·=·0x7f2213081d8d15 o5·=·0x7f477a7d0c7d
  
16 o5·:·Pointer16 o5·:·Pointer
  
17 i6·:·17 i6·:·
326 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/___Shared__Library.out
    
Offset 4, 10 lines modifiedOffset 4, 10 lines modified
  
4 o1·=·mpfr4 o1·=·mpfr
  
5 o1·:·SharedLibrary5 o1·:·SharedLibrary
  
6 i2·:·peek·mpfr6 i2·:·peek·mpfr
  
7 o2·=·SharedLibrary{0x7fa11dc8f550,·mpfr}7 o2·=·SharedLibrary{0x7f7e2e48f550,·mpfr}
  
8 i3·:·8 i3·:·
367 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/__st_spvoidstar_sp_eq_sp__Thing.out
    
Offset 4, 15 lines modifiedOffset 4, 15 lines modified
  
4 o1·=·54 o1·=·5
  
5 o1·:·ForeignObject·of·type·int325 o1·:·ForeignObject·of·type·int32
  
6 i2·:·ptr·=·address·x6 i2·:·ptr·=·address·x
  
7 o2·=·0x7f59dc9468e07 o2·=·0x7fc7cb42f720
  
8 o2·:·Pointer8 o2·:·Pointer
  
9 i3·:·*ptr·=·int·69 i3·:·*ptr·=·int·6
  
10 o3·=·610 o3·=·6
  
377 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/_address.out
    
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1 --·-*-·M2-comint·-*-·hash:·17301818843773735951 --·-*-·M2-comint·-*-·hash:·1730181884377373595
  
2 i1·:·address·int2 i1·:·address·int
  
3 o1·=·0x55fb750afac03 o1·=·0x56296d549ac0
  
4 o1·:·Pointer4 o1·:·Pointer
  
5 i2·:·address·int·55 i2·:·address·int·5
  
6 o2·=·0x7fb0084371506 o2·=·0x7fb645c9c480
  
7 o2·:·Pointer7 o2·:·Pointer
  
8 i3·:·8 i3·:·
370 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/_foreign__Function.out
    
Offset 78, 14 lines modifiedOffset 78, 14 lines modified
  
78 o16·=·free78 o16·=·free
  
79 o16·:·ForeignFunction79 o16·:·ForeignFunction
  
80 i17·:·x·=·malloc·880 i17·:·x·=·malloc·8
  
81 o17·=·0x7ff21c06a85081 o17·=·0x7fc6a406a850
  
82 o17·:·ForeignObject·of·type·void*82 o17·:·ForeignObject·of·type·void*
  
83 i18·:·registerFinalizer(x,·free)83 i18·:·registerFinalizer(x,·free)
  
84 i19·:·84 i19·:·
561 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/_get__Memory.out
    
Offset 1, 21 lines modifiedOffset 1, 21 lines modified
1 --·-*-·M2-comint·-*-·hash:·106479884127672803101 --·-*-·M2-comint·-*-·hash:·10647988412767280310
  
2 i1·:·ptr·=·getMemory·82 i1·:·ptr·=·getMemory·8
  
3 o1·=·0x7faaa5d813503 o1·=·0x7f158357d250
  
4 o1·:·ForeignObject·of·type·void*4 o1·:·ForeignObject·of·type·void*
  
5 i2·:·ptr·=·getMemory(8,·Atomic·=>·true)5 i2·:·ptr·=·getMemory(8,·Atomic·=>·true)
  
6 o2·=·0x7faaa42c00906 o2·=·0x7f1582234010
  
7 o2·:·ForeignObject·of·type·void*7 o2·:·ForeignObject·of·type·void*
  
8 i3·:·ptr·=·getMemory·int8 i3·:·ptr·=·getMemory·int
  
9 o3·=·0x7faaa3c0ffa09 o3·=·0x7f158225af10
  
10 o3·:·ForeignObject·of·type·void*10 o3·:·ForeignObject·of·type·void*
  
11 i4·:·11 i4·:·
1.02 KB
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/_register__Finalizer_lp__Foreign__Object_cm__Function_rp.out
    
Offset 17, 18 lines modifiedOffset 17, 18 lines modified
17 o3·=·finalizer17 o3·=·finalizer
  
18 o3·:·FunctionClosure18 o3·:·FunctionClosure
  
19 i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))19 i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))
  
20 i5·:·collectGarbage()20 i5·:·collectGarbage()
 21 freeing·memory·at·0x7f8b4c0709e0freeing·memory·at·0x7f8b4c065de0
21 freeing·memory·at·0x7f8f0c06aa4022 freeing·memory·at·0x7f8b4c06aa40
22 freeing·memory·at·0x7f8f0c072340 
23 freeing·memory·at·0x7f8f0c070cc0 
24 freeing·memory·at·0x7f8f0c0709e0 
25 freeing·memory·at·0x7f8f0c004f20 
26 freeing·memory·at·0x7f8f0c0705b0 
27 freeing·memory·at·0x7f8f0c06a85023 freeing·memory·at·0x7f8b4c06a850
 24 freeing·memory·at·0x7f8b4c070cc0
28 freeing·memory·at·0x7f8f0c070a0025 freeing·memory·at·0x7f8b4c070a00
 26 freeing·memory·at·0x7f8b4c072340
29 freeing·memory·at·0x7f8f0c065de027 freeing·memory·at·0x7f8b4c0705b0
 28 freeing·memory·at·0x7f8b4c0709e0
 29 freeing·memory·at·0x7f8b4c004f20
  
30 i6·:·30 i6·:·
493 B
./usr/share/doc/Macaulay2/ForeignFunctions/example-output/_value_lp__Foreign__Object_rp.out
    
Offset 20, 21 lines modifiedOffset 20, 21 lines modified
  
20 o4·=·520 o4·=·5
  
21 o4·:·RR·(of·precision·53)21 o4·:·RR·(of·precision·53)
  
22 i5·:·x·=·voidstar·address·int·522 i5·:·x·=·voidstar·address·int·5
  
23 o5·=·0x7efd6f731ec023 o5·=·0x7f2e8c6d96e0
  
24 o5·:·ForeignObject·of·type·void*24 o5·:·ForeignObject·of·type·void*
  
25 i6·:·value·x25 i6·:·value·x
  
26 o6·=·0x7efd6f731ec026 o6·=·0x7f2e8c6d96e0
  
27 o6·:·Pointer27 o6·:·Pointer
  
28 i7·:·x·=·charstar·"Hello,·world!"28 i7·:·x·=·charstar·"Hello,·world!"
  
29 o7·=·Hello,·world!29 o7·=·Hello,·world!
  
1.43 KB
./usr/share/doc/Macaulay2/ForeignFunctions/html/___Foreign__Object.html
    
Offset 64, 27 lines modifiedOffset 64, 27 lines modified
64 o1·:·ForeignObject·of·type·int32</code></pre>64 o1·:·ForeignObject·of·type·int32</code></pre>
65 ············</td>65 ············</td>
66 ··········</tr>66 ··········</tr>
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i2·:·peek·x69 ··············<pre><code·class="language-macaulay2">i2·:·peek·x
  
70 o2·=·int32{Address·=>·0x7f3a17455360}</code></pre>70 o2·=·int32{Address·=>·0x7fc1ce448300}</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ········</table>73 ········</table>
74 ········<div>74 ········<div>
75 ··········<p>To·get·this,·use·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p>75 ··········<p>To·get·this,·use·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p>
76 ········</div>76 ········</div>
77 ········<table·class="examples">77 ········<table·class="examples">
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i3·:·address·x80 ··············<pre><code·class="language-macaulay2">i3·:·address·x
  
81 o3·=·0x7f3a1745536081 o3·=·0x7fc1ce448300
  
82 o3·:·Pointer</code></pre>82 o3·:·Pointer</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ········</table>85 ········</table>
86 ········<div>86 ········<div>
87 ··········<p>Use·<a·title="class·of·an·object"·href="../../Macaulay2Doc/html/_class.html">class</a>·to·determine·the·type·of·the·object.</p>87 ··········<p>Use·<a·title="class·of·an·object"·href="../../Macaulay2Doc/html/_class.html">class</a>·to·determine·the·type·of·the·object.</p>
404 B
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10 i1·:·x·=·int·510 i1·:·x·=·int·5
  
11 o1·=·511 o1·=·5
  
12 o1·:·ForeignObject·of·type·int3212 o1·:·ForeignObject·of·type·int32
13 i2·:·peek·x13 i2·:·peek·x
  
14 o2·=·int32{Address·=>·0x7f3a17455360}14 o2·=·int32{Address·=>·0x7fc1ce448300}
15 To·get·this,·use·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s.15 To·get·this,·use·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s.
16 i3·:·address·x16 i3·:·address·x
  
17 o3·=·0x7f3a1745536017 o3·=·0x7fc1ce448300
  
18 o3·:·Pointer18 o3·:·Pointer
19 Use·_\x8c_\x8l_\x8a_\x8s_\x8s·to·determine·the·type·of·the·object.19 Use·_\x8c_\x8l_\x8a_\x8s_\x8s·to·determine·the·type·of·the·object.
20 i4·:·class·x20 i4·:·class·x
  
21 o4·=·int3221 o4·=·int32
  
1.32 KB
./usr/share/doc/Macaulay2/ForeignFunctions/html/___Foreign__Pointer__Array__Type.html
    
Offset 74, 15 lines modifiedOffset 74, 15 lines modified
74 o2·:·ForeignObject·of·type·char**</code></pre>74 o2·:·ForeignObject·of·type·char**</code></pre>
75 ············</td>75 ············</td>
76 ··········</tr>76 ··········</tr>
77 ··········<tr>77 ··········<tr>
78 ············<td>78 ············<td>
79 ··············<pre><code·class="language-macaulay2">i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}79 ··············<pre><code·class="language-macaulay2">i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}
  
80 o3·=·{0x7fe3d3ca8ab0,·0x7fe3d3ca8a90,·0x7fe3d3ca8a80}80 o3·=·{0x7fe0ab7d03b0,·0x7fe0ab7d03a0,·0x7fe0ab7d0390}
  
81 o3·:·ForeignObject·of·type·void**</code></pre>81 o3·:·ForeignObject·of·type·void**</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ········</table>84 ········</table>
85 ········<div>85 ········<div>
86 ··········<p>Foreign·pointer·arrays·may·be·subscripted·using·<a·title="a·binary·operator,·used·for·subscripting·and·access·to·elements"·href="../../Macaulay2Doc/html/__us.html">_</a>.</p>86 ··········<p>Foreign·pointer·arrays·may·be·subscripted·using·<a·title="a·binary·operator,·used·for·subscripting·and·access·to·elements"·href="../../Macaulay2Doc/html/__us.html">_</a>.</p>
507 B
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20 ·········"lazy",·"dog"}20 ·········"lazy",·"dog"}
  
21 o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog}21 o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog}
  
22 o2·:·ForeignObject·of·type·char**22 o2·:·ForeignObject·of·type·char**
23 i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}23 i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}
  
24 o3·=·{0x7fe3d3ca8ab0,·0x7fe3d3ca8a90,·0x7fe3d3ca8a80}24 o3·=·{0x7fe0ab7d03b0,·0x7fe0ab7d03a0,·0x7fe0ab7d0390}
  
25 o3·:·ForeignObject·of·type·void**25 o3·:·ForeignObject·of·type·void**
26 Foreign·pointer·arrays·may·be·subscripted·using·_\x8_.26 Foreign·pointer·arrays·may·be·subscripted·using·_\x8_.
27 i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"}27 i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"}
  
28 o4·=·{foo,·bar,·baz}28 o4·=·{foo,·bar,·baz}
  
1.21 KB
./usr/share/doc/Macaulay2/ForeignFunctions/html/___Foreign__Pointer__Array__Type_sp__Visible__List.html
    
Offset 82, 15 lines modifiedOffset 82, 15 lines modified
82 o1·:·ForeignObject·of·type·char**</code></pre>82 o1·:·ForeignObject·of·type·char**</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}87 ··············<pre><code·class="language-macaulay2">i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}
  
88 o2·=·{0x7f20bc884970,·0x7f20bc884960,·0x7f20bc884950}88 o2·=·{0x7f487a0d5f10,·0x7f487a0d5f00,·0x7f487a0d5ef0}
  
89 o2·:·ForeignObject·of·type·void**</code></pre>89 o2·:·ForeignObject·of·type·void**</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·int2star·=·foreignPointerArrayType(2·*·int)94 ··············<pre><code·class="language-macaulay2">i3·:·int2star·=·foreignPointerArrayType(2·*·int)
448 B
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20 i1·:·charstarstar·{"foo",·"bar"}20 i1·:·charstarstar·{"foo",·"bar"}
  
21 o1·=·{foo,·bar}21 o1·=·{foo,·bar}
  
22 o1·:·ForeignObject·of·type·char**22 o1·:·ForeignObject·of·type·char**
23 i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}23 i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2}
  
24 o2·=·{0x7f20bc884970,·0x7f20bc884960,·0x7f20bc884950}24 o2·=·{0x7f487a0d5f10,·0x7f487a0d5f00,·0x7f487a0d5ef0}
  
25 o2·:·ForeignObject·of·type·void**25 o2·:·ForeignObject·of·type·void**
26 i3·:·int2star·=·foreignPointerArrayType(2·*·int)26 i3·:·int2star·=·foreignPointerArrayType(2·*·int)
  
27 o3·=·int32[2]*27 o3·=·int32[2]*
  
28 o3·:·ForeignPointerArrayType28 o3·:·ForeignPointerArrayType
1.71 KB
./usr/share/doc/Macaulay2/ForeignFunctions/html/___Foreign__Pointer__Type_sp__Pointer.html
    
Offset 73, 24 lines modifiedOffset 73, 24 lines modified
73 ··········<p>To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the·type·followed·by·the·pointer.</p>73 ··········<p>To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the·type·followed·by·the·pointer.</p>
74 ········</div>74 ········</div>
75 ········<table·class="examples">75 ········<table·class="examples">
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i1·:·ptr·=·address·int·078 ··············<pre><code·class="language-macaulay2">i1·:·ptr·=·address·int·0
  
79 o1·=·0x7f39cb8d0ed079 o1·=·0x7ff3dd18c070
  
80 o1·:·Pointer</code></pre>80 o1·:·Pointer</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·voidstar·ptr85 ··············<pre><code·class="language-macaulay2">i2·:·voidstar·ptr
  
86 o2·=·0x7f39cb8d0ed086 o2·=·0x7ff3dd18c070
  
87 o2·:·ForeignObject·of·type·void*</code></pre>87 o2·:·ForeignObject·of·type·void*</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ········</table>90 ········</table>
91 ······</div>91 ······</div>
92 ······<div>92 ······<div>
873 B
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15 ····*·Outputs:15 ····*·Outputs:
16 ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,16 ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,
17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
18 To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the18 To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the
19 type·followed·by·the·pointer.19 type·followed·by·the·pointer.
20 i1·:·ptr·=·address·int·020 i1·:·ptr·=·address·int·0
  
21 o1·=·0x7f39cb8d0ed021 o1·=·0x7ff3dd18c070
  
22 o1·:·Pointer22 o1·:·Pointer
23 i2·:·voidstar·ptr23 i2·:·voidstar·ptr
  
24 o2·=·0x7f39cb8d0ed024 o2·=·0x7ff3dd18c070
  
25 o2·:·ForeignObject·of·type·void*25 o2·:·ForeignObject·of·type·void*
26 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
27 ····*·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·cast·a·Macaulay2·pointer·to·a·foreign27 ····*·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·cast·a·Macaulay2·pointer·to·a·foreign
28 ······pointer28 ······pointer
29 ===============================================================================29 ===============================================================================
30 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-30 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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82 o1·:·ForeignObject·of·type·int32</code></pre>82 o1·:·ForeignObject·of·type·int32</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x87 ··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x
  
88 o2·=·0x7f16e0c0f99088 o2·=·0x7f80484025c0
  
89 o2·:·Pointer</code></pre>89 o2·:·Pointer</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·int·ptr94 ··············<pre><code·class="language-macaulay2">i3·:·int·ptr
248 B
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18 i1·:·x·=·int·518 i1·:·x·=·int·5
  
19 o1·=·519 o1·=·5
  
20 o1·:·ForeignObject·of·type·int3220 o1·:·ForeignObject·of·type·int32
21 i2·:·ptr·=·address·x21 i2·:·ptr·=·address·x
  
22 o2·=·0x7f16e0c0f99022 o2·=·0x7f80484025c0
  
23 o2·:·Pointer23 o2·:·Pointer
24 i3·:·int·ptr24 i3·:·int·ptr
  
25 o3·=·525 o3·=·5
  
26 o3·:·ForeignObject·of·type·int3226 o3·:·ForeignObject·of·type·int32
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73 ··········<p>This·is·syntactic·sugar·for·<code·class="language-macaulay2">T·value·ptr</code>·(see·<a·title="dereference·a·pointer"·href="___Foreign__Type_sp__Pointer.html">ForeignType·Pointer</a>)·for·dereferencing·pointers.</p>73 ··········<p>This·is·syntactic·sugar·for·<code·class="language-macaulay2">T·value·ptr</code>·(see·<a·title="dereference·a·pointer"·href="___Foreign__Type_sp__Pointer.html">ForeignType·Pointer</a>)·for·dereferencing·pointers.</p>
74 ········</div>74 ········</div>
75 ········<table·class="examples">75 ········<table·class="examples">
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i1·:·ptr·=·voidstar·address·int·578 ··············<pre><code·class="language-macaulay2">i1·:·ptr·=·voidstar·address·int·5
  
79 o1·=·0x7fb46d42042079 o1·=·0x7f933a65adb0
  
80 o1·:·ForeignObject·of·type·void*</code></pre>80 o1·:·ForeignObject·of·type·void*</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·int·*·ptr85 ··············<pre><code·class="language-macaulay2">i2·:·int·*·ptr
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14 ····*·Outputs:14 ····*·Outputs:
15 ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,·of·type·T;15 ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,·of·type·T;
16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
17 This·is·syntactic·sugar·for·T·value·ptr·(see·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r)·for17 This·is·syntactic·sugar·for·T·value·ptr·(see·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r)·for
18 dereferencing·pointers.18 dereferencing·pointers.
19 i1·:·ptr·=·voidstar·address·int·519 i1·:·ptr·=·voidstar·address·int·5
  
20 o1·=·0x7fb46d42042020 o1·=·0x7f933a65adb0
  
21 o1·:·ForeignObject·of·type·void*21 o1·:·ForeignObject·of·type·void*
22 i2·:·int·*·ptr22 i2·:·int·*·ptr
  
23 o2·=·523 o2·=·5
  
24 o2·:·ForeignObject·of·type·int3224 o2·:·ForeignObject·of·type·int32
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82 o1·:·ForeignUnionType</code></pre>82 o1·:·ForeignUnionType</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i2·:·myunion·2787 ··············<pre><code·class="language-macaulay2">i2·:·myunion·27
  
88 o2·=·HashTable{&quot;bar&quot;·=>·6.94614e-310}88 o2·=·HashTable{&quot;bar&quot;·=>·6.92683e-310}
89 ···············&quot;foo&quot;·=>·2789 ···············&quot;foo&quot;·=>·27
  
90 o2·:·ForeignObject·of·type·myunion</code></pre>90 o2·:·ForeignObject·of·type·myunion</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
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20 i1·:·myunion·=·foreignUnionType("myunion",·{"foo"·=>·int,·"bar"·=>·double})20 i1·:·myunion·=·foreignUnionType("myunion",·{"foo"·=>·int,·"bar"·=>·double})
  
21 o1·=·myunion21 o1·=·myunion
  
22 o1·:·ForeignUnionType22 o1·:·ForeignUnionType
23 i2·:·myunion·2723 i2·:·myunion·27
  
24 o2·=·HashTable{"bar"·=>·6.94614e-310}24 o2·=·HashTable{"bar"·=>·6.92683e-310}
25 ···············"foo"·=>·2725 ···············"foo"·=>·27
  
26 o2·:·ForeignObject·of·type·myunion26 o2·:·ForeignObject·of·type·myunion
27 i3·:·myunion·pi27 i3·:·myunion·pi
  
28 o3·=·HashTable{"bar"·=>·3.14159···}28 o3·=·HashTable{"bar"·=>·3.14159···}
29 ···············"foo"·=>·141375413629 ···············"foo"·=>·1413754136
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64 o1·:·ForeignObject·of·type·int32</code></pre>64 o1·:·ForeignObject·of·type·int32</code></pre>
65 ············</td>65 ············</td>
66 ··········</tr>66 ··········</tr>
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i2·:·peek·x69 ··············<pre><code·class="language-macaulay2">i2·:·peek·x
  
70 o2·=·int32{Address·=>·0x7f2213081d90}</code></pre>70 o2·=·int32{Address·=>·0x7f477a7d0c80}</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ········</table>73 ········</table>
74 ········<div>74 ········<div>
75 ··········<p>These·pointers·can·be·accessed·using·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p>75 ··········<p>These·pointers·can·be·accessed·using·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p>
76 ········</div>76 ········</div>
77 ········<table·class="examples">77 ········<table·class="examples">
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i3·:·ptr·=·address·x80 ··············<pre><code·class="language-macaulay2">i3·:·ptr·=·address·x
  
81 o3·=·0x7f2213081d9081 o3·=·0x7f477a7d0c80
  
82 o3·:·Pointer</code></pre>82 o3·:·Pointer</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ········</table>85 ········</table>
86 ········<div>86 ········<div>
87 ··········<p>Simple·arithmetic·can·be·performed·on·pointers.</p>87 ··········<p>Simple·arithmetic·can·be·performed·on·pointers.</p>
88 ········</div>88 ········</div>
89 ········<table·class="examples">89 ········<table·class="examples">
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i4·:·ptr·+·592 ··············<pre><code·class="language-macaulay2">i4·:·ptr·+·5
  
93 o4·=·0x7f2213081d9593 o4·=·0x7f477a7d0c85
  
94 o4·:·Pointer</code></pre>94 o4·:·Pointer</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i5·:·ptr·-·399 ··············<pre><code·class="language-macaulay2">i5·:·ptr·-·3
  
100 o5·=·0x7f2213081d8d100 o5·=·0x7f477a7d0c7d
  
101 o5·:·Pointer</code></pre>101 o5·:·Pointer</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ········</table>104 ········</table>
105 ······</div>105 ······</div>
106 ······<div>106 ······<div>
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10 i1·:·x·=·int·2010 i1·:·x·=·int·20
  
11 o1·=·2011 o1·=·20
  
12 o1·:·ForeignObject·of·type·int3212 o1·:·ForeignObject·of·type·int32
13 i2·:·peek·x13 i2·:·peek·x
  
14 o2·=·int32{Address·=>·0x7f2213081d90}14 o2·=·int32{Address·=>·0x7f477a7d0c80}
15 These·pointers·can·be·accessed·using·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s.15 These·pointers·can·be·accessed·using·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s.
16 i3·:·ptr·=·address·x16 i3·:·ptr·=·address·x
  
17 o3·=·0x7f2213081d9017 o3·=·0x7f477a7d0c80
  
18 o3·:·Pointer18 o3·:·Pointer
19 Simple·arithmetic·can·be·performed·on·pointers.19 Simple·arithmetic·can·be·performed·on·pointers.
20 i4·:·ptr·+·520 i4·:·ptr·+·5
  
21 o4·=·0x7f2213081d9521 o4·=·0x7f477a7d0c85
  
22 o4·:·Pointer22 o4·:·Pointer
23 i5·:·ptr·-·323 i5·:·ptr·-·3
  
24 o5·=·0x7f2213081d8d24 o5·=·0x7f477a7d0c7d
  
25 o5·:·Pointer25 o5·:·Pointer
26 *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8*
27 ····*·_\x8n_\x8u_\x8l_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·the·null·pointer27 ····*·_\x8n_\x8u_\x8l_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·the·null·pointer
28 ····*·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s·--·pointer·to·type·or·object28 ····*·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s·--·pointer·to·type·or·object
29 ····*·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·dereference·a·pointer29 ····*·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·dereference·a·pointer
30 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·p\x8po\x8oi\x8in\x8nt\x8te\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*30 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·p\x8po\x8oi\x8in\x8nt\x8te\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
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64 o1·:·SharedLibrary</code></pre>64 o1·:·SharedLibrary</code></pre>
65 ············</td>65 ············</td>
66 ··········</tr>66 ··········</tr>
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i2·:·peek·mpfr69 ··············<pre><code·class="language-macaulay2">i2·:·peek·mpfr
  
70 o2·=·SharedLibrary{0x7fa11dc8f550,·mpfr}</code></pre>70 o2·=·SharedLibrary{0x7f7e2e48f550,·mpfr}</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ········</table>73 ········</table>
74 ······</div>74 ······</div>
75 ······<div>75 ······<div>
76 ········<h3>Menu</h3>76 ········<h3>Menu</h3>
77 ········<ul>77 ········<ul>
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12 i1·:·mpfr·=·openSharedLibrary·"mpfr"12 i1·:·mpfr·=·openSharedLibrary·"mpfr"
  
13 o1·=·mpfr13 o1·=·mpfr
  
14 o1·:·SharedLibrary14 o1·:·SharedLibrary
15 i2·:·peek·mpfr15 i2·:·peek·mpfr
  
16 o2·=·SharedLibrary{0x7fa11dc8f550,·mpfr}16 o2·=·SharedLibrary{0x7f7e2e48f550,·mpfr}
17 *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8*17 *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8*
18 ····*·_\x8o_\x8p_\x8e_\x8n_\x8S_\x8h_\x8a_\x8r_\x8e_\x8d_\x8L_\x8i_\x8b_\x8r_\x8a_\x8r_\x8y·--·open·a·shared·library18 ····*·_\x8o_\x8p_\x8e_\x8n_\x8S_\x8h_\x8a_\x8r_\x8e_\x8d_\x8L_\x8i_\x8b_\x8r_\x8a_\x8r_\x8y·--·open·a·shared·library
19 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*
20 ····*·_\x8o_\x8p_\x8e_\x8n_\x8S_\x8h_\x8a_\x8r_\x8e_\x8d_\x8L_\x8i_\x8b_\x8r_\x8a_\x8r_\x8y·--·open·a·shared·library20 ····*·_\x8o_\x8p_\x8e_\x8n_\x8S_\x8h_\x8a_\x8r_\x8e_\x8d_\x8L_\x8i_\x8b_\x8r_\x8a_\x8r_\x8y·--·open·a·shared·library
21 *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*21 *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*
22 ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType)·--·see22 ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType)·--·see
23 ······_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n·--·construct·a·foreign·function23 ······_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n·--·construct·a·foreign·function
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78 o1·:·ForeignObject·of·type·int32</code></pre>78 o1·:·ForeignObject·of·type·int32</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x83 ··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x
  
84 o2·=·0x7f59dc9468e084 o2·=·0x7fc7cb42f720
  
85 o2·:·Pointer</code></pre>85 o2·:·Pointer</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ··········<tr>88 ··········<tr>
89 ············<td>89 ············<td>
90 ··············<pre><code·class="language-macaulay2">i3·:·*ptr·=·int·690 ··············<pre><code·class="language-macaulay2">i3·:·*ptr·=·int·6
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16 i1·:·x·=·int·516 i1·:·x·=·int·5
  
17 o1·=·517 o1·=·5
  
18 o1·:·ForeignObject·of·type·int3218 o1·:·ForeignObject·of·type·int32
19 i2·:·ptr·=·address·x19 i2·:·ptr·=·address·x
  
20 o2·=·0x7f59dc9468e020 o2·=·0x7fc7cb42f720
  
21 o2·:·Pointer21 o2·:·Pointer
22 i3·:·*ptr·=·int·622 i3·:·*ptr·=·int·6
  
23 o3·=·623 o3·=·6
  
24 o3·:·ForeignObject·of·type·int3224 o3·:·ForeignObject·of·type·int32
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71 ··········<p>If·<span·class="tt">x</span>·is·a·foreign·type,·then·this·returns·the·address·to·the·<span·class="tt">ffi_type</span>·struct·used·by·<span·class="tt">libffi</span>·to·identify·the·type.</p>71 ··········<p>If·<span·class="tt">x</span>·is·a·foreign·type,·then·this·returns·the·address·to·the·<span·class="tt">ffi_type</span>·struct·used·by·<span·class="tt">libffi</span>·to·identify·the·type.</p>
72 ········</div>72 ········</div>
73 ········<table·class="examples">73 ········<table·class="examples">
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i1·:·address·int76 ··············<pre><code·class="language-macaulay2">i1·:·address·int
  
77 o1·=·0x55fb750afac077 o1·=·0x56296d549ac0
  
78 o1·:·Pointer</code></pre>78 o1·:·Pointer</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ········</table>81 ········</table>
82 ········<div>82 ········<div>
83 ··········<p>If·<span·class="tt">x</span>·is·a·foreign·object,·then·this·returns·the·address·to·the·object.··It·behaves·like·the·<span·class="tt">&amp;</span>·&quot;address-of&quot;·operator·in·C.</p>83 ··········<p>If·<span·class="tt">x</span>·is·a·foreign·object,·then·this·returns·the·address·to·the·object.··It·behaves·like·the·<span·class="tt">&amp;</span>·&quot;address-of&quot;·operator·in·C.</p>
84 ········</div>84 ········</div>
85 ········<table·class="examples">85 ········<table·class="examples">
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i2·:·address·int·588 ··············<pre><code·class="language-macaulay2">i2·:·address·int·5
  
89 o2·=·0x7fb00843715089 o2·=·0x7fb645c9c480
  
90 o2·:·Pointer</code></pre>90 o2·:·Pointer</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ········</table>93 ········</table>
94 ······</div>94 ······</div>
95 ······<div>95 ······<div>
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11 ····*·Outputs:11 ····*·Outputs:
12 ··········o·a·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r,12 ··········o·a·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r,
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 If·x·is·a·foreign·type,·then·this·returns·the·address·to·the·ffi_type·struct14 If·x·is·a·foreign·type,·then·this·returns·the·address·to·the·ffi_type·struct
15 used·by·libffi·to·identify·the·type.15 used·by·libffi·to·identify·the·type.
16 i1·:·address·int16 i1·:·address·int
  
17 o1·=·0x55fb750afac017 o1·=·0x56296d549ac0
  
18 o1·:·Pointer18 o1·:·Pointer
19 If·x·is·a·foreign·object,·then·this·returns·the·address·to·the·object.·It19 If·x·is·a·foreign·object,·then·this·returns·the·address·to·the·object.·It
20 behaves·like·the·&·"address-of"·operator·in·C.20 behaves·like·the·&·"address-of"·operator·in·C.
21 i2·:·address·int·521 i2·:·address·int·5
  
22 o2·=·0x7fb00843715022 o2·=·0x7fb645c9c480
  
23 o2·:·Pointer23 o2·:·Pointer
24 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ad\x8dd\x8dr\x8re\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*24 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ad\x8dd\x8dr\x8re\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
25 ····*·address(ForeignObject)25 ····*·address(ForeignObject)
26 ····*·address(ForeignType)26 ····*·address(ForeignType)
27 ····*·address(Nothing)·(missing·documentation)27 ····*·address(Nothing)·(missing·documentation)
28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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232 o16·:·ForeignFunction</code></pre>232 o16·:·ForeignFunction</code></pre>
233 ············</td>233 ············</td>
234 ··········</tr>234 ··········</tr>
235 ··········<tr>235 ··········<tr>
236 ············<td>236 ············<td>
237 ··············<pre><code·class="language-macaulay2">i17·:·x·=·malloc·8237 ··············<pre><code·class="language-macaulay2">i17·:·x·=·malloc·8
  
238 o17·=·0x7ff21c06a850238 o17·=·0x7fc6a406a850
  
239 o17·:·ForeignObject·of·type·void*</code></pre>239 o17·:·ForeignObject·of·type·void*</code></pre>
240 ············</td>240 ············</td>
241 ··········</tr>241 ··········</tr>
242 ··········<tr>242 ··········<tr>
243 ············<td>243 ············<td>
244 ··············<pre><code·class="language-macaulay2">i18·:·registerFinalizer(x,·free)</code></pre>244 ··············<pre><code·class="language-macaulay2">i18·:·registerFinalizer(x,·free)</code></pre>
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95 i16·:·free·=·foreignFunction("free",·void,·voidstar)95 i16·:·free·=·foreignFunction("free",·void,·voidstar)
  
96 o16·=·free96 o16·=·free
  
97 o16·:·ForeignFunction97 o16·:·ForeignFunction
98 i17·:·x·=·malloc·898 i17·:·x·=·malloc·8
  
99 o17·=·0x7ff21c06a85099 o17·=·0x7fc6a406a850
  
100 o17·:·ForeignObject·of·type·void*100 o17·:·ForeignObject·of·type·void*
101 i18·:·registerFinalizer(x,·free)101 i18·:·registerFinalizer(x,·free)
102 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fo\x8or\x8re\x8ei\x8ig\x8gn\x8nF\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8n:\x8:·*\x8**\x8**\x8**\x8**\x8*102 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fo\x8or\x8re\x8ei\x8ig\x8gn\x8nF\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8n:\x8:·*\x8**\x8**\x8**\x8**\x8*
103 ····*·foreignFunction(Pointer,String,ForeignType,VisibleList)103 ····*·foreignFunction(Pointer,String,ForeignType,VisibleList)
104 ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType)104 ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType)
105 ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList)105 ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList)
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77 ··········<p>Allocate·<span·class="tt">n</span>·bytes·of·memory·using·the·<a·href="../../Macaulay2Doc/html/___G__C_spgarbage_spcollector.html">GC·garbage·collector</a>.</p>77 ··········<p>Allocate·<span·class="tt">n</span>·bytes·of·memory·using·the·<a·href="../../Macaulay2Doc/html/___G__C_spgarbage_spcollector.html">GC·garbage·collector</a>.</p>
78 ········</div>78 ········</div>
79 ········<table·class="examples">79 ········<table·class="examples">
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i1·:·ptr·=·getMemory·882 ··············<pre><code·class="language-macaulay2">i1·:·ptr·=·getMemory·8
  
83 o1·=·0x7faaa5d8135083 o1·=·0x7f158357d250
  
84 o1·:·ForeignObject·of·type·void*</code></pre>84 o1·:·ForeignObject·of·type·void*</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ········</table>87 ········</table>
88 ········<div>88 ········<div>
89 ··········<p>If·the·memory·will·not·contain·any·pointers,·then·set·the·<span·class="tt">Atomic</span>·option·to·<a·href="../../Macaulay2Doc/html/_true.html">true</a>.</p>89 ··········<p>If·the·memory·will·not·contain·any·pointers,·then·set·the·<span·class="tt">Atomic</span>·option·to·<a·href="../../Macaulay2Doc/html/_true.html">true</a>.</p>
90 ········</div>90 ········</div>
91 ········<table·class="examples">91 ········<table·class="examples">
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i2·:·ptr·=·getMemory(8,·Atomic·=>·true)94 ··············<pre><code·class="language-macaulay2">i2·:·ptr·=·getMemory(8,·Atomic·=>·true)
  
95 o2·=·0x7faaa42c009095 o2·=·0x7f1582234010
  
96 o2·:·ForeignObject·of·type·void*</code></pre>96 o2·:·ForeignObject·of·type·void*</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ········</table>99 ········</table>
100 ········<div>100 ········<div>
101 ··········<p>Alternatively,·a·foreign·object·type·<span·class="tt">T</span>·may·be·specified.··In·this·case,·the·number·of·bytes·and·whether·the·<span·class="tt">Atomic</span>·option·should·be·set·will·be·determined·automatically.</p>101 ··········<p>Alternatively,·a·foreign·object·type·<span·class="tt">T</span>·may·be·specified.··In·this·case,·the·number·of·bytes·and·whether·the·<span·class="tt">Atomic</span>·option·should·be·set·will·be·determined·automatically.</p>
102 ········</div>102 ········</div>
103 ········<table·class="examples">103 ········<table·class="examples">
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i3·:·ptr·=·getMemory·int106 ··············<pre><code·class="language-macaulay2">i3·:·ptr·=·getMemory·int
  
107 o3·=·0x7faaa3c0ffa0107 o3·=·0x7f158225af10
  
108 o3·:·ForeignObject·of·type·void*</code></pre>108 o3·:·ForeignObject·of·type·void*</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ········</table>111 ········</table>
112 ······</div>112 ······</div>
113 ······<div>113 ······<div>
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14 ··········o·Atomic·=>·...,·default·value·false14 ··········o·Atomic·=>·...,·default·value·false
15 ····*·Outputs:15 ····*·Outputs:
16 ··········o·an·instance·of·the·type·_\x8v_\x8o_\x8i_\x8d_\x8s_\x8t_\x8a_\x8r,16 ··········o·an·instance·of·the·type·_\x8v_\x8o_\x8i_\x8d_\x8s_\x8t_\x8a_\x8r,
17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
18 Allocate·n·bytes·of·memory·using·the·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r.18 Allocate·n·bytes·of·memory·using·the·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r.
19 i1·:·ptr·=·getMemory·819 i1·:·ptr·=·getMemory·8
  
20 o1·=·0x7faaa5d8135020 o1·=·0x7f158357d250
  
21 o1·:·ForeignObject·of·type·void*21 o1·:·ForeignObject·of·type·void*
22 If·the·memory·will·not·contain·any·pointers,·then·set·the·Atomic·option·to22 If·the·memory·will·not·contain·any·pointers,·then·set·the·Atomic·option·to
23 _\x8t_\x8r_\x8u_\x8e.23 _\x8t_\x8r_\x8u_\x8e.
24 i2·:·ptr·=·getMemory(8,·Atomic·=>·true)24 i2·:·ptr·=·getMemory(8,·Atomic·=>·true)
  
25 o2·=·0x7faaa42c009025 o2·=·0x7f1582234010
  
26 o2·:·ForeignObject·of·type·void*26 o2·:·ForeignObject·of·type·void*
27 Alternatively,·a·foreign·object·type·T·may·be·specified.·In·this·case,·the27 Alternatively,·a·foreign·object·type·T·may·be·specified.·In·this·case,·the
28 number·of·bytes·and·whether·the·Atomic·option·should·be·set·will·be·determined28 number·of·bytes·and·whether·the·Atomic·option·should·be·set·will·be·determined
29 automatically.29 automatically.
30 i3·:·ptr·=·getMemory·int30 i3·:·ptr·=·getMemory·int
  
31 o3·=·0x7faaa3c0ffa031 o3·=·0x7f158225af10
  
32 o3·:·ForeignObject·of·type·void*32 o3·:·ForeignObject·of·type·void*
33 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*33 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
34 ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a34 ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a
35 ······foreign·object35 ······foreign·object
36 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8tM\x8Me\x8em\x8mo\x8or\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*36 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8tM\x8Me\x8em\x8mo\x8or\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*
37 ····*·getMemory(ForeignType)37 ····*·getMemory(ForeignType)
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100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))</code></pre>101 ··············<pre><code·class="language-macaulay2">i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i5·:·collectGarbage()106 ··············<pre><code·class="language-macaulay2">i5·:·collectGarbage()
 107 freeing·memory·at·0x7f8b4c0709e0freeing·memory·at·0x7f8b4c065de0
107 freeing·memory·at·0x7f8f0c06aa40108 freeing·memory·at·0x7f8b4c06aa40
108 freeing·memory·at·0x7f8f0c072340 
109 freeing·memory·at·0x7f8f0c070cc0 
110 freeing·memory·at·0x7f8f0c0709e0 
111 freeing·memory·at·0x7f8f0c004f20 
112 freeing·memory·at·0x7f8f0c0705b0 
113 freeing·memory·at·0x7f8f0c06a850109 freeing·memory·at·0x7f8b4c06a850
 110 freeing·memory·at·0x7f8b4c070cc0
114 freeing·memory·at·0x7f8f0c070a00111 freeing·memory·at·0x7f8b4c070a00
 112 freeing·memory·at·0x7f8b4c072340
 113 freeing·memory·at·0x7f8b4c0705b0
 114 freeing·memory·at·0x7f8b4c0709e0
115 freeing·memory·at·0x7f8f0c065de0</code></pre>115 freeing·memory·at·0x7f8b4c004f20</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ········</table>118 ········</table>
119 ······</div>119 ······</div>
120 ······<div>120 ······<div>
121 ········<h2>See·also</h2>121 ········<h2>See·also</h2>
122 ········<ul>122 ········<ul>
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31 i3·:·finalizer·=·x·->·(print("freeing·memory·at·"·|·net·x);·free·x)31 i3·:·finalizer·=·x·->·(print("freeing·memory·at·"·|·net·x);·free·x)
  
32 o3·=·finalizer32 o3·=·finalizer
  
33 o3·:·FunctionClosure33 o3·:·FunctionClosure
34 i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))34 i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))
35 i5·:·collectGarbage()35 i5·:·collectGarbage()
 36 freeing·memory·at·0x7f8b4c0709e0freeing·memory·at·0x7f8b4c065de0
36 freeing·memory·at·0x7f8f0c06aa4037 freeing·memory·at·0x7f8b4c06aa40
37 freeing·memory·at·0x7f8f0c072340 
38 freeing·memory·at·0x7f8f0c070cc0 
39 freeing·memory·at·0x7f8f0c0709e0 
40 freeing·memory·at·0x7f8f0c004f20 
41 freeing·memory·at·0x7f8f0c0705b0 
42 freeing·memory·at·0x7f8f0c06a85038 freeing·memory·at·0x7f8b4c06a850
 39 freeing·memory·at·0x7f8b4c070cc0
43 freeing·memory·at·0x7f8f0c070a0040 freeing·memory·at·0x7f8b4c070a00
 41 freeing·memory·at·0x7f8b4c072340
44 freeing·memory·at·0x7f8f0c065de042 freeing·memory·at·0x7f8b4c0705b0
 43 freeing·memory·at·0x7f8b4c0709e0
 44 freeing·memory·at·0x7f8b4c004f20
45 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*45 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
46 ····*·_\x8g_\x8e_\x8t_\x8M_\x8e_\x8m_\x8o_\x8r_\x8y·--·allocate·memory·using·the·garbage·collector46 ····*·_\x8g_\x8e_\x8t_\x8M_\x8e_\x8m_\x8o_\x8r_\x8y·--·allocate·memory·using·the·garbage·collector
47 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*47 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
48 ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a48 ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a
49 ······foreign·object49 ······foreign·object
50 ===============================================================================50 ===============================================================================
51 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-51 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
1.35 KB
./usr/share/doc/Macaulay2/ForeignFunctions/html/_value_lp__Foreign__Object_rp.html
    
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116 ··········<p>Foreign·pointer·objects·are·converted·to·<a·title="pointer·to·memory·address"·href="___Pointer.html">Pointer</a>·objects.</p>116 ··········<p>Foreign·pointer·objects·are·converted·to·<a·title="pointer·to·memory·address"·href="___Pointer.html">Pointer</a>·objects.</p>
117 ········</div>117 ········</div>
118 ········<table·class="examples">118 ········<table·class="examples">
119 ··········<tr>119 ··········<tr>
120 ············<td>120 ············<td>
121 ··············<pre><code·class="language-macaulay2">i5·:·x·=·voidstar·address·int·5121 ··············<pre><code·class="language-macaulay2">i5·:·x·=·voidstar·address·int·5
  
122 o5·=·0x7efd6f731ec0122 o5·=·0x7f2e8c6d96e0
  
123 o5·:·ForeignObject·of·type·void*</code></pre>123 o5·:·ForeignObject·of·type·void*</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i6·:·value·x128 ··············<pre><code·class="language-macaulay2">i6·:·value·x
  
129 o6·=·0x7efd6f731ec0129 o6·=·0x7f2e8c6d96e0
  
130 o6·:·Pointer</code></pre>130 o6·:·Pointer</code></pre>
131 ············</td>131 ············</td>
132 ··········</tr>132 ··········</tr>
133 ········</table>133 ········</table>
134 ········<div>134 ········<div>
135 ··········<p>Foreign·string·objects·are·converted·to·strings.</p>135 ··········<p>Foreign·string·objects·are·converted·to·strings.</p>
452 B
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Offset 34, 20 lines modifiedOffset 34, 20 lines modified
  
34 o4·=·534 o4·=·5
  
35 o4·:·RR·(of·precision·53)35 o4·:·RR·(of·precision·53)
36 Foreign·pointer·objects·are·converted·to·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·objects.36 Foreign·pointer·objects·are·converted·to·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·objects.
37 i5·:·x·=·voidstar·address·int·537 i5·:·x·=·voidstar·address·int·5
  
38 o5·=·0x7efd6f731ec038 o5·=·0x7f2e8c6d96e0
  
39 o5·:·ForeignObject·of·type·void*39 o5·:·ForeignObject·of·type·void*
40 i6·:·value·x40 i6·:·value·x
  
41 o6·=·0x7efd6f731ec041 o6·=·0x7f2e8c6d96e0
  
42 o6·:·Pointer42 o6·:·Pointer
43 Foreign·string·objects·are·converted·to·strings.43 Foreign·string·objects·are·converted·to·strings.
44 i7·:·x·=·charstar·"Hello,·world!"44 i7·:·x·=·charstar·"Hello,·world!"
  
45 o7·=·Hello,·world!45 o7·=·Hello,·world!
  
748 B
./usr/share/doc/Macaulay2/FormalGroupLaws/dump/rawdocumentation.dump
    
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724 B
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563 B
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Offset 6, 27 lines modifiedOffset 6, 27 lines modified
6 ·····|·1·2·3·4·|6 ·····|·1·2·3·4·|
  
7 ··············2·······47 ··············2·······4
8 o1·:·Matrix·ZZ··<--·ZZ8 o1·:·Matrix·ZZ··<--·ZZ
  
9 i2·:·s·=·temporaryFileName()9 i2·:·s·=·temporaryFileName()
  
10 o2·=·/tmp/M2-1129531-0/010 o2·=·/tmp/M2-1101458-0/0
  
11 i3·:·F·=·openOut(s)11 i3·:·F·=·openOut(s)
  
12 o3·=·/tmp/M2-1129531-0/012 o3·=·/tmp/M2-1101458-0/0
  
13 o3·:·File13 o3·:·File
  
14 i4·:·putMatrix(F,A)14 i4·:·putMatrix(F,A)
  
15 i5·:·close(F)15 i5·:·close(F)
  
16 o5·=·/tmp/M2-1129531-0/016 o5·=·/tmp/M2-1101458-0/0
  
17 o5·:·File17 o5·:·File
  
18 i6·:·getMatrix(s)18 i6·:·getMatrix(s)
  
19 o6·=·|·1·1·1·1·|19 o6·=·|·1·1·1·1·|
20 ·····|·1·2·3·4·|20 ·····|·1·2·3·4·|
1.57 KB
./usr/share/doc/Macaulay2/FourTiTwo/html/_put__Matrix.html
    
Offset 79, 36 lines modifiedOffset 79, 36 lines modified
79 o1·:·Matrix·ZZ··&lt;--·ZZ</code></pre>79 o1·:·Matrix·ZZ··&lt;--·ZZ</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i2·:·s·=·temporaryFileName()84 ··············<pre><code·class="language-macaulay2">i2·:·s·=·temporaryFileName()
  
85 o2·=·/tmp/M2-1129531-0/0</code></pre>85 o2·=·/tmp/M2-1101458-0/0</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ··········<tr>88 ··········<tr>
89 ············<td>89 ············<td>
90 ··············<pre><code·class="language-macaulay2">i3·:·F·=·openOut(s)90 ··············<pre><code·class="language-macaulay2">i3·:·F·=·openOut(s)
  
91 o3·=·/tmp/M2-1129531-0/091 o3·=·/tmp/M2-1101458-0/0
  
92 o3·:·File</code></pre>92 o3·:·File</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i4·:·putMatrix(F,A)</code></pre>97 ··············<pre><code·class="language-macaulay2">i4·:·putMatrix(F,A)</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i5·:·close(F)102 ··············<pre><code·class="language-macaulay2">i5·:·close(F)
  
103 o5·=·/tmp/M2-1129531-0/0103 o5·=·/tmp/M2-1101458-0/0
  
104 o5·:·File</code></pre>104 o5·:·File</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i6·:·getMatrix(s)109 ··············<pre><code·class="language-macaulay2">i6·:·getMatrix(s)
465 B
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18 ··············2·······418 ··············2·······4
19 o1·:·Matrix·ZZ··<--·ZZ19 o1·:·Matrix·ZZ··<--·ZZ
20 i2·:·s·=·temporaryFileName()20 i2·:·s·=·temporaryFileName()
  
21 o2·=·/tmp/M2-1129531-0/021 o2·=·/tmp/M2-1101458-0/0
22 i3·:·F·=·openOut(s)22 i3·:·F·=·openOut(s)
  
23 o3·=·/tmp/M2-1129531-0/023 o3·=·/tmp/M2-1101458-0/0
  
24 o3·:·File24 o3·:·File
25 i4·:·putMatrix(F,A)25 i4·:·putMatrix(F,A)
26 i5·:·close(F)26 i5·:·close(F)
  
27 o5·=·/tmp/M2-1129531-0/027 o5·=·/tmp/M2-1101458-0/0
  
28 o5·:·File28 o5·:·File
29 i6·:·getMatrix(s)29 i6·:·getMatrix(s)
  
30 o6·=·|·1·1·1·1·|30 o6·=·|·1·1·1·1·|
31 ·····|·1·2·3·4·|31 ·····|·1·2·3·4·|
  
734 B
./usr/share/doc/Macaulay2/FourierMotzkin/dump/rawdocumentation.dump
    
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6 #·End·of·header6 #·End·of·header
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767 B
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922 B
./usr/share/doc/Macaulay2/FrobeniusThresholds/example-output/_fpt.out
    
Offset 155, 31 lines modifiedOffset 155, 31 lines modified
155 i26·:·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)·--·FinalAttempt·improves·the·estimate·slightly155 i26·:·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)·--·FinalAttempt·improves·the·estimate·slightly
  
156 o26·=·{.142067,·.144}156 o26·=·{.142067,·.144}
  
157 o26·:·List157 o26·:·List
  
158 i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)158 i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)
159 ·--·used·1.8534s·(cpu);·1.1913s·(thread);·0s·(gc)159 ·--·used·2.24056s·(cpu);·1.26945s·(thread);·0s·(gc)
  
160 o27·=·{.142067,·.144}160 o27·=·{.142067,·.144}
  
161 o27·:·List161 o27·:·List
  
162 i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7)162 i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7)
163 ·--·used·1.10295s·(cpu);·0.747026s·(thread);·0s·(gc)163 ·--·used·1.17948s·(cpu);·0.740683s·(thread);·0s·(gc)
  
164 ······1164 ······1
165 o28·=·-165 o28·=·-
166 ······7166 ······7
  
167 o28·:·QQ167 o28·:·QQ
  
168 i29·:·time·fpt(f,·DepthOfSearch·=>·4)168 i29·:·time·fpt(f,·DepthOfSearch·=>·4)
169 ·--·used·0.933701s·(cpu);·0.607185s·(thread);·0s·(gc)169 ·--·used·1.06203s·(cpu);·0.669477s·(thread);·0s·(gc)
  
170 ······1170 ······1
171 o29·=·-171 o29·=·-
172 ······7172 ······7
  
173 o29·:·QQ173 o29·:·QQ
  
2.04 KB
./usr/share/doc/Macaulay2/FrobeniusThresholds/example-output/_frobenius__Nu.out
    
Offset 43, 34 lines modifiedOffset 43, 34 lines modified
43 o12·=·22043 o12·=·220
  
44 i13·:·R·=·ZZ/17[x,y,z];44 i13·:·R·=·ZZ/17[x,y,z];
  
45 i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial45 i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial
  
46 i15·:·time·frobeniusNu(3,·f)46 i15·:·time·frobeniusNu(3,·f)
47 ·--·used·0.00798509s·(cpu);·0.00493792s·(thread);·0s·(gc)47 ·--·used·0.00399559s·(cpu);·0.0041295s·(thread);·0s·(gc)
  
48 o15·=·375648 o15·=·3756
  
49 i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false)49 i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false)
50 ·--·used·0.297774s·(cpu);·0.234834s·(thread);·0s·(gc)50 ·--·used·0.344976s·(cpu);·0.234874s·(thread);·0s·(gc)
  
51 o16·=·375651 o16·=·3756
  
52 i17·:·R·=·ZZ/5[x,y,z];52 i17·:·R·=·ZZ/5[x,y,z];
  
53 i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;53 i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;
  
54 i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default54 i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default
55 ·--·used·0.293284s·(cpu);·0.195459s·(thread);·0s·(gc)55 ·--·used·0.367984s·(cpu);·0.23738s·(thread);·0s·(gc)
  
56 o19·=·49956 o19·=·499
  
57 i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower)57 i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower)
58 ·--·used·1.00661s·(cpu);·0.862033s·(thread);·0s·(gc)58 ·--·used·1.14677s·(cpu);·0.990673s·(thread);·0s·(gc)
  
59 o20·=·49959 o20·=·499
  
60 i21·:·R·=·ZZ/3[x,y];60 i21·:·R·=·ZZ/3[x,y];
  
61 i22·:·M·=·ideal(x,·y);61 i22·:·M·=·ideal(x,·y);
  
Offset 85, 34 lines modifiedOffset 85, 34 lines modified
85 o24·=·885 o24·=·8
  
86 i25·:·R·=·ZZ/5[x,y,z];86 i25·:·R·=·ZZ/5[x,y,z];
  
87 i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;87 i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;
  
88 i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default)88 i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default)
89 ·--·used·0.752781s·(cpu);·0.531304s·(thread);·0s·(gc)89 ·--·used·0.91517s·(cpu);·0.56781s·(thread);·0s·(gc)
  
90 o27·=·112490 o27·=·1124
  
91 i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear)91 i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear)
92 ·--·used·1.18633s·(cpu);·0.792731s·(thread);·0s·(gc)92 ·--·used·1.29612s·(cpu);·0.820717s·(thread);·0s·(gc)
  
93 o28·=·112493 o28·=·1124
  
94 i29·:·M·=·ideal(x,·y,·z);94 i29·:·M·=·ideal(x,·y,·z);
  
95 o29·:·Ideal·of·R95 o29·:·Ideal·of·R
  
96 i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default)96 i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default)
97 ·--·used·1.2229s·(cpu);·1.0664s·(thread);·0s·(gc)97 ·--·used·1.3603s·(cpu);·1.17619s·(thread);·0s·(gc)
  
98 o30·=·9798 o30·=·97
  
99 i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier99 i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier
100 ·--·used·0.464793s·(cpu);·0.39059s·(thread);·0s·(gc)100 ·--·used·0.503646s·(cpu);·0.415921s·(thread);·0s·(gc)
  
101 o31·=·97101 o31·=·97
  
102 i32·:·R·=·ZZ/7[x,y];102 i32·:·R·=·ZZ/7[x,y];
  
103 i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2;103 i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2;
  
2.53 KB
./usr/share/doc/Macaulay2/FrobeniusThresholds/html/_fpt.html
    
Offset 363, 37 lines modifiedOffset 363, 37 lines modified
363 ········<div>363 ········<div>
364 ··········<p>The·computations·performed·when·<span·class="tt">FinalAttempt</span>·is·set·to·<span·class="tt">true</span>·are·often·slow,·and·often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be·used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·<span·class="tt">Attempts</span>·or·<span·class="tt">DepthOfSearch</span>,·instead.</p>364 ··········<p>The·computations·performed·when·<span·class="tt">FinalAttempt</span>·is·set·to·<span·class="tt">true</span>·are·often·slow,·and·often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be·used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·<span·class="tt">Attempts</span>·or·<span·class="tt">DepthOfSearch</span>,·instead.</p>
365 ········</div>365 ········</div>
366 ········<table·class="examples">366 ········<table·class="examples">
367 ··········<tr>367 ··········<tr>
368 ············<td>368 ············<td>
369 ··············<pre><code·class="language-macaulay2">i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)369 ··············<pre><code·class="language-macaulay2">i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)
370 ·--·used·1.8534s·(cpu);·1.1913s·(thread);·0s·(gc)370 ·--·used·2.24056s·(cpu);·1.26945s·(thread);·0s·(gc)
  
371 o27·=·{.142067,·.144}371 o27·=·{.142067,·.144}
  
372 o27·:·List</code></pre>372 o27·:·List</code></pre>
373 ············</td>373 ············</td>
374 ··········</tr>374 ··········</tr>
375 ··········<tr>375 ··········<tr>
376 ············<td>376 ············<td>
377 ··············<pre><code·class="language-macaulay2">i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7)377 ··············<pre><code·class="language-macaulay2">i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7)
378 ·--·used·1.10295s·(cpu);·0.747026s·(thread);·0s·(gc)378 ·--·used·1.17948s·(cpu);·0.740683s·(thread);·0s·(gc)
  
379 ······1379 ······1
380 o28·=·-380 o28·=·-
381 ······7381 ······7
  
382 o28·:·QQ</code></pre>382 o28·:·QQ</code></pre>
383 ············</td>383 ············</td>
384 ··········</tr>384 ··········</tr>
385 ··········<tr>385 ··········<tr>
386 ············<td>386 ············<td>
387 ··············<pre><code·class="language-macaulay2">i29·:·time·fpt(f,·DepthOfSearch·=>·4)387 ··············<pre><code·class="language-macaulay2">i29·:·time·fpt(f,·DepthOfSearch·=>·4)
388 ·--·used·0.933701s·(cpu);·0.607185s·(thread);·0s·(gc)388 ·--·used·1.06203s·(cpu);·0.669477s·(thread);·0s·(gc)
  
389 ······1389 ······1
390 o29·=·-390 o29·=·-
391 ······7391 ······7
  
392 o29·:·QQ</code></pre>392 o29·:·QQ</code></pre>
393 ············</td>393 ············</td>
1010 B
html2text {}
    
Offset 228, 29 lines modifiedOffset 228, 29 lines modified
  
228 o26·:·List228 o26·:·List
229 The·computations·performed·when·FinalAttempt·is·set·to·true·are·often·slow,·and229 The·computations·performed·when·FinalAttempt·is·set·to·true·are·often·slow,·and
230 often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be230 often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be
231 used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·Attempts231 used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·Attempts
232 or·DepthOfSearch,·instead.232 or·DepthOfSearch,·instead.
233 i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)233 i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)
234 ·--·used·1.8534s·(cpu);·1.1913s·(thread);·0s·(gc)234 ·--·used·2.24056s·(cpu);·1.26945s·(thread);·0s·(gc)
  
235 o27·=·{.142067,·.144}235 o27·=·{.142067,·.144}
  
236 o27·:·List236 o27·:·List
237 i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7)237 i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7)
238 ·--·used·1.10295s·(cpu);·0.747026s·(thread);·0s·(gc)238 ·--·used·1.17948s·(cpu);·0.740683s·(thread);·0s·(gc)
  
239 ······1239 ······1
240 o28·=·-240 o28·=·-
241 ······7241 ······7
  
242 o28·:·QQ242 o28·:·QQ
243 i29·:·time·fpt(f,·DepthOfSearch·=>·4)243 i29·:·time·fpt(f,·DepthOfSearch·=>·4)
244 ·--·used·0.933701s·(cpu);·0.607185s·(thread);·0s·(gc)244 ·--·used·1.06203s·(cpu);·0.669477s·(thread);·0s·(gc)
  
245 ······1245 ······1
246 o29·=·-246 o29·=·-
247 ······7247 ······7
  
248 o29·:·QQ248 o29·:·QQ
249 As·seen·in·several·examples·above,·when·the·exact·answer·is·not·found,·a·list249 As·seen·in·several·examples·above,·when·the·exact·answer·is·not·found,·a·list
8.92 KB
./usr/share/doc/Macaulay2/FrobeniusThresholds/html/_frobenius__Nu.html
    
Offset 192, 23 lines modifiedOffset 192, 23 lines modified
192 ············<td>192 ············<td>
193 ··············<pre><code·class="language-macaulay2">i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial</code></pre>193 ··············<pre><code·class="language-macaulay2">i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial</code></pre>
194 ············</td>194 ············</td>
195 ··········</tr>195 ··········</tr>
196 ··········<tr>196 ··········<tr>
197 ············<td>197 ············<td>
198 ··············<pre><code·class="language-macaulay2">i15·:·time·frobeniusNu(3,·f)198 ··············<pre><code·class="language-macaulay2">i15·:·time·frobeniusNu(3,·f)
199 ·--·used·0.00798509s·(cpu);·0.00493792s·(thread);·0s·(gc)199 ·--·used·0.00399559s·(cpu);·0.0041295s·(thread);·0s·(gc)
  
200 o15·=·3756</code></pre>200 o15·=·3756</code></pre>
201 ············</td>201 ············</td>
202 ··········</tr>202 ··········</tr>
203 ··········<tr>203 ··········<tr>
204 ············<td>204 ············<td>
205 ··············<pre><code·class="language-macaulay2">i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false)205 ··············<pre><code·class="language-macaulay2">i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false)
206 ·--·used·0.297774s·(cpu);·0.234834s·(thread);·0s·(gc)206 ·--·used·0.344976s·(cpu);·0.234874s·(thread);·0s·(gc)
  
207 o16·=·3756</code></pre>207 o16·=·3756</code></pre>
208 ············</td>208 ············</td>
209 ··········</tr>209 ··········</tr>
210 ········</table>210 ········</table>
211 ········<div>211 ········<div>
212 ··········<p>The·valid·values·for·the·option·<span·class="tt">ContainmentTest</span>·are·<span·class="tt">FrobeniusPower</span>,·<span·class="tt">FrobeniusRoot</span>,·and·<span·class="tt">StandardPower</span>.·The·default·value·of·this·option·depends·on·what·is·passed·to·<span·class="tt">frobeniusNu</span>.·Indeed,·by·default,·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusRoot</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·a·ring·element·$f$,·and·is·set·to·<span·class="tt">StandardPower</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·an·ideal·$I$.·We·describe·the·consequences·of·setting·<span·class="tt">ContainmentTest</span>·to·each·of·these·values·below.</p>212 ··········<p>The·valid·values·for·the·option·<span·class="tt">ContainmentTest</span>·are·<span·class="tt">FrobeniusPower</span>,·<span·class="tt">FrobeniusRoot</span>,·and·<span·class="tt">StandardPower</span>.·The·default·value·of·this·option·depends·on·what·is·passed·to·<span·class="tt">frobeniusNu</span>.·Indeed,·by·default,·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusRoot</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·a·ring·element·$f$,·and·is·set·to·<span·class="tt">StandardPower</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·an·ideal·$I$.·We·describe·the·consequences·of·setting·<span·class="tt">ContainmentTest</span>·to·each·of·these·values·below.</p>
Offset 225, 23 lines modifiedOffset 225, 23 lines modified
225 ············<td>225 ············<td>
226 ··············<pre><code·class="language-macaulay2">i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;</code></pre>226 ··············<pre><code·class="language-macaulay2">i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;</code></pre>
227 ············</td>227 ············</td>
228 ··········</tr>228 ··········</tr>
229 ··········<tr>229 ··········<tr>
230 ············<td>230 ············<td>
231 ··············<pre><code·class="language-macaulay2">i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default231 ··············<pre><code·class="language-macaulay2">i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default
232 ·--·used·0.293284s·(cpu);·0.195459s·(thread);·0s·(gc)232 ·--·used·0.367984s·(cpu);·0.23738s·(thread);·0s·(gc)
  
233 o19·=·499</code></pre>233 o19·=·499</code></pre>
234 ············</td>234 ············</td>
235 ··········</tr>235 ··········</tr>
236 ··········<tr>236 ··········<tr>
237 ············<td>237 ············<td>
238 ··············<pre><code·class="language-macaulay2">i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower)238 ··············<pre><code·class="language-macaulay2">i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower)
239 ·--·used·1.00661s·(cpu);·0.862033s·(thread);·0s·(gc)239 ·--·used·1.14677s·(cpu);·0.990673s·(thread);·0s·(gc)
  
240 o20·=·499</code></pre>240 o20·=·499</code></pre>
241 ············</td>241 ············</td>
242 ··········</tr>242 ··········</tr>
243 ········</table>243 ········</table>
244 ········<div>244 ········<div>
245 ··········<p>Finally,·when·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusPower</span>,·then·instead·of·producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·<span·class="tt">frobeniusNu</span>·instead·outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius·power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the·$n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as·defined·in·the·paper·<i>Frobenius·Powers</i>·by·Hernández,·Teixeira,·and·Witt,·which·can·be·computed·with·the·function·<a·title="compute·a·(generalized)·Frobenius·power·of·an·ideal"·href="../../TestIdeals/html/_frobenius__Power.html">frobeniusPower</a>,·from·the·<a·title="a·package·for·calculations·of·singularities·in·positive·characteristic·"·href="../../TestIdeals/html/index.html">TestIdeals</a>·package.·In·particular,·<span·class="tt">frobeniusNu(e,I,J)</span>·and·<span·class="tt">frobeniusNu(e,I,J,ContainmentTest=>FrobeniusPower)</span>·need·not·agree.·However,·they·will·agree·when·$I$·is·a·principal·ideal.</p>245 ··········<p>Finally,·when·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusPower</span>,·then·instead·of·producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·<span·class="tt">frobeniusNu</span>·instead·outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius·power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the·$n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as·defined·in·the·paper·<i>Frobenius·Powers</i>·by·Hernández,·Teixeira,·and·Witt,·which·can·be·computed·with·the·function·<a·title="compute·a·(generalized)·Frobenius·power·of·an·ideal"·href="../../TestIdeals/html/_frobenius__Power.html">frobeniusPower</a>,·from·the·<a·title="a·package·for·calculations·of·singularities·in·positive·characteristic·"·href="../../TestIdeals/html/index.html">TestIdeals</a>·package.·In·particular,·<span·class="tt">frobeniusNu(e,I,J)</span>·and·<span·class="tt">frobeniusNu(e,I,J,ContainmentTest=>FrobeniusPower)</span>·need·not·agree.·However,·they·will·agree·when·$I$·is·a·principal·ideal.</p>
Offset 287, 46 lines modifiedOffset 287, 46 lines modified
287 ············<td>287 ············<td>
288 ··············<pre><code·class="language-macaulay2">i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;</code></pre>288 ··············<pre><code·class="language-macaulay2">i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;</code></pre>
289 ············</td>289 ············</td>
290 ··········</tr>290 ··········</tr>
291 ··········<tr>291 ··········<tr>
292 ············<td>292 ············<td>
293 ··············<pre><code·class="language-macaulay2">i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default)293 ··············<pre><code·class="language-macaulay2">i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default)
294 ·--·used·0.752781s·(cpu);·0.531304s·(thread);·0s·(gc)294 ·--·used·0.91517s·(cpu);·0.56781s·(thread);·0s·(gc)
  
295 o27·=·1124</code></pre>295 o27·=·1124</code></pre>
296 ············</td>296 ············</td>
297 ··········</tr>297 ··········</tr>
298 ··········<tr>298 ··········<tr>
299 ············<td>299 ············<td>
300 ··············<pre><code·class="language-macaulay2">i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear)300 ··············<pre><code·class="language-macaulay2">i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear)
301 ·--·used·1.18633s·(cpu);·0.792731s·(thread);·0s·(gc)301 ·--·used·1.29612s·(cpu);·0.820717s·(thread);·0s·(gc)
  
302 o28·=·1124</code></pre>302 o28·=·1124</code></pre>
303 ············</td>303 ············</td>
304 ··········</tr>304 ··········</tr>
305 ··········<tr>305 ··········<tr>
306 ············<td>306 ············<td>
307 ··············<pre><code·class="language-macaulay2">i29·:·M·=·ideal(x,·y,·z);307 ··············<pre><code·class="language-macaulay2">i29·:·M·=·ideal(x,·y,·z);
  
308 o29·:·Ideal·of·R</code></pre>308 o29·:·Ideal·of·R</code></pre>
309 ············</td>309 ············</td>
310 ··········</tr>310 ··········</tr>
311 ··········<tr>311 ··········<tr>
312 ············<td>312 ············<td>
313 ··············<pre><code·class="language-macaulay2">i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default)313 ··············<pre><code·class="language-macaulay2">i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default)
314 ·--·used·1.2229s·(cpu);·1.0664s·(thread);·0s·(gc)314 ·--·used·1.3603s·(cpu);·1.17619s·(thread);·0s·(gc)
  
315 o30·=·97</code></pre>315 o30·=·97</code></pre>
316 ············</td>316 ············</td>
317 ··········</tr>317 ··········</tr>
318 ··········<tr>318 ··········<tr>
319 ············<td>319 ············<td>
320 ··············<pre><code·class="language-macaulay2">i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier320 ··············<pre><code·class="language-macaulay2">i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier
321 ·--·used·0.464793s·(cpu);·0.39059s·(thread);·0s·(gc)321 ·--·used·0.503646s·(cpu);·0.415921s·(thread);·0s·(gc)
  
322 o31·=·97</code></pre>322 o31·=·97</code></pre>
323 ············</td>323 ············</td>
324 ··········</tr>324 ··········</tr>
325 ········</table>325 ········</table>
326 ········<div>326 ········<div>
327 ··········<p>The·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">true</span>)·can·be·turned·off·to·tell·<span·class="tt">frobeniusNu</span>·to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take·the·minimum.</p>327 ··········<p>The·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">true</span>)·can·be·turned·off·to·tell·<span·class="tt">frobeniusNu</span>·to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take·the·minimum.</p>
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106 algorithms,·namely·diagonal·polynomials,·binomials,·forms·in·two·variables,·and106 algorithms,·namely·diagonal·polynomials,·binomials,·forms·in·two·variables,·and
107 polynomials·whose·factors·are·in·simple·normal·crossing.·This·feature·can·be107 polynomials·whose·factors·are·in·simple·normal·crossing.·This·feature·can·be
108 disabled·by·setting·the·option·UseSpecialAlgorithms·(default·value·true)·to108 disabled·by·setting·the·option·UseSpecialAlgorithms·(default·value·true)·to
109 false.109 false.
110 i13·:·R·=·ZZ/17[x,y,z];110 i13·:·R·=·ZZ/17[x,y,z];
111 i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial111 i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial
112 i15·:·time·frobeniusNu(3,·f)112 i15·:·time·frobeniusNu(3,·f)
113 ·--·used·0.00798509s·(cpu);·0.00493792s·(thread);·0s·(gc)113 ·--·used·0.00399559s·(cpu);·0.0041295s·(thread);·0s·(gc)
  
114 o15·=·3756114 o15·=·3756
115 i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false)115 i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false)
116 ·--·used·0.297774s·(cpu);·0.234834s·(thread);·0s·(gc)116 ·--·used·0.344976s·(cpu);·0.234874s·(thread);·0s·(gc)
  
117 o16·=·3756117 o16·=·3756
118 The·valid·values·for·the·option·ContainmentTest·are·FrobeniusPower,118 The·valid·values·for·the·option·ContainmentTest·are·FrobeniusPower,
119 FrobeniusRoot,·and·StandardPower.·The·default·value·of·this·option·depends·on119 FrobeniusRoot,·and·StandardPower.·The·default·value·of·this·option·depends·on
120 what·is·passed·to·frobeniusNu.·Indeed,·by·default,·ContainmentTest·is·set·to120 what·is·passed·to·frobeniusNu.·Indeed,·by·default,·ContainmentTest·is·set·to
121 FrobeniusRoot·if·frobeniusNu·is·passed·a·ring·element·$f$,·and·is·set·to121 FrobeniusRoot·if·frobeniusNu·is·passed·a·ring·element·$f$,·and·is·set·to
122 StandardPower·if·frobeniusNu·is·passed·an·ideal·$I$.·We·describe·the122 StandardPower·if·frobeniusNu·is·passed·an·ideal·$I$.·We·describe·the
Offset 133, 19 lines modifiedOffset 133, 19 lines modified
133 is·contained·in·$J$.·The·output·is·unaffected,·but·this·option·often·speeds·up133 is·contained·in·$J$.·The·output·is·unaffected,·but·this·option·often·speeds·up
134 computations,·specially·when·a·polynomial·or·principal·ideal·is·passed·as·the134 computations,·specially·when·a·polynomial·or·principal·ideal·is·passed·as·the
135 second·argument.135 second·argument.
136 i17·:·R·=·ZZ/5[x,y,z];136 i17·:·R·=·ZZ/5[x,y,z];
137 i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;137 i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;
138 i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by138 i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by
139 default139 default
140 ·--·used·0.293284s·(cpu);·0.195459s·(thread);·0s·(gc)140 ·--·used·0.367984s·(cpu);·0.23738s·(thread);·0s·(gc)
  
141 o19·=·499141 o19·=·499
142 i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower)142 i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower)
143 ·--·used·1.00661s·(cpu);·0.862033s·(thread);·0s·(gc)143 ·--·used·1.14677s·(cpu);·0.990673s·(thread);·0s·(gc)
  
144 o20·=·499144 o20·=·499
145 Finally,·when·ContainmentTest·is·set·to·FrobeniusPower,·then·instead·of145 Finally,·when·ContainmentTest·is·set·to·FrobeniusPower,·then·instead·of
146 producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·frobeniusNu·instead146 producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·frobeniusNu·instead
147 outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius147 outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius
148 power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the148 power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the
149 $n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as149 $n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as
Offset 167, 31 lines modifiedOffset 167, 31 lines modified
167 The·function·frobeniusNu·works·by·searching·through·the·list·of·potential167 The·function·frobeniusNu·works·by·searching·through·the·list·of·potential
168 integers·$n$·and·checking·containments·of·$I^n$·in·the·specified·Frobenius168 integers·$n$·and·checking·containments·of·$I^n$·in·the·specified·Frobenius
169 power·of·$J$.·The·way·this·search·is·approached·is·specified·by·the·option169 power·of·$J$.·The·way·this·search·is·approached·is·specified·by·the·option
170 Search,·which·can·be·set·to·Binary·(the·default·value)·or·Linear.170 Search,·which·can·be·set·to·Binary·(the·default·value)·or·Linear.
171 i25·:·R·=·ZZ/5[x,y,z];171 i25·:·R·=·ZZ/5[x,y,z];
172 i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;172 i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;
173 i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default)173 i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default)
174 ·--·used·0.752781s·(cpu);·0.531304s·(thread);·0s·(gc)174 ·--·used·0.91517s·(cpu);·0.56781s·(thread);·0s·(gc)
  
175 o27·=·1124175 o27·=·1124
176 i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear)176 i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear)
177 ·--·used·1.18633s·(cpu);·0.792731s·(thread);·0s·(gc)177 ·--·used·1.29612s·(cpu);·0.820717s·(thread);·0s·(gc)
  
178 o28·=·1124178 o28·=·1124
179 i29·:·M·=·ideal(x,·y,·z);179 i29·:·M·=·ideal(x,·y,·z);
  
180 o29·:·Ideal·of·R180 o29·:·Ideal·of·R
181 i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default)181 i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default)
182 ·--·used·1.2229s·(cpu);·1.0664s·(thread);·0s·(gc)182 ·--·used·1.3603s·(cpu);·1.17619s·(thread);·0s·(gc)
  
183 o30·=·97183 o30·=·97
184 i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets184 i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets
185 luckier185 luckier
186 ·--·used·0.464793s·(cpu);·0.39059s·(thread);·0s·(gc)186 ·--·used·0.503646s·(cpu);·0.415921s·(thread);·0s·(gc)
  
187 o31·=·97187 o31·=·97
188 The·option·AtOrigin·(default·value·true)·can·be·turned·off·to·tell·frobeniusNu188 The·option·AtOrigin·(default·value·true)·can·be·turned·off·to·tell·frobeniusNu
189 to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take189 to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take
190 the·minimum.190 the·minimum.
191 i32·:·R·=·ZZ/7[x,y];191 i32·:·R·=·ZZ/7[x,y];
192 i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2;192 i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2;
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11 dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsiUlJFRk1l11 dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsiUlJFRk1l
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208 ······|·3/7·5/4·3/7··10···|208 ······|·3/7·5/4·3/7··10···|
209 ······|·6/7·2/9·5····3/2··|209 ······|·6/7·2/9·5····3/2··|
  
210 ···············3·······4210 ···············3·······4
211 o26·:·Matrix·QQ··<--·QQ211 o26·:·Matrix·QQ··<--·QQ
  
212 i27·:·time·C·=·orbitClosure(X,Mat)212 i27·:·time·C·=·orbitClosure(X,Mat)
213 ·--·used·31.2032s·(cpu);·3.89638s·(thread);·0s·(gc)213 ·--·used·27.6677s·(cpu);·3.49262s·(thread);·0s·(gc)
  
214 o27·=·an·"equivariant·K-class"·on·a·GKM·variety·214 o27·=·an·"equivariant·K-class"·on·a·GKM·variety·
  
215 o27·:·KClass215 o27·:·KClass
  
216 i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true)216 i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true)
217 ·--·used·33.1896s·(cpu);·4.48058s·(thread);·0s·(gc)217 ·--·used·28.8627s·(cpu);·4.12869s·(thread);·0s·(gc)
  
218 o28·=·an·"equivariant·K-class"·on·a·GKM·variety·218 o28·=·an·"equivariant·K-class"·on·a·GKM·variety·
  
219 o28·:·KClass219 o28·:·KClass
  
220 i29·:·220 i29·:·
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386 ···············3·······4386 ···············3·······4
387 o26·:·Matrix·QQ··&lt;--·QQ</code></pre>387 o26·:·Matrix·QQ··&lt;--·QQ</code></pre>
388 ············</td>388 ············</td>
389 ··········</tr>389 ··········</tr>
390 ··········<tr>390 ··········<tr>
391 ············<td>391 ············<td>
392 ··············<pre><code·class="language-macaulay2">i27·:·time·C·=·orbitClosure(X,Mat)392 ··············<pre><code·class="language-macaulay2">i27·:·time·C·=·orbitClosure(X,Mat)
393 ·--·used·31.2032s·(cpu);·3.89638s·(thread);·0s·(gc)393 ·--·used·27.6677s·(cpu);·3.49262s·(thread);·0s·(gc)
  
394 o27·=·an·&quot;equivariant·K-class&quot;·on·a·GKM·variety·394 o27·=·an·&quot;equivariant·K-class&quot;·on·a·GKM·variety·
  
395 o27·:·KClass</code></pre>395 o27·:·KClass</code></pre>
396 ············</td>396 ············</td>
397 ··········</tr>397 ··········</tr>
398 ··········<tr>398 ··········<tr>
399 ············<td>399 ············<td>
400 ··············<pre><code·class="language-macaulay2">i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true)400 ··············<pre><code·class="language-macaulay2">i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true)
401 ·--·used·33.1896s·(cpu);·4.48058s·(thread);·0s·(gc)401 ·--·used·28.8627s·(cpu);·4.12869s·(thread);·0s·(gc)
  
402 o28·=·an·&quot;equivariant·K-class&quot;·on·a·GKM·variety·402 o28·=·an·&quot;equivariant·K-class&quot;·on·a·GKM·variety·
  
403 o28·:·KClass</code></pre>403 o28·:·KClass</code></pre>
404 ············</td>404 ············</td>
405 ··········</tr>405 ··········</tr>
406 ········</table>406 ········</table>
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241 o26·=·|·7···6···3/10·10/9·|241 o26·=·|·7···6···3/10·10/9·|
242 ······|·3/7·5/4·3/7··10···|242 ······|·3/7·5/4·3/7··10···|
243 ······|·6/7·2/9·5····3/2··|243 ······|·6/7·2/9·5····3/2··|
  
244 ···············3·······4244 ···············3·······4
245 o26·:·Matrix·QQ··<--·QQ245 o26·:·Matrix·QQ··<--·QQ
246 i27·:·time·C·=·orbitClosure(X,Mat)246 i27·:·time·C·=·orbitClosure(X,Mat)
247 ·--·used·31.2032s·(cpu);·3.89638s·(thread);·0s·(gc)247 ·--·used·27.6677s·(cpu);·3.49262s·(thread);·0s·(gc)
  
248 o27·=·an·"equivariant·K-class"·on·a·GKM·variety248 o27·=·an·"equivariant·K-class"·on·a·GKM·variety
  
249 o27·:·KClass249 o27·:·KClass
250 i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true)250 i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true)
251 ·--·used·33.1896s·(cpu);·4.48058s·(thread);·0s·(gc)251 ·--·used·28.8627s·(cpu);·4.12869s·(thread);·0s·(gc)
  
252 o28·=·an·"equivariant·K-class"·on·a·GKM·variety252 o28·=·an·"equivariant·K-class"·on·a·GKM·variety
  
253 o28·:·KClass253 o28·:·KClass
254 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*254 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
255 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8l_\x8i_\x8z_\x8e_\x8d_\x8F_\x8l_\x8a_\x8g_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·makes·a·generalized·flag·variety·as·a·GKM255 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8l_\x8i_\x8z_\x8e_\x8d_\x8F_\x8l_\x8a_\x8g_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·makes·a·generalized·flag·variety·as·a·GKM
256 ······variety256 ······variety
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729 B
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734 B
./usr/share/doc/Macaulay2/Graphs/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/Graphs/example-output/_new__Digraph.out
    
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32 ·········································5·=>·{6}32 ·········································5·=>·{6}
33 ·········································6·=>·{}33 ·········································6·=>·{}
  
34 o2·:·SortedDigraph34 o2·:·SortedDigraph
  
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37 o3·:·List37 o3·:·List
  
38 i4·:·38 i4·:·
1.1 KB
./usr/share/doc/Macaulay2/Graphs/html/_new__Digraph.html
    
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95 o2·:·SortedDigraph</code></pre>95 o2·:·SortedDigraph</code></pre>
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97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
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104 ··········</tr>104 ··········</tr>
105 ········</table>105 ········</table>
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652 B
html2text {}
    
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36 ·········································4·=>·{}36 ·········································4·=>·{}
37 ·········································5·=>·{6}37 ·········································5·=>·{6}
38 ·········································6·=>·{}38 ·········································6·=>·{}
  
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41 o3·=·{digraph,·newDigraph,·map}41 o3·=·{map,·digraph,·newDigraph}
  
42 o3·:·List42 o3·:·List
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47 ······order·of·a·DAG.47 ······order·of·a·DAG.
742 B
./usr/share/doc/Macaulay2/GroebnerStrata/dump/rawdocumentation.dump
    
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8.33 KB
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79 ······+----------------------------------------------------------------------------------------+79 ······+-------------------------------------------------------------------------------------+
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81 ······+----------------------------------------------------------------------------------------+81 ······+-------------------------------------------------------------------------------------+
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87 ······+----------------------------------------------------------------------------------------+87 ······+-------------------------------------------------------------------------------------+
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91 ······+----------------------------------------------------------------------------------------+91 ······+-------------------------------------------------------------------------------------+
  
92 i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10)92 i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10)
  
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97 ······+--------------------------------------------------------------------------------------+97 ······+---------------------------------------------------------------------------------------+
98 ······||·24·-43·-8·-28·-37·48·45·16·34·47·20·-25·1·1·18·-44·40·-22·46·28·-18·-49·10·0·|······|98 ······||·-27·-3·-40·22·27·3·-28·-41·-12·-34·-10·40·46·29·30·24·-49·28·1·40·10·-22·-18·0·|·····|
99 ······+--------------------------------------------------------------------------------------+99 ······+---------------------------------------------------------------------------------------+
100 ······||·2·-44·10·47·22·42·-37·22·-39·-29·19·-42·-13·-39·0·-13·3·-41·-17·30·13·7·8·0·|·······|100 ······||·-26·-6·24·28·-27·26·34·47·13·50·3·-42·-17·5·4·-35·7·30·-13·3·8·-41·13·0·|············|
101 ······+--------------------------------------------------------------------------------------+101 ······+---------------------------------------------------------------------------------------+
102 ······||·-18·31·14·-11·-10·-1·7·-12·-36·3·-34·-2·49·-4·-1·45·-18·42·-46·-29·30·8·23·0·|······|102 ······||·49·-7·48·1·48·25·25·-10·49·36·-16·35·-46·-5·25·-33·8·-29·49·-18·23·42·30·0·|·········|
103 ······+--------------------------------------------------------------------------------------+103 ······+---------------------------------------------------------------------------------------+
104 ······||·22·22·21·25·-34·13·-42·42·34·7·-15·-2·-46·43·31·32·12·-18·-16·15·18·-28·27·0·|······|104 ······||·-35·28·-6·22·50·-49·2·-5·-11·-39·30·27·-16·34·-9·-34·-28·15·-46·12·27·-18·18·0·|·····|
105 ······+--------------------------------------------------------------------------------------+105 ······+---------------------------------------------------------------------------------------+
106 ······||·20·34·11·19·24·-34·-32·-18·-4·44·-43·-14·44·26·-43·9·-39·20·-23·23·-37·-21·19·0·|···|106 ······||·-49·-44·-16·-10·48·18·22·33·-35·-48·-28·-8·-23·-48·-25·-3·-21·23·44·-39·19·20·-37·0·||
107 ······+--------------------------------------------------------------------------------------+107 ······+---------------------------------------------------------------------------------------+
108 ······||·9·44·22·48·-27·-22·-41·22·17·48·3·27·-28·18·-9·27·6·-9·47·-47·-28·0·-33·0·|·········|108 ······||·-33·-14·-18·10·2·-43·-26·45·10·19·-15·25·47·9·-15·-22·0·-47·-28·6·-33·-9·-28·0·|·····|
109 ······+--------------------------------------------------------------------------------------+109 ······+---------------------------------------------------------------------------------------+
110 ······||·-45·5·15·-32·-3·-14·-30·44·10·44·-29·-48·-37·23·-14·-47·-33·-28·5·-29·26·28·42·0·|··|110 ······||·20·-27·-17·2·-47·-23·13·40·-19·-13·39·-23·5·-3·47·-6·28·-29·-37·-33·42·-28·26·0·|····|
111 ······+--------------------------------------------------------------------------------------+111 ······+---------------------------------------------------------------------------------------+
112 ······||·-2·-29·-50·-48·-22·17·-41·-21·-1·-4·13·17·5·-33·-5·47·-20·-13·22·30·4·44·-29·0·|····|112 ······||·19·10·-10·47·41·20·-43·-34·-43·2·44·29·22·35·-42·16·44·30·5·-20·-29·-13·4·0·|········|
113 ······+--------------------------------------------------------------------------------------+113 ······+---------------------------------------------------------------------------------------+
  
114 i15·:·114 i15·:·
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186 ··········<p>There·are·2·components.··We·attempt·to·find·points·on·each·of·these·two·components.·We·are·successful.··This·indicates·that·the·corresponding·varieties·are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we·want.</p>186 ··········<p>There·are·2·components.··We·attempt·to·find·points·on·each·of·these·two·components.·We·are·successful.··This·indicates·that·the·corresponding·varieties·are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we·want.</p>
187 ········</div>187 ········</div>
188 ········<table·class="examples">188 ········<table·class="examples">
189 ··········<tr>189 ··········<tr>
190 ············<td>190 ············<td>
191 ··············<pre><code·class="language-macaulay2">i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10)191 ··············<pre><code·class="language-macaulay2">i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10)
  
192 ······+----------------------------------------------------------------------------------------+192 ······+-------------------------------------------------------------------------------------+
193 o13·=·||·-15·9·-4·9·-47·-7·19·31·-22·-13·-23·-30·-38·-16·-19·39·-18·16·21·34·-47·19·-43·-39·|··|193 o13·=·||·13·15·3·36·2·48·44·-35·-34·39·5·-32·34·19·-42·-47·-16·-34·-39·-13·-18·-43·21·-38·|·|
194 ······+----------------------------------------------------------------------------------------+194 ······+-------------------------------------------------------------------------------------+
195 ······||·47·2·-38·-35·-49·-35·-20·48·-42·-48·-28·21·-15·-28·-10·-47·-34·49·38·2·22·16·-47·45·|·|195 ······||·-43·48·14·29·-47·-10·47·22·8·-47·15·-26·2·16·-49·22·-28·-18·45·-48·-34·-47·38·-15·||
196 ······+----------------------------------------------------------------------------------------+196 ······+-------------------------------------------------------------------------------------+
197 ······||·15·-40·-13·-45·-32·9·34·10·-2·-11·30·18·47·19·30·-16·-17·12·7·15·39·-23·48·43·|·······|197 ······||·-3·45·42·47·-50·16·-30·28·43·-16·24·19·15·-23·37·39·19·-8·43·-11·-17·48·7·47·|·····|
198 ······+----------------------------------------------------------------------------------------+198 ······+-------------------------------------------------------------------------------------+
199 ······||·-22·-35·14·-29·-36·-14·-18·-44·-50·1·14·16·36·35·5·11·-28·36·-38·33·11·40·-3·46·|·····|199 ······||·-49·7·32·-6·-30·-41·-10·2·44·11·-25·4·33·40·-19·11·35·-17·46·1·-28·-3·-38·36·|·····|
200 ······+----------------------------------------------------------------------------------------+200 ······+-------------------------------------------------------------------------------------+
201 ······||·13·-35·-39·35·16·-18·41·35·-15·-13·-26·-46·22·-47·-2·-23·-37·-50·-7·2·-47·29·-10·15·|·|201 ······||·35·-48·-2·45·-35·29·34·12·-32·-23·50·2·2·29·-3·-47·-47·-34·15·-13·-37·-10·-7·22·|··|
202 ······+----------------------------------------------------------------------------------------+202 ······+-------------------------------------------------------------------------------------+
203 ······||·19·-11·-23·-31·-35·-36·28·40·38·24·41·-47·30·-18·13·39·-20·15·27·-22·-9·32·-30·-32·|··|203 ······||·47·8·-14·6·-1·-13·-7·16·-20·39·-34·-22·-22·32·17·-9·-18·-6·-32·24·-20·-30·27·30·|··|
204 ······+----------------------------------------------------------------------------------------+204 ······+-------------------------------------------------------------------------------------+
205 ······||·41·29·49·14·-11·20·16·28·-48·-20·0·-5·-48·-15·-46·39·17·1·0·33·-33·-49·44·-19·|·······|205 ······||·-2·-36·-39·41·-6·34·-10·42·5·39·20·33·33·-49·-15·-33·-15·41·-19·-20·17·44·0·-48·|··|
206 ······+----------------------------------------------------------------------------------------+206 ······+-------------------------------------------------------------------------------------+
207 ······||·39·-35·49·20·-8·41·-3·19·23·-11·-4·-12·-39·36·46·9·-49·-35·-39·4·-26·13·-8·22·|·······|207 ······||·-30·37·-9·16·-36·19·-13·-14·-19·9·-33·5·4·13·44·-26·36·-12·22·-11·-49·-8·-39·-39·|·|
208 ······+----------------------------------------------------------------------------------------+208 ······+-------------------------------------------------------------------------------------+
209 ······||·27·-7·-28·31·30·41·-27·41·26·-6·22·-5·43·-8·-49·36·-28·-18·-3·-22·41·-30·35·16·|······|209 ······||·27·41·32·-44·40·-20·41·33·28·36·44·31·-22·-30·9·41·-8·30·16·-6·-28·35·-3·43·|······|
210 ······+----------------------------------------------------------------------------------------+210 ······+-------------------------------------------------------------------------------------+
211 ······||·36·-33·-45·-12·-50·-48·-13·-28·-15·-49·10·-31·-9·-35·-19·6·-41·33·40·3·25·-31·-13·-2·||211 ······||·37·-2·17·-42·-42·-12·18·-31·33·6·19·-31·3·-31·-11·25·-35·28·-2·-49·-41·-13·40·-9·|·|
212 ······+----------------------------------------------------------------------------------------+</code></pre>212 ······+-------------------------------------------------------------------------------------+</code></pre>
213 ············</td>213 ············</td>
214 ··········</tr>214 ··········</tr>
215 ··········<tr>215 ··········<tr>
216 ············<td>216 ············<td>
217 ··············<pre><code·class="language-macaulay2">i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10)217 ··············<pre><code·class="language-macaulay2">i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10)
  
218 ······+--------------------------------------------------------------------------------------+218 ······+---------------------------------------------------------------------------------------+
219 o14·=·||·-35·39·-4·-3·-26·4·20·45·43·-3·-44·23·-40·-50·-6·-24·37·-35·27·30·-47·4·-31·0·|·····|219 o14·=·||·-41·-1·-48·25·40·4·35·16·26·-41·-28·-16·27·-14·-39·4·4·30·-40·37·-31·-35·-47·0·|·····|
220 ······+--------------------------------------------------------------------------------------+220 ······+---------------------------------------------------------------------------------------+
221 ······||·-9·18·13·-46·44·-19·-4·10·-33·13·22·-48·-48·-33·-37·-8·30·-37·-29·-31·-48·-39·47·0·||221 ······||·-1·19·-3·12·50·3·4·25·48·50·34·-6·-29·6·-5·36·-39·-31·-48·30·47·-37·-48·0·|··········|
222 ······+--------------------------------------------------------------------------------------+222 ······+---------------------------------------------------------------------------------------+
223 ······||·24·-43·-8·-28·-37·48·45·16·34·47·20·-25·1·1·18·-44·40·-22·46·28·-18·-49·10·0·|······|223 ······||·-27·-3·-40·22·27·3·-28·-41·-12·-34·-10·40·46·29·30·24·-49·28·1·40·10·-22·-18·0·|·····|
224 ······+--------------------------------------------------------------------------------------+224 ······+---------------------------------------------------------------------------------------+
225 ······||·2·-44·10·47·22·42·-37·22·-39·-29·19·-42·-13·-39·0·-13·3·-41·-17·30·13·7·8·0·|·······|225 ······||·-26·-6·24·28·-27·26·34·47·13·50·3·-42·-17·5·4·-35·7·30·-13·3·8·-41·13·0·|············|
226 ······+--------------------------------------------------------------------------------------+226 ······+---------------------------------------------------------------------------------------+
227 ······||·-18·31·14·-11·-10·-1·7·-12·-36·3·-34·-2·49·-4·-1·45·-18·42·-46·-29·30·8·23·0·|······|227 ······||·49·-7·48·1·48·25·25·-10·49·36·-16·35·-46·-5·25·-33·8·-29·49·-18·23·42·30·0·|·········|
228 ······+--------------------------------------------------------------------------------------+228 ······+---------------------------------------------------------------------------------------+
229 ······||·22·22·21·25·-34·13·-42·42·34·7·-15·-2·-46·43·31·32·12·-18·-16·15·18·-28·27·0·|······|229 ······||·-35·28·-6·22·50·-49·2·-5·-11·-39·30·27·-16·34·-9·-34·-28·15·-46·12·27·-18·18·0·|·····|
230 ······+--------------------------------------------------------------------------------------+230 ······+---------------------------------------------------------------------------------------+
231 ······||·20·34·11·19·24·-34·-32·-18·-4·44·-43·-14·44·26·-43·9·-39·20·-23·23·-37·-21·19·0·|···|231 ······||·-49·-44·-16·-10·48·18·22·33·-35·-48·-28·-8·-23·-48·-25·-3·-21·23·44·-39·19·20·-37·0·||
232 ······+--------------------------------------------------------------------------------------+232 ······+---------------------------------------------------------------------------------------+
233 ······||·9·44·22·48·-27·-22·-41·22·17·48·3·27·-28·18·-9·27·6·-9·47·-47·-28·0·-33·0·|·········|233 ······||·-33·-14·-18·10·2·-43·-26·45·10·19·-15·25·47·9·-15·-22·0·-47·-28·6·-33·-9·-28·0·|·····|
234 ······+--------------------------------------------------------------------------------------+234 ······+---------------------------------------------------------------------------------------+
235 ······||·-45·5·15·-32·-3·-14·-30·44·10·44·-29·-48·-37·23·-14·-47·-33·-28·5·-29·26·28·42·0·|··|235 ······||·20·-27·-17·2·-47·-23·13·40·-19·-13·39·-23·5·-3·47·-6·28·-29·-37·-33·42·-28·26·0·|····|
236 ······+--------------------------------------------------------------------------------------+236 ······+---------------------------------------------------------------------------------------+
237 ······||·-2·-29·-50·-48·-22·17·-41·-21·-1·-4·13·17·5·-33·-5·47·-20·-13·22·30·4·44·-29·0·|····|237 ······||·19·10·-10·47·41·20·-43·-34·-43·2·44·29·22·35·-42·16·44·30·5·-20·-29·-13·4·0·|········|
238 ······+--------------------------------------------------------------------------------------+</code></pre>238 ······+---------------------------------------------------------------------------------------+</code></pre>
239 ············</td>239 ············</td>
240 ··········</tr>240 ··········</tr>
241 ········</table>241 ········</table>
242 ······</div>242 ······</div>
243 ······<div>243 ······<div>
244 ········<h2>Caveat</h2>244 ········<h2>Caveat</h2>
245 ········<div>245 ········<div>
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84 There·are·2·components.·We·attempt·to·find·points·on·each·of·these·two84 There·are·2·components.·We·attempt·to·find·points·on·each·of·these·two
85 components.·We·are·successful.·This·indicates·that·the·corresponding·varieties85 components.·We·are·successful.·This·indicates·that·the·corresponding·varieties
86 are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we86 are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we
87 want.87 want.
88 i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10)88 i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10)
  
89 ······+------------------------------------------------------------------------89 ······+------------------------------------------------------------------------
90 ----------------+90 -------------+
91 o13·=·||·-15·9·-4·9·-47·-7·19·31·-22·-13·-23·-30·-38·-16·-19·39·-18·16·21·34·- 
92 47·19·-43·-39·|··|91 o13·=·||·13·15·3·36·2·48·44·-35·-34·39·5·-32·34·19·-42·-47·-16·-34·-39·-13·-18
 92 -43·21·-38·|·|
93 ······+------------------------------------------------------------------------93 ······+------------------------------------------------------------------------
94 ----------------+94 -------------+
95 ······||·47·2·-38·-35·-49·-35·-20·48·-42·-48·-28·21·-15·-28·-10·-47·-34·49·38·2 
96 22·16·-47·45·|·|95 ······||·-43·48·14·29·-47·-10·47·22·8·-47·15·-26·2·16·-49·22·-28·-18·45·-48·-34
 96 -47·38·-15·||
97 ······+------------------------------------------------------------------------97 ······+------------------------------------------------------------------------
98 ----------------+98 -------------+
99 ······||·15·-40·-13·-45·-32·9·34·10·-2·-11·30·18·47·19·30·-16·-17·12·7·15·39·- 
100 23·48·43·|·······|99 ······||·-3·45·42·47·-50·16·-30·28·43·-16·24·19·15·-23·37·39·19·-8·43·-11·-17
 100 48·7·47·|·····|
101 ······+------------------------------------------------------------------------101 ······+------------------------------------------------------------------------
102 ----------------+102 -------------+
103 ······||·-22·-35·14·-29·-36·-14·-18·-44·-50·1·14·16·36·35·5·11·-28·36·-38·33·11103 ······||·-49·7·32·-6·-30·-41·-10·2·44·11·-25·4·33·40·-19·11·35·-17·46·1·-28·-
104 40·-3·46·|·····|104 3·-38·36·|·····|
105 ······+------------------------------------------------------------------------105 ······+------------------------------------------------------------------------
106 ----------------+106 -------------+
107 ······||·13·-35·-39·35·16·-18·41·35·-15·-13·-26·-46·22·-47·-2·-23·-37·-50·-7·2 
108 -47·29·-10·15·|·|107 ······||·35·-48·-2·45·-35·29·34·12·-32·-23·50·2·2·29·-3·-47·-47·-34·15·-13·-37
 108 -10·-7·22·|··|
109 ······+------------------------------------------------------------------------109 ······+------------------------------------------------------------------------
110 ----------------+110 -------------+
111 ······||·19·-11·-23·-31·-35·-36·28·40·38·24·41·-47·30·-18·13·39·-20·15·27·-22·- 
112 9·32·-30·-32·|··|111 ······||·47·8·-14·6·-1·-13·-7·16·-20·39·-34·-22·-22·32·17·-9·-18·-6·-32·24·-20
 112 -30·27·30·|··|
113 ······+------------------------------------------------------------------------113 ······+------------------------------------------------------------------------
114 ----------------+114 -------------+
115 ······||·41·29·49·14·-11·20·16·28·-48·-20·0·-5·-48·-15·-46·39·17·1·0·33·-33·-49 
116 44·-19·|·······|115 ······||·-2·-36·-39·41·-6·34·-10·42·5·39·20·33·33·-49·-15·-33·-15·41·-19·-20·17
 116 44·0·-48·|··|
117 ······+------------------------------------------------------------------------117 ······+------------------------------------------------------------------------
118 ----------------+118 -------------+
119 ······||·39·-35·49·20·-8·41·-3·19·23·-11·-4·-12·-39·36·46·9·-49·-35·-39·4·-26 
120 13·-8·22·|·······|119 ······||·-30·37·-9·16·-36·19·-13·-14·-19·9·-33·5·4·13·44·-26·36·-12·22·-11·-49
 120 -8·-39·-39·|·|
121 ······+------------------------------------------------------------------------121 ······+------------------------------------------------------------------------
122 ----------------+122 -------------+
123 ······||·27·-7·-28·31·30·41·-27·41·26·-6·22·-5·43·-8·-49·36·-28·-18·-3·-22·41·-123 ······||·27·41·32·-44·40·-20·41·33·28·36·44·31·-22·-30·9·41·-8·30·16·-6·-28·35
124 30·35·16·|······|124 -3·43·|······|
125 ······+------------------------------------------------------------------------125 ······+------------------------------------------------------------------------
126 ----------------+126 -------------+
127 ······||·36·-33·-45·-12·-50·-48·-13·-28·-15·-49·10·-31·-9·-35·-19·6·-41·33·40·3 
128 25·-31·-13·-2·||127 ······||·37·-2·17·-42·-42·-12·18·-31·33·6·19·-31·3·-31·-11·25·-35·28·-2·-49·-41
 128 -13·40·-9·|·|
129 ······+------------------------------------------------------------------------129 ······+------------------------------------------------------------------------
130 ----------------+130 -------------+
131 i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10)131 i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10)
  
132 ······+------------------------------------------------------------------------132 ······+------------------------------------------------------------------------
133 --------------+133 ---------------+
134 o14·=·||·-35·39·-4·-3·-26·4·20·45·43·-3·-44·23·-40·-50·-6·-24·37·-35·27·30·-47134 o14·=·||·-41·-1·-48·25·40·4·35·16·26·-41·-28·-16·27·-14·-39·4·4·30·-40·37·-31·-
135 4·-31·0·|·····|135 35·-47·0·|·····|
136 ······+------------------------------------------------------------------------136 ······+------------------------------------------------------------------------
137 --------------+137 ---------------+
138 ······||·-9·18·13·-46·44·-19·-4·10·-33·13·22·-48·-48·-33·-37·-8·30·-37·-29·-31 
139 -48·-39·47·0·||138 ······||·-1·19·-3·12·50·3·4·25·48·50·34·-6·-29·6·-5·36·-39·-31·-48·30·47·-37·-
 139 48·0·|··········|
140 ······+------------------------------------------------------------------------140 ······+------------------------------------------------------------------------
141 --------------+141 ---------------+
142 ······||·24·-43·-8·-28·-37·48·45·16·34·47·20·-25·1·1·18·-44·40·-22·46·28·-18·-142 ······||·-27·-3·-40·22·27·3·-28·-41·-12·-34·-10·40·46·29·30·24·-49·28·1·40·10·-
143 49·10·0·|······|143 22·-18·0·|·····|
144 ······+------------------------------------------------------------------------144 ······+------------------------------------------------------------------------
145 --------------+145 ---------------+
146 ······||·2·-44·10·47·22·42·-37·22·-39·-29·19·-42·-13·-39·0·-13·3·-41·-17·30·13 
147 7·8·0·|·······|146 ······||·-26·-6·24·28·-27·26·34·47·13·50·3·-42·-17·5·4·-35·7·30·-13·3·8·-41·13
 147 0·|············|
148 ······+------------------------------------------------------------------------148 ······+------------------------------------------------------------------------
149 --------------+149 ---------------+
150 ······||·-18·31·14·-11·-10·-1·7·-12·-36·3·-34·-2·49·-4·-1·45·-18·42·-46·-29·30150 ······||·49·-7·48·1·48·25·25·-10·49·36·-16·35·-46·-5·25·-33·8·-29·49·-18·23·42
151 8·23·0·|······|151 30·0·|·········|
152 ······+------------------------------------------------------------------------152 ······+------------------------------------------------------------------------
153 --------------+153 ---------------+
154 ······||·22·22·21·25·-34·13·-42·42·34·7·-15·-2·-46·43·31·32·12·-18·-16·15·18·-154 ······||·-35·28·-6·22·50·-49·2·-5·-11·-39·30·27·-16·34·-9·-34·-28·15·-46·12·27
155 28·27·0·|······|155 -18·18·0·|·····|
156 ······+------------------------------------------------------------------------156 ······+------------------------------------------------------------------------
157 --------------+157 ---------------+
158 ······||·20·34·11·19·24·-34·-32·-18·-4·44·-43·-14·44·26·-43·9·-39·20·-23·23·-37 
159 -21·19·0·|···|158 ······||·-49·-44·-16·-10·48·18·22·33·-35·-48·-28·-8·-23·-48·-25·-3·-21·23·44·-
 159 39·19·20·-37·0·||
160 ······+------------------------------------------------------------------------160 ······+------------------------------------------------------------------------
161 --------------+161 ---------------+
162 ······||·9·44·22·48·-27·-22·-41·22·17·48·3·27·-28·18·-9·27·6·-9·47·-47·-28·0·- 
163 33·0·|·········|162 ······||·-33·-14·-18·10·2·-43·-26·45·10·19·-15·25·47·9·-15·-22·0·-47·-28·6·-33
 163 -9·-28·0·|·····|
164 ······+------------------------------------------------------------------------164 ······+------------------------------------------------------------------------
165 --------------+165 ---------------+
166 ······||·-45·5·15·-32·-3·-14·-30·44·10·44·-29·-48·-37·23·-14·-47·-33·-28·5·-29 
167 26·28·42·0·|··|166 ······||·20·-27·-17·2·-47·-23·13·40·-19·-13·39·-23·5·-3·47·-6·28·-29·-37·-33·42
 167 -28·26·0·|····|
168 ······+------------------------------------------------------------------------168 ······+------------------------------------------------------------------------
169 --------------+169 ---------------+
170 ······||·-2·-29·-50·-48·-22·17·-41·-21·-1·-4·13·17·5·-33·-5·47·-20·-13·22·30·4 
171 44·-29·0·|····|170 ······||·19·10·-10·47·41·20·-43·-34·-43·2·44·29·22·35·-42·16·44·30·5·-20·-29·-
 171 13·4·0·|········|
172 ······+------------------------------------------------------------------------172 ······+------------------------------------------------------------------------
173 --------------+173 ---------------+
174 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*174 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
175 This·routine·expects·the·input·to·represent·an·irreducible·variety175 This·routine·expects·the·input·to·represent·an·irreducible·variety
176 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*176 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
177 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8O_\x8n_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8I_\x8d_\x8e_\x8a_\x8l_\x8)·--·find·a·random·point·on·a·variety177 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8O_\x8n_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8I_\x8d_\x8e_\x8a_\x8l_\x8)·--·find·a·random·point·on·a·variety
178 ······that·can·be·detected·to·be·rational178 ······that·can·be·detected·to·be·rational
179 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*179 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
180 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s_\x8O_\x8n_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8I_\x8d_\x8e_\x8a_\x8l_\x8,_\x8Z_\x8Z_\x8)·--·find·random·points·on·a180 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s_\x8O_\x8n_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8I_\x8d_\x8e_\x8a_\x8l_\x8,_\x8Z_\x8Z_\x8)·--·find·random·points·on·a
733 B
./usr/share/doc/Macaulay2/GroebnerWalk/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=167 #:len=16
8 c2V0V2Fsa1RyYWNlKFpaKQ==8 c2V0V2Fsa1RyYWNlKFpaKQ==
9 #:len=2519 #:len=251
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTYxLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTYxLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzZXRXYWxrVHJhY2UsWlopLCJzZXRXYWxrVHJhY2Uo11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzZXRXYWxrVHJhY2UsWlopLCJzZXRXYWxrVHJhY2Uo
634 B
./usr/share/doc/Macaulay2/GroebnerWalk/example-output/___Groebner__Walk.out
    
Offset 11, 21 lines modifiedOffset 11, 21 lines modified
11 i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}];11 i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}];
  
12 i4·:·I2·=·sub(I1,·R2);12 i4·:·I2·=·sub(I1,·R2);
  
13 o4·:·Ideal·of·R213 o4·:·Ideal·of·R2
  
14 i5·:·elapsedTime·gb·I214 i5·:·elapsedTime·gb·I2
15 ·--·1.84982s·elapsed15 ·--·6.82525s·elapsed
  
16 o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16]16 o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16]
  
17 o5·:·GroebnerBasis17 o5·:·GroebnerBasis
  
18 i6·:·elapsedTime·groebnerWalk(gb·I1,·R2)18 i6·:·elapsedTime·groebnerWalk(gb·I1,·R2)
19 ·--·1.48794s·elapsed19 ·--·3.6908s·elapsed
  
20 o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0]20 o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0]
  
21 o6·:·GroebnerBasis21 o6·:·GroebnerBasis
  
22 i7·:·22 i7·:·
1.88 KB
./usr/share/doc/Macaulay2/GroebnerWalk/html/index.html
    
Offset 92, 30 lines modifiedOffset 92, 30 lines modified
  
92 o4·:·Ideal·of·R2</code></pre>92 o4·:·Ideal·of·R2</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·gb·I297 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·gb·I2
98 ·--·1.84982s·elapsed98 ·--·6.82525s·elapsed
  
99 o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16]99 o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16]
  
100 o5·:·GroebnerBasis</code></pre>100 o5·:·GroebnerBasis</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ········</table>103 ········</table>
104 ········<div>104 ········<div>
105 ··········<p>but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the·Groebner·walk.</p>105 ··········<p>but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the·Groebner·walk.</p>
106 ········</div>106 ········</div>
107 ········<table·class="examples">107 ········<table·class="examples">
108 ··········<tr>108 ··········<tr>
109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·groebnerWalk(gb·I1,·R2)110 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·groebnerWalk(gb·I1,·R2)
111 ·--·1.48794s·elapsed111 ·--·3.6908s·elapsed
  
112 o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0]112 o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0]
  
113 o6·:·GroebnerBasis</code></pre>113 o6·:·GroebnerBasis</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ········</table>116 ········</table>
911 B
html2text {}
    
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38 using·a·different·weight·vector·and·then·graded·reverse·lexicographic·we·could38 using·a·different·weight·vector·and·then·graded·reverse·lexicographic·we·could
39 substitute·and·compute·directly,39 substitute·and·compute·directly,
40 i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}];40 i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}];
41 i4·:·I2·=·sub(I1,·R2);41 i4·:·I2·=·sub(I1,·R2);
  
42 o4·:·Ideal·of·R242 o4·:·Ideal·of·R2
43 i5·:·elapsedTime·gb·I243 i5·:·elapsedTime·gb·I2
44 ·--·1.84982s·elapsed44 ·--·6.82525s·elapsed
  
45 o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16]45 o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16]
  
46 o5·:·GroebnerBasis46 o5·:·GroebnerBasis
47 but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the47 but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the
48 Groebner·walk.48 Groebner·walk.
49 i6·:·elapsedTime·groebnerWalk(gb·I1,·R2)49 i6·:·elapsedTime·groebnerWalk(gb·I1,·R2)
50 ·--·1.48794s·elapsed50 ·--·3.6908s·elapsed
  
51 o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0]51 o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0]
  
52 o6·:·GroebnerBasis52 o6·:·GroebnerBasis
53 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*53 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
54 The·target·ring·must·be·the·same·ring·as·the·ring·of·the·starting·ideal,·except54 The·target·ring·must·be·the·same·ring·as·the·ring·of·the·starting·ideal,·except
55 with·different·monomial·order.·The·ring·must·be·a·polynomial·ring·over·a·field.55 with·different·monomial·order.·The·ring·must·be·a·polynomial·ring·over·a·field.
734 B
./usr/share/doc/Macaulay2/Hadamard/dump/rawdocumentation.dump
    
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2 #:version=1.12 #:version=1.1
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7 #:len=237 #:len=23
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11 dCBvZiBwb2ludHMiLCAibGluZW51bSIgPT4gNDI0LCBJbnB1dHMgPT4ge1NQQU57VFR7IkwifSwi11 dCBvZiBwb2ludHMiLCAibGluZW51bSIgPT4gNDI0LCBJbnB1dHMgPT4ge1NQQU57VFR7IkwifSwi
748 B
./usr/share/doc/Macaulay2/HigherCIOperators/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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11 b21wbGV0ZSBpbnRlcnNlY3Rpb24gdXNpbmcgaGlnaGVyIGNpLW9wZXJhdG9yc1wiIiwgImxpbmVu11 b21wbGV0ZSBpbnRlcnNlY3Rpb24gdXNpbmcgaGlnaGVyIGNpLW9wZXJhdG9yc1wiIiwgImxpbmVu
729 B
./usr/share/doc/Macaulay2/HighestWeights/dump/rawdocumentation.dump
    
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721 B
./usr/share/doc/Macaulay2/HodgeIntegrals/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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8 a2FwcGE=8 a2FwcGE=
9 #:len=13969 #:len=1396
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTWlsbGVyLU1vcml0YS1NdW1mb3JkIGNs10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTWlsbGVyLU1vcml0YS1NdW1mb3JkIGNs
11 YXNzZXMiLCAibGluZW51bSIgPT4gNzM3LCBJbnB1dHMgPT4ge1NQQU57VFR7ImEifSwiLCAiLFNQ11 YXNzZXMiLCAibGluZW51bSIgPT4gNzM3LCBJbnB1dHMgPT4ge1NQQU57VFR7ImEifSwiLCAiLFNQ
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./usr/share/doc/Macaulay2/HolonomicSystems/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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7 #:len=147 #:len=14
8 ZXVsZXJPcGVyYXRvcnM=8 ZXVsZXJPcGVyYXRvcnM=
9 #:len=19599 #:len=1959
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11 dW0iID0+IDE0MCwgSW5wdXRzID0+IHtTUEFOe1RUeyJBIn0sIiwgIixTUEFOeyJhICIsVE8ye25l11 dW0iID0+IDE0MCwgSW5wdXRzID0+IHtTUEFOe1RUeyJBIn0sIiwgIixTUEFOeyJhICIsVE8ye25l
925 B
./usr/share/doc/Macaulay2/HolonomicSystems/example-output/_css__Lead__Term.out
    
Offset 42, 19 lines modifiedOffset 42, 19 lines modified
42 i5·:·w·=·{9,1,99999,·9999999,·3,·999}42 i5·:·w·=·{9,1,99999,·9999999,·3,·999}
  
43 o5·=·{9,·1,·99999,·9999999,·3,·999}43 o5·=·{9,·1,·99999,·9999999,·3,·999}
  
44 o5·:·List44 o5·:·List
  
45 i6·:·netList·cssLeadTerm(Hbeta,·w)45 i6·:·netList·cssLeadTerm(Hbeta,·w)
 46 ·--·.000003837s·elapsed
 47 ·--·.000003868s·elapsed
 48 ·--·.000002745s·elapsed
 49 ·--·.000002936s·elapsed
46 ·--·.000003795s·elapsed50 ·--·.000003075s·elapsed
47 ·--·.000005829s·elapsed 
48 ·--·.000005508s·elapsed 
49 ·--·.000004517s·elapsed 
50 ·--·.000004267s·elapsed 
51 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.51 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.
52 Converting·to·Naive·algorithm.52 Converting·to·Naive·algorithm.
  
53 ·····+----------------------------------------------------+53 ·····+----------------------------------------------------+
54 ·····|···1·5···5·5········································|54 ·····|···1·5···5·5········································|
55 ·····|·-·-·-·-·-·-········································|55 ·····|·-·-·-·-·-·-········································|
56 ·····|···2·2···2·2········································|56 ·····|···2·2···2·2········································|
1.47 KB
./usr/share/doc/Macaulay2/HolonomicSystems/example-output/_solve__Frobenius__Ideal.out
    
Offset 3, 15 lines modifiedOffset 3, 15 lines modified
3 i1·:·R·=·QQ[t_1..t_5];3 i1·:·R·=·QQ[t_1..t_5];
  
4 i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,·t_2*t_4);4 i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,·t_2*t_4);
  
5 o2·:·Ideal·of·R5 o2·:·Ideal·of·R
  
6 i3·:·solveFrobeniusIdeal·I6 i3·:·solveFrobeniusIdeal·I
7 ·--·.000003725s·elapsed7 ·--·.000005941s·elapsed
8 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.8 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.
9 Converting·to·Naive·algorithm.9 Converting·to·Naive·algorithm.
  
10 ·············································································10 ·············································································
11 o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,11 o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,
12 ················0········1········2·······3········0·······1·······2·······4·12 ················0········1········2·······3········0·······1·······2·······4·
13 ·····------------------------------------------------------------------------13 ·····------------------------------------------------------------------------
Offset 24, 15 lines modifiedOffset 24, 15 lines modified
24 ·······2····4····0···4····4····1···2····4····2···4····4····3·······424 ·······2····4····0···4····4····1···2····4····2···4····4····3·······4
  
25 o3·:·List25 o3·:·List
  
26 i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);26 i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);
  
27 i5·:·solveFrobeniusIdeal(I,·W)27 i5·:·solveFrobeniusIdeal(I,·W)
28 ·--·.000003905s·elapsed28 ·--·.00000522s·elapsed
29 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.29 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.
30 Converting·to·Naive·algorithm.30 Converting·to·Naive·algorithm.
  
31 ·············································································31 ·············································································
32 o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,32 o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,
33 ················0········1········2·······3········0·······1·······2·······4·33 ················0········1········2·······3········0·······1·······2·······4·
34 ·····------------------------------------------------------------------------34 ·····------------------------------------------------------------------------
1.69 KB
./usr/share/doc/Macaulay2/HolonomicSystems/html/_css__Lead__Term.html
    
Offset 132, 19 lines modifiedOffset 132, 19 lines modified
  
132 o5·:·List</code></pre>132 o5·:·List</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i6·:·netList·cssLeadTerm(Hbeta,·w)137 ··············<pre><code·class="language-macaulay2">i6·:·netList·cssLeadTerm(Hbeta,·w)
 138 ·--·.000003837s·elapsed
 139 ·--·.000003868s·elapsed
 140 ·--·.000002745s·elapsed
 141 ·--·.000002936s·elapsed
138 ·--·.000003795s·elapsed142 ·--·.000003075s·elapsed
139 ·--·.000005829s·elapsed 
140 ·--·.000005508s·elapsed 
141 ·--·.000004517s·elapsed 
142 ·--·.000004267s·elapsed 
143 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.143 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.
144 Converting·to·Naive·algorithm.144 Converting·to·Naive·algorithm.
  
145 ·····+----------------------------------------------------+145 ·····+----------------------------------------------------+
146 ·····|···1·5···5·5········································|146 ·····|···1·5···5·5········································|
147 ·····|·-·-·-·-·-·-········································|147 ·····|·-·-·-·-·-·-········································|
148 ·····|···2·2···2·2········································|148 ·····|···2·2···2·2········································|
764 B
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Offset 54, 19 lines modifiedOffset 54, 19 lines modified
54 ··················1···6···1···654 ··················1···6···1···6
55 i5·:·w·=·{9,1,99999,·9999999,·3,·999}55 i5·:·w·=·{9,1,99999,·9999999,·3,·999}
  
56 o5·=·{9,·1,·99999,·9999999,·3,·999}56 o5·=·{9,·1,·99999,·9999999,·3,·999}
  
57 o5·:·List57 o5·:·List
58 i6·:·netList·cssLeadTerm(Hbeta,·w)58 i6·:·netList·cssLeadTerm(Hbeta,·w)
 59 ·--·.000003837s·elapsed
 60 ·--·.000003868s·elapsed
 61 ·--·.000002745s·elapsed
 62 ·--·.000002936s·elapsed
59 ·--·.000003795s·elapsed63 ·--·.000003075s·elapsed
60 ·--·.000005829s·elapsed 
61 ·--·.000005508s·elapsed 
62 ·--·.000004517s·elapsed 
63 ·--·.000004267s·elapsed 
64 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or64 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or
65 inhomogeneous·ideal.65 inhomogeneous·ideal.
66 Converting·to·Naive·algorithm.66 Converting·to·Naive·algorithm.
  
67 ·····+----------------------------------------------------+67 ·····+----------------------------------------------------+
68 ·····|···1·5···5·5········································|68 ·····|···1·5···5·5········································|
69 ·····|·-·-·-·-·-·-········································|69 ·····|·-·-·-·-·-·-········································|
2.8 KB
./usr/share/doc/Macaulay2/HolonomicSystems/html/_solve__Frobenius__Ideal.html
    
Offset 84, 15 lines modifiedOffset 84, 15 lines modified
  
84 o2·:·Ideal·of·R</code></pre>84 o2·:·Ideal·of·R</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i3·:·solveFrobeniusIdeal·I89 ··············<pre><code·class="language-macaulay2">i3·:·solveFrobeniusIdeal·I
90 ·--·.000003725s·elapsed90 ·--·.000005941s·elapsed
91 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.91 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.
92 Converting·to·Naive·algorithm.92 Converting·to·Naive·algorithm.
  
93 ·············································································93 ·············································································
94 o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,94 o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,
95 ················0········1········2·······3········0·······1·······2·······4·95 ················0········1········2·······3········0·······1·······2·······4·
96 ·····------------------------------------------------------------------------96 ·····------------------------------------------------------------------------
Offset 113, 15 lines modifiedOffset 113, 15 lines modified
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);</code></pre>114 ··············<pre><code·class="language-macaulay2">i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i5·:·solveFrobeniusIdeal(I,·W)119 ··············<pre><code·class="language-macaulay2">i5·:·solveFrobeniusIdeal(I,·W)
120 ·--·.000003905s·elapsed120 ·--·.00000522s·elapsed
121 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.121 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal.
122 Converting·to·Naive·algorithm.122 Converting·to·Naive·algorithm.
  
123 ·············································································123 ·············································································
124 o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,124 o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,
125 ················0········1········2·······3········0·······1·······2·······4·125 ················0········1········2·······3········0·······1·······2·······4·
126 ·····------------------------------------------------------------------------126 ·····------------------------------------------------------------------------
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html2text {}
    
Offset 17, 15 lines modifiedOffset 17, 15 lines modified
17 Here·is·[_\x8S_\x8S_\x8T,·Example·2.3.16]:17 Here·is·[_\x8S_\x8S_\x8T,·Example·2.3.16]:
18 i1·:·R·=·QQ[t_1..t_5];18 i1·:·R·=·QQ[t_1..t_5];
19 i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,19 i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,
20 t_2*t_4);20 t_2*t_4);
  
21 o2·:·Ideal·of·R21 o2·:·Ideal·of·R
22 i3·:·solveFrobeniusIdeal·I22 i3·:·solveFrobeniusIdeal·I
23 ·--·.000003725s·elapsed23 ·--·.000005941s·elapsed
24 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or24 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or
25 inhomogeneous·ideal.25 inhomogeneous·ideal.
26 Converting·to·Naive·algorithm.26 Converting·to·Naive·algorithm.
  
  
27 o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,27 o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,
28 ················0········1········2·······3········0·······1·······2·······428 ················0········1········2·······3········0·······1·······2·······4
Offset 37, 15 lines modifiedOffset 37, 15 lines modified
37 ·······1·············1·············1·············3·················237 ·······1·············1·············1·············3·················2
38 ·····-·-logX·logX··-·-logX·logX··-·-logX·logX··-·-logX·logX··+·logX·}38 ·····-·-logX·logX··-·-logX·logX··-·-logX·logX··-·-logX·logX··+·logX·}
39 ·······2····4····0···4····4····1···2····4····2···4····4····3·······439 ·······2····4····0···4····4····1···2····4····2···4····4····3·······4
  
40 o3·:·List40 o3·:·List
41 i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);41 i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);
42 i5·:·solveFrobeniusIdeal(I,·W)42 i5·:·solveFrobeniusIdeal(I,·W)
43 ·--·.000003905s·elapsed43 ·--·.00000522s·elapsed
44 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or44 Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or
45 inhomogeneous·ideal.45 inhomogeneous·ideal.
46 Converting·to·Naive·algorithm.46 Converting·to·Naive·algorithm.
  
  
47 o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,47 o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·,
48 ················0········1········2·······3········0·······1·······2·······448 ················0········1········2·······3········0·······1·······2·······4
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=217 #:len=21
8 YWxsZ2VucyhER0FsZ2VicmEsWlop8 YWxsZ2VucyhER0FsZ2VicmEsWlop
9 #:len=2699 #:len=269
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY5LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY5LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbGxnZW5zLERHQWxnZWJyYSxaWiksImFsbGdlbnMo11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbGxnZW5zLERHQWxnZWJyYSxaWiksImFsbGdlbnMo
8.72 KB
./usr/share/doc/Macaulay2/HomotopyLieAlgebra/example-output/_bracket.out
    
Offset 85, 82 lines modifiedOffset 85, 82 lines modified
  
85 o13·=·60085 o13·=·600
  
86 i14·:·H'·=·select(keys·H,·k->H#k·!=·0);86 i14·:·H'·=·select(keys·H,·k->H#k·!=·0);
  
87 i15·:·H'87 i15·:·H'
  
88 o15·=·{({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··-88 o15·=·{({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·T·T··-·z*T···+
89 ··········1···8······3·6····5·7····1·8······12······14······4···9····4·9··89 ··········4···8······2·7····4·8······12······14······3···9····3·9······15··
90 ······-----------------------------------------------------------------------90 ······-----------------------------------------------------------------------
91 ······T·T···-·z*T···+·z*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T·},·-91 ······y*T··),·({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·-
92 ·······5·10······17······19······2···8······2·8····5·9······15······5···7····92 ·········17······3···6······3·6····5·7····1·8······12······14······1···7····
93 ······-----------------------------------------------------------------------93 ······-----------------------------------------------------------------------
94 ······T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+ 
95 ·······3·6····5·7····1·8······12······14······4···9····2·6····3·8····4·9··94 ······T·T··+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T··},·-·T·T··+
 95 ·······1·7······13······5···9······2·8····5·9······15······3···10······4·8··
96 ······-----------------------------------------------------------------------96 ······-----------------------------------------------------------------------
97 ······y*T···-·z*T··),·({T·,·T··},·T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T·}, 
98 ·········14······17······3···10····5·6····3·10······18······20······5···6··97 ······T·T···-·z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),
 98 ·······3·10······18······19······2···7······2·7····4·8······12······14··
99 ······-----------------------------------------------------------------------99 ······-----------------------------------------------------------------------
100 ······T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T··},·-·T·T··-·T·T···+·z*T···+100 ······({T·,·T·},·-·T·T··+·T·T···-·z*T···+·x*T··),·({T·,·T··},·-·T·T··-·T·T··
101 ·······5·6····3·10······18······20······4···10······5·7····4·10······12··101 ·········4···8······4·8····3·10······18······19······2···10······5·8····2·10
102 ······-----------------------------------------------------------------------102 ······-----------------------------------------------------------------------
103 ······z*T··),·({T·,·T·},·-·T·T··-·T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··- 
104 ·········20······1···6······1·6····4·7······11······3···9····5·8····3·9··103 ······+·y*T··),·({T·,·T··},·-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T···+
 104 ···········19······4···10······4·10······18······5···8······5·8····2·10··
105 ······-----------------------------------------------------------------------105 ······-----------------------------------------------------------------------
106 ······z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T··},·-106 ······y*T··),·({T·,·T·},·T·T··+·x*T···-·z*T··),·({T·,·T·},·-·T·T··-·T·T··-
107 ·········15······16······4···6····4·6····3·7······11······13······5···10····107 ·········19······3···8····3·8······15······17······1···8······3·6····5·7··
108 ······-----------------------------------------------------------------------108 ······-----------------------------------------------------------------------
109 ······T·T···+·y*T··),·({T·,·T·},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-109 ······T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··-·T·T···-·z*T···+·z*T··),·({T·,
110 ·······5·10······18······4···6····4·6····1·10······20······4···7······1·6··110 ·······1·8······12······14······4···9····4·9····5·10······17······19······2·
111 ······-----------------------------------------------------------------------111 ······-----------------------------------------------------------------------
112 ······T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·, 
113 ·······4·7······11······2···6····2·6····3·8····4·9······14······17······5·112 ······T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+
 113 ·······8······2·8····5·9······15······5···7······3·6····5·7····1·8······12··
114 ······-----------------------------------------------------------------------114 ······-----------------------------------------------------------------------
115 ······T··},·T·T··-·T·T···-·z*T···+·z*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+ 
116 ·······10····4·9····5·10······17······19······3···8····2·6····3·8····4·9··115 ······x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T··},
 116 ·········14······4···9····2·6····3·8····4·9······14······17······3···10··
117 ······-----------------------------------------------------------------------117 ······-----------------------------------------------------------------------
118 ······y*T···-·z*T··),·({T·,·T·},·T·T··+·y*T···-·z*T··),·({T·,·T·},·-·T·T··- 
119 ·········14······17······3···6····3·6······11······12······5···7······5·7··118 ······T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T·},·T·T··+·T·T···-·z*T···+
 119 ·······5·6····3·10······18······20······5···6····5·6····3·10······18··
120 ······-----------------------------------------------------------------------120 ······-----------------------------------------------------------------------
121 ······T·T···+·z*T···+·z*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·, 
122 ·······4·10······12······20······3···7····4·6····3·7······11······13······2·121 ······y*T··),·({T·,·T··},·-·T·T··-·T·T···+·z*T···+·z*T··),·({T·,·T·},·-·T·T·
 122 ·········20······4···10······5·7····4·10······12······20······1···6······1·6
123 ······-----------------------------------------------------------------------123 ······-----------------------------------------------------------------------
124 ······T·},·-·T·T··+·y*T··),·({T·,·T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,124 ······-·T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·x*T··),·({T·,·T·},
125 ·······9······2·9······16······1···9······5·6····1·9······14······17······4·125 ·········4·7······11······3···9····5·8····3·9······15······16······4···6··
126 ······-----------------------------------------------------------------------126 ······-----------------------------------------------------------------------
127 ······T·},·-·T·T··+·z*T··),·({T·,·T··},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-127 ······T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T··},·-·T·T···+·y*T··),·({T·,·T·},
128 ·······7······4·7······13······1···10····4·6····1·10······20······5···9····128 ·······4·6····3·7······11······13······5···10······5·10······18······4···6··
129 ······-----------------------------------------------------------------------129 ······-----------------------------------------------------------------------
130 ······T·T··+·z*T··),·({T·,·T·},·T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··- 
131 ·······5·9······16······3···7····3·7······11······12······5···6······5·6··130 ······T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·x*T··),·({T·,·T·},
 131 ·······4·6····1·10······20······4···7······1·6····4·7······11······2···6··
132 ······-----------------------------------------------------------------------132 ······-----------------------------------------------------------------------
133 ······T·T··-·z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·x*T··),·({T·, 
134 ·······1·9······14······17······5···8····5·8····3·9······15······16······4·133 ······T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T··},·T·T··-·T·T···-·z*T···+
 134 ·······2·6····3·8····4·9······14······17······5···10····4·9····5·10······17··
135 ······-----------------------------------------------------------------------135 ······-----------------------------------------------------------------------
136 ······T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·T·T··-·z*T···+·y*T··), 
137 ·······8······2·7····4·8······12······14······3···9····3·9······15······17··136 ······z*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T·},·T·T·
 137 ·········19······3···8····2·6····3·8····4·9······14······17······3···6····3·6
138 ······-----------------------------------------------------------------------138 ······-----------------------------------------------------------------------
139 ······({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·-·T·T··+ 
140 ·········3···6······3·6····5·7····1·8······12······14······1···7······1·7··139 ······+·y*T···-·z*T··),·({T·,·T·},·-·T·T··-·T·T···+·z*T···+·z*T··),·({T·,
 140 ···········11······12······5···7······5·7····4·10······12······20······3·
141 ······-----------------------------------------------------------------------141 ······-----------------------------------------------------------------------
142 ······x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T··},·-·T·T··+·T·T···- 
143 ·········13······5···9······2·8····5·9······15······3···10······4·8····3·10··142 ······T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T·},·-·T·T··+·y*T··),·({T·,
 143 ·······7····4·6····3·7······11······13······2···9······2·9······16······1·
144 ······-----------------------------------------------------------------------144 ······-----------------------------------------------------------------------
145 ······z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·- 
146 ·········18······19······2···7······2·7····4·8······12······14······4···8····145 ······T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··+·z*T··),·({T·,
 146 ·······9······5·6····1·9······14······17······4···7······4·7······13······1·
147 ······-----------------------------------------------------------------------147 ······-----------------------------------------------------------------------
148 ······T·T··+·T·T···-·z*T···+·x*T··),·({T·,·T··},·-·T·T··-·T·T···+·y*T··),148 ······T··},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··+·z*T··),·({T·,·T·},
149 ·······4·8····3·10······18······19······2···10······5·8····2·10······19··149 ·······10····4·6····1·10······20······5···9······5·9······16······3···7··
150 ······-----------------------------------------------------------------------150 ······-----------------------------------------------------------------------
151 ······({T·,·T··},·-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T···+·y*T··),·({T·,151 ······T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,
152 ·········4···10······4·10······18······5···8······5·8····2·10······19······3·152 ·······3·7······11······12······5···6······5·6····1·9······14······17······5·
153 ······-----------------------------------------------------------------------153 ······-----------------------------------------------------------------------
154 ······T·},·T·T··+·x*T···-·z*T··)}154 ······T·},·T·T··+·T·T··-·z*T···+·x*T··)}
155 ·······8····3·8······15······17155 ·······8····5·8····3·9······15······16
  
156 o15·:·List156 o15·:·List
  
157 i16·:·H#(H'_0)157 i16·:·H#(H'_0)
  
158 o16·=·-1158 o16·=·-1
  
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./usr/share/doc/Macaulay2/HomotopyLieAlgebra/html/_bracket.html
    
Offset 215, 82 lines modifiedOffset 215, 82 lines modified
215 ··············<pre><code·class="language-macaulay2">i14·:·H'·=·select(keys·H,·k->H#k·!=·0);</code></pre>215 ··············<pre><code·class="language-macaulay2">i14·:·H'·=·select(keys·H,·k->H#k·!=·0);</code></pre>
216 ············</td>216 ············</td>
217 ··········</tr>217 ··········</tr>
218 ··········<tr>218 ··········<tr>
219 ············<td>219 ············<td>
220 ··············<pre><code·class="language-macaulay2">i15·:·H'220 ··············<pre><code·class="language-macaulay2">i15·:·H'
  
221 o15·=·{({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··-221 o15·=·{({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·T·T··-·z*T···+
222 ··········1···8······3·6····5·7····1·8······12······14······4···9····4·9··222 ··········4···8······2·7····4·8······12······14······3···9····3·9······15··
223 ······-----------------------------------------------------------------------223 ······-----------------------------------------------------------------------
224 ······T·T···-·z*T···+·z*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T·},·-224 ······y*T··),·({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·-
225 ·······5·10······17······19······2···8······2·8····5·9······15······5···7····225 ·········17······3···6······3·6····5·7····1·8······12······14······1···7····
226 ······-----------------------------------------------------------------------226 ······-----------------------------------------------------------------------
227 ······T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+ 
228 ·······3·6····5·7····1·8······12······14······4···9····2·6····3·8····4·9··227 ······T·T··+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T··},·-·T·T··+
 228 ·······1·7······13······5···9······2·8····5·9······15······3···10······4·8··
229 ······-----------------------------------------------------------------------229 ······-----------------------------------------------------------------------
230 ······y*T···-·z*T··),·({T·,·T··},·T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T·}, 
231 ·········14······17······3···10····5·6····3·10······18······20······5···6··230 ······T·T···-·z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),
 231 ·······3·10······18······19······2···7······2·7····4·8······12······14··
232 ······-----------------------------------------------------------------------232 ······-----------------------------------------------------------------------
233 ······T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T··},·-·T·T··-·T·T···+·z*T···+233 ······({T·,·T·},·-·T·T··+·T·T···-·z*T···+·x*T··),·({T·,·T··},·-·T·T··-·T·T··
234 ·······5·6····3·10······18······20······4···10······5·7····4·10······12··234 ·········4···8······4·8····3·10······18······19······2···10······5·8····2·10
235 ······-----------------------------------------------------------------------235 ······-----------------------------------------------------------------------
236 ······z*T··),·({T·,·T·},·-·T·T··-·T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··- 
237 ·········20······1···6······1·6····4·7······11······3···9····5·8····3·9··236 ······+·y*T··),·({T·,·T··},·-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T···+
 237 ···········19······4···10······4·10······18······5···8······5·8····2·10··
238 ······-----------------------------------------------------------------------238 ······-----------------------------------------------------------------------
239 ······z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T··},·-239 ······y*T··),·({T·,·T·},·T·T··+·x*T···-·z*T··),·({T·,·T·},·-·T·T··-·T·T··-
240 ·········15······16······4···6····4·6····3·7······11······13······5···10····240 ·········19······3···8····3·8······15······17······1···8······3·6····5·7··
241 ······-----------------------------------------------------------------------241 ······-----------------------------------------------------------------------
242 ······T·T···+·y*T··),·({T·,·T·},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-242 ······T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··-·T·T···-·z*T···+·z*T··),·({T·,
243 ·······5·10······18······4···6····4·6····1·10······20······4···7······1·6··243 ·······1·8······12······14······4···9····4·9····5·10······17······19······2·
244 ······-----------------------------------------------------------------------244 ······-----------------------------------------------------------------------
245 ······T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·, 
246 ·······4·7······11······2···6····2·6····3·8····4·9······14······17······5·245 ······T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+
 246 ·······8······2·8····5·9······15······5···7······3·6····5·7····1·8······12··
247 ······-----------------------------------------------------------------------247 ······-----------------------------------------------------------------------
248 ······T··},·T·T··-·T·T···-·z*T···+·z*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+ 
249 ·······10····4·9····5·10······17······19······3···8····2·6····3·8····4·9··248 ······x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T··},
 249 ·········14······4···9····2·6····3·8····4·9······14······17······3···10··
250 ······-----------------------------------------------------------------------250 ······-----------------------------------------------------------------------
251 ······y*T···-·z*T··),·({T·,·T·},·T·T··+·y*T···-·z*T··),·({T·,·T·},·-·T·T··- 
252 ·········14······17······3···6····3·6······11······12······5···7······5·7··251 ······T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T·},·T·T··+·T·T···-·z*T···+
 252 ·······5·6····3·10······18······20······5···6····5·6····3·10······18··
253 ······-----------------------------------------------------------------------253 ······-----------------------------------------------------------------------
254 ······T·T···+·z*T···+·z*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·, 
255 ·······4·10······12······20······3···7····4·6····3·7······11······13······2·254 ······y*T··),·({T·,·T··},·-·T·T··-·T·T···+·z*T···+·z*T··),·({T·,·T·},·-·T·T·
 255 ·········20······4···10······5·7····4·10······12······20······1···6······1·6
256 ······-----------------------------------------------------------------------256 ······-----------------------------------------------------------------------
257 ······T·},·-·T·T··+·y*T··),·({T·,·T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,257 ······-·T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·x*T··),·({T·,·T·},
258 ·······9······2·9······16······1···9······5·6····1·9······14······17······4·258 ·········4·7······11······3···9····5·8····3·9······15······16······4···6··
259 ······-----------------------------------------------------------------------259 ······-----------------------------------------------------------------------
260 ······T·},·-·T·T··+·z*T··),·({T·,·T··},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-260 ······T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T··},·-·T·T···+·y*T··),·({T·,·T·},
261 ·······7······4·7······13······1···10····4·6····1·10······20······5···9····261 ·······4·6····3·7······11······13······5···10······5·10······18······4···6··
262 ······-----------------------------------------------------------------------262 ······-----------------------------------------------------------------------
263 ······T·T··+·z*T··),·({T·,·T·},·T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··- 
264 ·······5·9······16······3···7····3·7······11······12······5···6······5·6··263 ······T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·x*T··),·({T·,·T·},
 264 ·······4·6····1·10······20······4···7······1·6····4·7······11······2···6··
265 ······-----------------------------------------------------------------------265 ······-----------------------------------------------------------------------
266 ······T·T··-·z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·x*T··),·({T·, 
267 ·······1·9······14······17······5···8····5·8····3·9······15······16······4·266 ······T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T··},·T·T··-·T·T···-·z*T···+
 267 ·······2·6····3·8····4·9······14······17······5···10····4·9····5·10······17··
268 ······-----------------------------------------------------------------------268 ······-----------------------------------------------------------------------
269 ······T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·T·T··-·z*T···+·y*T··), 
270 ·······8······2·7····4·8······12······14······3···9····3·9······15······17··269 ······z*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T·},·T·T·
 270 ·········19······3···8····2·6····3·8····4·9······14······17······3···6····3·6
271 ······-----------------------------------------------------------------------271 ······-----------------------------------------------------------------------
272 ······({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·-·T·T··+ 
273 ·········3···6······3·6····5·7····1·8······12······14······1···7······1·7··272 ······+·y*T···-·z*T··),·({T·,·T·},·-·T·T··-·T·T···+·z*T···+·z*T··),·({T·,
 273 ···········11······12······5···7······5·7····4·10······12······20······3·
274 ······-----------------------------------------------------------------------274 ······-----------------------------------------------------------------------
275 ······x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T··},·-·T·T··+·T·T···- 
276 ·········13······5···9······2·8····5·9······15······3···10······4·8····3·10··275 ······T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T·},·-·T·T··+·y*T··),·({T·,
 276 ·······7····4·6····3·7······11······13······2···9······2·9······16······1·
277 ······-----------------------------------------------------------------------277 ······-----------------------------------------------------------------------
278 ······z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·- 
279 ·········18······19······2···7······2·7····4·8······12······14······4···8····278 ······T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··+·z*T··),·({T·,
 279 ·······9······5·6····1·9······14······17······4···7······4·7······13······1·
280 ······-----------------------------------------------------------------------280 ······-----------------------------------------------------------------------
281 ······T·T··+·T·T···-·z*T···+·x*T··),·({T·,·T··},·-·T·T··-·T·T···+·y*T··),281 ······T··},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··+·z*T··),·({T·,·T·},
282 ·······4·8····3·10······18······19······2···10······5·8····2·10······19··282 ·······10····4·6····1·10······20······5···9······5·9······16······3···7··
283 ······-----------------------------------------------------------------------283 ······-----------------------------------------------------------------------
284 ······({T·,·T··},·-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T···+·y*T··),·({T·,284 ······T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,
285 ·········4···10······4·10······18······5···8······5·8····2·10······19······3·285 ·······3·7······11······12······5···6······5·6····1·9······14······17······5·
286 ······-----------------------------------------------------------------------286 ······-----------------------------------------------------------------------
287 ······T·},·T·T··+·x*T···-·z*T··)}287 ······T·},·T·T··+·T·T··-·z*T···+·x*T··)}
288 ·······8····3·8······15······17288 ·······8····5·8····3·9······15······16
  
289 o15·:·List</code></pre>289 o15·:·List</code></pre>
290 ············</td>290 ············</td>
291 ··········</tr>291 ··········</tr>
292 ··········<tr>292 ··········<tr>
293 ············<td>293 ············<td>
294 ··············<pre><code·class="language-macaulay2">i16·:·H#(H'_0)294 ··············<pre><code·class="language-macaulay2">i16·:·H#(H'_0)
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Offset 118, 82 lines modifiedOffset 118, 82 lines modified
118 37···38···39···40···41···42···43···44118 37···38···39···40···41···42···43···44
119 i13·:·#keys·H119 i13·:·#keys·H
  
120 o13·=·600120 o13·=·600
121 i14·:·H'·=·select(keys·H,·k->H#k·!=·0);121 i14·:·H'·=·select(keys·H,·k->H#k·!=·0);
122 i15·:·H'122 i15·:·H'
  
123 o15·=·{({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··-123 o15·=·{({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·T·T··-·z*T···+
124 ··········1···8······3·6····5·7····1·8······12······14······4···9····4·9124 ··········4···8······2·7····4·8······12······14······3···9····3·9······15
125 ······-----------------------------------------------------------------------125 ······-----------------------------------------------------------------------
126 ······T·T···-·z*T···+·z*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T·},·-126 ······y*T··),·({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·-
127 ·······5·10······17······19······2···8······2·8····5·9······15······5···7127 ·········17······3···6······3·6····5·7····1·8······12······14······1···7
128 ······-----------------------------------------------------------------------128 ······-----------------------------------------------------------------------
129 ······T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+ 
130 ·······3·6····5·7····1·8······12······14······4···9····2·6····3·8····4·9129 ······T·T··+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T··},·-·T·T··+
 130 ·······1·7······13······5···9······2·8····5·9······15······3···10······4·8
131 ······-----------------------------------------------------------------------131 ······-----------------------------------------------------------------------
132 ······y*T···-·z*T··),·({T·,·T··},·T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T·}, 
133 ·········14······17······3···10····5·6····3·10······18······20······5···6132 ······T·T···-·z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),
 133 ·······3·10······18······19······2···7······2·7····4·8······12······14
134 ······-----------------------------------------------------------------------134 ······-----------------------------------------------------------------------
135 ······T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T··},·-·T·T··-·T·T···+·z*T···+135 ······({T·,·T·},·-·T·T··+·T·T···-·z*T···+·x*T··),·({T·,·T··},·-·T·T··-·T·T
136 ·······5·6····3·10······18······20······4···10······5·7····4·10······12136 ·········4···8······4·8····3·10······18······19······2···10······5·8····2·10
137 ······-----------------------------------------------------------------------137 ······-----------------------------------------------------------------------
138 ······z*T··),·({T·,·T·},·-·T·T··-·T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··- 
139 ·········20······1···6······1·6····4·7······11······3···9····5·8····3·9138 ······+·y*T··),·({T·,·T··},·-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T···+
 139 ···········19······4···10······4·10······18······5···8······5·8····2·10
140 ······-----------------------------------------------------------------------140 ······-----------------------------------------------------------------------
141 ······z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T··},·-141 ······y*T··),·({T·,·T·},·T·T··+·x*T···-·z*T··),·({T·,·T·},·-·T·T··-·T·T··-
142 ·········15······16······4···6····4·6····3·7······11······13······5···10142 ·········19······3···8····3·8······15······17······1···8······3·6····5·7
143 ······-----------------------------------------------------------------------143 ······-----------------------------------------------------------------------
144 ······T·T···+·y*T··),·({T·,·T·},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-144 ······T·T··+·z*T···+·x*T··),·({T·,·T·},·T·T··-·T·T···-·z*T···+·z*T··),·({T·,
145 ·······5·10······18······4···6····4·6····1·10······20······4···7······1·6145 ·······1·8······12······14······4···9····4·9····5·10······17······19······2
146 ······-----------------------------------------------------------------------146 ······-----------------------------------------------------------------------
147 ······T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·, 
148 ·······4·7······11······2···6····2·6····3·8····4·9······14······17······5147 ······T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+
 148 ·······8······2·8····5·9······15······5···7······3·6····5·7····1·8······12
149 ······-----------------------------------------------------------------------149 ······-----------------------------------------------------------------------
150 ······T··},·T·T··-·T·T···-·z*T···+·z*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+ 
151 ·······10····4·9····5·10······17······19······3···8····2·6····3·8····4·9150 ······x*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T··},
 151 ·········14······4···9····2·6····3·8····4·9······14······17······3···10
152 ······-----------------------------------------------------------------------152 ······-----------------------------------------------------------------------
153 ······y*T···-·z*T··),·({T·,·T·},·T·T··+·y*T···-·z*T··),·({T·,·T·},·-·T·T··- 
154 ·········14······17······3···6····3·6······11······12······5···7······5·7153 ······T·T··+·T·T···-·z*T···+·y*T··),·({T·,·T·},·T·T··+·T·T···-·z*T···+
 154 ·······5·6····3·10······18······20······5···6····5·6····3·10······18
155 ······-----------------------------------------------------------------------155 ······-----------------------------------------------------------------------
156 ······T·T···+·z*T···+·z*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·, 
157 ·······4·10······12······20······3···7····4·6····3·7······11······13······2156 ······y*T··),·({T·,·T··},·-·T·T··-·T·T···+·z*T···+·z*T··),·({T·,·T·},·-·T·T
 157 ·········20······4···10······5·7····4·10······12······20······1···6······1·6
158 ······-----------------------------------------------------------------------158 ······-----------------------------------------------------------------------
159 ······T·},·-·T·T··+·y*T··),·({T·,·T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,159 ······-·T·T··+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·x*T··),·({T·,·T·},
160 ·······9······2·9······16······1···9······5·6····1·9······14······17······4160 ·········4·7······11······3···9····5·8····3·9······15······16······4···6
161 ······-----------------------------------------------------------------------161 ······-----------------------------------------------------------------------
162 ······T·},·-·T·T··+·z*T··),·({T·,·T··},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-162 ······T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T··},·-·T·T···+·y*T··),·({T·,·T·},
163 ·······7······4·7······13······1···10····4·6····1·10······20······5···9163 ·······4·6····3·7······11······13······5···10······5·10······18······4···6
164 ······-----------------------------------------------------------------------164 ······-----------------------------------------------------------------------
165 ······T·T··+·z*T··),·({T·,·T·},·T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··- 
166 ·······5·9······16······3···7····3·7······11······12······5···6······5·6165 ······T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·x*T··),·({T·,·T·},
 166 ·······4·6····1·10······20······4···7······1·6····4·7······11······2···6
167 ······-----------------------------------------------------------------------167 ······-----------------------------------------------------------------------
168 ······T·T··-·z*T···+·x*T··),·({T·,·T·},·T·T··+·T·T··-·z*T···+·x*T··),·({T·, 
169 ·······1·9······14······17······5···8····5·8····3·9······15······16······4168 ······T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T··},·T·T··-·T·T···-·z*T···+
 169 ·······2·6····3·8····4·9······14······17······5···10····4·9····5·10······17
170 ······-----------------------------------------------------------------------170 ······-----------------------------------------------------------------------
171 ······T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·T·T··-·z*T···+·y*T··), 
172 ·······8······2·7····4·8······12······14······3···9····3·9······15······17171 ······z*T··),·({T·,·T·},·T·T··+·T·T··+·T·T··+·y*T···-·z*T··),·({T·,·T·},·T·T
 172 ·········19······3···8····2·6····3·8····4·9······14······17······3···6····3·6
173 ······-----------------------------------------------------------------------173 ······-----------------------------------------------------------------------
174 ······({T·,·T·},·-·T·T··-·T·T··-·T·T··+·z*T···+·x*T··),·({T·,·T·},·-·T·T··+ 
175 ·········3···6······3·6····5·7····1·8······12······14······1···7······1·7174 ······+·y*T···-·z*T··),·({T·,·T·},·-·T·T··-·T·T···+·z*T···+·z*T··),·({T·,
 175 ···········11······12······5···7······5·7····4·10······12······20······3
176 ······-----------------------------------------------------------------------176 ······-----------------------------------------------------------------------
177 ······x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T··),·({T·,·T··},·-·T·T··+·T·T···- 
178 ·········13······5···9······2·8····5·9······15······3···10······4·8····3·10177 ······T·},·T·T··+·T·T··-·z*T···+·y*T··),·({T·,·T·},·-·T·T··+·y*T··),·({T·,
 178 ·······7····4·6····3·7······11······13······2···9······2·9······16······1
179 ······-----------------------------------------------------------------------179 ······-----------------------------------------------------------------------
180 ······z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··+·y*T···+·z*T··),·({T·,·T·},·- 
181 ·········18······19······2···7······2·7····4·8······12······14······4···8180 ······T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··+·z*T··),·({T·,
 181 ·······9······5·6····1·9······14······17······4···7······4·7······13······1
182 ······-----------------------------------------------------------------------182 ······-----------------------------------------------------------------------
183 ······T·T··+·T·T···-·z*T···+·x*T··),·({T·,·T··},·-·T·T··-·T·T···+·y*T··),183 ······T··},·T·T··-·T·T···+·x*T··),·({T·,·T·},·-·T·T··+·z*T··),·({T·,·T·},
184 ·······4·8····3·10······18······19······2···10······5·8····2·10······19184 ·······10····4·6····1·10······20······5···9······5·9······16······3···7
185 ······-----------------------------------------------------------------------185 ······-----------------------------------------------------------------------
186 ······({T·,·T··},·-·T·T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T···+·y*T··),·({T·,186 ······T·T··-·z*T···+·x*T··),·({T·,·T·},·-·T·T··-·T·T··-·z*T···+·x*T··),·({T·,
187 ·········4···10······4·10······18······5···8······5·8····2·10······19······3187 ·······3·7······11······12······5···6······5·6····1·9······14······17······5
188 ······-----------------------------------------------------------------------188 ······-----------------------------------------------------------------------
189 ······T·},·T·T··+·x*T···-·z*T··)}189 ······T·},·T·T··+·T·T··-·z*T···+·x*T··)}
190 ·······8····3·8······15······17190 ·······8····5·8····3·9······15······16
  
191 o15·:·List191 o15·:·List
192 i16·:·H#(H'_0)192 i16·:·H#(H'_0)
  
193 o16·=·-1193 o16·=·-1
  
194 o16·:·S[T·..T··]194 o16·:·S[T·..T··]
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./usr/share/doc/Macaulay2/HyperplaneArrangements/example-output/_euler__Restriction_lp__Central__Arrangement_cm__List_cm__Z__Z_rp.out
    
Offset 59, 16 lines modifiedOffset 59, 16 lines modified
  
59 o11·:·QQ[y..z]-module,·free,·degrees·{2:3}59 o11·:·QQ[y..z]-module,·free,·degrees·{2:3}
  
60 i12·:·A·=·arrangement·"bracelet";60 i12·:·A·=·arrangement·"bracelet";
  
61 i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0)61 i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0)
  
62 o13·=·({x·,·x·,·x··+·x··+·x·,·x··+·x·,·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1})62 o13·=·({x·,·x··+·x·,·x·,·x·,·x··+·x··+·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1})
63 ·········3···4···2····3····4···2····4···2···3····463 ·········2···3····4···3···4···2····3····4···2····4
  
64 o13·:·Sequence64 o13·:·Sequence
  
65 i14·:·C·=·restriction(A,0)65 i14·:·C·=·restriction(A,0)
  
66 o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·}66 o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·}
67 ········2···3···4···2····4···3····4···2····4···3····4···2····3····467 ········2···3···4···2····4···3····4···2····4···3····4···2····3····4
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./usr/share/doc/Macaulay2/HyperplaneArrangements/html/_euler__Restriction_lp__Central__Arrangement_cm__List_cm__Z__Z_rp.html
    
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181 ··············<pre><code·class="language-macaulay2">i12·:·A·=·arrangement·&quot;bracelet&quot;;</code></pre>181 ··············<pre><code·class="language-macaulay2">i12·:·A·=·arrangement·&quot;bracelet&quot;;</code></pre>
182 ············</td>182 ············</td>
183 ··········</tr>183 ··········</tr>
184 ··········<tr>184 ··········<tr>
185 ············<td>185 ············<td>
186 ··············<pre><code·class="language-macaulay2">i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0)186 ··············<pre><code·class="language-macaulay2">i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0)
  
187 o13·=·({x·,·x·,·x··+·x··+·x·,·x··+·x·,·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1})187 o13·=·({x·,·x··+·x·,·x·,·x·,·x··+·x··+·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1})
188 ·········3···4···2····3····4···2····4···2···3····4188 ·········2···3····4···3···4···2····3····4···2····4
  
189 o13·:·Sequence</code></pre>189 o13·:·Sequence</code></pre>
190 ············</td>190 ············</td>
191 ··········</tr>191 ··········</tr>
192 ··········<tr>192 ··········<tr>
193 ············<td>193 ············<td>
194 ··············<pre><code·class="language-macaulay2">i14·:·C·=·restriction(A,0)194 ··············<pre><code·class="language-macaulay2">i14·:·C·=·restriction(A,0)
718 B
html2text {}
    
Offset 80, 16 lines modifiedOffset 80, 16 lines modified
  
80 o11·:·QQ[y..z]-module,·free,·degrees·{2:3}80 o11·:·QQ[y..z]-module,·free,·degrees·{2:3}
81 It·may·be·the·case·that·the·Euler·restriction·is·free,·while·the·naive81 It·may·be·the·case·that·the·Euler·restriction·is·free,·while·the·naive
82 restriction·is·not:82 restriction·is·not:
83 i12·:·A·=·arrangement·"bracelet";83 i12·:·A·=·arrangement·"bracelet";
84 i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0)84 i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0)
  
85 o13·=·({x·,·x·,·x··+·x··+·x·,·x··+·x·,·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1})85 o13·=·({x·,·x··+·x·,·x·,·x·,·x··+·x··+·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1})
86 ·········3···4···2····3····4···2····4···2···3····486 ·········2···3····4···3···4···2····3····4···2····4
  
87 o13·:·Sequence87 o13·:·Sequence
88 i14·:·C·=·restriction(A,0)88 i14·:·C·=·restriction(A,0)
  
89 o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·}89 o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·}
90 ········2···3···4···2····4···3····4···2····4···3····4···2····3····490 ········2···3···4···2····4···3····4···2····4···3····4···2····3····4
  
788 B
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11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1thZGFwdGVkTW9ub21pYWxPcmRlcixGaWVsZF0sImFk11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1thZGFwdGVkTW9ub21pYWxPcmRlcixGaWVsZF0sImFk
760 B
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6.19 KB
./usr/share/doc/Macaulay2/IntegralClosure/example-output/_integral__Closure_lp..._cm__Strategy_eq_gt..._rp.out
    
Offset 16, 15 lines modifiedOffset 16, 15 lines modified
16 i3·:·R·=·S/f16 i3·:·R·=·S/f
  
17 o3·=·R17 o3·=·R
  
18 o3·:·QuotientRing18 o3·:·QuotientRing
  
19 i4·:·time·R'·=·integralClosure·R19 i4·:·time·R'·=·integralClosure·R
20 ·--·used·0.643287s·(cpu);·0.33729s·(thread);·0s·(gc)20 ·--·used·0.812045s·(cpu);·0.3767s·(thread);·0s·(gc)
  
21 o4·=·R'21 o4·=·R'
  
22 o4·:·QuotientRing22 o4·:·QuotientRing
  
23 i5·:·netList·(ideal·R')_*23 i5·:·netList·(ideal·R')_*
  
Offset 83, 15 lines modifiedOffset 83, 15 lines modified
83 i9·:·R·=·S/f83 i9·:·R·=·S/f
  
84 o9·=·R84 o9·=·R
  
85 o9·:·QuotientRing85 o9·:·QuotientRing
  
86 i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)86 i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)
87 ·--·used·0.625821s·(cpu);·0.333342s·(thread);·0s·(gc)87 ·--·used·0.74952s·(cpu);·0.388643s·(thread);·0s·(gc)
  
88 o10·=·R'88 o10·=·R'
  
89 o10·:·QuotientRing89 o10·:·QuotientRing
  
90 i11·:·netList·(ideal·R')_*90 i11·:·netList·(ideal·R')_*
  
Offset 150, 15 lines modifiedOffset 150, 15 lines modified
150 i15·:·R·=·S/f150 i15·:·R·=·S/f
  
151 o15·=·R151 o15·=·R
  
152 o15·:·QuotientRing152 o15·:·QuotientRing
  
153 i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions)153 i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions)
154 ·--·used·0.421983s·(cpu);·0.299816s·(thread);·0s·(gc)154 ·--·used·0.543345s·(cpu);·0.379768s·(thread);·0s·(gc)
  
155 o16·=·R'155 o16·=·R'
  
156 o16·:·QuotientRing156 o16·:·QuotientRing
  
157 i17·:·netList·(ideal·R')_*157 i17·:·netList·(ideal·R')_*
  
Offset 208, 15 lines modifiedOffset 208, 15 lines modified
208 i20·:·R·=·S/f208 i20·:·R·=·S/f
  
209 o20·=·R209 o20·=·R
  
210 o20·:·QuotientRing210 o20·:·QuotientRing
  
211 i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions)211 i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions)
212 ·--·used·0.320174s·(cpu);·0.285186s·(thread);·0s·(gc)212 ·--·used·0.346577s·(cpu);·0.291285s·(thread);·0s·(gc)
  
213 o21·=·R'213 o21·=·R'
  
214 o21·:·QuotientRing214 o21·:·QuotientRing
  
215 i22·:·netList·(ideal·R')_*215 i22·:·netList·(ideal·R')_*
  
Offset 266, 15 lines modifiedOffset 266, 15 lines modified
266 i25·:·R·=·S/f266 i25·:·R·=·S/f
  
267 o25·=·R267 o25·=·R
  
268 o25·:·QuotientRing268 o25·:·QuotientRing
  
269 i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1)269 i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1)
270 ·--·used·0.615555s·(cpu);·0.478354s·(thread);·0s·(gc)270 ·--·used·0.692438s·(cpu);·0.538288s·(thread);·0s·(gc)
  
271 o26·=·R'271 o26·=·R'
  
272 o26·:·QuotientRing272 o26·:·QuotientRing
  
273 i27·:·netList·(ideal·R')_*273 i27·:·netList·(ideal·R')_*
  
Offset 324, 15 lines modifiedOffset 324, 15 lines modified
324 i30·:·R·=·S/f324 i30·:·R·=·S/f
  
325 o30·=·R325 o30·=·R
  
326 o30·:·QuotientRing326 o30·:·QuotientRing
  
327 i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos)327 i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos)
328 ·--·used·0.300116s·(cpu);·0.255461s·(thread);·0s·(gc)328 ·--·used·0.347929s·(cpu);·0.297721s·(thread);·0s·(gc)
  
329 o31·=·R'329 o31·=·R'
  
330 o31·:·QuotientRing330 o31·:·QuotientRing
  
331 i32·:·netList·(ideal·R')_*331 i32·:·netList·(ideal·R')_*
  
Offset 382, 15 lines modifiedOffset 382, 15 lines modified
382 i35·:·R·=·S/f382 i35·:·R·=·S/f
  
383 o35·=·R383 o35·=·R
  
384 o35·:·QuotientRing384 o35·:·QuotientRing
  
385 i36·:·time·R'·=·integralClosure·R385 i36·:·time·R'·=·integralClosure·R
386 ·--·used·0.0360022s·(cpu);·0.0373263s·(thread);·0s·(gc)386 ·--·used·0.0474003s·(cpu);·0.0458357s·(thread);·0s·(gc)
  
387 o36·=·R'387 o36·=·R'
  
388 o36·:·QuotientRing388 o36·:·QuotientRing
  
389 i37·:·netList·(ideal·R')_*389 i37·:·netList·(ideal·R')_*
  
Offset 432, 15 lines modifiedOffset 432, 15 lines modified
432 i40·:·R·=·S/I432 i40·:·R·=·S/I
  
433 o40·=·R433 o40·=·R
  
434 o40·:·QuotientRing434 o40·:·QuotientRing
  
435 i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)435 i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)
436 ·--·used·0.107357s·(cpu);·0.0695835s·(thread);·0s·(gc)436 ·--·used·0.133641s·(cpu);·0.0731088s·(thread);·0s·(gc)
  
437 o41·=·R'437 o41·=·R'
  
438 o41·:·QuotientRing438 o41·:·QuotientRing
  
439 i42·:·icFractions·R439 i42·:·icFractions·R
  
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./usr/share/doc/Macaulay2/IntegralClosure/example-output/_integral__Closure_lp..._cm__Verbosity_eq_gt..._rp.out
    
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1 --·-*-·M2-comint·-*-·hash:·131779540694346152731 --·-*-·M2-comint·-*-·hash:·13177954069434615273
  
2 i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);2 i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);
  
3 i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2)3 i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2)
4 ·[jacobian·time·.000880965·sec·#minors·3]4 ·[jacobian·time·.00260525·sec·#minors·3]
5 integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·25 integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2
  
6 ·[step·0:·6 ·[step·0:·
7 ······radical·(use·minprimes)·.00399937·seconds7 ······radical·(use·minprimes)·0·seconds
8 ······idlizer1:··.00555663·seconds8 ······idlizer1:··.00800214·seconds
9 ······idlizer2:··.00942649·seconds9 ······idlizer2:··.00800336·seconds
10 ······minpres:···.0622194·seconds10 ······minpres:···.065727·seconds
11 ··time·.0875184·sec··#fractions·4]11 ··time·.0937245·sec··#fractions·4]
12 ·[step·1:·12 ·[step·1:·
13 ······radical·(use·minprimes)·.00399929·seconds13 ······radical·(use·minprimes)·0·seconds
14 ······idlizer1:··.00800009·seconds 
15 ······idlizer2:··.0119997·seconds14 ······idlizer1:··.0115569·seconds
 15 ······idlizer2:··.0133081·seconds
16 ······minpres:···.0654003·seconds16 ······minpres:···.0775545·seconds
17 ··time·.0969859·sec··#fractions·4]17 ··time·.110013·sec··#fractions·4]
18 ·[step·2:·18 ·[step·2:·
19 ······radical·(use·minprimes)·.00400076·seconds19 ······radical·(use·minprimes)·.00399458·seconds
20 ······idlizer1:··.0119986·seconds20 ······idlizer1:··.0120099·seconds
21 ······idlizer2:··.0646385·seconds21 ······idlizer2:··.0986425·seconds
22 ······minpres:···.00796869·seconds22 ······minpres:···.0119984·seconds
23 ··time·.0988024·sec··#fractions·5]23 ··time·.134639·sec··#fractions·5]
24 ·[step·3:·24 ·[step·3:·
25 ······radical·(use·minprimes)·.00399856·seconds25 ······radical·(use·minprimes)·.00398756·seconds
26 ······idlizer1:··.0160234·seconds26 ······idlizer1:··.0160219·seconds
27 ······idlizer2:··.0680807·seconds27 ······idlizer2:··.0786332·seconds
28 ······minpres:···.0160647·seconds28 ······minpres:···.0199656·seconds
29 ··time·.111514·sec··#fractions·5]29 ··time·.126533·sec··#fractions·5]
30 ·[step·4:·30 ·[step·4:·
31 ······radical·(use·minprimes)·.00385243·seconds31 ······radical·(use·minprimes)·.00393502·seconds
32 ······idlizer1:··.00910461·seconds32 ······idlizer1:··.0121068·seconds
33 ······idlizer2:··.0760828·seconds33 ······idlizer2:··.101829·seconds
34 ······minpres:···.0119969·seconds34 ······minpres:···.0126668·seconds
35 ··time·.112259·sec··#fractions·5]35 ··time·.141479·sec··#fractions·5]
36 ·[step·5:·36 ·[step·5:·
37 ······radical·(use·minprimes)·0·seconds37 ······radical·(use·minprimes)·.00403653·seconds
38 ······idlizer1:···--·used·0.528614s·(cpu);·0.32721s·(thread);·0s·(gc)38 ······idlizer1:···--·used·0.630461s·(cpu);·0.358897s·(thread);·0s·(gc)
39 .00399852·seconds39 .012026·seconds
40 ··time·.0159976·sec··#fractions·5]40 ··time·.0200928·sec··#fractions·5]
  
41 o2·=·R'41 o2·=·R'
  
42 o2·:·QuotientRing42 o2·:·QuotientRing
  
43 i3·:·trim·ideal·R'43 i3·:·trim·ideal·R'
  
1.33 KB
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13 ················2······2····2········2···2·2·····213 ················2······2····2········2···2·2·····2
14 o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·)14 o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·)
  
15 o3·:·Ideal·of·S15 o3·:·Ideal·of·S
  
16 i4·:·time·integralClosure·J16 i4·:·time·integralClosure·J
17 ·--·used·6.4986s·(cpu);·1.30959s·(thread);·0s·(gc)17 ·--·used·5.88464s·(cpu);·1.21039s·(thread);·0s·(gc)
  
18 ·············2·2··············2·2················2··········2···2·····18 ·············2·2··············2·2················2··········2···2·····
19 o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-19 o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-
20 ·····------------------------------------------------------------------------20 ·····------------------------------------------------------------------------
21 ···········2···3···············2·2·····2···521 ···········2···3···············2·2·····2···5
22 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)22 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)
  
23 o4·:·Ideal·of·S23 o4·:·Ideal·of·S
  
24 i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1})24 i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1})
25 ·--·used·9.31893s·(cpu);·1.55133s·(thread);·0s·(gc)25 ·--·used·8.03561s·(cpu);·1.40195s·(thread);·0s·(gc)
  
26 ·············2·2··············2·2················2··········2···2·····26 ·············2·2··············2·2················2··········2···2·····
27 o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-27 o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-
28 ·····------------------------------------------------------------------------28 ·····------------------------------------------------------------------------
29 ···········2···3···············2·2·····2···529 ···········2···3···············2·2·····2···5
30 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)30 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)
  
15.5 KB
./usr/share/doc/Macaulay2/IntegralClosure/html/_integral__Closure_lp..._cm__Strategy_eq_gt..._rp.html
    
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99 o3·:·QuotientRing</code></pre>99 o3·:·QuotientRing</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i4·:·time·R'·=·integralClosure·R104 ··············<pre><code·class="language-macaulay2">i4·:·time·R'·=·integralClosure·R
105 ·--·used·0.643287s·(cpu);·0.33729s·(thread);·0s·(gc)105 ·--·used·0.812045s·(cpu);·0.3767s·(thread);·0s·(gc)
  
106 o4·=·R'106 o4·=·R'
  
107 o4·:·QuotientRing</code></pre>107 o4·:·QuotientRing</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
Offset 186, 15 lines modifiedOffset 186, 15 lines modified
  
186 o9·:·QuotientRing</code></pre>186 o9·:·QuotientRing</code></pre>
187 ············</td>187 ············</td>
188 ··········</tr>188 ··········</tr>
189 ··········<tr>189 ··········<tr>
190 ············<td>190 ············<td>
191 ··············<pre><code·class="language-macaulay2">i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)191 ··············<pre><code·class="language-macaulay2">i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)
192 ·--·used·0.625821s·(cpu);·0.333342s·(thread);·0s·(gc)192 ·--·used·0.74952s·(cpu);·0.388643s·(thread);·0s·(gc)
  
193 o10·=·R'193 o10·=·R'
  
194 o10·:·QuotientRing</code></pre>194 o10·:·QuotientRing</code></pre>
195 ············</td>195 ············</td>
196 ··········</tr>196 ··········</tr>
197 ··········<tr>197 ··········<tr>
Offset 273, 15 lines modifiedOffset 273, 15 lines modified
  
273 o15·:·QuotientRing</code></pre>273 o15·:·QuotientRing</code></pre>
274 ············</td>274 ············</td>
275 ··········</tr>275 ··········</tr>
276 ··········<tr>276 ··········<tr>
277 ············<td>277 ············<td>
278 ··············<pre><code·class="language-macaulay2">i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions)278 ··············<pre><code·class="language-macaulay2">i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions)
279 ·--·used·0.421983s·(cpu);·0.299816s·(thread);·0s·(gc)279 ·--·used·0.543345s·(cpu);·0.379768s·(thread);·0s·(gc)
  
280 o16·=·R'280 o16·=·R'
  
281 o16·:·QuotientRing</code></pre>281 o16·:·QuotientRing</code></pre>
282 ············</td>282 ············</td>
283 ··········</tr>283 ··········</tr>
284 ··········<tr>284 ··········<tr>
Offset 348, 15 lines modifiedOffset 348, 15 lines modified
  
348 o20·:·QuotientRing</code></pre>348 o20·:·QuotientRing</code></pre>
349 ············</td>349 ············</td>
350 ··········</tr>350 ··········</tr>
351 ··········<tr>351 ··········<tr>
352 ············<td>352 ············<td>
353 ··············<pre><code·class="language-macaulay2">i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions)353 ··············<pre><code·class="language-macaulay2">i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions)
354 ·--·used·0.320174s·(cpu);·0.285186s·(thread);·0s·(gc)354 ·--·used·0.346577s·(cpu);·0.291285s·(thread);·0s·(gc)
  
355 o21·=·R'355 o21·=·R'
  
356 o21·:·QuotientRing</code></pre>356 o21·:·QuotientRing</code></pre>
357 ············</td>357 ············</td>
358 ··········</tr>358 ··········</tr>
359 ··········<tr>359 ··········<tr>
Offset 423, 15 lines modifiedOffset 423, 15 lines modified
  
423 o25·:·QuotientRing</code></pre>423 o25·:·QuotientRing</code></pre>
424 ············</td>424 ············</td>
425 ··········</tr>425 ··········</tr>
426 ··········<tr>426 ··········<tr>
427 ············<td>427 ············<td>
428 ··············<pre><code·class="language-macaulay2">i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1)428 ··············<pre><code·class="language-macaulay2">i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1)
429 ·--·used·0.615555s·(cpu);·0.478354s·(thread);·0s·(gc)429 ·--·used·0.692438s·(cpu);·0.538288s·(thread);·0s·(gc)
  
430 o26·=·R'430 o26·=·R'
  
431 o26·:·QuotientRing</code></pre>431 o26·:·QuotientRing</code></pre>
432 ············</td>432 ············</td>
433 ··········</tr>433 ··········</tr>
434 ··········<tr>434 ··········<tr>
Offset 498, 15 lines modifiedOffset 498, 15 lines modified
  
498 o30·:·QuotientRing</code></pre>498 o30·:·QuotientRing</code></pre>
499 ············</td>499 ············</td>
500 ··········</tr>500 ··········</tr>
501 ··········<tr>501 ··········<tr>
502 ············<td>502 ············<td>
503 ··············<pre><code·class="language-macaulay2">i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos)503 ··············<pre><code·class="language-macaulay2">i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos)
504 ·--·used·0.300116s·(cpu);·0.255461s·(thread);·0s·(gc)504 ·--·used·0.347929s·(cpu);·0.297721s·(thread);·0s·(gc)
  
505 o31·=·R'505 o31·=·R'
  
506 o31·:·QuotientRing</code></pre>506 o31·:·QuotientRing</code></pre>
507 ············</td>507 ············</td>
508 ··········</tr>508 ··········</tr>
509 ··········<tr>509 ··········<tr>
Offset 573, 15 lines modifiedOffset 573, 15 lines modified
  
573 o35·:·QuotientRing</code></pre>573 o35·:·QuotientRing</code></pre>
574 ············</td>574 ············</td>
575 ··········</tr>575 ··········</tr>
576 ··········<tr>576 ··········<tr>
577 ············<td>577 ············<td>
578 ··············<pre><code·class="language-macaulay2">i36·:·time·R'·=·integralClosure·R578 ··············<pre><code·class="language-macaulay2">i36·:·time·R'·=·integralClosure·R
579 ·--·used·0.0360022s·(cpu);·0.0373263s·(thread);·0s·(gc)579 ·--·used·0.0474003s·(cpu);·0.0458357s·(thread);·0s·(gc)
  
580 o36·=·R'580 o36·=·R'
  
581 o36·:·QuotientRing</code></pre>581 o36·:·QuotientRing</code></pre>
582 ············</td>582 ············</td>
583 ··········</tr>583 ··········</tr>
584 ··········<tr>584 ··········<tr>
Offset 643, 15 lines modifiedOffset 643, 15 lines modified
  
643 o40·:·QuotientRing</code></pre>643 o40·:·QuotientRing</code></pre>
644 ············</td>644 ············</td>
645 ··········</tr>645 ··········</tr>
646 ··········<tr>646 ··········<tr>
647 ············<td>647 ············<td>
648 ··············<pre><code·class="language-macaulay2">i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)648 ··············<pre><code·class="language-macaulay2">i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)
649 ·--·used·0.107357s·(cpu);·0.0695835s·(thread);·0s·(gc)649 ·--·used·0.133641s·(cpu);·0.0731088s·(thread);·0s·(gc)
  
650 o41·=·R'650 o41·=·R'
  
651 o41·:·QuotientRing</code></pre>651 o41·:·QuotientRing</code></pre>
652 ············</td>652 ············</td>
653 ··········</tr>653 ··········</tr>
654 ··········<tr>654 ··········<tr>
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Offset 48, 15 lines modifiedOffset 48, 15 lines modified
48 o2·:·Ideal·of·S48 o2·:·Ideal·of·S
49 i3·:·R·=·S/f49 i3·:·R·=·S/f
  
50 o3·=·R50 o3·=·R
  
51 o3·:·QuotientRing51 o3·:·QuotientRing
52 i4·:·time·R'·=·integralClosure·R52 i4·:·time·R'·=·integralClosure·R
53 ·--·used·0.643287s·(cpu);·0.33729s·(thread);·0s·(gc)53 ·--·used·0.812045s·(cpu);·0.3767s·(thread);·0s·(gc)
  
54 o4·=·R'54 o4·=·R'
  
55 o4·:·QuotientRing55 o4·:·QuotientRing
56 i5·:·netList·(ideal·R')_*56 i5·:·netList·(ideal·R')_*
  
57 ·····+------------------------------------------------------------------------+57 ·····+------------------------------------------------------------------------+
Offset 109, 15 lines modifiedOffset 109, 15 lines modified
109 o8·:·Ideal·of·S109 o8·:·Ideal·of·S
110 i9·:·R·=·S/f110 i9·:·R·=·S/f
  
111 o9·=·R111 o9·=·R
  
112 o9·:·QuotientRing112 o9·:·QuotientRing
113 i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)113 i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)
114 ·--·used·0.625821s·(cpu);·0.333342s·(thread);·0s·(gc)114 ·--·used·0.74952s·(cpu);·0.388643s·(thread);·0s·(gc)
  
115 o10·=·R'115 o10·=·R'
  
116 o10·:·QuotientRing116 o10·:·QuotientRing
117 i11·:·netList·(ideal·R')_*117 i11·:·netList·(ideal·R')_*
  
118 ······+------------------------------------------------------------------------118 ······+------------------------------------------------------------------------
Offset 199, 15 lines modifiedOffset 199, 15 lines modified
199 o14·:·Ideal·of·S199 o14·:·Ideal·of·S
200 i15·:·R·=·S/f200 i15·:·R·=·S/f
  
201 o15·=·R201 o15·=·R
  
202 o15·:·QuotientRing202 o15·:·QuotientRing
203 i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions)203 i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions)
204 ·--·used·0.421983s·(cpu);·0.299816s·(thread);·0s·(gc)204 ·--·used·0.543345s·(cpu);·0.379768s·(thread);·0s·(gc)
  
205 o16·=·R'205 o16·=·R'
  
206 o16·:·QuotientRing206 o16·:·QuotientRing
207 i17·:·netList·(ideal·R')_*207 i17·:·netList·(ideal·R')_*
  
208 ······+------------------------------------------------------------------------208 ······+------------------------------------------------------------------------
Offset 281, 15 lines modifiedOffset 281, 15 lines modified
281 o19·:·Ideal·of·S281 o19·:·Ideal·of·S
282 i20·:·R·=·S/f282 i20·:·R·=·S/f
  
283 o20·=·R283 o20·=·R
  
284 o20·:·QuotientRing284 o20·:·QuotientRing
285 i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions)285 i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions)
286 ·--·used·0.320174s·(cpu);·0.285186s·(thread);·0s·(gc)286 ·--·used·0.346577s·(cpu);·0.291285s·(thread);·0s·(gc)
  
287 o21·=·R'287 o21·=·R'
  
288 o21·:·QuotientRing288 o21·:·QuotientRing
289 i22·:·netList·(ideal·R')_*289 i22·:·netList·(ideal·R')_*
  
290 ······+------------------------------------------------------------------------290 ······+------------------------------------------------------------------------
Offset 363, 15 lines modifiedOffset 363, 15 lines modified
363 o24·:·Ideal·of·S363 o24·:·Ideal·of·S
364 i25·:·R·=·S/f364 i25·:·R·=·S/f
  
365 o25·=·R365 o25·=·R
  
366 o25·:·QuotientRing366 o25·:·QuotientRing
367 i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1)367 i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1)
368 ·--·used·0.615555s·(cpu);·0.478354s·(thread);·0s·(gc)368 ·--·used·0.692438s·(cpu);·0.538288s·(thread);·0s·(gc)
  
369 o26·=·R'369 o26·=·R'
  
370 o26·:·QuotientRing370 o26·:·QuotientRing
371 i27·:·netList·(ideal·R')_*371 i27·:·netList·(ideal·R')_*
  
372 ······+------------------------------------------------------------------------372 ······+------------------------------------------------------------------------
Offset 445, 15 lines modifiedOffset 445, 15 lines modified
445 o29·:·Ideal·of·S445 o29·:·Ideal·of·S
446 i30·:·R·=·S/f446 i30·:·R·=·S/f
  
447 o30·=·R447 o30·=·R
  
448 o30·:·QuotientRing448 o30·:·QuotientRing
449 i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos)449 i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos)
450 ·--·used·0.300116s·(cpu);·0.255461s·(thread);·0s·(gc)450 ·--·used·0.347929s·(cpu);·0.297721s·(thread);·0s·(gc)
  
451 o31·=·R'451 o31·=·R'
  
452 o31·:·QuotientRing452 o31·:·QuotientRing
453 i32·:·netList·(ideal·R')_*453 i32·:·netList·(ideal·R')_*
  
454 ······+------------------------------------------------------------------------454 ······+------------------------------------------------------------------------
Offset 527, 15 lines modifiedOffset 527, 15 lines modified
527 o34·:·Ideal·of·S527 o34·:·Ideal·of·S
528 i35·:·R·=·S/f528 i35·:·R·=·S/f
  
529 o35·=·R529 o35·=·R
  
530 o35·:·QuotientRing530 o35·:·QuotientRing
531 i36·:·time·R'·=·integralClosure·R531 i36·:·time·R'·=·integralClosure·R
532 ·--·used·0.0360022s·(cpu);·0.0373263s·(thread);·0s·(gc)532 ·--·used·0.0474003s·(cpu);·0.0458357s·(thread);·0s·(gc)
  
533 o36·=·R'533 o36·=·R'
  
534 o36·:·QuotientRing534 o36·:·QuotientRing
535 i37·:·netList·(ideal·R')_*535 i37·:·netList·(ideal·R')_*
  
536 ······+-----------+536 ······+-----------+
Offset 573, 15 lines modifiedOffset 573, 15 lines modified
573 o39·:·Ideal·of·S573 o39·:·Ideal·of·S
574 i40·:·R·=·S/I574 i40·:·R·=·S/I
  
575 o40·=·R575 o40·=·R
  
576 o40·:·QuotientRing576 o40·:·QuotientRing
577 i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)577 i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical)
578 ·--·used·0.107357s·(cpu);·0.0695835s·(thread);·0s·(gc)578 ·--·used·0.133641s·(cpu);·0.0731088s·(thread);·0s·(gc)
  
579 o41·=·R'579 o41·=·R'
  
580 o41·:·QuotientRing580 o41·:·QuotientRing
581 i42·:·icFractions·R581 i42·:·icFractions·R
  
582 ········2582 ········2
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Offset 71, 52 lines modifiedOffset 71, 52 lines modified
71 ············<td>71 ············<td>
72 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);</code></pre>72 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);</code></pre>
73 ············</td>73 ············</td>
74 ··········</tr>74 ··········</tr>
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2)77 ··············<pre><code·class="language-macaulay2">i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2)
78 ·[jacobian·time·.000880965·sec·#minors·3]78 ·[jacobian·time·.00260525·sec·#minors·3]
79 integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·279 integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2
  
80 ·[step·0:·80 ·[step·0:·
81 ······radical·(use·minprimes)·.00399937·seconds81 ······radical·(use·minprimes)·0·seconds
82 ······idlizer1:··.00555663·seconds82 ······idlizer1:··.00800214·seconds
83 ······idlizer2:··.00942649·seconds83 ······idlizer2:··.00800336·seconds
84 ······minpres:···.0622194·seconds84 ······minpres:···.065727·seconds
85 ··time·.0875184·sec··#fractions·4]85 ··time·.0937245·sec··#fractions·4]
86 ·[step·1:·86 ·[step·1:·
87 ······radical·(use·minprimes)·.00399929·seconds87 ······radical·(use·minprimes)·0·seconds
88 ······idlizer1:··.00800009·seconds 
89 ······idlizer2:··.0119997·seconds88 ······idlizer1:··.0115569·seconds
 89 ······idlizer2:··.0133081·seconds
90 ······minpres:···.0654003·seconds90 ······minpres:···.0775545·seconds
91 ··time·.0969859·sec··#fractions·4]91 ··time·.110013·sec··#fractions·4]
92 ·[step·2:·92 ·[step·2:·
93 ······radical·(use·minprimes)·.00400076·seconds93 ······radical·(use·minprimes)·.00399458·seconds
94 ······idlizer1:··.0119986·seconds94 ······idlizer1:··.0120099·seconds
95 ······idlizer2:··.0646385·seconds95 ······idlizer2:··.0986425·seconds
96 ······minpres:···.00796869·seconds96 ······minpres:···.0119984·seconds
97 ··time·.0988024·sec··#fractions·5]97 ··time·.134639·sec··#fractions·5]
98 ·[step·3:·98 ·[step·3:·
99 ······radical·(use·minprimes)·.00399856·seconds99 ······radical·(use·minprimes)·.00398756·seconds
100 ······idlizer1:··.0160234·seconds100 ······idlizer1:··.0160219·seconds
101 ······idlizer2:··.0680807·seconds101 ······idlizer2:··.0786332·seconds
102 ······minpres:···.0160647·seconds102 ······minpres:···.0199656·seconds
103 ··time·.111514·sec··#fractions·5]103 ··time·.126533·sec··#fractions·5]
104 ·[step·4:·104 ·[step·4:·
105 ······radical·(use·minprimes)·.00385243·seconds105 ······radical·(use·minprimes)·.00393502·seconds
106 ······idlizer1:··.00910461·seconds106 ······idlizer1:··.0121068·seconds
107 ······idlizer2:··.0760828·seconds107 ······idlizer2:··.101829·seconds
108 ······minpres:···.0119969·seconds108 ······minpres:···.0126668·seconds
109 ··time·.112259·sec··#fractions·5]109 ··time·.141479·sec··#fractions·5]
110 ·[step·5:·110 ·[step·5:·
111 ······radical·(use·minprimes)·0·seconds111 ······radical·(use·minprimes)·.00403653·seconds
112 ······idlizer1:···--·used·0.528614s·(cpu);·0.32721s·(thread);·0s·(gc)112 ······idlizer1:···--·used·0.630461s·(cpu);·0.358897s·(thread);·0s·(gc)
113 .00399852·seconds113 .012026·seconds
114 ··time·.0159976·sec··#fractions·5]114 ··time·.0200928·sec··#fractions·5]
  
115 o2·=·R'115 o2·=·R'
  
116 o2·:·QuotientRing</code></pre>116 o2·:·QuotientRing</code></pre>
117 ············</td>117 ············</td>
118 ··········</tr>118 ··········</tr>
119 ··········<tr>119 ··········<tr>
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12 ············displayed.·A·value·of·0·means:·keep·quiet.12 ············displayed.·A·value·of·0·means:·keep·quiet.
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 When·the·computation·takes·a·considerable·time,·this·function·can·be·used·to14 When·the·computation·takes·a·considerable·time,·this·function·can·be·used·to
15 decide·if·it·will·ever·finish,·or·to·get·a·feel·for·what·is·happening·during15 decide·if·it·will·ever·finish,·or·to·get·a·feel·for·what·is·happening·during
16 the·computation.16 the·computation.
17 i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);17 i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3);
18 i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2)18 i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2)
19 ·[jacobian·time·.000880965·sec·#minors·3]19 ·[jacobian·time·.00260525·sec·#minors·3]
20 integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·220 integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2
  
21 ·[step·0:21 ·[step·0:
22 ······radical·(use·minprimes)·.00399937·seconds22 ······radical·(use·minprimes)·0·seconds
23 ······idlizer1:··.00555663·seconds23 ······idlizer1:··.00800214·seconds
24 ······idlizer2:··.00942649·seconds24 ······idlizer2:··.00800336·seconds
25 ······minpres:···.0622194·seconds25 ······minpres:···.065727·seconds
26 ··time·.0875184·sec··#fractions·4]26 ··time·.0937245·sec··#fractions·4]
27 ·[step·1:27 ·[step·1:
28 ······radical·(use·minprimes)·.00399929·seconds28 ······radical·(use·minprimes)·0·seconds
29 ······idlizer1:··.00800009·seconds 
30 ······idlizer2:··.0119997·seconds29 ······idlizer1:··.0115569·seconds
 30 ······idlizer2:··.0133081·seconds
31 ······minpres:···.0654003·seconds31 ······minpres:···.0775545·seconds
32 ··time·.0969859·sec··#fractions·4]32 ··time·.110013·sec··#fractions·4]
33 ·[step·2:33 ·[step·2:
34 ······radical·(use·minprimes)·.00400076·seconds34 ······radical·(use·minprimes)·.00399458·seconds
35 ······idlizer1:··.0119986·seconds35 ······idlizer1:··.0120099·seconds
36 ······idlizer2:··.0646385·seconds36 ······idlizer2:··.0986425·seconds
37 ······minpres:···.00796869·seconds37 ······minpres:···.0119984·seconds
38 ··time·.0988024·sec··#fractions·5]38 ··time·.134639·sec··#fractions·5]
39 ·[step·3:39 ·[step·3:
40 ······radical·(use·minprimes)·.00399856·seconds40 ······radical·(use·minprimes)·.00398756·seconds
41 ······idlizer1:··.0160234·seconds41 ······idlizer1:··.0160219·seconds
42 ······idlizer2:··.0680807·seconds42 ······idlizer2:··.0786332·seconds
43 ······minpres:···.0160647·seconds43 ······minpres:···.0199656·seconds
44 ··time·.111514·sec··#fractions·5]44 ··time·.126533·sec··#fractions·5]
45 ·[step·4:45 ·[step·4:
46 ······radical·(use·minprimes)·.00385243·seconds46 ······radical·(use·minprimes)·.00393502·seconds
47 ······idlizer1:··.00910461·seconds47 ······idlizer1:··.0121068·seconds
48 ······idlizer2:··.0760828·seconds48 ······idlizer2:··.101829·seconds
49 ······minpres:···.0119969·seconds49 ······minpres:···.0126668·seconds
50 ··time·.112259·sec··#fractions·5]50 ··time·.141479·sec··#fractions·5]
51 ·[step·5:51 ·[step·5:
52 ······radical·(use·minprimes)·0·seconds52 ······radical·(use·minprimes)·.00403653·seconds
53 ······idlizer1:···--·used·0.528614s·(cpu);·0.32721s·(thread);·0s·(gc)53 ······idlizer1:···--·used·0.630461s·(cpu);·0.358897s·(thread);·0s·(gc)
54 .00399852·seconds54 .012026·seconds
55 ··time·.0159976·sec··#fractions·5]55 ··time·.0200928·sec··#fractions·5]
  
56 o2·=·R'56 o2·=·R'
  
57 o2·:·QuotientRing57 o2·:·QuotientRing
58 i3·:·trim·ideal·R'58 i3·:·trim·ideal·R'
  
59 ·····················3···2·····················2·2····4···········459 ·····················3···2·····················2·2····4···········4
2.62 KB
./usr/share/doc/Macaulay2/IntegralClosure/html/_integral__Closure_lp__Ideal_cm__Ring__Element_cm__Z__Z_rp.html
    
Offset 109, 29 lines modifiedOffset 109, 29 lines modified
  
109 o3·:·Ideal·of·S</code></pre>109 o3·:·Ideal·of·S</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i4·:·time·integralClosure·J114 ··············<pre><code·class="language-macaulay2">i4·:·time·integralClosure·J
115 ·--·used·6.4986s·(cpu);·1.30959s·(thread);·0s·(gc)115 ·--·used·5.88464s·(cpu);·1.21039s·(thread);·0s·(gc)
  
116 ·············2·2··············2·2················2··········2···2·····116 ·············2·2··············2·2················2··········2···2·····
117 o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-117 o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-
118 ·····------------------------------------------------------------------------118 ·····------------------------------------------------------------------------
119 ···········2···3···············2·2·····2···5119 ···········2···3···············2·2·····2···5
120 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)120 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)
  
121 o4·:·Ideal·of·S</code></pre>121 o4·:·Ideal·of·S</code></pre>
122 ············</td>122 ············</td>
123 ··········</tr>123 ··········</tr>
124 ··········<tr>124 ··········<tr>
125 ············<td>125 ············<td>
126 ··············<pre><code·class="language-macaulay2">i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1})126 ··············<pre><code·class="language-macaulay2">i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1})
127 ·--·used·9.31893s·(cpu);·1.55133s·(thread);·0s·(gc)127 ·--·used·8.03561s·(cpu);·1.40195s·(thread);·0s·(gc)
  
128 ·············2·2··············2·2················2··········2···2·····128 ·············2·2··············2·2················2··········2···2·····
129 o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-129 o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-
130 ·····------------------------------------------------------------------------130 ·····------------------------------------------------------------------------
131 ···········2···3···············2·2·····2···5131 ···········2···3···············2·2·····2···5
132 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)132 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)
  
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html2text {}
    
Offset 46, 25 lines modifiedOffset 46, 25 lines modified
46 i3·:·J·=·ideal·jacobian·ideal·F46 i3·:·J·=·ideal·jacobian·ideal·F
  
47 ················2······2····2········2···2·2·····247 ················2······2····2········2···2·2·····2
48 o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·)48 o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·)
  
49 o3·:·Ideal·of·S49 o3·:·Ideal·of·S
50 i4·:·time·integralClosure·J50 i4·:·time·integralClosure·J
51 ·--·used·6.4986s·(cpu);·1.30959s·(thread);·0s·(gc)51 ·--·used·5.88464s·(cpu);·1.21039s·(thread);·0s·(gc)
  
52 ·············2·2··············2·2················2··········2···252 ·············2·2··············2·2················2··········2···2
53 o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-53 o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-
54 ·····------------------------------------------------------------------------54 ·····------------------------------------------------------------------------
55 ···········2···3···············2·2·····2···555 ···········2···3···············2·2·····2···5
56 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)56 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)
  
57 o4·:·Ideal·of·S57 o4·:·Ideal·of·S
58 i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1})58 i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1})
59 ·--·used·9.31893s·(cpu);·1.55133s·(thread);·0s·(gc)59 ·--·used·8.03561s·(cpu);·1.40195s·(thread);·0s·(gc)
  
60 ·············2·2··············2·2················2··········2···260 ·············2·2··············2·2················2··········2···2
61 o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-61 o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·-
62 ·····------------------------------------------------------------------------62 ·····------------------------------------------------------------------------
63 ···········2···3···············2·2·····2···563 ···········2···3···············2·2·····2···5
64 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)64 ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c)
  
732 B
./usr/share/doc/Macaulay2/InvariantRing/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=137 #:len=13
8 c2NocmVpZXJHcmFwaA==8 c2NocmVpZXJHcmFwaA==
9 #:len=17129 #:len=1712
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU2NocmVpZXIgZ3JhcGggb2YgYSBmaW5p10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU2NocmVpZXIgZ3JhcGggb2YgYSBmaW5p
11 dGUgZ3JvdXAiLCAibGluZW51bSIgPT4gMjYxLCBJbnB1dHMgPT4ge1NQQU57VFR7IkcifSwiLCAi11 dGUgZ3JvdXAiLCAibGluZW51bSIgPT4gMjYxLCBJbnB1dHMgPT4ge1NQQU57VFR7IkcifSwiLCAi
1.0 KB
./usr/share/doc/Macaulay2/InvariantRing/example-output/_equivariant__Hilbert.out
    
Offset 25, 15 lines modifiedOffset 25, 15 lines modified
25 o3·:·DiagonalAction25 o3·:·DiagonalAction
  
26 i4·:·T.cache.?equivariantHilbert26 i4·:·T.cache.?equivariantHilbert
  
27 o4·=·false27 o4·=·false
  
28 i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5)28 i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5)
29 ·--·.00249221s·elapsed29 ·--·.00671914s·elapsed
  
30 ··················-1····-1·······2·2··············-2····-1·-1····-2··2··30 ··················-1····-1·······2·2··············-2····-1·-1····-2··2··
31 o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+31 o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+
32 ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······32 ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······
33 ·····------------------------------------------------------------------------33 ·····------------------------------------------------------------------------
34 ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··334 ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3
35 ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T·35 ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T·
Offset 51, 10 lines modifiedOffset 51, 10 lines modified
51 ·········0···151 ·········0···1
  
52 i6·:·T.cache.?equivariantHilbert52 i6·:·T.cache.?equivariantHilbert
  
53 o6·=·true53 o6·=·true
  
54 i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5);54 i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5);
55 ·--·.000424852s·elapsed55 ·--·.00461842s·elapsed
  
56 i8·:·56 i8·:·
2.06 KB
./usr/share/doc/Macaulay2/InvariantRing/example-output/_hsop_spalgorithms.out
    
Offset 23, 23 lines modifiedOffset 23, 23 lines modified
23 o3·=·QQ[x..z]·<-·{|·0·-1·0··|,·|·0·-1·0·|}23 o3·=·QQ[x..z]·<-·{|·0·-1·0··|,·|·0·-1·0·|}
24 ··················|·1·0··0··|··|·1·0··0·|24 ··················|·1·0··0··|··|·1·0··0·|
25 ··················|·0·0··-1·|··|·0·0··1·|25 ··················|·0·0··-1·|··|·0·0··1·|
  
26 o3·:·FiniteGroupAction26 o3·:·FiniteGroupAction
  
27 i4·:·time·P1=primaryInvariants·C4xC227 i4·:·time·P1=primaryInvariants·C4xC2
28 ·--·used·0.627438s·(cpu);·0.465944s·(thread);·0s·(gc)28 ·--·used·0.744955s·(cpu);·0.515285s·(thread);·0s·(gc)
  
29 ·······2····2···2···2·229 ·······2····2···2···2·2
30 o4·=·{x··+·y·,·z·,·x·y·}30 o4·=·{x··+·y·,·z·,·x·y·}
  
31 o4·:·List31 o4·:·List
  
32 i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true)32 i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true)
33 ·--·used·0.470632s·(cpu);·0.320446s·(thread);·0s·(gc)33 ·--·used·0.586342s·(cpu);·0.340307s·(thread);·0s·(gc)
  
34 ···················8·················7···················6·2··34 ···················8·················7···················6·2··
35 o5·=·{656100000000x··-·4738500000000x·y·+·10209037500000x·y··-35 o5·=·{656100000000x··-·4738500000000x·y·+·10209037500000x·y··-
36 ·····------------------------------------------------------------------------36 ·····------------------------------------------------------------------------
37 ···················5·3··················4·4·················3·5··37 ···················5·3··················4·4·················3·5··
38 ·····1232156250000x·y··-·14757374609375x·y··+·1232156250000x·y··+38 ·····1232156250000x·y··-·14757374609375x·y··+·1232156250000x·y··+
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
Offset 90, 23 lines modifiedOffset 90, 23 lines modified
90 ·····------------------------------------------------------------------------90 ·····------------------------------------------------------------------------
91 ········2·6····891 ········2·6····8
92 ·····90y·z··+·z·}92 ·····90y·z··+·z·}
  
93 o5·:·List93 o5·:·List
  
94 i6·:·time·secondaryInvariants(P1,C4xC2)94 i6·:·time·secondaryInvariants(P1,C4xC2)
95 ·--·used·0.0739605s·(cpu);·0.0428423s·(thread);·0s·(gc)95 ·--·used·0.091396s·(cpu);·0.0450058s·(thread);·0s·(gc)
  
96 ··········3·······396 ··········3·······3
97 o6·=·{1,·x·y·-·x*y·}97 o6·=·{1,·x·y·-·x*y·}
  
98 o6·:·List98 o6·:·List
  
99 i7·:·time·secondaryInvariants(P2,C4xC2)99 i7·:·time·secondaryInvariants(P2,C4xC2)
100 ·--·used·1.48389s·(cpu);·1.10702s·(thread);·0s·(gc)100 ·--·used·1.85678s·(cpu);·1.3179s·(thread);·0s·(gc)
  
101 ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4··101 ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4··
102 o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+102 o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+
103 ·····------------------------------------------------------------------------103 ·····------------------------------------------------------------------------
104 ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6104 ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6
105 ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x·105 ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x·
106 ·····------------------------------------------------------------------------106 ·····------------------------------------------------------------------------
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./usr/share/doc/Macaulay2/InvariantRing/example-output/_invariants_lp..._cm__Degree__Bound_eq_gt..._rp.out
    
Offset 14, 28 lines modifiedOffset 14, 28 lines modified
14 ···········|·1·0·0·0·|··|·1·0·0·0·|14 ···········|·1·0·0·0·|··|·1·0·0·0·|
15 ···········|·0·0·1·0·|··|·0·1·0·0·|15 ···········|·0·0·1·0·|··|·0·1·0·0·|
16 ···········|·0·0·0·1·|··|·0·0·1·0·|16 ···········|·0·0·0·1·|··|·0·0·1·0·|
  
17 o3·:·FiniteGroupAction17 o3·:·FiniteGroupAction
  
18 i4·:·elapsedTime·invariants·S418 i4·:·elapsedTime·invariants·S4
19 ·--·.532913s·elapsed19 ·--·1.68084s·elapsed
  
20 ··························2····2····2····2···3····3····3····3···4····4····4··20 ··························2····2····2····2···3····3····3····3···4····4····4··
21 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+21 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+
22 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··22 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··
23 ·····------------------------------------------------------------------------23 ·····------------------------------------------------------------------------
24 ······424 ······4
25 ·····x·}25 ·····x·}
26 ······426 ······4
  
27 o4·:·List27 o4·:·List
  
28 i5·:·elapsedTime·invariants(S4,DegreeBound=>4)28 i5·:·elapsedTime·invariants(S4,DegreeBound=>4)
29 ·--·.408506s·elapsed29 ·--·1.17532s·elapsed
  
30 Warning:·stopping·condition·not·met!30 Warning:·stopping·condition·not·met!
31 Output·may·not·generate·the·entire·ring·of·invariants.31 Output·may·not·generate·the·entire·ring·of·invariants.
32 Increase·value·of·DegreeBound.32 Increase·value·of·DegreeBound.
  
  
33 ··························2····2····2····2···3····3····3····3···4····4····4··33 ··························2····2····2····2···3····3····3····3···4····4····4··
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14 ···········|·1·0·0·0·|··|·1·0·0·0·|14 ···········|·1·0·0·0·|··|·1·0·0·0·|
15 ···········|·0·0·1·0·|··|·0·1·0·0·|15 ···········|·0·0·1·0·|··|·0·1·0·0·|
16 ···········|·0·0·0·1·|··|·0·0·1·0·|16 ···········|·0·0·0·1·|··|·0·0·1·0·|
  
17 o3·:·FiniteGroupAction17 o3·:·FiniteGroupAction
  
18 i4·:·elapsedTime·invariants·S418 i4·:·elapsedTime·invariants·S4
19 ·--·.952763s·elapsed19 ·--·1.97876s·elapsed
  
20 ··························2····2····2····2···3····3····3····3···4····4····4··20 ··························2····2····2····2···3····3····3····3···4····4····4··
21 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+21 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+
22 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··22 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··
23 ·····------------------------------------------------------------------------23 ·····------------------------------------------------------------------------
24 ······424 ······4
25 ·····x·}25 ·····x·}
26 ······426 ······4
  
27 o4·:·List27 o4·:·List
  
28 i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true)28 i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true)
29 ·--·.138036s·elapsed29 ·--·.207228s·elapsed
  
30 o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+30 o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+
31 ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3··31 ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3··
32 ·····------------------------------------------------------------------------32 ·····------------------------------------------------------------------------
33 ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·}33 ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·}
34 ······1·2·4····1·3·4····2·3·4···1·2·3·434 ······1·2·4····1·3·4····2·3·4···1·2·3·4
  
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16 ··················|·0·0·1·|··|·1·0·0·|16 ··················|·0·0·1·|··|·1·0·0·|
17 ··················|·1·0·0·|··|·0·0·1·|17 ··················|·1·0·0·|··|·0·0·1·|
  
18 o3·:·FiniteGroupAction18 o3·:·FiniteGroupAction
  
19 i4·:·primaryInvariants·S319 i4·:·primaryInvariants·S3
  
20 ··················2····2····2···2·······2····2·····2·······2······2 
21 o4·=·{x·+·y·+·z,·x··+·y··+·z·,·x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·}20 ···································3····3····3
 21 o4·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·}
  
22 o4·:·List22 o4·:·List
  
23 i5·:·K=GF(101)23 i5·:·K=GF(101)
  
24 o5·=·K24 o5·=·K
  
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16 ··················|·0·0·1·|··|·1·0·0·|16 ··················|·0·0·1·|··|·1·0·0·|
17 ··················|·1·0·0·|··|·0·0·1·|17 ··················|·1·0·0·|··|·0·0·1·|
  
18 o3·:·FiniteGroupAction18 o3·:·FiniteGroupAction
  
19 i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4})19 i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4})
  
20 ·······2·······2····2·····2·······2······2··········4····4····420 ·······3····3····3···2·······2····2·····2·······2······2···4····4····4
21 o4·=·{x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x*y*z,·x··+·y··+·z·}21 o4·=·{x··+·y··+·z·,·x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x··+·y··+·z·}
  
22 o4·:·List22 o4·:·List
  
23 i5·:·23 i5·:·
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Offset 92, 15 lines modifiedOffset 92, 15 lines modified
  
92 o4·=·false</code></pre>92 o4·=·false</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5)97 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5)
98 ·--·.00249221s·elapsed98 ·--·.00671914s·elapsed
  
99 ··················-1····-1·······2·2··············-2····-1·-1····-2··2··99 ··················-1····-1·······2·2··············-2····-1·-1····-2··2··
100 o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+100 o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+
101 ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······101 ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······
102 ·····------------------------------------------------------------------------102 ·····------------------------------------------------------------------------
103 ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3103 ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3
104 ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T·104 ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T·
Offset 124, 15 lines modifiedOffset 124, 15 lines modified
  
124 o6·=·true</code></pre>124 o6·=·true</code></pre>
125 ············</td>125 ············</td>
126 ··········</tr>126 ··········</tr>
127 ··········<tr>127 ··········<tr>
128 ············<td>128 ············<td>
129 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5);129 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5);
130 ·--·.000424852s·elapsed</code></pre>130 ·--·.00461842s·elapsed</code></pre>
131 ············</td>131 ············</td>
132 ··········</tr>132 ··········</tr>
133 ········</table>133 ········</table>
134 ······</div>134 ······</div>
135 ······<div>135 ······<div>
136 ········<div·class="waystouse">136 ········<div·class="waystouse">
137 ··········<h2>For·the·programmer</h2>137 ··········<h2>For·the·programmer</h2>
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30 ·····|·0··-1·1·|30 ·····|·0··-1·1·|
  
31 o3·:·DiagonalAction31 o3·:·DiagonalAction
32 i4·:·T.cache.?equivariantHilbert32 i4·:·T.cache.?equivariantHilbert
  
33 o4·=·false33 o4·=·false
34 i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5)34 i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5)
35 ·--·.00249221s·elapsed35 ·--·.00671914s·elapsed
  
36 ··················-1····-1·······2·2··············-2····-1·-1····-2··236 ··················-1····-1·······2·2··············-2····-1·-1····-2··2
37 o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+37 o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+
38 ···········0·1····1·····0········0·1····0····1····1·····0··1·····038 ···········0·1····1·····0········0·1····0····1····1·····0··1·····0
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
40 ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··340 ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3
41 ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T41 ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T
Offset 54, 13 lines modifiedOffset 54, 13 lines modified
  
54 o5·:·ZZ[z·..z·][T]54 o5·:·ZZ[z·..z·][T]
55 ·········0···155 ·········0···1
56 i6·:·T.cache.?equivariantHilbert56 i6·:·T.cache.?equivariantHilbert
  
57 o6·=·true57 o6·=·true
58 i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5);58 i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5);
59 ·--·.000424852s·elapsed59 ·--·.00461842s·elapsed
60 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*60 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
61 The·object·_\x8e_\x8q_\x8u_\x8i_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8H_\x8i_\x8l_\x8b_\x8e_\x8r_\x8t·is·a·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l.61 The·object·_\x8e_\x8q_\x8u_\x8i_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8H_\x8i_\x8l_\x8b_\x8e_\x8r_\x8t·is·a·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l.
62 ===============================================================================62 ===============================================================================
63 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-63 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
64 1.25.06+ds/M2/Macaulay2/packages/InvariantRing/AbelianGroupsDoc.m2:185:0.64 1.25.06+ds/M2/Macaulay2/packages/InvariantRing/AbelianGroupsDoc.m2:185:0.
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92 ··········</tr>92 ··········</tr>
93 ········</table>93 ········</table>
94 ········<p>The·two·algorithms·used·in·<a·title="computes·a·list·of·primary·invariants·for·the·invariant·ring·of·a·finite·group"·href="_primary__Invariants.html">primaryInvariants</a>·are·timed.·One·sees·that·the·Dade·algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·8·and·have·ugly·coefficients.</p>94 ········<p>The·two·algorithms·used·in·<a·title="computes·a·list·of·primary·invariants·for·the·invariant·ring·of·a·finite·group"·href="_primary__Invariants.html">primaryInvariants</a>·are·timed.·One·sees·that·the·Dade·algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·8·and·have·ugly·coefficients.</p>
95 ········<table·class="examples">95 ········<table·class="examples">
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i4·:·time·P1=primaryInvariants·C4xC298 ··············<pre><code·class="language-macaulay2">i4·:·time·P1=primaryInvariants·C4xC2
99 ·--·used·0.627438s·(cpu);·0.465944s·(thread);·0s·(gc)99 ·--·used·0.744955s·(cpu);·0.515285s·(thread);·0s·(gc)
  
100 ·······2····2···2···2·2100 ·······2····2···2···2·2
101 o4·=·{x··+·y·,·z·,·x·y·}101 o4·=·{x··+·y·,·z·,·x·y·}
  
102 o4·:·List</code></pre>102 o4·:·List</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true)107 ··············<pre><code·class="language-macaulay2">i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true)
108 ·--·used·0.470632s·(cpu);·0.320446s·(thread);·0s·(gc)108 ·--·used·0.586342s·(cpu);·0.340307s·(thread);·0s·(gc)
  
109 ···················8·················7···················6·2··109 ···················8·················7···················6·2··
110 o5·=·{656100000000x··-·4738500000000x·y·+·10209037500000x·y··-110 o5·=·{656100000000x··-·4738500000000x·y·+·10209037500000x·y··-
111 ·····------------------------------------------------------------------------111 ·····------------------------------------------------------------------------
112 ···················5·3··················4·4·················3·5··112 ···················5·3··················4·4·················3·5··
113 ·····1232156250000x·y··-·14757374609375x·y··+·1232156250000x·y··+113 ·····1232156250000x·y··-·14757374609375x·y··+·1232156250000x·y··+
114 ·····------------------------------------------------------------------------114 ·····------------------------------------------------------------------------
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168 ··········</tr>168 ··········</tr>
169 ········</table>169 ········</table>
170 ········<p>The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is·rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding·secondary·invariants.··In·fact,·it·has·proved·quicker·overall·to·calculate·the·invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm.</p>170 ········<p>The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is·rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding·secondary·invariants.··In·fact,·it·has·proved·quicker·overall·to·calculate·the·invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm.</p>
171 ········<table·class="examples">171 ········<table·class="examples">
172 ··········<tr>172 ··········<tr>
173 ············<td>173 ············<td>
174 ··············<pre><code·class="language-macaulay2">i6·:·time·secondaryInvariants(P1,C4xC2)174 ··············<pre><code·class="language-macaulay2">i6·:·time·secondaryInvariants(P1,C4xC2)
175 ·--·used·0.0739605s·(cpu);·0.0428423s·(thread);·0s·(gc)175 ·--·used·0.091396s·(cpu);·0.0450058s·(thread);·0s·(gc)
  
176 ··········3·······3176 ··········3·······3
177 o6·=·{1,·x·y·-·x*y·}177 o6·=·{1,·x·y·-·x*y·}
  
178 o6·:·List</code></pre>178 o6·:·List</code></pre>
179 ············</td>179 ············</td>
180 ··········</tr>180 ··········</tr>
181 ··········<tr>181 ··········<tr>
182 ············<td>182 ············<td>
183 ··············<pre><code·class="language-macaulay2">i7·:·time·secondaryInvariants(P2,C4xC2)183 ··············<pre><code·class="language-macaulay2">i7·:·time·secondaryInvariants(P2,C4xC2)
184 ·--·used·1.48389s·(cpu);·1.10702s·(thread);·0s·(gc)184 ·--·used·1.85678s·(cpu);·1.3179s·(thread);·0s·(gc)
  
185 ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4··185 ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4··
186 o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+186 o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+
187 ·····------------------------------------------------------------------------187 ·····------------------------------------------------------------------------
188 ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6188 ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6
189 ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x·189 ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x·
190 ·····------------------------------------------------------------------------190 ·····------------------------------------------------------------------------
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69 ··················|·0·0··-1·|··|·0·0··1·|69 ··················|·0·0··-1·|··|·0·0··1·|
  
70 o3·:·FiniteGroupAction70 o3·:·FiniteGroupAction
71 The·two·algorithms·used·in·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·are·timed.·One·sees·that·the·Dade71 The·two·algorithms·used·in·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·are·timed.·One·sees·that·the·Dade
72 algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·872 algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·8
73 and·have·ugly·coefficients.73 and·have·ugly·coefficients.
74 i4·:·time·P1=primaryInvariants·C4xC274 i4·:·time·P1=primaryInvariants·C4xC2
75 ·--·used·0.627438s·(cpu);·0.465944s·(thread);·0s·(gc)75 ·--·used·0.744955s·(cpu);·0.515285s·(thread);·0s·(gc)
  
76 ·······2····2···2···2·276 ·······2····2···2···2·2
77 o4·=·{x··+·y·,·z·,·x·y·}77 o4·=·{x··+·y·,·z·,·x·y·}
  
78 o4·:·List78 o4·:·List
79 i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true)79 i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true)
80 ·--·used·0.470632s·(cpu);·0.320446s·(thread);·0s·(gc)80 ·--·used·0.586342s·(cpu);·0.340307s·(thread);·0s·(gc)
  
81 ···················8·················7···················6·281 ···················8·················7···················6·2
82 o5·=·{656100000000x··-·4738500000000x·y·+·10209037500000x·y··-82 o5·=·{656100000000x··-·4738500000000x·y·+·10209037500000x·y··-
83 ·····------------------------------------------------------------------------83 ·····------------------------------------------------------------------------
84 ···················5·3··················4·4·················3·584 ···················5·3··················4·4·················3·5
85 ·····1232156250000x·y··-·14757374609375x·y··+·1232156250000x·y··+85 ·····1232156250000x·y··-·14757374609375x·y··+·1232156250000x·y··+
86 ·····------------------------------------------------------------------------86 ·····------------------------------------------------------------------------
Offset 138, 22 lines modifiedOffset 138, 22 lines modified
  
138 o5·:·List138 o5·:·List
139 The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is139 The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is
140 rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding140 rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding
141 secondary·invariants.·In·fact,·it·has·proved·quicker·overall·to·calculate·the141 secondary·invariants.·In·fact,·it·has·proved·quicker·overall·to·calculate·the
142 invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm.142 invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm.
143 i6·:·time·secondaryInvariants(P1,C4xC2)143 i6·:·time·secondaryInvariants(P1,C4xC2)
144 ·--·used·0.0739605s·(cpu);·0.0428423s·(thread);·0s·(gc)144 ·--·used·0.091396s·(cpu);·0.0450058s·(thread);·0s·(gc)
  
145 ··········3·······3145 ··········3·······3
146 o6·=·{1,·x·y·-·x*y·}146 o6·=·{1,·x·y·-·x*y·}
  
147 o6·:·List147 o6·:·List
148 i7·:·time·secondaryInvariants(P2,C4xC2)148 i7·:·time·secondaryInvariants(P2,C4xC2)
149 ·--·used·1.48389s·(cpu);·1.10702s·(thread);·0s·(gc)149 ·--·used·1.85678s·(cpu);·1.3179s·(thread);·0s·(gc)
  
150 ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4150 ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4
151 o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+151 o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+
152 ·····------------------------------------------------------------------------152 ·····------------------------------------------------------------------------
153 ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6153 ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6
154 ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x154 ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x
155 ·····------------------------------------------------------------------------155 ·····------------------------------------------------------------------------
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Offset 96, 15 lines modifiedOffset 96, 15 lines modified
  
96 o3·:·FiniteGroupAction</code></pre>96 o3·:·FiniteGroupAction</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4101 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4
102 ·--·.532913s·elapsed102 ·--·1.68084s·elapsed
  
103 ··························2····2····2····2···3····3····3····3···4····4····4··103 ··························2····2····2····2···3····3····3····3···4····4····4··
104 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+104 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+
105 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··105 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··
106 ·····------------------------------------------------------------------------106 ·····------------------------------------------------------------------------
107 ······4107 ······4
108 ·····x·}108 ·····x·}
Offset 112, 15 lines modifiedOffset 112, 15 lines modified
  
112 o4·:·List</code></pre>112 o4·:·List</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,DegreeBound=>4)117 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,DegreeBound=>4)
118 ·--·.408506s·elapsed118 ·--·1.17532s·elapsed
  
119 Warning:·stopping·condition·not·met!119 Warning:·stopping·condition·not·met!
120 Output·may·not·generate·the·entire·ring·of·invariants.120 Output·may·not·generate·the·entire·ring·of·invariants.
121 Increase·value·of·DegreeBound.121 Increase·value·of·DegreeBound.
  
  
122 ··························2····2····2····2···3····3····3····3···4····4····4··122 ··························2····2····2····2···3····3····3····3···4····4····4··
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Offset 33, 27 lines modifiedOffset 33, 27 lines modified
33 o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|}33 o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|}
34 ···········|·1·0·0·0·|··|·1·0·0·0·|34 ···········|·1·0·0·0·|··|·1·0·0·0·|
35 ···········|·0·0·1·0·|··|·0·1·0·0·|35 ···········|·0·0·1·0·|··|·0·1·0·0·|
36 ···········|·0·0·0·1·|··|·0·0·1·0·|36 ···········|·0·0·0·1·|··|·0·0·1·0·|
  
37 o3·:·FiniteGroupAction37 o3·:·FiniteGroupAction
38 i4·:·elapsedTime·invariants·S438 i4·:·elapsedTime·invariants·S4
39 ·--·.532913s·elapsed39 ·--·1.68084s·elapsed
  
40 ··························2····2····2····2···3····3····3····3···4····4····440 ··························2····2····2····2···3····3····3····3···4····4····4
41 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+41 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+
42 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····342 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3
43 ·····------------------------------------------------------------------------43 ·····------------------------------------------------------------------------
44 ······444 ······4
45 ·····x·}45 ·····x·}
46 ······446 ······4
  
47 o4·:·List47 o4·:·List
48 i5·:·elapsedTime·invariants(S4,DegreeBound=>4)48 i5·:·elapsedTime·invariants(S4,DegreeBound=>4)
49 ·--·.408506s·elapsed49 ·--·1.17532s·elapsed
  
50 Warning:·stopping·condition·not·met!50 Warning:·stopping·condition·not·met!
51 Output·may·not·generate·the·entire·ring·of·invariants.51 Output·may·not·generate·the·entire·ring·of·invariants.
52 Increase·value·of·DegreeBound.52 Increase·value·of·DegreeBound.
  
  
53 ··························2····2····2····2···3····3····3····3···4····4····453 ··························2····2····2····2···3····3····3····3···4····4····4
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Offset 96, 15 lines modifiedOffset 96, 15 lines modified
  
96 o3·:·FiniteGroupAction</code></pre>96 o3·:·FiniteGroupAction</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4101 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4
102 ·--·.952763s·elapsed102 ·--·1.97876s·elapsed
  
103 ··························2····2····2····2···3····3····3····3···4····4····4··103 ··························2····2····2····2···3····3····3····3···4····4····4··
104 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+104 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+
105 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··105 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3··
106 ·····------------------------------------------------------------------------106 ·····------------------------------------------------------------------------
107 ······4107 ······4
108 ·····x·}108 ·····x·}
Offset 112, 15 lines modifiedOffset 112, 15 lines modified
  
112 o4·:·List</code></pre>112 o4·:·List</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true)117 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true)
118 ·--·.138036s·elapsed118 ·--·.207228s·elapsed
  
119 o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+119 o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+
120 ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3··120 ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3··
121 ·····------------------------------------------------------------------------121 ·····------------------------------------------------------------------------
122 ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·}122 ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·}
123 ······1·2·4····1·3·4····2·3·4···1·2·3·4123 ······1·2·4····1·3·4····2·3·4···1·2·3·4
  
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Offset 35, 27 lines modifiedOffset 35, 27 lines modified
35 o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|}35 o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|}
36 ···········|·1·0·0·0·|··|·1·0·0·0·|36 ···········|·1·0·0·0·|··|·1·0·0·0·|
37 ···········|·0·0·1·0·|··|·0·1·0·0·|37 ···········|·0·0·1·0·|··|·0·1·0·0·|
38 ···········|·0·0·0·1·|··|·0·0·1·0·|38 ···········|·0·0·0·1·|··|·0·0·1·0·|
  
39 o3·:·FiniteGroupAction39 o3·:·FiniteGroupAction
40 i4·:·elapsedTime·invariants·S440 i4·:·elapsedTime·invariants·S4
41 ·--·.952763s·elapsed41 ·--·1.97876s·elapsed
  
42 ··························2····2····2····2···3····3····3····3···4····4····442 ··························2····2····2····2···3····3····3····3···4····4····4
43 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+43 o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+
44 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····344 ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3
45 ·····------------------------------------------------------------------------45 ·····------------------------------------------------------------------------
46 ······446 ······4
47 ·····x·}47 ·····x·}
48 ······448 ······4
  
49 o4·:·List49 o4·:·List
50 i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true)50 i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true)
51 ·--·.138036s·elapsed51 ·--·.207228s·elapsed
  
52 o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+52 o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+
53 ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·353 ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3
54 ·····------------------------------------------------------------------------54 ·····------------------------------------------------------------------------
55 ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·}55 ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·}
56 ······1·2·4····1·3·4····2·3·4···1·2·3·456 ······1·2·4····1·3·4····2·3·4···1·2·3·4
  
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Offset 101, 16 lines modifiedOffset 101, 16 lines modified
101 o3·:·FiniteGroupAction</code></pre>101 o3·:·FiniteGroupAction</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants·S3106 ··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants·S3
  
107 ··················2····2····2···2·······2····2·····2·······2······2 
108 o4·=·{x·+·y·+·z,·x··+·y··+·z·,·x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·}107 ···································3····3····3
 108 o4·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·}
  
109 o4·:·List</code></pre>109 o4·:·List</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ········</table>112 ········</table>
113 ········<p>Below,·the·invariant·ring·<span·class="tt">QQ[x,y,z]</span><sup><span·class="tt">S3</span></sup>·is·calculated·with·<span·class="tt">K</span>·being·the·field·with·101·elements.</p>113 ········<p>Below,·the·invariant·ring·<span·class="tt">QQ[x,y,z]</span><sup><span·class="tt">S3</span></sup>·is·calculated·with·<span·class="tt">K</span>·being·the·field·with·101·elements.</p>
114 ········<table·class="examples">114 ········<table·class="examples">
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Offset 38, 16 lines modifiedOffset 38, 16 lines modified
38 o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|}38 o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|}
39 ··················|·0·0·1·|··|·1·0·0·|39 ··················|·0·0·1·|··|·1·0·0·|
40 ··················|·1·0·0·|··|·0·0·1·|40 ··················|·1·0·0·|··|·0·0·1·|
  
41 o3·:·FiniteGroupAction41 o3·:·FiniteGroupAction
42 i4·:·primaryInvariants·S342 i4·:·primaryInvariants·S3
  
43 ··················2····2····2···2·······2····2·····2·······2······2 
44 o4·=·{x·+·y·+·z,·x··+·y··+·z·,·x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·}43 ···································3····3····3
 44 o4·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·}
  
45 o4·:·List45 o4·:·List
46 Below,·the·invariant·ring·QQ[x,y,z]S3·is·calculated·with·K·being·the·field·with46 Below,·the·invariant·ring·QQ[x,y,z]S3·is·calculated·with·K·being·the·field·with
47 101·elements.47 101·elements.
48 i5·:·K=GF(101)48 i5·:·K=GF(101)
  
49 o5·=·K49 o5·=·K
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Offset 97, 16 lines modifiedOffset 97, 16 lines modified
97 o3·:·FiniteGroupAction</code></pre>97 o3·:·FiniteGroupAction</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4})102 ··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4})
  
103 ·······2·······2····2·····2·······2······2··········4····4····4103 ·······3····3····3···2·······2····2·····2·······2······2···4····4····4
104 o4·=·{x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x*y*z,·x··+·y··+·z·}104 o4·=·{x··+·y··+·z·,·x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x··+·y··+·z·}
  
105 o4·:·List</code></pre>105 o4·:·List</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ········</table>108 ········</table>
109 ······</div>109 ······</div>
110 ······<div>110 ······<div>
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Offset 34, 16 lines modifiedOffset 34, 16 lines modified
34 o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|}34 o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|}
35 ··················|·0·0·1·|··|·1·0·0·|35 ··················|·0·0·1·|··|·1·0·0·|
36 ··················|·1·0·0·|··|·0·0·1·|36 ··················|·1·0·0·|··|·0·0·1·|
  
37 o3·:·FiniteGroupAction37 o3·:·FiniteGroupAction
38 i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4})38 i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4})
  
39 ·······2·······2····2·····2·······2······2··········4····4····439 ·······3····3····3···2·······2····2·····2·······2······2···4····4····4
40 o4·=·{x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x*y*z,·x··+·y··+·z·}40 o4·=·{x··+·y··+·z·,·x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x··+·y··+·z·}
  
41 o4·:·List41 o4·:·List
42 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*42 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
43 Currently·users·can·only·use·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·to·calculate·a·hsop·for·the43 Currently·users·can·only·use·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·to·calculate·a·hsop·for·the
44 invariant·ring·over·a·finite·field·by·using·the·Dade·algorithm.·Users·should44 invariant·ring·over·a·finite·field·by·using·the·Dade·algorithm.·Users·should
45 enter·the·finite·field·as·a·_\x8G_\x8a_\x8l_\x8o_\x8i_\x8s_\x8F_\x8i_\x8e_\x8l_\x8d·or·a·quotient·field·of·the·form·_\x8Z_\x8Z/45 enter·the·finite·field·as·a·_\x8G_\x8a_\x8l_\x8o_\x8i_\x8s_\x8F_\x8i_\x8e_\x8l_\x8d·or·a·quotient·field·of·the·form·_\x8Z_\x8Z/
46 p·and·are·advised·to·ensure·that·the·ground·field·has·cardinality·greater·than46 p·and·are·advised·to·ensure·that·the·ground·field·has·cardinality·greater·than
737 B
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156 ···················{-1}·|·0·0·0··0·0·0·0·0·0·0··0·0··0·0··0·0·0··0·0·0·0··0·0·0·0···0···0···0···0···0···0····0····0···0···0····0···0···0····0····0···0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····x_2··x_1··x_0··|··{-1}·|·0···0····0···0····0···0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0····0····0····0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····x_0··0····0····0····0····0····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····x_2·x_1·x_0^2·|156 ···················{-1}·|·0·0·0··0·0·0·0·0·0·0··0·0··0·0··0·0·0··0·0·0·0··0·0·0·0···0···0···0···0···0···0····0····0···0···0····0···0···0····0····0···0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····x_2··x_1··x_0··|··{-1}·|·0···0····0···0····0···0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0····0····0····0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····x_0··0····0····0····0····0····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····x_2·x_1·x_0^2·|
157 ···················{-1}·|·0·0·0··0·0·0·0·0·0·0··0·0··0·0··0·0·0··0·0·0·0··0·0·1·0···0···0···0···0···0···0····0····0···0···0····0···0···0····0····0···0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····|··{-1}·|·0···0····0···0····0···0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0····0····0····0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····0····x_0··-x_2·x_1··-x_3·x_2··0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····x_3·x_2·x_1^2·|157 ···················{-1}·|·0·0·0··0·0·0·0·0·0·0··0·0··0·0··0·0·0··0·0·0·0··0·0·1·0···0···0···0···0···0···0····0····0···0···0····0···0···0····0····0···0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····0····|··{-1}·|·0···0····0···0····0···0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····0···0····0····0····0····0····0····0····0····0····0····0····0···0····0····0····0····0····0···0····0····0····0····0····0····0····0····x_0··-x_2·x_1··-x_3·x_2··0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····x_3·x_2·x_1^2·|
  
158 ································40158 ································40
159 o22·:·S-module,·subquotient·of·S159 o22·:·S-module,·subquotient·of·S
  
160 i23·:·elapsedTime·isIsomorphic(T1,·T2)160 i23·:·elapsedTime·isIsomorphic(T1,·T2)
161 ·--·1.49674s·elapsed161 ·--·5.20073s·elapsed
  
162 o23·=·true162 o23·=·true
  
163 i24·:·elapsedTime·isomorphism(T1,·T2)163 i24·:·elapsedTime·isomorphism(T1,·T2)
164 ·--·.000019419s·elapsed164 ·--·.000023303s·elapsed
  
165 o24·=·{-1}·|·1······-3976··-13490·13495··-2886··2577···14757··-881···7677··165 o24·=·{-1}·|·1······-3976··-13490·13495··-2886··2577···14757··-881···7677··
166 ······{-1}·|·-2527··-13566·2778···-6934··-14806·4619···-13099·6022···-10907166 ······{-1}·|·-2527··-13566·2778···-6934··-14806·4619···-13099·6022···-10907
167 ······{-1}·|·-15420·5642···1489···1354···4591···11881··-5253··7296···-1098·167 ······{-1}·|·-15420·5642···1489···1354···4591···11881··-5253··7296···-1098·
168 ······{-1}·|·7909···-12428·-2260··-8465··12113··-6893··8411···4186···-9393·168 ······{-1}·|·7909···-12428·-2260··-8465··12113··-6893··8411···4186···-9393·
169 ······{-1}·|·-9615··2934···10440··5015···8145···-5585··1360···3295···12851·169 ······{-1}·|·-9615··2934···10440··5015···8145···-5585··1360···3295···12851·
170 ······{-1}·|·-4881··-7984··12700··-10391·-10009·-14538·13207··262····-6500·170 ······{-1}·|·-4881··-7984··12700··-10391·-10009·-14538·13207··262····-6500·
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./usr/share/doc/Macaulay2/Isomorphism/html/_is__Isomorphic.html
    
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328 ································40328 ································40
329 o22·:·S-module,·subquotient·of·S</code></pre>329 o22·:·S-module,·subquotient·of·S</code></pre>
330 ············</td>330 ············</td>
331 ··········</tr>331 ··········</tr>
332 ··········<tr>332 ··········<tr>
333 ············<td>333 ············<td>
334 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isIsomorphic(T1,·T2)334 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isIsomorphic(T1,·T2)
335 ·--·1.49674s·elapsed335 ·--·5.20073s·elapsed
  
336 o23·=·true</code></pre>336 o23·=·true</code></pre>
337 ············</td>337 ············</td>
338 ··········</tr>338 ··········</tr>
339 ··········<tr>339 ··········<tr>
340 ············<td>340 ············<td>
341 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isomorphism(T1,·T2)341 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isomorphism(T1,·T2)
342 ·--·.000019419s·elapsed342 ·--·.000023303s·elapsed
  
343 o24·=·{-1}·|·1······-3976··-13490·13495··-2886··2577···14757··-881···7677··343 o24·=·{-1}·|·1······-3976··-13490·13495··-2886··2577···14757··-881···7677··
344 ······{-1}·|·-2527··-13566·2778···-6934··-14806·4619···-13099·6022···-10907344 ······{-1}·|·-2527··-13566·2778···-6934··-14806·4619···-13099·6022···-10907
345 ······{-1}·|·-15420·5642···1489···1354···4591···11881··-5253··7296···-1098·345 ······{-1}·|·-15420·5642···1489···1354···4591···11881··-5253··7296···-1098·
346 ······{-1}·|·7909···-12428·-2260··-8465··12113··-6893··8411···4186···-9393·346 ······{-1}·|·7909···-12428·-2260··-8465··12113··-6893··8411···4186···-9393·
347 ······{-1}·|·-9615··2934···10440··5015···8145···-5585··1360···3295···12851·347 ······{-1}·|·-9615··2934···10440··5015···8145···-5585··1360···3295···12851·
348 ······{-1}·|·-4881··-7984··12700··-10391·-10009·-14538·13207··262····-6500·348 ······{-1}·|·-4881··-7984··12700··-10391·-10009·-14538·13207··262····-6500·
956 B
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684 0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0684 0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0
685 0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0685 0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0·····0···0···0
686 0···0···0·····x_3·x_2·x_1^2·|686 0···0···0·····x_3·x_2·x_1^2·|
  
687 ································40687 ································40
688 o22·:·S-module,·subquotient·of·S688 o22·:·S-module,·subquotient·of·S
689 i23·:·elapsedTime·isIsomorphic(T1,·T2)689 i23·:·elapsedTime·isIsomorphic(T1,·T2)
690 ·--·1.49674s·elapsed690 ·--·5.20073s·elapsed
  
691 o23·=·true691 o23·=·true
692 i24·:·elapsedTime·isomorphism(T1,·T2)692 i24·:·elapsedTime·isomorphism(T1,·T2)
693 ·--·.000019419s·elapsed693 ·--·.000023303s·elapsed
  
694 o24·=·{-1}·|·1······-3976··-13490·13495··-2886··2577···14757··-881···7677694 o24·=·{-1}·|·1······-3976··-13490·13495··-2886··2577···14757··-881···7677
695 ······{-1}·|·-2527··-13566·2778···-6934··-14806·4619···-13099·6022···-10907695 ······{-1}·|·-2527··-13566·2778···-6934··-14806·4619···-13099·6022···-10907
696 ······{-1}·|·-15420·5642···1489···1354···4591···11881··-5253··7296···-1098696 ······{-1}·|·-15420·5642···1489···1354···4591···11881··-5253··7296···-1098
697 ······{-1}·|·7909···-12428·-2260··-8465··12113··-6893··8411···4186···-9393697 ······{-1}·|·7909···-12428·-2260··-8465··12113··-6893··8411···4186···-9393
698 ······{-1}·|·-9615··2934···10440··5015···8145···-5585··1360···3295···12851698 ······{-1}·|·-9615··2934···10440··5015···8145···-5585··1360···3295···12851
699 ······{-1}·|·-4881··-7984··12700··-10391·-10009·-14538·13207··262····-6500699 ······{-1}·|·-4881··-7984··12700··-10391·-10009·-14538·13207··262····-6500
713 B
./usr/share/doc/Macaulay2/JSON/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=137 #:len=13
8 TmFtZVNlcGFyYXRvcg==8 TmFtZVNlcGFyYXRvcg==
9 #:len=2109 #:len=210
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJOYW1lU2VwYXJhdG9yIiwiTmFtZVNlcGFyYXRvciIs11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJOYW1lU2VwYXJhdG9yIiwiTmFtZVNlcGFyYXRvciIs
483 B
./usr/share/doc/Macaulay2/JSON/example-output/_from__J__S__O__N.out
    
Offset 39, 19 lines modifiedOffset 39, 19 lines modified
  
39 o8·=·{1,·2,·3}39 o8·=·{1,·2,·3}
  
40 o8·:·List40 o8·:·List
  
41 i9·:·jsonFile·=·temporaryFileName()·|·".json"41 i9·:·jsonFile·=·temporaryFileName()·|·".json"
  
42 o9·=·/tmp/M2-1340029-0/0.json42 o9·=·/tmp/M2-1409306-0/0.json
  
43 i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close43 i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close
  
44 o10·=·/tmp/M2-1340029-0/0.json44 o10·=·/tmp/M2-1409306-0/0.json
  
45 o10·:·File45 o10·:·File
  
46 i11·:·fromJSON·openIn·jsonFile46 i11·:·fromJSON·openIn·jsonFile
  
47 o11·=·{1,·2,·3}47 o11·=·{1,·2,·3}
  
1.33 KB
./usr/share/doc/Macaulay2/JSON/html/_from__J__S__O__N.html
    
Offset 167, 22 lines modifiedOffset 167, 22 lines modified
167 ··········<p>The·input·may·also·be·a·file·containing·JSON·data.</p>167 ··········<p>The·input·may·also·be·a·file·containing·JSON·data.</p>
168 ········</div>168 ········</div>
169 ········<table·class="examples">169 ········<table·class="examples">
170 ··········<tr>170 ··········<tr>
171 ············<td>171 ············<td>
172 ··············<pre><code·class="language-macaulay2">i9·:·jsonFile·=·temporaryFileName()·|·&quot;.json&quot;172 ··············<pre><code·class="language-macaulay2">i9·:·jsonFile·=·temporaryFileName()·|·&quot;.json&quot;
  
173 o9·=·/tmp/M2-1340029-0/0.json</code></pre>173 o9·=·/tmp/M2-1409306-0/0.json</code></pre>
174 ············</td>174 ············</td>
175 ··········</tr>175 ··········</tr>
176 ··········<tr>176 ··········<tr>
177 ············<td>177 ············<td>
178 ··············<pre><code·class="language-macaulay2">i10·:·jsonFile·&lt;&lt;·&quot;[1,·2,·3]&quot;·&lt;&lt;·endl·&lt;&lt;·close178 ··············<pre><code·class="language-macaulay2">i10·:·jsonFile·&lt;&lt;·&quot;[1,·2,·3]&quot;·&lt;&lt;·endl·&lt;&lt;·close
  
179 o10·=·/tmp/M2-1340029-0/0.json179 o10·=·/tmp/M2-1409306-0/0.json
  
180 o10·:·File</code></pre>180 o10·:·File</code></pre>
181 ············</td>181 ············</td>
182 ··········</tr>182 ··········</tr>
183 ··········<tr>183 ··········<tr>
184 ············<td>184 ············<td>
185 ··············<pre><code·class="language-macaulay2">i11·:·fromJSON·openIn·jsonFile185 ··············<pre><code·class="language-macaulay2">i11·:·fromJSON·openIn·jsonFile
431 B
html2text {}
    
Offset 53, 18 lines modifiedOffset 53, 18 lines modified
  
53 o8·=·{1,·2,·3}53 o8·=·{1,·2,·3}
  
54 o8·:·List54 o8·:·List
55 The·input·may·also·be·a·file·containing·JSON·data.55 The·input·may·also·be·a·file·containing·JSON·data.
56 i9·:·jsonFile·=·temporaryFileName()·|·".json"56 i9·:·jsonFile·=·temporaryFileName()·|·".json"
  
57 o9·=·/tmp/M2-1340029-0/0.json57 o9·=·/tmp/M2-1409306-0/0.json
58 i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close58 i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close
  
59 o10·=·/tmp/M2-1340029-0/0.json59 o10·=·/tmp/M2-1409306-0/0.json
  
60 o10·:·File60 o10·:·File
61 i11·:·fromJSON·openIn·jsonFile61 i11·:·fromJSON·openIn·jsonFile
  
62 o11·=·{1,·2,·3}62 o11·=·{1,·2,·3}
  
63 o11·:·List63 o11·:·List
726 B
./usr/share/doc/Macaulay2/Jets/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=227 #:len=22
8 amV0cyhaWixBZmZpbmVWYXJpZXR5KQ==8 amV0cyhaWixBZmZpbmVWYXJpZXR5KQ==
9 #:len=24699 #:len=2469
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGpldHMgb2YgYW4gYWZmaW5lIHZh10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGpldHMgb2YgYW4gYWZmaW5lIHZh
11 cmlldHkiLCAibGluZW51bSIgPT4gMTY2NiwgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT11 cmlldHkiLCAibGluZW51bSIgPT4gMTY2NiwgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT
1.06 KB
./usr/share/doc/Macaulay2/Jets/example-output/___Example_sp1.out
    
Offset 17, 24 lines modifiedOffset 17, 24 lines modified
17 o3·=·ideal·(y0*z0*x2·+·x0*z0*y2·+·x0*y0*z2·+·z0*x1*y1·+·y0*x1*z1·+·x0*y1*z1,17 o3·=·ideal·(y0*z0*x2·+·x0*z0*y2·+·x0*y0*z2·+·z0*x1*y1·+·y0*x1*z1·+·x0*y1*z1,
18 ·····------------------------------------------------------------------------18 ·····------------------------------------------------------------------------
19 ·····y0*z0*x1·+·x0*z0*y1·+·x0*y0*z1,·x0*y0*z0)19 ·····y0*z0*x1·+·x0*z0*y1·+·x0*y0*z1,·x0*y0*z0)
  
20 o3·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]20 o3·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]
  
21 i4·:·elapsedTime·jetsRadical(2,I)21 i4·:·elapsedTime·jetsRadical(2,I)
22 ·--·.00199911s·elapsed22 ·--·.00211829s·elapsed
  
23 o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1,23 o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1,
24 ·····------------------------------------------------------------------------24 ·····------------------------------------------------------------------------
25 ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0)25 ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0)
  
26 o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]26 o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]
  
27 i5·:·elapsedTime·radical·J2I27 i5·:·elapsedTime·radical·J2I
28 ·--·.596959s·elapsed28 ·--·.590252s·elapsed
  
29 o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1,29 o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1,
30 ·····------------------------------------------------------------------------30 ·····------------------------------------------------------------------------
31 ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2)31 ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2)
  
32 o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]32 o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]
  
2.77 KB
./usr/share/doc/Macaulay2/Jets/example-output/___Storing_sp__Computations.out
    
Offset 33, 15 lines modifiedOffset 33, 15 lines modified
33 o6·:·Ideal·of·R33 o6·:·Ideal·of·R
  
34 i7·:·I.cache.?jet34 i7·:·I.cache.?jet
  
35 o7·=·false35 o7·=·false
  
36 i8·:·elapsedTime·jets(3,I)36 i8·:·elapsedTime·jets(3,I)
37 ·--·.0282062s·elapsed37 ·--·.0328445s·elapsed
  
38 ··················································2·················238 ··················································2·················2
39 o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)39 o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
40 o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]40 o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]
  
41 i9·:·I.cache.?jet41 i9·:·I.cache.?jet
Offset 53, 23 lines modifiedOffset 53, 23 lines modified
53 o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|}53 o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|}
54 ·······························|·2x0x2-y2+x1^2··|54 ·······························|·2x0x2-y2+x1^2··|
55 ·······························|·2x0x1-y1·······|55 ·······························|·2x0x1-y1·······|
56 ·······························|·x0^2-y0········|56 ·······························|·x0^2-y0········|
57 ·················jetsMaxOrder·=>·357 ·················jetsMaxOrder·=>·3
  
58 i11·:·elapsedTime·jets(3,I)58 i11·:·elapsedTime·jets(3,I)
59 ·--·.00203857s·elapsed59 ·--·.0108973s·elapsed
  
60 ···················································2·················260 ···················································2·················2
61 o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)61 o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
62 o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]62 o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]
  
63 i12·:·elapsedTime·jets(2,I)63 i12·:·elapsedTime·jets(2,I)
64 ·--·.00212051s·elapsed64 ·--·.0020789s·elapsed
  
65 ·····························2·················265 ·····························2·················2
66 o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)66 o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
67 o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]67 o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]
  
68 i13·:·Q·=·R/I68 i13·:·Q·=·R/I
Offset 148, 15 lines modifiedOffset 148, 15 lines modified
148 o22·=·true148 o22·=·true
  
149 i23·:·f.cache.?jet149 i23·:·f.cache.?jet
  
150 o23·=·false150 o23·=·false
  
151 i24·:·elapsedTime·jets(3,f)151 i24·:·elapsedTime·jets(3,f)
152 ·--·.0118552s·elapsed152 ·--·.0606728s·elapsed
  
153 ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2153 ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2
154 o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})154 o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})
155 ······································································2·················2155 ······································································2·················2
156 ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)156 ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
157 ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]157 ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]
Offset 173, 15 lines modifiedOffset 173, 15 lines modified
173 o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|}173 o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|}
174 ·······························|·t2·2t0t2+t1^2··|174 ·······························|·t2·2t0t2+t1^2··|
175 ·······························|·t1·2t0t1·······|175 ·······························|·t1·2t0t1·······|
176 ·······························|·t0·t0^2········|176 ·······························|·t0·t0^2········|
177 ·················jetsMaxOrder·=>·3177 ·················jetsMaxOrder·=>·3
  
178 i27·:·elapsedTime·jets(2,f)178 i27·:·elapsedTime·jets(2,f)
179 ·--·.000664914s·elapsed179 ·--·.000659236s·elapsed
  
180 ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2180 ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2
181 o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})181 o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})
182 ············································2·················2182 ············································2·················2
183 ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)183 ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
184 ·········································QQ[x0,·y0][x1,·y1][x2,·y2]184 ·········································QQ[x0,·y0][x1,·y1][x2,·y2]
2.67 KB
./usr/share/doc/Macaulay2/Jets/html/___Example_sp1.html
    
Offset 87, 27 lines modifiedOffset 87, 27 lines modified
87 ········<div>87 ········<div>
88 ··········<p>However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial·ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is·generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This·observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of·monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in·Macaulay2.</p>88 ··········<p>However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial·ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is·generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This·observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of·monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in·Macaulay2.</p>
89 ········</div>89 ········</div>
90 ········<table·class="examples">90 ········<table·class="examples">
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jetsRadical(2,I)93 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jetsRadical(2,I)
94 ·--·.00199911s·elapsed94 ·--·.00211829s·elapsed
  
95 o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1,95 o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1,
96 ·····------------------------------------------------------------------------96 ·····------------------------------------------------------------------------
97 ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0)97 ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0)
  
98 o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre>98 o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·radical·J2I103 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·radical·J2I
104 ·--·.596959s·elapsed104 ·--·.590252s·elapsed
  
105 o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1,105 o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1,
106 ·····------------------------------------------------------------------------106 ·····------------------------------------------------------------------------
107 ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2)107 ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2)
  
108 o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre>108 o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre>
109 ············</td>109 ············</td>
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Offset 27, 23 lines modifiedOffset 27, 23 lines modified
27 However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial27 However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial
28 ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is28 ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is
29 generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This29 generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This
30 observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of30 observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of
31 monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in31 monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in
32 Macaulay2.32 Macaulay2.
33 i4·:·elapsedTime·jetsRadical(2,I)33 i4·:·elapsedTime·jetsRadical(2,I)
34 ·--·.00199911s·elapsed34 ·--·.00211829s·elapsed
  
35 o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1,35 o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1,
36 ·····------------------------------------------------------------------------36 ·····------------------------------------------------------------------------
37 ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0)37 ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0)
  
38 o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]38 o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]
39 i5·:·elapsedTime·radical·J2I39 i5·:·elapsedTime·radical·J2I
40 ·--·.596959s·elapsed40 ·--·.590252s·elapsed
  
41 o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1,41 o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1,
42 ·····------------------------------------------------------------------------42 ·····------------------------------------------------------------------------
43 ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2)43 ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2)
  
44 o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]44 o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]
45 For·a·monomial·hypersurface,·[GS06,·Theorem·3.2]·describes·the·minimal·primes45 For·a·monomial·hypersurface,·[GS06,·Theorem·3.2]·describes·the·minimal·primes
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Offset 117, 15 lines modifiedOffset 117, 15 lines modified
  
117 o7·=·false</code></pre>117 o7·=·false</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·jets(3,I)122 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·jets(3,I)
123 ·--·.0282062s·elapsed123 ·--·.0328445s·elapsed
  
124 ··················································2·················2124 ··················································2·················2
125 o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)125 o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
126 o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre>126 o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
Offset 146, 26 lines modifiedOffset 146, 26 lines modified
146 ·······························|·x0^2-y0········|146 ·······························|·x0^2-y0········|
147 ·················jetsMaxOrder·=>·3</code></pre>147 ·················jetsMaxOrder·=>·3</code></pre>
148 ············</td>148 ············</td>
149 ··········</tr>149 ··········</tr>
150 ··········<tr>150 ··········<tr>
151 ············<td>151 ············<td>
152 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·jets(3,I)152 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·jets(3,I)
153 ·--·.00203857s·elapsed153 ·--·.0108973s·elapsed
  
154 ···················································2·················2154 ···················································2·················2
155 o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)155 o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
156 o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre>156 o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre>
157 ············</td>157 ············</td>
158 ··········</tr>158 ··········</tr>
159 ··········<tr>159 ··········<tr>
160 ············<td>160 ············<td>
161 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·jets(2,I)161 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·jets(2,I)
162 ·--·.00212051s·elapsed162 ·--·.0020789s·elapsed
  
163 ·····························2·················2163 ·····························2·················2
164 o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)164 o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
165 o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]</code></pre>165 o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]</code></pre>
166 ············</td>166 ············</td>
167 ··········</tr>167 ··········</tr>
Offset 290, 15 lines modifiedOffset 290, 15 lines modified
  
290 o23·=·false</code></pre>290 o23·=·false</code></pre>
291 ············</td>291 ············</td>
292 ··········</tr>292 ··········</tr>
293 ··········<tr>293 ··········<tr>
294 ············<td>294 ············<td>
295 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·jets(3,f)295 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·jets(3,f)
296 ·--·.0118552s·elapsed296 ·--·.0606728s·elapsed
  
297 ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2297 ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2
298 o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})298 o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})
299 ······································································2·················2299 ······································································2·················2
300 ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)300 ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
301 ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]301 ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]
Offset 324, 15 lines modifiedOffset 324, 15 lines modified
324 ·······························|·t0·t0^2········|324 ·······························|·t0·t0^2········|
325 ·················jetsMaxOrder·=>·3</code></pre>325 ·················jetsMaxOrder·=>·3</code></pre>
326 ············</td>326 ············</td>
327 ··········</tr>327 ··········</tr>
328 ··········<tr>328 ··········<tr>
329 ············<td>329 ············<td>
330 ··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·jets(2,f)330 ··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·jets(2,f)
331 ·--·.000664914s·elapsed331 ·--·.000659236s·elapsed
  
332 ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2332 ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2
333 o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})333 o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})
334 ············································2·················2334 ············································2·················2
335 ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)335 ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
336 ·········································QQ[x0,·y0][x1,·y1][x2,·y2]336 ·········································QQ[x0,·y0][x1,·y1][x2,·y2]
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Offset 41, 15 lines modifiedOffset 41, 15 lines modified
41 o6·=·ideal(x··-·y)41 o6·=·ideal(x··-·y)
  
42 o6·:·Ideal·of·R42 o6·:·Ideal·of·R
43 i7·:·I.cache.?jet43 i7·:·I.cache.?jet
  
44 o7·=·false44 o7·=·false
45 i8·:·elapsedTime·jets(3,I)45 i8·:·elapsedTime·jets(3,I)
46 ·--·.0282062s·elapsed46 ·--·.0328445s·elapsed
  
47 ··················································2·················247 ··················································2·················2
48 o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)48 o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
49 o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]49 o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]
50 i9·:·I.cache.?jet50 i9·:·I.cache.?jet
  
Offset 58, 22 lines modifiedOffset 58, 22 lines modified
  
58 o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|}58 o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|}
59 ·······························|·2x0x2-y2+x1^2··|59 ·······························|·2x0x2-y2+x1^2··|
60 ·······························|·2x0x1-y1·······|60 ·······························|·2x0x1-y1·······|
61 ·······························|·x0^2-y0········|61 ·······························|·x0^2-y0········|
62 ·················jetsMaxOrder·=>·362 ·················jetsMaxOrder·=>·3
63 i11·:·elapsedTime·jets(3,I)63 i11·:·elapsedTime·jets(3,I)
64 ·--·.00203857s·elapsed64 ·--·.0108973s·elapsed
  
65 ···················································2·················265 ···················································2·················2
66 o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)66 o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
67 o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]67 o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]
68 i12·:·elapsedTime·jets(2,I)68 i12·:·elapsedTime·jets(2,I)
69 ·--·.00212051s·elapsed69 ·--·.0020789s·elapsed
  
70 ·····························2·················270 ·····························2·················2
71 o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)71 o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
  
72 o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]72 o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]
73 For·quotient·rings,·data·is·stored·under·*.jet.·Each·jets·order·gives·rise·to·a73 For·quotient·rings,·data·is·stored·under·*.jet.·Each·jets·order·gives·rise·to·a
74 different·quotient·that·is·stored·separately·under·*.jet.jetsRing·(order·zero74 different·quotient·that·is·stored·separately·under·*.jet.jetsRing·(order·zero
Offset 153, 15 lines modifiedOffset 153, 15 lines modified
153 i22·:·isWellDefined·f153 i22·:·isWellDefined·f
  
154 o22·=·true154 o22·=·true
155 i23·:·f.cache.?jet155 i23·:·f.cache.?jet
  
156 o23·=·false156 o23·=·false
157 i24·:·elapsedTime·jets(3,f)157 i24·:·elapsedTime·jets(3,f)
158 ·--·.0118552s·elapsed158 ·--·.0606728s·elapsed
  
159 ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,159 ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,
160 y3]······················································2····················2160 y3]······················································2····················2
161 o24·=·map·(QQ[t0][t1][t2][t3],·------------------------------------------------161 o24·=·map·(QQ[t0][t1][t2][t3],·------------------------------------------------
162 ----------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})162 ----------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})
163 ······································································2163 ······································································2
164 2164 2
Offset 183, 15 lines modifiedOffset 183, 15 lines modified
  
183 o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|}183 o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|}
184 ·······························|·t2·2t0t2+t1^2··|184 ·······························|·t2·2t0t2+t1^2··|
185 ·······························|·t1·2t0t1·······|185 ·······························|·t1·2t0t1·······|
186 ·······························|·t0·t0^2········|186 ·······························|·t0·t0^2········|
187 ·················jetsMaxOrder·=>·3187 ·················jetsMaxOrder·=>·3
188 i27·:·elapsedTime·jets(2,f)188 i27·:·elapsedTime·jets(2,f)
189 ·--·.000664914s·elapsed189 ·--·.000659236s·elapsed
  
190 ···································QQ[x0,·y0][x1,·y1][x2,·y2]190 ···································QQ[x0,·y0][x1,·y1][x2,·y2]
191 2····················2191 2····················2
192 o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,192 o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,
193 2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})193 2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·})
194 ············································2·················2194 ············································2·················2
195 ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)195 ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0)
759 B
./usr/share/doc/Macaulay2/K3Carpets/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=417 #:len=41
8 Y2Fub25pY2FsSG9tb3RvcGllcyguLi4sRmluZUdyYWRpbmc9Pi4uLik=8 Y2Fub25pY2FsSG9tb3RvcGllcyguLi4sRmluZUdyYWRpbmc9Pi4uLik=
9 #:len=2989 #:len=298
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTU5Niwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTU5Niwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbY2Fub25pY2FsSG9tb3RvcGllcyxGaW5lR3JhZGlu11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbY2Fub25pY2FsSG9tb3RvcGllcyxGaW5lR3JhZGlu
1.9 KB
./usr/share/doc/Macaulay2/K3Carpets/example-output/_analyze__Strand.out
    
Offset 19, 15 lines modifiedOffset 19, 15 lines modified
19 ······32003··0···5···0···5·········32003··0···5···0···5··········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5··········32003··0···5···0···519 ······32003··0···5···0···5·········32003··0···5···0···5··········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5··········32003··0···5···0···5
20 ·························································································································································································································································································20 ·························································································································································································································································································
21 ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························921 ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························9
  
22 o3·:·Complex22 o3·:·Complex
  
23 i4·:·L·=·analyzeStrand(F,a);·#L23 i4·:·L·=·analyzeStrand(F,a);·#L
24 ·--·.0231855s·elapsed24 ·--·.0235921s·elapsed
  
25 o5·=·35025 o5·=·350
  
26 i6·:·betti·F_a,·betti·F26 i6·:·betti·F_a,·betti·F
  
27 ···············0·········0··1···2···3···4···5···6···7··8·927 ···············0·········0··1···2···3···4···5···6···7··8·9
28 o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7)28 o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7)
Offset 46, 19 lines modifiedOffset 46, 19 lines modified
46 o7·:·Expression·of·class·Product46 o7·:·Expression·of·class·Product
  
47 i8·:·L3·=·select(L,c->c%3==0);·#L347 i8·:·L3·=·select(L,c->c%3==0);·#L3
  
48 o9·=·1448 o9·=·14
  
49 i10·:·carpetBettiTable(a,b,3)49 i10·:·carpetBettiTable(a,b,3)
50 ·--·.00229029s·elapsed50 ·--·.00225909s·elapsed
51 ·--·.00620931s·elapsed 
52 ·--·.0216891s·elapsed 
53 ·--·.00901705s·elapsed 
54 ·--·.00332008s·elapsed51 ·--·.0325001s·elapsed
 52 ·--·.142543s·elapsed
 53 ·--·.033065s·elapsed
 54 ·--·.00877626s·elapsed
  
55 ·············0··1···2···3···4···5···6···7··8·955 ·············0··1···2···3···4···5···6···7··8·9
56 o10·=·total:·1·36·160·315·302·302·315·160·36·156 o10·=·total:·1·36·160·315·302·302·315·160·36·1
57 ··········0:·1··.···.···.···.···.···.···.··.·.57 ··········0:·1··.···.···.···.···.···.···.··.·.
58 ··········1:·.·36·160·315·288··14···.···.··.·.58 ··········1:·.·36·160·315·288··14···.···.··.·.
59 ··········2:·.··.···.···.··14·288·315·160·36·.59 ··········2:·.··.···.···.··14·288·315·160·36·.
60 ··········3:·.··.···.···.···.···.···.···.··.·160 ··········3:·.··.···.···.···.···.···.···.··.·1
2.12 KB
./usr/share/doc/Macaulay2/K3Carpets/example-output/_carpet__Betti__Table.out
    
Offset 3, 20 lines modifiedOffset 3, 20 lines modified
3 i1·:·a=5,b=53 i1·:·a=5,b=5
  
4 o1·=·(5,·5)4 o1·=·(5,·5)
  
5 o1·:·Sequence5 o1·:·Sequence
  
6 i2·:·elapsedTime·T=carpetBettiTable(a,b,3)6 i2·:·elapsedTime·T=carpetBettiTable(a,b,3)
7 ·--·.00229022s·elapsed7 ·--·.0022327s·elapsed
8 ·--·.00589389s·elapsed8 ·--·.00637437s·elapsed
9 ·--·.0200426s·elapsed9 ·--·.0242551s·elapsed
 10 ·--·.0239844s·elapsed
10 ·--·.0108043s·elapsed11 ·--·.00340232s·elapsed
11 ·--·.00417078s·elapsed 
12 ·--·.379713s·elapsed12 ·--·.589799s·elapsed
  
13 ············0··1···2···3···4···5···6···7··8·913 ············0··1···2···3···4···5···6···7··8·9
14 o2·=·total:·1·36·160·315·302·302·315·160·36·114 o2·=·total:·1·36·160·315·302·302·315·160·36·1
15 ·········0:·1··.···.···.···.···.···.···.··.·.15 ·········0:·1··.···.···.···.···.···.···.··.·.
16 ·········1:·.·36·160·315·288··14···.···.··.·.16 ·········1:·.·36·160·315·288··14···.···.··.·.
17 ·········2:·.··.···.···.··14·288·315·160·36·.17 ·········2:·.··.···.···.··14·288·315·160·36·.
18 ·········3:·.··.···.···.···.···.···.···.··.·118 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 26, 15 lines modifiedOffset 26, 15 lines modified
26 i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);26 i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);
  
27 ··············ZZ27 ··············ZZ
28 o3·:·Ideal·of·--[x·..x·,·y·..y·]28 o3·:·Ideal·of·--[x·..x·,·y·..y·]
29 ···············3··0···5···0···529 ···············3··0···5···0···5
  
30 i4·:·elapsedTime·T'=minimalBetti·J30 i4·:·elapsedTime·T'=minimalBetti·J
31 ·--·.153688s·elapsed31 ·--·.391788s·elapsed
  
32 ············0··1···2···3···4···5···6···7··8·932 ············0··1···2···3···4···5···6···7··8·9
33 o4·=·total:·1·36·160·315·302·302·315·160·36·133 o4·=·total:·1·36·160·315·302·302·315·160·36·1
34 ·········0:·1··.···.···.···.···.···.···.··.·.34 ·········0:·1··.···.···.···.···.···.···.··.·.
35 ·········1:·.·36·160·315·288··14···.···.··.·.35 ·········1:·.·36·160·315·288··14···.···.··.·.
36 ·········2:·.··.···.···.··14·288·315·160·36·.36 ·········2:·.··.···.···.··14·288·315·160·36·.
37 ·········3:·.··.···.···.···.···.···.···.··.·137 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 48, 22 lines modifiedOffset 48, 22 lines modified
48 ·········1:·.·.·.·.·.·.·.·.·.·.48 ·········1:·.·.·.·.·.·.·.·.·.·.
49 ·········2:·.·.·.·.·.·.·.·.·.·.49 ·········2:·.·.·.·.·.·.·.·.·.·.
50 ·········3:·.·.·.·.·.·.·.·.·.·.50 ·········3:·.·.·.·.·.·.·.·.·.·.
  
51 o5·:·BettiTally51 o5·:·BettiTally
  
52 i6·:·elapsedTime·h=carpetBettiTables(6,6);52 i6·:·elapsedTime·h=carpetBettiTables(6,6);
53 ·--·.00417813s·elapsed53 ·--·.00461858s·elapsed
54 ·--·.0158662s·elapsed54 ·--·.0150988s·elapsed
55 ·--·.0814004s·elapsed55 ·--·.235104s·elapsed
 56 ·--·2.04057s·elapsed
56 ·--·1.12458s·elapsed57 ·--·1.12205s·elapsed
57 ·--·.463825s·elapsed 
58 ·--·.06896s·elapsed58 ·--·.0992913s·elapsed
59 ·--·.00799867s·elapsed59 ·--·.0279594s·elapsed
60 ·--·5.41283s·elapsed60 ·--·9.8142s·elapsed
  
61 i7·:·carpetBettiTable(h,7)61 i7·:·carpetBettiTable(h,7)
  
62 ············0··1···2···3····4····5····6····7···8···9·10·1162 ············0··1···2···3····4····5····6····7···8···9·10·11
63 o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··163 o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1
64 ·········0:·1··.···.···.····.····.····.····.···.···.··.··.64 ·········0:·1··.···.···.····.····.····.····.···.···.··.··.
65 ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··.65 ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··.
1.93 KB
./usr/share/doc/Macaulay2/K3Carpets/example-output/_carpet__Betti__Tables.out
    
Offset 3, 19 lines modifiedOffset 3, 19 lines modified
3 i1·:·a=5,b=53 i1·:·a=5,b=5
  
4 o1·=·(5,·5)4 o1·=·(5,·5)
  
5 o1·:·Sequence5 o1·:·Sequence
  
6 i2·:·h=carpetBettiTables(a,b)6 i2·:·h=carpetBettiTables(a,b)
7 ·--·.00219233s·elapsed7 ·--·.010296s·elapsed
8 ·--·.00577272s·elapsed 
9 ·--·.0247876s·elapsed 
10 ·--·.00920855s·elapsed 
11 ·--·.00327452s·elapsed8 ·--·.0303972s·elapsed
 9 ·--·.0663514s·elapsed
 10 ·--·.0394736s·elapsed
 11 ·--·.0164669s·elapsed
  
12 ···························0··1···2···3···4···5···6···7··8·912 ···························0··1···2···3···4···5···6···7··8·9
13 o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}13 o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}
14 ························0:·1··.···.···.···.···.···.···.··.·.14 ························0:·1··.···.···.···.···.···.···.··.·.
15 ························1:·.·36·160·315·288···.···.···.··.·.15 ························1:·.·36·160·315·288···.···.···.··.·.
16 ························2:·.··.···.···.···.·288·315·160·36·.16 ························2:·.··.···.···.···.·288·315·160·36·.
17 ························3:·.··.···.···.···.···.···.···.··.·117 ························3:·.··.···.···.···.···.···.···.··.·1
Offset 48, 15 lines modifiedOffset 48, 15 lines modified
48 i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);48 i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);
  
49 ··············ZZ49 ··············ZZ
50 o4·:·Ideal·of·--[x·..x·,·y·..y·]50 o4·:·Ideal·of·--[x·..x·,·y·..y·]
51 ···············3··0···5···0···551 ···············3··0···5···0···5
  
52 i5·:·elapsedTime·T'=minimalBetti·J52 i5·:·elapsedTime·T'=minimalBetti·J
53 ·--·.205189s·elapsed53 ·--·.698075s·elapsed
  
54 ············0··1···2···3···4···5···6···7··8·954 ············0··1···2···3···4···5···6···7··8·9
55 o5·=·total:·1·36·160·315·302·302·315·160·36·155 o5·=·total:·1·36·160·315·302·302·315·160·36·1
56 ·········0:·1··.···.···.···.···.···.···.··.·.56 ·········0:·1··.···.···.···.···.···.···.··.·.
57 ·········1:·.·36·160·315·288··14···.···.··.·.57 ·········1:·.·36·160·315·288··14···.···.··.·.
58 ·········2:·.··.···.···.··14·288·315·160·36·.58 ·········2:·.··.···.···.··14·288·315·160·36·.
59 ·········3:·.··.···.···.···.···.···.···.··.·159 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 70, 22 lines modifiedOffset 70, 22 lines modified
70 ·········1:·.·.·.·.·.·.·.·.·.·.70 ·········1:·.·.·.·.·.·.·.·.·.·.
71 ·········2:·.·.·.·.·.·.·.·.·.·.71 ·········2:·.·.·.·.·.·.·.·.·.·.
72 ·········3:·.·.·.·.·.·.·.·.·.·.72 ·········3:·.·.·.·.·.·.·.·.·.·.
  
73 o6·:·BettiTally73 o6·:·BettiTally
  
74 i7·:·elapsedTime·h=carpetBettiTables(6,6);74 i7·:·elapsedTime·h=carpetBettiTables(6,6);
75 ·--·.0040965s·elapsed75 ·--·.00840979s·elapsed
76 ·--·.0173441s·elapsed 
77 ·--·.0819195s·elapsed76 ·--·.140268s·elapsed
 77 ·--·.323611s·elapsed
78 ·--·.883274s·elapsed78 ·--·3.43027s·elapsed
79 ·--·.390992s·elapsed79 ·--·1.28678s·elapsed
 80 ·--·.419351s·elapsed
80 ·--·.0432806s·elapsed81 ·--·.0264281s·elapsed
81 ·--·.0057332s·elapsed 
82 ·--·4.93324s·elapsed82 ·--·15.5409s·elapsed
  
83 i8·:·keys·h83 i8·:·keys·h
  
84 o8·=·{0,·2,·3,·5}84 o8·=·{0,·2,·3,·5}
  
85 o8·:·List85 o8·:·List
  
1.61 KB
./usr/share/doc/Macaulay2/K3Carpets/example-output/_carpet__Det.out
    
Offset 3, 42 lines modifiedOffset 3, 42 lines modified
3 i1·:·a=4,b=43 i1·:·a=4,b=4
  
4 o1·=·(4,·4)4 o1·=·(4,·4)
  
5 o1·:·Sequence5 o1·:·Sequence
  
6 i2·:·d=carpetDet(a,b)6 i2·:·d=carpetDet(a,b)
7 ·--·.00671651s·elapsed 
8 ·--·.0166392s·elapsed7 ·--·.0273009s·elapsed
 8 ·--·.0559471s·elapsed
9 ·--·.000223808s·elapsed9 ·--·.000278993s·elapsed
10 ·--·.000143466s·elapsed10 ·--·.000240541s·elapsed
11 ·--·.000129015s·elapsed11 ·--·.000272971s·elapsed
12 ·--·.000115755s·elapsed 
13 ·--·.000134844s·elapsed 
14 ·--·.000146711s·elapsed 
15 ·--·.000135925s·elapsed 
16 ·--·.000176226s·elapsed 
17 ·--·.000128094s·elapsed12 ·--·.000218069s·elapsed
18 ·--·.00025175s·elapsed13 ·--·.000237075s·elapsed
19 ·--·.000257558s·elapsed 
20 ·--·.000187694s·elapsed 
21 ·--·.000120011s·elapsed 
22 ·--·.000120693s·elapsed14 ·--·.000262863s·elapsed
23 ·--·.000140633s·elapsed15 ·--·.000247033s·elapsed
 16 ·--·.000326061s·elapsed
 17 ·--·.000277881s·elapsed
24 ·--·.00011939s·elapsed18 ·--·.000216906s·elapsed
25 ·--·.000179951s·elapsed19 ·--·.000322484s·elapsed
26 ·--·.000132009s·elapsed20 ·--·.00020803s·elapsed
 21 ·--·.000203201s·elapsed
27 ·--·.000138769s·elapsed22 ·--·.00017579s·elapsed
28 ·--·.000136035s·elapsed23 ·--·.000283722s·elapsed
29 ·--·.000129945s·elapsed24 ·--·.012245s·elapsed
30 ·--·.000147231s·elapsed25 ·--·.000219903s·elapsed
31 ·--·.000113842s·elapsed26 ·--·.000195677s·elapsed
32 ·--·.000124758s·elapsed27 ·--·.000243747s·elapsed
33 ·--·.000123916s·elapsed28 ·--·.000205916s·elapsed
34 ·--·.000138049s·elapsed29 ·--·.000212589s·elapsed
 30 ·--·.000183615s·elapsed
 31 ·--·.000219061s·elapsed
 32 ·--·.000196879s·elapsed
 33 ·--·.000223419s·elapsed
 34 ·--·.000184236s·elapsed
35 (number·Of·blocks,·26)35 (number·Of·blocks,·26)
36 136 1
37 137 1
38 138 1
39 139 1
40 240 2
41 ·241 ·2
524 B
./usr/share/doc/Macaulay2/K3Carpets/example-output/_compute__Bound.out
    
Offset 3, 17 lines modifiedOffset 3, 17 lines modified
3 i1·:·(a,b)=computeBound(6,4,3)3 i1·:·(a,b)=computeBound(6,4,3)
  
4 o1·=·(9,·7)4 o1·=·(9,·7)
  
5 o1·:·Sequence5 o1·:·Sequence
  
6 i2·:·computeBound·36 i2·:·computeBound·3
7 ·--·.974793s·elapsed7 ·--·2.09744s·elapsed
8 ·--·.755559s·elapsed 
9 ·--·.421012s·elapsed 
10 ·--·1.16935s·elapsed 
11 ·--·.865335s·elapsed 
12 ·--·1.22015s·elapsed8 ·--·1.50152s·elapsed
 9 ·--·.64122s·elapsed
 10 ·--·2.575s·elapsed
 11 ·--·1.4336s·elapsed
 12 ·--·1.94991s·elapsed
  
13 o2·=·613 o2·=·6
  
14 i3·:·14 i3·:·
2.03 KB
./usr/share/doc/Macaulay2/K3Carpets/example-output/_degenerate__K3__Betti__Tables.out
    
Offset 9, 19 lines modifiedOffset 9, 19 lines modified
9 i2·:·e=(-1,5)9 i2·:·e=(-1,5)
  
10 o2·=·(-1,·5)10 o2·=·(-1,·5)
  
11 o2·:·Sequence11 o2·:·Sequence
  
12 i3·:·h=degenerateK3BettiTables(a,b,e)12 i3·:·h=degenerateK3BettiTables(a,b,e)
 13 ·--·.0112985s·elapsed
 14 ·--·.02254s·elapsed
 15 ·--·.078953s·elapsed
 16 ·--·.0543006s·elapsed
13 ·--·.00230618s·elapsed17 ·--·.0236152s·elapsed
14 ·--·.0050692s·elapsed 
15 ·--·.0267149s·elapsed 
16 ·--·.00811787s·elapsed 
17 ·--·.00311321s·elapsed 
  
18 ···························0··1···2···3···4···5···6···7··8·918 ···························0··1···2···3···4···5···6···7··8·9
19 o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}19 o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}
20 ························0:·1··.···.···.···.···.···.···.··.·.20 ························0:·1··.···.···.···.···.···.···.··.·.
21 ························1:·.·36·160·315·288···.···.···.··.·.21 ························1:·.·36·160·315·288···.···.···.··.·.
22 ························2:·.··.···.···.···.·288·315·160·36·.22 ························2:·.··.···.···.···.·288·315·160·36·.
23 ························3:·.··.···.···.···.···.···.···.··.·123 ························3:·.··.···.···.···.···.···.···.··.·1
Offset 49, 15 lines modifiedOffset 49, 15 lines modified
49 i4·:·keys·h49 i4·:·keys·h
  
50 o4·=·{0,·2,·3,·5}50 o4·=·{0,·2,·3,·5}
  
51 o4·:·List51 o4·:·List
  
52 i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5)52 i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5)
53 ·--·.361527s·elapsed53 ·--·.966198s·elapsed
  
54 ············0··1···2···3···4···5···6···7··8·954 ············0··1···2···3···4···5···6···7··8·9
55 o5·=·total:·1·36·167·370·476·476·370·167·36·155 o5·=·total:·1·36·167·370·476·476·370·167·36·1
56 ·········0:·1··.···.···.···.···.···.···.··.·.56 ·········0:·1··.···.···.···.···.···.···.··.·.
57 ·········1:·.·36·160·322·336·140··48···7··.·.57 ·········1:·.·36·160·322·336·140··48···7··.·.
58 ·········2:·.··.···7··48·140·336·322·160·36·.58 ·········2:·.··.···7··48·140·336·322·160·36·.
59 ·········3:·.··.···.···.···.···.···.···.··.·159 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 77, 19 lines modifiedOffset 77, 19 lines modified
77 i7·:·e=(-1,5^2)77 i7·:·e=(-1,5^2)
  
78 o7·=·(-1,·25)78 o7·=·(-1,·25)
  
79 o7·:·Sequence79 o7·:·Sequence
  
80 i8·:·h=degenerateK3BettiTables(a,b,e)80 i8·:·h=degenerateK3BettiTables(a,b,e)
 81 ·--·.0189008s·elapsed
81 ·--·.00241335s·elapsed82 ·--·.0302941s·elapsed
82 ·--·.00521724s·elapsed83 ·--·.0988654s·elapsed
83 ·--·.0265308s·elapsed84 ·--·.0520845s·elapsed
84 ·--·.00789618s·elapsed85 ·--·.0208928s·elapsed
85 ·--·.00316001s·elapsed 
  
86 ···························0··1···2···3···4···5···6···7··8·986 ···························0··1···2···3···4···5···6···7··8·9
87 o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····}87 o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····}
88 ························0:·1··.···.···.···.···.···.···.··.·.88 ························0:·1··.···.···.···.···.···.···.··.·.
89 ························1:·.·36·160·315·288···.···.···.··.·.89 ························1:·.·36·160·315·288···.···.···.··.·.
90 ························2:·.··.···.···.···.·288·315·160·36·.90 ························2:·.··.···.···.···.·288·315·160·36·.
91 ························3:·.··.···.···.···.···.···.···.··.·191 ························3:·.··.···.···.···.···.···.···.··.·1
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./usr/share/doc/Macaulay2/K3Carpets/example-output/_resonance__Det.out
    
Offset 1, 33 lines modifiedOffset 1, 33 lines modified
1 --·-*-·M2-comint·-*-·hash:·17291828916907047381 --·-*-·M2-comint·-*-·hash:·1729182891690704738
  
2 i1·:·a=42 i1·:·a=4
  
3 o1·=·43 o1·=·4
  
4 i2·:·(d1,d2)=resonanceDet(a)4 i2·:·(d1,d2)=resonanceDet(a)
5 ·--·.0132832s·elapsed5 ·--·.0635816s·elapsed
6 ·--·.000031908s·elapsed6 ·--·.000036839s·elapsed
7 ·--·.000073011s·elapsed 
8 ·--·.000071427s·elapsed7 ·--·.000092985s·elapsed
9 ·--·.000067151s·elapsed8 ·--·.000071595s·elapsed
10 ·--·.000078099s·elapsed9 ·--·.0000904s·elapsed
11 ·--·.000073761s·elapsed 
12 ·--·.000023926s·elapsed10 ·--·.000094297s·elapsed
13 ·--·.000057276s·elapsed 
14 ·--·.000072018s·elapsed11 ·--·.000097213s·elapsed
 12 ·--·.000024486s·elapsed
 13 ·--·.000073498s·elapsed
15 ·--·.000089795s·elapsed14 ·--·.000089769s·elapsed
16 ·--·.000084979s·elapsed15 ·--·.000092093s·elapsed
17 ·--·.000073202s·elapsed 
18 ·--·.000060211s·elapsed 
19 ·--·.000054452s·elapsed 
20 ·--·.000055884s·elapsed 
21 ·--·.000039369s·elapsed 
22 ·--·.000084427s·elapsed16 ·--·.000087444s·elapsed
 17 ·--·.000081864s·elapsed
23 ·--·.00001979s·elapsed18 ·--·.000079148s·elapsed
 19 ·--·.000078397s·elapsed
 20 ·--·.000066474s·elapsed
 21 ·--·.000038321s·elapsed
 22 ·--·.000084218s·elapsed
 23 ·--·.000025148s·elapsed
24 (number·of·blocks=·,·18)24 (number·of·blocks=·,·18)
25 (size·of·the·matrices,·Tally{1·=>·4})25 (size·of·the·matrices,·Tally{1·=>·4})
26 ·····························2·=>·626 ·····························2·=>·6
27 ·····························3·=>·227 ·····························3·=>·2
28 ·····························4·=>·628 ·····························4·=>·6
29 ·······0·129 ·······0·1
30 total:·1·130 total:·1·1
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./usr/share/doc/Macaulay2/K3Carpets/html/_analyze__Strand.html
    
Offset 102, 15 lines modifiedOffset 102, 15 lines modified
  
102 o3·:·Complex</code></pre>102 o3·:·Complex</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i4·:·L·=·analyzeStrand(F,a);·#L107 ··············<pre><code·class="language-macaulay2">i4·:·L·=·analyzeStrand(F,a);·#L
108 ·--·.0231855s·elapsed108 ·--·.0235921s·elapsed
  
109 o5·=·350</code></pre>109 o5·=·350</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i6·:·betti·F_a,·betti·F114 ··············<pre><code·class="language-macaulay2">i6·:·betti·F_a,·betti·F
Offset 141, 19 lines modifiedOffset 141, 19 lines modified
  
141 o9·=·14</code></pre>141 o9·=·14</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ··········<tr>144 ··········<tr>
145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i10·:·carpetBettiTable(a,b,3)146 ··············<pre><code·class="language-macaulay2">i10·:·carpetBettiTable(a,b,3)
147 ·--·.00229029s·elapsed147 ·--·.00225909s·elapsed
148 ·--·.00620931s·elapsed 
149 ·--·.0216891s·elapsed 
150 ·--·.00901705s·elapsed 
151 ·--·.00332008s·elapsed148 ·--·.0325001s·elapsed
 149 ·--·.142543s·elapsed
 150 ·--·.033065s·elapsed
 151 ·--·.00877626s·elapsed
  
152 ·············0··1···2···3···4···5···6···7··8·9152 ·············0··1···2···3···4···5···6···7··8·9
153 o10·=·total:·1·36·160·315·302·302·315·160·36·1153 o10·=·total:·1·36·160·315·302·302·315·160·36·1
154 ··········0:·1··.···.···.···.···.···.···.··.·.154 ··········0:·1··.···.···.···.···.···.···.··.·.
155 ··········1:·.·36·160·315·288··14···.···.··.·.155 ··········1:·.·36·160·315·288··14···.···.··.·.
156 ··········2:·.··.···.···.··14·288·315·160·36·.156 ··········2:·.··.···.···.··14·288·315·160·36·.
157 ··········3:·.··.···.···.···.···.···.···.··.·1157 ··········3:·.··.···.···.···.···.···.···.··.·1
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Offset 49, 15 lines modifiedOffset 49, 15 lines modified
49 ·····0····························1·····························249 ·····0····························1·····························2
50 3······························4······························550 3······························4······························5
51 6······························7······························851 6······························7······························8
52 952 9
  
53 o3·:·Complex53 o3·:·Complex
54 i4·:·L·=·analyzeStrand(F,a);·#L54 i4·:·L·=·analyzeStrand(F,a);·#L
55 ·--·.0231855s·elapsed55 ·--·.0235921s·elapsed
  
56 o5·=·35056 o5·=·350
57 i6·:·betti·F_a,·betti·F57 i6·:·betti·F_a,·betti·F
  
58 ···············0·········0··1···2···3···4···5···6···7··8·958 ···············0·········0··1···2···3···4···5···6···7··8·9
59 o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7)59 o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7)
60 ··········6:·350······0:·1··.···.···.···.···.···.···.··.·.60 ··········6:·350······0:·1··.···.···.···.···.···.···.··.·.
Offset 72, 19 lines modifiedOffset 72, 19 lines modified
72 o7·=·2···372 o7·=·2···3
  
73 o7·:·Expression·of·class·Product73 o7·:·Expression·of·class·Product
74 i8·:·L3·=·select(L,c->c%3==0);·#L374 i8·:·L3·=·select(L,c->c%3==0);·#L3
  
75 o9·=·1475 o9·=·14
76 i10·:·carpetBettiTable(a,b,3)76 i10·:·carpetBettiTable(a,b,3)
77 ·--·.00229029s·elapsed77 ·--·.00225909s·elapsed
78 ·--·.00620931s·elapsed 
79 ·--·.0216891s·elapsed 
80 ·--·.00901705s·elapsed 
81 ·--·.00332008s·elapsed78 ·--·.0325001s·elapsed
 79 ·--·.142543s·elapsed
 80 ·--·.033065s·elapsed
 81 ·--·.00877626s·elapsed
  
82 ·············0··1···2···3···4···5···6···7··8·982 ·············0··1···2···3···4···5···6···7··8·9
83 o10·=·total:·1·36·160·315·302·302·315·160·36·183 o10·=·total:·1·36·160·315·302·302·315·160·36·1
84 ··········0:·1··.···.···.···.···.···.···.··.·.84 ··········0:·1··.···.···.···.···.···.···.··.·.
85 ··········1:·.·36·160·315·288··14···.···.··.·.85 ··········1:·.·36·160·315·288··14···.···.··.·.
86 ··········2:·.··.···.···.··14·288·315·160·36·.86 ··········2:·.··.···.···.··14·288·315·160·36·.
87 ··········3:·.··.···.···.···.···.···.···.··.·187 ··········3:·.··.···.···.···.···.···.···.··.·1
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./usr/share/doc/Macaulay2/K3Carpets/html/_carpet__Betti__Table.html
    
Offset 83, 20 lines modifiedOffset 83, 20 lines modified
  
83 o1·:·Sequence</code></pre>83 o1·:·Sequence</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·T=carpetBettiTable(a,b,3)88 ··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·T=carpetBettiTable(a,b,3)
89 ·--·.00229022s·elapsed89 ·--·.0022327s·elapsed
90 ·--·.00589389s·elapsed90 ·--·.00637437s·elapsed
91 ·--·.0200426s·elapsed91 ·--·.0242551s·elapsed
 92 ·--·.0239844s·elapsed
92 ·--·.0108043s·elapsed93 ·--·.00340232s·elapsed
93 ·--·.00417078s·elapsed 
94 ·--·.379713s·elapsed94 ·--·.589799s·elapsed
  
95 ············0··1···2···3···4···5···6···7··8·995 ············0··1···2···3···4···5···6···7··8·9
96 o2·=·total:·1·36·160·315·302·302·315·160·36·196 o2·=·total:·1·36·160·315·302·302·315·160·36·1
97 ·········0:·1··.···.···.···.···.···.···.··.·.97 ·········0:·1··.···.···.···.···.···.···.··.·.
98 ·········1:·.·36·160·315·288··14···.···.··.·.98 ·········1:·.·36·160·315·288··14···.···.··.·.
99 ·········2:·.··.···.···.··14·288·315·160·36·.99 ·········2:·.··.···.···.··14·288·315·160·36·.
100 ·········3:·.··.···.···.···.···.···.···.··.·1100 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 112, 15 lines modifiedOffset 112, 15 lines modified
112 o3·:·Ideal·of·--[x·..x·,·y·..y·]112 o3·:·Ideal·of·--[x·..x·,·y·..y·]
113 ···············3··0···5···0···5</code></pre>113 ···············3··0···5···0···5</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ··········<tr>116 ··········<tr>
117 ············<td>117 ············<td>
118 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·T'=minimalBetti·J118 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·T'=minimalBetti·J
119 ·--·.153688s·elapsed119 ·--·.391788s·elapsed
  
120 ············0··1···2···3···4···5···6···7··8·9120 ············0··1···2···3···4···5···6···7··8·9
121 o4·=·total:·1·36·160·315·302·302·315·160·36·1121 o4·=·total:·1·36·160·315·302·302·315·160·36·1
122 ·········0:·1··.···.···.···.···.···.···.··.·.122 ·········0:·1··.···.···.···.···.···.···.··.·.
123 ·········1:·.·36·160·315·288··14···.···.··.·.123 ·········1:·.·36·160·315·288··14···.···.··.·.
124 ·········2:·.··.···.···.··14·288·315·160·36·.124 ·········2:·.··.···.···.··14·288·315·160·36·.
125 ·········3:·.··.···.···.···.···.···.···.··.·1125 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 140, 22 lines modifiedOffset 140, 22 lines modified
  
140 o5·:·BettiTally</code></pre>140 o5·:·BettiTally</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
143 ··········<tr>143 ··········<tr>
144 ············<td>144 ············<td>
145 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·h=carpetBettiTables(6,6);145 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·h=carpetBettiTables(6,6);
146 ·--·.00417813s·elapsed146 ·--·.00461858s·elapsed
147 ·--·.0158662s·elapsed147 ·--·.0150988s·elapsed
148 ·--·.0814004s·elapsed148 ·--·.235104s·elapsed
 149 ·--·2.04057s·elapsed
149 ·--·1.12458s·elapsed150 ·--·1.12205s·elapsed
150 ·--·.463825s·elapsed 
151 ·--·.06896s·elapsed151 ·--·.0992913s·elapsed
152 ·--·.00799867s·elapsed152 ·--·.0279594s·elapsed
153 ·--·5.41283s·elapsed</code></pre>153 ·--·9.8142s·elapsed</code></pre>
154 ············</td>154 ············</td>
155 ··········</tr>155 ··········</tr>
156 ··········<tr>156 ··········<tr>
157 ············<td>157 ············<td>
158 ··············<pre><code·class="language-macaulay2">i7·:·carpetBettiTable(h,7)158 ··············<pre><code·class="language-macaulay2">i7·:·carpetBettiTable(h,7)
  
159 ············0··1···2···3····4····5····6····7···8···9·10·11159 ············0··1···2···3····4····5····6····7···8···9·10·11
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Offset 25, 20 lines modifiedOffset 25, 20 lines modified
25 resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes.25 resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes.
26 i1·:·a=5,b=526 i1·:·a=5,b=5
  
27 o1·=·(5,·5)27 o1·=·(5,·5)
  
28 o1·:·Sequence28 o1·:·Sequence
29 i2·:·elapsedTime·T=carpetBettiTable(a,b,3)29 i2·:·elapsedTime·T=carpetBettiTable(a,b,3)
30 ·--·.00229022s·elapsed30 ·--·.0022327s·elapsed
31 ·--·.00589389s·elapsed31 ·--·.00637437s·elapsed
32 ·--·.0200426s·elapsed32 ·--·.0242551s·elapsed
 33 ·--·.0239844s·elapsed
33 ·--·.0108043s·elapsed34 ·--·.00340232s·elapsed
34 ·--·.00417078s·elapsed 
35 ·--·.379713s·elapsed35 ·--·.589799s·elapsed
  
36 ············0··1···2···3···4···5···6···7··8·936 ············0··1···2···3···4···5···6···7··8·9
37 o2·=·total:·1·36·160·315·302·302·315·160·36·137 o2·=·total:·1·36·160·315·302·302·315·160·36·1
38 ·········0:·1··.···.···.···.···.···.···.··.·.38 ·········0:·1··.···.···.···.···.···.···.··.·.
39 ·········1:·.·36·160·315·288··14···.···.··.·.39 ·········1:·.·36·160·315·288··14···.···.··.·.
40 ·········2:·.··.···.···.··14·288·315·160·36·.40 ·········2:·.··.···.···.··14·288·315·160·36·.
41 ·········3:·.··.···.···.···.···.···.···.··.·141 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 46, 15 lines modifiedOffset 46, 15 lines modified
46 o2·:·BettiTally46 o2·:·BettiTally
47 i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);47 i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);
  
48 ··············ZZ48 ··············ZZ
49 o3·:·Ideal·of·--[x·..x·,·y·..y·]49 o3·:·Ideal·of·--[x·..x·,·y·..y·]
50 ···············3··0···5···0···550 ···············3··0···5···0···5
51 i4·:·elapsedTime·T'=minimalBetti·J51 i4·:·elapsedTime·T'=minimalBetti·J
52 ·--·.153688s·elapsed52 ·--·.391788s·elapsed
  
53 ············0··1···2···3···4···5···6···7··8·953 ············0··1···2···3···4···5···6···7··8·9
54 o4·=·total:·1·36·160·315·302·302·315·160·36·154 o4·=·total:·1·36·160·315·302·302·315·160·36·1
55 ·········0:·1··.···.···.···.···.···.···.··.·.55 ·········0:·1··.···.···.···.···.···.···.··.·.
56 ·········1:·.·36·160·315·288··14···.···.··.·.56 ·········1:·.·36·160·315·288··14···.···.··.·.
57 ·········2:·.··.···.···.··14·288·315·160·36·.57 ·········2:·.··.···.···.··14·288·315·160·36·.
58 ·········3:·.··.···.···.···.···.···.···.··.·158 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 66, 22 lines modifiedOffset 66, 22 lines modified
66 o5·=·total:·.·.·.·.·.·.·.·.·.·.66 o5·=·total:·.·.·.·.·.·.·.·.·.·.
67 ·········1:·.·.·.·.·.·.·.·.·.·.67 ·········1:·.·.·.·.·.·.·.·.·.·.
68 ·········2:·.·.·.·.·.·.·.·.·.·.68 ·········2:·.·.·.·.·.·.·.·.·.·.
69 ·········3:·.·.·.·.·.·.·.·.·.·.69 ·········3:·.·.·.·.·.·.·.·.·.·.
  
70 o5·:·BettiTally70 o5·:·BettiTally
71 i6·:·elapsedTime·h=carpetBettiTables(6,6);71 i6·:·elapsedTime·h=carpetBettiTables(6,6);
72 ·--·.00417813s·elapsed72 ·--·.00461858s·elapsed
73 ·--·.0158662s·elapsed73 ·--·.0150988s·elapsed
74 ·--·.0814004s·elapsed74 ·--·.235104s·elapsed
 75 ·--·2.04057s·elapsed
75 ·--·1.12458s·elapsed76 ·--·1.12205s·elapsed
76 ·--·.463825s·elapsed 
77 ·--·.06896s·elapsed77 ·--·.0992913s·elapsed
78 ·--·.00799867s·elapsed78 ·--·.0279594s·elapsed
79 ·--·5.41283s·elapsed79 ·--·9.8142s·elapsed
80 i7·:·carpetBettiTable(h,7)80 i7·:·carpetBettiTable(h,7)
  
81 ············0··1···2···3····4····5····6····7···8···9·10·1181 ············0··1···2···3····4····5····6····7···8···9·10·11
82 o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··182 o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1
83 ·········0:·1··.···.···.····.····.····.····.···.···.··.··.83 ·········0:·1··.···.···.····.····.····.····.···.···.··.··.
84 ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··.84 ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··.
85 ·········2:·.··.···.···.····.····.·1155·1408·891·320·55··.85 ·········2:·.··.···.···.····.····.·1155·1408·891·320·55··.
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Offset 80, 19 lines modifiedOffset 80, 19 lines modified
  
80 o1·:·Sequence</code></pre>80 o1·:·Sequence</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·h=carpetBettiTables(a,b)85 ··············<pre><code·class="language-macaulay2">i2·:·h=carpetBettiTables(a,b)
86 ·--·.00219233s·elapsed86 ·--·.010296s·elapsed
87 ·--·.00577272s·elapsed 
88 ·--·.0247876s·elapsed 
89 ·--·.00920855s·elapsed 
90 ·--·.00327452s·elapsed87 ·--·.0303972s·elapsed
 88 ·--·.0663514s·elapsed
 89 ·--·.0394736s·elapsed
 90 ·--·.0164669s·elapsed
  
91 ···························0··1···2···3···4···5···6···7··8·991 ···························0··1···2···3···4···5···6···7··8·9
92 o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}92 o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}
93 ························0:·1··.···.···.···.···.···.···.··.·.93 ························0:·1··.···.···.···.···.···.···.··.·.
94 ························1:·.·36·160·315·288···.···.···.··.·.94 ························1:·.·36·160·315·288···.···.···.··.·.
95 ························2:·.··.···.···.···.·288·315·160·36·.95 ························2:·.··.···.···.···.·288·315·160·36·.
96 ························3:·.··.···.···.···.···.···.···.··.·196 ························3:·.··.···.···.···.···.···.···.··.·1
Offset 134, 15 lines modifiedOffset 134, 15 lines modified
134 o4·:·Ideal·of·--[x·..x·,·y·..y·]134 o4·:·Ideal·of·--[x·..x·,·y·..y·]
135 ···············3··0···5···0···5</code></pre>135 ···············3··0···5···0···5</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ··········<tr>138 ··········<tr>
139 ············<td>139 ············<td>
140 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T'=minimalBetti·J140 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T'=minimalBetti·J
141 ·--·.205189s·elapsed141 ·--·.698075s·elapsed
  
142 ············0··1···2···3···4···5···6···7··8·9142 ············0··1···2···3···4···5···6···7··8·9
143 o5·=·total:·1·36·160·315·302·302·315·160·36·1143 o5·=·total:·1·36·160·315·302·302·315·160·36·1
144 ·········0:·1··.···.···.···.···.···.···.··.·.144 ·········0:·1··.···.···.···.···.···.···.··.·.
145 ·········1:·.·36·160·315·288··14···.···.··.·.145 ·········1:·.·36·160·315·288··14···.···.··.·.
146 ·········2:·.··.···.···.··14·288·315·160·36·.146 ·········2:·.··.···.···.··14·288·315·160·36·.
147 ·········3:·.··.···.···.···.···.···.···.··.·1147 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 162, 22 lines modifiedOffset 162, 22 lines modified
  
162 o6·:·BettiTally</code></pre>162 o6·:·BettiTally</code></pre>
163 ············</td>163 ············</td>
164 ··········</tr>164 ··········</tr>
165 ··········<tr>165 ··········<tr>
166 ············<td>166 ············<td>
167 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·h=carpetBettiTables(6,6);167 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·h=carpetBettiTables(6,6);
168 ·--·.0040965s·elapsed168 ·--·.00840979s·elapsed
169 ·--·.0173441s·elapsed 
170 ·--·.0819195s·elapsed169 ·--·.140268s·elapsed
 170 ·--·.323611s·elapsed
171 ·--·.883274s·elapsed171 ·--·3.43027s·elapsed
172 ·--·.390992s·elapsed172 ·--·1.28678s·elapsed
 173 ·--·.419351s·elapsed
173 ·--·.0432806s·elapsed174 ·--·.0264281s·elapsed
174 ·--·.0057332s·elapsed 
175 ·--·4.93324s·elapsed</code></pre>175 ·--·15.5409s·elapsed</code></pre>
176 ············</td>176 ············</td>
177 ··········</tr>177 ··········</tr>
178 ··········<tr>178 ··········<tr>
179 ············<td>179 ············<td>
180 ··············<pre><code·class="language-macaulay2">i8·:·keys·h180 ··············<pre><code·class="language-macaulay2">i8·:·keys·h
  
181 o8·=·{0,·2,·3,·5}181 o8·=·{0,·2,·3,·5}
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Offset 21, 19 lines modifiedOffset 21, 19 lines modified
21 resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes.21 resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes.
22 i1·:·a=5,b=522 i1·:·a=5,b=5
  
23 o1·=·(5,·5)23 o1·=·(5,·5)
  
24 o1·:·Sequence24 o1·:·Sequence
25 i2·:·h=carpetBettiTables(a,b)25 i2·:·h=carpetBettiTables(a,b)
26 ·--·.00219233s·elapsed26 ·--·.010296s·elapsed
27 ·--·.00577272s·elapsed 
28 ·--·.0247876s·elapsed 
29 ·--·.00920855s·elapsed 
30 ·--·.00327452s·elapsed27 ·--·.0303972s·elapsed
 28 ·--·.0663514s·elapsed
 29 ·--·.0394736s·elapsed
 30 ·--·.0164669s·elapsed
  
31 ···························0··1···2···3···4···5···6···7··8·931 ···························0··1···2···3···4···5···6···7··8·9
32 o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}32 o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}
33 ························0:·1··.···.···.···.···.···.···.··.·.33 ························0:·1··.···.···.···.···.···.···.··.·.
34 ························1:·.·36·160·315·288···.···.···.··.·.34 ························1:·.·36·160·315·288···.···.···.··.·.
35 ························2:·.··.···.···.···.·288·315·160·36·.35 ························2:·.··.···.···.···.·288·315·160·36·.
36 ························3:·.··.···.···.···.···.···.···.··.·136 ························3:·.··.···.···.···.···.···.···.··.·1
Offset 63, 15 lines modifiedOffset 63, 15 lines modified
63 o3·:·BettiTally63 o3·:·BettiTally
64 i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);64 i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3);
  
65 ··············ZZ65 ··············ZZ
66 o4·:·Ideal·of·--[x·..x·,·y·..y·]66 o4·:·Ideal·of·--[x·..x·,·y·..y·]
67 ···············3··0···5···0···567 ···············3··0···5···0···5
68 i5·:·elapsedTime·T'=minimalBetti·J68 i5·:·elapsedTime·T'=minimalBetti·J
69 ·--·.205189s·elapsed69 ·--·.698075s·elapsed
  
70 ············0··1···2···3···4···5···6···7··8·970 ············0··1···2···3···4···5···6···7··8·9
71 o5·=·total:·1·36·160·315·302·302·315·160·36·171 o5·=·total:·1·36·160·315·302·302·315·160·36·1
72 ·········0:·1··.···.···.···.···.···.···.··.·.72 ·········0:·1··.···.···.···.···.···.···.··.·.
73 ·········1:·.·36·160·315·288··14···.···.··.·.73 ·········1:·.·36·160·315·288··14···.···.··.·.
74 ·········2:·.··.···.···.··14·288·315·160·36·.74 ·········2:·.··.···.···.··14·288·315·160·36·.
75 ·········3:·.··.···.···.···.···.···.···.··.·175 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 83, 22 lines modifiedOffset 83, 22 lines modified
83 o6·=·total:·.·.·.·.·.·.·.·.·.·.83 o6·=·total:·.·.·.·.·.·.·.·.·.·.
84 ·········1:·.·.·.·.·.·.·.·.·.·.84 ·········1:·.·.·.·.·.·.·.·.·.·.
85 ·········2:·.·.·.·.·.·.·.·.·.·.85 ·········2:·.·.·.·.·.·.·.·.·.·.
86 ·········3:·.·.·.·.·.·.·.·.·.·.86 ·········3:·.·.·.·.·.·.·.·.·.·.
  
87 o6·:·BettiTally87 o6·:·BettiTally
88 i7·:·elapsedTime·h=carpetBettiTables(6,6);88 i7·:·elapsedTime·h=carpetBettiTables(6,6);
89 ·--·.0040965s·elapsed89 ·--·.00840979s·elapsed
90 ·--·.0173441s·elapsed 
91 ·--·.0819195s·elapsed90 ·--·.140268s·elapsed
 91 ·--·.323611s·elapsed
92 ·--·.883274s·elapsed92 ·--·3.43027s·elapsed
93 ·--·.390992s·elapsed93 ·--·1.28678s·elapsed
 94 ·--·.419351s·elapsed
94 ·--·.0432806s·elapsed95 ·--·.0264281s·elapsed
95 ·--·.0057332s·elapsed 
96 ·--·4.93324s·elapsed96 ·--·15.5409s·elapsed
97 i8·:·keys·h97 i8·:·keys·h
  
98 o8·=·{0,·2,·3,·5}98 o8·=·{0,·2,·3,·5}
  
99 o8·:·List99 o8·:·List
100 i9·:·carpetBettiTable(h,7)100 i9·:·carpetBettiTable(h,7)
  
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Offset 80, 42 lines modifiedOffset 80, 42 lines modified
  
80 o1·:·Sequence</code></pre>80 o1·:·Sequence</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·d=carpetDet(a,b)85 ··············<pre><code·class="language-macaulay2">i2·:·d=carpetDet(a,b)
86 ·--·.00671651s·elapsed 
87 ·--·.0166392s·elapsed86 ·--·.0273009s·elapsed
 87 ·--·.0559471s·elapsed
88 ·--·.000223808s·elapsed88 ·--·.000278993s·elapsed
89 ·--·.000143466s·elapsed89 ·--·.000240541s·elapsed
90 ·--·.000129015s·elapsed90 ·--·.000272971s·elapsed
91 ·--·.000115755s·elapsed 
92 ·--·.000134844s·elapsed 
93 ·--·.000146711s·elapsed 
94 ·--·.000135925s·elapsed 
95 ·--·.000176226s·elapsed 
96 ·--·.000128094s·elapsed91 ·--·.000218069s·elapsed
97 ·--·.00025175s·elapsed92 ·--·.000237075s·elapsed
98 ·--·.000257558s·elapsed 
99 ·--·.000187694s·elapsed 
100 ·--·.000120011s·elapsed 
101 ·--·.000120693s·elapsed93 ·--·.000262863s·elapsed
102 ·--·.000140633s·elapsed94 ·--·.000247033s·elapsed
 95 ·--·.000326061s·elapsed
 96 ·--·.000277881s·elapsed
103 ·--·.00011939s·elapsed97 ·--·.000216906s·elapsed
104 ·--·.000179951s·elapsed98 ·--·.000322484s·elapsed
105 ·--·.000132009s·elapsed99 ·--·.00020803s·elapsed
 100 ·--·.000203201s·elapsed
106 ·--·.000138769s·elapsed101 ·--·.00017579s·elapsed
107 ·--·.000136035s·elapsed102 ·--·.000283722s·elapsed
108 ·--·.000129945s·elapsed103 ·--·.012245s·elapsed
109 ·--·.000147231s·elapsed104 ·--·.000219903s·elapsed
110 ·--·.000113842s·elapsed105 ·--·.000195677s·elapsed
111 ·--·.000124758s·elapsed106 ·--·.000243747s·elapsed
112 ·--·.000123916s·elapsed107 ·--·.000205916s·elapsed
113 ·--·.000138049s·elapsed108 ·--·.000212589s·elapsed
 109 ·--·.000183615s·elapsed
 110 ·--·.000219061s·elapsed
 111 ·--·.000196879s·elapsed
 112 ·--·.000223419s·elapsed
 113 ·--·.000184236s·elapsed
114 (number·Of·blocks,·26)114 (number·Of·blocks,·26)
115 1115 1
116 1116 1
117 1117 1
118 1118 1
119 2119 2
120 ·2120 ·2
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Offset 19, 42 lines modifiedOffset 19, 42 lines modified
19 determinants·and·return·their·product.19 determinants·and·return·their·product.
20 i1·:·a=4,b=420 i1·:·a=4,b=4
  
21 o1·=·(4,·4)21 o1·=·(4,·4)
  
22 o1·:·Sequence22 o1·:·Sequence
23 i2·:·d=carpetDet(a,b)23 i2·:·d=carpetDet(a,b)
24 ·--·.00671651s·elapsed 
25 ·--·.0166392s·elapsed24 ·--·.0273009s·elapsed
 25 ·--·.0559471s·elapsed
26 ·--·.000223808s·elapsed26 ·--·.000278993s·elapsed
27 ·--·.000143466s·elapsed27 ·--·.000240541s·elapsed
28 ·--·.000129015s·elapsed28 ·--·.000272971s·elapsed
29 ·--·.000115755s·elapsed 
30 ·--·.000134844s·elapsed 
31 ·--·.000146711s·elapsed 
32 ·--·.000135925s·elapsed 
33 ·--·.000176226s·elapsed 
34 ·--·.000128094s·elapsed29 ·--·.000218069s·elapsed
35 ·--·.00025175s·elapsed30 ·--·.000237075s·elapsed
36 ·--·.000257558s·elapsed 
37 ·--·.000187694s·elapsed 
38 ·--·.000120011s·elapsed 
39 ·--·.000120693s·elapsed31 ·--·.000262863s·elapsed
40 ·--·.000140633s·elapsed32 ·--·.000247033s·elapsed
 33 ·--·.000326061s·elapsed
 34 ·--·.000277881s·elapsed
41 ·--·.00011939s·elapsed35 ·--·.000216906s·elapsed
42 ·--·.000179951s·elapsed36 ·--·.000322484s·elapsed
43 ·--·.000132009s·elapsed37 ·--·.00020803s·elapsed
 38 ·--·.000203201s·elapsed
44 ·--·.000138769s·elapsed39 ·--·.00017579s·elapsed
45 ·--·.000136035s·elapsed40 ·--·.000283722s·elapsed
46 ·--·.000129945s·elapsed41 ·--·.012245s·elapsed
47 ·--·.000147231s·elapsed42 ·--·.000219903s·elapsed
48 ·--·.000113842s·elapsed43 ·--·.000195677s·elapsed
49 ·--·.000124758s·elapsed44 ·--·.000243747s·elapsed
50 ·--·.000123916s·elapsed45 ·--·.000205916s·elapsed
51 ·--·.000138049s·elapsed46 ·--·.000212589s·elapsed
 47 ·--·.000183615s·elapsed
 48 ·--·.000219061s·elapsed
 49 ·--·.000196879s·elapsed
 50 ·--·.000223419s·elapsed
 51 ·--·.000184236s·elapsed
52 (number·Of·blocks,·26)52 (number·Of·blocks,·26)
53 153 1
54 154 1
55 155 1
56 156 1
57 257 2
58 ·258 ·2
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Offset 85, 20 lines modifiedOffset 85, 20 lines modified
  
85 o1·:·Sequence</code></pre>85 o1·:·Sequence</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ··········<tr>88 ··········<tr>
89 ············<td>89 ············<td>
90 ··············<pre><code·class="language-macaulay2">i2·:·computeBound·390 ··············<pre><code·class="language-macaulay2">i2·:·computeBound·3
91 ·--·.974793s·elapsed91 ·--·2.09744s·elapsed
92 ·--·.755559s·elapsed 
93 ·--·.421012s·elapsed 
94 ·--·1.16935s·elapsed 
95 ·--·.865335s·elapsed 
96 ·--·1.22015s·elapsed92 ·--·1.50152s·elapsed
 93 ·--·.64122s·elapsed
 94 ·--·2.575s·elapsed
 95 ·--·1.4336s·elapsed
 96 ·--·1.94991s·elapsed
  
97 o2·=·6</code></pre>97 o2·=·6</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ········</table>100 ········</table>
101 ······</div>101 ······</div>
102 ······<div>102 ······<div>
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Offset 25, 20 lines modifiedOffset 25, 20 lines modified
25 classes·mod·k.·We·conjecture·that·c=k^2-k.25 classes·mod·k.·We·conjecture·that·c=k^2-k.
26 i1·:·(a,b)=computeBound(6,4,3)26 i1·:·(a,b)=computeBound(6,4,3)
  
27 o1·=·(9,·7)27 o1·=·(9,·7)
  
28 o1·:·Sequence28 o1·:·Sequence
29 i2·:·computeBound·329 i2·:·computeBound·3
30 ·--·.974793s·elapsed30 ·--·2.09744s·elapsed
31 ·--·.755559s·elapsed 
32 ·--·.421012s·elapsed 
33 ·--·1.16935s·elapsed 
34 ·--·.865335s·elapsed 
35 ·--·1.22015s·elapsed31 ·--·1.50152s·elapsed
 32 ·--·.64122s·elapsed
 33 ·--·2.575s·elapsed
 34 ·--·1.4336s·elapsed
 35 ·--·1.94991s·elapsed
  
36 o2·=·636 o2·=·6
37 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*37 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
38 ····*·_\x8r_\x8e_\x8l_\x8a_\x8t_\x8i_\x8v_\x8e_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·compute·the·relative·quadrics38 ····*·_\x8r_\x8e_\x8l_\x8a_\x8t_\x8i_\x8v_\x8e_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·compute·the·relative·quadrics
39 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8eB\x8Bo\x8ou\x8un\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8eB\x8Bo\x8ou\x8un\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
40 ····*·computeBound(ZZ)40 ····*·computeBound(ZZ)
41 ····*·computeBound(ZZ,ZZ,ZZ)41 ····*·computeBound(ZZ,ZZ,ZZ)
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Offset 90, 19 lines modifiedOffset 90, 19 lines modified
  
90 o2·:·Sequence</code></pre>90 o2·:·Sequence</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i3·:·h=degenerateK3BettiTables(a,b,e)95 ··············<pre><code·class="language-macaulay2">i3·:·h=degenerateK3BettiTables(a,b,e)
 96 ·--·.0112985s·elapsed
 97 ·--·.02254s·elapsed
 98 ·--·.078953s·elapsed
 99 ·--·.0543006s·elapsed
96 ·--·.00230618s·elapsed100 ·--·.0236152s·elapsed
97 ·--·.0050692s·elapsed 
98 ·--·.0267149s·elapsed 
99 ·--·.00811787s·elapsed 
100 ·--·.00311321s·elapsed 
  
101 ···························0··1···2···3···4···5···6···7··8·9101 ···························0··1···2···3···4···5···6···7··8·9
102 o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}102 o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}
103 ························0:·1··.···.···.···.···.···.···.··.·.103 ························0:·1··.···.···.···.···.···.···.··.·.
104 ························1:·.·36·160·315·288···.···.···.··.·.104 ························1:·.·36·160·315·288···.···.···.··.·.
105 ························2:·.··.···.···.···.·288·315·160·36·.105 ························2:·.··.···.···.···.·288·315·160·36·.
106 ························3:·.··.···.···.···.···.···.···.··.·1106 ························3:·.··.···.···.···.···.···.···.··.·1
Offset 136, 15 lines modifiedOffset 136, 15 lines modified
  
136 o4·:·List</code></pre>136 o4·:·List</code></pre>
137 ············</td>137 ············</td>
138 ··········</tr>138 ··········</tr>
139 ··········<tr>139 ··········<tr>
140 ············<td>140 ············<td>
141 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5)141 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5)
142 ·--·.361527s·elapsed142 ·--·.966198s·elapsed
  
143 ············0··1···2···3···4···5···6···7··8·9143 ············0··1···2···3···4···5···6···7··8·9
144 o5·=·total:·1·36·167·370·476·476·370·167·36·1144 o5·=·total:·1·36·167·370·476·476·370·167·36·1
145 ·········0:·1··.···.···.···.···.···.···.··.·.145 ·········0:·1··.···.···.···.···.···.···.··.·.
146 ·········1:·.·36·160·322·336·140··48···7··.·.146 ·········1:·.·36·160·322·336·140··48···7··.·.
147 ·········2:·.··.···7··48·140·336·322·160·36·.147 ·········2:·.··.···7··48·140·336·322·160·36·.
148 ·········3:·.··.···.···.···.···.···.···.··.·1148 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 178, 19 lines modifiedOffset 178, 19 lines modified
  
178 o7·:·Sequence</code></pre>178 o7·:·Sequence</code></pre>
179 ············</td>179 ············</td>
180 ··········</tr>180 ··········</tr>
181 ··········<tr>181 ··········<tr>
182 ············<td>182 ············<td>
183 ··············<pre><code·class="language-macaulay2">i8·:·h=degenerateK3BettiTables(a,b,e)183 ··············<pre><code·class="language-macaulay2">i8·:·h=degenerateK3BettiTables(a,b,e)
 184 ·--·.0189008s·elapsed
184 ·--·.00241335s·elapsed185 ·--·.0302941s·elapsed
185 ·--·.00521724s·elapsed186 ·--·.0988654s·elapsed
186 ·--·.0265308s·elapsed187 ·--·.0520845s·elapsed
187 ·--·.00789618s·elapsed188 ·--·.0208928s·elapsed
188 ·--·.00316001s·elapsed 
  
189 ···························0··1···2···3···4···5···6···7··8·9189 ···························0··1···2···3···4···5···6···7··8·9
190 o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····}190 o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····}
191 ························0:·1··.···.···.···.···.···.···.··.·.191 ························0:·1··.···.···.···.···.···.···.··.·.
192 ························1:·.·36·160·315·288···.···.···.··.·.192 ························1:·.·36·160·315·288···.···.···.··.·.
193 ························2:·.··.···.···.···.·288·315·160·36·.193 ························2:·.··.···.···.···.·288·315·160·36·.
194 ························3:·.··.···.···.···.···.···.···.··.·1194 ························3:·.··.···.···.···.···.···.···.··.·1
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Offset 27, 19 lines modifiedOffset 27, 19 lines modified
27 o1·:·Sequence27 o1·:·Sequence
28 i2·:·e=(-1,5)28 i2·:·e=(-1,5)
  
29 o2·=·(-1,·5)29 o2·=·(-1,·5)
  
30 o2·:·Sequence30 o2·:·Sequence
31 i3·:·h=degenerateK3BettiTables(a,b,e)31 i3·:·h=degenerateK3BettiTables(a,b,e)
 32 ·--·.0112985s·elapsed
 33 ·--·.02254s·elapsed
 34 ·--·.078953s·elapsed
 35 ·--·.0543006s·elapsed
32 ·--·.00230618s·elapsed36 ·--·.0236152s·elapsed
33 ·--·.0050692s·elapsed 
34 ·--·.0267149s·elapsed 
35 ·--·.00811787s·elapsed 
36 ·--·.00311321s·elapsed 
  
37 ···························0··1···2···3···4···5···6···7··8·937 ···························0··1···2···3···4···5···6···7··8·9
38 o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}38 o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1}
39 ························0:·1··.···.···.···.···.···.···.··.·.39 ························0:·1··.···.···.···.···.···.···.··.·.
40 ························1:·.·36·160·315·288···.···.···.··.·.40 ························1:·.·36·160·315·288···.···.···.··.·.
41 ························2:·.··.···.···.···.·288·315·160·36·.41 ························2:·.··.···.···.···.·288·315·160·36·.
42 ························3:·.··.···.···.···.···.···.···.··.·142 ························3:·.··.···.···.···.···.···.···.··.·1
Offset 65, 15 lines modifiedOffset 65, 15 lines modified
65 o3·:·HashTable65 o3·:·HashTable
66 i4·:·keys·h66 i4·:·keys·h
  
67 o4·=·{0,·2,·3,·5}67 o4·=·{0,·2,·3,·5}
  
68 o4·:·List68 o4·:·List
69 i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5)69 i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5)
70 ·--·.361527s·elapsed70 ·--·.966198s·elapsed
  
71 ············0··1···2···3···4···5···6···7··8·971 ············0··1···2···3···4···5···6···7··8·9
72 o5·=·total:·1·36·167·370·476·476·370·167·36·172 o5·=·total:·1·36·167·370·476·476·370·167·36·1
73 ·········0:·1··.···.···.···.···.···.···.··.·.73 ·········0:·1··.···.···.···.···.···.···.··.·.
74 ·········1:·.·36·160·322·336·140··48···7··.·.74 ·········1:·.·36·160·322·336·140··48···7··.·.
75 ·········2:·.··.···7··48·140·336·322·160·36·.75 ·········2:·.··.···7··48·140·336·322·160·36·.
76 ·········3:·.··.···.···.···.···.···.···.··.·176 ·········3:·.··.···.···.···.···.···.···.··.·1
Offset 94, 19 lines modifiedOffset 94, 19 lines modified
94 these·mistakes.94 these·mistakes.
95 i7·:·e=(-1,5^2)95 i7·:·e=(-1,5^2)
  
96 o7·=·(-1,·25)96 o7·=·(-1,·25)
  
97 o7·:·Sequence97 o7·:·Sequence
98 i8·:·h=degenerateK3BettiTables(a,b,e)98 i8·:·h=degenerateK3BettiTables(a,b,e)
 99 ·--·.0189008s·elapsed
99 ·--·.00241335s·elapsed100 ·--·.0302941s·elapsed
100 ·--·.00521724s·elapsed101 ·--·.0988654s·elapsed
101 ·--·.0265308s·elapsed102 ·--·.0520845s·elapsed
102 ·--·.00789618s·elapsed103 ·--·.0208928s·elapsed
103 ·--·.00316001s·elapsed 
  
104 ···························0··1···2···3···4···5···6···7··8·9104 ···························0··1···2···3···4···5···6···7··8·9
105 o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····}105 o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····}
106 ························0:·1··.···.···.···.···.···.···.··.·.106 ························0:·1··.···.···.···.···.···.···.··.·.
107 ························1:·.·36·160·315·288···.···.···.··.·.107 ························1:·.·36·160·315·288···.···.···.··.·.
108 ························2:·.··.···.···.···.·288·315·160·36·.108 ························2:·.··.···.···.···.·288·315·160·36·.
109 ························3:·.··.···.···.···.···.···.···.··.·1109 ························3:·.··.···.···.···.···.···.···.··.·1
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Offset 78, 33 lines modifiedOffset 78, 33 lines modified
  
78 o1·=·4</code></pre>78 o1·=·4</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i2·:·(d1,d2)=resonanceDet(a)83 ··············<pre><code·class="language-macaulay2">i2·:·(d1,d2)=resonanceDet(a)
84 ·--·.0132832s·elapsed84 ·--·.0635816s·elapsed
85 ·--·.000031908s·elapsed85 ·--·.000036839s·elapsed
86 ·--·.000073011s·elapsed 
87 ·--·.000071427s·elapsed86 ·--·.000092985s·elapsed
88 ·--·.000067151s·elapsed87 ·--·.000071595s·elapsed
89 ·--·.000078099s·elapsed88 ·--·.0000904s·elapsed
90 ·--·.000073761s·elapsed 
91 ·--·.000023926s·elapsed89 ·--·.000094297s·elapsed
92 ·--·.000057276s·elapsed 
93 ·--·.000072018s·elapsed90 ·--·.000097213s·elapsed
 91 ·--·.000024486s·elapsed
 92 ·--·.000073498s·elapsed
94 ·--·.000089795s·elapsed93 ·--·.000089769s·elapsed
95 ·--·.000084979s·elapsed94 ·--·.000092093s·elapsed
96 ·--·.000073202s·elapsed 
97 ·--·.000060211s·elapsed 
98 ·--·.000054452s·elapsed 
99 ·--·.000055884s·elapsed 
100 ·--·.000039369s·elapsed 
101 ·--·.000084427s·elapsed95 ·--·.000087444s·elapsed
 96 ·--·.000081864s·elapsed
102 ·--·.00001979s·elapsed97 ·--·.000079148s·elapsed
 98 ·--·.000078397s·elapsed
 99 ·--·.000066474s·elapsed
 100 ·--·.000038321s·elapsed
 101 ·--·.000084218s·elapsed
 102 ·--·.000025148s·elapsed
103 (number·of·blocks=·,·18)103 (number·of·blocks=·,·18)
104 (size·of·the·matrices,·Tally{1·=>·4})104 (size·of·the·matrices,·Tally{1·=>·4})
105 ·····························2·=>·6105 ·····························2·=>·6
106 ·····························3·=>·2106 ·····························3·=>·2
107 ·····························4·=>·6107 ·····························4·=>·6
108 ·······0·1108 ·······0·1
109 total:·1·1109 total:·1·1
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Offset 19, 33 lines modifiedOffset 19, 33 lines modified
19 grading.·Viewed·as·a·resolution·over·QQ(e_1,e_2),·this·resolution·is·non-19 grading.·Viewed·as·a·resolution·over·QQ(e_1,e_2),·this·resolution·is·non-
20 minimal·and·carries·further·gradings.·We·decompose·the·crucial·map·of·the·a-th20 minimal·and·carries·further·gradings.·We·decompose·the·crucial·map·of·the·a-th
21 strand·into·blocks,·compute·their·determinants,·and·factor·the·product.21 strand·into·blocks,·compute·their·determinants,·and·factor·the·product.
22 i1·:·a=422 i1·:·a=4
  
23 o1·=·423 o1·=·4
24 i2·:·(d1,d2)=resonanceDet(a)24 i2·:·(d1,d2)=resonanceDet(a)
25 ·--·.0132832s·elapsed25 ·--·.0635816s·elapsed
26 ·--·.000031908s·elapsed26 ·--·.000036839s·elapsed
27 ·--·.000073011s·elapsed 
28 ·--·.000071427s·elapsed27 ·--·.000092985s·elapsed
29 ·--·.000067151s·elapsed28 ·--·.000071595s·elapsed
30 ·--·.000078099s·elapsed29 ·--·.0000904s·elapsed
31 ·--·.000073761s·elapsed 
32 ·--·.000023926s·elapsed30 ·--·.000094297s·elapsed
33 ·--·.000057276s·elapsed 
34 ·--·.000072018s·elapsed31 ·--·.000097213s·elapsed
 32 ·--·.000024486s·elapsed
 33 ·--·.000073498s·elapsed
35 ·--·.000089795s·elapsed34 ·--·.000089769s·elapsed
36 ·--·.000084979s·elapsed35 ·--·.000092093s·elapsed
37 ·--·.000073202s·elapsed 
38 ·--·.000060211s·elapsed 
39 ·--·.000054452s·elapsed 
40 ·--·.000055884s·elapsed 
41 ·--·.000039369s·elapsed 
42 ·--·.000084427s·elapsed36 ·--·.000087444s·elapsed
 37 ·--·.000081864s·elapsed
43 ·--·.00001979s·elapsed38 ·--·.000079148s·elapsed
 39 ·--·.000078397s·elapsed
 40 ·--·.000066474s·elapsed
 41 ·--·.000038321s·elapsed
 42 ·--·.000084218s·elapsed
 43 ·--·.000025148s·elapsed
44 (number·of·blocks=·,·18)44 (number·of·blocks=·,·18)
45 (size·of·the·matrices,·Tally{1·=>·4})45 (size·of·the·matrices,·Tally{1·=>·4})
46 ·····························2·=>·646 ·····························2·=>·6
47 ·····························3·=>·247 ·····························3·=>·2
48 ·····························4·=>·648 ·····························4·=>·6
49 ·······0·149 ·······0·1
50 total:·1·150 total:·1·1
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Offset 1, 11 lines modifiedOffset 1, 11 lines modified
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./usr/share/doc/Macaulay2/LLLBases/example-output/___L__L__L_lp..._cm__Strategy_eq_gt..._rp.out
    
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7 i2·:·m·=·syz·m1;7 i2·:·m·=·syz·m1;
  
8 ··············50·······478 ··············50·······47
9 o2·:·Matrix·ZZ···<--·ZZ9 o2·:·Matrix·ZZ···<--·ZZ
  
10 i3·:·time·LLL·m;10 i3·:·time·LLL·m;
11 ·--·used·0.00514805s·(cpu);·0.00684702s·(thread);·0s·(gc)11 ·--·used·0.00632111s·(cpu);·0.00734694s·(thread);·0s·(gc)
  
12 ··············50·······4712 ··············50·······47
13 o3·:·Matrix·ZZ···<--·ZZ13 o3·:·Matrix·ZZ···<--·ZZ
  
14 i4·:·time·LLL(m,·Strategy=>CohenEngine);14 i4·:·time·LLL(m,·Strategy=>CohenEngine);
15 ·--·used·0.0212743s·(cpu);·0.0232361s·(thread);·0s·(gc)15 ·--·used·0.0211834s·(cpu);·0.0246533s·(thread);·0s·(gc)
  
16 ··············50·······4716 ··············50·······47
17 o4·:·Matrix·ZZ···<--·ZZ17 o4·:·Matrix·ZZ···<--·ZZ
  
18 i5·:·time·LLL(m,·Strategy=>CohenTopLevel);18 i5·:·time·LLL(m,·Strategy=>CohenTopLevel);
19 ·--·used·0.0880007s·(cpu);·0.0882364s·(thread);·0s·(gc)19 ·--·used·0.114255s·(cpu);·0.115505s·(thread);·0s·(gc)
  
20 ··············50·······4720 ··············50·······47
21 o5·:·Matrix·ZZ···<--·ZZ21 o5·:·Matrix·ZZ···<--·ZZ
  
22 i6·:·time·LLL(m,·Strategy=>{Givens,RealFP});22 i6·:·time·LLL(m,·Strategy=>{Givens,RealFP});
23 ·--·used·0.00745862s·(cpu);·0.00989982s·(thread);·0s·(gc)23 ·--·used·0.00806965s·(cpu);·0.0110965s·(thread);·0s·(gc)
  
24 ··············50·······4724 ··············50·······47
25 o6·:·Matrix·ZZ···<--·ZZ25 o6·:·Matrix·ZZ···<--·ZZ
  
26 i7·:·time·LLL(m,·Strategy=>{Givens,RealQP});26 i7·:·time·LLL(m,·Strategy=>{Givens,RealQP});
27 ·--·used·0.0491971s·(cpu);·0.0515237s·(thread);·0s·(gc)27 ·--·used·0.0492734s·(cpu);·0.0510739s·(thread);·0s·(gc)
  
28 ··············50·······4728 ··············50·······47
29 o7·:·Matrix·ZZ···<--·ZZ29 o7·:·Matrix·ZZ···<--·ZZ
  
30 i8·:·time·LLL(m,·Strategy=>{Givens,RealXD});30 i8·:·time·LLL(m,·Strategy=>{Givens,RealXD});
31 ·--·used·0.0532887s·(cpu);·0.0553984s·(thread);·0s·(gc)31 ·--·used·0.0517295s·(cpu);·0.054476s·(thread);·0s·(gc)
  
32 ··············50·······4732 ··············50·······47
33 o8·:·Matrix·ZZ···<--·ZZ33 o8·:·Matrix·ZZ···<--·ZZ
  
34 i9·:·time·LLL(m,·Strategy=>{Givens,RealRR});34 i9·:·time·LLL(m,·Strategy=>{Givens,RealRR});
35 ·--·used·0.255805s·(cpu);·0.258473s·(thread);·0s·(gc)35 ·--·used·0.259991s·(cpu);·0.26342s·(thread);·0s·(gc)
  
36 ··············50·······4736 ··············50·······47
37 o9·:·Matrix·ZZ···<--·ZZ37 o9·:·Matrix·ZZ···<--·ZZ
  
38 i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP});38 i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP});
39 ·--·used·0.126576s·(cpu);·0.126763s·(thread);·0s·(gc)39 ·--·used·0.116913s·(cpu);·0.120578s·(thread);·0s·(gc)
  
40 ···············50·······4740 ···············50·······47
41 o10·:·Matrix·ZZ···<--·ZZ41 o10·:·Matrix·ZZ···<--·ZZ
  
42 i11·:·42 i11·:·
5.08 KB
./usr/share/doc/Macaulay2/LLLBases/html/___L__L__L_lp..._cm__Strategy_eq_gt..._rp.html
    
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139 ··············50·······47139 ··············50·······47
140 o2·:·Matrix·ZZ···&lt;--·ZZ</code></pre>140 o2·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
143 ··········<tr>143 ··········<tr>
144 ············<td>144 ············<td>
145 ··············<pre><code·class="language-macaulay2">i3·:·time·LLL·m;145 ··············<pre><code·class="language-macaulay2">i3·:·time·LLL·m;
146 ·--·used·0.00514805s·(cpu);·0.00684702s·(thread);·0s·(gc)146 ·--·used·0.00632111s·(cpu);·0.00734694s·(thread);·0s·(gc)
  
147 ··············50·······47147 ··············50·······47
148 o3·:·Matrix·ZZ···&lt;--·ZZ</code></pre>148 o3·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
152 ············<td>152 ············<td>
153 ··············<pre><code·class="language-macaulay2">i4·:·time·LLL(m,·Strategy=>CohenEngine);153 ··············<pre><code·class="language-macaulay2">i4·:·time·LLL(m,·Strategy=>CohenEngine);
154 ·--·used·0.0212743s·(cpu);·0.0232361s·(thread);·0s·(gc)154 ·--·used·0.0211834s·(cpu);·0.0246533s·(thread);·0s·(gc)
  
155 ··············50·······47155 ··············50·······47
156 o4·:·Matrix·ZZ···&lt;--·ZZ</code></pre>156 o4·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
157 ············</td>157 ············</td>
158 ··········</tr>158 ··········</tr>
159 ··········<tr>159 ··········<tr>
160 ············<td>160 ············<td>
161 ··············<pre><code·class="language-macaulay2">i5·:·time·LLL(m,·Strategy=>CohenTopLevel);161 ··············<pre><code·class="language-macaulay2">i5·:·time·LLL(m,·Strategy=>CohenTopLevel);
162 ·--·used·0.0880007s·(cpu);·0.0882364s·(thread);·0s·(gc)162 ·--·used·0.114255s·(cpu);·0.115505s·(thread);·0s·(gc)
  
163 ··············50·······47163 ··············50·······47
164 o5·:·Matrix·ZZ···&lt;--·ZZ</code></pre>164 o5·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
165 ············</td>165 ············</td>
166 ··········</tr>166 ··········</tr>
167 ··········<tr>167 ··········<tr>
168 ············<td>168 ············<td>
169 ··············<pre><code·class="language-macaulay2">i6·:·time·LLL(m,·Strategy=>{Givens,RealFP});169 ··············<pre><code·class="language-macaulay2">i6·:·time·LLL(m,·Strategy=>{Givens,RealFP});
170 ·--·used·0.00745862s·(cpu);·0.00989982s·(thread);·0s·(gc)170 ·--·used·0.00806965s·(cpu);·0.0110965s·(thread);·0s·(gc)
  
171 ··············50·······47171 ··············50·······47
172 o6·:·Matrix·ZZ···&lt;--·ZZ</code></pre>172 o6·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
173 ············</td>173 ············</td>
174 ··········</tr>174 ··········</tr>
175 ··········<tr>175 ··········<tr>
176 ············<td>176 ············<td>
177 ··············<pre><code·class="language-macaulay2">i7·:·time·LLL(m,·Strategy=>{Givens,RealQP});177 ··············<pre><code·class="language-macaulay2">i7·:·time·LLL(m,·Strategy=>{Givens,RealQP});
178 ·--·used·0.0491971s·(cpu);·0.0515237s·(thread);·0s·(gc)178 ·--·used·0.0492734s·(cpu);·0.0510739s·(thread);·0s·(gc)
  
179 ··············50·······47179 ··············50·······47
180 o7·:·Matrix·ZZ···&lt;--·ZZ</code></pre>180 o7·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
181 ············</td>181 ············</td>
182 ··········</tr>182 ··········</tr>
183 ··········<tr>183 ··········<tr>
184 ············<td>184 ············<td>
185 ··············<pre><code·class="language-macaulay2">i8·:·time·LLL(m,·Strategy=>{Givens,RealXD});185 ··············<pre><code·class="language-macaulay2">i8·:·time·LLL(m,·Strategy=>{Givens,RealXD});
186 ·--·used·0.0532887s·(cpu);·0.0553984s·(thread);·0s·(gc)186 ·--·used·0.0517295s·(cpu);·0.054476s·(thread);·0s·(gc)
  
187 ··············50·······47187 ··············50·······47
188 o8·:·Matrix·ZZ···&lt;--·ZZ</code></pre>188 o8·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
189 ············</td>189 ············</td>
190 ··········</tr>190 ··········</tr>
191 ··········<tr>191 ··········<tr>
192 ············<td>192 ············<td>
193 ··············<pre><code·class="language-macaulay2">i9·:·time·LLL(m,·Strategy=>{Givens,RealRR});193 ··············<pre><code·class="language-macaulay2">i9·:·time·LLL(m,·Strategy=>{Givens,RealRR});
194 ·--·used·0.255805s·(cpu);·0.258473s·(thread);·0s·(gc)194 ·--·used·0.259991s·(cpu);·0.26342s·(thread);·0s·(gc)
  
195 ··············50·······47195 ··············50·······47
196 o9·:·Matrix·ZZ···&lt;--·ZZ</code></pre>196 o9·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
197 ············</td>197 ············</td>
198 ··········</tr>198 ··········</tr>
199 ··········<tr>199 ··········<tr>
200 ············<td>200 ············<td>
201 ··············<pre><code·class="language-macaulay2">i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP});201 ··············<pre><code·class="language-macaulay2">i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP});
202 ·--·used·0.126576s·(cpu);·0.126763s·(thread);·0s·(gc)202 ·--·used·0.116913s·(cpu);·0.120578s·(thread);·0s·(gc)
  
203 ···············50·······47203 ···············50·······47
204 o10·:·Matrix·ZZ···&lt;--·ZZ</code></pre>204 o10·:·Matrix·ZZ···&lt;--·ZZ</code></pre>
205 ············</td>205 ············</td>
206 ··········</tr>206 ··········</tr>
207 ········</table>207 ········</table>
208 ······</div>208 ······</div>
2.04 KB
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115 ··············50·······50115 ··············50·······50
116 o1·:·Matrix·ZZ···<--·ZZ116 o1·:·Matrix·ZZ···<--·ZZ
117 i2·:·m·=·syz·m1;117 i2·:·m·=·syz·m1;
  
118 ··············50·······47118 ··············50·······47
119 o2·:·Matrix·ZZ···<--·ZZ119 o2·:·Matrix·ZZ···<--·ZZ
120 i3·:·time·LLL·m;120 i3·:·time·LLL·m;
121 ·--·used·0.00514805s·(cpu);·0.00684702s·(thread);·0s·(gc)121 ·--·used·0.00632111s·(cpu);·0.00734694s·(thread);·0s·(gc)
  
122 ··············50·······47122 ··············50·······47
123 o3·:·Matrix·ZZ···<--·ZZ123 o3·:·Matrix·ZZ···<--·ZZ
124 i4·:·time·LLL(m,·Strategy=>CohenEngine);124 i4·:·time·LLL(m,·Strategy=>CohenEngine);
125 ·--·used·0.0212743s·(cpu);·0.0232361s·(thread);·0s·(gc)125 ·--·used·0.0211834s·(cpu);·0.0246533s·(thread);·0s·(gc)
  
126 ··············50·······47126 ··············50·······47
127 o4·:·Matrix·ZZ···<--·ZZ127 o4·:·Matrix·ZZ···<--·ZZ
128 i5·:·time·LLL(m,·Strategy=>CohenTopLevel);128 i5·:·time·LLL(m,·Strategy=>CohenTopLevel);
129 ·--·used·0.0880007s·(cpu);·0.0882364s·(thread);·0s·(gc)129 ·--·used·0.114255s·(cpu);·0.115505s·(thread);·0s·(gc)
  
130 ··············50·······47130 ··············50·······47
131 o5·:·Matrix·ZZ···<--·ZZ131 o5·:·Matrix·ZZ···<--·ZZ
132 i6·:·time·LLL(m,·Strategy=>{Givens,RealFP});132 i6·:·time·LLL(m,·Strategy=>{Givens,RealFP});
133 ·--·used·0.00745862s·(cpu);·0.00989982s·(thread);·0s·(gc)133 ·--·used·0.00806965s·(cpu);·0.0110965s·(thread);·0s·(gc)
  
134 ··············50·······47134 ··············50·······47
135 o6·:·Matrix·ZZ···<--·ZZ135 o6·:·Matrix·ZZ···<--·ZZ
136 i7·:·time·LLL(m,·Strategy=>{Givens,RealQP});136 i7·:·time·LLL(m,·Strategy=>{Givens,RealQP});
137 ·--·used·0.0491971s·(cpu);·0.0515237s·(thread);·0s·(gc)137 ·--·used·0.0492734s·(cpu);·0.0510739s·(thread);·0s·(gc)
  
138 ··············50·······47138 ··············50·······47
139 o7·:·Matrix·ZZ···<--·ZZ139 o7·:·Matrix·ZZ···<--·ZZ
140 i8·:·time·LLL(m,·Strategy=>{Givens,RealXD});140 i8·:·time·LLL(m,·Strategy=>{Givens,RealXD});
141 ·--·used·0.0532887s·(cpu);·0.0553984s·(thread);·0s·(gc)141 ·--·used·0.0517295s·(cpu);·0.054476s·(thread);·0s·(gc)
  
142 ··············50·······47142 ··············50·······47
143 o8·:·Matrix·ZZ···<--·ZZ143 o8·:·Matrix·ZZ···<--·ZZ
144 i9·:·time·LLL(m,·Strategy=>{Givens,RealRR});144 i9·:·time·LLL(m,·Strategy=>{Givens,RealRR});
145 ·--·used·0.255805s·(cpu);·0.258473s·(thread);·0s·(gc)145 ·--·used·0.259991s·(cpu);·0.26342s·(thread);·0s·(gc)
  
146 ··············50·······47146 ··············50·······47
147 o9·:·Matrix·ZZ···<--·ZZ147 o9·:·Matrix·ZZ···<--·ZZ
148 i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP});148 i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP});
149 ·--·used·0.126576s·(cpu);·0.126763s·(thread);·0s·(gc)149 ·--·used·0.116913s·(cpu);·0.120578s·(thread);·0s·(gc)
  
150 ···············50·······47150 ···············50·······47
151 o10·:·Matrix·ZZ···<--·ZZ151 o10·:·Matrix·ZZ···<--·ZZ
152 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*152 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
153 For·most·of·the·options,·the·columns·do·not·need·to·be·linearly·independent.153 For·most·of·the·options,·the·columns·do·not·need·to·be·linearly·independent.
154 The·strategies·CohenEngine·and·CohenTopLevel·currently·require·the·columns·to154 The·strategies·CohenEngine·and·CohenTopLevel·currently·require·the·columns·to
155 be·linearly·independent.155 be·linearly·independent.
757 B
./usr/share/doc/Macaulay2/LatticePolytopes/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/LatticePolytopes/example-output/_are__Isomorphic.out
    
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16 ··············3·······816 ··············3·······8
17 o4·:·Matrix·ZZ··<--·ZZ17 o4·:·Matrix·ZZ··<--·ZZ
  
18 i5·:·P·=·convexHull(M);18 i5·:·P·=·convexHull(M);
  
19 i6·:·time·areIsomorphic(P,P);19 i6·:·time·areIsomorphic(P,P);
20 ·--·used·5.15257s·(cpu);·0.902843s·(thread);·0s·(gc)20 ·--·used·4.78516s·(cpu);·0.926804s·(thread);·0s·(gc)
  
21 i7·:·time·areIsomorphic(P,P,smoothTest=>false);21 i7·:·time·areIsomorphic(P,P,smoothTest=>false);
22 ·--·used·2.87546s·(cpu);·0.48611s·(thread);·0s·(gc)22 ·--·used·2.78067s·(cpu);·0.520684s·(thread);·0s·(gc)
  
23 i8·:·23 i8·:·
24 ·····24 ·····
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./usr/share/doc/Macaulay2/LatticePolytopes/html/_are__Isomorphic.html
    
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120 ············<td>120 ············<td>
121 ··············<pre><code·class="language-macaulay2">i5·:·P·=·convexHull(M);</code></pre>121 ··············<pre><code·class="language-macaulay2">i5·:·P·=·convexHull(M);</code></pre>
122 ············</td>122 ············</td>
123 ··········</tr>123 ··········</tr>
124 ··········<tr>124 ··········<tr>
125 ············<td>125 ············<td>
126 ··············<pre><code·class="language-macaulay2">i6·:·time·areIsomorphic(P,P);126 ··············<pre><code·class="language-macaulay2">i6·:·time·areIsomorphic(P,P);
127 ·--·used·5.15257s·(cpu);·0.902843s·(thread);·0s·(gc)</code></pre>127 ·--·used·4.78516s·(cpu);·0.926804s·(thread);·0s·(gc)</code></pre>
128 ············</td>128 ············</td>
129 ··········</tr>129 ··········</tr>
130 ··········<tr>130 ··········<tr>
131 ············<td>131 ············<td>
132 ··············<pre><code·class="language-macaulay2">i7·:·time·areIsomorphic(P,P,smoothTest=>false);132 ··············<pre><code·class="language-macaulay2">i7·:·time·areIsomorphic(P,P,smoothTest=>false);
133 ·--·used·2.87546s·(cpu);·0.48611s·(thread);·0s·(gc)</code></pre>133 ·--·used·2.78067s·(cpu);·0.520684s·(thread);·0s·(gc)</code></pre>
134 ············</td>134 ············</td>
135 ··········</tr>135 ··········</tr>
136 ········</table>136 ········</table>
137 ······</div>137 ······</div>
138 ······<div>138 ······<div>
139 ········<div·class="waystouse">139 ········<div·class="waystouse">
140 ··········<h2>Ways·to·use·<span·class="tt">areIsomorphic</span>:</h2>140 ··········<h2>Ways·to·use·<span·class="tt">areIsomorphic</span>:</h2>
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35 ·····|·0·0·1·0·1·0·1·1·|35 ·····|·0·0·1·0·1·0·1·1·|
36 ·····|·0·0·0·1·0·1·1·1·|36 ·····|·0·0·0·1·0·1·1·1·|
  
37 ··············3·······837 ··············3·······8
38 o4·:·Matrix·ZZ··<--·ZZ38 o4·:·Matrix·ZZ··<--·ZZ
39 i5·:·P·=·convexHull(M);39 i5·:·P·=·convexHull(M);
40 i6·:·time·areIsomorphic(P,P);40 i6·:·time·areIsomorphic(P,P);
41 ·--·used·5.15257s·(cpu);·0.902843s·(thread);·0s·(gc)41 ·--·used·4.78516s·(cpu);·0.926804s·(thread);·0s·(gc)
42 i7·:·time·areIsomorphic(P,P,smoothTest=>false);42 i7·:·time·areIsomorphic(P,P,smoothTest=>false);
43 ·--·used·2.87546s·(cpu);·0.48611s·(thread);·0s·(gc)43 ·--·used·2.78067s·(cpu);·0.520684s·(thread);·0s·(gc)
44 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ar\x8re\x8eI\x8Is\x8so\x8om\x8mo\x8or\x8rp\x8ph\x8hi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8*44 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ar\x8re\x8eI\x8Is\x8so\x8om\x8mo\x8or\x8rp\x8ph\x8hi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8*
45 ····*·areIsomorphic(Matrix,Matrix)45 ····*·areIsomorphic(Matrix,Matrix)
46 ····*·areIsomorphic(Polyhedron,Polyhedron)46 ····*·areIsomorphic(Polyhedron,Polyhedron)
47 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*47 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
48 The·object·_\x8a_\x8r_\x8e_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.48 The·object·_\x8a_\x8r_\x8e_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
49 ===============================================================================49 ===============================================================================
50 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-50 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
714 B
./usr/share/doc/Macaulay2/LexIdeals/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/LieTypes/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/LinearTruncations/example-output/_find__Region.out
    
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29 i5·:·findRegion({{0,0},{4,4}},M,f)29 i5·:·findRegion({{0,0},{4,4}},M,f)
  
30 o5·=·{{1,·2},·{3,·1}}30 o5·=·{{1,·2},·{3,·1}}
  
31 o5·:·List31 o5·:·List
  
32 i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f)32 i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f)
33 ·--·.0811806s·elapsed33 ·--·.208038s·elapsed
  
34 o6·=·{{1,·2},·{3,·1}}34 o6·=·{{1,·2},·{3,·1}}
  
35 o6·:·List35 o6·:·List
  
36 i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}})36 i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}})
37 ·--·.0121642s·elapsed37 ·--·.041296s·elapsed
  
38 o7·=·{{1,·2},·{3,·1}}38 o7·=·{{1,·2},·{3,·1}}
  
39 o7·:·List39 o7·:·List
  
40 i8·:·40 i8·:·
585 B
./usr/share/doc/Macaulay2/LinearTruncations/example-output/_linear__Truncations__Bound.out
    
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30 i5·:·apply(L,·d·->·isLinearComplex·res·prune·truncate(d,M))30 i5·:·apply(L,·d·->·isLinearComplex·res·prune·truncate(d,M))
  
31 o5·=·{true,·true}31 o5·=·{true,·true}
  
32 o5·:·List32 o5·:·List
  
33 i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M)33 i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M)
34 ·--·57.5593s·elapsed34 ·--·89.6722s·elapsed
  
35 o6·=·{{4,·3,·3},·{4,·4,·2}}35 o6·=·{{4,·3,·3},·{4,·4,·2}}
  
36 o6·:·List36 o6·:·List
  
37 i7·:·elapsedTime·linearTruncationsBound·M37 i7·:·elapsedTime·linearTruncationsBound·M
38 ·--·.0540957s·elapsed38 ·--·.12853s·elapsed
  
39 o7·=·{{4,·3,·3},·{4,·4,·2}}39 o7·=·{{4,·3,·3},·{4,·4,·2}}
  
40 o7·:·List40 o7·:·List
  
41 i8·:·41 i8·:·
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./usr/share/doc/Macaulay2/LinearTruncations/html/_find__Region.html
    
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125 ········<div>125 ········<div>
126 ··········<p>If·some·degrees·<span·class="tt">d</span>·are·known·to·satisfy·<span·class="tt">f(d,M)</span>,·then·they·can·be·specified·using·the·option·<span·class="tt">Inner</span>·in·order·to·expedite·the·computation.··Similarly,·degrees·not·above·those·given·in·<span·class="tt">Outer</span>·will·be·assumed·not·to·satisfy·<span·class="tt">f(d,M)</span>.·If·<span·class="tt">f</span>·takes·options·these·can·also·be·given·to·<span·class="tt">findRegion</span>.</p>126 ··········<p>If·some·degrees·<span·class="tt">d</span>·are·known·to·satisfy·<span·class="tt">f(d,M)</span>,·then·they·can·be·specified·using·the·option·<span·class="tt">Inner</span>·in·order·to·expedite·the·computation.··Similarly,·degrees·not·above·those·given·in·<span·class="tt">Outer</span>·will·be·assumed·not·to·satisfy·<span·class="tt">f(d,M)</span>.·If·<span·class="tt">f</span>·takes·options·these·can·also·be·given·to·<span·class="tt">findRegion</span>.</p>
127 ········</div>127 ········</div>
128 ········<table·class="examples">128 ········<table·class="examples">
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f)131 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f)
132 ·--·.0811806s·elapsed132 ·--·.208038s·elapsed
  
133 o6·=·{{1,·2},·{3,·1}}133 o6·=·{{1,·2},·{3,·1}}
  
134 o6·:·List</code></pre>134 o6·:·List</code></pre>
135 ············</td>135 ············</td>
136 ··········</tr>136 ··········</tr>
137 ··········<tr>137 ··········<tr>
138 ············<td>138 ············<td>
139 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}})139 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}})
140 ·--·.0121642s·elapsed140 ·--·.041296s·elapsed
  
141 o7·=·{{1,·2},·{3,·1}}141 o7·=·{{1,·2},·{3,·1}}
  
142 o7·:·List</code></pre>142 o7·:·List</code></pre>
143 ············</td>143 ············</td>
144 ··········</tr>144 ··········</tr>
145 ········</table>145 ········</table>
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48 o5·:·List48 o5·:·List
49 If·some·degrees·d·are·known·to·satisfy·f(d,M),·then·they·can·be·specified·using49 If·some·degrees·d·are·known·to·satisfy·f(d,M),·then·they·can·be·specified·using
50 the·option·Inner·in·order·to·expedite·the·computation.·Similarly,·degrees·not50 the·option·Inner·in·order·to·expedite·the·computation.·Similarly,·degrees·not
51 above·those·given·in·Outer·will·be·assumed·not·to·satisfy·f(d,M).·If·f·takes51 above·those·given·in·Outer·will·be·assumed·not·to·satisfy·f(d,M).·If·f·takes
52 options·these·can·also·be·given·to·findRegion.52 options·these·can·also·be·given·to·findRegion.
53 i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f)53 i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f)
54 ·--·.0811806s·elapsed54 ·--·.208038s·elapsed
  
55 o6·=·{{1,·2},·{3,·1}}55 o6·=·{{1,·2},·{3,·1}}
  
56 o6·:·List56 o6·:·List
57 i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{57 i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{
58 {1,1}})58 {1,1}})
59 ·--·.0121642s·elapsed59 ·--·.041296s·elapsed
  
60 o7·=·{{1,·2},·{3,·1}}60 o7·=·{{1,·2},·{3,·1}}
  
61 o7·:·List61 o7·:·List
62 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nt\x8tr\x8ri\x8ib\x8bu\x8ut\x8to\x8or\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8*62 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nt\x8tr\x8ri\x8ib\x8bu\x8ut\x8to\x8or\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8*
63 Mahrud·Sayrafi·contributed·to·the·code·for·this·function.63 Mahrud·Sayrafi·contributed·to·the·code·for·this·function.
64 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*64 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
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123 ········<div>123 ········<div>
124 ··········<p>The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the·positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in·the·<span·class="tt">i</span>-th·step·of·the·resolution·of·$M$.</p>124 ··········<p>The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the·positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in·the·<span·class="tt">i</span>-th·step·of·the·resolution·of·$M$.</p>
125 ········</div>125 ········</div>
126 ········<table·class="examples">126 ········<table·class="examples">
127 ··········<tr>127 ··········<tr>
128 ············<td>128 ············<td>
129 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M)129 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M)
130 ·--·57.5593s·elapsed130 ·--·89.6722s·elapsed
  
131 o6·=·{{4,·3,·3},·{4,·4,·2}}131 o6·=·{{4,·3,·3},·{4,·4,·2}}
  
132 o6·:·List</code></pre>132 o6·:·List</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·linearTruncationsBound·M137 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·linearTruncationsBound·M
138 ·--·.0540957s·elapsed138 ·--·.12853s·elapsed
  
139 o7·=·{{4,·3,·3},·{4,·4,·2}}139 o7·=·{{4,·3,·3},·{4,·4,·2}}
  
140 o7·:·List</code></pre>140 o7·:·List</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
143 ········</table>143 ········</table>
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48 o5·=·{true,·true}48 o5·=·{true,·true}
  
49 o5·:·List49 o5·:·List
50 The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the50 The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the
51 positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in51 positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in
52 the·i-th·step·of·the·resolution·of·$M$.52 the·i-th·step·of·the·resolution·of·$M$.
53 i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M)53 i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M)
54 ·--·57.5593s·elapsed54 ·--·89.6722s·elapsed
  
55 o6·=·{{4,·3,·3},·{4,·4,·2}}55 o6·=·{{4,·3,·3},·{4,·4,·2}}
  
56 o6·:·List56 o6·:·List
57 i7·:·elapsedTime·linearTruncationsBound·M57 i7·:·elapsedTime·linearTruncationsBound·M
58 ·--·.0540957s·elapsed58 ·--·.12853s·elapsed
  
59 o7·=·{{4,·3,·3},·{4,·4,·2}}59 o7·=·{{4,·3,·3},·{4,·4,·2}}
  
60 o7·:·List60 o7·:·List
61 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*61 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
62 In·general·linearTruncationsBound·will·not·find·the·minimal·degrees·where·$M$62 In·general·linearTruncationsBound·will·not·find·the·minimal·degrees·where·$M$
63 has·a·linear·resolution·but·will·be·faster·than·repeatedly·truncating·$M$.63 has·a·linear·resolution·but·will·be·faster·than·repeatedly·truncating·$M$.
722 B
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15 o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·|15 o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·|
  
16 ······························116 ······························1
17 o4·:·RP-module,·quotient·of·RP17 o4·:·RP-module,·quotient·of·RP
  
18 i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6)18 i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6)
19 ·--·.140873s·elapsed19 ·--·.547341s·elapsed
  
20 o5·=·{1,·3,·6,·7,·6,·3,·1}20 o5·=·{1,·3,·6,·7,·6,·3,·1}
  
21 o5·:·List21 o5·:·List
  
22 i6·:·oo//sum22 i6·:·oo//sum
  
Offset 44, 21 lines modifiedOffset 44, 21 lines modified
  
44 ··············2···344 ··············2···3
45 o10·=·ideal·(x·,·y·)45 o10·=·ideal·(x·,·y·)
  
46 o10·:·Ideal·of·RP46 o10·:·Ideal·of·RP
  
47 i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds47 i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds
48 ·--·.0148455s·elapsed48 ·--·.0398274s·elapsed
  
49 o11·=·{1,·2,·3,·4,·5,·6}49 o11·=·{1,·2,·3,·4,·5,·6}
  
50 o11·:·List50 o11·:·List
  
51 i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds51 i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds
52 ·--·.220556s·elapsed52 ·--·.672747s·elapsed
  
53 o12·=·{6,·12,·18,·24,·30,·36}53 o12·=·{6,·12,·18,·24,·30,·36}
  
54 o12·:·List54 o12·:·List
  
55 i13·:·55 i13·:·
2.16 KB
./usr/share/doc/Macaulay2/LocalRings/html/_hilbert__Samuel__Function.html
    
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111 ······························1111 ······························1
112 o4·:·RP-module,·quotient·of·RP</code></pre>112 o4·:·RP-module,·quotient·of·RP</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6)117 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6)
118 ·--·.140873s·elapsed118 ·--·.547341s·elapsed
  
119 o5·=·{1,·3,·6,·7,·6,·3,·1}119 o5·=·{1,·3,·6,·7,·6,·3,·1}
  
120 o5·:·List</code></pre>120 o5·:·List</code></pre>
121 ············</td>121 ············</td>
122 ··········</tr>122 ··········</tr>
123 ··········<tr>123 ··········<tr>
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163 o10·:·Ideal·of·RP</code></pre>163 o10·:·Ideal·of·RP</code></pre>
164 ············</td>164 ············</td>
165 ··········</tr>165 ··········</tr>
166 ··········<tr>166 ··········<tr>
167 ············<td>167 ············<td>
168 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds168 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds
169 ·--·.0148455s·elapsed169 ·--·.0398274s·elapsed
  
170 o11·=·{1,·2,·3,·4,·5,·6}170 o11·=·{1,·2,·3,·4,·5,·6}
  
171 o11·:·List</code></pre>171 o11·:·List</code></pre>
172 ············</td>172 ············</td>
173 ··········</tr>173 ··········</tr>
174 ··········<tr>174 ··········<tr>
175 ············<td>175 ············<td>
176 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds176 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds
177 ·--·.220556s·elapsed177 ·--·.672747s·elapsed
  
178 o12·=·{6,·12,·18,·24,·30,·36}178 o12·=·{6,·12,·18,·24,·30,·36}
  
179 o12·:·List</code></pre>179 o12·:·List</code></pre>
180 ············</td>180 ············</td>
181 ··········</tr>181 ··········</tr>
182 ········</table>182 ········</table>
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41 i4·:·M·=·RP^1/I41 i4·:·M·=·RP^1/I
  
42 o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·|42 o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·|
  
43 ······························143 ······························1
44 o4·:·RP-module,·quotient·of·RP44 o4·:·RP-module,·quotient·of·RP
45 i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6)45 i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6)
46 ·--·.140873s·elapsed46 ·--·.547341s·elapsed
  
47 o5·=·{1,·3,·6,·7,·6,·3,·1}47 o5·=·{1,·3,·6,·7,·6,·3,·1}
  
48 o5·:·List48 o5·:·List
49 i6·:·oo//sum49 i6·:·oo//sum
  
50 o6·=·2750 o6·=·27
Offset 65, 21 lines modifiedOffset 65, 21 lines modified
65 i10·:·q·=·ideal"x2,y3"65 i10·:·q·=·ideal"x2,y3"
  
66 ··············2···366 ··············2···3
67 o10·=·ideal·(x·,·y·)67 o10·=·ideal·(x·,·y·)
  
68 o10·:·Ideal·of·RP68 o10·:·Ideal·of·RP
69 i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds69 i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds
70 ·--·.0148455s·elapsed70 ·--·.0398274s·elapsed
  
71 o11·=·{1,·2,·3,·4,·5,·6}71 o11·=·{1,·2,·3,·4,·5,·6}
  
72 o11·:·List72 o11·:·List
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74 ·--·.220556s·elapsed74 ·--·.672747s·elapsed
  
75 o12·=·{6,·12,·18,·24,·30,·36}75 o12·=·{6,·12,·18,·24,·30,·36}
  
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78 Hilbert-Samuel·function·with·respect·to·a·parameter·ideal·other·than·the78 Hilbert-Samuel·function·with·respect·to·a·parameter·ideal·other·than·the
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7 ···············"heapSize"·=>·2247270407 ···············"heapSize"·=>·224940032
8 ···············"numGCs"·=>·7878 ···············"numGCs"·=>·787
9 ···············"numGCThreads"·=>·129 ···············"numGCThreads"·=>·12
  
10 o1·:·HashTable10 o1·:·HashTable
  
11 i2·:·s#"heapSize"11 i2·:·s#"heapSize"
  
12 o2·=·22472704012 o2·=·224940032
  
13 i3·:·13 i3·:·
690 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/___Minimal__Generators.out
    
Offset 40, 20 lines modifiedOffset 40, 20 lines modified
40 o6·:·PolynomialRing40 o6·:·PolynomialRing
  
41 i7·:·I·=·monomialCurveIdeal(R,·{1,4,5,9});41 i7·:·I·=·monomialCurveIdeal(R,·{1,4,5,9});
  
42 o7·:·Ideal·of·R42 o7·:·Ideal·of·R
  
43 i8·:·time·J·=·truncate(8,·I,·MinimalGenerators·=>·false);43 i8·:·time·J·=·truncate(8,·I,·MinimalGenerators·=>·false);
44 ·--·used·0.00468382s·(cpu);·0.00468123s·(thread);·0s·(gc)44 ·--·used·0.00460115s·(cpu);·0.00459974s·(thread);·0s·(gc)
  
45 o8·:·Ideal·of·R45 o8·:·Ideal·of·R
  
46 i9·:·time·K·=·truncate(8,·I,·MinimalGenerators·=>·true);46 i9·:·time·K·=·truncate(8,·I,·MinimalGenerators·=>·true);
47 ·--·used·0.0413581s·(cpu);·0.0413685s·(thread);·0s·(gc)47 ·--·used·0.0483026s·(cpu);·0.04824s·(thread);·0s·(gc)
  
48 o9·:·Ideal·of·R48 o9·:·Ideal·of·R
  
49 i10·:·numgens·J49 i10·:·numgens·J
  
50 o10·=·106750 o10·=·1067
  
657 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/___S__V__D_lp..._cm__Divide__Conquer_eq_gt..._rp.out
    
Offset 3, 13 lines modifiedOffset 3, 13 lines modified
3 i1·:·M·=·random(RR^200,·RR^200);3 i1·:·M·=·random(RR^200,·RR^200);
  
4 ················200·········2004 ················200·········200
5 o1·:·Matrix·RR······<--·RR5 o1·:·Matrix·RR······<--·RR
6 ··············53··········536 ··············53··········53
  
7 i2·:·time·SVD(M);7 i2·:·time·SVD(M);
8 ·--·used·0.0294049s·(cpu);·0.0294053s·(thread);·0s·(gc)8 ·--·used·0.0345343s·(cpu);·0.0345229s·(thread);·0s·(gc)
  
9 i3·:·time·SVD(M,·DivideConquer=>true);9 i3·:·time·SVD(M,·DivideConquer=>true);
10 ·--·used·0.0301216s·(cpu);·0.0301329s·(thread);·0s·(gc)10 ·--·used·0.0363766s·(cpu);·0.0363847s·(thread);·0s·(gc)
  
11 i4·:·11 i4·:·
686 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_a_spfirst_sp__Macaulay2_spsession.out
    
Offset 351, 15 lines modifiedOffset 351, 15 lines modified
351 ···············|·b·e·h·k·n·q·|351 ···············|·b·e·h·k·n·q·|
352 ···············|·c·f·i·l·o·r·|352 ···············|·c·f·i·l·o·r·|
  
353 ·····························3353 ·····························3
354 o58·:·R-module,·quotient·of·R354 o58·:·R-module,·quotient·of·R
  
355 i59·:·time·C·=·resolution·M355 i59·:·time·C·=·resolution·M
356 ·--·used·0.00212478s·(cpu);·0.00211824s·(thread);·0s·(gc)356 ·--·used·0.00156858s·(cpu);·0.00156277s·(thread);·0s·(gc)
  
357 ·······3······6······15······18······6357 ·······3······6······15······18······6
358 o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0358 o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0
359 ············································359 ············································
360 ······0······1······2·······3·······4······5360 ······0······1······2·······3·······4······5
  
361 o59·:·ChainComplex361 o59·:·ChainComplex
291 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_at__End__Of__File_lp__File_rp.out
    
Offset 14, 10 lines modifiedOffset 14, 10 lines modified
  
14 i4·:·peek·read·f14 i4·:·peek·read·f
  
15 o4·=·"hi·there"15 o4·=·"hi·there"
  
16 i5·:·atEndOfFile·f16 i5·:·atEndOfFile·f
  
17 o5·=·false17 o5·=·true
  
18 i6·:·18 i6·:·
322 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_benchmark.out
    
Offset 1, 9 lines modifiedOffset 1, 9 lines modified
1 --·-*-·M2-comint·-*-·hash:·13303793594201 --·-*-·M2-comint·-*-·hash:·1330379359420
  
2 i1·:·benchmark·"sqrt·2p100000"2 i1·:·benchmark·"sqrt·2p100000"
  
3 o1·=·.00035200856551976543 o1·=·.0003361085814274754
  
4 o1·:·RR·(of·precision·53)4 o1·:·RR·(of·precision·53)
  
5 i2·:·5 i2·:·
595 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_caching_spcomputation_spresults.out
    
Offset 4, 20 lines modifiedOffset 4, 20 lines modified
  
4 i2·:·R·=·QQ[x,y,z];4 i2·:·R·=·QQ[x,y,z];
  
5 i3·:·M·=·coker·vars·R;5 i3·:·M·=·coker·vars·R;
  
6 i4·:·elapsedTime·pdim'·M6 i4·:·elapsedTime·pdim'·M
7 ·--·computing·pdim'7 ·--·computing·pdim'
8 ·--·.00329091s·elapsed8 ·--·.0154865s·elapsed
  
9 o4·=·39 o4·=·3
  
10 i5·:·elapsedTime·pdim'·M10 i5·:·elapsedTime·pdim'·M
11 ·--·.000001483s·elapsed11 ·--·.000001704s·elapsed
  
12 o5·=·312 o5·=·3
  
13 i6·:·peek·M.cache13 i6·:·peek·M.cache
  
14 o6·=·CacheTable{cache·=>·MutableHashTable{}··············································}14 o6·=·CacheTable{cache·=>·MutableHashTable{}··············································}
15 ················isHomogeneous·=>·true15 ················isHomogeneous·=>·true
751 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_cancel__Task_lp__Task_rp.out
    
Offset 18, 57 lines modifiedOffset 18, 57 lines modified
  
18 o4·=·<<task,·running>>18 o4·=·<<task,·running>>
  
19 o4·:·Task19 o4·:·Task
  
20 i5·:·n20 i5·:·n
  
21 o5·=·95236121 o5·=·960378
  
22 i6·:·sleep·122 i6·:·sleep·1
  
23 o6·=·023 o6·=·0
  
24 i7·:·t24 i7·:·t
  
25 o7·=·<<task,·running>>25 o7·=·<<task,·running>>
  
26 o7·:·Task26 o7·:·Task
  
27 i8·:·n27 i8·:·n
  
28 o8·=·192407928 o8·=·1924465
  
29 i9·:·isReady·t29 i9·:·isReady·t
  
30 o9·=·false30 o9·=·false
  
31 i10·:·cancelTask·t31 i10·:·cancelTask·t
  
32 i11·:·sleep·232 i11·:·sleep·2
33 stdio:2:38:(3):[1]:·error:·interrupted33 stdio:2:25:(3):[1]:·error:·interrupted
  
34 o11·=·034 o11·=·0
  
35 i12·:·t35 i12·:·t
  
36 o12·=·<<task,·canceled>>36 o12·=·<<task,·canceled>>
  
37 o12·:·Task37 o12·:·Task
  
38 i13·:·n38 i13·:·n
  
39 o13·=·192423139 o13·=·1924656
  
40 i14·:·sleep·140 i14·:·sleep·1
  
41 o14·=·041 o14·=·0
  
42 i15·:·n42 i15·:·n
  
43 o15·=·192423143 o15·=·1924656
  
44 i16·:·isReady·t44 i16·:·isReady·t
  
45 o16·=·false45 o16·=·false
  
46 i17·:·46 i17·:·
558 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_change__Directory.out
    
Offset 1, 19 lines modifiedOffset 1, 19 lines modified
1 --·-*-·M2-comint·-*-·hash:·85355102461401752781 --·-*-·M2-comint·-*-·hash:·8535510246140175278
  
2 i1·:·dir·=·temporaryFileName()2 i1·:·dir·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1077179-0/03 o1·=·/tmp/M2-985150-0/0
  
4 i2·:·makeDirectory·dir4 i2·:·makeDirectory·dir
  
5 o2·=·/tmp/M2-1077179-0/05 o2·=·/tmp/M2-985150-0/0
  
6 i3·:·changeDirectory·dir6 i3·:·changeDirectory·dir
  
7 o3·=·/tmp/M2-1077179-0/0/7 o3·=·/tmp/M2-985150-0/0/
  
8 i4·:·currentDirectory()8 i4·:·currentDirectory()
  
9 o4·=·/tmp/M2-1077179-0/0/9 o4·=·/tmp/M2-985150-0/0/
  
10 i5·:·10 i5·:·
2.25 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_check.out
    
Offset 4, 51 lines modifiedOffset 4, 51 lines modified
  
4 o1·=·FirstPackage4 o1·=·FirstPackage
  
5 o1·:·Package5 o1·:·Package
  
6 i2·:·check_1·FirstPackage6 i2·:·check_1·FirstPackage
7 ·--·warning:·reloading·FirstPackage;·recreate·instances·of·types·from·this·package7 ·--·warning:·reloading·FirstPackage;·recreate·instances·of·types·from·this·package
8 ·--·capturing·check(1,·"FirstPackage")········--·.112117s·elapsed8 ·--·capturing·check(1,·"FirstPackage")········--·.332184s·elapsed
  
9 i3·:·check·FirstPackage9 i3·:·check·FirstPackage
10 ·--·capturing·check(0,·"FirstPackage")········--·.117408s·elapsed10 ·--·capturing·check(0,·"FirstPackage")········--·.466856s·elapsed
11 ·--·capturing·check(1,·"FirstPackage")········--·.110957s·elapsed11 ·--·capturing·check(1,·"FirstPackage")········--·.391457s·elapsed
  
12 i4·:·check_1·"FirstPackage"12 i4·:·check_1·"FirstPackage"
13 ·--·capturing·check(1,·"FirstPackage")········--·.113437s·elapsed13 ·--·capturing·check(1,·"FirstPackage")········--·.321593s·elapsed
  
14 i5·:·check·"FirstPackage"14 i5·:·check·"FirstPackage"
15 ·--·capturing·check(0,·"FirstPackage")········--·.109372s·elapsed15 ·--·capturing·check(0,·"FirstPackage")········--·.351501s·elapsed
16 ·--·capturing·check(1,·"FirstPackage")········--·.11024s·elapsed16 ·--·capturing·check(1,·"FirstPackage")········--·.444128s·elapsed
  
17 i6·:·tests(1,·"FirstPackage")17 i6·:·tests(1,·"FirstPackage")
  
18 o6·=·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]18 o6·=·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]
  
19 o6·:·TestInput19 o6·:·TestInput
  
20 i7·:·check·oo20 i7·:·check·oo
21 ·--·capturing·check(1,·"FirstPackage")········--·.109679s·elapsed21 ·--·capturing·check(1,·"FirstPackage")········--·.333943s·elapsed
  
22 i8·:·tests·"FirstPackage"22 i8·:·tests·"FirstPackage"
  
23 o8·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}23 o8·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}
24 ·····{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}24 ·····{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}
  
25 o8·:·NumberedVerticalList25 o8·:·NumberedVerticalList
  
26 i9·:·check·oo26 i9·:·check·oo
27 ·--·capturing·check(0,·"FirstPackage")········--·.115759s·elapsed27 ·--·capturing·check(0,·"FirstPackage")········--·.391343s·elapsed
28 ·--·capturing·check(1,·"FirstPackage")········--·.115056s·elapsed28 ·--·capturing·check(1,·"FirstPackage")········--·.360842s·elapsed
  
29 i10·:·tests·"FirstPackage"29 i10·:·tests·"FirstPackage"
  
30 o10·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}30 o10·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}
31 ······{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}31 ······{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}
  
32 o10·:·NumberedVerticalList32 o10·:·NumberedVerticalList
  
33 i11·:·check·133 i11·:·check·1
34 ·--·capturing·check(1,·"FirstPackage")········--·.111649s·elapsed34 ·--·capturing·check(1,·"FirstPackage")········--·.445743s·elapsed
  
35 i12·:·35 i12·:·
988 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_communicating_spwith_spprograms.out
    
Offset 1, 26 lines modifiedOffset 1, 26 lines modified
1 --·-*-·M2-comint·-*-·hash:·109865180196083357191 --·-*-·M2-comint·-*-·hash:·10986518019608335719
  
2 i1·:·run·"uname·-a"2 i1·:·run·"uname·-a"
3 Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.140-1·(2025-05-22)·x86_64·GNU/Linux3 Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux
  
4 o1·=·04 o1·=·0
  
5 i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close5 i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close
6 ·ba·6 ·ba·
7 ·ad·7 ·ad·
  
8 o2·=·!grep·a8 o2·=·!grep·a
  
9 o2·:·File9 o2·:·File
  
10 i3·:·peek·get·"!uname·-a"10 i3·:·peek·get·"!uname·-a"
  
11 o3·=·"Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian11 o3·=·"Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC
12 ·····6.1.140-1·(2025-05-22)·x86_64·GNU/Linux\n"12 ·····Debian·6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux\n"
  
13 i4·:·f·=·openInOut·"!egrep·'^in'"13 i4·:·f·=·openInOut·"!egrep·'^in'"
  
14 o4·=·!egrep·'^in'14 o4·=·!egrep·'^in'
  
15 o4·:·File15 o4·:·File
  
1.32 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_computing_sp__Groebner_spbases.out
    
Offset 126, 15 lines modifiedOffset 126, 15 lines modified
  
126 ················ZZ126 ················ZZ
127 o23·:·Ideal·of·----[x..z,·w]127 o23·:·Ideal·of·----[x..z,·w]
128 ···············1277128 ···············1277
  
129 i24·:·gb·I129 i24·:·gb·I
  
130 ···--·registering·gb·5·at·0x7fd41f6061c0130 ···--·registering·gb·5·at·0x7f82257de1c0
  
131 ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4131 ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4
132 ···--·number·of·monomials················=·8132 ···--·number·of·monomials················=·8
133 ···--·#reduction·steps·=·2133 ···--·#reduction·steps·=·2
134 ···--·#spairs·done·=·6134 ···--·#spairs·done·=·6
135 ···--·ncalls·=·0135 ···--·ncalls·=·0
136 ···--·nloop·=·0136 ···--·nloop·=·0
Offset 177, 15 lines modifiedOffset 177, 15 lines modified
  
177 i32·:·f·=·random(R^1,R^{-3,-3,-5,-6});177 i32·:·f·=·random(R^1,R^{-3,-3,-5,-6});
  
178 ··············1······4178 ··············1······4
179 o32·:·Matrix·R··<--·R179 o32·:·Matrix·R··<--·R
  
180 i33·:·time·betti·gb·f180 i33·:·time·betti·gb·f
181 ·--·used·0.140209s·(cpu);·0.138647s·(thread);·0s·(gc)181 ·--·used·0.224213s·(cpu);·0.223398s·(thread);·0s·(gc)
  
182 ·············0··1182 ·············0··1
183 o33·=·total:·1·53183 o33·=·total:·1·53
184 ··········0:·1··.184 ··········0:·1··.
185 ··········1:·.··.185 ··········1:·.··.
186 ··········2:·.··2186 ··········2:·.··2
187 ··········3:·.··1187 ··········3:·.··1
Offset 208, 15 lines modifiedOffset 208, 15 lines modified
  
208 ············3····5·····8·····9····12·····14····17208 ············3····5·····8·····9····12·····14····17
209 o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T209 o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T
  
210 o35·:·ZZ[T]210 o35·:·ZZ[T]
  
211 i36·:·time·betti·gb·f211 i36·:·time·betti·gb·f
212 ·--·used·0.000929549s·(cpu);·0.00282705s·(thread);·0s·(gc)212 ·--·used·0.000680076s·(cpu);·0.00277309s·(thread);·0s·(gc)
  
213 ·············0··1213 ·············0··1
214 o36·=·total:·1·53214 o36·=·total:·1·53
215 ··········0:·1··.215 ··········0:·1··.
216 ··········1:·.··.216 ··········1:·.··.
217 ··········2:·.··2217 ··········2:·.··2
218 ··········3:·.··1218 ··········3:·.··1
3.04 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_copy__Directory_lp__String_cm__String_rp.out
    
Offset 1, 76 lines modifiedOffset 1, 76 lines modified
1 --·-*-·M2-comint·-*-·hash:·114227932945643102731 --·-*-·M2-comint·-*-·hash:·11422793294564310273
  
2 i1·:·src·=·temporaryFileName()·|·"/"2 i1·:·src·=·temporaryFileName()·|·"/"
  
3 o1·=·/tmp/M2-1083836-0/0/3 o1·=·/tmp/M2-1017254-0/0/
  
4 i2·:·dst·=·temporaryFileName()·|·"/"4 i2·:·dst·=·temporaryFileName()·|·"/"
  
5 o2·=·/tmp/M2-1083836-0/1/5 o2·=·/tmp/M2-1017254-0/1/
  
6 i3·:·makeDirectory·(src|"a/")6 i3·:·makeDirectory·(src|"a/")
  
7 o3·=·/tmp/M2-1083836-0/0/a/7 o3·=·/tmp/M2-1017254-0/0/a/
  
8 i4·:·makeDirectory·(src|"b/")8 i4·:·makeDirectory·(src|"b/")
  
9 o4·=·/tmp/M2-1083836-0/0/b/9 o4·=·/tmp/M2-1017254-0/0/b/
  
10 i5·:·makeDirectory·(src|"b/c/")10 i5·:·makeDirectory·(src|"b/c/")
  
11 o5·=·/tmp/M2-1083836-0/0/b/c/11 o5·=·/tmp/M2-1017254-0/0/b/c/
  
12 i6·:·src|"a/f"·<<·"hi·there"·<<·close12 i6·:·src|"a/f"·<<·"hi·there"·<<·close
  
13 o6·=·/tmp/M2-1083836-0/0/a/f13 o6·=·/tmp/M2-1017254-0/0/a/f
  
14 o6·:·File14 o6·:·File
  
15 i7·:·src|"a/g"·<<·"hi·there"·<<·close15 i7·:·src|"a/g"·<<·"hi·there"·<<·close
  
16 o7·=·/tmp/M2-1083836-0/0/a/g16 o7·=·/tmp/M2-1017254-0/0/a/g
  
17 o7·:·File17 o7·:·File
  
18 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close18 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close
  
19 o8·=·/tmp/M2-1083836-0/0/b/c/g19 o8·=·/tmp/M2-1017254-0/0/b/c/g
  
20 o8·:·File20 o8·:·File
  
21 i9·:·stack·findFiles·src21 i9·:·stack·findFiles·src
  
22 o9·=·/tmp/M2-1083836-0/0/22 o9·=·/tmp/M2-1017254-0/0/
23 ·····/tmp/M2-1083836-0/0/b/23 ·····/tmp/M2-1017254-0/0/b/
24 ·····/tmp/M2-1083836-0/0/b/c/24 ·····/tmp/M2-1017254-0/0/b/c/
25 ·····/tmp/M2-1083836-0/0/b/c/g25 ·····/tmp/M2-1017254-0/0/b/c/g
26 ·····/tmp/M2-1083836-0/0/a/26 ·····/tmp/M2-1017254-0/0/a/
27 ·····/tmp/M2-1083836-0/0/a/f 
28 ·····/tmp/M2-1083836-0/0/a/g27 ·····/tmp/M2-1017254-0/0/a/g
 28 ·····/tmp/M2-1017254-0/0/a/f
  
29 i10·:·copyDirectory(src,dst,Verbose=>true)29 i10·:·copyDirectory(src,dst,Verbose=>true)
30 ·--·copying:·/tmp/M2-1083836-0/0/b/c/g·->·/tmp/M2-1083836-0/1/b/c/g30 ·--·copying:·/tmp/M2-1017254-0/0/b/c/g·->·/tmp/M2-1017254-0/1/b/c/g
31 ·--·copying:·/tmp/M2-1083836-0/0/a/f·->·/tmp/M2-1083836-0/1/a/f 
32 ·--·copying:·/tmp/M2-1083836-0/0/a/g·->·/tmp/M2-1083836-0/1/a/g31 ·--·copying:·/tmp/M2-1017254-0/0/a/g·->·/tmp/M2-1017254-0/1/a/g
 32 ·--·copying:·/tmp/M2-1017254-0/0/a/f·->·/tmp/M2-1017254-0/1/a/f
  
33 i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true)33 i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true)
34 ·--·skipping:·/tmp/M2-1083836-0/0/b/c/g·not·newer·than·/tmp/M2-1083836-0/1/b/c/g34 ·--·skipping:·/tmp/M2-1017254-0/0/b/c/g·not·newer·than·/tmp/M2-1017254-0/1/b/c/g
35 ·--·skipping:·/tmp/M2-1083836-0/0/a/f·not·newer·than·/tmp/M2-1083836-0/1/a/f 
36 ·--·skipping:·/tmp/M2-1083836-0/0/a/g·not·newer·than·/tmp/M2-1083836-0/1/a/g35 ·--·skipping:·/tmp/M2-1017254-0/0/a/g·not·newer·than·/tmp/M2-1017254-0/1/a/g
 36 ·--·skipping:·/tmp/M2-1017254-0/0/a/f·not·newer·than·/tmp/M2-1017254-0/1/a/f
  
37 i12·:·stack·findFiles·dst37 i12·:·stack·findFiles·dst
  
38 o12·=·/tmp/M2-1083836-0/1/38 o12·=·/tmp/M2-1017254-0/1/
39 ······/tmp/M2-1083836-0/1/b/39 ······/tmp/M2-1017254-0/1/b/
40 ······/tmp/M2-1083836-0/1/b/c/40 ······/tmp/M2-1017254-0/1/b/c/
41 ······/tmp/M2-1083836-0/1/b/c/g41 ······/tmp/M2-1017254-0/1/b/c/g
42 ······/tmp/M2-1083836-0/1/a/42 ······/tmp/M2-1017254-0/1/a/
43 ······/tmp/M2-1083836-0/1/a/f 
44 ······/tmp/M2-1083836-0/1/a/g43 ······/tmp/M2-1017254-0/1/a/g
 44 ······/tmp/M2-1017254-0/1/a/f
  
45 i13·:·get·(dst|"b/c/g")45 i13·:·get·(dst|"b/c/g")
  
46 o13·=·ho·there46 o13·=·ho·there
  
47 i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d47 i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d
  
1.24 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_copy__File_lp__String_cm__String_rp.out
    
Offset 1, 41 lines modifiedOffset 1, 41 lines modified
1 --·-*-·M2-comint·-*-·hash:·115394754201557751101 --·-*-·M2-comint·-*-·hash:·11539475420155775110
  
2 i1·:·src·=·temporaryFileName()2 i1·:·src·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1083285-0/03 o1·=·/tmp/M2-997314-0/0
  
4 i2·:·dst·=·temporaryFileName()4 i2·:·dst·=·temporaryFileName()
  
5 o2·=·/tmp/M2-1083285-0/15 o2·=·/tmp/M2-997314-0/1
  
6 i3·:·src·<<·"hi·there"·<<·close6 i3·:·src·<<·"hi·there"·<<·close
  
7 o3·=·/tmp/M2-1083285-0/07 o3·=·/tmp/M2-997314-0/0
  
8 o3·:·File8 o3·:·File
  
9 i4·:·copyFile(src,dst,Verbose=>true)9 i4·:·copyFile(src,dst,Verbose=>true)
10 ·--·copying:·/tmp/M2-1083285-0/0·->·/tmp/M2-1083285-0/110 ·--·copying:·/tmp/M2-997314-0/0·->·/tmp/M2-997314-0/1
  
11 i5·:·get·dst11 i5·:·get·dst
  
12 o5·=·hi·there12 o5·=·hi·there
  
13 i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)13 i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)
14 ·--·skipping:·/tmp/M2-1083285-0/0·not·newer·than·/tmp/M2-1083285-0/114 ·--·skipping:·/tmp/M2-997314-0/0·not·newer·than·/tmp/M2-997314-0/1
  
15 i7·:·src·<<·"ho·there"·<<·close15 i7·:·src·<<·"ho·there"·<<·close
  
16 o7·=·/tmp/M2-1083285-0/016 o7·=·/tmp/M2-997314-0/0
  
17 o7·:·File17 o7·:·File
  
18 i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)18 i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)
19 ·--·skipping:·/tmp/M2-1083285-0/0·not·newer·than·/tmp/M2-1083285-0/119 ·--·skipping:·/tmp/M2-997314-0/0·not·newer·than·/tmp/M2-997314-0/1
  
20 i9·:·get·dst20 i9·:·get·dst
  
21 o9·=·hi·there21 o9·=·hi·there
  
22 i10·:·removeFile·src22 i10·:·removeFile·src
  
549 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_cpu__Time.out
    
Offset 1, 23 lines modifiedOffset 1, 23 lines modified
1 --·-*-·M2-comint·-*-·hash:·155081537832322324531 --·-*-·M2-comint·-*-·hash:·15508153783232232453
  
2 i1·:·t1·=·cpuTime()2 i1·:·t1·=·cpuTime()
  
3 o1·=·271.9705256093 o1·=·274.517090533
  
4 o1·:·RR·(of·precision·53)4 o1·:·RR·(of·precision·53)
  
5 i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;5 i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;
  
6 i3·:·t2·=·cpuTime()6 i3·:·t2·=·cpuTime()
  
7 o3·=·272.9311938547 o3·=·275.549827006
  
8 o3·:·RR·(of·precision·53)8 o3·:·RR·(of·precision·53)
  
9 i4·:·t2-t19 i4·:·t2-t1
  
10 o4·=·.960668245000022110 o4·=·1.032736473
  
11 o4·:·RR·(of·precision·53)11 o4·:·RR·(of·precision·53)
  
12 i5·:·12 i5·:·
611 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_current__Time.out
    
Offset 1, 24 lines modifiedOffset 1, 24 lines modified
1 --·-*-·M2-comint·-*-·hash:·36608394761079672591 --·-*-·M2-comint·-*-·hash:·3660839476107967259
  
2 i1·:·currentTime()2 i1·:·currentTime()
  
3 o1·=·17492072983 o1·=·1783629092
  
4 i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·)4 i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·)
  
5 o2·=·55.430172660528195 o2·=·56.52095588952952
  
6 o2·:·RR·(of·precision·53)6 o2·:·RR·(of·precision·53)
  
7 i3·:·12·*·(oo·-·floor·oo)7 i3·:·12·*·(oo·-·floor·oo)
  
8 o3·=·5.1620719263382288 o3·=·6.251470674354209
  
9 o3·:·RR·(of·precision·53)9 o3·:·RR·(of·precision·53)
  
10 i4·:·run·"date"10 i4·:·run·"date"
11 Thu·Jun··5·22:54:58·-12·202511 Fri·Jul·10·10:31:32·+14·2026
  
12 o4·=·012 o4·=·0
  
13 i5·:·13 i5·:·
293 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_elapsed__Time.out
    
Offset 1, 8 lines modifiedOffset 1, 8 lines modified
1 --·-*-·M2-comint·-*-·hash:·13305659580251 --·-*-·M2-comint·-*-·hash:·1330565958025
  
2 i1·:·elapsedTime·sleep·12 i1·:·elapsedTime·sleep·1
3 ·--·1.00016s·elapsed3 ·--·1.00515s·elapsed
  
4 o1·=·04 o1·=·0
  
5 i2·:·5 i2·:·
390 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_elapsed__Timing.out
    
Offset 1, 14 lines modifiedOffset 1, 14 lines modified
1 --·-*-·M2-comint·-*-·hash:·17311068032072987151 --·-*-·M2-comint·-*-·hash:·1731106803207298715
  
2 i1·:·elapsedTiming·sleep·12 i1·:·elapsedTiming·sleep·1
  
3 o1·=·03 o1·=·0
4 ·····--·1.00015·seconds4 ·····--·1.00411·seconds
  
5 o1·:·Time5 o1·:·Time
  
6 i2·:·peek·oo6 i2·:·peek·oo
  
7 o2·=·Time{1.00015,·0}7 o2·=·Time{1.00411,·0}
  
8 i3·:·8 i3·:·
4.01 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_elimination_spof_spvariables.out
    
Offset 6, 15 lines modifiedOffset 6, 15 lines modified
  
6 ···············3···················3·····2···············36 ···············3···················3·····2···············3
7 o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z)7 o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z)
  
8 o2·:·Ideal·of·R8 o2·:·Ideal·of·R
  
9 i3·:·time·leadTerm·gens·gb·I9 i3·:·time·leadTerm·gens·gb·I
10 ·--·used·0.103026s·(cpu);·0.103026s·(thread);·0s·(gc)10 ·--·used·0.114498s·(cpu);·0.114348s·(thread);·0s·(gc)
  
11 o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy411 o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4
12 ·····------------------------------------------------------------------------12 ·····------------------------------------------------------------------------
13 ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z213 ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2
14 ·····------------------------------------------------------------------------14 ·····------------------------------------------------------------------------
15 ·····267076255345488270sy3z4·5256861933965245618410txyz615 ·····267076255345488270sy3z4·5256861933965245618410txyz6
16 ·····------------------------------------------------------------------------16 ·····------------------------------------------------------------------------
Offset 85, 15 lines modifiedOffset 85, 15 lines modified
  
85 ···············3···················3·····2···············385 ···············3···················3·····2···············3
86 o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z)86 o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z)
  
87 o7·:·Ideal·of·R87 o7·:·Ideal·of·R
  
88 i8·:·time·G·=·eliminate(I,{s,t})88 i8·:·time·G·=·eliminate(I,{s,t})
89 ·--·used·0.313091s·(cpu);·0.134462s·(thread);·0s·(gc)89 ·--·used·0.284413s·(cpu);·0.136539s·(thread);·0s·(gc)
  
90 ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···90 ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···
91 o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+91 o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+
92 ·····------------------------------------------------------------------------92 ·····------------------------------------------------------------------------
93 ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·93 ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·
94 ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z94 ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z
95 ·····------------------------------------------------------------------------95 ·····------------------------------------------------------------------------
Offset 154, 15 lines modifiedOffset 154, 15 lines modified
154 i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}];154 i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}];
  
155 i11·:·I1·=·substitute(I,R1);155 i11·:·I1·=·substitute(I,R1);
  
156 o11·:·Ideal·of·R1156 o11·:·Ideal·of·R1
  
157 i12·:·time·G·=·eliminate(I1,{s,t})157 i12·:·time·G·=·eliminate(I1,{s,t})
158 ·--·used·0.0276051s·(cpu);·0.0276072s·(thread);·0s·(gc)158 ·--·used·0.0290221s·(cpu);·0.0290301s·(thread);·0s·(gc)
  
159 ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7··159 ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7··
160 o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··-160 o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··-
161 ······-----------------------------------------------------------------------161 ······-----------------------------------------------------------------------
162 ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2··162 ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2··
163 ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··-163 ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··-
164 ······-----------------------------------------------------------------------164 ······-----------------------------------------------------------------------
Offset 228, 15 lines modifiedOffset 228, 15 lines modified
  
228 ···················3·············3·····2·········3228 ···················3·············3·····2·········3
229 o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·})229 o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·})
  
230 o16·:·RingMap·A·<--·B230 o16·:·RingMap·A·<--·B
  
231 i17·:·time·G·=·kernel·F231 i17·:·time·G·=·kernel·F
232 ·--·used·0.0903451s·(cpu);·0.0901412s·(thread);·0s·(gc)232 ·--·used·0.0957037s·(cpu);·0.0955438s·(thread);·0s·(gc)
  
233 ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···233 ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···
234 o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+234 o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+
235 ······-----------------------------------------------------------------------235 ······-----------------------------------------------------------------------
236 ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·236 ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·
237 ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z237 ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z
238 ······-----------------------------------------------------------------------238 ······-----------------------------------------------------------------------
Offset 297, 23 lines modifiedOffset 297, 23 lines modified
297 i19·:·use·ring·I297 i19·:·use·ring·I
  
298 o19·=·R298 o19·=·R
  
299 o19·:·PolynomialRing299 o19·:·PolynomialRing
  
300 i20·:·time·f1·=·resultant(I_0,I_2,s)300 i20·:·time·f1·=·resultant(I_0,I_2,s)
301 ·--·used·0.00138135s·(cpu);·0.00137906s·(thread);·0s·(gc)301 ·--·used·0.00152956s·(cpu);·0.00152337s·(thread);·0s·(gc)
  
302 ·········9····9······7····3302 ·········9····9······7····3
303 o20·=·x*t··-·t··-·z*t··-·z303 o20·=·x*t··-·t··-·z*t··-·z
  
304 o20·:·R304 o20·:·R
  
305 i21·:·time·f2·=·resultant(I_1,f1,t)305 i21·:·time·f2·=·resultant(I_1,f1,t)
306 ·--·used·0.235795s·(cpu);·0.0644657s·(thread);·0s·(gc)306 ·--·used·0.199214s·(cpu);·0.0630954s·(thread);·0s·(gc)
  
307 ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2··307 ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2··
308 o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+308 o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+
309 ······-----------------------------------------------------------------------309 ······-----------------------------------------------------------------------
310 ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8···310 ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8···
311 ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+311 ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+
312 ······-----------------------------------------------------------------------312 ······-----------------------------------------------------------------------
870 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_end__Package.out
    
Offset 59, 15 lines modifiedOffset 59, 15 lines modified
59 ····································Version·=>·0.059 ····································Version·=>·0.0
60 ·············package·prefix·=>·/usr/60 ·············package·prefix·=>·/usr/
61 ·············PackageIsLoaded·=>·true61 ·············PackageIsLoaded·=>·true
62 ·············pkgname·=>·Foo62 ·············pkgname·=>·Foo
63 ·············private·dictionary·=>·Foo#"private·dictionary"63 ·············private·dictionary·=>·Foo#"private·dictionary"
64 ·············processed·documentation·=>·MutableHashTable{}64 ·············processed·documentation·=>·MutableHashTable{}
65 ·············raw·documentation·=>·MutableHashTable{}65 ·············raw·documentation·=>·MutableHashTable{}
66 ·············source·directory·=>·/tmp/M2-1075204-0/91-rundir/66 ·············source·directory·=>·/tmp/M2-980911-0/91-rundir/
67 ·············source·file·=>·stdio67 ·············source·file·=>·stdio
68 ·············test·inputs·=>·MutableList{}68 ·············test·inputs·=>·MutableList{}
  
69 i7·:·dictionaryPath69 i7·:·dictionaryPath
  
70 o7·=·{Foo.Dictionary,·Varieties.Dictionary,·Isomorphism.Dictionary,70 o7·=·{Foo.Dictionary,·Varieties.Dictionary,·Isomorphism.Dictionary,
71 ·····------------------------------------------------------------------------71 ·····------------------------------------------------------------------------
467 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_file__Exists.out
    
Offset 1, 20 lines modifiedOffset 1, 20 lines modified
1 --·-*-·M2-comint·-*-·hash:·74750389365702248991 --·-*-·M2-comint·-*-·hash:·7475038936570224899
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1079473-0/03 o1·=·/tmp/M2-986105-0/0
  
4 i2·:·fileExists·fn4 i2·:·fileExists·fn
  
5 o2·=·false5 o2·=·false
  
6 i3·:·fn·<<·"hi·there"·<<·close6 i3·:·fn·<<·"hi·there"·<<·close
  
7 o3·=·/tmp/M2-1079473-0/07 o3·=·/tmp/M2-986105-0/0
  
8 o3·:·File8 o3·:·File
  
9 i4·:·fileExists·fn9 i4·:·fileExists·fn
  
10 o4·=·true10 o4·=·true
  
580 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_file__Length.out
    
Offset 1, 28 lines modifiedOffset 1, 28 lines modified
1 --·-*-·M2-comint·-*-·hash:·12166954471952379941 --·-*-·M2-comint·-*-·hash:·1216695447195237994
  
2 i1·:·f·=·temporaryFileName()·<<·"hi·there"2 i1·:·f·=·temporaryFileName()·<<·"hi·there"
  
3 o1·=·/tmp/M2-1101145-0/03 o1·=·/tmp/M2-1059327-0/0
  
4 o1·:·File4 o1·:·File
  
5 i2·:·fileLength·f5 i2·:·fileLength·f
  
6 o2·=·86 o2·=·8
  
7 i3·:·close·f7 i3·:·close·f
  
8 o3·=·/tmp/M2-1101145-0/08 o3·=·/tmp/M2-1059327-0/0
  
9 o3·:·File9 o3·:·File
  
10 i4·:·filename·=·toString·f10 i4·:·filename·=·toString·f
  
11 o4·=·/tmp/M2-1101145-0/011 o4·=·/tmp/M2-1059327-0/0
  
12 i5·:·fileLength·filename12 i5·:·fileLength·filename
  
13 o5·=·813 o5·=·8
  
14 i6·:·get·filename14 i6·:·get·filename
  
557 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_file__Mode_lp__File_rp.out
    
Offset 1, 25 lines modifiedOffset 1, 25 lines modified
1 --·-*-·M2-comint·-*-·hash:·112021406211239936331 --·-*-·M2-comint·-*-·hash:·11202140621123993633
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1084758-0/03 o1·=·/tmp/M2-1040725-0/0
  
4 i2·:·f·=·fn·<<·"hi·there"4 i2·:·f·=·fn·<<·"hi·there"
  
5 o2·=·/tmp/M2-1084758-0/05 o2·=·/tmp/M2-1040725-0/0
  
6 o2·:·File6 o2·:·File
  
7 i3·:·fileMode·f7 i3·:·fileMode·f
  
8 o3·=·4208 o3·=·420
  
9 i4·:·close·f9 i4·:·close·f
  
10 o4·=·/tmp/M2-1084758-0/010 o4·=·/tmp/M2-1040725-0/0
  
11 o4·:·File11 o4·:·File
  
12 i5·:·removeFile·fn12 i5·:·removeFile·fn
  
13 i6·:·13 i6·:·
452 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_file__Mode_lp__String_rp.out
    
Offset 1, 16 lines modifiedOffset 1, 16 lines modified
1 --·-*-·M2-comint·-*-·hash:·47825702021974645321 --·-*-·M2-comint·-*-·hash:·4782570202197464532
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1083316-0/03 o1·=·/tmp/M2-997476-0/0
  
4 i2·:·fn·<<·"hi·there"·<<·close4 i2·:·fn·<<·"hi·there"·<<·close
  
5 o2·=·/tmp/M2-1083316-0/05 o2·=·/tmp/M2-997476-0/0
  
6 o2·:·File6 o2·:·File
  
7 i3·:·fileMode·fn7 i3·:·fileMode·fn
  
8 o3·=·4208 o3·=·420
  
636 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_file__Mode_lp__Z__Z_cm__File_rp.out
    
Offset 1, 16 lines modifiedOffset 1, 16 lines modified
1 --·-*-·M2-comint·-*-·hash:·174738782678455754421 --·-*-·M2-comint·-*-·hash:·17473878267845575442
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1083073-0/03 o1·=·/tmp/M2-996452-0/0
  
4 i2·:·f·=·fn·<<·"hi·there"4 i2·:·f·=·fn·<<·"hi·there"
  
5 o2·=·/tmp/M2-1083073-0/05 o2·=·/tmp/M2-996452-0/0
  
6 o2·:·File6 o2·:·File
  
7 i3·:·m·=·7·+·7*8·+·7*647 i3·:·m·=·7·+·7*8·+·7*64
  
8 o3·=·5118 o3·=·511
  
Offset 18, 15 lines modifiedOffset 18, 15 lines modified
  
18 i5·:·fileMode·f18 i5·:·fileMode·f
  
19 o5·=·51119 o5·=·511
  
20 i6·:·close·f20 i6·:·close·f
  
21 o6·=·/tmp/M2-1083073-0/021 o6·=·/tmp/M2-996452-0/0
  
22 o6·:·File22 o6·:·File
  
23 i7·:·fileMode·fn23 i7·:·fileMode·fn
  
24 o7·=·51124 o7·=·511
  
477 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_file__Mode_lp__Z__Z_cm__String_rp.out
    
Offset 1, 16 lines modifiedOffset 1, 16 lines modified
1 --·-*-·M2-comint·-*-·hash:·167727843907993347231 --·-*-·M2-comint·-*-·hash:·16772784390799334723
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1095448-0/03 o1·=·/tmp/M2-1056337-0/0
  
4 i2·:·fn·<<·"hi·there"·<<·close4 i2·:·fn·<<·"hi·there"·<<·close
  
5 o2·=·/tmp/M2-1095448-0/05 o2·=·/tmp/M2-1056337-0/0
  
6 o2·:·File6 o2·:·File
  
7 i3·:·m·=·fileMode·fn7 i3·:·m·=·fileMode·fn
  
8 o3·=·4208 o3·=·420
  
263 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_file__Time.out
    
Offset 1, 7 lines modifiedOffset 1, 7 lines modified
1 --·-*-·M2-comint·-*-·hash:·13313107110751 --·-*-·M2-comint·-*-·hash:·1331310711075
  
2 i1·:·currentTime()·-·fileTime·"."2 i1·:·currentTime()·-·fileTime·"."
  
3 o1·=·403 o1·=·112
  
4 i2·:·4 i2·:·
640 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_force__G__B_lp..._cm__Syzygy__Matrix_eq_gt..._rp.out
    
Offset 29, 15 lines modifiedOffset 29, 15 lines modified
29 ·····{4}·|·0·····x2-3··y3-1··|29 ·····{4}·|·0·····x2-3··y3-1··|
  
30 ·············3······330 ·············3······3
31 o6·:·Matrix·R··<--·R31 o6·:·Matrix·R··<--·R
  
32 i7·:·syz·f32 i7·:·syz·f
  
33 ···--·registering·gb·0·at·0x7f83660f6a8033 ···--·registering·gb·0·at·0x7f45a0acda80
  
34 ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·334 ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3
35 ···--·number·of·monomials················=·935 ···--·number·of·monomials················=·9
36 ···--·#reduction·steps·=·636 ···--·#reduction·steps·=·6
37 ···--·#spairs·done·=·637 ···--·#spairs·done·=·6
38 ···--·ncalls·=·038 ···--·ncalls·=·0
39 ···--·nloop·=·039 ···--·nloop·=·0
295 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_get.out
    
Offset 10, 11 lines modifiedOffset 10, 11 lines modified
  
10 o2·=·hi·there10 o2·=·hi·there
  
11 i3·:·removeFile·"test-file"11 i3·:·removeFile·"test-file"
  
12 i4·:·get·"!date"12 i4·:·get·"!date"
  
13 o4·=·Thu·Jun··5·22:54:30·-12·202513 o4·=·Fri·Jul·10·10:30:33·+14·2026
  
  
14 i5·:·14 i5·:·
254 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_group__I__D.out
    
Offset 1, 7 lines modifiedOffset 1, 7 lines modified
1 --·-*-·M2-comint·-*-·hash:·13309756143231 --·-*-·M2-comint·-*-·hash:·1330975614323
  
2 i1·:·groupID()2 i1·:·groupID()
  
3 o1·=·10362373 o1·=·732624
  
4 i2·:·4 i2·:·
351 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_is__Canceled_lp__Task_rp.out
    
Offset 2, 15 lines modifiedOffset 2, 15 lines modified
  
2 i1·:·n·=·02 i1·:·n·=·0
  
3 o1·=·03 o1·=·0
  
4 i2·:·t·=·schedule(()·->·while·true·do·n·=·n·+·1)4 i2·:·t·=·schedule(()·->·while·true·do·n·=·n·+·1)
  
5 o2·=·<<task,·created>>5 o2·=·<<task,·running>>
  
6 o2·:·Task6 o2·:·Task
  
7 i3·:·sleep·17 i3·:·sleep·1
  
8 o3·=·08 o3·=·0
  
424 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_is__Directory.out
    
Offset 2, 19 lines modifiedOffset 2, 19 lines modified
  
2 i1·:·isDirectory·"."2 i1·:·isDirectory·"."
  
3 o1·=·true3 o1·=·true
  
4 i2·:·fn·=·temporaryFileName()4 i2·:·fn·=·temporaryFileName()
  
5 o2·=·/tmp/M2-1076282-0/05 o2·=·/tmp/M2-984625-0/0
  
6 i3·:·fn·<<·"hi·there"·<<·close6 i3·:·fn·<<·"hi·there"·<<·close
  
7 o3·=·/tmp/M2-1076282-0/07 o3·=·/tmp/M2-984625-0/0
  
8 o3·:·File8 o3·:·File
  
9 i4·:·isDirectory·fn9 i4·:·isDirectory·fn
  
10 o4·=·false10 o4·=·false
  
848 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_is__Pseudoprime_lp__Z__Z_rp.out
    
Offset 75, 15 lines modifiedOffset 75, 15 lines modified
75 o17·=·false75 o17·=·false
  
76 i18·:·isPrime(m*m*m1*m1*m2^6)76 i18·:·isPrime(m*m*m1*m1*m2^6)
  
77 o18·=·false77 o18·=·false
  
78 i19·:·elapsedTime·facs·=·factor(m*m1)78 i19·:·elapsedTime·facs·=·factor(m*m1)
79 ·--·4.05952s·elapsed79 ·--·16.2161s·elapsed
  
80 o19·=·1000000000000000000000000000057*100000000000000000001000000008380 o19·=·1000000000000000000000000000057*1000000000000000000010000000083
  
81 o19·:·Expression·of·class·Product81 o19·:·Expression·of·class·Product
  
82 i20·:·facs·=·facs//toList/toList82 i20·:·facs·=·facs//toList/toList
  
Offset 97, 17 lines modifiedOffset 97, 17 lines modified
  
97 i22·:·m3·=·nextPrime·(m^3)97 i22·:·m3·=·nextPrime·(m^3)
  
98 o22·=·1000000000000000000000000000171000000000000000000000000009747000000000098 o22·=·10000000000000000000000000001710000000000000000000000000097470000000000
99 ······0000000000000018561399 ······00000000000000185613
  
100 i23·:·elapsedTime·isPrime·m3100 i23·:·elapsedTime·isPrime·m3
101 ·--·.0614478s·elapsed101 ·--·.124756s·elapsed
  
102 o23·=·true102 o23·=·true
  
103 i24·:·elapsedTime·isPseudoprime·m3103 i24·:·elapsedTime·isPseudoprime·m3
104 ·--·.000133883s·elapsed104 ·--·.000143308s·elapsed
  
105 o24·=·true105 o24·=·true
  
106 i25·:·106 i25·:·
446 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_is__Regular__File.out
    
Offset 1, 16 lines modifiedOffset 1, 16 lines modified
1 --·-*-·M2-comint·-*-·hash:·47822052457580536291 --·-*-·M2-comint·-*-·hash:·4782205245758053629
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1101217-0/03 o1·=·/tmp/M2-1060387-0/0
  
4 i2·:·fn·<<·"hi·there"·<<·close4 i2·:·fn·<<·"hi·there"·<<·close
  
5 o2·=·/tmp/M2-1101217-0/05 o2·=·/tmp/M2-1060387-0/0
  
6 o2·:·File6 o2·:·File
  
7 i3·:·isRegularFile·fn7 i3·:·isRegularFile·fn
  
8 o3·=·true8 o3·=·true
  
544 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_make__Directory_lp__String_rp.out
    
Offset 1, 16 lines modifiedOffset 1, 16 lines modified
1 --·-*-·M2-comint·-*-·hash:·51133721592045717461 --·-*-·M2-comint·-*-·hash:·5113372159204571746
  
2 i1·:·dir·=·temporaryFileName()2 i1·:·dir·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1082841-0/03 o1·=·/tmp/M2-994788-0/0
  
4 i2·:·makeDirectory·(dir|"/a/b/c")4 i2·:·makeDirectory·(dir|"/a/b/c")
  
5 o2·=·/tmp/M2-1082841-0/0/a/b/c5 o2·=·/tmp/M2-994788-0/0/a/b/c
  
6 i3·:·removeDirectory·(dir|"/a/b/c")6 i3·:·removeDirectory·(dir|"/a/b/c")
  
7 i4·:·removeDirectory·(dir|"/a/b")7 i4·:·removeDirectory·(dir|"/a/b")
  
8 i5·:·removeDirectory·(dir|"/a")8 i5·:·removeDirectory·(dir|"/a")
  
812 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_memoize.out
    
Offset 3, 31 lines modifiedOffset 3, 31 lines modified
3 i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2)3 i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2)
  
4 o1·=·fib4 o1·=·fib
  
5 o1·:·FunctionClosure5 o1·:·FunctionClosure
  
6 i2·:·time·fib·286 i2·:·time·fib·28
7 ·--·used·0.871376s·(cpu);·0.561091s·(thread);·0s·(gc)7 ·--·used·0.904923s·(cpu);·0.594351s·(thread);·0s·(gc)
  
8 o2·=·5142298 o2·=·514229
  
9 i3·:·fib·=·memoize·fib9 i3·:·fib·=·memoize·fib
  
10 o3·=·fib10 o3·=·fib
  
11 o3·:·FunctionClosure11 o3·:·FunctionClosure
  
12 i4·:·time·fib·2812 i4·:·time·fib·28
13 ·--·used·6.1743e-05s·(cpu);·6.007e-05s·(thread);·0s·(gc)13 ·--·used·6.409e-05s·(cpu);·6.9e-05s·(thread);·0s·(gc)
  
14 o4·=·51422914 o4·=·514229
  
15 i5·:·time·fib·2815 i5·:·time·fib·28
16 ·--·used·1.482e-06s·(cpu);·1.382e-06s·(thread);·0s·(gc)16 ·--·used·7.034e-06s·(cpu);·4.98e-06s·(thread);·0s·(gc)
  
17 o5·=·51422917 o5·=·514229
  
18 i6·:·fib·=·memoize(·n·->·fib(n-1)·+·fib(n-2)·)18 i6·:·fib·=·memoize(·n·->·fib(n-1)·+·fib(n-2)·)
  
19 o6·=·fib19 o6·=·fib
  
4.18 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_methods.out
    
Offset 17, 20 lines modifiedOffset 17, 20 lines modified
17 ·····{12·=>·(poincare,·BettiTally)································}17 ·····{12·=>·(poincare,·BettiTally)································}
18 ·····{13·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················}18 ·····{13·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················}
19 ·····{14·=>·(degree,·BettiTally)··································}19 ·····{14·=>·(degree,·BettiTally)··································}
20 ·····{15·=>·(hilbertSeries,·ZZ,·BettiTally)·······················}20 ·····{15·=>·(hilbertSeries,·ZZ,·BettiTally)·······················}
21 ·····{16·=>·(pdim,·BettiTally)····································}21 ·····{16·=>·(pdim,·BettiTally)····································}
22 ·····{17·=>·(regularity,·BettiTally)······························}22 ·····{17·=>·(regularity,·BettiTally)······························}
23 ·····{18·=>·(mathML,·BettiTally)··································}23 ·····{18·=>·(mathML,·BettiTally)··································}
24 ·····{19·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)} 
25 ·····{20·=>·(dual,·BettiTally)····································}24 ·····{19·=>·(dual,·BettiTally)····································}
 25 ·····{20·=>·(truncate,·BettiTally,·ZZ,·ZZ)························}
26 ·····{21·=>·(codim,·BettiTally)···································}26 ·····{21·=>·(codim,·BettiTally)···································}
27 ·····{22·=>·(truncate,·BettiTally,·ZZ,·ZZ)························} 
28 ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············}27 ·····{22·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············}
29 ·····{24·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············}28 ·····{23·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············}
 29 ·····{24·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)}
30 ·····{25·=>·(^,·Ring,·BettiTally)·································}30 ·····{25·=>·(^,·Ring,·BettiTally)·································}
  
31 o1·:·NumberedVerticalList31 o1·:·NumberedVerticalList
  
32 i2·:·methods·resolution32 i2·:·methods·resolution
  
33 o2·=·{0·=>·(resolution,·Ideal)·}33 o2·=·{0·=>·(resolution,·Ideal)·}
Offset 61, 19 lines modifiedOffset 61, 19 lines modified
61 ·····{2·=>·(++,·Module,·Module)······}61 ·····{2·=>·(++,·Module,·Module)······}
  
62 o4·:·NumberedVerticalList62 o4·:·NumberedVerticalList
  
63 i5·:·methods(·Matrix,·Matrix·)63 i5·:·methods(·Matrix,·Matrix·)
  
64 o5·=·{0·=>·(contract',·Matrix,·Matrix)···························}64 o5·=·{0·=>·(contract',·Matrix,·Matrix)···························}
65 ·····{1·=>·(diff',·Matrix,·Matrix)·······························} 
66 ·····{2·=>·(diff,·Matrix,·Matrix)································} 
67 ·····{3·=>·(+,·Matrix,·Matrix)···································}65 ·····{1·=>·(+,·Matrix,·Matrix)···································}
 66 ·····{2·=>·(-,·Matrix,·Matrix)···································}
 67 ·····{3·=>·(diff',·Matrix,·Matrix)·······························}
68 ·····{4·=>·(contract,·Matrix,·Matrix)····························}68 ·····{4·=>·(contract,·Matrix,·Matrix)····························}
69 ·····{5·=>·(-,·Matrix,·Matrix)···································}69 ·····{5·=>·(diff,·Matrix,·Matrix)································}
70 ·····{6·=>·(markedGB,·Matrix,·Matrix)····························}70 ·····{6·=>·(markedGB,·Matrix,·Matrix)····························}
71 ·····{7·=>·(Hom,·Matrix,·Matrix)·································}71 ·····{7·=>·(Hom,·Matrix,·Matrix)·································}
72 ·····{8·=>·(==,·Matrix,·Matrix)··································}72 ·····{8·=>·(==,·Matrix,·Matrix)··································}
73 ·····{9·=>·(*,·Matrix,·Matrix)···································}73 ·····{9·=>·(*,·Matrix,·Matrix)···································}
74 ·····{10·=>·(|,·Matrix,·Matrix)··································}74 ·····{10·=>·(|,·Matrix,·Matrix)··································}
75 ·····{11·=>·(||,·Matrix,·Matrix)·································}75 ·····{11·=>·(||,·Matrix,·Matrix)·································}
76 ·····{12·=>·(subquotient,·Matrix,·Matrix)························}76 ·····{12·=>·(subquotient,·Matrix,·Matrix)························}
Offset 88, 18 lines modifiedOffset 88, 18 lines modified
88 ·····{21·=>·(quotient,·Matrix,·Matrix)···························}88 ·····{21·=>·(quotient,·Matrix,·Matrix)···························}
89 ·····{22·=>·(quotient',·Matrix,·Matrix)··························}89 ·····{22·=>·(quotient',·Matrix,·Matrix)··························}
90 ·····{23·=>·(remainder',·Matrix,·Matrix)·························}90 ·····{23·=>·(remainder',·Matrix,·Matrix)·························}
91 ·····{24·=>·(%,·Matrix,·Matrix)··································}91 ·····{24·=>·(%,·Matrix,·Matrix)··································}
92 ·····{25·=>·(remainder,·Matrix,·Matrix)··························}92 ·····{25·=>·(remainder,·Matrix,·Matrix)··························}
93 ·····{26·=>·(pushout,·Matrix,·Matrix)····························}93 ·····{26·=>·(pushout,·Matrix,·Matrix)····························}
94 ·····{27·=>·(solve,·Matrix,·Matrix)······························}94 ·····{27·=>·(solve,·Matrix,·Matrix)······························}
95 ·····{28·=>·(intersect,·Matrix,·Matrix)··························}95 ·····{28·=>·(pullback,·Matrix,·Matrix)···························}
96 ·····{29·=>·(tensor,·Matrix,·Matrix)·····························}96 ·····{29·=>·(tensor,·Matrix,·Matrix)·····························}
97 ·····{30·=>·(pullback,·Matrix,·Matrix)···························} 
98 ·····{31·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)··········}97 ·····{30·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)··········}
 98 ·····{31·=>·(intersect,·Matrix,·Matrix)··························}
99 ·····{32·=>·(substitute,·Matrix,·Matrix)·························}99 ·····{32·=>·(substitute,·Matrix,·Matrix)·························}
100 ·····{33·=>·(yonedaProduct,·Matrix,·Matrix)······················}100 ·····{33·=>·(yonedaProduct,·Matrix,·Matrix)······················}
101 ·····{34·=>·(isShortExactSequence,·Matrix,·Matrix)···············}101 ·····{34·=>·(isShortExactSequence,·Matrix,·Matrix)···············}
102 ·····{35·=>·(horseshoeResolution,·Matrix,·Matrix)················}102 ·····{35·=>·(horseshoeResolution,·Matrix,·Matrix)················}
103 ·····{36·=>·(connectingExtMap,·Module,·Matrix,·Matrix)···········}103 ·····{36·=>·(connectingExtMap,·Module,·Matrix,·Matrix)···········}
104 ·····{37·=>·(connectingExtMap,·Matrix,·Matrix,·Module)···········}104 ·····{37·=>·(connectingExtMap,·Matrix,·Matrix,·Module)···········}
105 ·····{38·=>·(connectingTorMap,·Module,·Matrix,·Matrix)···········}105 ·····{38·=>·(connectingTorMap,·Module,·Matrix,·Matrix)···········}
1.61 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_minimal__Betti.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 i2·:·S·=·ring·I9 i2·:·S·=·ring·I
  
10 o2·=·S10 o2·=·S
  
11 o2·:·PolynomialRing11 o2·:·PolynomialRing
  
12 i3·:·elapsedTime·C·=·minimalBetti·I12 i3·:·elapsedTime·C·=·minimalBetti·I
13 ·--·2.01874s·elapsed13 ·--·3.14153s·elapsed
  
14 ············0··1···2···3···4····5···6···7···8··9·1014 ············0··1···2···3···4····5···6···7···8··9·10
15 o3·=·total:·1·35·140·385·819·1080·819·385·140·35··115 o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1
16 ·········0:·1··.···.···.···.····.···.···.···.··.··.16 ·········0:·1··.···.···.···.····.···.···.···.··.··.
17 ·········1:·.·35·140·189··84····.···.···.···.··.··.17 ·········1:·.·35·140·189··84····.···.···.···.··.··.
18 ·········2:·.··.···.·196·735·1080·735·196···.··.··.18 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
19 ·········3:·.··.···.···.···.····.··84·189·140·35··.19 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 26, 44 lines modifiedOffset 26, 44 lines modified
26 o3·:·BettiTally26 o3·:·BettiTally
  
27 i4·:·I·=·ideal·I_*;27 i4·:·I·=·ideal·I_*;
  
28 o4·:·Ideal·of·S28 o4·:·Ideal·of·S
  
29 i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2)29 i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2)
30 ·--·.787739s·elapsed30 ·--·1.29119s·elapsed
  
31 ············0··1···2···3···4····5···6···731 ············0··1···2···3···4····5···6···7
32 o5·=·total:·1·35·140·385·819·1080·735·19632 o5·=·total:·1·35·140·385·819·1080·735·196
33 ·········0:·1··.···.···.···.····.···.···.33 ·········0:·1··.···.···.···.····.···.···.
34 ·········1:·.·35·140·189··84····.···.···.34 ·········1:·.·35·140·189··84····.···.···.
35 ·········2:·.··.···.·196·735·1080·735·19635 ·········2:·.··.···.·196·735·1080·735·196
  
36 o5·:·BettiTally36 o5·:·BettiTally
  
37 i6·:·I·=·ideal·I_*;37 i6·:·I·=·ideal·I_*;
  
38 o6·:·Ideal·of·S38 o6·:·Ideal·of·S
  
39 i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5)39 i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5)
40 ·--·.0299097s·elapsed40 ·--·.0295357s·elapsed
  
41 ············0··1···2···3··441 ············0··1···2···3··4
42 o7·=·total:·1·35·140·189·8442 o7·=·total:·1·35·140·189·84
43 ·········0:·1··.···.···.··.43 ·········0:·1··.···.···.··.
44 ·········1:·.·35·140·189·8444 ·········1:·.·35·140·189·84
  
45 o7·:·BettiTally45 o7·:·BettiTally
  
46 i8·:·I·=·ideal·I_*;46 i8·:·I·=·ideal·I_*;
  
47 o8·:·Ideal·of·S47 o8·:·Ideal·of·S
  
48 i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5)48 i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5)
49 ·--·1.23548s·elapsed49 ·--·1.76861s·elapsed
  
50 ············0··1···2···3···4····550 ············0··1···2···3···4····5
51 o9·=·total:·1·35·140·385·819·108051 o9·=·total:·1·35·140·385·819·1080
52 ·········0:·1··.···.···.···.····.52 ·········0:·1··.···.···.···.····.
53 ·········1:·.·35·140·189··84····.53 ·········1:·.·35·140·189··84····.
54 ·········2:·.··.···.·196·735·108054 ·········2:·.··.···.·196·735·1080
  
495 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_mkdir.out
    
Offset 1, 22 lines modifiedOffset 1, 22 lines modified
1 --·-*-·M2-comint·-*-·hash:·155552268095099331351 --·-*-·M2-comint·-*-·hash:·15555226809509933135
  
2 i1·:·p·=·temporaryFileName()·|·"/"2 i1·:·p·=·temporaryFileName()·|·"/"
  
3 o1·=·/tmp/M2-1082878-0/0/3 o1·=·/tmp/M2-995497-0/0/
  
4 i2·:·mkdir·p4 i2·:·mkdir·p
  
5 i3·:·isDirectory·p5 i3·:·isDirectory·p
  
6 o3·=·true6 o3·=·true
  
7 i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close7 i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close
  
8 o4·=·/tmp/M2-1082878-0/0/foo8 o4·=·/tmp/M2-995497-0/0/foo
  
9 o4·:·File9 o4·:·File
  
10 i5·:·get·fn10 i5·:·get·fn
  
11 o5·=·hi·there11 o5·=·hi·there
  
938 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_move__File_lp__String_cm__String_rp.out
    
Offset 1, 31 lines modifiedOffset 1, 31 lines modified
1 --·-*-·M2-comint·-*-·hash:·48579440424710932181 --·-*-·M2-comint·-*-·hash:·4857944042471093218
  
2 i1·:·src·=·temporaryFileName()2 i1·:·src·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1081082-0/03 o1·=·/tmp/M2-987774-0/0
  
4 i2·:·dst·=·temporaryFileName()4 i2·:·dst·=·temporaryFileName()
  
5 o2·=·/tmp/M2-1081082-0/15 o2·=·/tmp/M2-987774-0/1
  
6 i3·:·src·<<·"hi·there"·<<·close6 i3·:·src·<<·"hi·there"·<<·close
  
7 o3·=·/tmp/M2-1081082-0/07 o3·=·/tmp/M2-987774-0/0
  
8 o3·:·File8 o3·:·File
  
9 i4·:·moveFile(src,dst,Verbose=>true)9 i4·:·moveFile(src,dst,Verbose=>true)
10 --moving:·/tmp/M2-1081082-0/0·->·/tmp/M2-1081082-0/110 --moving:·/tmp/M2-987774-0/0·->·/tmp/M2-987774-0/1
  
11 i5·:·get·dst11 i5·:·get·dst
  
12 o5·=·hi·there12 o5·=·hi·there
  
13 i6·:·bak·=·moveFile(dst,Verbose=>true)13 i6·:·bak·=·moveFile(dst,Verbose=>true)
14 --backup·file·created:·/tmp/M2-1081082-0/1.bak14 --backup·file·created:·/tmp/M2-987774-0/1.bak
  
15 o6·=·/tmp/M2-1081082-0/1.bak15 o6·=·/tmp/M2-987774-0/1.bak
  
16 i7·:·removeFile·bak16 i7·:·removeFile·bak
  
17 i8·:·17 i8·:·
297 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_nanosleep.out
    
Offset 1, 8 lines modifiedOffset 1, 8 lines modified
1 --·-*-·M2-comint·-*-·hash:·13311146124411 --·-*-·M2-comint·-*-·hash:·1331114612441
  
2 i1·:·elapsedTime·nanosleep·5000000002 i1·:·elapsedTime·nanosleep·500000000
3 ·--·.500168s·elapsed3 ·--·.500097s·elapsed
  
4 o1·=·04 o1·=·0
  
5 i2·:·5 i2·:·
2.65 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_options_lp__Function_rp.out
    
Offset 21, 54 lines modifiedOffset 21, 54 lines modified
  
21 o3·=·OptionTable{Generic·=>·false}21 o3·=·OptionTable{Generic·=>·false}
  
22 o3·:·OptionTable22 o3·:·OptionTable
  
23 i4·:·methods·codim23 i4·:·methods·codim
  
24 o4·=·{0·=>·(codim,·CoherentSheaf)·} 
25 ·····{1·=>·(codim,·MonomialIdeal)·}24 o4·=·{0·=>·(codim,·MonomialIdeal)·}
26 ·····{2·=>·(codim,·Variety)·······}25 ·····{1·=>·(codim,·Variety)·······}
27 ·····{3·=>·(codim,·Module)········}26 ·····{2·=>·(codim,·Module)········}
28 ·····{4·=>·(codim,·QuotientRing)··}27 ·····{3·=>·(codim,·QuotientRing)··}
29 ·····{5·=>·(codim,·Ideal)·········}28 ·····{4·=>·(codim,·Ideal)·········}
30 ·····{6·=>·(codim,·BettiTally)····}29 ·····{5·=>·(codim,·BettiTally)····}
31 ·····{7·=>·(codim,·PolynomialRing)}30 ·····{6·=>·(codim,·PolynomialRing)}
 31 ·····{7·=>·(codim,·CoherentSheaf)·}
  
32 o4·:·NumberedVerticalList32 o4·:·NumberedVerticalList
  
33 i5·:·options·oo33 i5·:·options·oo
  
34 o5·=·{0·=>·(OptionTable{Generic·=>·false})}34 o5·=·{0·=>·(OptionTable{Generic·=>·false})}
35 ·····{1·=>·(OptionTable{Generic·=>·false})}35 ·····{1·=>·(OptionTable{Generic·=>·false})}
36 ·····{2·=>·(OptionTable{Generic·=>·false})}36 ·····{2·=>·(OptionTable{Generic·=>·false})}
37 ·····{3·=>·(OptionTable{Generic·=>·false})}37 ·····{3·=>·(OptionTable{Generic·=>·false})}
38 ·····{4·=>·(OptionTable{Generic·=>·false})}38 ·····{4·=>·(OptionTable{Generic·=>·false})}
39 ·····{5·=>·(OptionTable{Generic·=>·false})} 
40 ·····{6·=>·(OptionTable{})················}39 ·····{5·=>·(OptionTable{})················}
 40 ·····{6·=>·(OptionTable{Generic·=>·false})}
41 ·····{7·=>·(OptionTable{Generic·=>·false})}41 ·····{7·=>·(OptionTable{Generic·=>·false})}
  
42 o5·:·NumberedVerticalList42 o5·:·NumberedVerticalList
  
43 i6·:·methods·intersect43 i6·:·methods·intersect
  
44 o6·=·{0·=>·(intersect,·List)··························}44 o6·=·{0·=>·(intersect,·List)··························}
45 ·····{1·=>·(intersect,·Set,·Set)······················} 
46 ·····{2·=>·(intersect,·Ideal)·························}45 ·····{1·=>·(intersect,·Ideal)·························}
 46 ·····{2·=>·(intersect,·Set,·Set)······················}
47 ·····{3·=>·(intersect,·RRi,·RRi)······················}47 ·····{3·=>·(intersect,·RRi,·RRi)······················}
48 ·····{4·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)}48 ·····{4·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)}
49 ·····{5·=>·(intersect,·Polyhedron,·Cone)··············}49 ·····{5·=>·(intersect,·Polyhedron,·Cone)··············}
50 ·····{6·=>·(intersect,·Cone,·Polyhedron)··············}50 ·····{6·=>·(intersect,·Cone,·Polyhedron)··············}
51 ·····{7·=>·(intersect,·Matrix)························}51 ·····{7·=>·(intersect,·Matrix)························}
52 ·····{8·=>·(intersect,·Module,·Module)················}52 ·····{8·=>·(intersect,·Module,·Module)················}
53 ·····{9·=>·(intersect,·RRi)···························}53 ·····{9·=>·(intersect,·RRi)···························}
54 ·····{10·=>·(intersect,·Ideal,·Ideal)·················} 
55 ·····{11·=>·(intersect,·Polyhedron,·Polyhedron)·······}54 ·····{10·=>·(intersect,·Polyhedron,·Polyhedron)·······}
56 ·····{12·=>·(intersect,·Cone,·Cone)···················}55 ·····{11·=>·(intersect,·Cone,·Cone)···················}
57 ·····{13·=>·(intersect,·Matrix,·Matrix)···············}56 ·····{12·=>·(intersect,·Matrix,·Matrix)···············}
 57 ·····{13·=>·(intersect,·Ideal,·Ideal)·················}
58 ·····{14·=>·(intersect,·Module)·······················}58 ·····{14·=>·(intersect,·Module)·······················}
59 ·····{15·=>·(intersect,·Sequence)·····················}59 ·····{15·=>·(intersect,·Sequence)·····················}
  
60 o6·:·NumberedVerticalList60 o6·:·NumberedVerticalList
  
61 i7·:·options·061 i7·:·options·0
  
1.22 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_parallel_spprogramming_spwith_spthreads_spand_sptasks.out
    
Offset 5, 18 lines modifiedOffset 5, 18 lines modified
5 o1·=·{1,·2,·6,·24,·120,·720,·5040,·40320,·362880,·3628800}5 o1·=·{1,·2,·6,·24,·120,·720,·5040,·40320,·362880,·3628800}
  
6 o1·:·List6 o1·:·List
  
7 i2·:·L·=·random·toList·(1..10000);7 i2·:·L·=·random·toList·(1..10000);
  
8 i3·:·elapsedTime·········apply(1..100,·n·->·sort·L);8 i3·:·elapsedTime·········apply(1..100,·n·->·sort·L);
9 ·--·.682304s·elapsed9 ·--·1.89611s·elapsed
  
10 i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L);10 i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L);
11 ·--·.185652s·elapsed11 ·--·.525755s·elapsed
  
12 i5·:·allowableThreads12 i5·:·allowableThreads
  
13 o5·=·513 o5·=·5
  
14 i6·:·allowableThreads·=·maxAllowableThreads14 i6·:·allowableThreads·=·maxAllowableThreads
  
Offset 41, 15 lines modifiedOffset 41, 15 lines modified
  
41 o10·=·<<task,·created>>41 o10·=·<<task,·created>>
  
42 o10·:·Task42 o10·:·Task
  
43 i11·:·t43 i11·:·t
  
44 o11·=·<<task,·running>>44 o11·=·<<task,·created>>
  
45 o11·:·Task45 o11·:·Task
  
46 i12·:·isReady·t46 i12·:·isReady·t
  
47 o12·=·false47 o12·=·false
  
Offset 74, 15 lines modifiedOffset 74, 15 lines modified
  
74 o16·:·Task74 o16·:·Task
  
75 i17·:·schedule·t';75 i17·:·schedule·t';
  
76 i18·:·t'76 i18·:·t'
  
77 o18·=·<<task,·created>>77 o18·=·<<task,·running>>
  
78 o18·:·Task78 o18·:·Task
  
79 i19·:·taskResult·t'79 i19·:·taskResult·t'
  
80 o19·=·|·980z2-18y-201z+13·35yz-4y+2z-1·10y2-y-12z+1·5x2-4y+2z-1·|80 o19·=·|·980z2-18y-201z+13·35yz-4y+2z-1·10y2-y-12z+1·5x2-4y+2z-1·|
  
Offset 101, 15 lines modifiedOffset 101, 15 lines modified
  
101 o21·:·Task101 o21·:·Task
  
102 i22·:·addStartTask(F,G)102 i22·:·addStartTask(F,G)
  
103 i23·:·schedule·F103 i23·:·schedule·F
  
104 o23·=·<<task,·created>>104 o23·=·<<task,·result·available,·task·done>>
  
105 o23·:·Task105 o23·:·Task
  
106 i24·:·taskResult·F106 i24·:·taskResult·F
  
107 o24·=·result·of·F107 o24·=·result·of·F
  
4.3 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_parallelism_spin_spengine_spcomputations.out
    
Offset 67, 15 lines modifiedOffset 67, 15 lines modified
67 i3·:·S·=·ring·I67 i3·:·S·=·ring·I
  
68 o3·=·S68 o3·=·S
  
69 o3·:·PolynomialRing69 o3·:·PolynomialRing
  
70 i4·:·elapsedTime·minimalBetti·I70 i4·:·elapsedTime·minimalBetti·I
71 ·--·1.87001s·elapsed71 ·--·11.8923s·elapsed
  
72 ············0··1···2···3···4····5···6···7···8··9·1072 ············0··1···2···3···4····5···6···7···8··9·10
73 o4·=·total:·1·35·140·385·819·1080·819·385·140·35··173 o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1
74 ·········0:·1··.···.···.···.····.···.···.···.··.··.74 ·········0:·1··.···.···.···.····.···.···.···.··.··.
75 ·········1:·.·35·140·189··84····.···.···.···.··.··.75 ·········1:·.·35·140·189··84····.···.···.···.··.··.
76 ·········2:·.··.···.·196·735·1080·735·196···.··.··.76 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
77 ·········3:·.··.···.···.···.····.··84·189·140·35··.77 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 84, 15 lines modifiedOffset 84, 15 lines modified
84 o4·:·BettiTally84 o4·:·BettiTally
  
85 i5·:·I·=·ideal·I_*;85 i5·:·I·=·ideal·I_*;
  
86 o5·:·Ideal·of·S86 o5·:·Ideal·of·S
  
87 i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true)87 i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true)
88 ·--·1.81656s·elapsed88 ·--·5.03134s·elapsed
  
89 ············0··1···2···3···4····5···6···7···8··9·1089 ············0··1···2···3···4····5···6···7···8··9·10
90 o6·=·total:·1·35·140·385·819·1080·819·385·140·35··190 o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1
91 ·········0:·1··.···.···.···.····.···.···.···.··.··.91 ·········0:·1··.···.···.···.····.···.···.···.··.··.
92 ·········1:·.·35·140·189··84····.···.···.···.··.··.92 ·········1:·.·35·140·189··84····.···.···.···.··.··.
93 ·········2:·.··.···.·196·735·1080·735·196···.··.··.93 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
94 ·········3:·.··.···.···.···.····.··84·189·140·35··.94 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 105, 15 lines modifiedOffset 105, 15 lines modified
105 o7·:·Ideal·of·S105 o7·:·Ideal·of·S
  
106 i8·:·numTBBThreads·=·1106 i8·:·numTBBThreads·=·1
  
107 o8·=·1107 o8·=·1
  
108 i9·:·elapsedTime·minimalBetti(I)108 i9·:·elapsedTime·minimalBetti(I)
109 ·--·1.76207s·elapsed109 ·--·6.04471s·elapsed
  
110 ············0··1···2···3···4····5···6···7···8··9·10110 ············0··1···2···3···4····5···6···7···8··9·10
111 o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1111 o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1
112 ·········0:·1··.···.···.···.····.···.···.···.··.··.112 ·········0:·1··.···.···.···.····.···.···.···.··.··.
113 ·········1:·.·35·140·189··84····.···.···.···.··.··.113 ·········1:·.·35·140·189··84····.···.···.···.··.··.
114 ·········2:·.··.···.·196·735·1080·735·196···.··.··.114 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
115 ·········3:·.··.···.···.···.····.··84·189·140·35··.115 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 132, 15 lines modifiedOffset 132, 15 lines modified
132 o11·=·0132 o11·=·0
  
133 i12·:·I·=·ideal·I_*;133 i12·:·I·=·ideal·I_*;
  
134 o12·:·Ideal·of·S134 o12·:·Ideal·of·S
  
135 i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)135 i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)
136 ·--·2.08299s·elapsed136 ·--·6.77885s·elapsed
  
137 ·······1······35······241······841······1781······2464······2294······1432······576······135······14137 ·······1······35······241······841······1781······2464······2294······1432······576······135······14
138 o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S138 o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S
139 ··································································································139 ··································································································
140 ······0······1·······2········3········4·········5·········6·········7·········8········9········10140 ······0······1·······2········3········4·········5·········6·········7·········8········9········10
  
141 o13·:·Complex141 o13·:·Complex
Offset 150, 15 lines modifiedOffset 150, 15 lines modified
150 o14·=·1150 o14·=·1
  
151 i15·:·I·=·ideal·I_*;151 i15·:·I·=·ideal·I_*;
  
152 o15·:·Ideal·of·S152 o15·:·Ideal·of·S
  
153 i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)153 i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)
154 ·--·1.97957s·elapsed154 ·--·7.46347s·elapsed
  
155 ·······1······35······241······841······1781······2464······2294······1432······576······135······14155 ·······1······35······241······841······1781······2464······2294······1432······576······135······14
156 o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S156 o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S
157 ··································································································157 ··································································································
158 ······0······1·······2········3········4·········5·········6·········7·········8········9········10158 ······0······1·······2········3········4·········5·········6·········7·········8········9········10
  
159 o16·:·Complex159 o16·:·Complex
Offset 174, 43 lines modifiedOffset 174, 43 lines modified
174 o18·:·PolynomialRing174 o18·:·PolynomialRing
  
175 i19·:·I·=·ideal·random(S^1,·S^{4:-5});175 i19·:·I·=·ideal·random(S^1,·S^{4:-5});
  
176 o19·:·Ideal·of·S176 o19·:·Ideal·of·S
  
177 i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");177 i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");
178 ·--·3.10387s·elapsed178 ·--·8.49594s·elapsed
  
179 ··············1······108179 ··············1······108
180 o20·:·Matrix·S··<--·S180 o20·:·Matrix·S··<--·S
  
181 i21·:·numTBBThreads·=·1181 i21·:·numTBBThreads·=·1
  
182 o21·=·1182 o21·=·1
  
183 i22·:·I·=·ideal·I_*;183 i22·:·I·=·ideal·I_*;
  
184 o22·:·Ideal·of·S184 o22·:·Ideal·of·S
  
185 i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");185 i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");
186 ·--·6.09094s·elapsed186 ·--·26.4761s·elapsed
  
187 ··············1······108187 ··············1······108
188 o23·:·Matrix·S··<--·S188 o23·:·Matrix·S··<--·S
  
189 i24·:·numTBBThreads·=·10189 i24·:·numTBBThreads·=·10
  
190 o24·=·10190 o24·=·10
  
191 i25·:·I·=·ideal·I_*;191 i25·:·I·=·ideal·I_*;
  
192 o25·:·Ideal·of·S192 o25·:·Ideal·of·S
  
193 i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");193 i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");
194 ·--·2.92069s·elapsed194 ·--·8.21435s·elapsed
  
195 ··············1······108195 ··············1······108
196 o26·:·Matrix·S··<--·S196 o26·:·Matrix·S··<--·S
  
197 i27·:·needsPackage·"AssociativeAlgebras"197 i27·:·needsPackage·"AssociativeAlgebras"
  
198 o27·=·AssociativeAlgebras198 o27·=·AssociativeAlgebras
Offset 233, 15 lines modifiedOffset 233, 15 lines modified
233 o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·)233 o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·)
  
234 ················ZZ234 ················ZZ
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2.88 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_poincare.out
    
Offset 146, 65 lines modifiedOffset 146, 65 lines modified
146 o26·:·ZZ[T]146 o26·:·ZZ[T]
  
147 i27·:·gbTrace·=·3147 i27·:·gbTrace·=·3
  
148 o27·=·3148 o27·=·3
  
149 i28·:·time·poincare·I149 i28·:·time·poincare·I
150 ·--·used·0.00145017s·(cpu);·7.802e-06s·(thread);·0s·(gc)150 ·--·used·0.00319799s·(cpu);·2.9034e-05s·(thread);·0s·(gc)
  
151 ············3·····6····9151 ············3·····6····9
152 o28·=·1·-·3T··+·3T··-·T152 o28·=·1·-·3T··+·3T··-·T
  
153 o28·:·ZZ[T]153 o28·:·ZZ[T]
  
154 i29·:·time·gens·gb·I;154 i29·:·time·gens·gb·I;
  
155 ···--·registering·gb·19·at·0x7f749535a540155 ···--·registering·gb·19·at·0x7f8bad70e540
  
156 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11156 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11
157 ···--·number·of·monomials················=·4186157 ···--·number·of·monomials················=·4186
158 ···--·#reduction·steps·=·38158 ···--·#reduction·steps·=·38
159 ···--·#spairs·done·=·11159 ···--·#spairs·done·=·11
160 ···--·ncalls·=·10160 ···--·ncalls·=·10
161 ···--·nloop·=·29161 ···--·nloop·=·29
162 ···--·nsaved·=·0162 ···--·nsaved·=·0
163 ···--··--·used·0.00903704s·(cpu);·0.0101512s·(thread);·0s·(gc)163 ···--··--·used·0.0101535s·(cpu);·0.0127548s·(thread);·0s·(gc)
  
164 ··············1······11164 ··············1······11
165 o29·:·Matrix·R··<--·R165 o29·:·Matrix·R··<--·R
  
166 i30·:·R·=·QQ[a..d];166 i30·:·R·=·QQ[a..d];
  
167 i31·:·I·=·ideal·random(R^1,·R^{3:-3});167 i31·:·I·=·ideal·random(R^1,·R^{3:-3});
  
168 ···--·registering·gb·20·at·0x7f749535a380168 ···--·registering·gb·20·at·0x7f8bad70e380
  
169 ···--·[gb]number·of·(nonminimal)·gb·elements·=·0169 ···--·[gb]number·of·(nonminimal)·gb·elements·=·0
170 ···--·number·of·monomials················=·0170 ···--·number·of·monomials················=·0
171 ···--·#reduction·steps·=·0171 ···--·#reduction·steps·=·0
172 ···--·#spairs·done·=·0172 ···--·#spairs·done·=·0
173 ···--·ncalls·=·0173 ···--·ncalls·=·0
174 ···--·nloop·=·0174 ···--·nloop·=·0
175 ···--·nsaved·=·0175 ···--·nsaved·=·0
176 ···--·176 ···--·
177 o31·:·Ideal·of·R177 o31·:·Ideal·of·R
  
178 i32·:·time·p·=·poincare·I178 i32·:·time·p·=·poincare·I
  
179 ···--·registering·gb·21·at·0x7f749535a1c0179 ···--·registering·gb·21·at·0x7f8bad70e1c0
  
180 ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11180 ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11
181 ···--·number·of·monomials················=·267181 ···--·number·of·monomials················=·267
182 ···--·#reduction·steps·=·236182 ···--·#reduction·steps·=·236
183 ···--·#spairs·done·=·30183 ···--·#spairs·done·=·30
184 ···--·ncalls·=·10184 ···--·ncalls·=·10
185 ···--·nloop·=·20185 ···--·nloop·=·20
186 ···--·nsaved·=·0186 ···--·nsaved·=·0
187 ···--··--·used·0.00566835s·(cpu);·0.00489106s·(thread);·0s·(gc)187 ···--··--·used·0.00530603s·(cpu);·0.00629818s·(thread);·0s·(gc)
  
188 ············3·····6····9188 ············3·····6····9
189 o32·=·1·-·3T··+·3T··-·T189 o32·=·1·-·3T··+·3T··-·T
  
190 o32·:·ZZ[T]190 o32·:·ZZ[T]
  
191 i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2]191 i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2]
Offset 254, 27 lines modifiedOffset 254, 27 lines modified
  
254 i36·:·gbTrace·=·3254 i36·:·gbTrace·=·3
  
255 o36·=·3255 o36·=·3
  
256 i37·:·time·gens·gb·J;256 i37·:·time·gens·gb·J;
  
257 ···--·registering·gb·22·at·0x7f749535a000257 ···--·registering·gb·22·at·0x7f8bad70e000
  
258 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m258 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m
259 ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m259 ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m
260 ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m260 ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m
261 ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39261 ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39
262 ···--·number·of·monomials················=·1051262 ···--·number·of·monomials················=·1051
263 ···--·#reduction·steps·=·284263 ···--·#reduction·steps·=·284
264 ···--·#spairs·done·=·53264 ···--·#spairs·done·=·53
265 ···--·ncalls·=·46265 ···--·ncalls·=·46
266 ···--·nloop·=·54266 ···--·nloop·=·54
267 ···--·nsaved·=·0267 ···--·nsaved·=·0
268 ···--··--·used·0.0464432s·(cpu);·0.0480922s·(thread);·0s·(gc)268 ···--··--·used·0.059633s·(cpu);·0.0564652s·(thread);·0s·(gc)
  
269 ··············1······39269 ··············1······39
270 o37·:·Matrix·S··<--·S270 o37·:·Matrix·S··<--·S
  
271 i38·:·selectInSubring(1,·gens·gb·J)271 i38·:·selectInSubring(1,·gens·gb·J)
  
272 o38·=·|·188529931266160087758259645374082357642621166724936033369975727480205272 o38·=·|·188529931266160087758259645374082357642621166724936033369975727480205
1.03 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_printing_spto_spa_spfile.out
    
Offset 12, 19 lines modifiedOffset 12, 19 lines modified
  
12 o2·=·stdio12 o2·=·stdio
  
13 o2·:·File13 o2·:·File
  
14 i3·:·fn·=·temporaryFileName()14 i3·:·fn·=·temporaryFileName()
  
15 o3·=·/tmp/M2-1083217-0/015 o3·=·/tmp/M2-997039-0/0
  
16 i4·:·fn·<<·"hi·there"·<<·endl·<<·close16 i4·:·fn·<<·"hi·there"·<<·endl·<<·close
  
17 o4·=·/tmp/M2-1083217-0/017 o4·=·/tmp/M2-997039-0/0
  
18 o4·:·File18 o4·:·File
  
19 i5·:·get·fn19 i5·:·get·fn
  
20 o5·=·hi·there20 o5·=·hi·there
  
Offset 49, 27 lines modifiedOffset 49, 27 lines modified
49 x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·149 x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·1
50 o8·=·stdio50 o8·=·stdio
  
51 o8·:·File51 o8·:·File
  
52 i9·:·fn·<<·f·<<·close52 i9·:·fn·<<·f·<<·close
  
53 o9·=·/tmp/M2-1083217-0/053 o9·=·/tmp/M2-997039-0/0
  
54 o9·:·File54 o9·:·File
  
55 i10·:·get·fn55 i10·:·get·fn
  
56 o10·=··10······9······8·······7·······6·······5·······4·······3······256 o10·=··10······9······8·······7·······6·······5·······4·······3······2
57 ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x57 ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x
58 ······+·158 ······+·1
  
59 i11·:·fn·<<·toExternalString·f·<<·close59 i11·:·fn·<<·toExternalString·f·<<·close
  
60 o11·=·/tmp/M2-1083217-0/060 o11·=·/tmp/M2-997039-0/0
  
61 o11·:·File61 o11·:·File
  
62 i12·:·get·fn62 i12·:·get·fn
  
63 o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+63 o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+
64 ······164 ······1
260 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_process__I__D.out
    
Offset 1, 7 lines modifiedOffset 1, 7 lines modified
1 --·-*-·M2-comint·-*-·hash:·13305136305631 --·-*-·M2-comint·-*-·hash:·1330513630563
  
2 i1·:·processID()2 i1·:·processID()
  
3 o1·=·10752043 o1·=·980911
  
4 i2·:·4 i2·:·
2.64 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_profile.out
    
Offset 9, 35 lines modifiedOffset 9, 35 lines modified
  
9 ··············4·······59 ··············4·······5
10 o1·:·Matrix·ZZ··<--·ZZ10 o1·:·Matrix·ZZ··<--·ZZ
  
11 i2·:·profileSummary11 i2·:·profileSummary
  
12 o2·=·#run··%time···position·························12 o2·=·#run··%time···position·························
13 ·····1·····91.8····../../m2/matrix1.m2:279:4-282:58·13 ·····1·····92.19···../../m2/matrix1.m2:279:4-282:58·
14 ·····1·····88.55···../../m2/matrix1.m2:281:22-281:4314 ·····1·····89.48···../../m2/matrix1.m2:281:22-281:43
15 ·····1·····44.03···../../m2/matrix1.m2:193:25-193:5215 ·····1·····43.48···../../m2/matrix1.m2:193:25-193:52
16 ·····1·····29.76···../../m2/matrix1.m2:114:5-156:72·16 ·····1·····30.15···../../m2/matrix1.m2:114:5-156:72·
17 ·····1·····28.41···../../m2/matrix1.m2:140:10-155:1617 ·····1·····28.93···../../m2/matrix1.m2:140:10-155:16
18 ·····1·····21.43···../../m2/matrix1.m2:181:4-181:42·18 ·····1·····21.92···../../m2/matrix1.m2:181:4-181:42·
19 ·····1·····19.82···../../m2/set.m2:122:5-122:61·····19 ·····1·····20.36···../../m2/set.m2:122:5-122:61·····
20 ·····1·····18.68···../../m2/matrix1.m2:45:10-49:22··20 ·····1·····20.09···../../m2/matrix1.m2:45:10-49:22··
21 ·····1·····3.22····../../m2/matrix1.m2:112:5-112:29·21 ·····1·····3.32····../../m2/matrix1.m2:112:5-112:29·
22 ·····1·····2.81····../../m2/matrix1.m2:141:13-141:7822 ·····1·····2.45····../../m2/matrix1.m2:141:13-141:78
23 ·····1·····2.07····../../m2/matrix1.m2:96:5-109:11··23 ·····1·····2.09····../../m2/matrix1.m2:96:5-109:11··
24 ·····1·····1.97····../../m2/matrix1.m2:281:7-281:16·24 ·····1·····1.67····../../m2/matrix1.m2:281:7-281:16·
25 ·····1·····1.75····../../m2/modules.m2:278:4-278:52· 
26 ·····1·····1.69····../../m2/matrix1.m2:147:20-147:6425 ·····1·····1.43····../../m2/matrix1.m2:147:20-147:64
27 ·····1·····1.59····../../m2/matrix1.m2:276:4-277:73·26 ·····1·····1.40····../../m2/matrix1.m2:276:4-277:73·
28 ·····1·····1.3·····../../m2/matrix1.m2:111:5-111:91·27 ·····1·····1.22····../../m2/matrix1.m2:111:5-111:91·
29 ·····1·····1.12····../../m2/matrix1.m2:182:4-184:74· 
30 ·····1·····1.04····../../m2/matrix1.m2:98:10-98:46··28 ·····1·····1.06····../../m2/matrix1.m2:98:10-98:46··
 29 ·····1·····1.05····../../m2/matrix1.m2:182:4-184:74·
 30 ·····1·····.86·····../../m2/modules.m2:278:4-278:52·
31 ·····20····.91·····../../m2/matrix1.m2:191:14-192:6731 ·····20····.70·····../../m2/matrix1.m2:191:14-192:67
32 ·····20····.56·····../../m2/matrix1.m2:47:43-47:71··32 ·····1·····.35·····../../m2/matrix1.m2:152:66-152:98
33 ·····1·····.0015s··elapsed·total····················33 ·····1·····.0026s··elapsed·total····················
  
34 i3·:·coverageSummary34 i3·:·coverageSummary
  
35 o3·=·covered·lines:35 o3·=·covered·lines:
36 ·····../../m2/lists.m2:145:24-145:3236 ·····../../m2/lists.m2:145:24-145:32
37 ·····../../m2/lists.m2:145:34-145:5837 ·····../../m2/lists.m2:145:34-145:58
38 ·····../../m2/matrix.m2:12:5-12:3538 ·····../../m2/matrix.m2:12:5-12:35
1.26 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_random__K__Rational__Point.out
    
Offset 13, 15 lines modifiedOffset 13, 15 lines modified
13 i5·:·codim·I,·degree·I13 i5·:·codim·I,·degree·I
  
14 o5·=·(2,·10)14 o5·=·(2,·10)
  
15 o5·:·Sequence15 o5·:·Sequence
  
16 i6·:·time·randomKRationalPoint(I)16 i6·:·time·randomKRationalPoint(I)
17 ·--·used·0.138948s·(cpu);·0.0717858s·(thread);·0s·(gc)17 ·--·used·0.119735s·(cpu);·0.0842559s·(thread);·0s·(gc)
  
18 o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·)18 o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·)
19 ·············2······3···1·····3···0·····319 ·············2······3···1·····3···0·····3
  
20 o6·:·Ideal·of·R20 o6·:·Ideal·of·R
  
21 i7·:·R=kk[x_0..x_5];21 i7·:·R=kk[x_0..x_5];
Offset 33, 15 lines modifiedOffset 33, 15 lines modified
33 i9·:·codim·I,·degree·I33 i9·:·codim·I,·degree·I
  
34 o9·=·(3,·10)34 o9·=·(3,·10)
  
35 o9·:·Sequence35 o9·:·Sequence
  
36 i10·:·time·randomKRationalPoint(I)36 i10·:·time·randomKRationalPoint(I)
37 ·--·used·0.538065s·(cpu);·0.203857s·(thread);·0s·(gc)37 ·--·used·0.677037s·(cpu);·0.278406s·(thread);·0s·(gc)
  
38 o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·)38 o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·)
39 ··············4······5···3······5···2·····5···1······5···0······539 ··············4······5···3······5···2·····5···1······5···0······5
  
40 o10·:·Ideal·of·R40 o10·:·Ideal·of·R
  
41 i11·:·p=10007,kk=ZZ/p,R=kk[x_0..x_2]41 i11·:·p=10007,kk=ZZ/p,R=kk[x_0..x_2]
Offset 58, 12 lines modifiedOffset 58, 12 lines modified
  
58 i14·:·I=ideal·random(n,R);58 i14·:·I=ideal·random(n,R);
  
59 o14·:·Ideal·of·R59 o14·:·Ideal·of·R
  
60 i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c);60 i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c);
61 ·····················#select(degs,d->d==1))),f->f>0))61 ·····················#select(degs,d->d==1))),f->f>0))
62 ·--·used·2.87793s·(cpu);·1.4543s·(thread);·0s·(gc)62 ·--·used·3.16003s·(cpu);·1.77636s·(thread);·0s·(gc)
  
63 o15·=·5863 o15·=·58
  
64 i16·:·64 i16·:·
642 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_read__Directory.out
    
Offset 1, 26 lines modifiedOffset 1, 26 lines modified
1 --·-*-·M2-comint·-*-·hash:·209107367040705141 --·-*-·M2-comint·-*-·hash:·20910736704070514
  
2 i1·:·dir·=·temporaryFileName()2 i1·:·dir·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1092406-0/03 o1·=·/tmp/M2-1048456-0/0
  
4 i2·:·makeDirectory·dir4 i2·:·makeDirectory·dir
  
5 o2·=·/tmp/M2-1092406-0/05 o2·=·/tmp/M2-1048456-0/0
  
6 i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close6 i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close
  
7 o3·=·/tmp/M2-1092406-0/0/foo7 o3·=·/tmp/M2-1048456-0/0/foo
  
8 o3·:·File8 o3·:·File
  
9 i4·:·readDirectory·dir9 i4·:·readDirectory·dir
  
10 o4·=·{..,·.,·foo}10 o4·=·{foo,·.,·..}
  
11 o4·:·List11 o4·:·List
  
12 i5·:·removeFile·fn12 i5·:·removeFile·fn
  
13 i6·:·removeDirectory·dir13 i6·:·removeDirectory·dir
  
836 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_reading_spfiles.out
    
Offset 1, 16 lines modifiedOffset 1, 16 lines modified
1 --·-*-·M2-comint·-*-·hash:·135135551042009447961 --·-*-·M2-comint·-*-·hash:·13513555104200944796
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1083684-0/03 o1·=·/tmp/M2-1004559-0/0
  
4 i2·:·fn·<<·"z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"·<<·endl·<<·close4 i2·:·fn·<<·"z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"·<<·endl·<<·close
  
5 o2·=·/tmp/M2-1083684-0/05 o2·=·/tmp/M2-1004559-0/0
  
6 o2·:·File6 o2·:·File
  
7 i3·:·get·fn7 i3·:·get·fn
  
8 o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^28 o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2
9 ·····+8*y^39 ·····+8*y^3
Offset 38, 15 lines modifiedOffset 38, 15 lines modified
  
38 o6·:·Expression·of·class·Product38 o6·:·Expression·of·class·Product
  
39 i7·:·fn·<<·"sample·=·2^10039 i7·:·fn·<<·"sample·=·2^100
40 ·····print·sample40 ·····print·sample
41 ·····"·<<·close41 ·····"·<<·close
  
42 o7·=·/tmp/M2-1083684-0/042 o7·=·/tmp/M2-1004559-0/0
  
43 o7·:·File43 o7·:·File
  
44 i8·:·get·fn44 i8·:·get·fn
  
45 o8·=·sample·=·2^10045 o8·=·sample·=·2^100
46 ·····print·sample46 ·····print·sample
351 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_readlink.out
    
Offset 1, 12 lines modifiedOffset 1, 12 lines modified
1 --·-*-·M2-comint·-*-·hash:·44086396114787811301 --·-*-·M2-comint·-*-·hash:·4408639611478781130
  
2 i1·:·p·=·temporaryFileName·()2 i1·:·p·=·temporaryFileName·()
  
3 o1·=·/tmp/M2-1093698-0/03 o1·=·/tmp/M2-1054229-0/0
  
4 i2·:·symlinkFile·("foo",·p)4 i2·:·symlinkFile·("foo",·p)
  
5 i3·:·readlink·p5 i3·:·readlink·p
  
6 o3·=·foo6 o3·=·foo
  
866 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_realpath.out
    
Offset 1, 39 lines modifiedOffset 1, 39 lines modified
1 --·-*-·M2-comint·-*-·hash:·3240723472132246561 --·-*-·M2-comint·-*-·hash:·324072347213224656
  
2 i1·:·realpath·"."2 i1·:·realpath·"."
  
3 o1·=·/tmp/M2-1075204-0/86-rundir/3 o1·=·/tmp/M2-980911-0/86-rundir/
  
4 i2·:·p·=·temporaryFileName()4 i2·:·p·=·temporaryFileName()
  
5 o2·=·/tmp/M2-1093886-0/05 o2·=·/tmp/M2-1054831-0/0
  
6 i3·:·q·=·temporaryFileName()6 i3·:·q·=·temporaryFileName()
  
7 o3·=·/tmp/M2-1093886-0/17 o3·=·/tmp/M2-1054831-0/1
  
8 i4·:·symlinkFile(p,q)8 i4·:·symlinkFile(p,q)
  
9 i5·:·p·<<·close9 i5·:·p·<<·close
  
10 o5·=·/tmp/M2-1093886-0/010 o5·=·/tmp/M2-1054831-0/0
  
11 o5·:·File11 o5·:·File
  
12 i6·:·readlink·q12 i6·:·readlink·q
  
13 o6·=·/tmp/M2-1093886-0/013 o6·=·/tmp/M2-1054831-0/0
  
14 i7·:·realpath·q14 i7·:·realpath·q
  
15 o7·=·/tmp/M2-1093886-0/015 o7·=·/tmp/M2-1054831-0/0
  
16 i8·:·removeFile·p16 i8·:·removeFile·p
  
17 i9·:·removeFile·q17 i9·:·removeFile·q
  
18 i10·:·realpath·""18 i10·:·realpath·""
  
19 o10·=·/tmp/M2-1075204-0/86-rundir/19 o10·=·/tmp/M2-980911-0/86-rundir/
  
20 i11·:·20 i11·:·
1.09 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_register__Finalizer.out
    
Offset 1, 15 lines modifiedOffset 1, 15 lines modified
1 --·-*-·M2-comint·-*-·hash:·17293843743726626931 --·-*-·M2-comint·-*-·hash:·1729384374372662693
  
2 i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"--·finalizing·sequence·#"|i|"·--"))2 i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"--·finalizing·sequence·#"|i|"·--"))
  
3 i2·:·collectGarbage()·3 i2·:·collectGarbage()·
4 --finalization:·(1)[1]:·--·finalizing·sequence·#2·-- 
5 --finalization:·(2)[7]:·--·finalizing·sequence·#8·-- 
6 --finalization:·(3)[4]:·--·finalizing·sequence·#5·-- 
7 --finalization:·(4)[3]:·--·finalizing·sequence·#4·-- 
8 --finalization:·(5)[0]:·--·finalizing·sequence·#1·-- 
9 --finalization:·(6)[6]:·--·finalizing·sequence·#7·--4 --finalization:·(1)[6]:·--·finalizing·sequence·#7·--
 5 --finalization:·(2)[3]:·--·finalizing·sequence·#4·--
 6 --finalization:·(3)[0]:·--·finalizing·sequence·#1·--
 7 --finalization:·(4)[7]:·--·finalizing·sequence·#8·--
 8 --finalization:·(5)[4]:·--·finalizing·sequence·#5·--
 9 --finalization:·(6)[1]:·--·finalizing·sequence·#2·--
10 --finalization:·(7)[5]:·--·finalizing·sequence·#6·--10 --finalization:·(7)[5]:·--·finalizing·sequence·#6·--
11 --finalization:·(8)[2]:·--·finalizing·sequence·#3·--11 --finalization:·(8)[2]:·--·finalizing·sequence·#3·--
  
12 i3·:·12 i3·:·
490 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_remove__Directory.out
    
Offset 1, 19 lines modifiedOffset 1, 19 lines modified
1 --·-*-·M2-comint·-*-·hash:·85329803100970600891 --·-*-·M2-comint·-*-·hash:·8532980310097060089
  
2 i1·:·dir·=·temporaryFileName()2 i1·:·dir·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1082943-0/03 o1·=·/tmp/M2-996065-0/0
  
4 i2·:·makeDirectory·dir4 i2·:·makeDirectory·dir
  
5 o2·=·/tmp/M2-1082943-0/05 o2·=·/tmp/M2-996065-0/0
  
6 i3·:·readDirectory·dir6 i3·:·readDirectory·dir
  
7 o3·=·{..,·.}7 o3·=·{.,·..}
  
8 o3·:·List8 o3·:·List
  
9 i4·:·removeDirectory·dir9 i4·:·removeDirectory·dir
  
10 i5·:·10 i5·:·
374 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_root__Path.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·17314202321481493871 --·-*-·M2-comint·-*-·hash:·1731420232148149387
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1076046-0/03 o1·=·/tmp/M2-982439-0/0
  
4 i2·:·rootPath·|·fn4 i2·:·rootPath·|·fn
  
5 o2·=·/tmp/M2-1076046-0/05 o2·=·/tmp/M2-982439-0/0
  
6 i3·:·6 i3·:·
395 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_root__U__R__I.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·17314202315255729681 --·-*-·M2-comint·-*-·hash:·1731420231525572968
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1086087-0/03 o1·=·/tmp/M2-1047499-0/0
  
4 i2·:·rootURI·|·fn4 i2·:·rootURI·|·fn
  
5 o2·=·file:///tmp/M2-1086087-0/05 o2·=·file:///tmp/M2-1047499-0/0
  
6 i3·:·6 i3·:·
679 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_saving_sppolynomials_spand_spmatrices_spin_spfiles.out
    
Offset 25, 19 lines modifiedOffset 25, 19 lines modified
25 o4·=·image·|·x2·x2-y2·xyz7·|25 o4·=·image·|·x2·x2-y2·xyz7·|
  
26 ·····························126 ·····························1
27 o4·:·R-module,·submodule·of·R27 o4·:·R-module,·submodule·of·R
  
28 i5·:·f·=·temporaryFileName()28 i5·:·f·=·temporaryFileName()
  
29 o5·=·/tmp/M2-1084627-0/029 o5·=·/tmp/M2-1040535-0/0
  
30 i6·:·f·<<·toString·(p,m,M)·<<·close30 i6·:·f·<<·toString·(p,m,M)·<<·close
  
31 o6·=·/tmp/M2-1084627-0/031 o6·=·/tmp/M2-1040535-0/0
  
32 o6·:·File32 o6·:·File
  
33 i7·:·get·f33 i7·:·get·f
  
34 o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2,34 o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2,
35 ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}})35 ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}})
328 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_schedule.out
    
Offset 10, 15 lines modifiedOffset 10, 15 lines modified
  
10 o2·=·<<task,·created>>10 o2·=·<<task,·created>>
  
11 o2·:·Task11 o2·:·Task
  
12 i3·:·schedule·t12 i3·:·schedule·t
  
13 o3·=·<<task,·created>>13 o3·=·<<task,·result·available,·task·done>>
  
14 o3·:·Task14 o3·:·Task
  
15 i4·:·taskResult·t15 i4·:·taskResult·t
  
16 o4·=·816 o4·=·8
  
1.19 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_solve.out
    
Offset 189, 18 lines modifiedOffset 189, 18 lines modified
189 o25·=·40189 o25·=·40
  
190 i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;190 i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;
  
191 i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;191 i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;
  
192 i30·:·time·X·=·solve(A,B);192 i30·:·time·X·=·solve(A,B);
193 ·--·used·0.000120261s·(cpu);·0.00011242s·(thread);·0s·(gc)193 ·--·used·0.000573995s·(cpu);·0.00059232s·(thread);·0s·(gc)
  
194 i31·:·time·X·=·solve(A,B,·MaximalRank=>true);194 i31·:·time·X·=·solve(A,B,·MaximalRank=>true);
195 ·--·used·7.266e-05s·(cpu);·7.271e-05s·(thread);·0s·(gc)195 ·--·used·0.000120916s·(cpu);·0.000120496s·(thread);·0s·(gc)
  
196 i32·:·norm(A*X-B)196 i32·:·norm(A*X-B)
  
197 o32·=·5.111850690840453e-15197 o32·=·5.111850690840453e-15
  
198 o32·:·RR·(of·precision·53)198 o32·:·RR·(of·precision·53)
  
Offset 209, 18 lines modifiedOffset 209, 18 lines modified
209 o33·=·100209 o33·=·100
  
210 i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;210 i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;
  
211 i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;211 i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;
  
212 i38·:·time·X·=·solve(A,B);212 i38·:·time·X·=·solve(A,B);
213 ·--·used·0.306572s·(cpu);·0.140883s·(thread);·0s·(gc)213 ·--·used·0.295576s·(cpu);·0.154725s·(thread);·0s·(gc)
  
214 i39·:·time·X·=·solve(A,B,·MaximalRank=>true);214 i39·:·time·X·=·solve(A,B,·MaximalRank=>true);
215 ·--·used·0.106319s·(cpu);·0.106326s·(thread);·0s·(gc)215 ·--·used·0.120689s·(cpu);·0.120669s·(thread);·0s·(gc)
  
216 i40·:·norm(A*X-B)216 i40·:·norm(A*X-B)
  
217 o40·=·1.491578274689709814082355885932e-28217 o40·=·1.491578274689709814082355885932e-28
  
218 o40·:·RR·(of·precision·100)218 o40·:·RR·(of·precision·100)
  
2.01 KB
    
Offset 1, 60 lines modifiedOffset 1, 60 lines modified
1 --·-*-·M2-comint·-*-·hash:·29895135282135576911 --·-*-·M2-comint·-*-·hash:·2989513528213557691
  
2 i1·:·src·=·temporaryFileName()·|·"/"2 i1·:·src·=·temporaryFileName()·|·"/"
  
3 o1·=·/tmp/M2-1083759-0/0/3 o1·=·/tmp/M2-1012869-0/0/
  
4 i2·:·dst·=·temporaryFileName()·|·"/"4 i2·:·dst·=·temporaryFileName()·|·"/"
  
5 o2·=·/tmp/M2-1083759-0/1/5 o2·=·/tmp/M2-1012869-0/1/
  
6 i3·:·makeDirectory·(src|"a/")6 i3·:·makeDirectory·(src|"a/")
  
7 o3·=·/tmp/M2-1083759-0/0/a/7 o3·=·/tmp/M2-1012869-0/0/a/
  
8 i4·:·makeDirectory·(src|"b/")8 i4·:·makeDirectory·(src|"b/")
  
9 o4·=·/tmp/M2-1083759-0/0/b/9 o4·=·/tmp/M2-1012869-0/0/b/
  
10 i5·:·makeDirectory·(src|"b/c/")10 i5·:·makeDirectory·(src|"b/c/")
  
11 o5·=·/tmp/M2-1083759-0/0/b/c/11 o5·=·/tmp/M2-1012869-0/0/b/c/
  
12 i6·:·src|"a/f"·<<·"hi·there"·<<·close12 i6·:·src|"a/f"·<<·"hi·there"·<<·close
  
13 o6·=·/tmp/M2-1083759-0/0/a/f13 o6·=·/tmp/M2-1012869-0/0/a/f
  
14 o6·:·File14 o6·:·File
  
15 i7·:·src|"a/g"·<<·"hi·there"·<<·close15 i7·:·src|"a/g"·<<·"hi·there"·<<·close
  
16 o7·=·/tmp/M2-1083759-0/0/a/g16 o7·=·/tmp/M2-1012869-0/0/a/g
  
17 o7·:·File17 o7·:·File
  
18 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close18 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close
  
19 o8·=·/tmp/M2-1083759-0/0/b/c/g19 o8·=·/tmp/M2-1012869-0/0/b/c/g
  
20 o8·:·File20 o8·:·File
  
21 i9·:·symlinkDirectory(src,dst,Verbose=>true)21 i9·:·symlinkDirectory(src,dst,Verbose=>true)
22 --symlinking:·../../../0/b/c/g·->·/tmp/M2-1083759-0/1/b/c/g22 --symlinking:·../../../0/b/c/g·->·/tmp/M2-1012869-0/1/b/c/g
23 --symlinking:·../../0/a/f·->·/tmp/M2-1083759-0/1/a/f 
24 --symlinking:·../../0/a/g·->·/tmp/M2-1083759-0/1/a/g23 --symlinking:·../../0/a/g·->·/tmp/M2-1012869-0/1/a/g
 24 --symlinking:·../../0/a/f·->·/tmp/M2-1012869-0/1/a/f
  
25 i10·:·get·(dst|"b/c/g")25 i10·:·get·(dst|"b/c/g")
  
26 o10·=·ho·there26 o10·=·ho·there
  
27 i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true)27 i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true)
28 --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-1083759-0/1/b/c/g28 --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-1012869-0/1/b/c/g
29 --unsymlinking:·../../0/a/f·->·/tmp/M2-1083759-0/1/a/f 
30 --unsymlinking:·../../0/a/g·->·/tmp/M2-1083759-0/1/a/g29 --unsymlinking:·../../0/a/g·->·/tmp/M2-1012869-0/1/a/g
 30 --unsymlinking:·../../0/a/f·->·/tmp/M2-1012869-0/1/a/f
  
31 i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d31 i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d
  
32 o12·=·rm32 o12·=·rm
  
33 o12·:·FunctionClosure33 o12·:·FunctionClosure
  
368 B
    
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1 --·-*-·M2-comint·-*-·hash:·93438446729403065951 --·-*-·M2-comint·-*-·hash:·9343844672940306595
  
2 i1·:·fn·=·temporaryFileName()2 i1·:·fn·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1083870-0/03 o1·=·/tmp/M2-1018263-0/0
  
4 i2·:·symlinkFile("qwert",·fn)4 i2·:·symlinkFile("qwert",·fn)
  
5 i3·:·fileExists·fn5 i3·:·fileExists·fn
  
6 o3·=·false6 o3·=·false
  
438 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_temporary__File__Name.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·17319265312913021061 --·-*-·M2-comint·-*-·hash:·1731926531291302106
  
2 i1·:·temporaryFileName·()·|·".tex"2 i1·:·temporaryFileName·()·|·".tex"
  
3 o1·=·/tmp/M2-1101176-0/0.tex3 o1·=·/tmp/M2-1060134-0/0.tex
  
4 i2·:·temporaryFileName·()·|·".html"4 i2·:·temporaryFileName·()·|·".html"
  
5 o2·=·/tmp/M2-1101176-0/1.html5 o2·=·/tmp/M2-1060134-0/1.html
  
6 i3·:·6 i3·:·
349 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_time.out
    
Offset 1, 8 lines modifiedOffset 1, 8 lines modified
1 --·-*-·M2-comint·-*-·hash:·13324355007231 --·-*-·M2-comint·-*-·hash:·1332435500723
  
2 i1·:·time·3^302 i1·:·time·3^30
3 ·--·used·1.5744e-05s·(cpu);·4.767e-06s·(thread);·0s·(gc)3 ·--·used·1.597e-05s·(cpu);·5.33e-06s·(thread);·0s·(gc)
  
4 o1·=·2058911320946494 o1·=·205891132094649
  
5 i2·:·5 i2·:·
416 B
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_timing.out
    
Offset 1, 14 lines modifiedOffset 1, 14 lines modified
1 --·-*-·M2-comint·-*-·hash:·17309883004690986031 --·-*-·M2-comint·-*-·hash:·1730988300469098603
  
2 i1·:·timing·3^302 i1·:·timing·3^30
  
3 o1·=·2058911320946493 o1·=·205891132094649
4 ·····--·.000012869·seconds4 ·····--·.000013385·seconds
  
5 o1·:·Time5 o1·:·Time
  
6 i2·:·peek·oo6 i2·:·peek·oo
  
7 o2·=·Time{.000012869,·205891132094649}7 o2·=·Time{.000013385,·205891132094649}
  
8 i3·:·8 i3·:·
5.09 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/example-output/_version.out
    
Offset 34, 15 lines modifiedOffset 34, 15 lines modified
34 ···············"memtailor·version"·=>·1.034 ···············"memtailor·version"·=>·1.0
35 ···············"mpfi·version"·=>·1.5.435 ···············"mpfi·version"·=>·1.5.4
36 ···············"mpfr·version"·=>·4.2.236 ···············"mpfr·version"·=>·4.2.2
37 ···············"mpsolve·version"·=>·3.2.137 ···············"mpsolve·version"·=>·3.2.1
38 ···············"mysql·version"·=>·not·present38 ···············"mysql·version"·=>·not·present
39 ···············"normaliz·version"·=>·3.10.439 ···············"normaliz·version"·=>·3.10.4
40 ···············"ntl·version"·=>·11.5.140 ···············"ntl·version"·=>·11.5.1
41 ···············"operating·system·release"·=>·6.1.0-37-cloud-amd6441 ···············"operating·system·release"·=>·6.12.22+bpo-amd64
42 ···············"operating·system"·=>·Linux42 ···············"operating·system"·=>·Linux
43 ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic·Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition·FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·ConnectionMatrices·Depth·Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements·LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings·SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone·ChainComplexExtras·Varieties·Schubert2·PushForward·LocalRings·PruneComplex·BoijSoederberg·BGG·Bruns·InvolutiveBases·ConwayPolynomials·EdgeIdeals·FourTiTwo·StatePolytope·Polyhedra·Truncations·Polymake·gfanInterface·PieriMaps·Normaliz·Posets·XML·OpenMath·SCSCP·RationalPoints·MapleInterface·ConvexInterface·SRdeformations·NumericalAlgebraicGeometry·BeginningMacaulay2·FormalGroupLaws·Graphics·WeylGroups·HodgeIntegrals·Cyclotomic·Binomials·Kronecker·Nauty·ToricVectorBundles·ModuleDeformations·PHCpack·SimplicialDecomposability·BooleanGB·AdjointIdeal·Parametrization·Serialization·NAGtypes·NormalToricVarieties·DGAlgebras·Graphs·GraphicalModels·BIBasis·KustinMiller·Units·NautyGraphs·VersalDeformations·CharacteristicClasses·RandomIdeals·RandomObjects·RandomPlaneCurves·RandomSpaceCurves·RandomGenus14Curves·RandomCanonicalCurves·RandomCurves·TensorComplexes·MonomialAlgebras·QthPower·EliminationMatrices·EllipticIntegrals·Triplets·CompleteIntersectionResolutions·EagonResolution·MCMApproximations·MultiplierIdeals·InvariantRing·QuillenSuslin·EnumerationCurves·Book3264Examples·Divisor·EllipticCurves·HighestWeights·MinimalPrimes·Bertini·TorAlgebra·Permanents·BinomialEdgeIdeals·TateOnProducts·LatticePolytopes·FiniteFittingIdeals·HigherCIOperators·LieTypes·ConformalBlocks·M0nbar·AnalyzeSheafOnP1·MultiplierIdealsDim2·RunExternalM2·NumericalSchubertCalculus·ToricTopology·Cremona·Resultants·VectorFields·SLPexpressions·Miura·ResidualIntersections·Visualize·EquivariantGB·ExampleSystems·RationalMaps·FastMinors·RandomPoints·SwitchingFields·SpectralSequences·SectionRing·OldPolyhedra·OldToricVectorBundles·K3Carpets·ChainComplexOperations·NumericalCertification·PhylogeneticTrees·MonodromySolver·ReactionNetworks·PackageCitations·NumericSolutions·GradedLieAlgebras·InverseSystems·Pullback·EngineTests·SVDComplexes·RandomComplexes·CohomCalg·Topcom·Triangulations·ReflexivePolytopesDB·AbstractToricVarieties·TestIdeals·FrobeniusThresholds·Seminormalization·AlgebraicSplines·TriangularSets·Chordal·Tropical·SymbolicPowers·Complexes·OldChainComplexes·GroebnerWalk·RandomMonomialIdeals·Matroids·NumericalImplicitization·NonminimalComplexes·CoincidentRootLoci·RelativeCanonicalResolution·RandomCurvesOverVerySmallFiniteFields·StronglyStableIdeals·SLnEquivariantMatrices·CorrespondenceScrolls·NCAlgebra·SpaceCurves·ExteriorIdeals·ToricInvariants·SegreClasses·SemidefiniteProgramming·SumsOfSquares·MultiGradedRationalMap·AssociativeAlgebras·VirtualResolutions·Quasidegrees·DiffAlg·DeterminantalRepresentations·FGLM·SpechtModule·SchurComplexes·SimplicialPosets·SlackIdeals·PositivityToricBundles·SparseResultants·DecomposableSparseSystems·MixedMultiplicity·PencilsOfQuadrics·ThreadedGB·AdjunctionForSurfaces·VectorGraphics·GKMVarieties·MonomialIntegerPrograms·NoetherianOperators·Hadamard·StatGraphs·GraphicalModelsMLE·EigenSolver·MultiplicitySequence·ResolutionsOfStanleyReisnerRings·NumericalLinearAlgebra·ResLengthThree·MonomialOrbits·MultiprojectiveVarieties·SpecialFanoFourfolds·RationalPoints2·SuperLinearAlgebra·SubalgebraBases·AInfinity·LinearTruncations·ThinSincereQuivers·Python·BettiCharacters·Jets·FunctionFieldDesingularization·HomotopyLieAlgebra·TSpreadIdeals·RealRoots·ExteriorModules·K3Surfaces·GroebnerStrata·QuaternaryQuartics·CotangentSchubert·OnlineLookup·MergeTeX·Probability·Isomorphism·CodingTheory·WhitneyStratifications·JSON·ForeignFunctions·GeometricDecomposability·PseudomonomialPrimaryDecomposition·PolyominoIdeals·MatchingFields·CellularResolutions·SagbiGbDetection·A1BrouwerDegrees·QuadraticIdealExamplesByRoos·TerraciniLoci·MatrixSchubert·RInterface·OIGroebnerBases·PlaneCurveLinearSeries·Valuations·SchurVeronese·VNumber·TropicalToric·MultigradedBGG·AbstractSimplicialComplexes·MultigradedImplicitization·Msolve·Permutations·SCMAlgebras·NumericalSemigroups·Oscillators·IncidenceCorrespondenceCohomology·ToricHigherDirectImages·Brackets·IntegerProgramming·GameTheory·AllMarkovBases43 ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic·Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition·FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·ConnectionMatrices·Depth·Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements·LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings·SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone·ChainComplexExtras·Varieties·Schubert2·PushForward·LocalRings·PruneComplex·BoijSoederberg·BGG·Bruns·InvolutiveBases·ConwayPolynomials·EdgeIdeals·FourTiTwo·StatePolytope·Polyhedra·Truncations·Polymake·gfanInterface·PieriMaps·Normaliz·Posets·XML·OpenMath·SCSCP·RationalPoints·MapleInterface·ConvexInterface·SRdeformations·NumericalAlgebraicGeometry·BeginningMacaulay2·FormalGroupLaws·Graphics·WeylGroups·HodgeIntegrals·Cyclotomic·Binomials·Kronecker·Nauty·ToricVectorBundles·ModuleDeformations·PHCpack·SimplicialDecomposability·BooleanGB·AdjointIdeal·Parametrization·Serialization·NAGtypes·NormalToricVarieties·DGAlgebras·Graphs·GraphicalModels·BIBasis·KustinMiller·Units·NautyGraphs·VersalDeformations·CharacteristicClasses·RandomIdeals·RandomObjects·RandomPlaneCurves·RandomSpaceCurves·RandomGenus14Curves·RandomCanonicalCurves·RandomCurves·TensorComplexes·MonomialAlgebras·QthPower·EliminationMatrices·EllipticIntegrals·Triplets·CompleteIntersectionResolutions·EagonResolution·MCMApproximations·MultiplierIdeals·InvariantRing·QuillenSuslin·EnumerationCurves·Book3264Examples·Divisor·EllipticCurves·HighestWeights·MinimalPrimes·Bertini·TorAlgebra·Permanents·BinomialEdgeIdeals·TateOnProducts·LatticePolytopes·FiniteFittingIdeals·HigherCIOperators·LieTypes·ConformalBlocks·M0nbar·AnalyzeSheafOnP1·MultiplierIdealsDim2·RunExternalM2·NumericalSchubertCalculus·ToricTopology·Cremona·Resultants·VectorFields·SLPexpressions·Miura·ResidualIntersections·Visualize·EquivariantGB·ExampleSystems·RationalMaps·FastMinors·RandomPoints·SwitchingFields·SpectralSequences·SectionRing·OldPolyhedra·OldToricVectorBundles·K3Carpets·ChainComplexOperations·NumericalCertification·PhylogeneticTrees·MonodromySolver·ReactionNetworks·PackageCitations·NumericSolutions·GradedLieAlgebras·InverseSystems·Pullback·EngineTests·SVDComplexes·RandomComplexes·CohomCalg·Topcom·Triangulations·ReflexivePolytopesDB·AbstractToricVarieties·TestIdeals·FrobeniusThresholds·Seminormalization·AlgebraicSplines·TriangularSets·Chordal·Tropical·SymbolicPowers·Complexes·OldChainComplexes·GroebnerWalk·RandomMonomialIdeals·Matroids·NumericalImplicitization·NonminimalComplexes·CoincidentRootLoci·RelativeCanonicalResolution·RandomCurvesOverVerySmallFiniteFields·StronglyStableIdeals·SLnEquivariantMatrices·CorrespondenceScrolls·NCAlgebra·SpaceCurves·ExteriorIdeals·ToricInvariants·SegreClasses·SemidefiniteProgramming·SumsOfSquares·MultiGradedRationalMap·AssociativeAlgebras·VirtualResolutions·Quasidegrees·DiffAlg·DeterminantalRepresentations·FGLM·SpechtModule·SchurComplexes·SimplicialPosets·SlackIdeals·PositivityToricBundles·SparseResultants·DecomposableSparseSystems·MixedMultiplicity·PencilsOfQuadrics·ThreadedGB·AdjunctionForSurfaces·VectorGraphics·GKMVarieties·MonomialIntegerPrograms·NoetherianOperators·Hadamard·StatGraphs·GraphicalModelsMLE·EigenSolver·MultiplicitySequence·ResolutionsOfStanleyReisnerRings·NumericalLinearAlgebra·ResLengthThree·MonomialOrbits·MultiprojectiveVarieties·SpecialFanoFourfolds·RationalPoints2·SuperLinearAlgebra·SubalgebraBases·AInfinity·LinearTruncations·ThinSincereQuivers·Python·BettiCharacters·Jets·FunctionFieldDesingularization·HomotopyLieAlgebra·TSpreadIdeals·RealRoots·ExteriorModules·K3Surfaces·GroebnerStrata·QuaternaryQuartics·CotangentSchubert·OnlineLookup·MergeTeX·Probability·Isomorphism·CodingTheory·WhitneyStratifications·JSON·ForeignFunctions·GeometricDecomposability·PseudomonomialPrimaryDecomposition·PolyominoIdeals·MatchingFields·CellularResolutions·SagbiGbDetection·A1BrouwerDegrees·QuadraticIdealExamplesByRoos·TerraciniLoci·MatrixSchubert·RInterface·OIGroebnerBases·PlaneCurveLinearSeries·Valuations·SchurVeronese·VNumber·TropicalToric·MultigradedBGG·AbstractSimplicialComplexes·MultigradedImplicitization·Msolve·Permutations·SCMAlgebras·NumericalSemigroups·Oscillators·IncidenceCorrespondenceCohomology·ToricHigherDirectImages·Brackets·IntegerProgramming·GameTheory·AllMarkovBases
44 ···············"pointer·size"·=>·844 ···············"pointer·size"·=>·8
45 ···············"python·version"·=>·3.13.445 ···············"python·version"·=>·3.13.4
46 ···············"readline·version"·=>·8.246 ···············"readline·version"·=>·8.2
47 ···············"scscp·version"·=>·not·present47 ···············"scscp·version"·=>·not·present
48 ···············"tbb·version"·=>·2022.148 ···············"tbb·version"·=>·2022.1
1.15 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/html/___Command.html
    
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84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·(c·=·Command·&quot;date&quot;;)</code></pre>85 ··············<pre><code·class="language-macaulay2">i3·:·(c·=·Command·&quot;date&quot;;)</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ··········<tr>88 ··········<tr>
89 ············<td>89 ············<td>
90 ··············<pre><code·class="language-macaulay2">i4·:·c90 ··············<pre><code·class="language-macaulay2">i4·:·c
91 Thu·Jun··5·22:54:15·-12·202591 Fri·Jul·10·10:29:58·+14·2026
  
92 o4·=·0</code></pre>92 o4·=·0</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ········</table>95 ········</table>
96 ······</div>96 ······</div>
97 ······<div>97 ······<div>
625 B
html2text {}
    
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19 in·a·file),·then·it·gets·executed·with·empty·argument·list.19 in·a·file),·then·it·gets·executed·with·empty·argument·list.
20 i1·:·(f·=·Command·(·()·->·2^30·);)20 i1·:·(f·=·Command·(·()·->·2^30·);)
21 i2·:·f21 i2·:·f
  
22 o2·=·107374182422 o2·=·1073741824
23 i3·:·(c·=·Command·"date";)23 i3·:·(c·=·Command·"date";)
24 i4·:·c24 i4·:·c
25 Thu·Jun··5·22:54:15·-12·202525 Fri·Jul·10·10:29:58·+14·2026
  
26 o4·=·026 o4·=·0
27 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*27 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
28 ····*·_\x8r_\x8u_\x8n·--·run·an·external·command28 ····*·_\x8r_\x8u_\x8n·--·run·an·external·command
29 ····*·_\x8A_\x8f_\x8t_\x8e_\x8r_\x8E_\x8v_\x8a_\x8l·--·top·level·method·applied·after·evaluation29 ····*·_\x8A_\x8f_\x8t_\x8e_\x8r_\x8E_\x8v_\x8a_\x8l·--·top·level·method·applied·after·evaluation
30 *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·c\x8co\x8om\x8mm\x8ma\x8an\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*30 *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·c\x8co\x8om\x8mm\x8ma\x8an\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
31 ····*·code(Command)·--·see·_\x8c_\x8o_\x8d_\x8e·--·display·source·code31 ····*·code(Command)·--·see·_\x8c_\x8o_\x8d_\x8e·--·display·source·code
1.94 KB
./usr/share/doc/Macaulay2/Macaulay2Doc/html/___Database.html
    
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52 ······<div>52 ······<div>
53 ········<h2>Description</h2>53 ········<h2>Description</h2>
54 A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have·to·be·strings.··In·this·example·we·create·a·database·file,·store·a·few·entries,·remove·an·entry·with·<a·title="remove·an·entry·from·a·mutable·hash·table,·list,·or·database"·href="_remove.html">remove</a>,·close·the·file,·and·then·remove·the·file.········<table·class="examples">54 A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have·to·be·strings.··In·this·example·we·create·a·database·file,·store·a·few·entries,·remove·an·entry·with·<a·title="remove·an·entry·from·a·mutable·hash·table,·list,·or·database"·href="_remove.html">remove</a>,·close·the·file,·and·then·remove·the·file.········<table·class="examples">
55 ··········<tr>55 ··········<tr>
56 ············<td>56 ············<td>
57 ··············<pre><code·class="language-macaulay2">i1·:·filename·=·temporaryFileName·()·|·&quot;.dbm&quot;57 ··············<pre><code·class="language-macaulay2">i1·:·filename·=·temporaryFileName·()·|·&quot;.dbm&quot;
  
58 o1·=·/tmp/M2-1093010-0/0.dbm</code></pre>58 o1·=·/tmp/M2-1049387-0/0.dbm</code></pre>
59 ············</td>59 ············</td>
60 ··········</tr>60 ··········</tr>
61 ··········<tr>61 ··········<tr>
62 ············<td>62 ············<td>
63 ··············<pre><code·class="language-macaulay2">i2·:·x·=·openDatabaseOut·filename63 ··············<pre><code·class="language-macaulay2">i2·:·x·=·openDatabaseOut·filename
  
64 o2·=·/tmp/M2-1093010-0/0.dbm64 o2·=·/tmp/M2-1049387-0/0.dbm
  
65 o2·:·Database</code></pre>65 o2·:·Database</code></pre>
66 ············</td>66 ············</td>
67 ··········</tr>67 ··········</tr>
68 ··········<tr>68 ··········<tr>
69 ············<td>69 ············<td>
70 ··············<pre><code·class="language-macaulay2">i3·:·x#&quot;first&quot;·=·&quot;hi·there&quot;70 ··············<pre><code·class="language-macaulay2">i3·:·x#&quot;first&quot;·=·&quot;hi·there&quot;
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7 *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8Da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·-\x8--\x8-·t\x8th\x8he\x8e·c\x8cl\x8la\x8as\x8ss\x8s·o\x8of\x8f·a\x8al\x8ll\x8l·d\x8da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·f\x8fi\x8il\x8le\x8es\x8s·*\x8**\x8**\x8**\x8**\x8**\x8*7 *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8Da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·-\x8--\x8-·t\x8th\x8he\x8e·c\x8cl\x8la\x8as\x8ss\x8s·o\x8of\x8f·a\x8al\x8ll\x8l·d\x8da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·f\x8fi\x8il\x8le\x8es\x8s·*\x8**\x8**\x8**\x8**\x8**\x8*
8 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*8 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
9 A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have9 A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have
10 to·be·strings.·In·this·example·we·create·a·database·file,·store·a·few·entries,10 to·be·strings.·In·this·example·we·create·a·database·file,·store·a·few·entries,
11 remove·an·entry·with·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e,·close·the·file,·and·then·remove·the·file.11 remove·an·entry·with·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e,·close·the·file,·and·then·remove·the·file.
12 i1·:·filename·=·temporaryFileName·()·|·".dbm"12 i1·:·filename·=·temporaryFileName·()·|·".dbm"
  
13 o1·=·/tmp/M2-1093010-0/0.dbm13 o1·=·/tmp/M2-1049387-0/0.dbm
14 i2·:·x·=·openDatabaseOut·filename14 i2·:·x·=·openDatabaseOut·filename
  
15 o2·=·/tmp/M2-1093010-0/0.dbm15 o2·=·/tmp/M2-1049387-0/0.dbm
  
16 o2·:·Database16 o2·:·Database
17 i3·:·x#"first"·=·"hi·there"17 i3·:·x#"first"·=·"hi·there"
  
18 o3·=·hi·there18 o3·=·hi·there
19 i4·:·x#"first"19 i4·:·x#"first"
  
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53 ········<h2>Description</h2>53 ········<h2>Description</h2>
54 ········<p>Macaulay2·uses·the·Hans·Boehm·<a·href="___G__C_spgarbage_spcollector.html">garbage·collector</a>·to·reclaim·unused·memory.··The·function·<span·class="tt">GCstats</span>·provides·information·about·its·status,·such·as·the·total·number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage·collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu·time·spent·in·garbage·collection,·etc.</p>54 ········<p>Macaulay2·uses·the·Hans·Boehm·<a·href="___G__C_spgarbage_spcollector.html">garbage·collector</a>·to·reclaim·unused·memory.··The·function·<span·class="tt">GCstats</span>·provides·information·about·its·status,·such·as·the·total·number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage·collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu·time·spent·in·garbage·collection,·etc.</p>
55 ········<table·class="examples">55 ········<table·class="examples">
56 ··········<tr>56 ··········<tr>
57 ············<td>57 ············<td>
58 ··············<pre><code·class="language-macaulay2">i1·:·s·=·GCstats()58 ··············<pre><code·class="language-macaulay2">i1·:·s·=·GCstats()
  
59 o1·=·HashTable{&quot;bytesAlloc&quot;·=>·42573633514········}59 o1·=·HashTable{&quot;bytesAlloc&quot;·=>·42614349306········}
60 ···············&quot;GC_free_space_divisor&quot;·=>·360 ···············&quot;GC_free_space_divisor&quot;·=>·3
61 ···············&quot;GC_LARGE_ALLOC_WARN_INTERVAL&quot;·=>·161 ···············&quot;GC_LARGE_ALLOC_WARN_INTERVAL&quot;·=>·1
62 ···············&quot;gcCpuTimeSecs&quot;·=>·062 ···············&quot;gcCpuTimeSecs&quot;·=>·0
63 ···············&quot;heapSize&quot;·=>·22472704063 ···············&quot;heapSize&quot;·=>·224940032
64 ···············&quot;numGCs&quot;·=>·78764 ···············&quot;numGCs&quot;·=>·787
65 ···············&quot;numGCThreads&quot;·=>·1265 ···············&quot;numGCThreads&quot;·=>·12
  
66 o1·:·HashTable</code></pre>66 o1·:·HashTable</code></pre>
67 ············</td>67 ············</td>
68 ··········</tr>68 ··········</tr>
69 ········</table>69 ········</table>
70 ········<p>The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information·can·be·easily·extracted,·as·follows.</p>70 ········<p>The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information·can·be·easily·extracted,·as·follows.</p>
71 ········<table·class="examples">71 ········<table·class="examples">
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i2·:·s#&quot;heapSize&quot;74 ··············<pre><code·class="language-macaulay2">i2·:·s#&quot;heapSize&quot;
  
75 o2·=·224727040</code></pre>75 o2·=·224940032</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ········</table>78 ········</table>
79 ········<p>Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment·variables·affecting·the·operation·of·the·garbage·collector·that·have·been·specified·by·the·user.</p>79 ········<p>Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment·variables·affecting·the·operation·of·the·garbage·collector·that·have·been·specified·by·the·user.</p>
80 ········<p>For·further·information·about·the·individual·items·in·the·table,·we·refer·the·user·to·the·source·code·and·documentation·of·the·garbage·collector.</p>80 ········<p>For·further·information·about·the·individual·items·in·the·table,·we·refer·the·user·to·the·source·code·and·documentation·of·the·garbage·collector.</p>
81 ······</div>81 ······</div>
82 ······<div>82 ······<div>
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9 Macaulay2·uses·the·Hans·Boehm·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r·to·reclaim·unused·memory.·The9 Macaulay2·uses·the·Hans·Boehm·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r·to·reclaim·unused·memory.·The
10 function·GCstats·provides·information·about·its·status,·such·as·the·total10 function·GCstats·provides·information·about·its·status,·such·as·the·total
11 number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage11 number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage
12 collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu12 collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu
13 time·spent·in·garbage·collection,·etc.13 time·spent·in·garbage·collection,·etc.
14 i1·:·s·=·GCstats()14 i1·:·s·=·GCstats()
  
15 o1·=·HashTable{"bytesAlloc"·=>·42573633514········}15 o1·=·HashTable{"bytesAlloc"·=>·42614349306········}
16 ···············"GC_free_space_divisor"·=>·316 ···············"GC_free_space_divisor"·=>·3
17 ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·117 ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1
18 ···············"gcCpuTimeSecs"·=>·018 ···············"gcCpuTimeSecs"·=>·0
19 ···············"heapSize"·=>·22472704019 ···············"heapSize"·=>·224940032
20 ···············"numGCs"·=>·78720 ···············"numGCs"·=>·787
21 ···············"numGCThreads"·=>·1221 ···············"numGCThreads"·=>·12
  
22 o1·:·HashTable22 o1·:·HashTable
23 The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information23 The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information
24 can·be·easily·extracted,·as·follows.24 can·be·easily·extracted,·as·follows.
25 i2·:·s#"heapSize"25 i2·:·s#"heapSize"
  
26 o2·=·22472704026 o2·=·224940032
27 Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment27 Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment
28 variables·affecting·the·operation·of·the·garbage·collector·that·have·been28 variables·affecting·the·operation·of·the·garbage·collector·that·have·been
29 specified·by·the·user.29 specified·by·the·user.
30 For·further·information·about·the·individual·items·in·the·table,·we·refer·the30 For·further·information·about·the·individual·items·in·the·table,·we·refer·the
31 user·to·the·source·code·and·documentation·of·the·garbage·collector.31 user·to·the·source·code·and·documentation·of·the·garbage·collector.
32 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*32 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
33 ····*·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r33 ····*·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r
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128 o7·:·Ideal·of·R</code></pre>128 o7·:·Ideal·of·R</code></pre>
129 ············</td>129 ············</td>
130 ··········</tr>130 ··········</tr>
131 ··········<tr>131 ··········<tr>
132 ············<td>132 ············<td>
133 ··············<pre><code·class="language-macaulay2">i8·:·time·J·=·truncate(8,·I,·MinimalGenerators·=>·false);133 ··············<pre><code·class="language-macaulay2">i8·:·time·J·=·truncate(8,·I,·MinimalGenerators·=>·false);
134 ·--·used·0.00468382s·(cpu);·0.00468123s·(thread);·0s·(gc)134 ·--·used·0.00460115s·(cpu);·0.00459974s·(thread);·0s·(gc)
  
135 o8·:·Ideal·of·R</code></pre>135 o8·:·Ideal·of·R</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ··········<tr>138 ··········<tr>
139 ············<td>139 ············<td>
140 ··············<pre><code·class="language-macaulay2">i9·:·time·K·=·truncate(8,·I,·MinimalGenerators·=>·true);140 ··············<pre><code·class="language-macaulay2">i9·:·time·K·=·truncate(8,·I,·MinimalGenerators·=>·true);
141 ·--·used·0.0413581s·(cpu);·0.0413685s·(thread);·0s·(gc)141 ·--·used·0.0483026s·(cpu);·0.04824s·(thread);·0s·(gc)
  
142 o9·:·Ideal·of·R</code></pre>142 o9·:·Ideal·of·R</code></pre>
143 ············</td>143 ············</td>
144 ··········</tr>144 ··········</tr>
145 ··········<tr>145 ··········<tr>
146 ············<td>146 ············<td>
147 ··············<pre><code·class="language-macaulay2">i10·:·numgens·J147 ··············<pre><code·class="language-macaulay2">i10·:·numgens·J
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46 o6·=·R46 o6·=·R
  
47 o6·:·PolynomialRing47 o6·:·PolynomialRing
48 i7·:·I·=·monomialCurveIdeal(R,·{1,4,5,9});48 i7·:·I·=·monomialCurveIdeal(R,·{1,4,5,9});
  
49 o7·:·Ideal·of·R49 o7·:·Ideal·of·R
50 i8·:·time·J·=·truncate(8,·I,·MinimalGenerators·=>·false);50 i8·:·time·J·=·truncate(8,·I,·MinimalGenerators·=>·false);
51 ·--·used·0.00468382s·(cpu);·0.00468123s·(thread);·0s·(gc)51 ·--·used·0.00460115s·(cpu);·0.00459974s·(thread);·0s·(gc)
  
52 o8·:·Ideal·of·R52 o8·:·Ideal·of·R
53 i9·:·time·K·=·truncate(8,·I,·MinimalGenerators·=>·true);53 i9·:·time·K·=·truncate(8,·I,·MinimalGenerators·=>·true);
54 ·--·used·0.0413581s·(cpu);·0.0413685s·(thread);·0s·(gc)54 ·--·used·0.0483026s·(cpu);·0.04824s·(thread);·0s·(gc)
  
55 o9·:·Ideal·of·R55 o9·:·Ideal·of·R
56 i10·:·numgens·J56 i10·:·numgens·J
  
57 o10·=·106757 o10·=·1067
58 i11·:·numgens·K58 i11·:·numgens·K
  
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68 o1·:·Matrix·RR······&lt;--·RR68 o1·:·Matrix·RR······&lt;--·RR
69 ··············53··········53</code></pre>69 ··············53··········53</code></pre>
70 ············</td>70 ············</td>
71 ··········</tr>71 ··········</tr>
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i2·:·time·SVD(M);74 ··············<pre><code·class="language-macaulay2">i2·:·time·SVD(M);
75 ·--·used·0.0294049s·(cpu);·0.0294053s·(thread);·0s·(gc)</code></pre>75 ·--·used·0.0345343s·(cpu);·0.0345229s·(thread);·0s·(gc)</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i3·:·time·SVD(M,·DivideConquer=>true);80 ··············<pre><code·class="language-macaulay2">i3·:·time·SVD(M,·DivideConquer=>true);
81 ·--·used·0.0301216s·(cpu);·0.0301329s·(thread);·0s·(gc)</code></pre>81 ·--·used·0.0363766s·(cpu);·0.0363847s·(thread);·0s·(gc)</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ········</table>84 ········</table>
85 ······</div>85 ······</div>
86 ······<div>86 ······<div>
87 ········<div>87 ········<div>
88 ··········<h2>Functions·with·optional·argument·named·<span·class="tt">DivideConquer</span>:</h2>88 ··········<h2>Functions·with·optional·argument·named·<span·class="tt">DivideConquer</span>:</h2>
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11 For·large·matrices,·this·algorithm·is·often·much·faster.11 For·large·matrices,·this·algorithm·is·often·much·faster.
12 i1·:·M·=·random(RR^200,·RR^200);12 i1·:·M·=·random(RR^200,·RR^200);
  
13 ················200·········20013 ················200·········200
14 o1·:·Matrix·RR······<--·RR14 o1·:·Matrix·RR······<--·RR
15 ··············53··········5315 ··············53··········53
16 i2·:·time·SVD(M);16 i2·:·time·SVD(M);
17 ·--·used·0.0294049s·(cpu);·0.0294053s·(thread);·0s·(gc)17 ·--·used·0.0345343s·(cpu);·0.0345229s·(thread);·0s·(gc)
18 i3·:·time·SVD(M,·DivideConquer=>true);18 i3·:·time·SVD(M,·DivideConquer=>true);
19 ·--·used·0.0301216s·(cpu);·0.0301329s·(thread);·0s·(gc)19 ·--·used·0.0363766s·(cpu);·0.0363847s·(thread);·0s·(gc)
20 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·D\x8Di\x8iv\x8vi\x8id\x8de\x8eC\x8Co\x8on\x8nq\x8qu\x8ue\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·D\x8Di\x8iv\x8vi\x8id\x8de\x8eC\x8Co\x8on\x8nq\x8qu\x8ue\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
21 ····*·_\x8S_\x8V_\x8D_\x8(_\x8._\x8._\x8._\x8,_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r_\x8=_\x8>_\x8._\x8._\x8._\x8)·--·whether·to·use·the·LAPACK·divide·and21 ····*·_\x8S_\x8V_\x8D_\x8(_\x8._\x8._\x8._\x8,_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r_\x8=_\x8>_\x8._\x8._\x8._\x8)·--·whether·to·use·the·LAPACK·divide·and
22 ······conquer·SVD·algorithm22 ······conquer·SVD·algorithm
23 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
24 ····*·Default·value:·_\x8t_\x8r_\x8u_\x8e24 ····*·Default·value:·_\x8t_\x8r_\x8u_\x8e
25 ····*·Function:·_\x8S_\x8V_\x8D·--·singular·value·decomposition·of·a·matrix25 ····*·Function:·_\x8S_\x8V_\x8D·--·singular·value·decomposition·of·a·matrix
26 ····*·Option·key:·_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r·--·an·optional·argument26 ····*·Option·key:·_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r·--·an·optional·argument
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826 ········<div>826 ········<div>
827 ··········<p>We·may·use·<a·title="projective·resolution"·href="../../OldChainComplexes/html/_resolution.html">resolution</a>·to·produce·a·projective·resolution·of·it,·and·<a·title="time·a·computation"·href="_time.html">time</a>·to·report·the·time·required.</p>827 ··········<p>We·may·use·<a·title="projective·resolution"·href="../../OldChainComplexes/html/_resolution.html">resolution</a>·to·produce·a·projective·resolution·of·it,·and·<a·title="time·a·computation"·href="_time.html">time</a>·to·report·the·time·required.</p>
828 ········</div>828 ········</div>
829 ········<table·class="examples">829 ········<table·class="examples">
830 ··········<tr>830 ··········<tr>
831 ············<td>831 ············<td>
832 ··············<pre><code·class="language-macaulay2">i59·:·time·C·=·resolution·M832 ··············<pre><code·class="language-macaulay2">i59·:·time·C·=·resolution·M
833 ·--·used·0.00212478s·(cpu);·0.00211824s·(thread);·0s·(gc)833 ·--·used·0.00156858s·(cpu);·0.00156277s·(thread);·0s·(gc)
  
834 ·······3······6······15······18······6834 ·······3······6······15······18······6
835 o59·=·R··&lt;--·R··&lt;--·R···&lt;--·R···&lt;--·R··&lt;--·0835 o59·=·R··&lt;--·R··&lt;--·R···&lt;--·R···&lt;--·R··&lt;--·0
836 ············································836 ············································
837 ······0······1······2·······3·······4······5837 ······0······1······2·······3·······4······5
  
838 o59·:·ChainComplex</code></pre>838 o59·:·ChainComplex</code></pre>
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390 ···············|·c·f·i·l·o·r·|390 ···············|·c·f·i·l·o·r·|
  
391 ·····························3391 ·····························3
392 o58·:·R-module,·quotient·of·R392 o58·:·R-module,·quotient·of·R
393 We·may·use·_\x8r_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n·to·produce·a·projective·resolution·of·it,·and·_\x8t_\x8i_\x8m_\x8e·to393 We·may·use·_\x8r_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n·to·produce·a·projective·resolution·of·it,·and·_\x8t_\x8i_\x8m_\x8e·to
394 report·the·time·required.394 report·the·time·required.
395 i59·:·time·C·=·resolution·M395 i59·:·time·C·=·resolution·M
396 ·--·used·0.00212478s·(cpu);·0.00211824s·(thread);·0s·(gc)396 ·--·used·0.00156858s·(cpu);·0.00156277s·(thread);·0s·(gc)
  
397 ·······3······6······15······18······6397 ·······3······6······15······18······6
398 o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0398 o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0
  
399 ······0······1······2·······3·······4······5399 ······0······1······2·······3·······4······5
  
400 o59·:·ChainComplex400 o59·:·ChainComplex
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97 o4·=·&quot;hi·there&quot;</code></pre>97 o4·=·&quot;hi·there&quot;</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i5·:·atEndOfFile·f102 ··············<pre><code·class="language-macaulay2">i5·:·atEndOfFile·f
  
103 o5·=·false</code></pre>103 o5·=·true</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ········</table>106 ········</table>
107 ······</div>107 ······</div>
108 ······<div>108 ······<div>
109 ········<div·class="waystouse">109 ········<div·class="waystouse">
110 ··········<h2>Ways·to·use·this·method:</h2>110 ··········<h2>Ways·to·use·this·method:</h2>
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23 o3·=·false23 o3·=·false
24 i4·:·peek·read·f24 i4·:·peek·read·f
  
25 o4·=·"hi·there"25 o4·=·"hi·there"
26 i5·:·atEndOfFile·f26 i5·:·atEndOfFile·f
  
27 o5·=·false27 o5·=·true
28 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
29 ····*·_\x8a_\x8t_\x8E_\x8n_\x8d_\x8O_\x8f_\x8F_\x8i_\x8l_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·test·for·end·of·file29 ····*·_\x8a_\x8t_\x8E_\x8n_\x8d_\x8O_\x8f_\x8F_\x8i_\x8l_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·test·for·end·of·file
30 ===============================================================================30 ===============================================================================
31 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-31 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
32 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_files.m2:374:0.32 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_files.m2:374:0.
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68 ······<div>68 ······<div>
69 ········<h2>Description</h2>69 ········<h2>Description</h2>
70 Produces·an·accurate·timing·for·the·code·contained·in·the·string·<span·class="tt">s</span>.··The·value·returned·is·the·number·of·seconds.········<table·class="examples">70 Produces·an·accurate·timing·for·the·code·contained·in·the·string·<span·class="tt">s</span>.··The·value·returned·is·the·number·of·seconds.········<table·class="examples">
71 ··········<tr>71 ··········<tr>
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i1·:·benchmark·&quot;sqrt·2p100000&quot;73 ··············<pre><code·class="language-macaulay2">i1·:·benchmark·&quot;sqrt·2p100000&quot;
  
74 o1·=·.000352008565519765474 o1·=·.0003361085814274754
  
75 o1·:·RR·(of·precision·53)</code></pre>75 o1·:·RR·(of·precision·53)</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ········</table>78 ········</table>
79 The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully·on·the·clock,·and·the·garbage·collector·will·be·called·beforehand.······</div>79 The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully·on·the·clock,·and·the·garbage·collector·will·be·called·beforehand.······</div>
80 ······<div>80 ······<div>
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12 ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·it·takes·to·evaluate·the·code12 ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·it·takes·to·evaluate·the·code
13 ············in·s13 ············in·s
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 Produces·an·accurate·timing·for·the·code·contained·in·the·string·s.·The·value15 Produces·an·accurate·timing·for·the·code·contained·in·the·string·s.·The·value
16 returned·is·the·number·of·seconds.16 returned·is·the·number·of·seconds.
17 i1·:·benchmark·"sqrt·2p100000"17 i1·:·benchmark·"sqrt·2p100000"
  
18 o1·=·.000352008565519765418 o1·=·.0003361085814274754
  
19 o1·:·RR·(of·precision·53)19 o1·:·RR·(of·precision·53)
20 The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully20 The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully
21 on·the·clock,·and·the·garbage·collector·will·be·called·beforehand.21 on·the·clock,·and·the·garbage·collector·will·be·called·beforehand.
22 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*22 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
23 The·object·_\x8b_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k·is·a·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8c_\x8l_\x8o_\x8s_\x8u_\x8r_\x8e.23 The·object·_\x8b_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k·is·a·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8c_\x8l_\x8o_\x8s_\x8u_\x8r_\x8e.
24 ===============================================================================24 ===============================================================================
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69 ··············<pre><code·class="language-macaulay2">i3·:·M·=·coker·vars·R;</code></pre>69 ··············<pre><code·class="language-macaulay2">i3·:·M·=·coker·vars·R;</code></pre>
70 ············</td>70 ············</td>
71 ··········</tr>71 ··········</tr>
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·pdim'·M74 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·pdim'·M
75 ·--·computing·pdim'75 ·--·computing·pdim'
76 ·--·.00329091s·elapsed76 ·--·.0154865s·elapsed
  
77 o4·=·3</code></pre>77 o4·=·3</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·pdim'·M82 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·pdim'·M
83 ·--·.000001483s·elapsed83 ·--·.000001704s·elapsed
  
84 o5·=·3</code></pre>84 o5·=·3</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i6·:·peek·M.cache89 ··············<pre><code·class="language-macaulay2">i6·:·peek·M.cache
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8 Here·is·a·simple·example·of·caching·a·computation·in·a·_\x8C_\x8a_\x8c_\x8h_\x8e_\x8T_\x8a_\x8b_\x8l_\x8e,·using·the8 Here·is·a·simple·example·of·caching·a·computation·in·a·_\x8C_\x8a_\x8c_\x8h_\x8e_\x8T_\x8a_\x8b_\x8l_\x8e,·using·the
9 augmented·null·coalescing·operator·_\x8?_\x8?_\x8=.9 augmented·null·coalescing·operator·_\x8?_\x8?_\x8=.
10 i1·:·pdim'·=·M·->·M.cache.pdim'·??=·(·printerr·"computing·pdim'";·pdim·M·);10 i1·:·pdim'·=·M·->·M.cache.pdim'·??=·(·printerr·"computing·pdim'";·pdim·M·);
11 i2·:·R·=·QQ[x,y,z];11 i2·:·R·=·QQ[x,y,z];
12 i3·:·M·=·coker·vars·R;12 i3·:·M·=·coker·vars·R;
13 i4·:·elapsedTime·pdim'·M13 i4·:·elapsedTime·pdim'·M
14 ·--·computing·pdim'14 ·--·computing·pdim'
15 ·--·.00329091s·elapsed15 ·--·.0154865s·elapsed
  
16 o4·=·316 o4·=·3
17 i5·:·elapsedTime·pdim'·M17 i5·:·elapsedTime·pdim'·M
18 ·--·.000001483s·elapsed18 ·--·.000001704s·elapsed
  
19 o5·=·319 o5·=·3
20 i6·:·peek·M.cache20 i6·:·peek·M.cache
  
21 o6·=·CacheTable{cache·=>·MutableHashTable{}21 o6·=·CacheTable{cache·=>·MutableHashTable{}
22 }22 }
23 ················isHomogeneous·=>·true23 ················isHomogeneous·=>·true
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104 o4·:·Task</code></pre>104 o4·:·Task</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i5·:·n109 ··············<pre><code·class="language-macaulay2">i5·:·n
  
110 o5·=·952361</code></pre>110 o5·=·960378</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i6·:·sleep·1115 ··············<pre><code·class="language-macaulay2">i6·:·sleep·1
  
116 o6·=·0</code></pre>116 o6·=·0</code></pre>
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127 o7·:·Task</code></pre>127 o7·:·Task</code></pre>
128 ············</td>128 ············</td>
129 ··········</tr>129 ··········</tr>
130 ··········<tr>130 ··········<tr>
131 ············<td>131 ············<td>
132 ··············<pre><code·class="language-macaulay2">i8·:·n132 ··············<pre><code·class="language-macaulay2">i8·:·n
  
133 o8·=·1924079</code></pre>133 o8·=·1924465</code></pre>
134 ············</td>134 ············</td>
135 ··········</tr>135 ··········</tr>
136 ··········<tr>136 ··········<tr>
137 ············<td>137 ············<td>
138 ··············<pre><code·class="language-macaulay2">i9·:·isReady·t138 ··············<pre><code·class="language-macaulay2">i9·:·isReady·t
  
139 o9·=·false</code></pre>139 o9·=·false</code></pre>
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145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i10·:·cancelTask·t</code></pre>146 ··············<pre><code·class="language-macaulay2">i10·:·cancelTask·t</code></pre>
147 ············</td>147 ············</td>
148 ··········</tr>148 ··········</tr>
149 ··········<tr>149 ··········<tr>
150 ············<td>150 ············<td>
151 ··············<pre><code·class="language-macaulay2">i11·:·sleep·2151 ··············<pre><code·class="language-macaulay2">i11·:·sleep·2
152 stdio:2:38:(3):[1]:·error:·interrupted152 stdio:2:25:(3):[1]:·error:·interrupted
  
153 o11·=·0</code></pre>153 o11·=·0</code></pre>
154 ············</td>154 ············</td>
155 ··········</tr>155 ··········</tr>
156 ··········<tr>156 ··········<tr>
157 ············<td>157 ············<td>
158 ··············<pre><code·class="language-macaulay2">i12·:·t158 ··············<pre><code·class="language-macaulay2">i12·:·t
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163 o12·:·Task</code></pre>163 o12·:·Task</code></pre>
164 ············</td>164 ············</td>
165 ··········</tr>165 ··········</tr>
166 ··········<tr>166 ··········<tr>
167 ············<td>167 ············<td>
168 ··············<pre><code·class="language-macaulay2">i13·:·n168 ··············<pre><code·class="language-macaulay2">i13·:·n
  
169 o13·=·1924231</code></pre>169 o13·=·1924656</code></pre>
170 ············</td>170 ············</td>
171 ··········</tr>171 ··········</tr>
172 ··········<tr>172 ··········<tr>
173 ············<td>173 ············<td>
174 ··············<pre><code·class="language-macaulay2">i14·:·sleep·1174 ··············<pre><code·class="language-macaulay2">i14·:·sleep·1
  
175 o14·=·0</code></pre>175 o14·=·0</code></pre>
176 ············</td>176 ············</td>
177 ··········</tr>177 ··········</tr>
178 ··········<tr>178 ··········<tr>
179 ············<td>179 ············<td>
180 ··············<pre><code·class="language-macaulay2">i15·:·n180 ··············<pre><code·class="language-macaulay2">i15·:·n
  
181 o15·=·1924231</code></pre>181 o15·=·1924656</code></pre>
182 ············</td>182 ············</td>
183 ··········</tr>183 ··········</tr>
184 ··········<tr>184 ··········<tr>
185 ············<td>185 ············<td>
186 ··············<pre><code·class="language-macaulay2">i16·:·isReady·t186 ··············<pre><code·class="language-macaulay2">i16·:·isReady·t
  
187 o16·=·false</code></pre>187 o16·=·false</code></pre>
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28 i4·:·t28 i4·:·t
  
29 o4·=·<<task,·running>>29 o4·=·<<task,·running>>
  
30 o4·:·Task30 o4·:·Task
31 i5·:·n31 i5·:·n
  
32 o5·=·95236132 o5·=·960378
33 i6·:·sleep·133 i6·:·sleep·1
  
34 o6·=·034 o6·=·0
35 i7·:·t35 i7·:·t
  
36 o7·=·<<task,·running>>36 o7·=·<<task,·running>>
  
37 o7·:·Task37 o7·:·Task
38 i8·:·n38 i8·:·n
  
39 o8·=·192407939 o8·=·1924465
40 i9·:·isReady·t40 i9·:·isReady·t
  
41 o9·=·false41 o9·=·false
42 i10·:·cancelTask·t42 i10·:·cancelTask·t
43 i11·:·sleep·243 i11·:·sleep·2
44 stdio:2:38:(3):[1]:·error:·interrupted44 stdio:2:25:(3):[1]:·error:·interrupted
  
45 o11·=·045 o11·=·0
46 i12·:·t46 i12·:·t
  
47 o12·=·<<task,·canceled>>47 o12·=·<<task,·canceled>>
  
48 o12·:·Task48 o12·:·Task
49 i13·:·n49 i13·:·n
  
50 o13·=·192423150 o13·=·1924656
51 i14·:·sleep·151 i14·:·sleep·1
  
52 o14·=·052 o14·=·0
53 i15·:·n53 i15·:·n
  
54 o15·=·192423154 o15·=·1924656
55 i16·:·isReady·t55 i16·:·isReady·t
  
56 o16·=·false56 o16·=·false
57 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*57 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
58 ····*·_\x8c_\x8a_\x8n_\x8c_\x8e_\x8l_\x8T_\x8a_\x8s_\x8k_\x8(_\x8T_\x8a_\x8s_\x8k_\x8)·--·stop·a·task58 ····*·_\x8c_\x8a_\x8n_\x8c_\x8e_\x8l_\x8T_\x8a_\x8s_\x8k_\x8(_\x8T_\x8a_\x8s_\x8k_\x8)·--·stop·a·task
59 ===============================================================================59 ===============================================================================
60 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-60 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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71 ··········<p>Change·the·current·working·directory·to·<var>dir</var>.</p>71 ··········<p>Change·the·current·working·directory·to·<var>dir</var>.</p>
72 ········</div>72 ········</div>
73 ········<table·class="examples">73 ········<table·class="examples">
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()76 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()
  
77 o1·=·/tmp/M2-1077179-0/0</code></pre>77 o1·=·/tmp/M2-985150-0/0</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir82 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir
  
83 o2·=·/tmp/M2-1077179-0/0</code></pre>83 o2·=·/tmp/M2-985150-0/0</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·changeDirectory·dir88 ··············<pre><code·class="language-macaulay2">i3·:·changeDirectory·dir
  
89 o3·=·/tmp/M2-1077179-0/0/</code></pre>89 o3·=·/tmp/M2-985150-0/0/</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i4·:·currentDirectory()94 ··············<pre><code·class="language-macaulay2">i4·:·currentDirectory()
  
95 o4·=·/tmp/M2-1077179-0/0/</code></pre>95 o4·=·/tmp/M2-985150-0/0/</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ········</table>98 ········</table>
99 ········<div>99 ········<div>
100 ··········<p>If·<var>dir</var>·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's·home·directory.</p>100 ··········<p>If·<var>dir</var>·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's·home·directory.</p>
101 ········</div>101 ········</div>
102 ······</div>102 ······</div>
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11 ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,11 ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,
12 ····*·Outputs:12 ····*·Outputs:
13 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·new·working·directory;13 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·new·working·directory;
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 Change·the·current·working·directory·to·dir.15 Change·the·current·working·directory·to·dir.
16 i1·:·dir·=·temporaryFileName()16 i1·:·dir·=·temporaryFileName()
  
17 o1·=·/tmp/M2-1077179-0/017 o1·=·/tmp/M2-985150-0/0
18 i2·:·makeDirectory·dir18 i2·:·makeDirectory·dir
  
19 o2·=·/tmp/M2-1077179-0/019 o2·=·/tmp/M2-985150-0/0
20 i3·:·changeDirectory·dir20 i3·:·changeDirectory·dir
  
21 o3·=·/tmp/M2-1077179-0/0/21 o3·=·/tmp/M2-985150-0/0/
22 i4·:·currentDirectory()22 i4·:·currentDirectory()
  
23 o4·=·/tmp/M2-1077179-0/0/23 o4·=·/tmp/M2-985150-0/0/
24 If·dir·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's24 If·dir·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's
25 home·directory.25 home·directory.
26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
27 ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·current·working·directory27 ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·current·working·directory
28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
29 The·object·_\x8c_\x8h_\x8a_\x8n_\x8g_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.29 The·object·_\x8c_\x8h_\x8a_\x8n_\x8g_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
30 ===============================================================================30 ===============================================================================
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95 o1·:·Package</code></pre>95 o1·:·Package</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i2·:·check_1·FirstPackage100 ··············<pre><code·class="language-macaulay2">i2·:·check_1·FirstPackage
101 ·--·warning:·reloading·FirstPackage;·recreate·instances·of·types·from·this·package101 ·--·warning:·reloading·FirstPackage;·recreate·instances·of·types·from·this·package
102 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.112117s·elapsed</code></pre>102 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.332184s·elapsed</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i3·:·check·FirstPackage107 ··············<pre><code·class="language-macaulay2">i3·:·check·FirstPackage
108 ·--·capturing·check(0,·&quot;FirstPackage&quot;)········--·.117408s·elapsed108 ·--·capturing·check(0,·&quot;FirstPackage&quot;)········--·.466856s·elapsed
109 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.110957s·elapsed</code></pre>109 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.391457s·elapsed</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ········</table>112 ········</table>
113 ········<div>113 ········<div>
114 ··········<p>Alternatively,·if·the·package·is·installed·somewhere·accessible,·one·can·do·the·following.</p>114 ··········<p>Alternatively,·if·the·package·is·installed·somewhere·accessible,·one·can·do·the·following.</p>
115 ········</div>115 ········</div>
116 ········<table·class="examples">116 ········<table·class="examples">
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i4·:·check_1·&quot;FirstPackage&quot;119 ··············<pre><code·class="language-macaulay2">i4·:·check_1·&quot;FirstPackage&quot;
120 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.113437s·elapsed</code></pre>120 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.321593s·elapsed</code></pre>
121 ············</td>121 ············</td>
122 ··········</tr>122 ··········</tr>
123 ··········<tr>123 ··········<tr>
124 ············<td>124 ············<td>
125 ··············<pre><code·class="language-macaulay2">i5·:·check·&quot;FirstPackage&quot;125 ··············<pre><code·class="language-macaulay2">i5·:·check·&quot;FirstPackage&quot;
126 ·--·capturing·check(0,·&quot;FirstPackage&quot;)········--·.109372s·elapsed126 ·--·capturing·check(0,·&quot;FirstPackage&quot;)········--·.351501s·elapsed
127 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.11024s·elapsed</code></pre>127 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.444128s·elapsed</code></pre>
128 ············</td>128 ············</td>
129 ··········</tr>129 ··········</tr>
130 ········</table>130 ········</table>
131 ········<div>131 ········<div>
132 ··········<p>A·<a·title="locate·a·package's·tests"·href="_tests.html">TestInput</a>·object·(or·a·list·of·such·objects)·can·also·be·run·directly.</p>132 ··········<p>A·<a·title="locate·a·package's·tests"·href="_tests.html">TestInput</a>·object·(or·a·list·of·such·objects)·can·also·be·run·directly.</p>
133 ········</div>133 ········</div>
134 ········<table·class="examples">134 ········<table·class="examples">
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140 o6·:·TestInput</code></pre>140 o6·:·TestInput</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
143 ··········<tr>143 ··········<tr>
144 ············<td>144 ············<td>
145 ··············<pre><code·class="language-macaulay2">i7·:·check·oo145 ··············<pre><code·class="language-macaulay2">i7·:·check·oo
146 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.109679s·elapsed</code></pre>146 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.333943s·elapsed</code></pre>
147 ············</td>147 ············</td>
148 ··········</tr>148 ··········</tr>
149 ··········<tr>149 ··········<tr>
150 ············<td>150 ············<td>
151 ··············<pre><code·class="language-macaulay2">i8·:·tests·&quot;FirstPackage&quot;151 ··············<pre><code·class="language-macaulay2">i8·:·tests·&quot;FirstPackage&quot;
  
152 o8·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}152 o8·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}
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156 o8·:·NumberedVerticalList</code></pre>156 o8·:·NumberedVerticalList</code></pre>
157 ············</td>157 ············</td>
158 ··········</tr>158 ··········</tr>
159 ··········<tr>159 ··········<tr>
160 ············<td>160 ············<td>
161 ··············<pre><code·class="language-macaulay2">i9·:·check·oo161 ··············<pre><code·class="language-macaulay2">i9·:·check·oo
162 ·--·capturing·check(0,·&quot;FirstPackage&quot;)········--·.115759s·elapsed162 ·--·capturing·check(0,·&quot;FirstPackage&quot;)········--·.391343s·elapsed
163 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.115056s·elapsed</code></pre>163 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.360842s·elapsed</code></pre>
164 ············</td>164 ············</td>
165 ··········</tr>165 ··········</tr>
166 ········</table>166 ········</table>
167 ········<div>167 ········<div>
168 ··········<p>If·only·an·integer·is·passed·as·an·argument,·then·the·test·with·that·index·from·the·last·call·to·<a·title="locate·a·package's·tests"·href="_tests.html">tests</a>·is·run.</p>168 ··········<p>If·only·an·integer·is·passed·as·an·argument,·then·the·test·with·that·index·from·the·last·call·to·<a·title="locate·a·package's·tests"·href="_tests.html">tests</a>·is·run.</p>
169 ········</div>169 ········</div>
170 ········<table·class="examples">170 ········<table·class="examples">
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178 o10·:·NumberedVerticalList</code></pre>178 o10·:·NumberedVerticalList</code></pre>
179 ············</td>179 ············</td>
180 ··········</tr>180 ··········</tr>
181 ··········<tr>181 ··········<tr>
182 ············<td>182 ············<td>
183 ··············<pre><code·class="language-macaulay2">i11·:·check·1183 ··············<pre><code·class="language-macaulay2">i11·:·check·1
184 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.111649s·elapsed</code></pre>184 ·--·capturing·check(1,·&quot;FirstPackage&quot;)········--·.445743s·elapsed</code></pre>
185 ············</td>185 ············</td>
186 ··········</tr>186 ··········</tr>
187 ········</table>187 ········</table>
188 ······</div>188 ······</div>
189 ······<div>189 ······<div>
190 ········<h2>Caveat</h2>190 ········<h2>Caveat</h2>
191 ········<div>191 ········<div>
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42 o1·=·FirstPackage42 o1·=·FirstPackage
  
43 o1·:·Package43 o1·:·Package
44 i2·:·check_1·FirstPackage44 i2·:·check_1·FirstPackage
45 ·--·warning:·reloading·FirstPackage;·recreate·instances·of·types·from·this45 ·--·warning:·reloading·FirstPackage;·recreate·instances·of·types·from·this
46 package46 package
47 ·--·capturing·check(1,·"FirstPackage")········--·.112117s·elapsed47 ·--·capturing·check(1,·"FirstPackage")········--·.332184s·elapsed
48 i3·:·check·FirstPackage48 i3·:·check·FirstPackage
49 ·--·capturing·check(0,·"FirstPackage")········--·.117408s·elapsed49 ·--·capturing·check(0,·"FirstPackage")········--·.466856s·elapsed
50 ·--·capturing·check(1,·"FirstPackage")········--·.110957s·elapsed50 ·--·capturing·check(1,·"FirstPackage")········--·.391457s·elapsed
51 Alternatively,·if·the·package·is·installed·somewhere·accessible,·one·can·do·the51 Alternatively,·if·the·package·is·installed·somewhere·accessible,·one·can·do·the
52 following.52 following.
53 i4·:·check_1·"FirstPackage"53 i4·:·check_1·"FirstPackage"
54 ·--·capturing·check(1,·"FirstPackage")········--·.113437s·elapsed54 ·--·capturing·check(1,·"FirstPackage")········--·.321593s·elapsed
55 i5·:·check·"FirstPackage"55 i5·:·check·"FirstPackage"
56 ·--·capturing·check(0,·"FirstPackage")········--·.109372s·elapsed56 ·--·capturing·check(0,·"FirstPackage")········--·.351501s·elapsed
57 ·--·capturing·check(1,·"FirstPackage")········--·.11024s·elapsed57 ·--·capturing·check(1,·"FirstPackage")········--·.444128s·elapsed
58 A·_\x8T_\x8e_\x8s_\x8t_\x8I_\x8n_\x8p_\x8u_\x8t·object·(or·a·list·of·such·objects)·can·also·be·run·directly.58 A·_\x8T_\x8e_\x8s_\x8t_\x8I_\x8n_\x8p_\x8u_\x8t·object·(or·a·list·of·such·objects)·can·also·be·run·directly.
59 i6·:·tests(1,·"FirstPackage")59 i6·:·tests(1,·"FirstPackage")
  
60 o6·=·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]60 o6·=·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]
  
61 o6·:·TestInput61 o6·:·TestInput
62 i7·:·check·oo62 i7·:·check·oo
63 ·--·capturing·check(1,·"FirstPackage")········--·.109679s·elapsed63 ·--·capturing·check(1,·"FirstPackage")········--·.333943s·elapsed
64 i8·:·tests·"FirstPackage"64 i8·:·tests·"FirstPackage"
  
65 o8·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}65 o8·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}
66 ·····{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}66 ·····{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}
  
67 o8·:·NumberedVerticalList67 o8·:·NumberedVerticalList
68 i9·:·check·oo68 i9·:·check·oo
69 ·--·capturing·check(0,·"FirstPackage")········--·.115759s·elapsed69 ·--·capturing·check(0,·"FirstPackage")········--·.391343s·elapsed
70 ·--·capturing·check(1,·"FirstPackage")········--·.115056s·elapsed70 ·--·capturing·check(1,·"FirstPackage")········--·.360842s·elapsed
71 If·only·an·integer·is·passed·as·an·argument,·then·the·test·with·that·index·from71 If·only·an·integer·is·passed·as·an·argument,·then·the·test·with·that·index·from
72 the·last·call·to·_\x8t_\x8e_\x8s_\x8t_\x8s·is·run.72 the·last·call·to·_\x8t_\x8e_\x8s_\x8t_\x8s·is·run.
73 i10·:·tests·"FirstPackage"73 i10·:·tests·"FirstPackage"
  
74 o10·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}74 o10·=·{0·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:54:5-56:3]}
75 ······{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}75 ······{1·=>·TestInput[/usr/share/Macaulay2/FirstPackage.m2:58:5-60:3]}
  
76 o10·:·NumberedVerticalList76 o10·:·NumberedVerticalList
77 i11·:·check·177 i11·:·check·1
78 ·--·capturing·check(1,·"FirstPackage")········--·.111649s·elapsed78 ·--·capturing·check(1,·"FirstPackage")········--·.445743s·elapsed
79 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*79 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
80 Currently,·if·the·package·was·only·partially·loaded·because·the·documentation80 Currently,·if·the·package·was·only·partially·loaded·because·the·documentation
81 was·obtainable·from·a·database·(see·_\x8b_\x8e_\x8g_\x8i_\x8n_\x8D_\x8o_\x8c_\x8u_\x8m_\x8e_\x8n_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n),·then·the·package·will81 was·obtainable·from·a·database·(see·_\x8b_\x8e_\x8g_\x8i_\x8n_\x8D_\x8o_\x8c_\x8u_\x8m_\x8e_\x8n_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n),·then·the·package·will
82 be·reloaded,·this·time·completely,·to·ensure·that·all·tests·are·considered;82 be·reloaded,·this·time·completely,·to·ensure·that·all·tests·are·considered;
83 this·may·affect·user·objects·of·types·declared·by·the·package,·as·they·may·be83 this·may·affect·user·objects·of·types·declared·by·the·package,·as·they·may·be
84 not·usable·by·the·new·instance·of·the·package.·In·a·future·version,·either·the84 not·usable·by·the·new·instance·of·the·package.·In·a·future·version,·either·the
85 tests·and·the·documentation·will·both·be·cached,·or·neither·will.85 tests·and·the·documentation·will·both·be·cached,·or·neither·will.
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50 ····<div>50 ····<div>
51 ······<h1>communicating·with·programs</h1>51 ······<h1>communicating·with·programs</h1>
52 ······<div>52 ······<div>
53 The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it·communicate·directly·with·the·user,·and·wait·for·it·to·finish.··This·is·done·with·the·<a·title="run·an·external·command"·href="_run.html">run</a>·command.········<table·class="examples">53 The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it·communicate·directly·with·the·user,·and·wait·for·it·to·finish.··This·is·done·with·the·<a·title="run·an·external·command"·href="_run.html">run</a>·command.········<table·class="examples">
54 ··········<tr>54 ··········<tr>
55 ············<td>55 ············<td>
56 ··············<pre><code·class="language-macaulay2">i1·:·run·&quot;uname·-a&quot;56 ··············<pre><code·class="language-macaulay2">i1·:·run·&quot;uname·-a&quot;
57 Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.140-1·(2025-05-22)·x86_64·GNU/Linux57 Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux
  
58 o1·=·0</code></pre>58 o1·=·0</code></pre>
59 ············</td>59 ············</td>
60 ··········</tr>60 ··········</tr>
61 ········</table>61 ········</table>
62 To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·<a·title="a·binary·operator,·used·for·bit·shifting·or·file·output"·href="__lt_lt.html">&lt;&lt;</a>,·with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the·file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example.········<table·class="examples">62 To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·<a·title="a·binary·operator,·used·for·bit·shifting·or·file·output"·href="__lt_lt.html">&lt;&lt;</a>,·with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the·file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example.········<table·class="examples">
63 ··········<tr>63 ··········<tr>
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74 ··········</tr>74 ··········</tr>
75 ········</table>75 ········</table>
76 More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the·output·from·the·other·program.··If·the·program·requires·no·input·data,·then·we·can·use·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·with·a·file·name·whose·first·character·is·an·exclamation·point.··In·the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a·newline·character.········<table·class="examples">76 More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the·output·from·the·other·program.··If·the·program·requires·no·input·data,·then·we·can·use·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·with·a·file·name·whose·first·character·is·an·exclamation·point.··In·the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a·newline·character.········<table·class="examples">
77 ··········<tr>77 ··········<tr>
78 ············<td>78 ············<td>
79 ··············<pre><code·class="language-macaulay2">i3·:·peek·get·&quot;!uname·-a&quot;79 ··············<pre><code·class="language-macaulay2">i3·:·peek·get·&quot;!uname·-a&quot;
  
80 o3·=·&quot;Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian80 o3·=·&quot;Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC
81 ·····6.1.140-1·(2025-05-22)·x86_64·GNU/Linux\n&quot;</code></pre>81 ·····Debian·6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux\n&quot;</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ········</table>84 ········</table>
85 Bidirectional·communication·with·a·program·is·also·possible.··We·use·<a·title="open·an·input·output·file"·href="_open__In__Out.html">openInOut</a>·to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.··That·file·is·called·an·input·output·file.··In·this·example·we·open·a·connection·to·the·unix·utility·<span·class="tt">egrep</span>·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that·begin·with·<span·class="tt">in</span>.········<table·class="examples">85 Bidirectional·communication·with·a·program·is·also·possible.··We·use·<a·title="open·an·input·output·file"·href="_open__In__Out.html">openInOut</a>·to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.··That·file·is·called·an·input·output·file.··In·this·example·we·open·a·connection·to·the·unix·utility·<span·class="tt">egrep</span>·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that·begin·with·<span·class="tt">in</span>.········<table·class="examples">
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i4·:·f·=·openInOut·&quot;!egrep·'^in'&quot;88 ··············<pre><code·class="language-macaulay2">i4·:·f·=·openInOut·&quot;!egrep·'^in'&quot;
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5 _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c5 _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c
6 ===============================================================================6 ===============================================================================
7 *\x8**\x8**\x8**\x8**\x8**\x8*·c\x8co\x8om\x8mm\x8mu\x8un\x8ni\x8ic\x8ca\x8at\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8ms\x8s·*\x8**\x8**\x8**\x8**\x8**\x8*7 *\x8**\x8**\x8**\x8**\x8**\x8*·c\x8co\x8om\x8mm\x8mu\x8un\x8ni\x8ic\x8ca\x8at\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8ms\x8s·*\x8**\x8**\x8**\x8**\x8**\x8*
8 The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it8 The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it
9 communicate·directly·with·the·user,·and·wait·for·it·to·finish.·This·is·done9 communicate·directly·with·the·user,·and·wait·for·it·to·finish.·This·is·done
10 with·the·_\x8r_\x8u_\x8n·command.10 with·the·_\x8r_\x8u_\x8n·command.
11 i1·:·run·"uname·-a"11 i1·:·run·"uname·-a"
12 Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.140- 
13 1·(2025-05-22)·x86_64·GNU/Linux12 Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian
 13 6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux
  
14 o1·=·014 o1·=·0
15 To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·_\x8<_\x8<,15 To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·_\x8<_\x8<,
16 with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the16 with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the
17 file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example.17 file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example.
18 i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close18 i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close
19 ·ba19 ·ba
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26 More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the26 More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the
27 output·from·the·other·program.·If·the·program·requires·no·input·data,·then·we27 output·from·the·other·program.·If·the·program·requires·no·input·data,·then·we
28 can·use·_\x8g_\x8e_\x8t·with·a·file·name·whose·first·character·is·an·exclamation·point.·In28 can·use·_\x8g_\x8e_\x8t·with·a·file·name·whose·first·character·is·an·exclamation·point.·In
29 the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a29 the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a
30 newline·character.30 newline·character.
31 i3·:·peek·get·"!uname·-a"31 i3·:·peek·get·"!uname·-a"
  
32 o3·=·"Linux·infom01-amd64·6.1.0-37-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian32 o3·=·"Linux·i-capture-the-hostname·6.12.22+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC
33 ·····6.1.140-1·(2025-05-22)·x86_64·GNU/Linux\n"33 ·····Debian·6.12.22-1~bpo12+1·(2025-04-25)·x86_64·GNU/Linux\n"
34 Bidirectional·communication·with·a·program·is·also·possible.·We·use·_\x8o_\x8p_\x8e_\x8n_\x8I_\x8n_\x8O_\x8u_\x8t34 Bidirectional·communication·with·a·program·is·also·possible.·We·use·_\x8o_\x8p_\x8e_\x8n_\x8I_\x8n_\x8O_\x8u_\x8t
35 to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.·That35 to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.·That
36 file·is·called·an·input·output·file.·In·this·example·we·open·a·connection·to36 file·is·called·an·input·output·file.·In·this·example·we·open·a·connection·to
37 the·unix·utility·egrep·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that37 the·unix·utility·egrep·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that
38 begin·with·in.38 begin·with·in.
39 i4·:·f·=·openInOut·"!egrep·'^in'"39 i4·:·f·=·openInOut·"!egrep·'^in'"
  
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269 ···············1277</code></pre>269 ···············1277</code></pre>
270 ············</td>270 ············</td>
271 ··········</tr>271 ··········</tr>
272 ··········<tr>272 ··········<tr>
273 ············<td>273 ············<td>
274 ··············<pre><code·class="language-macaulay2">i24·:·gb·I274 ··············<pre><code·class="language-macaulay2">i24·:·gb·I
  
275 ···--·registering·gb·5·at·0x7fd41f6061c0275 ···--·registering·gb·5·at·0x7f82257de1c0
  
276 ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4276 ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4
277 ···--·number·of·monomials················=·8277 ···--·number·of·monomials················=·8
278 ···--·#reduction·steps·=·2278 ···--·#reduction·steps·=·2
279 ···--·#spairs·done·=·6279 ···--·#spairs·done·=·6
280 ···--·ncalls·=·0280 ···--·ncalls·=·0
281 ···--·nloop·=·0281 ···--·nloop·=·0
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373 ··············1······4373 ··············1······4
374 o32·:·Matrix·R··&lt;--·R</code></pre>374 o32·:·Matrix·R··&lt;--·R</code></pre>
375 ············</td>375 ············</td>
376 ··········</tr>376 ··········</tr>
377 ··········<tr>377 ··········<tr>
378 ············<td>378 ············<td>
379 ··············<pre><code·class="language-macaulay2">i33·:·time·betti·gb·f379 ··············<pre><code·class="language-macaulay2">i33·:·time·betti·gb·f
380 ·--·used·0.140209s·(cpu);·0.138647s·(thread);·0s·(gc)380 ·--·used·0.224213s·(cpu);·0.223398s·(thread);·0s·(gc)
  
381 ·············0··1381 ·············0··1
382 o33·=·total:·1·53382 o33·=·total:·1·53
383 ··········0:·1··.383 ··········0:·1··.
384 ··········1:·.··.384 ··········1:·.··.
385 ··········2:·.··2385 ··········2:·.··2
386 ··········3:·.··1386 ··········3:·.··1
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417 o35·:·ZZ[T]</code></pre>417 o35·:·ZZ[T]</code></pre>
418 ············</td>418 ············</td>
419 ··········</tr>419 ··········</tr>
420 ··········<tr>420 ··········<tr>
421 ············<td>421 ············<td>
422 ··············<pre><code·class="language-macaulay2">i36·:·time·betti·gb·f422 ··············<pre><code·class="language-macaulay2">i36·:·time·betti·gb·f
423 ·--·used·0.000929549s·(cpu);·0.00282705s·(thread);·0s·(gc)423 ·--·used·0.000680076s·(cpu);·0.00277309s·(thread);·0s·(gc)
  
424 ·············0··1424 ·············0··1
425 o36·=·total:·1·53425 o36·=·total:·1·53
426 ··········0:·1··.426 ··········0:·1··.
427 ··········1:·.··.427 ··········1:·.··.
428 ··········2:·.··2428 ··········2:·.··2
429 ··········3:·.··1429 ··········3:·.··1
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140 o23·=·ideal·(x*y·-·z·,·y··-·w·)140 o23·=·ideal·(x*y·-·z·,·y··-·w·)
  
141 ················ZZ141 ················ZZ
142 o23·:·Ideal·of·----[x..z,·w]142 o23·:·Ideal·of·----[x..z,·w]
143 ···············1277143 ···············1277
144 i24·:·gb·I144 i24·:·gb·I
  
145 ···--·registering·gb·5·at·0x7fd41f6061c0145 ···--·registering·gb·5·at·0x7f82257de1c0
  
146 ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4146 ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4
147 ···--·number·of·monomials················=·8147 ···--·number·of·monomials················=·8
148 ···--·#reduction·steps·=·2148 ···--·#reduction·steps·=·2
149 ···--·#spairs·done·=·6149 ···--·#spairs·done·=·6
150 ···--·ncalls·=·0150 ···--·ncalls·=·0
151 ···--·nloop·=·0151 ···--·nloop·=·0
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213 o31·:·ZZ[T]213 o31·:·ZZ[T]
214 i32·:·f·=·random(R^1,R^{-3,-3,-5,-6});214 i32·:·f·=·random(R^1,R^{-3,-3,-5,-6});
  
215 ··············1······4215 ··············1······4
216 o32·:·Matrix·R··<--·R216 o32·:·Matrix·R··<--·R
217 i33·:·time·betti·gb·f217 i33·:·time·betti·gb·f
218 ·--·used·0.140209s·(cpu);·0.138647s·(thread);·0s·(gc)218 ·--·used·0.224213s·(cpu);·0.223398s·(thread);·0s·(gc)
  
219 ·············0··1219 ·············0··1
220 o33·=·total:·1·53220 o33·=·total:·1·53
221 ··········0:·1··.221 ··········0:·1··.
222 ··········1:·.··.222 ··········1:·.··.
223 ··········2:·.··2223 ··········2:·.··2
224 ··········3:·.··1224 ··········3:·.··1
Offset 245, 15 lines modifiedOffset 245, 15 lines modified
245 i35·:·poincare·cokernel·f·=·(1-T^3)*(1-T^3)*(1-T^5)*(1-T^6)·--·cache·poincare245 i35·:·poincare·cokernel·f·=·(1-T^3)*(1-T^3)*(1-T^5)*(1-T^6)·--·cache·poincare
  
246 ············3····5·····8·····9····12·····14····17246 ············3····5·····8·····9····12·····14····17
247 o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T247 o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T
  
248 o35·:·ZZ[T]248 o35·:·ZZ[T]
249 i36·:·time·betti·gb·f249 i36·:·time·betti·gb·f
250 ·--·used·0.000929549s·(cpu);·0.00282705s·(thread);·0s·(gc)250 ·--·used·0.000680076s·(cpu);·0.00277309s·(thread);·0s·(gc)
  
251 ·············0··1251 ·············0··1
252 o36·=·total:·1·53252 o36·=·total:·1·53
253 ··········0:·1··.253 ··········0:·1··.
254 ··········1:·.··.254 ··········1:·.··.
255 ··········2:·.··2255 ··········2:·.··2
256 ··········3:·.··1256 ··········3:·.··1
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./usr/share/doc/Macaulay2/Macaulay2Doc/html/_copy__Directory_lp__String_cm__String_rp.html
    
Offset 80, 112 lines modifiedOffset 80, 112 lines modified
80 ······<div>80 ······<div>
81 ········<h2>Description</h2>81 ········<h2>Description</h2>
82 ········<table·class="examples">82 ········<table·class="examples">
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·&quot;/&quot;85 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·&quot;/&quot;
  
86 o1·=·/tmp/M2-1083836-0/0/</code></pre>86 o1·=·/tmp/M2-1017254-0/0/</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·&quot;/&quot;91 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·&quot;/&quot;
  
92 o2·=·/tmp/M2-1083836-0/1/</code></pre>92 o2·=·/tmp/M2-1017254-0/1/</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|&quot;a/&quot;)97 ··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|&quot;a/&quot;)
  
98 o3·=·/tmp/M2-1083836-0/0/a/</code></pre>98 o3·=·/tmp/M2-1017254-0/0/a/</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|&quot;b/&quot;)103 ··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|&quot;b/&quot;)
  
104 o4·=·/tmp/M2-1083836-0/0/b/</code></pre>104 o4·=·/tmp/M2-1017254-0/0/b/</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|&quot;b/c/&quot;)109 ··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|&quot;b/c/&quot;)
  
110 o5·=·/tmp/M2-1083836-0/0/b/c/</code></pre>110 o5·=·/tmp/M2-1017254-0/0/b/c/</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i6·:·src|&quot;a/f&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close115 ··············<pre><code·class="language-macaulay2">i6·:·src|&quot;a/f&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
116 o6·=·/tmp/M2-1083836-0/0/a/f116 o6·=·/tmp/M2-1017254-0/0/a/f
  
117 o6·:·File</code></pre>117 o6·:·File</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i7·:·src|&quot;a/g&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close122 ··············<pre><code·class="language-macaulay2">i7·:·src|&quot;a/g&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
123 o7·=·/tmp/M2-1083836-0/0/a/g123 o7·=·/tmp/M2-1017254-0/0/a/g
  
124 o7·:·File</code></pre>124 o7·:·File</code></pre>
125 ············</td>125 ············</td>
126 ··········</tr>126 ··········</tr>
127 ··········<tr>127 ··········<tr>
128 ············<td>128 ············<td>
129 ··············<pre><code·class="language-macaulay2">i8·:·src|&quot;b/c/g&quot;·&lt;&lt;·&quot;ho·there&quot;·&lt;&lt;·close129 ··············<pre><code·class="language-macaulay2">i8·:·src|&quot;b/c/g&quot;·&lt;&lt;·&quot;ho·there&quot;·&lt;&lt;·close
  
130 o8·=·/tmp/M2-1083836-0/0/b/c/g130 o8·=·/tmp/M2-1017254-0/0/b/c/g
  
131 o8·:·File</code></pre>131 o8·:·File</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i9·:·stack·findFiles·src136 ··············<pre><code·class="language-macaulay2">i9·:·stack·findFiles·src
  
137 o9·=·/tmp/M2-1083836-0/0/137 o9·=·/tmp/M2-1017254-0/0/
138 ·····/tmp/M2-1083836-0/0/b/138 ·····/tmp/M2-1017254-0/0/b/
139 ·····/tmp/M2-1083836-0/0/b/c/139 ·····/tmp/M2-1017254-0/0/b/c/
140 ·····/tmp/M2-1083836-0/0/b/c/g140 ·····/tmp/M2-1017254-0/0/b/c/g
141 ·····/tmp/M2-1083836-0/0/a/141 ·····/tmp/M2-1017254-0/0/a/
142 ·····/tmp/M2-1083836-0/0/a/f142 ·····/tmp/M2-1017254-0/0/a/g
143 ·····/tmp/M2-1083836-0/0/a/g</code></pre>143 ·····/tmp/M2-1017254-0/0/a/f</code></pre>
144 ············</td>144 ············</td>
145 ··········</tr>145 ··········</tr>
146 ··········<tr>146 ··········<tr>
147 ············<td>147 ············<td>
148 ··············<pre><code·class="language-macaulay2">i10·:·copyDirectory(src,dst,Verbose=>true)148 ··············<pre><code·class="language-macaulay2">i10·:·copyDirectory(src,dst,Verbose=>true)
149 ·--·copying:·/tmp/M2-1083836-0/0/b/c/g·->·/tmp/M2-1083836-0/1/b/c/g149 ·--·copying:·/tmp/M2-1017254-0/0/b/c/g·->·/tmp/M2-1017254-0/1/b/c/g
150 ·--·copying:·/tmp/M2-1083836-0/0/a/f·->·/tmp/M2-1083836-0/1/a/f150 ·--·copying:·/tmp/M2-1017254-0/0/a/g·->·/tmp/M2-1017254-0/1/a/g
151 ·--·copying:·/tmp/M2-1083836-0/0/a/g·->·/tmp/M2-1083836-0/1/a/g</code></pre>151 ·--·copying:·/tmp/M2-1017254-0/0/a/f·->·/tmp/M2-1017254-0/1/a/f</code></pre>
152 ············</td>152 ············</td>
153 ··········</tr>153 ··········</tr>
154 ··········<tr>154 ··········<tr>
155 ············<td>155 ············<td>
156 ··············<pre><code·class="language-macaulay2">i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true)156 ··············<pre><code·class="language-macaulay2">i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true)
157 ·--·skipping:·/tmp/M2-1083836-0/0/b/c/g·not·newer·than·/tmp/M2-1083836-0/1/b/c/g157 ·--·skipping:·/tmp/M2-1017254-0/0/b/c/g·not·newer·than·/tmp/M2-1017254-0/1/b/c/g
158 ·--·skipping:·/tmp/M2-1083836-0/0/a/f·not·newer·than·/tmp/M2-1083836-0/1/a/f158 ·--·skipping:·/tmp/M2-1017254-0/0/a/g·not·newer·than·/tmp/M2-1017254-0/1/a/g
159 ·--·skipping:·/tmp/M2-1083836-0/0/a/g·not·newer·than·/tmp/M2-1083836-0/1/a/g</code></pre>159 ·--·skipping:·/tmp/M2-1017254-0/0/a/f·not·newer·than·/tmp/M2-1017254-0/1/a/f</code></pre>
160 ············</td>160 ············</td>
161 ··········</tr>161 ··········</tr>
162 ··········<tr>162 ··········<tr>
163 ············<td>163 ············<td>
164 ··············<pre><code·class="language-macaulay2">i12·:·stack·findFiles·dst164 ··············<pre><code·class="language-macaulay2">i12·:·stack·findFiles·dst
  
165 o12·=·/tmp/M2-1083836-0/1/165 o12·=·/tmp/M2-1017254-0/1/
166 ······/tmp/M2-1083836-0/1/b/166 ······/tmp/M2-1017254-0/1/b/
167 ······/tmp/M2-1083836-0/1/b/c/167 ······/tmp/M2-1017254-0/1/b/c/
168 ······/tmp/M2-1083836-0/1/b/c/g168 ······/tmp/M2-1017254-0/1/b/c/g
169 ······/tmp/M2-1083836-0/1/a/169 ······/tmp/M2-1017254-0/1/a/
170 ······/tmp/M2-1083836-0/1/a/f170 ······/tmp/M2-1017254-0/1/a/g
171 ······/tmp/M2-1083836-0/1/a/g</code></pre>171 ······/tmp/M2-1017254-0/1/a/f</code></pre>
172 ············</td>172 ············</td>
173 ··········</tr>173 ··········</tr>
174 ··········<tr>174 ··········<tr>
175 ············<td>175 ············<td>
176 ··············<pre><code·class="language-macaulay2">i13·:·get·(dst|&quot;b/c/g&quot;)176 ··············<pre><code·class="language-macaulay2">i13·:·get·(dst|&quot;b/c/g&quot;)
  
177 o13·=·ho·there</code></pre>177 o13·=·ho·there</code></pre>
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Offset 25, 69 lines modifiedOffset 25, 69 lines modified
25 ············individual·file·operations25 ············individual·file·operations
26 ····*·Consequences:26 ····*·Consequences:
27 ··········o·a·copy·of·the·directory·tree·rooted·at·src·is·created,·rooted·at27 ··········o·a·copy·of·the·directory·tree·rooted·at·src·is·created,·rooted·at
28 ············dst28 ············dst
29 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
30 i1·:·src·=·temporaryFileName()·|·"/"30 i1·:·src·=·temporaryFileName()·|·"/"
  
31 o1·=·/tmp/M2-1083836-0/0/31 o1·=·/tmp/M2-1017254-0/0/
32 i2·:·dst·=·temporaryFileName()·|·"/"32 i2·:·dst·=·temporaryFileName()·|·"/"
  
33 o2·=·/tmp/M2-1083836-0/1/33 o2·=·/tmp/M2-1017254-0/1/
34 i3·:·makeDirectory·(src|"a/")34 i3·:·makeDirectory·(src|"a/")
  
35 o3·=·/tmp/M2-1083836-0/0/a/35 o3·=·/tmp/M2-1017254-0/0/a/
36 i4·:·makeDirectory·(src|"b/")36 i4·:·makeDirectory·(src|"b/")
  
37 o4·=·/tmp/M2-1083836-0/0/b/37 o4·=·/tmp/M2-1017254-0/0/b/
38 i5·:·makeDirectory·(src|"b/c/")38 i5·:·makeDirectory·(src|"b/c/")
  
39 o5·=·/tmp/M2-1083836-0/0/b/c/39 o5·=·/tmp/M2-1017254-0/0/b/c/
40 i6·:·src|"a/f"·<<·"hi·there"·<<·close40 i6·:·src|"a/f"·<<·"hi·there"·<<·close
  
41 o6·=·/tmp/M2-1083836-0/0/a/f41 o6·=·/tmp/M2-1017254-0/0/a/f
  
42 o6·:·File42 o6·:·File
43 i7·:·src|"a/g"·<<·"hi·there"·<<·close43 i7·:·src|"a/g"·<<·"hi·there"·<<·close
  
44 o7·=·/tmp/M2-1083836-0/0/a/g44 o7·=·/tmp/M2-1017254-0/0/a/g
  
45 o7·:·File45 o7·:·File
46 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close46 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close
  
47 o8·=·/tmp/M2-1083836-0/0/b/c/g47 o8·=·/tmp/M2-1017254-0/0/b/c/g
  
48 o8·:·File48 o8·:·File
49 i9·:·stack·findFiles·src49 i9·:·stack·findFiles·src
  
50 o9·=·/tmp/M2-1083836-0/0/50 o9·=·/tmp/M2-1017254-0/0/
51 ·····/tmp/M2-1083836-0/0/b/51 ·····/tmp/M2-1017254-0/0/b/
52 ·····/tmp/M2-1083836-0/0/b/c/52 ·····/tmp/M2-1017254-0/0/b/c/
53 ·····/tmp/M2-1083836-0/0/b/c/g53 ·····/tmp/M2-1017254-0/0/b/c/g
54 ·····/tmp/M2-1083836-0/0/a/54 ·····/tmp/M2-1017254-0/0/a/
55 ·····/tmp/M2-1083836-0/0/a/f 
56 ·····/tmp/M2-1083836-0/0/a/g55 ·····/tmp/M2-1017254-0/0/a/g
 56 ·····/tmp/M2-1017254-0/0/a/f
57 i10·:·copyDirectory(src,dst,Verbose=>true)57 i10·:·copyDirectory(src,dst,Verbose=>true)
58 ·--·copying:·/tmp/M2-1083836-0/0/b/c/g·->·/tmp/M2-1083836-0/1/b/c/g58 ·--·copying:·/tmp/M2-1017254-0/0/b/c/g·->·/tmp/M2-1017254-0/1/b/c/g
59 ·--·copying:·/tmp/M2-1083836-0/0/a/f·->·/tmp/M2-1083836-0/1/a/f 
60 ·--·copying:·/tmp/M2-1083836-0/0/a/g·->·/tmp/M2-1083836-0/1/a/g59 ·--·copying:·/tmp/M2-1017254-0/0/a/g·->·/tmp/M2-1017254-0/1/a/g
 60 ·--·copying:·/tmp/M2-1017254-0/0/a/f·->·/tmp/M2-1017254-0/1/a/f
61 i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true)61 i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true)
62 ·--·skipping:·/tmp/M2-1083836-0/0/b/c/g·not·newer·than·/tmp/M2-1083836-0/1/b/c/62 ·--·skipping:·/tmp/M2-1017254-0/0/b/c/g·not·newer·than·/tmp/M2-1017254-0/1/b/c/
63 g63 g
64 ·--·skipping:·/tmp/M2-1083836-0/0/a/f·not·newer·than·/tmp/M2-1083836-0/1/a/f 
65 ·--·skipping:·/tmp/M2-1083836-0/0/a/g·not·newer·than·/tmp/M2-1083836-0/1/a/g64 ·--·skipping:·/tmp/M2-1017254-0/0/a/g·not·newer·than·/tmp/M2-1017254-0/1/a/g
 65 ·--·skipping:·/tmp/M2-1017254-0/0/a/f·not·newer·than·/tmp/M2-1017254-0/1/a/f
66 i12·:·stack·findFiles·dst66 i12·:·stack·findFiles·dst
  
67 o12·=·/tmp/M2-1083836-0/1/67 o12·=·/tmp/M2-1017254-0/1/
68 ······/tmp/M2-1083836-0/1/b/68 ······/tmp/M2-1017254-0/1/b/
69 ······/tmp/M2-1083836-0/1/b/c/69 ······/tmp/M2-1017254-0/1/b/c/
70 ······/tmp/M2-1083836-0/1/b/c/g70 ······/tmp/M2-1017254-0/1/b/c/g
71 ······/tmp/M2-1083836-0/1/a/71 ······/tmp/M2-1017254-0/1/a/
72 ······/tmp/M2-1083836-0/1/a/f 
73 ······/tmp/M2-1083836-0/1/a/g72 ······/tmp/M2-1017254-0/1/a/g
 73 ······/tmp/M2-1017254-0/1/a/f
74 i13·:·get·(dst|"b/c/g")74 i13·:·get·(dst|"b/c/g")
  
75 o13·=·ho·there75 o13·=·ho·there
76 Now·we·remove·the·files·and·directories·we·created.76 Now·we·remove·the·files·and·directories·we·created.
77 i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d77 i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d
  
78 o14·=·rm78 o14·=·rm
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Offset 78, 65 lines modifiedOffset 78, 65 lines modified
78 ······<div>78 ······<div>
79 ········<h2>Description</h2>79 ········<h2>Description</h2>
80 ········<table·class="examples">80 ········<table·class="examples">
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()83 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()
  
84 o1·=·/tmp/M2-1083285-0/0</code></pre>84 o1·=·/tmp/M2-997314-0/0</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()89 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()
  
90 o2·=·/tmp/M2-1083285-0/1</code></pre>90 o2·=·/tmp/M2-997314-0/1</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i3·:·src·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close95 ··············<pre><code·class="language-macaulay2">i3·:·src·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
96 o3·=·/tmp/M2-1083285-0/096 o3·=·/tmp/M2-997314-0/0
  
97 o3·:·File</code></pre>97 o3·:·File</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i4·:·copyFile(src,dst,Verbose=>true)102 ··············<pre><code·class="language-macaulay2">i4·:·copyFile(src,dst,Verbose=>true)
103 ·--·copying:·/tmp/M2-1083285-0/0·->·/tmp/M2-1083285-0/1</code></pre>103 ·--·copying:·/tmp/M2-997314-0/0·->·/tmp/M2-997314-0/1</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i5·:·get·dst108 ··············<pre><code·class="language-macaulay2">i5·:·get·dst
  
109 o5·=·hi·there</code></pre>109 o5·=·hi·there</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)114 ··············<pre><code·class="language-macaulay2">i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)
115 ·--·skipping:·/tmp/M2-1083285-0/0·not·newer·than·/tmp/M2-1083285-0/1</code></pre>115 ·--·skipping:·/tmp/M2-997314-0/0·not·newer·than·/tmp/M2-997314-0/1</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ··········<tr>118 ··········<tr>
119 ············<td>119 ············<td>
120 ··············<pre><code·class="language-macaulay2">i7·:·src·&lt;&lt;·&quot;ho·there&quot;·&lt;&lt;·close120 ··············<pre><code·class="language-macaulay2">i7·:·src·&lt;&lt;·&quot;ho·there&quot;·&lt;&lt;·close
  
121 o7·=·/tmp/M2-1083285-0/0121 o7·=·/tmp/M2-997314-0/0
  
122 o7·:·File</code></pre>122 o7·:·File</code></pre>
123 ············</td>123 ············</td>
124 ··········</tr>124 ··········</tr>
125 ··········<tr>125 ··········<tr>
126 ············<td>126 ············<td>
127 ··············<pre><code·class="language-macaulay2">i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)127 ··············<pre><code·class="language-macaulay2">i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)
128 ·--·skipping:·/tmp/M2-1083285-0/0·not·newer·than·/tmp/M2-1083285-0/1</code></pre>128 ·--·skipping:·/tmp/M2-997314-0/0·not·newer·than·/tmp/M2-997314-0/1</code></pre>
129 ············</td>129 ············</td>
130 ··········</tr>130 ··········</tr>
131 ··········<tr>131 ··········<tr>
132 ············<td>132 ············<td>
133 ··············<pre><code·class="language-macaulay2">i9·:·get·dst133 ··············<pre><code·class="language-macaulay2">i9·:·get·dst
  
134 o9·=·hi·there</code></pre>134 o9·=·hi·there</code></pre>
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18 ··········o·Verbose·=>·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·default·value·false,·whether·to·report18 ··········o·Verbose·=>·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·default·value·false,·whether·to·report
19 ············individual·file·operations19 ············individual·file·operations
20 ····*·Consequences:20 ····*·Consequences:
21 ··········o·the·file·may·be·copied21 ··········o·the·file·may·be·copied
22 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*22 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
23 i1·:·src·=·temporaryFileName()23 i1·:·src·=·temporaryFileName()
  
24 o1·=·/tmp/M2-1083285-0/024 o1·=·/tmp/M2-997314-0/0
25 i2·:·dst·=·temporaryFileName()25 i2·:·dst·=·temporaryFileName()
  
26 o2·=·/tmp/M2-1083285-0/126 o2·=·/tmp/M2-997314-0/1
27 i3·:·src·<<·"hi·there"·<<·close27 i3·:·src·<<·"hi·there"·<<·close
  
28 o3·=·/tmp/M2-1083285-0/028 o3·=·/tmp/M2-997314-0/0
  
29 o3·:·File29 o3·:·File
30 i4·:·copyFile(src,dst,Verbose=>true)30 i4·:·copyFile(src,dst,Verbose=>true)
31 ·--·copying:·/tmp/M2-1083285-0/0·->·/tmp/M2-1083285-0/131 ·--·copying:·/tmp/M2-997314-0/0·->·/tmp/M2-997314-0/1
32 i5·:·get·dst32 i5·:·get·dst
  
33 o5·=·hi·there33 o5·=·hi·there
34 i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)34 i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)
35 ·--·skipping:·/tmp/M2-1083285-0/0·not·newer·than·/tmp/M2-1083285-0/135 ·--·skipping:·/tmp/M2-997314-0/0·not·newer·than·/tmp/M2-997314-0/1
36 i7·:·src·<<·"ho·there"·<<·close36 i7·:·src·<<·"ho·there"·<<·close
  
37 o7·=·/tmp/M2-1083285-0/037 o7·=·/tmp/M2-997314-0/0
  
38 o7·:·File38 o7·:·File
39 i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)39 i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true)
40 ·--·skipping:·/tmp/M2-1083285-0/0·not·newer·than·/tmp/M2-1083285-0/140 ·--·skipping:·/tmp/M2-997314-0/0·not·newer·than·/tmp/M2-997314-0/1
41 i9·:·get·dst41 i9·:·get·dst
  
42 o9·=·hi·there42 o9·=·hi·there
43 i10·:·removeFile·src43 i10·:·removeFile·src
44 i11·:·removeFile·dst44 i11·:·removeFile·dst
45 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*45 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
46 ····*·_\x8c_\x8o_\x8p_\x8y_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y46 ····*·_\x8c_\x8o_\x8p_\x8y_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y
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Offset 64, 38 lines modifiedOffset 64, 38 lines modified
64 ······<div>64 ······<div>
65 ········<h2>Description</h2>65 ········<h2>Description</h2>
66 ········<table·class="examples">66 ········<table·class="examples">
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i1·:·t1·=·cpuTime()69 ··············<pre><code·class="language-macaulay2">i1·:·t1·=·cpuTime()
  
70 o1·=·271.97052560970 o1·=·274.517090533
  
71 o1·:·RR·(of·precision·53)</code></pre>71 o1·:·RR·(of·precision·53)</code></pre>
72 ············</td>72 ············</td>
73 ··········</tr>73 ··········</tr>
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;</code></pre>76 ··············<pre><code·class="language-macaulay2">i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i3·:·t2·=·cpuTime()81 ··············<pre><code·class="language-macaulay2">i3·:·t2·=·cpuTime()
  
82 o3·=·272.93119385482 o3·=·275.549827006
  
83 o3·:·RR·(of·precision·53)</code></pre>83 o3·:·RR·(of·precision·53)</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i4·:·t2-t188 ··············<pre><code·class="language-macaulay2">i4·:·t2-t1
  
89 o4·=·.960668245000022189 o4·=·1.032736473
  
90 o4·:·RR·(of·precision·53)</code></pre>90 o4·:·RR·(of·precision·53)</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ········</table>93 ········</table>
94 ······</div>94 ······</div>
95 ······<div>95 ······<div>
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9 ············cpuTime()9 ············cpuTime()
10 ····*·Outputs:10 ····*·Outputs:
11 ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·of·cpu·time·used·since·the11 ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·of·cpu·time·used·since·the
12 ············program·was·started12 ············program·was·started
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 i1·:·t1·=·cpuTime()14 i1·:·t1·=·cpuTime()
  
15 o1·=·271.97052560915 o1·=·274.517090533
  
16 o1·:·RR·(of·precision·53)16 o1·:·RR·(of·precision·53)
17 i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;17 i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;
18 i3·:·t2·=·cpuTime()18 i3·:·t2·=·cpuTime()
  
19 o3·=·272.93119385419 o3·=·275.549827006
  
20 o3·:·RR·(of·precision·53)20 o3·:·RR·(of·precision·53)
21 i4·:·t2-t121 i4·:·t2-t1
  
22 o4·=·.960668245000022122 o4·=·1.032736473
  
23 o4·:·RR·(of·precision·53)23 o4·:·RR·(of·precision·53)
24 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*24 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
25 ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation25 ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation
26 ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation26 ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation
27 ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time27 ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time
28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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64 ······<div>64 ······<div>
65 ········<h2>Description</h2>65 ········<h2>Description</h2>
66 ········<table·class="examples">66 ········<table·class="examples">
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i1·:·currentTime()69 ··············<pre><code·class="language-macaulay2">i1·:·currentTime()
  
70 o1·=·1749207298</code></pre>70 o1·=·1783629092</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ········</table>73 ········</table>
74 ········<p>We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.</p>74 ········<p>We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.</p>
75 ········<table·class="examples">75 ········<table·class="examples">
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·)78 ··············<pre><code·class="language-macaulay2">i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·)
  
79 o2·=·55.4301726605281979 o2·=·56.52095588952952
  
80 o2·:·RR·(of·precision·53)</code></pre>80 o2·:·RR·(of·precision·53)</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ········</table>83 ········</table>
84 ········<p>We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that·number.</p>84 ········<p>We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that·number.</p>
85 ········<table·class="examples">85 ········<table·class="examples">
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·12·*·(oo·-·floor·oo)88 ··············<pre><code·class="language-macaulay2">i3·:·12·*·(oo·-·floor·oo)
  
89 o3·=·5.16207192633822889 o3·=·6.251470674354209
  
90 o3·:·RR·(of·precision·53)</code></pre>90 o3·:·RR·(of·precision·53)</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ········</table>93 ········</table>
94 ········<p>Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.</p>94 ········<p>Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.</p>
95 ········<table·class="examples">95 ········<table·class="examples">
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i4·:·run·&quot;date&quot;98 ··············<pre><code·class="language-macaulay2">i4·:·run·&quot;date&quot;
99 Thu·Jun··5·22:54:58·-12·202599 Fri·Jul·10·10:31:32·+14·2026
  
100 o4·=·0</code></pre>100 o4·=·0</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ········</table>103 ········</table>
104 ······</div>104 ······</div>
105 ······<div>105 ······<div>
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9 ············currentTime()9 ············currentTime()
10 ····*·Outputs:10 ····*·Outputs:
11 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·current·time,·in·seconds·since·00:00:00·1970-01-0111 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·current·time,·in·seconds·since·00:00:00·1970-01-01
12 ············UTC,·the·beginning·of·the·epoch12 ············UTC,·the·beginning·of·the·epoch
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 i1·:·currentTime()14 i1·:·currentTime()
  
15 o1·=·174920729815 o1·=·1783629092
16 We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.16 We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.
17 i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·)17 i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·)
  
18 o2·=·55.4301726605281918 o2·=·56.52095588952952
  
19 o2·:·RR·(of·precision·53)19 o2·:·RR·(of·precision·53)
20 We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that20 We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that
21 number.21 number.
22 i3·:·12·*·(oo·-·floor·oo)22 i3·:·12·*·(oo·-·floor·oo)
  
23 o3·=·5.16207192633822823 o3·=·6.251470674354209
  
24 o3·:·RR·(of·precision·53)24 o3·:·RR·(of·precision·53)
25 Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.25 Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.
26 i4·:·run·"date"26 i4·:·run·"date"
27 Thu·Jun··5·22:54:58·-12·202527 Fri·Jul·10·10:31:32·+14·2026
  
28 o4·=·028 o4·=·0
29 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
30 The·object·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.30 The·object·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
31 ===============================================================================31 ===============================================================================
32 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-32 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
33 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_system.m2:1849:0.33 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_system.m2:1849:0.
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59 ······</ul>59 ······</ul>
60 ······<div>60 ······<div>
61 ········<h2>Description</h2>61 ········<h2>Description</h2>
62 <span·class="tt">elapsedTime·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·time·elapsed,·and·returns·the·value·of·<span·class="tt">e</span>.········<table·class="examples">62 <span·class="tt">elapsedTime·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·time·elapsed,·and·returns·the·value·of·<span·class="tt">e</span>.········<table·class="examples">
63 ··········<tr>63 ··········<tr>
64 ············<td>64 ············<td>
65 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·sleep·165 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·sleep·1
66 ·--·1.00016s·elapsed66 ·--·1.00515s·elapsed
  
67 o1·=·0</code></pre>67 o1·=·0</code></pre>
68 ············</td>68 ············</td>
69 ··········</tr>69 ··········</tr>
70 ········</table>70 ········</table>
71 ······</div>71 ······</div>
72 ······<div>72 ······<div>
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7 *\x8**\x8**\x8**\x8**\x8**\x8*·e\x8el\x8la\x8ap\x8ps\x8se\x8ed\x8dT\x8Ti\x8im\x8me\x8e·-\x8--\x8-·t\x8ti\x8im\x8me\x8e·a\x8a·c\x8co\x8om\x8mp\x8pu\x8ut\x8ta\x8at\x8ti\x8io\x8on\x8n·i\x8in\x8nc\x8cl\x8lu\x8ud\x8di\x8in\x8ng\x8g·t\x8ti\x8im\x8me\x8e·e\x8el\x8la\x8ap\x8ps\x8se\x8ed\x8d·*\x8**\x8**\x8**\x8**\x8**\x8*7 *\x8**\x8**\x8**\x8**\x8**\x8*·e\x8el\x8la\x8ap\x8ps\x8se\x8ed\x8dT\x8Ti\x8im\x8me\x8e·-\x8--\x8-·t\x8ti\x8im\x8me\x8e·a\x8a·c\x8co\x8om\x8mp\x8pu\x8ut\x8ta\x8at\x8ti\x8io\x8on\x8n·i\x8in\x8nc\x8cl\x8lu\x8ud\x8di\x8in\x8ng\x8g·t\x8ti\x8im\x8me\x8e·e\x8el\x8la\x8ap\x8ps\x8se\x8ed\x8d·*\x8**\x8**\x8**\x8**\x8**\x8*
8 ····*···Usage:8 ····*···Usage:
9 ············elapsedTime·e9 ············elapsedTime·e
10 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*10 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
11 elapsedTime·e·evaluates·e,·prints·the·amount·of·time·elapsed,·and·returns·the11 elapsedTime·e·evaluates·e,·prints·the·amount·of·time·elapsed,·and·returns·the
12 value·of·e.12 value·of·e.
13 i1·:·elapsedTime·sleep·113 i1·:·elapsedTime·sleep·1
14 ·--·1.00016s·elapsed14 ·--·1.00515s·elapsed
  
15 o1·=·015 o1·=·0
16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
17 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed17 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed
18 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began18 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began
19 ····*·_\x8G_\x8C_\x8s_\x8t_\x8a_\x8t_\x8s·--·information·about·the·status·of·the·garbage·collector19 ····*·_\x8G_\x8C_\x8s_\x8t_\x8a_\x8t_\x8s·--·information·about·the·status·of·the·garbage·collector
20 ····*·_\x8p_\x8a_\x8r_\x8a_\x8l_\x8l_\x8e_\x8l_\x8·_\x8p_\x8r_\x8o_\x8g_\x8r_\x8a_\x8m_\x8m_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8t_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s_\x8·_\x8a_\x8n_\x8d_\x8·_\x8t_\x8a_\x8s_\x8k_\x8s20 ····*·_\x8p_\x8a_\x8r_\x8a_\x8l_\x8l_\x8e_\x8l_\x8·_\x8p_\x8r_\x8o_\x8g_\x8r_\x8a_\x8m_\x8m_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8t_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s_\x8·_\x8a_\x8n_\x8d_\x8·_\x8t_\x8a_\x8s_\x8k_\x8s
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54 <span·class="tt">elapsedTiming·e</span>·evaluates·<span·class="tt">e</span>·and·returns·a·list·of·type·<a·title="the·class·of·all·timing·results"·href="___Time.html">Time</a>·of·the·form·<span·class="tt">{t,v}</span>,·where·<span·class="tt">t</span>·is·the·number·of·seconds·of·time·elapsed,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p>54 <span·class="tt">elapsedTiming·e</span>·evaluates·<span·class="tt">e</span>·and·returns·a·list·of·type·<a·title="the·class·of·all·timing·results"·href="___Time.html">Time</a>·of·the·form·<span·class="tt">{t,v}</span>,·where·<span·class="tt">t</span>·is·the·number·of·seconds·of·time·elapsed,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p>
55 The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples">55 The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples">
56 ··········<tr>56 ··········<tr>
57 ············<td>57 ············<td>
58 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTiming·sleep·158 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTiming·sleep·1
  
59 o1·=·059 o1·=·0
60 ·····--·1.00015·seconds60 ·····--·1.00411·seconds
  
61 o1·:·Time</code></pre>61 o1·:·Time</code></pre>
62 ············</td>62 ············</td>
63 ··········</tr>63 ··········</tr>
64 ··········<tr>64 ··········<tr>
65 ············<td>65 ············<td>
66 ··············<pre><code·class="language-macaulay2">i2·:·peek·oo66 ··············<pre><code·class="language-macaulay2">i2·:·peek·oo
  
67 o2·=·Time{1.00015,·0}</code></pre>67 o2·=·Time{1.00411,·0}</code></pre>
68 ············</td>68 ············</td>
69 ··········</tr>69 ··········</tr>
70 ········</table>70 ········</table>
71 ······</div>71 ······</div>
72 ······<div>72 ······<div>
73 ········<h2>See·also</h2>73 ········<h2>See·also</h2>
74 ········<ul>74 ········<ul>
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10 where·t·is·the·number·of·seconds·of·time·elapsed,·and·v·is·the·value·of·the10 where·t·is·the·number·of·seconds·of·time·elapsed,·and·v·is·the·value·of·the
11 expression.11 expression.
12 The·default·method·for·printing·such·timing·results·is·to·display·the·timing12 The·default·method·for·printing·such·timing·results·is·to·display·the·timing
13 separately·in·a·comment·below·the·computed·value.13 separately·in·a·comment·below·the·computed·value.
14 i1·:·elapsedTiming·sleep·114 i1·:·elapsedTiming·sleep·1
  
15 o1·=·015 o1·=·0
16 ·····--·1.00015·seconds16 ·····--·1.00411·seconds
  
17 o1·:·Time17 o1·:·Time
18 i2·:·peek·oo18 i2·:·peek·oo
  
19 o2·=·Time{1.00015,·0}19 o2·=·Time{1.00411,·0}
20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
21 ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results21 ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results
22 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed22 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed
23 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began23 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began
24 ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation24 ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation
25 ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation25 ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation
26 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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65 o2·:·Ideal·of·R</code></pre>65 o2·:·Ideal·of·R</code></pre>
66 ············</td>66 ············</td>
67 ··········</tr>67 ··········</tr>
68 ··········<tr>68 ··········<tr>
69 ············<td>69 ············<td>
70 ··············<pre><code·class="language-macaulay2">i3·:·time·leadTerm·gens·gb·I70 ··············<pre><code·class="language-macaulay2">i3·:·time·leadTerm·gens·gb·I
71 ·--·used·0.103026s·(cpu);·0.103026s·(thread);·0s·(gc)71 ·--·used·0.114498s·(cpu);·0.114348s·(thread);·0s·(gc)
  
72 o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy472 o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4
73 ·····------------------------------------------------------------------------73 ·····------------------------------------------------------------------------
74 ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z274 ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2
75 ·····------------------------------------------------------------------------75 ·····------------------------------------------------------------------------
76 ·····267076255345488270sy3z4·5256861933965245618410txyz676 ·····267076255345488270sy3z4·5256861933965245618410txyz6
77 ·····------------------------------------------------------------------------77 ·····------------------------------------------------------------------------
Offset 162, 15 lines modifiedOffset 162, 15 lines modified
  
162 o7·:·Ideal·of·R</code></pre>162 o7·:·Ideal·of·R</code></pre>
163 ············</td>163 ············</td>
164 ··········</tr>164 ··········</tr>
165 ··········<tr>165 ··········<tr>
166 ············<td>166 ············<td>
167 ··············<pre><code·class="language-macaulay2">i8·:·time·G·=·eliminate(I,{s,t})167 ··············<pre><code·class="language-macaulay2">i8·:·time·G·=·eliminate(I,{s,t})
168 ·--·used·0.313091s·(cpu);·0.134462s·(thread);·0s·(gc)168 ·--·used·0.284413s·(cpu);·0.136539s·(thread);·0s·(gc)
  
169 ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···169 ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···
170 o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+170 o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+
171 ·····------------------------------------------------------------------------171 ·····------------------------------------------------------------------------
172 ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·172 ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·
173 ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z173 ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z
174 ·····------------------------------------------------------------------------174 ·····------------------------------------------------------------------------
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245 o11·:·Ideal·of·R1</code></pre>245 o11·:·Ideal·of·R1</code></pre>
246 ············</td>246 ············</td>
247 ··········</tr>247 ··········</tr>
248 ··········<tr>248 ··········<tr>
249 ············<td>249 ············<td>
250 ··············<pre><code·class="language-macaulay2">i12·:·time·G·=·eliminate(I1,{s,t})250 ··············<pre><code·class="language-macaulay2">i12·:·time·G·=·eliminate(I1,{s,t})
251 ·--·used·0.0276051s·(cpu);·0.0276072s·(thread);·0s·(gc)251 ·--·used·0.0290221s·(cpu);·0.0290301s·(thread);·0s·(gc)
  
252 ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7··252 ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7··
253 o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··-253 o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··-
254 ······-----------------------------------------------------------------------254 ······-----------------------------------------------------------------------
255 ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2··255 ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2··
256 ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··-256 ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··-
257 ······-----------------------------------------------------------------------257 ······-----------------------------------------------------------------------
Offset 337, 15 lines modifiedOffset 337, 15 lines modified
  
337 o16·:·RingMap·A·&lt;--·B</code></pre>337 o16·:·RingMap·A·&lt;--·B</code></pre>
338 ············</td>338 ············</td>
339 ··········</tr>339 ··········</tr>
340 ··········<tr>340 ··········<tr>
341 ············<td>341 ············<td>
342 ··············<pre><code·class="language-macaulay2">i17·:·time·G·=·kernel·F342 ··············<pre><code·class="language-macaulay2">i17·:·time·G·=·kernel·F
343 ·--·used·0.0903451s·(cpu);·0.0901412s·(thread);·0s·(gc)343 ·--·used·0.0957037s·(cpu);·0.0955438s·(thread);·0s·(gc)
  
344 ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···344 ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8···
345 o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+345 o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+
346 ······-----------------------------------------------------------------------346 ······-----------------------------------------------------------------------
347 ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·347 ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7·
348 ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z348 ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z
349 ······-----------------------------------------------------------------------349 ······-----------------------------------------------------------------------
Offset 418, 26 lines modifiedOffset 418, 26 lines modified
  
418 o19·:·PolynomialRing</code></pre>418 o19·:·PolynomialRing</code></pre>
419 ············</td>419 ············</td>
420 ··········</tr>420 ··········</tr>
421 ··········<tr>421 ··········<tr>
422 ············<td>422 ············<td>
423 ··············<pre><code·class="language-macaulay2">i20·:·time·f1·=·resultant(I_0,I_2,s)423 ··············<pre><code·class="language-macaulay2">i20·:·time·f1·=·resultant(I_0,I_2,s)
424 ·--·used·0.00138135s·(cpu);·0.00137906s·(thread);·0s·(gc)424 ·--·used·0.00152956s·(cpu);·0.00152337s·(thread);·0s·(gc)
  
425 ·········9····9······7····3425 ·········9····9······7····3
426 o20·=·x*t··-·t··-·z*t··-·z426 o20·=·x*t··-·t··-·z*t··-·z
  
427 o20·:·R</code></pre>427 o20·:·R</code></pre>
428 ············</td>428 ············</td>
429 ··········</tr>429 ··········</tr>
430 ··········<tr>430 ··········<tr>
431 ············<td>431 ············<td>
432 ··············<pre><code·class="language-macaulay2">i21·:·time·f2·=·resultant(I_1,f1,t)432 ··············<pre><code·class="language-macaulay2">i21·:·time·f2·=·resultant(I_1,f1,t)
433 ·--·used·0.235795s·(cpu);·0.0644657s·(thread);·0s·(gc)433 ·--·used·0.199214s·(cpu);·0.0630954s·(thread);·0s·(gc)
  
434 ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2··434 ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2··
435 o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+435 o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+
436 ······-----------------------------------------------------------------------436 ······-----------------------------------------------------------------------
437 ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8···437 ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8···
438 ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+438 ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+
439 ······-----------------------------------------------------------------------439 ······-----------------------------------------------------------------------
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Offset 13, 15 lines modifiedOffset 13, 15 lines modified
13 i2·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3)13 i2·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3)
  
14 ···············3···················3·····2···············314 ···············3···················3·····2···············3
15 o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z)15 o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z)
  
16 o2·:·Ideal·of·R16 o2·:·Ideal·of·R
17 i3·:·time·leadTerm·gens·gb·I17 i3·:·time·leadTerm·gens·gb·I
18 ·--·used·0.103026s·(cpu);·0.103026s·(thread);·0s·(gc)18 ·--·used·0.114498s·(cpu);·0.114348s·(thread);·0s·(gc)
  
19 o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy419 o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4
20 ·····------------------------------------------------------------------------20 ·····------------------------------------------------------------------------
21 ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z221 ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2
22 ·····------------------------------------------------------------------------22 ·····------------------------------------------------------------------------
23 ·····267076255345488270sy3z4·5256861933965245618410txyz623 ·····267076255345488270sy3z4·5256861933965245618410txyz6
24 ·····------------------------------------------------------------------------24 ·····------------------------------------------------------------------------
Offset 89, 15 lines modifiedOffset 89, 15 lines modified
89 i7·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3)89 i7·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3)
  
90 ···············3···················3·····2···············390 ···············3···················3·····2···············3
91 o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z)91 o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z)
  
92 o7·:·Ideal·of·R92 o7·:·Ideal·of·R
93 i8·:·time·G·=·eliminate(I,{s,t})93 i8·:·time·G·=·eliminate(I,{s,t})
94 ·--·used·0.313091s·(cpu);·0.134462s·(thread);·0s·(gc)94 ·--·used·0.284413s·(cpu);·0.136539s·(thread);·0s·(gc)
  
95 ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········895 ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8
96 o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+96 o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+
97 ·····------------------------------------------------------------------------97 ·····------------------------------------------------------------------------
98 ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······798 ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7
99 ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z99 ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z
100 ·····------------------------------------------------------------------------100 ·····------------------------------------------------------------------------
Offset 156, 15 lines modifiedOffset 156, 15 lines modified
156 Sometimes·giving·the·variables·different·degrees·will·speed·up·the156 Sometimes·giving·the·variables·different·degrees·will·speed·up·the
157 computations.·Here,·we·set·the·degrees·of·x,·y,·and·z·to·be·the·total·degrees.157 computations.·Here,·we·set·the·degrees·of·x,·y,·and·z·to·be·the·total·degrees.
158 i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}];158 i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}];
159 i11·:·I1·=·substitute(I,R1);159 i11·:·I1·=·substitute(I,R1);
  
160 o11·:·Ideal·of·R1160 o11·:·Ideal·of·R1
161 i12·:·time·G·=·eliminate(I1,{s,t})161 i12·:·time·G·=·eliminate(I1,{s,t})
162 ·--·used·0.0276051s·(cpu);·0.0276072s·(thread);·0s·(gc)162 ·--·used·0.0290221s·(cpu);·0.0290301s·(thread);·0s·(gc)
  
163 ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7163 ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7
164 o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··-164 o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··-
165 ······-----------------------------------------------------------------------165 ······-----------------------------------------------------------------------
166 ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2166 ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2
167 ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··-167 ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··-
168 ······-----------------------------------------------------------------------168 ······-----------------------------------------------------------------------
Offset 227, 15 lines modifiedOffset 227, 15 lines modified
227 i16·:·F·=·map(A,B,{s^3+s*t+1,·t^3+3*t^2+t,·s*t^3})227 i16·:·F·=·map(A,B,{s^3+s*t+1,·t^3+3*t^2+t,·s*t^3})
  
228 ···················3·············3·····2·········3228 ···················3·············3·····2·········3
229 o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·})229 o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·})
  
230 o16·:·RingMap·A·<--·B230 o16·:·RingMap·A·<--·B
231 i17·:·time·G·=·kernel·F231 i17·:·time·G·=·kernel·F
232 ·--·used·0.0903451s·(cpu);·0.0901412s·(thread);·0s·(gc)232 ·--·used·0.0957037s·(cpu);·0.0955438s·(thread);·0s·(gc)
  
233 ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8233 ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8
234 o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+234 o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+
235 ······-----------------------------------------------------------------------235 ······-----------------------------------------------------------------------
236 ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7236 ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7
237 ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z237 ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z
238 ······-----------------------------------------------------------------------238 ······-----------------------------------------------------------------------
Offset 296, 22 lines modifiedOffset 296, 22 lines modified
296 involve·the·variables·s·and·t.296 involve·the·variables·s·and·t.
297 i19·:·use·ring·I297 i19·:·use·ring·I
  
298 o19·=·R298 o19·=·R
  
299 o19·:·PolynomialRing299 o19·:·PolynomialRing
300 i20·:·time·f1·=·resultant(I_0,I_2,s)300 i20·:·time·f1·=·resultant(I_0,I_2,s)
301 ·--·used·0.00138135s·(cpu);·0.00137906s·(thread);·0s·(gc)301 ·--·used·0.00152956s·(cpu);·0.00152337s·(thread);·0s·(gc)
  
302 ·········9····9······7····3302 ·········9····9······7····3
303 o20·=·x*t··-·t··-·z*t··-·z303 o20·=·x*t··-·t··-·z*t··-·z
  
304 o20·:·R304 o20·:·R
305 i21·:·time·f2·=·resultant(I_1,f1,t)305 i21·:·time·f2·=·resultant(I_1,f1,t)
306 ·--·used·0.235795s·(cpu);·0.0644657s·(thread);·0s·(gc)306 ·--·used·0.199214s·(cpu);·0.0630954s·(thread);·0s·(gc)
  
307 ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2307 ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2
308 o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+308 o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+
309 ······-----------------------------------------------------------------------309 ······-----------------------------------------------------------------------
310 ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8310 ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8
311 ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+311 ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+
312 ······-----------------------------------------------------------------------312 ······-----------------------------------------------------------------------
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Offset 154, 15 lines modifiedOffset 154, 15 lines modified
154 ····································Version·=>·0.0154 ····································Version·=>·0.0
155 ·············package·prefix·=>·/usr/155 ·············package·prefix·=>·/usr/
156 ·············PackageIsLoaded·=>·true156 ·············PackageIsLoaded·=>·true
157 ·············pkgname·=>·Foo157 ·············pkgname·=>·Foo
158 ·············private·dictionary·=>·Foo#&quot;private·dictionary&quot;158 ·············private·dictionary·=>·Foo#&quot;private·dictionary&quot;
159 ·············processed·documentation·=>·MutableHashTable{}159 ·············processed·documentation·=>·MutableHashTable{}
160 ·············raw·documentation·=>·MutableHashTable{}160 ·············raw·documentation·=>·MutableHashTable{}
161 ·············source·directory·=>·/tmp/M2-1075204-0/91-rundir/161 ·············source·directory·=>·/tmp/M2-980911-0/91-rundir/
162 ·············source·file·=>·stdio162 ·············source·file·=>·stdio
163 ·············test·inputs·=>·MutableList{}</code></pre>163 ·············test·inputs·=>·MutableList{}</code></pre>
164 ············</td>164 ············</td>
165 ··········</tr>165 ··········</tr>
166 ··········<tr>166 ··········<tr>
167 ············<td>167 ············<td>
168 ··············<pre><code·class="language-macaulay2">i7·:·dictionaryPath168 ··············<pre><code·class="language-macaulay2">i7·:·dictionaryPath
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Offset 77, 15 lines modifiedOffset 77, 15 lines modified
77 ····································Version·=>·0.077 ····································Version·=>·0.0
78 ·············package·prefix·=>·/usr/78 ·············package·prefix·=>·/usr/
79 ·············PackageIsLoaded·=>·true79 ·············PackageIsLoaded·=>·true
80 ·············pkgname·=>·Foo80 ·············pkgname·=>·Foo
81 ·············private·dictionary·=>·Foo#"private·dictionary"81 ·············private·dictionary·=>·Foo#"private·dictionary"
82 ·············processed·documentation·=>·MutableHashTable{}82 ·············processed·documentation·=>·MutableHashTable{}
83 ·············raw·documentation·=>·MutableHashTable{}83 ·············raw·documentation·=>·MutableHashTable{}
84 ·············source·directory·=>·/tmp/M2-1075204-0/91-rundir/84 ·············source·directory·=>·/tmp/M2-980911-0/91-rundir/
85 ·············source·file·=>·stdio85 ·············source·file·=>·stdio
86 ·············test·inputs·=>·MutableList{}86 ·············test·inputs·=>·MutableList{}
87 i7·:·dictionaryPath87 i7·:·dictionaryPath
  
88 o7·=·{Foo.Dictionary,·Varieties.Dictionary,·Isomorphism.Dictionary,88 o7·=·{Foo.Dictionary,·Varieties.Dictionary,·Isomorphism.Dictionary,
89 ·····------------------------------------------------------------------------89 ·····------------------------------------------------------------------------
90 ·····Truncations.Dictionary,·Polyhedra.Dictionary,·Saturation.Dictionary,90 ·····Truncations.Dictionary,·Polyhedra.Dictionary,·Saturation.Dictionary,
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Offset 68, 29 lines modifiedOffset 68, 29 lines modified
68 ······<div>68 ······<div>
69 ········<h2>Description</h2>69 ········<h2>Description</h2>
70 ········<table·class="examples">70 ········<table·class="examples">
71 ··········<tr>71 ··········<tr>
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()73 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
74 o1·=·/tmp/M2-1079473-0/0</code></pre>74 o1·=·/tmp/M2-986105-0/0</code></pre>
75 ············</td>75 ············</td>
76 ··········</tr>76 ··········</tr>
77 ··········<tr>77 ··········<tr>
78 ············<td>78 ············<td>
79 ··············<pre><code·class="language-macaulay2">i2·:·fileExists·fn79 ··············<pre><code·class="language-macaulay2">i2·:·fileExists·fn
  
80 o2·=·false</code></pre>80 o2·=·false</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close85 ··············<pre><code·class="language-macaulay2">i3·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
86 o3·=·/tmp/M2-1079473-0/086 o3·=·/tmp/M2-986105-0/0
  
87 o3·:·File</code></pre>87 o3·:·File</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i4·:·fileExists·fn92 ··············<pre><code·class="language-macaulay2">i4·:·fileExists·fn
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Offset 10, 21 lines modifiedOffset 10, 21 lines modified
10 ····*·Inputs:10 ····*·Inputs:
11 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g11 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g
12 ····*·Outputs:12 ····*·Outputs:
13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·a·file·with·the·filename·or·path·fn·exists13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·a·file·with·the·filename·or·path·fn·exists
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 i1·:·fn·=·temporaryFileName()15 i1·:·fn·=·temporaryFileName()
  
16 o1·=·/tmp/M2-1079473-0/016 o1·=·/tmp/M2-986105-0/0
17 i2·:·fileExists·fn17 i2·:·fileExists·fn
  
18 o2·=·false18 o2·=·false
19 i3·:·fn·<<·"hi·there"·<<·close19 i3·:·fn·<<·"hi·there"·<<·close
  
20 o3·=·/tmp/M2-1079473-0/020 o3·=·/tmp/M2-986105-0/0
  
21 o3·:·File21 o3·:·File
22 i4·:·fileExists·fn22 i4·:·fileExists·fn
  
23 o4·=·true23 o4·=·true
24 i5·:·removeFile·fn24 i5·:·removeFile·fn
25 If·fn·refers·to·a·symbolic·link,·then·whether·the·file·exists·is·determined·by25 If·fn·refers·to·a·symbolic·link,·then·whether·the·file·exists·is·determined·by
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69 ········<h2>Description</h2>69 ········<h2>Description</h2>
70 ········<p>The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the·number·of·bytes·written·so·far.</p>70 ········<p>The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the·number·of·bytes·written·so·far.</p>
71 ········<table·class="examples">71 ········<table·class="examples">
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i1·:·f·=·temporaryFileName()·&lt;&lt;·&quot;hi·there&quot;74 ··············<pre><code·class="language-macaulay2">i1·:·f·=·temporaryFileName()·&lt;&lt;·&quot;hi·there&quot;
  
75 o1·=·/tmp/M2-1101145-0/075 o1·=·/tmp/M2-1059327-0/0
  
76 o1·:·File</code></pre>76 o1·:·File</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i2·:·fileLength·f81 ··············<pre><code·class="language-macaulay2">i2·:·fileLength·f
Offset 85, 24 lines modifiedOffset 85, 24 lines modified
85 o2·=·8</code></pre>85 o2·=·8</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ··········<tr>88 ··········<tr>
89 ············<td>89 ············<td>
90 ··············<pre><code·class="language-macaulay2">i3·:·close·f90 ··············<pre><code·class="language-macaulay2">i3·:·close·f
  
91 o3·=·/tmp/M2-1101145-0/091 o3·=·/tmp/M2-1059327-0/0
  
92 o3·:·File</code></pre>92 o3·:·File</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i4·:·filename·=·toString·f97 ··············<pre><code·class="language-macaulay2">i4·:·filename·=·toString·f
  
98 o4·=·/tmp/M2-1101145-0/0</code></pre>98 o4·=·/tmp/M2-1059327-0/0</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i5·:·fileLength·filename103 ··············<pre><code·class="language-macaulay2">i5·:·fileLength·filename
  
104 o5·=·8</code></pre>104 o5·=·8</code></pre>
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12 ····*·Outputs:12 ····*·Outputs:
13 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·length·of·the·file·f·or·the·file·whose·name·is·f13 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·length·of·the·file·f·or·the·file·whose·name·is·f
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the15 The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the
16 number·of·bytes·written·so·far.16 number·of·bytes·written·so·far.
17 i1·:·f·=·temporaryFileName()·<<·"hi·there"17 i1·:·f·=·temporaryFileName()·<<·"hi·there"
  
18 o1·=·/tmp/M2-1101145-0/018 o1·=·/tmp/M2-1059327-0/0
  
19 o1·:·File19 o1·:·File
20 i2·:·fileLength·f20 i2·:·fileLength·f
  
21 o2·=·821 o2·=·8
22 i3·:·close·f22 i3·:·close·f
  
23 o3·=·/tmp/M2-1101145-0/023 o3·=·/tmp/M2-1059327-0/0
  
24 o3·:·File24 o3·:·File
25 i4·:·filename·=·toString·f25 i4·:·filename·=·toString·f
  
26 o4·=·/tmp/M2-1101145-0/026 o4·=·/tmp/M2-1059327-0/0
27 i5·:·fileLength·filename27 i5·:·fileLength·filename
  
28 o5·=·828 o5·=·8
29 i6·:·get·filename29 i6·:·get·filename
  
30 o6·=·hi·there30 o6·=·hi·there
31 i7·:·length·oo31 i7·:·length·oo
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Offset 69, 22 lines modifiedOffset 69, 22 lines modified
69 ······<div>69 ······<div>
70 ········<h2>Description</h2>70 ········<h2>Description</h2>
71 ········<table·class="examples">71 ········<table·class="examples">
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()74 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
75 o1·=·/tmp/M2-1084758-0/0</code></pre>75 o1·=·/tmp/M2-1040725-0/0</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·&lt;&lt;·&quot;hi·there&quot;80 ··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·&lt;&lt;·&quot;hi·there&quot;
  
81 o2·=·/tmp/M2-1084758-0/081 o2·=·/tmp/M2-1040725-0/0
  
82 o2·:·File</code></pre>82 o2·:·File</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i3·:·fileMode·f87 ··············<pre><code·class="language-macaulay2">i3·:·fileMode·f
Offset 92, 15 lines modifiedOffset 92, 15 lines modified
92 o3·=·420</code></pre>92 o3·=·420</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i4·:·close·f97 ··············<pre><code·class="language-macaulay2">i4·:·close·f
  
98 o4·=·/tmp/M2-1084758-0/098 o4·=·/tmp/M2-1040725-0/0
  
99 o4·:·File</code></pre>99 o4·:·File</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre>104 ··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre>
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11 ····*·Inputs:11 ····*·Inputs:
12 ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e12 ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e
13 ····*·Outputs:13 ····*·Outputs:
14 ··········o·the·mode·of·the·open·file·f14 ··········o·the·mode·of·the·open·file·f
15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
16 i1·:·fn·=·temporaryFileName()16 i1·:·fn·=·temporaryFileName()
  
17 o1·=·/tmp/M2-1084758-0/017 o1·=·/tmp/M2-1040725-0/0
18 i2·:·f·=·fn·<<·"hi·there"18 i2·:·f·=·fn·<<·"hi·there"
  
19 o2·=·/tmp/M2-1084758-0/019 o2·=·/tmp/M2-1040725-0/0
  
20 o2·:·File20 o2·:·File
21 i3·:·fileMode·f21 i3·:·fileMode·f
  
22 o3·=·42022 o3·=·420
23 i4·:·close·f23 i4·:·close·f
  
24 o4·=·/tmp/M2-1084758-0/024 o4·=·/tmp/M2-1040725-0/0
  
25 o4·:·File25 o4·:·File
26 i5·:·removeFile·fn26 i5·:·removeFile·fn
27 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*27 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
28 ····*·_\x8f_\x8i_\x8l_\x8e_\x8M_\x8o_\x8d_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·get·file·mode28 ····*·_\x8f_\x8i_\x8l_\x8e_\x8M_\x8o_\x8d_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·get·file·mode
29 ===============================================================================29 ===============================================================================
30 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-30 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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69 ······<div>69 ······<div>
70 ········<h2>Description</h2>70 ········<h2>Description</h2>
71 ········<table·class="examples">71 ········<table·class="examples">
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()74 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
75 o1·=·/tmp/M2-1083316-0/0</code></pre>75 o1·=·/tmp/M2-997476-0/0</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close80 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
81 o2·=·/tmp/M2-1083316-0/081 o2·=·/tmp/M2-997476-0/0
  
82 o2·:·File</code></pre>82 o2·:·File</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i3·:·fileMode·fn87 ··············<pre><code·class="language-macaulay2">i3·:·fileMode·fn
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11 ····*·Inputs:11 ····*·Inputs:
12 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g12 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g
13 ····*·Outputs:13 ····*·Outputs:
14 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·mode·of·the·file·located·at·the·filename·or·path·fn14 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·mode·of·the·file·located·at·the·filename·or·path·fn
15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
16 i1·:·fn·=·temporaryFileName()16 i1·:·fn·=·temporaryFileName()
  
17 o1·=·/tmp/M2-1083316-0/017 o1·=·/tmp/M2-997476-0/0
18 i2·:·fn·<<·"hi·there"·<<·close18 i2·:·fn·<<·"hi·there"·<<·close
  
19 o2·=·/tmp/M2-1083316-0/019 o2·=·/tmp/M2-997476-0/0
  
20 o2·:·File20 o2·:·File
21 i3·:·fileMode·fn21 i3·:·fileMode·fn
  
22 o3·=·42022 o3·=·420
23 i4·:·removeFile·fn23 i4·:·removeFile·fn
24 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*24 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
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73 ······<div>73 ······<div>
74 ········<h2>Description</h2>74 ········<h2>Description</h2>
75 ········<table·class="examples">75 ········<table·class="examples">
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()78 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
79 o1·=·/tmp/M2-1083073-0/0</code></pre>79 o1·=·/tmp/M2-996452-0/0</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·&lt;&lt;·&quot;hi·there&quot;84 ··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·&lt;&lt;·&quot;hi·there&quot;
  
85 o2·=·/tmp/M2-1083073-0/085 o2·=·/tmp/M2-996452-0/0
  
86 o2·:·File</code></pre>86 o2·:·File</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i3·:·m·=·7·+·7*8·+·7*6491 ··············<pre><code·class="language-macaulay2">i3·:·m·=·7·+·7*8·+·7*64
Offset 108, 15 lines modifiedOffset 108, 15 lines modified
108 o5·=·511</code></pre>108 o5·=·511</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i6·:·close·f113 ··············<pre><code·class="language-macaulay2">i6·:·close·f
  
114 o6·=·/tmp/M2-1083073-0/0114 o6·=·/tmp/M2-996452-0/0
  
115 o6·:·File</code></pre>115 o6·:·File</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ··········<tr>118 ··········<tr>
119 ············<td>119 ············<td>
120 ··············<pre><code·class="language-macaulay2">i7·:·fileMode·fn120 ··············<pre><code·class="language-macaulay2">i7·:·fileMode·fn
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12 ··········o·mo,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r12 ··········o·mo,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r
13 ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e13 ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e
14 ····*·Consequences:14 ····*·Consequences:
15 ··········o·the·mode·of·the·open·file·f·is·set·to·mo15 ··········o·the·mode·of·the·open·file·f·is·set·to·mo
16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
17 i1·:·fn·=·temporaryFileName()17 i1·:·fn·=·temporaryFileName()
  
18 o1·=·/tmp/M2-1083073-0/018 o1·=·/tmp/M2-996452-0/0
19 i2·:·f·=·fn·<<·"hi·there"19 i2·:·f·=·fn·<<·"hi·there"
  
20 o2·=·/tmp/M2-1083073-0/020 o2·=·/tmp/M2-996452-0/0
  
21 o2·:·File21 o2·:·File
22 i3·:·m·=·7·+·7*8·+·7*6422 i3·:·m·=·7·+·7*8·+·7*64
  
23 o3·=·51123 o3·=·511
24 i4·:·fileMode(m,f)24 i4·:·fileMode(m,f)
25 i5·:·fileMode·f25 i5·:·fileMode·f
  
26 o5·=·51126 o5·=·511
27 i6·:·close·f27 i6·:·close·f
  
28 o6·=·/tmp/M2-1083073-0/028 o6·=·/tmp/M2-996452-0/0
  
29 o6·:·File29 o6·:·File
30 i7·:·fileMode·fn30 i7·:·fileMode·fn
  
31 o7·=·51131 o7·=·511
32 i8·:·removeFile·fn32 i8·:·removeFile·fn
33 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*33 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
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74 ········<h2>Description</h2>74 ········<h2>Description</h2>
75 ········<table·class="examples">75 ········<table·class="examples">
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()78 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
79 o1·=·/tmp/M2-1095448-0/0</code></pre>79 o1·=·/tmp/M2-1056337-0/0</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close84 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
85 o2·=·/tmp/M2-1095448-0/085 o2·=·/tmp/M2-1056337-0/0
  
86 o2·:·File</code></pre>86 o2·:·File</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i3·:·m·=·fileMode·fn91 ··············<pre><code·class="language-macaulay2">i3·:·m·=·fileMode·fn
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13 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g13 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g
14 ····*·Consequences:14 ····*·Consequences:
15 ··········o·the·mode·of·the·file·located·at·the·filename·or·path·fn·is·set·to15 ··········o·the·mode·of·the·file·located·at·the·filename·or·path·fn·is·set·to
16 ············mo16 ············mo
17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
18 i1·:·fn·=·temporaryFileName()18 i1·:·fn·=·temporaryFileName()
  
19 o1·=·/tmp/M2-1095448-0/019 o1·=·/tmp/M2-1056337-0/0
20 i2·:·fn·<<·"hi·there"·<<·close20 i2·:·fn·<<·"hi·there"·<<·close
  
21 o2·=·/tmp/M2-1095448-0/021 o2·=·/tmp/M2-1056337-0/0
  
22 o2·:·File22 o2·:·File
23 i3·:·m·=·fileMode·fn23 i3·:·m·=·fileMode·fn
  
24 o3·=·42024 o3·=·420
25 i4·:·fileMode(m|7,fn)25 i4·:·fileMode(m|7,fn)
26 i5·:·fileMode·fn26 i5·:·fileMode·fn
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76 ······<div>76 ······<div>
77 ········<h2>Description</h2>77 ········<h2>Description</h2>
78 The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning·of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may·be·found·by·using·the·following·code.········<table·class="examples">78 The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning·of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may·be·found·by·using·the·following·code.········<table·class="examples">
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i1·:·currentTime()·-·fileTime·&quot;.&quot;81 ··············<pre><code·class="language-macaulay2">i1·:·currentTime()·-·fileTime·&quot;.&quot;
  
82 o1·=·40</code></pre>82 o1·=·112</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ········</table>85 ········</table>
86 ······</div>86 ······</div>
87 ······<div>87 ······<div>
88 ········<h2>See·also</h2>88 ········<h2>See·also</h2>
89 ········<ul>89 ········<ul>
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18 ············returns·null·if·no·error·occurs18 ············returns·null·if·no·error·occurs
19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
20 The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning20 The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning
21 of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may21 of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may
22 be·found·by·using·the·following·code.22 be·found·by·using·the·following·code.
23 i1·:·currentTime()·-·fileTime·"."23 i1·:·currentTime()·-·fileTime·"."
  
24 o1·=·4024 o1·=·112
25 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*25 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
26 ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time26 ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time
27 ····*·_\x8f_\x8i_\x8l_\x8e_\x8·_\x8m_\x8a_\x8n_\x8i_\x8p_\x8u_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n·--·Unix·file·manipulation·functions27 ····*·_\x8f_\x8i_\x8l_\x8e_\x8·_\x8m_\x8a_\x8n_\x8i_\x8p_\x8u_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n·--·Unix·file·manipulation·functions
28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
29 The·object·_\x8f_\x8i_\x8l_\x8e_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.29 The·object·_\x8f_\x8i_\x8l_\x8e_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
30 ===============================================================================30 ===============================================================================
31 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-31 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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120 o6·:·Matrix·R··&lt;--·R</code></pre>120 o6·:·Matrix·R··&lt;--·R</code></pre>
121 ············</td>121 ············</td>
122 ··········</tr>122 ··········</tr>
123 ··········<tr>123 ··········<tr>
124 ············<td>124 ············<td>
125 ··············<pre><code·class="language-macaulay2">i7·:·syz·f125 ··············<pre><code·class="language-macaulay2">i7·:·syz·f
  
126 ···--·registering·gb·0·at·0x7f83660f6a80126 ···--·registering·gb·0·at·0x7f45a0acda80
  
127 ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3127 ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3
128 ···--·number·of·monomials················=·9128 ···--·number·of·monomials················=·9
129 ···--·#reduction·steps·=·6129 ···--·#reduction·steps·=·6
130 ···--·#spairs·done·=·6130 ···--·#spairs·done·=·6
131 ···--·ncalls·=·0131 ···--·ncalls·=·0
132 ···--·nloop·=·0132 ···--·nloop·=·0
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37 ·····{3}·|·x2-3··0·····-z4+2·|37 ·····{3}·|·x2-3··0·····-z4+2·|
38 ·····{4}·|·0·····x2-3··y3-1··|38 ·····{4}·|·0·····x2-3··y3-1··|
  
39 ·············3······339 ·············3······3
40 o6·:·Matrix·R··<--·R40 o6·:·Matrix·R··<--·R
41 i7·:·syz·f41 i7·:·syz·f
  
42 ···--·registering·gb·0·at·0x7f83660f6a8042 ···--·registering·gb·0·at·0x7f45a0acda80
  
43 ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb43 ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb
44 elements·=·344 elements·=·3
45 ···--·number·of·monomials················=·945 ···--·number·of·monomials················=·9
46 ···--·#reduction·steps·=·646 ···--·#reduction·steps·=·6
47 ···--·#spairs·done·=·647 ···--·#spairs·done·=·6
48 ···--·ncalls·=·048 ···--·ncalls·=·0
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96 ··············<pre><code·class="language-macaulay2">i3·:·removeFile·&quot;test-file&quot;</code></pre>96 ··············<pre><code·class="language-macaulay2">i3·:·removeFile·&quot;test-file&quot;</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·get·&quot;!date&quot;101 ··············<pre><code·class="language-macaulay2">i4·:·get·&quot;!date&quot;
  
102 o4·=·Thu·Jun··5·22:54:30·-12·2025</code></pre>102 o4·=·Fri·Jul·10·10:30:33·+14·2026</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ········</table>105 ········</table>
106 ······</div>106 ······</div>
107 ······<div>107 ······<div>
108 ········<h2>See·also</h2>108 ········<h2>See·also</h2>
109 ········<ul>109 ········<ul>
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25 o1·:·File25 o1·:·File
26 i2·:·get·"test-file"26 i2·:·get·"test-file"
  
27 o2·=·hi·there27 o2·=·hi·there
28 i3·:·removeFile·"test-file"28 i3·:·removeFile·"test-file"
29 i4·:·get·"!date"29 i4·:·get·"!date"
  
30 o4·=·Thu·Jun··5·22:54:30·-12·202530 o4·=·Fri·Jul·10·10:30:33·+14·2026
31 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*31 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
32 ····*·_\x8r_\x8e_\x8a_\x8d·--·read·from·a·file32 ····*·_\x8r_\x8e_\x8a_\x8d·--·read·from·a·file
33 ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file33 ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file
34 ····*·_\x8c_\x8l_\x8o_\x8s_\x8e·--·close·a·file34 ····*·_\x8c_\x8l_\x8o_\x8s_\x8e·--·close·a·file
35 ····*·_\x8F_\x8i_\x8l_\x8e_\x8·_\x8<_\x8<_\x8·_\x8T_\x8h_\x8i_\x8n_\x8g·--·print·to·a·file35 ····*·_\x8F_\x8i_\x8l_\x8e_\x8·_\x8<_\x8<_\x8·_\x8T_\x8h_\x8i_\x8n_\x8g·--·print·to·a·file
36 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*36 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*
37 ····*·get(File)37 ····*·get(File)
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64 ······<div>64 ······<div>
65 ········<h2>Description</h2>65 ········<h2>Description</h2>
66 ········<table·class="examples">66 ········<table·class="examples">
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i1·:·groupID()69 ··············<pre><code·class="language-macaulay2">i1·:·groupID()
  
70 o1·=·1036237</code></pre>70 o1·=·732624</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ········</table>73 ········</table>
74 ······</div>74 ······</div>
75 ······<div>75 ······<div>
76 ········<h2>See·also</h2>76 ········<h2>See·also</h2>
77 ········<ul>77 ········<ul>
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9 ············groupID()9 ············groupID()
10 ····*·Outputs:10 ····*·Outputs:
11 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·group·identifier·of·the·current·Macaulay211 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·group·identifier·of·the·current·Macaulay2
12 ············process12 ············process
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 i1·:·groupID()14 i1·:·groupID()
  
15 o1·=·103623715 o1·=·732624
16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
17 ····*·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·--·the·process·identifier17 ····*·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·--·the·process·identifier
18 ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier18 ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier
19 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
20 The·object·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.20 The·object·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
21 ===============================================================================21 ===============================================================================
22 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-22 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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76 o1·=·0</code></pre>76 o1·=·0</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i2·:·t·=·schedule(()·->·while·true·do·n·=·n·+·1)81 ··············<pre><code·class="language-macaulay2">i2·:·t·=·schedule(()·->·while·true·do·n·=·n·+·1)
  
82 o2·=·&lt;&lt;task,·created>>82 o2·=·&lt;&lt;task,·running>>
  
83 o2·:·Task</code></pre>83 o2·:·Task</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·sleep·188 ··············<pre><code·class="language-macaulay2">i3·:·sleep·1
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14 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·the·task·t·has·been·canceled14 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·the·task·t·has·been·canceled
15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
16 i1·:·n·=·016 i1·:·n·=·0
  
17 o1·=·017 o1·=·0
18 i2·:·t·=·schedule(()·->·while·true·do·n·=·n·+·1)18 i2·:·t·=·schedule(()·->·while·true·do·n·=·n·+·1)
  
19 o2·=·<<task,·created>>19 o2·=·<<task,·running>>
  
20 o2·:·Task20 o2·:·Task
21 i3·:·sleep·121 i3·:·sleep·1
  
22 o3·=·022 o3·=·0
23 i4·:·isCanceled·t23 i4·:·isCanceled·t
  
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75 o1·=·true</code></pre>75 o1·=·true</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i2·:·fn·=·temporaryFileName()80 ··············<pre><code·class="language-macaulay2">i2·:·fn·=·temporaryFileName()
  
81 o2·=·/tmp/M2-1076282-0/0</code></pre>81 o2·=·/tmp/M2-984625-0/0</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i3·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close86 ··············<pre><code·class="language-macaulay2">i3·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
87 o3·=·/tmp/M2-1076282-0/087 o3·=·/tmp/M2-984625-0/0
  
88 o3·:·File</code></pre>88 o3·:·File</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·isDirectory·fn93 ··············<pre><code·class="language-macaulay2">i4·:·isDirectory·fn
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13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·directory13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·directory
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 i1·:·isDirectory·"."15 i1·:·isDirectory·"."
  
16 o1·=·true16 o1·=·true
17 i2·:·fn·=·temporaryFileName()17 i2·:·fn·=·temporaryFileName()
  
18 o2·=·/tmp/M2-1076282-0/018 o2·=·/tmp/M2-984625-0/0
19 i3·:·fn·<<·"hi·there"·<<·close19 i3·:·fn·<<·"hi·there"·<<·close
  
20 o3·=·/tmp/M2-1076282-0/020 o3·=·/tmp/M2-984625-0/0
  
21 o3·:·File21 o3·:·File
22 i4·:·isDirectory·fn22 i4·:·isDirectory·fn
  
23 o4·=·false23 o4·=·false
24 i5·:·removeFile·fn24 i5·:·removeFile·fn
25 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*25 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
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211 o18·=·false</code></pre>211 o18·=·false</code></pre>
212 ············</td>212 ············</td>
213 ··········</tr>213 ··········</tr>
214 ··········<tr>214 ··········<tr>
215 ············<td>215 ············<td>
216 ··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·facs·=·factor(m*m1)216 ··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·facs·=·factor(m*m1)
217 ·--·4.05952s·elapsed217 ·--·16.2161s·elapsed
  
218 o19·=·1000000000000000000000000000057*1000000000000000000010000000083218 o19·=·1000000000000000000000000000057*1000000000000000000010000000083
  
219 o19·:·Expression·of·class·Product</code></pre>219 o19·:·Expression·of·class·Product</code></pre>
220 ············</td>220 ············</td>
221 ··········</tr>221 ··········</tr>
222 ··········<tr>222 ··········<tr>
Offset 245, 23 lines modifiedOffset 245, 23 lines modified
245 o22·=·10000000000000000000000000001710000000000000000000000000097470000000000245 o22·=·10000000000000000000000000001710000000000000000000000000097470000000000
246 ······00000000000000185613</code></pre>246 ······00000000000000185613</code></pre>
247 ············</td>247 ············</td>
248 ··········</tr>248 ··········</tr>
249 ··········<tr>249 ··········<tr>
250 ············<td>250 ············<td>
251 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·m3251 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·m3
252 ·--·.0614478s·elapsed252 ·--·.124756s·elapsed
  
253 o23·=·true</code></pre>253 o23·=·true</code></pre>
254 ············</td>254 ············</td>
255 ··········</tr>255 ··········</tr>
256 ··········<tr>256 ··········<tr>
257 ············<td>257 ············<td>
258 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isPseudoprime·m3258 ··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isPseudoprime·m3
259 ·--·.000133883s·elapsed259 ·--·.000143308s·elapsed
  
260 o24·=·true</code></pre>260 o24·=·true</code></pre>
261 ············</td>261 ············</td>
262 ··········</tr>262 ··········</tr>
263 ········</table>263 ········</table>
264 ······</div>264 ······</div>
265 ······<div>265 ······<div>
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80 i17·:·isPrime·(m*m1)80 i17·:·isPrime·(m*m1)
  
81 o17·=·false81 o17·=·false
82 i18·:·isPrime(m*m*m1*m1*m2^6)82 i18·:·isPrime(m*m*m1*m1*m2^6)
  
83 o18·=·false83 o18·=·false
84 i19·:·elapsedTime·facs·=·factor(m*m1)84 i19·:·elapsedTime·facs·=·factor(m*m1)
85 ·--·4.05952s·elapsed85 ·--·16.2161s·elapsed
  
86 o19·=·1000000000000000000000000000057*100000000000000000001000000008386 o19·=·1000000000000000000000000000057*1000000000000000000010000000083
  
87 o19·:·Expression·of·class·Product87 o19·:·Expression·of·class·Product
88 i20·:·facs·=·facs//toList/toList88 i20·:·facs·=·facs//toList/toList
  
89 o20·=·{{1000000000000000000000000000057,·1},89 o20·=·{{1000000000000000000000000000057,·1},
Offset 98, 19 lines modifiedOffset 98, 19 lines modified
98 o20·:·List98 o20·:·List
99 i21·:·assert(set·facs·===·set·{{m,1},·{m1,1}})99 i21·:·assert(set·facs·===·set·{{m,1},·{m1,1}})
100 i22·:·m3·=·nextPrime·(m^3)100 i22·:·m3·=·nextPrime·(m^3)
  
101 o22·=·10000000000000000000000000001710000000000000000000000000097470000000000101 o22·=·10000000000000000000000000001710000000000000000000000000097470000000000
102 ······00000000000000185613102 ······00000000000000185613
103 i23·:·elapsedTime·isPrime·m3103 i23·:·elapsedTime·isPrime·m3
104 ·--·.0614478s·elapsed104 ·--·.124756s·elapsed
  
105 o23·=·true105 o23·=·true
106 i24·:·elapsedTime·isPseudoprime·m3106 i24·:·elapsedTime·isPseudoprime·m3
107 ·--·.000133883s·elapsed107 ·--·.000143308s·elapsed
  
108 o24·=·true108 o24·=·true
109 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*109 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
110 ····*·_\x8i_\x8s_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8Z_\x8Z_\x8)·--·whether·a·integer·or·polynomial·is·prime110 ····*·_\x8i_\x8s_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8Z_\x8Z_\x8)·--·whether·a·integer·or·polynomial·is·prime
111 ····*·_\x8f_\x8a_\x8c_\x8t_\x8o_\x8r_\x8(_\x8Z_\x8Z_\x8)·--·factor·a·ring·element111 ····*·_\x8f_\x8a_\x8c_\x8t_\x8o_\x8r_\x8(_\x8Z_\x8Z_\x8)·--·factor·a·ring·element
112 ····*·_\x8n_\x8e_\x8x_\x8t_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8N_\x8u_\x8m_\x8b_\x8e_\x8r_\x8)·--·compute·the·smallest·prime·greater·than·or·equal·to112 ····*·_\x8n_\x8e_\x8x_\x8t_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8N_\x8u_\x8m_\x8b_\x8e_\x8r_\x8)·--·compute·the·smallest·prime·greater·than·or·equal·to
113 ······a·given·number113 ······a·given·number
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68 ······<div>68 ······<div>
69 ········<h2>Description</h2>69 ········<h2>Description</h2>
70 In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.··Special·files·include·symbolic·links·and·directories.··A·regular·file·is·a·sequence·of·bytes·stored·permanently·in·a·file·system.········<table·class="examples">70 In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.··Special·files·include·symbolic·links·and·directories.··A·regular·file·is·a·sequence·of·bytes·stored·permanently·in·a·file·system.········<table·class="examples">
71 ··········<tr>71 ··········<tr>
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()73 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
74 o1·=·/tmp/M2-1101217-0/0</code></pre>74 o1·=·/tmp/M2-1060387-0/0</code></pre>
75 ············</td>75 ············</td>
76 ··········</tr>76 ··········</tr>
77 ··········<tr>77 ··········<tr>
78 ············<td>78 ············<td>
79 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close79 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
80 o2·=·/tmp/M2-1101217-0/080 o2·=·/tmp/M2-1060387-0/0
  
81 o2·:·File</code></pre>81 o2·:·File</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i3·:·isRegularFile·fn86 ··············<pre><code·class="language-macaulay2">i3·:·isRegularFile·fn
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13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·regular·file13 ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·regular·file
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.·Special·files15 In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.·Special·files
16 include·symbolic·links·and·directories.·A·regular·file·is·a·sequence·of·bytes16 include·symbolic·links·and·directories.·A·regular·file·is·a·sequence·of·bytes
17 stored·permanently·in·a·file·system.17 stored·permanently·in·a·file·system.
18 i1·:·fn·=·temporaryFileName()18 i1·:·fn·=·temporaryFileName()
  
19 o1·=·/tmp/M2-1101217-0/019 o1·=·/tmp/M2-1060387-0/0
20 i2·:·fn·<<·"hi·there"·<<·close20 i2·:·fn·<<·"hi·there"·<<·close
  
21 o2·=·/tmp/M2-1101217-0/021 o2·=·/tmp/M2-1060387-0/0
  
22 o2·:·File22 o2·:·File
23 i3·:·isRegularFile·fn23 i3·:·isRegularFile·fn
  
24 o3·=·true24 o3·=·true
25 i4·:·removeFile·fn25 i4·:·removeFile·fn
26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
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76 ······<div>76 ······<div>
77 ········<h2>Description</h2>77 ········<h2>Description</h2>
78 ········<table·class="examples">78 ········<table·class="examples">
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()81 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()
  
82 o1·=·/tmp/M2-1082841-0/0</code></pre>82 o1·=·/tmp/M2-994788-0/0</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·(dir|&quot;/a/b/c&quot;)87 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·(dir|&quot;/a/b/c&quot;)
  
88 o2·=·/tmp/M2-1082841-0/0/a/b/c</code></pre>88 o2·=·/tmp/M2-994788-0/0/a/b/c</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i3·:·removeDirectory·(dir|&quot;/a/b/c&quot;)</code></pre>93 ··············<pre><code·class="language-macaulay2">i3·:·removeDirectory·(dir|&quot;/a/b/c&quot;)</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
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13 ····*·Outputs:13 ····*·Outputs:
14 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·name·of·the·newly·made·directory14 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·name·of·the·newly·made·directory
15 ····*·Consequences:15 ····*·Consequences:
16 ··········o·the·directory·is·made,·with·as·many·new·path·components·as·needed16 ··········o·the·directory·is·made,·with·as·many·new·path·components·as·needed
17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
18 i1·:·dir·=·temporaryFileName()18 i1·:·dir·=·temporaryFileName()
  
19 o1·=·/tmp/M2-1082841-0/019 o1·=·/tmp/M2-994788-0/0
20 i2·:·makeDirectory·(dir|"/a/b/c")20 i2·:·makeDirectory·(dir|"/a/b/c")
  
21 o2·=·/tmp/M2-1082841-0/0/a/b/c21 o2·=·/tmp/M2-994788-0/0/a/b/c
22 i3·:·removeDirectory·(dir|"/a/b/c")22 i3·:·removeDirectory·(dir|"/a/b/c")
23 i4·:·removeDirectory·(dir|"/a/b")23 i4·:·removeDirectory·(dir|"/a/b")
24 i5·:·removeDirectory·(dir|"/a")24 i5·:·removeDirectory·(dir|"/a")
25 A·filename·starting·with·~/·will·have·the·tilde·replaced·by·the·home·directory.25 A·filename·starting·with·~/·will·have·the·tilde·replaced·by·the·home·directory.
26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
27 ····*·_\x8m_\x8k_\x8d_\x8i_\x8r27 ····*·_\x8m_\x8k_\x8d_\x8i_\x8r
28 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
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61 o1·:·FunctionClosure</code></pre>61 o1·:·FunctionClosure</code></pre>
62 ············</td>62 ············</td>
63 ··········</tr>63 ··········</tr>
64 ··········<tr>64 ··········<tr>
65 ············<td>65 ············<td>
66 ··············<pre><code·class="language-macaulay2">i2·:·time·fib·2866 ··············<pre><code·class="language-macaulay2">i2·:·time·fib·28
67 ·--·used·0.871376s·(cpu);·0.561091s·(thread);·0s·(gc)67 ·--·used·0.904923s·(cpu);·0.594351s·(thread);·0s·(gc)
  
68 o2·=·514229</code></pre>68 o2·=·514229</code></pre>
69 ············</td>69 ············</td>
70 ··········</tr>70 ··········</tr>
71 ··········<tr>71 ··········<tr>
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i3·:·fib·=·memoize·fib73 ··············<pre><code·class="language-macaulay2">i3·:·fib·=·memoize·fib
Offset 78, 23 lines modifiedOffset 78, 23 lines modified
  
78 o3·:·FunctionClosure</code></pre>78 o3·:·FunctionClosure</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i4·:·time·fib·2883 ··············<pre><code·class="language-macaulay2">i4·:·time·fib·28
84 ·--·used·6.1743e-05s·(cpu);·6.007e-05s·(thread);·0s·(gc)84 ·--·used·6.409e-05s·(cpu);·6.9e-05s·(thread);·0s·(gc)
  
85 o4·=·514229</code></pre>85 o4·=·514229</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ··········<tr>88 ··········<tr>
89 ············<td>89 ············<td>
90 ··············<pre><code·class="language-macaulay2">i5·:·time·fib·2890 ··············<pre><code·class="language-macaulay2">i5·:·time·fib·28
91 ·--·used·1.482e-06s·(cpu);·1.382e-06s·(thread);·0s·(gc)91 ·--·used·7.034e-06s·(cpu);·4.98e-06s·(thread);·0s·(gc)
  
92 o5·=·514229</code></pre>92 o5·=·514229</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ········</table>95 ········</table>
96 ········<p>An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each·of·the·form·<span·class="tt">x·=>·v</span>,·where·<span·class="tt">v</span>·is·the·value·to·be·provided·for·the·argument·<span·class="tt">x</span>.</p>96 ········<p>An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each·of·the·form·<span·class="tt">x·=>·v</span>,·where·<span·class="tt">v</span>·is·the·value·to·be·provided·for·the·argument·<span·class="tt">x</span>.</p>
97 ········<p>Alternatively,·values·can·be·provided·after·defining·the·memoized·function·using·the·syntax·<span·class="tt">f·x·=·v</span>.·A·slightly·more·efficient·implementation·of·the·above·would·be</p>97 ········<p>Alternatively,·values·can·be·provided·after·defining·the·memoized·function·using·the·syntax·<span·class="tt">f·x·=·v</span>.·A·slightly·more·efficient·implementation·of·the·above·would·be</p>
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Offset 11, 28 lines modifiedOffset 11, 28 lines modified
11 arguments·are·presented.11 arguments·are·presented.
12 i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2)12 i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2)
  
13 o1·=·fib13 o1·=·fib
  
14 o1·:·FunctionClosure14 o1·:·FunctionClosure
15 i2·:·time·fib·2815 i2·:·time·fib·28
16 ·--·used·0.871376s·(cpu);·0.561091s·(thread);·0s·(gc)16 ·--·used·0.904923s·(cpu);·0.594351s·(thread);·0s·(gc)
  
17 o2·=·51422917 o2·=·514229
18 i3·:·fib·=·memoize·fib18 i3·:·fib·=·memoize·fib
  
19 o3·=·fib19 o3·=·fib
  
20 o3·:·FunctionClosure20 o3·:·FunctionClosure
21 i4·:·time·fib·2821 i4·:·time·fib·28
22 ·--·used·6.1743e-05s·(cpu);·6.007e-05s·(thread);·0s·(gc)22 ·--·used·6.409e-05s·(cpu);·6.9e-05s·(thread);·0s·(gc)
  
23 o4·=·51422923 o4·=·514229
24 i5·:·time·fib·2824 i5·:·time·fib·28
25 ·--·used·1.482e-06s·(cpu);·1.382e-06s·(thread);·0s·(gc)25 ·--·used·7.034e-06s·(cpu);·4.98e-06s·(thread);·0s·(gc)
  
26 o5·=·51422926 o5·=·514229
27 An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each27 An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each
28 of·the·form·x·=>·v,·where·v·is·the·value·to·be·provided·for·the·argument·x.28 of·the·form·x·=>·v,·where·v·is·the·value·to·be·provided·for·the·argument·x.
29 Alternatively,·values·can·be·provided·after·defining·the·memoized·function29 Alternatively,·values·can·be·provided·after·defining·the·memoized·function
30 using·the·syntax·f·x·=·v.·A·slightly·more·efficient·implementation·of·the·above30 using·the·syntax·f·x·=·v.·A·slightly·more·efficient·implementation·of·the·above
31 would·be31 would·be
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./usr/share/doc/Macaulay2/Macaulay2Doc/html/_methods.html
    
Offset 89, 20 lines modifiedOffset 89, 20 lines modified
89 ·····{12·=>·(poincare,·BettiTally)································}89 ·····{12·=>·(poincare,·BettiTally)································}
90 ·····{13·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················}90 ·····{13·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················}
91 ·····{14·=>·(degree,·BettiTally)··································}91 ·····{14·=>·(degree,·BettiTally)··································}
92 ·····{15·=>·(hilbertSeries,·ZZ,·BettiTally)·······················}92 ·····{15·=>·(hilbertSeries,·ZZ,·BettiTally)·······················}
93 ·····{16·=>·(pdim,·BettiTally)····································}93 ·····{16·=>·(pdim,·BettiTally)····································}
94 ·····{17·=>·(regularity,·BettiTally)······························}94 ·····{17·=>·(regularity,·BettiTally)······························}
95 ·····{18·=>·(mathML,·BettiTally)··································}95 ·····{18·=>·(mathML,·BettiTally)··································}
96 ·····{19·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)} 
97 ·····{20·=>·(dual,·BettiTally)····································}96 ·····{19·=>·(dual,·BettiTally)····································}
 97 ·····{20·=>·(truncate,·BettiTally,·ZZ,·ZZ)························}
98 ·····{21·=>·(codim,·BettiTally)···································}98 ·····{21·=>·(codim,·BettiTally)···································}
99 ·····{22·=>·(truncate,·BettiTally,·ZZ,·ZZ)························} 
100 ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············}99 ·····{22·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············}
101 ·····{24·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············}100 ·····{23·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············}
 101 ·····{24·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)}
102 ·····{25·=>·(^,·Ring,·BettiTally)·································}102 ·····{25·=>·(^,·Ring,·BettiTally)·································}
  
103 o1·:·NumberedVerticalList</code></pre>103 o1·:·NumberedVerticalList</code></pre>
104 ··············</td>104 ··············</td>
105 ············</tr>105 ············</tr>
106 ············<tr>106 ············<tr>
107 ··············<td>107 ··············<td>
Offset 189, 19 lines modifiedOffset 189, 19 lines modified
189 ··········</ul>189 ··········</ul>
190 ··········<table·class="examples">190 ··········<table·class="examples">
191 ············<tr>191 ············<tr>
192 ··············<td>192 ··············<td>
193 ················<pre><code·class="language-macaulay2">i5·:·methods(·Matrix,·Matrix·)193 ················<pre><code·class="language-macaulay2">i5·:·methods(·Matrix,·Matrix·)
  
194 o5·=·{0·=>·(contract',·Matrix,·Matrix)···························}194 o5·=·{0·=>·(contract',·Matrix,·Matrix)···························}
195 ·····{1·=>·(diff',·Matrix,·Matrix)·······························} 
196 ·····{2·=>·(diff,·Matrix,·Matrix)································} 
197 ·····{3·=>·(+,·Matrix,·Matrix)···································}195 ·····{1·=>·(+,·Matrix,·Matrix)···································}
 196 ·····{2·=>·(-,·Matrix,·Matrix)···································}
 197 ·····{3·=>·(diff',·Matrix,·Matrix)·······························}
198 ·····{4·=>·(contract,·Matrix,·Matrix)····························}198 ·····{4·=>·(contract,·Matrix,·Matrix)····························}
199 ·····{5·=>·(-,·Matrix,·Matrix)···································}199 ·····{5·=>·(diff,·Matrix,·Matrix)································}
200 ·····{6·=>·(markedGB,·Matrix,·Matrix)····························}200 ·····{6·=>·(markedGB,·Matrix,·Matrix)····························}
201 ·····{7·=>·(Hom,·Matrix,·Matrix)·································}201 ·····{7·=>·(Hom,·Matrix,·Matrix)·································}
202 ·····{8·=>·(==,·Matrix,·Matrix)··································}202 ·····{8·=>·(==,·Matrix,·Matrix)··································}
203 ·····{9·=>·(*,·Matrix,·Matrix)···································}203 ·····{9·=>·(*,·Matrix,·Matrix)···································}
204 ·····{10·=>·(|,·Matrix,·Matrix)··································}204 ·····{10·=>·(|,·Matrix,·Matrix)··································}
205 ·····{11·=>·(||,·Matrix,·Matrix)·································}205 ·····{11·=>·(||,·Matrix,·Matrix)·································}
206 ·····{12·=>·(subquotient,·Matrix,·Matrix)························}206 ·····{12·=>·(subquotient,·Matrix,·Matrix)························}
Offset 216, 18 lines modifiedOffset 216, 18 lines modified
216 ·····{21·=>·(quotient,·Matrix,·Matrix)···························}216 ·····{21·=>·(quotient,·Matrix,·Matrix)···························}
217 ·····{22·=>·(quotient',·Matrix,·Matrix)··························}217 ·····{22·=>·(quotient',·Matrix,·Matrix)··························}
218 ·····{23·=>·(remainder',·Matrix,·Matrix)·························}218 ·····{23·=>·(remainder',·Matrix,·Matrix)·························}
219 ·····{24·=>·(%,·Matrix,·Matrix)··································}219 ·····{24·=>·(%,·Matrix,·Matrix)··································}
220 ·····{25·=>·(remainder,·Matrix,·Matrix)··························}220 ·····{25·=>·(remainder,·Matrix,·Matrix)··························}
221 ·····{26·=>·(pushout,·Matrix,·Matrix)····························}221 ·····{26·=>·(pushout,·Matrix,·Matrix)····························}
222 ·····{27·=>·(solve,·Matrix,·Matrix)······························}222 ·····{27·=>·(solve,·Matrix,·Matrix)······························}
223 ·····{28·=>·(intersect,·Matrix,·Matrix)··························}223 ·····{28·=>·(pullback,·Matrix,·Matrix)···························}
224 ·····{29·=>·(tensor,·Matrix,·Matrix)·····························}224 ·····{29·=>·(tensor,·Matrix,·Matrix)·····························}
225 ·····{30·=>·(pullback,·Matrix,·Matrix)···························} 
226 ·····{31·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)··········}225 ·····{30·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)··········}
 226 ·····{31·=>·(intersect,·Matrix,·Matrix)··························}
227 ·····{32·=>·(substitute,·Matrix,·Matrix)·························}227 ·····{32·=>·(substitute,·Matrix,·Matrix)·························}
228 ·····{33·=>·(yonedaProduct,·Matrix,·Matrix)······················}228 ·····{33·=>·(yonedaProduct,·Matrix,·Matrix)······················}
229 ·····{34·=>·(isShortExactSequence,·Matrix,·Matrix)···············}229 ·····{34·=>·(isShortExactSequence,·Matrix,·Matrix)···············}
230 ·····{35·=>·(horseshoeResolution,·Matrix,·Matrix)················}230 ·····{35·=>·(horseshoeResolution,·Matrix,·Matrix)················}
231 ·····{36·=>·(connectingExtMap,·Module,·Matrix,·Matrix)···········}231 ·····{36·=>·(connectingExtMap,·Module,·Matrix,·Matrix)···········}
232 ·····{37·=>·(connectingExtMap,·Matrix,·Matrix,·Module)···········}232 ·····{37·=>·(connectingExtMap,·Matrix,·Matrix,·Module)···········}
233 ·····{38·=>·(connectingTorMap,·Module,·Matrix,·Matrix)···········}233 ·····{38·=>·(connectingTorMap,·Module,·Matrix,·Matrix)···········}
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Offset 29, 20 lines modifiedOffset 29, 20 lines modified
29 ·····{12·=>·(poincare,·BettiTally)································}29 ·····{12·=>·(poincare,·BettiTally)································}
30 ·····{13·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················}30 ·····{13·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················}
31 ·····{14·=>·(degree,·BettiTally)··································}31 ·····{14·=>·(degree,·BettiTally)··································}
32 ·····{15·=>·(hilbertSeries,·ZZ,·BettiTally)·······················}32 ·····{15·=>·(hilbertSeries,·ZZ,·BettiTally)·······················}
33 ·····{16·=>·(pdim,·BettiTally)····································}33 ·····{16·=>·(pdim,·BettiTally)····································}
34 ·····{17·=>·(regularity,·BettiTally)······························}34 ·····{17·=>·(regularity,·BettiTally)······························}
35 ·····{18·=>·(mathML,·BettiTally)··································}35 ·····{18·=>·(mathML,·BettiTally)··································}
36 ·····{19·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)} 
37 ·····{20·=>·(dual,·BettiTally)····································}36 ·····{19·=>·(dual,·BettiTally)····································}
 37 ·····{20·=>·(truncate,·BettiTally,·ZZ,·ZZ)························}
38 ·····{21·=>·(codim,·BettiTally)···································}38 ·····{21·=>·(codim,·BettiTally)···································}
39 ·····{22·=>·(truncate,·BettiTally,·ZZ,·ZZ)························} 
40 ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············}39 ·····{22·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············}
41 ·····{24·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············}40 ·····{23·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············}
 41 ·····{24·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)}
42 ·····{25·=>·(^,·Ring,·BettiTally)·································}42 ·····{25·=>·(^,·Ring,·BettiTally)·································}
  
43 o1·:·NumberedVerticalList43 o1·:·NumberedVerticalList
44 i2·:·methods·resolution44 i2·:·methods·resolution
  
45 o2·=·{0·=>·(resolution,·Ideal)·}45 o2·=·{0·=>·(resolution,·Ideal)·}
46 ·····{1·=>·(resolution,·Module)}46 ·····{1·=>·(resolution,·Module)}
Offset 86, 19 lines modifiedOffset 86, 19 lines modified
86 ··········o·X,·a·_\x8t_\x8y_\x8p_\x8e86 ··········o·X,·a·_\x8t_\x8y_\x8p_\x8e
87 ··········o·Y,·a·_\x8t_\x8y_\x8p_\x8e87 ··········o·Y,·a·_\x8t_\x8y_\x8p_\x8e
88 ····*·Outputs:88 ····*·Outputs:
89 ··········o·a·_\x8v_\x8e_\x8r_\x8t_\x8i_\x8c_\x8a_\x8l_\x8·_\x8l_\x8i_\x8s_\x8t·of·those·methods·associated·with89 ··········o·a·_\x8v_\x8e_\x8r_\x8t_\x8i_\x8c_\x8a_\x8l_\x8·_\x8l_\x8i_\x8s_\x8t·of·those·methods·associated·with
90 i5·:·methods(·Matrix,·Matrix·)90 i5·:·methods(·Matrix,·Matrix·)
  
91 o5·=·{0·=>·(contract',·Matrix,·Matrix)···························}91 o5·=·{0·=>·(contract',·Matrix,·Matrix)···························}
92 ·····{1·=>·(diff',·Matrix,·Matrix)·······························} 
93 ·····{2·=>·(diff,·Matrix,·Matrix)································} 
94 ·····{3·=>·(+,·Matrix,·Matrix)···································}92 ·····{1·=>·(+,·Matrix,·Matrix)···································}
 93 ·····{2·=>·(-,·Matrix,·Matrix)···································}
 94 ·····{3·=>·(diff',·Matrix,·Matrix)·······························}
95 ·····{4·=>·(contract,·Matrix,·Matrix)····························}95 ·····{4·=>·(contract,·Matrix,·Matrix)····························}
96 ·····{5·=>·(-,·Matrix,·Matrix)···································}96 ·····{5·=>·(diff,·Matrix,·Matrix)································}
97 ·····{6·=>·(markedGB,·Matrix,·Matrix)····························}97 ·····{6·=>·(markedGB,·Matrix,·Matrix)····························}
98 ·····{7·=>·(Hom,·Matrix,·Matrix)·································}98 ·····{7·=>·(Hom,·Matrix,·Matrix)·································}
99 ·····{8·=>·(==,·Matrix,·Matrix)··································}99 ·····{8·=>·(==,·Matrix,·Matrix)··································}
100 ·····{9·=>·(*,·Matrix,·Matrix)···································}100 ·····{9·=>·(*,·Matrix,·Matrix)···································}
101 ·····{10·=>·(|,·Matrix,·Matrix)··································}101 ·····{10·=>·(|,·Matrix,·Matrix)··································}
102 ·····{11·=>·(||,·Matrix,·Matrix)·································}102 ·····{11·=>·(||,·Matrix,·Matrix)·································}
103 ·····{12·=>·(subquotient,·Matrix,·Matrix)························}103 ·····{12·=>·(subquotient,·Matrix,·Matrix)························}
Offset 113, 18 lines modifiedOffset 113, 18 lines modified
113 ·····{21·=>·(quotient,·Matrix,·Matrix)···························}113 ·····{21·=>·(quotient,·Matrix,·Matrix)···························}
114 ·····{22·=>·(quotient',·Matrix,·Matrix)··························}114 ·····{22·=>·(quotient',·Matrix,·Matrix)··························}
115 ·····{23·=>·(remainder',·Matrix,·Matrix)·························}115 ·····{23·=>·(remainder',·Matrix,·Matrix)·························}
116 ·····{24·=>·(%,·Matrix,·Matrix)··································}116 ·····{24·=>·(%,·Matrix,·Matrix)··································}
117 ·····{25·=>·(remainder,·Matrix,·Matrix)··························}117 ·····{25·=>·(remainder,·Matrix,·Matrix)··························}
118 ·····{26·=>·(pushout,·Matrix,·Matrix)····························}118 ·····{26·=>·(pushout,·Matrix,·Matrix)····························}
119 ·····{27·=>·(solve,·Matrix,·Matrix)······························}119 ·····{27·=>·(solve,·Matrix,·Matrix)······························}
120 ·····{28·=>·(intersect,·Matrix,·Matrix)··························}120 ·····{28·=>·(pullback,·Matrix,·Matrix)···························}
121 ·····{29·=>·(tensor,·Matrix,·Matrix)·····························}121 ·····{29·=>·(tensor,·Matrix,·Matrix)·····························}
122 ·····{30·=>·(pullback,·Matrix,·Matrix)···························} 
123 ·····{31·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)··········}122 ·····{30·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)··········}
 123 ·····{31·=>·(intersect,·Matrix,·Matrix)··························}
124 ·····{32·=>·(substitute,·Matrix,·Matrix)·························}124 ·····{32·=>·(substitute,·Matrix,·Matrix)·························}
125 ·····{33·=>·(yonedaProduct,·Matrix,·Matrix)······················}125 ·····{33·=>·(yonedaProduct,·Matrix,·Matrix)······················}
126 ·····{34·=>·(isShortExactSequence,·Matrix,·Matrix)···············}126 ·····{34·=>·(isShortExactSequence,·Matrix,·Matrix)···············}
127 ·····{35·=>·(horseshoeResolution,·Matrix,·Matrix)················}127 ·····{35·=>·(horseshoeResolution,·Matrix,·Matrix)················}
128 ·····{36·=>·(connectingExtMap,·Module,·Matrix,·Matrix)···········}128 ·····{36·=>·(connectingExtMap,·Module,·Matrix,·Matrix)···········}
129 ·····{37·=>·(connectingExtMap,·Matrix,·Matrix,·Module)···········}129 ·····{37·=>·(connectingExtMap,·Matrix,·Matrix,·Module)···········}
130 ·····{38·=>·(connectingTorMap,·Module,·Matrix,·Matrix)···········}130 ·····{38·=>·(connectingTorMap,·Module,·Matrix,·Matrix)···········}
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Offset 97, 15 lines modifiedOffset 97, 15 lines modified
  
97 o2·:·PolynomialRing</code></pre>97 o2·:·PolynomialRing</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·minimalBetti·I102 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·minimalBetti·I
103 ·--·2.01874s·elapsed103 ·--·3.14153s·elapsed
  
104 ············0··1···2···3···4····5···6···7···8··9·10104 ············0··1···2···3···4····5···6···7···8··9·10
105 o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1105 o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1
106 ·········0:·1··.···.···.···.····.···.···.···.··.··.106 ·········0:·1··.···.···.···.····.···.···.···.··.··.
107 ·········1:·.·35·140·189··84····.···.···.···.··.··.107 ·········1:·.·35·140·189··84····.···.···.···.··.··.
108 ·········2:·.··.···.·196·735·1080·735·196···.··.··.108 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
109 ·········3:·.··.···.···.···.····.··84·189·140·35··.109 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 125, 15 lines modifiedOffset 125, 15 lines modified
  
125 o4·:·Ideal·of·S</code></pre>125 o4·:·Ideal·of·S</code></pre>
126 ············</td>126 ············</td>
127 ··········</tr>127 ··········</tr>
128 ··········<tr>128 ··········<tr>
129 ············<td>129 ············<td>
130 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2)130 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2)
131 ·--·.787739s·elapsed131 ·--·1.29119s·elapsed
  
132 ············0··1···2···3···4····5···6···7132 ············0··1···2···3···4····5···6···7
133 o5·=·total:·1·35·140·385·819·1080·735·196133 o5·=·total:·1·35·140·385·819·1080·735·196
134 ·········0:·1··.···.···.···.····.···.···.134 ·········0:·1··.···.···.···.····.···.···.
135 ·········1:·.·35·140·189··84····.···.···.135 ·········1:·.·35·140·189··84····.···.···.
136 ·········2:·.··.···.·196·735·1080·735·196136 ·········2:·.··.···.·196·735·1080·735·196
  
Offset 146, 15 lines modifiedOffset 146, 15 lines modified
  
146 o6·:·Ideal·of·S</code></pre>146 o6·:·Ideal·of·S</code></pre>
147 ············</td>147 ············</td>
148 ··········</tr>148 ··········</tr>
149 ··········<tr>149 ··········<tr>
150 ············<td>150 ············<td>
151 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5)151 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5)
152 ·--·.0299097s·elapsed152 ·--·.0295357s·elapsed
  
153 ············0··1···2···3··4153 ············0··1···2···3··4
154 o7·=·total:·1·35·140·189·84154 o7·=·total:·1·35·140·189·84
155 ·········0:·1··.···.···.··.155 ·········0:·1··.···.···.··.
156 ·········1:·.·35·140·189·84156 ·········1:·.·35·140·189·84
  
157 o7·:·BettiTally</code></pre>157 o7·:·BettiTally</code></pre>
Offset 166, 15 lines modifiedOffset 166, 15 lines modified
  
166 o8·:·Ideal·of·S</code></pre>166 o8·:·Ideal·of·S</code></pre>
167 ············</td>167 ············</td>
168 ··········</tr>168 ··········</tr>
169 ··········<tr>169 ··········<tr>
170 ············<td>170 ············<td>
171 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5)171 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5)
172 ·--·1.23548s·elapsed172 ·--·1.76861s·elapsed
  
173 ············0··1···2···3···4····5173 ············0··1···2···3···4····5
174 o9·=·total:·1·35·140·385·819·1080174 o9·=·total:·1·35·140·385·819·1080
175 ·········0:·1··.···.···.···.····.175 ·········0:·1··.···.···.···.····.
176 ·········1:·.·35·140·189··84····.176 ·········1:·.·35·140·189··84····.
177 ·········2:·.··.···.·196·735·1080177 ·········2:·.··.···.·196·735·1080
  
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43 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,643 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6
44 i2·:·S·=·ring·I44 i2·:·S·=·ring·I
  
45 o2·=·S45 o2·=·S
  
46 o2·:·PolynomialRing46 o2·:·PolynomialRing
47 i3·:·elapsedTime·C·=·minimalBetti·I47 i3·:·elapsedTime·C·=·minimalBetti·I
48 ·--·2.01874s·elapsed48 ·--·3.14153s·elapsed
  
49 ············0··1···2···3···4····5···6···7···8··9·1049 ············0··1···2···3···4····5···6···7···8··9·10
50 o3·=·total:·1·35·140·385·819·1080·819·385·140·35··150 o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1
51 ·········0:·1··.···.···.···.····.···.···.···.··.··.51 ·········0:·1··.···.···.···.····.···.···.···.··.··.
52 ·········1:·.·35·140·189··84····.···.···.···.··.··.52 ·········1:·.·35·140·189··84····.···.···.···.··.··.
53 ·········2:·.··.···.·196·735·1080·735·196···.··.··.53 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
54 ·········3:·.··.···.···.···.····.··84·189·140·35··.54 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 60, 40 lines modifiedOffset 60, 40 lines modified
60 o3·:·BettiTally60 o3·:·BettiTally
61 One·can·compute·smaller·parts·of·the·Betti·table,·by·using·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·and/or61 One·can·compute·smaller·parts·of·the·Betti·table,·by·using·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·and/or
62 _\x8L_\x8e_\x8n_\x8g_\x8t_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t.62 _\x8L_\x8e_\x8n_\x8g_\x8t_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t.
63 i4·:·I·=·ideal·I_*;63 i4·:·I·=·ideal·I_*;
  
64 o4·:·Ideal·of·S64 o4·:·Ideal·of·S
65 i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2)65 i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2)
66 ·--·.787739s·elapsed66 ·--·1.29119s·elapsed
  
67 ············0··1···2···3···4····5···6···767 ············0··1···2···3···4····5···6···7
68 o5·=·total:·1·35·140·385·819·1080·735·19668 o5·=·total:·1·35·140·385·819·1080·735·196
69 ·········0:·1··.···.···.···.····.···.···.69 ·········0:·1··.···.···.···.····.···.···.
70 ·········1:·.·35·140·189··84····.···.···.70 ·········1:·.·35·140·189··84····.···.···.
71 ·········2:·.··.···.·196·735·1080·735·19671 ·········2:·.··.···.·196·735·1080·735·196
  
72 o5·:·BettiTally72 o5·:·BettiTally
73 i6·:·I·=·ideal·I_*;73 i6·:·I·=·ideal·I_*;
  
74 o6·:·Ideal·of·S74 o6·:·Ideal·of·S
75 i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5)75 i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5)
76 ·--·.0299097s·elapsed76 ·--·.0295357s·elapsed
  
77 ············0··1···2···3··477 ············0··1···2···3··4
78 o7·=·total:·1·35·140·189·8478 o7·=·total:·1·35·140·189·84
79 ·········0:·1··.···.···.··.79 ·········0:·1··.···.···.··.
80 ·········1:·.·35·140·189·8480 ·········1:·.·35·140·189·84
  
81 o7·:·BettiTally81 o7·:·BettiTally
82 i8·:·I·=·ideal·I_*;82 i8·:·I·=·ideal·I_*;
  
83 o8·:·Ideal·of·S83 o8·:·Ideal·of·S
84 i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5)84 i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5)
85 ·--·1.23548s·elapsed85 ·--·1.76861s·elapsed
  
86 ············0··1···2···3···4····586 ············0··1···2···3···4····5
87 o9·=·total:·1·35·140·385·819·108087 o9·=·total:·1·35·140·385·819·1080
88 ·········0:·1··.···.···.···.····.88 ·········0:·1··.···.···.···.····.
89 ·········1:·.·35·140·189··84····.89 ·········1:·.·35·140·189··84····.
90 ·········2:·.··.···.·196·735·108090 ·········2:·.··.···.·196·735·1080
  
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Offset 72, 15 lines modifiedOffset 72, 15 lines modified
72 ········<h2>Description</h2>72 ········<h2>Description</h2>
73 ········<p>Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the·last·must·already·exist.</p>73 ········<p>Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the·last·must·already·exist.</p>
74 ········<table·class="examples">74 ········<table·class="examples">
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName()·|·&quot;/&quot;77 ··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName()·|·&quot;/&quot;
  
78 o1·=·/tmp/M2-1082878-0/0/</code></pre>78 o1·=·/tmp/M2-995497-0/0/</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i2·:·mkdir·p</code></pre>83 ··············<pre><code·class="language-macaulay2">i2·:·mkdir·p</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
Offset 91, 15 lines modifiedOffset 91, 15 lines modified
91 o3·=·true</code></pre>91 o3·=·true</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i4·:·(fn·=·p·|·&quot;foo&quot;)·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close96 ··············<pre><code·class="language-macaulay2">i4·:·(fn·=·p·|·&quot;foo&quot;)·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
97 o4·=·/tmp/M2-1082878-0/0/foo97 o4·=·/tmp/M2-995497-0/0/foo
  
98 o4·:·File</code></pre>98 o4·:·File</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i5·:·get·fn103 ··············<pre><code·class="language-macaulay2">i5·:·get·fn
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12 ····*·Consequences:12 ····*·Consequences:
13 ··········o·a·directory·will·be·created·at·the·path·p13 ··········o·a·directory·will·be·created·at·the·path·p
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the15 Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the
16 last·must·already·exist.16 last·must·already·exist.
17 i1·:·p·=·temporaryFileName()·|·"/"17 i1·:·p·=·temporaryFileName()·|·"/"
  
18 o1·=·/tmp/M2-1082878-0/0/18 o1·=·/tmp/M2-995497-0/0/
19 i2·:·mkdir·p19 i2·:·mkdir·p
20 i3·:·isDirectory·p20 i3·:·isDirectory·p
  
21 o3·=·true21 o3·=·true
22 i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close22 i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close
  
23 o4·=·/tmp/M2-1082878-0/0/foo23 o4·=·/tmp/M2-995497-0/0/foo
  
24 o4·:·File24 o4·:·File
25 i5·:·get·fn25 i5·:·get·fn
  
26 o5·=·hi·there26 o5·=·hi·there
27 i6·:·removeFile·fn27 i6·:·removeFile·fn
28 i7·:·removeDirectory·p28 i7·:·removeDirectory·p
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Offset 81, 52 lines modifiedOffset 81, 52 lines modified
81 ······<div>81 ······<div>
82 ········<h2>Description</h2>82 ········<h2>Description</h2>
83 ········<table·class="examples">83 ········<table·class="examples">
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()86 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()
  
87 o1·=·/tmp/M2-1081082-0/0</code></pre>87 o1·=·/tmp/M2-987774-0/0</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()92 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()
  
93 o2·=·/tmp/M2-1081082-0/1</code></pre>93 o2·=·/tmp/M2-987774-0/1</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i3·:·src·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close98 ··············<pre><code·class="language-macaulay2">i3·:·src·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
99 o3·=·/tmp/M2-1081082-0/099 o3·=·/tmp/M2-987774-0/0
  
100 o3·:·File</code></pre>100 o3·:·File</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i4·:·moveFile(src,dst,Verbose=>true)105 ··············<pre><code·class="language-macaulay2">i4·:·moveFile(src,dst,Verbose=>true)
106 --moving:·/tmp/M2-1081082-0/0·->·/tmp/M2-1081082-0/1</code></pre>106 --moving:·/tmp/M2-987774-0/0·->·/tmp/M2-987774-0/1</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ··········<tr>109 ··········<tr>
110 ············<td>110 ············<td>
111 ··············<pre><code·class="language-macaulay2">i5·:·get·dst111 ··············<pre><code·class="language-macaulay2">i5·:·get·dst
  
112 o5·=·hi·there</code></pre>112 o5·=·hi·there</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i6·:·bak·=·moveFile(dst,Verbose=>true)117 ··············<pre><code·class="language-macaulay2">i6·:·bak·=·moveFile(dst,Verbose=>true)
118 --backup·file·created:·/tmp/M2-1081082-0/1.bak118 --backup·file·created:·/tmp/M2-987774-0/1.bak
  
119 o6·=·/tmp/M2-1081082-0/1.bak</code></pre>119 o6·=·/tmp/M2-987774-0/1.bak</code></pre>
120 ············</td>120 ············</td>
121 ··········</tr>121 ··········</tr>
122 ··········<tr>122 ··········<tr>
123 ············<td>123 ············<td>
124 ··············<pre><code·class="language-macaulay2">i7·:·removeFile·bak</code></pre>124 ··············<pre><code·class="language-macaulay2">i7·:·removeFile·bak</code></pre>
125 ············</td>125 ············</td>
126 ··········</tr>126 ··········</tr>
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20 ··········o·the·name·of·the·backup·file·if·one·was·created,·or·_\x8n_\x8u_\x8l_\x8l20 ··········o·the·name·of·the·backup·file·if·one·was·created,·or·_\x8n_\x8u_\x8l_\x8l
21 ····*·Consequences:21 ····*·Consequences:
22 ··········o·the·file·will·be·moved·by·creating·a·new·link·to·the·file·and22 ··········o·the·file·will·be·moved·by·creating·a·new·link·to·the·file·and
23 ············removing·the·old·one23 ············removing·the·old·one
24 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*24 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
25 i1·:·src·=·temporaryFileName()25 i1·:·src·=·temporaryFileName()
  
26 o1·=·/tmp/M2-1081082-0/026 o1·=·/tmp/M2-987774-0/0
27 i2·:·dst·=·temporaryFileName()27 i2·:·dst·=·temporaryFileName()
  
28 o2·=·/tmp/M2-1081082-0/128 o2·=·/tmp/M2-987774-0/1
29 i3·:·src·<<·"hi·there"·<<·close29 i3·:·src·<<·"hi·there"·<<·close
  
30 o3·=·/tmp/M2-1081082-0/030 o3·=·/tmp/M2-987774-0/0
  
31 o3·:·File31 o3·:·File
32 i4·:·moveFile(src,dst,Verbose=>true)32 i4·:·moveFile(src,dst,Verbose=>true)
33 --moving:·/tmp/M2-1081082-0/0·->·/tmp/M2-1081082-0/133 --moving:·/tmp/M2-987774-0/0·->·/tmp/M2-987774-0/1
34 i5·:·get·dst34 i5·:·get·dst
  
35 o5·=·hi·there35 o5·=·hi·there
36 i6·:·bak·=·moveFile(dst,Verbose=>true)36 i6·:·bak·=·moveFile(dst,Verbose=>true)
37 --backup·file·created:·/tmp/M2-1081082-0/1.bak37 --backup·file·created:·/tmp/M2-987774-0/1.bak
  
38 o6·=·/tmp/M2-1081082-0/1.bak38 o6·=·/tmp/M2-987774-0/1.bak
39 i7·:·removeFile·bak39 i7·:·removeFile·bak
40 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*40 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
41 ····*·_\x8c_\x8o_\x8p_\x8y_\x8F_\x8i_\x8l_\x8e41 ····*·_\x8c_\x8o_\x8p_\x8y_\x8F_\x8i_\x8l_\x8e
42 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*42 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
43 ····*·moveFile(String)43 ····*·moveFile(String)
44 ····*·_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e_\x8(_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8,_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8)44 ····*·_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e_\x8(_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8,_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8)
45 ===============================================================================45 ===============================================================================
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./usr/share/doc/Macaulay2/Macaulay2Doc/html/_nanosleep.html
    
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51 ······<h1>nanosleep·--·sleep·for·a·given·number·of·nanoseconds</h1>51 ······<h1>nanosleep·--·sleep·for·a·given·number·of·nanoseconds</h1>
52 ······<div>52 ······<div>
53 ········<h2>Description</h2>53 ········<h2>Description</h2>
54 <span·class="tt">nanosleep·n</span>·--·sleeps·for·<span·class="tt">n</span>·nanoseconds.········<table·class="examples">54 <span·class="tt">nanosleep·n</span>·--·sleeps·for·<span·class="tt">n</span>·nanoseconds.········<table·class="examples">
55 ··········<tr>55 ··········<tr>
56 ············<td>56 ············<td>
57 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nanosleep·50000000057 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nanosleep·500000000
58 ·--·.500168s·elapsed58 ·--·.500097s·elapsed
  
59 o1·=·0</code></pre>59 o1·=·0</code></pre>
60 ············</td>60 ············</td>
61 ··········</tr>61 ··········</tr>
62 ········</table>62 ········</table>
63 ······</div>63 ······</div>
64 ······<div>64 ······<div>
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4 [q···················]4 [q···················]
5 _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c5 _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c
6 ===============================================================================6 ===============================================================================
7 *\x8**\x8**\x8**\x8**\x8**\x8*·n\x8na\x8an\x8no\x8os\x8sl\x8le\x8ee\x8ep\x8p·-\x8--\x8-·s\x8sl\x8le\x8ee\x8ep\x8p·f\x8fo\x8or\x8r·a\x8a·g\x8gi\x8iv\x8ve\x8en\x8n·n\x8nu\x8um\x8mb\x8be\x8er\x8r·o\x8of\x8f·n\x8na\x8an\x8no\x8os\x8se\x8ec\x8co\x8on\x8nd\x8ds\x8s·*\x8**\x8**\x8**\x8**\x8**\x8*7 *\x8**\x8**\x8**\x8**\x8**\x8*·n\x8na\x8an\x8no\x8os\x8sl\x8le\x8ee\x8ep\x8p·-\x8--\x8-·s\x8sl\x8le\x8ee\x8ep\x8p·f\x8fo\x8or\x8r·a\x8a·g\x8gi\x8iv\x8ve\x8en\x8n·n\x8nu\x8um\x8mb\x8be\x8er\x8r·o\x8of\x8f·n\x8na\x8an\x8no\x8os\x8se\x8ec\x8co\x8on\x8nd\x8ds\x8s·*\x8**\x8**\x8**\x8**\x8**\x8*
8 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*8 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
9 nanosleep·n·--·sleeps·for·n·nanoseconds.9 nanosleep·n·--·sleeps·for·n·nanoseconds.
10 i1·:·elapsedTime·nanosleep·50000000010 i1·:·elapsedTime·nanosleep·500000000
11 ·--·.500168s·elapsed11 ·--·.500097s·elapsed
  
12 o1·=·012 o1·=·0
13 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
14 ····*·_\x8s_\x8l_\x8e_\x8e_\x8p·--·sleep·for·a·while14 ····*·_\x8s_\x8l_\x8e_\x8e_\x8p·--·sleep·for·a·while
15 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
16 The·object·_\x8n_\x8a_\x8n_\x8o_\x8s_\x8l_\x8e_\x8e_\x8p·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.16 The·object·_\x8n_\x8a_\x8n_\x8o_\x8s_\x8l_\x8e_\x8e_\x8p·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
17 ===============================================================================17 ===============================================================================
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./usr/share/doc/Macaulay2/Macaulay2Doc/html/_options_lp__Function_rp.html
    
Offset 104, 60 lines modifiedOffset 104, 60 lines modified
104 o3·:·OptionTable</code></pre>104 o3·:·OptionTable</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i4·:·methods·codim109 ··············<pre><code·class="language-macaulay2">i4·:·methods·codim
  
110 o4·=·{0·=>·(codim,·CoherentSheaf)·} 
111 ·····{1·=>·(codim,·MonomialIdeal)·}110 o4·=·{0·=>·(codim,·MonomialIdeal)·}
112 ·····{2·=>·(codim,·Variety)·······}111 ·····{1·=>·(codim,·Variety)·······}
113 ·····{3·=>·(codim,·Module)········}112 ·····{2·=>·(codim,·Module)········}
114 ·····{4·=>·(codim,·QuotientRing)··}113 ·····{3·=>·(codim,·QuotientRing)··}
115 ·····{5·=>·(codim,·Ideal)·········}114 ·····{4·=>·(codim,·Ideal)·········}
116 ·····{6·=>·(codim,·BettiTally)····}115 ·····{5·=>·(codim,·BettiTally)····}
117 ·····{7·=>·(codim,·PolynomialRing)}116 ·····{6·=>·(codim,·PolynomialRing)}
 117 ·····{7·=>·(codim,·CoherentSheaf)·}
  
118 o4·:·NumberedVerticalList</code></pre>118 o4·:·NumberedVerticalList</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i5·:·options·oo123 ··············<pre><code·class="language-macaulay2">i5·:·options·oo
  
124 o5·=·{0·=>·(OptionTable{Generic·=>·false})}124 o5·=·{0·=>·(OptionTable{Generic·=>·false})}
125 ·····{1·=>·(OptionTable{Generic·=>·false})}125 ·····{1·=>·(OptionTable{Generic·=>·false})}
126 ·····{2·=>·(OptionTable{Generic·=>·false})}126 ·····{2·=>·(OptionTable{Generic·=>·false})}
127 ·····{3·=>·(OptionTable{Generic·=>·false})}127 ·····{3·=>·(OptionTable{Generic·=>·false})}
128 ·····{4·=>·(OptionTable{Generic·=>·false})}128 ·····{4·=>·(OptionTable{Generic·=>·false})}
129 ·····{5·=>·(OptionTable{Generic·=>·false})} 
130 ·····{6·=>·(OptionTable{})················}129 ·····{5·=>·(OptionTable{})················}
 130 ·····{6·=>·(OptionTable{Generic·=>·false})}
131 ·····{7·=>·(OptionTable{Generic·=>·false})}131 ·····{7·=>·(OptionTable{Generic·=>·false})}
  
132 o5·:·NumberedVerticalList</code></pre>132 o5·:·NumberedVerticalList</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i6·:·methods·intersect137 ··············<pre><code·class="language-macaulay2">i6·:·methods·intersect
  
138 o6·=·{0·=>·(intersect,·List)··························}138 o6·=·{0·=>·(intersect,·List)··························}
139 ·····{1·=>·(intersect,·Set,·Set)······················} 
140 ·····{2·=>·(intersect,·Ideal)·························}139 ·····{1·=>·(intersect,·Ideal)·························}
 140 ·····{2·=>·(intersect,·Set,·Set)······················}
141 ·····{3·=>·(intersect,·RRi,·RRi)······················}141 ·····{3·=>·(intersect,·RRi,·RRi)······················}
142 ·····{4·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)}142 ·····{4·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)}
143 ·····{5·=>·(intersect,·Polyhedron,·Cone)··············}143 ·····{5·=>·(intersect,·Polyhedron,·Cone)··············}
144 ·····{6·=>·(intersect,·Cone,·Polyhedron)··············}144 ·····{6·=>·(intersect,·Cone,·Polyhedron)··············}
145 ·····{7·=>·(intersect,·Matrix)························}145 ·····{7·=>·(intersect,·Matrix)························}
146 ·····{8·=>·(intersect,·Module,·Module)················}146 ·····{8·=>·(intersect,·Module,·Module)················}
147 ·····{9·=>·(intersect,·RRi)···························}147 ·····{9·=>·(intersect,·RRi)···························}
148 ·····{10·=>·(intersect,·Ideal,·Ideal)·················} 
149 ·····{11·=>·(intersect,·Polyhedron,·Polyhedron)·······}148 ·····{10·=>·(intersect,·Polyhedron,·Polyhedron)·······}
150 ·····{12·=>·(intersect,·Cone,·Cone)···················}149 ·····{11·=>·(intersect,·Cone,·Cone)···················}
151 ·····{13·=>·(intersect,·Matrix,·Matrix)···············}150 ·····{12·=>·(intersect,·Matrix,·Matrix)···············}
 151 ·····{13·=>·(intersect,·Ideal,·Ideal)·················}
152 ·····{14·=>·(intersect,·Module)·······················}152 ·····{14·=>·(intersect,·Module)·······················}
153 ·····{15·=>·(intersect,·Sequence)·····················}153 ·····{15·=>·(intersect,·Sequence)·····················}
  
154 o6·:·NumberedVerticalList</code></pre>154 o6·:·NumberedVerticalList</code></pre>
155 ············</td>155 ············</td>
156 ··········</tr>156 ··········</tr>
157 ··········<tr>157 ··········<tr>
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35 i3·:·options(codim,·Ideal)35 i3·:·options(codim,·Ideal)
  
36 o3·=·OptionTable{Generic·=>·false}36 o3·=·OptionTable{Generic·=>·false}
  
37 o3·:·OptionTable37 o3·:·OptionTable
38 i4·:·methods·codim38 i4·:·methods·codim
  
39 o4·=·{0·=>·(codim,·CoherentSheaf)·} 
40 ·····{1·=>·(codim,·MonomialIdeal)·}39 o4·=·{0·=>·(codim,·MonomialIdeal)·}
41 ·····{2·=>·(codim,·Variety)·······}40 ·····{1·=>·(codim,·Variety)·······}
42 ·····{3·=>·(codim,·Module)········}41 ·····{2·=>·(codim,·Module)········}
43 ·····{4·=>·(codim,·QuotientRing)··}42 ·····{3·=>·(codim,·QuotientRing)··}
44 ·····{5·=>·(codim,·Ideal)·········}43 ·····{4·=>·(codim,·Ideal)·········}
45 ·····{6·=>·(codim,·BettiTally)····}44 ·····{5·=>·(codim,·BettiTally)····}
46 ·····{7·=>·(codim,·PolynomialRing)}45 ·····{6·=>·(codim,·PolynomialRing)}
 46 ·····{7·=>·(codim,·CoherentSheaf)·}
  
47 o4·:·NumberedVerticalList47 o4·:·NumberedVerticalList
48 i5·:·options·oo48 i5·:·options·oo
  
49 o5·=·{0·=>·(OptionTable{Generic·=>·false})}49 o5·=·{0·=>·(OptionTable{Generic·=>·false})}
50 ·····{1·=>·(OptionTable{Generic·=>·false})}50 ·····{1·=>·(OptionTable{Generic·=>·false})}
51 ·····{2·=>·(OptionTable{Generic·=>·false})}51 ·····{2·=>·(OptionTable{Generic·=>·false})}
52 ·····{3·=>·(OptionTable{Generic·=>·false})}52 ·····{3·=>·(OptionTable{Generic·=>·false})}
53 ·····{4·=>·(OptionTable{Generic·=>·false})}53 ·····{4·=>·(OptionTable{Generic·=>·false})}
54 ·····{5·=>·(OptionTable{Generic·=>·false})} 
55 ·····{6·=>·(OptionTable{})················}54 ·····{5·=>·(OptionTable{})················}
 55 ·····{6·=>·(OptionTable{Generic·=>·false})}
56 ·····{7·=>·(OptionTable{Generic·=>·false})}56 ·····{7·=>·(OptionTable{Generic·=>·false})}
  
57 o5·:·NumberedVerticalList57 o5·:·NumberedVerticalList
58 i6·:·methods·intersect58 i6·:·methods·intersect
  
59 o6·=·{0·=>·(intersect,·List)··························}59 o6·=·{0·=>·(intersect,·List)··························}
60 ·····{1·=>·(intersect,·Set,·Set)······················} 
61 ·····{2·=>·(intersect,·Ideal)·························}60 ·····{1·=>·(intersect,·Ideal)·························}
 61 ·····{2·=>·(intersect,·Set,·Set)······················}
62 ·····{3·=>·(intersect,·RRi,·RRi)······················}62 ·····{3·=>·(intersect,·RRi,·RRi)······················}
63 ·····{4·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)}63 ·····{4·=>·(intersect,·Matrix,·Matrix,·Matrix,·Matrix)}
64 ·····{5·=>·(intersect,·Polyhedron,·Cone)··············}64 ·····{5·=>·(intersect,·Polyhedron,·Cone)··············}
65 ·····{6·=>·(intersect,·Cone,·Polyhedron)··············}65 ·····{6·=>·(intersect,·Cone,·Polyhedron)··············}
66 ·····{7·=>·(intersect,·Matrix)························}66 ·····{7·=>·(intersect,·Matrix)························}
67 ·····{8·=>·(intersect,·Module,·Module)················}67 ·····{8·=>·(intersect,·Module,·Module)················}
68 ·····{9·=>·(intersect,·RRi)···························}68 ·····{9·=>·(intersect,·RRi)···························}
69 ·····{10·=>·(intersect,·Ideal,·Ideal)·················} 
70 ·····{11·=>·(intersect,·Polyhedron,·Polyhedron)·······}69 ·····{10·=>·(intersect,·Polyhedron,·Polyhedron)·······}
71 ·····{12·=>·(intersect,·Cone,·Cone)···················}70 ·····{11·=>·(intersect,·Cone,·Cone)···················}
72 ·····{13·=>·(intersect,·Matrix,·Matrix)···············}71 ·····{12·=>·(intersect,·Matrix,·Matrix)···············}
 72 ·····{13·=>·(intersect,·Ideal,·Ideal)·················}
73 ·····{14·=>·(intersect,·Module)·······················}73 ·····{14·=>·(intersect,·Module)·······················}
74 ·····{15·=>·(intersect,·Sequence)·····················}74 ·····{15·=>·(intersect,·Sequence)·····················}
  
75 o6·:·NumberedVerticalList75 o6·:·NumberedVerticalList
76 i7·:·options·076 i7·:·options·0
  
77 o7·=·OptionTable{}77 o7·=·OptionTable{}
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Offset 72, 21 lines modifiedOffset 72, 21 lines modified
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i2·:·L·=·random·toList·(1..10000);</code></pre>73 ··············<pre><code·class="language-macaulay2">i2·:·L·=·random·toList·(1..10000);</code></pre>
74 ············</td>74 ············</td>
75 ··········</tr>75 ··········</tr>
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·········apply(1..100,·n·->·sort·L);78 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·········apply(1..100,·n·->·sort·L);
79 ·--·.682304s·elapsed</code></pre>79 ·--·1.89611s·elapsed</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L);84 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L);
85 ·--·.185652s·elapsed</code></pre>85 ·--·.525755s·elapsed</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ········</table>88 ········</table>
89 ········<div>89 ········<div>
90 ··········<p>You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.</p>90 ··········<p>You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.</p>
91 ··········<p>Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is·not·&quot;thread·safe&quot;,·meaning·they·make·modifications·to·memory·without·ensuring·the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can·slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and·mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists.·Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be·thread·safe.</p>91 ··········<p>Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is·not·&quot;thread·safe&quot;,·meaning·they·make·modifications·to·memory·without·ensuring·the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can·slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and·mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists.·Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be·thread·safe.</p>
92 ··········<p>The·rest·of·this·document·describes·how·to·control·parallel·tasks·more·directly.</p>92 ··········<p>The·rest·of·this·document·describes·how·to·control·parallel·tasks·more·directly.</p>
Offset 150, 15 lines modifiedOffset 150, 15 lines modified
150 ··········<p>Note·that·<a·title="schedule·a·task·for·execution"·href="_schedule.html">schedule</a>·returns·a·task,·not·the·result·of·the·computation,·which·will·be·accessible·only·after·the·task·has·completed·the·computation.</p>150 ··········<p>Note·that·<a·title="schedule·a·task·for·execution"·href="_schedule.html">schedule</a>·returns·a·task,·not·the·result·of·the·computation,·which·will·be·accessible·only·after·the·task·has·completed·the·computation.</p>
151 ········</div>151 ········</div>
152 ········<table·class="examples">152 ········<table·class="examples">
153 ··········<tr>153 ··········<tr>
154 ············<td>154 ············<td>
155 ··············<pre><code·class="language-macaulay2">i11·:·t155 ··············<pre><code·class="language-macaulay2">i11·:·t
  
156 o11·=·&lt;&lt;task,·running>>156 o11·=·&lt;&lt;task,·created>>
  
157 o11·:·Task</code></pre>157 o11·:·Task</code></pre>
158 ············</td>158 ············</td>
159 ··········</tr>159 ··········</tr>
160 ········</table>160 ········</table>
161 ········<div>161 ········<div>
162 ··········<p>Use·<a·title="whether·a·file·has·data·available·for·reading"·href="_is__Ready_lp__File_rp.html">isReady</a>·to·check·whether·the·result·is·available·yet.</p>162 ··········<p>Use·<a·title="whether·a·file·has·data·available·for·reading"·href="_is__Ready_lp__File_rp.html">isReady</a>·to·check·whether·the·result·is·available·yet.</p>
Offset 224, 15 lines modifiedOffset 224, 15 lines modified
224 ··············<pre><code·class="language-macaulay2">i17·:·schedule·t';</code></pre>224 ··············<pre><code·class="language-macaulay2">i17·:·schedule·t';</code></pre>
225 ············</td>225 ············</td>
226 ··········</tr>226 ··········</tr>
227 ··········<tr>227 ··········<tr>
228 ············<td>228 ············<td>
229 ··············<pre><code·class="language-macaulay2">i18·:·t'229 ··············<pre><code·class="language-macaulay2">i18·:·t'
  
230 o18·=·&lt;&lt;task,·created>>230 o18·=·&lt;&lt;task,·running>>
  
231 o18·:·Task</code></pre>231 o18·:·Task</code></pre>
232 ············</td>232 ············</td>
233 ··········</tr>233 ··········</tr>
234 ··········<tr>234 ··········<tr>
235 ············<td>235 ············<td>
236 ··············<pre><code·class="language-macaulay2">i19·:·taskResult·t'236 ··············<pre><code·class="language-macaulay2">i19·:·taskResult·t'
Offset 271, 15 lines modifiedOffset 271, 15 lines modified
271 ··············<pre><code·class="language-macaulay2">i22·:·addStartTask(F,G)</code></pre>271 ··············<pre><code·class="language-macaulay2">i22·:·addStartTask(F,G)</code></pre>
272 ············</td>272 ············</td>
273 ··········</tr>273 ··········</tr>
274 ··········<tr>274 ··········<tr>
275 ············<td>275 ············<td>
276 ··············<pre><code·class="language-macaulay2">i23·:·schedule·F276 ··············<pre><code·class="language-macaulay2">i23·:·schedule·F
  
277 o23·=·&lt;&lt;task,·created>>277 o23·=·&lt;&lt;task,·result·available,·task·done>>
  
278 o23·:·Task</code></pre>278 o23·:·Task</code></pre>
279 ············</td>279 ············</td>
280 ··········</tr>280 ··········</tr>
281 ··········<tr>281 ··········<tr>
282 ············<td>282 ············<td>
283 ··············<pre><code·class="language-macaulay2">i24·:·taskResult·F283 ··············<pre><code·class="language-macaulay2">i24·:·taskResult·F
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Offset 17, 17 lines modifiedOffset 17, 17 lines modified
17 big·computation.·If·the·list·is·long,·it·will·be·split·into·chunks·for·each17 big·computation.·If·the·list·is·long,·it·will·be·split·into·chunks·for·each
18 core,·reducing·the·overhead.·But·the·speedup·is·still·limited·by·the·different18 core,·reducing·the·overhead.·But·the·speedup·is·still·limited·by·the·different
19 threads·competing·for·memory,·including·cpu·caches;·it·is·like·running19 threads·competing·for·memory,·including·cpu·caches;·it·is·like·running
20 Macaulay2·on·a·computer·that·is·running·other·big·programs·at·the·same·time.·We20 Macaulay2·on·a·computer·that·is·running·other·big·programs·at·the·same·time.·We
21 can·see·this·using·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e.21 can·see·this·using·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e.
22 i2·:·L·=·random·toList·(1..10000);22 i2·:·L·=·random·toList·(1..10000);
23 i3·:·elapsedTime·········apply(1..100,·n·->·sort·L);23 i3·:·elapsedTime·········apply(1..100,·n·->·sort·L);
24 ·--·.682304s·elapsed24 ·--·1.89611s·elapsed
25 i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L);25 i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L);
26 ·--·.185652s·elapsed26 ·--·.525755s·elapsed
27 You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.27 You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.
28 Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is28 Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is
29 not·"thread·safe",·meaning·they·make·modifications·to·memory·without·ensuring29 not·"thread·safe",·meaning·they·make·modifications·to·memory·without·ensuring
30 the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can30 the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can
31 slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and31 slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and
32 mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists.32 mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists.
33 Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be33 Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be
Offset 62, 15 lines modifiedOffset 62, 15 lines modified
62 o10·=·<<task,·created>>62 o10·=·<<task,·created>>
  
63 o10·:·Task63 o10·:·Task
64 Note·that·_\x8s_\x8c_\x8h_\x8e_\x8d_\x8u_\x8l_\x8e·returns·a·task,·not·the·result·of·the·computation,·which64 Note·that·_\x8s_\x8c_\x8h_\x8e_\x8d_\x8u_\x8l_\x8e·returns·a·task,·not·the·result·of·the·computation,·which
65 will·be·accessible·only·after·the·task·has·completed·the·computation.65 will·be·accessible·only·after·the·task·has·completed·the·computation.
66 i11·:·t66 i11·:·t
  
67 o11·=·<<task,·running>>67 o11·=·<<task,·created>>
  
68 o11·:·Task68 o11·:·Task
69 Use·_\x8i_\x8s_\x8R_\x8e_\x8a_\x8d_\x8y·to·check·whether·the·result·is·available·yet.69 Use·_\x8i_\x8s_\x8R_\x8e_\x8a_\x8d_\x8y·to·check·whether·the·result·is·available·yet.
70 i12·:·isReady·t70 i12·:·isReady·t
  
71 o12·=·false71 o12·=·false
72 To·wait·for·the·result·and·then·retrieve·it,·use·_\x8t_\x8a_\x8s_\x8k_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t.72 To·wait·for·the·result·and·then·retrieve·it,·use·_\x8t_\x8a_\x8s_\x8k_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t.
Offset 92, 15 lines modifiedOffset 92, 15 lines modified
92 o16·=·<<task,·created>>92 o16·=·<<task,·created>>
  
93 o16·:·Task93 o16·:·Task
94 Start·it·running·with·_\x8s_\x8c_\x8h_\x8e_\x8d_\x8u_\x8l_\x8e.94 Start·it·running·with·_\x8s_\x8c_\x8h_\x8e_\x8d_\x8u_\x8l_\x8e.
95 i17·:·schedule·t';95 i17·:·schedule·t';
96 i18·:·t'96 i18·:·t'
  
97 o18·=·<<task,·created>>97 o18·=·<<task,·running>>
  
98 o18·:·Task98 o18·:·Task
99 i19·:·taskResult·t'99 i19·:·taskResult·t'
  
100 o19·=·|·980z2-18y-201z+13·35yz-4y+2z-1·10y2-y-12z+1·5x2-4y+2z-1·|100 o19·=·|·980z2-18y-201z+13·35yz-4y+2z-1·10y2-y-12z+1·5x2-4y+2z-1·|
  
101 ··············1······4101 ··············1······4
Offset 116, 15 lines modifiedOffset 116, 15 lines modified
  
116 o21·=·<<task,·created>>116 o21·=·<<task,·created>>
  
117 o21·:·Task117 o21·:·Task
118 i22·:·addStartTask(F,G)118 i22·:·addStartTask(F,G)
119 i23·:·schedule·F119 i23·:·schedule·F
  
120 o23·=·<<task,·created>>120 o23·=·<<task,·result·available,·task·done>>
  
121 o23·:·Task121 o23·:·Task
122 i24·:·taskResult·F122 i24·:·taskResult·F
  
123 o24·=·result·of·F123 o24·=·result·of·F
124 i25·:·taskResult·G124 i25·:·taskResult·G
  
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Offset 137, 15 lines modifiedOffset 137, 15 lines modified
  
137 o3·:·PolynomialRing</code></pre>137 o3·:·PolynomialRing</code></pre>
138 ············</td>138 ············</td>
139 ··········</tr>139 ··········</tr>
140 ··········<tr>140 ··········<tr>
141 ············<td>141 ············<td>
142 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalBetti·I142 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalBetti·I
143 ·--·1.87001s·elapsed143 ·--·11.8923s·elapsed
  
144 ············0··1···2···3···4····5···6···7···8··9·10144 ············0··1···2···3···4····5···6···7···8··9·10
145 o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1145 o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1
146 ·········0:·1··.···.···.···.····.···.···.···.··.··.146 ·········0:·1··.···.···.···.····.···.···.···.··.··.
147 ·········1:·.·35·140·189··84····.···.···.···.··.··.147 ·········1:·.·35·140·189··84····.···.···.···.··.··.
148 ·········2:·.··.···.·196·735·1080·735·196···.··.··.148 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
149 ·········3:·.··.···.···.···.····.··84·189·140·35··.149 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 160, 15 lines modifiedOffset 160, 15 lines modified
  
160 o5·:·Ideal·of·S</code></pre>160 o5·:·Ideal·of·S</code></pre>
161 ············</td>161 ············</td>
162 ··········</tr>162 ··········</tr>
163 ··········<tr>163 ··········<tr>
164 ············<td>164 ············<td>
165 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true)165 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true)
166 ·--·1.81656s·elapsed166 ·--·5.03134s·elapsed
  
167 ············0··1···2···3···4····5···6···7···8··9·10167 ············0··1···2···3···4····5···6···7···8··9·10
168 o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1168 o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1
169 ·········0:·1··.···.···.···.····.···.···.···.··.··.169 ·········0:·1··.···.···.···.····.···.···.···.··.··.
170 ·········1:·.·35·140·189··84····.···.···.···.··.··.170 ·········1:·.·35·140·189··84····.···.···.···.··.··.
171 ·········2:·.··.···.·196·735·1080·735·196···.··.··.171 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
172 ·········3:·.··.···.···.···.····.··84·189·140·35··.172 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 190, 15 lines modifiedOffset 190, 15 lines modified
  
190 o8·=·1</code></pre>190 o8·=·1</code></pre>
191 ············</td>191 ············</td>
192 ··········</tr>192 ··········</tr>
193 ··········<tr>193 ··········<tr>
194 ············<td>194 ············<td>
195 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·minimalBetti(I)195 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·minimalBetti(I)
196 ·--·1.76207s·elapsed196 ·--·6.04471s·elapsed
  
197 ············0··1···2···3···4····5···6···7···8··9·10197 ············0··1···2···3···4····5···6···7···8··9·10
198 o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1198 o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1
199 ·········0:·1··.···.···.···.····.···.···.···.··.··.199 ·········0:·1··.···.···.···.····.···.···.···.··.··.
200 ·········1:·.·35·140·189··84····.···.···.···.··.··.200 ·········1:·.·35·140·189··84····.···.···.···.··.··.
201 ·········2:·.··.···.·196·735·1080·735·196···.··.··.201 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
202 ·········3:·.··.···.···.···.····.··84·189·140·35··.202 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 231, 15 lines modifiedOffset 231, 15 lines modified
  
231 o12·:·Ideal·of·S</code></pre>231 o12·:·Ideal·of·S</code></pre>
232 ············</td>232 ············</td>
233 ··········</tr>233 ··········</tr>
234 ··········<tr>234 ··········<tr>
235 ············<td>235 ············<td>
236 ··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)236 ··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)
237 ·--·2.08299s·elapsed237 ·--·6.77885s·elapsed
  
238 ·······1······35······241······841······1781······2464······2294······1432······576······135······14238 ·······1······35······241······841······1781······2464······2294······1432······576······135······14
239 o13·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S239 o13·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S
240 ··································································································240 ··································································································
241 ······0······1·······2········3········4·········5·········6·········7·········8········9········10241 ······0······1·······2········3········4·········5·········6·········7·········8········9········10
  
242 o13·:·Complex</code></pre>242 o13·:·Complex</code></pre>
Offset 258, 15 lines modifiedOffset 258, 15 lines modified
  
258 o15·:·Ideal·of·S</code></pre>258 o15·:·Ideal·of·S</code></pre>
259 ············</td>259 ············</td>
260 ··········</tr>260 ··········</tr>
261 ··········<tr>261 ··········<tr>
262 ············<td>262 ············<td>
263 ··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)263 ··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)
264 ·--·1.97957s·elapsed264 ·--·7.46347s·elapsed
  
265 ·······1······35······241······841······1781······2464······2294······1432······576······135······14265 ·······1······35······241······841······1781······2464······2294······1432······576······135······14
266 o16·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S266 o16·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S
267 ··································································································267 ··································································································
268 ······0······1·······2········3········4·········5·········6·········7·········8········9········10268 ······0······1·······2········3········4·········5·········6·········7·········8········9········10
  
269 o16·:·Complex</code></pre>269 o16·:·Complex</code></pre>
Offset 299, 15 lines modifiedOffset 299, 15 lines modified
  
299 o19·:·Ideal·of·S</code></pre>299 o19·:·Ideal·of·S</code></pre>
300 ············</td>300 ············</td>
301 ··········</tr>301 ··········</tr>
302 ··········<tr>302 ··········<tr>
303 ············<td>303 ············<td>
304 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·&quot;F4&quot;);304 ··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·&quot;F4&quot;);
305 ·--·3.10387s·elapsed305 ·--·8.49594s·elapsed
  
306 ··············1······108306 ··············1······108
307 o20·:·Matrix·S··&lt;--·S</code></pre>307 o20·:·Matrix·S··&lt;--·S</code></pre>
308 ············</td>308 ············</td>
309 ··········</tr>309 ··········</tr>
310 ··········<tr>310 ··········<tr>
311 ············<td>311 ············<td>
Offset 322, 15 lines modifiedOffset 322, 15 lines modified
  
322 o22·:·Ideal·of·S</code></pre>322 o22·:·Ideal·of·S</code></pre>
323 ············</td>323 ············</td>
324 ··········</tr>324 ··········</tr>
325 ··········<tr>325 ··········<tr>
326 ············<td>326 ············<td>
327 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·&quot;F4&quot;);327 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·&quot;F4&quot;);
328 ·--·6.09094s·elapsed328 ·--·26.4761s·elapsed
  
329 ··············1······108329 ··············1······108
330 o23·:·Matrix·S··&lt;--·S</code></pre>330 o23·:·Matrix·S··&lt;--·S</code></pre>
331 ············</td>331 ············</td>
332 ··········</tr>332 ··········</tr>
333 ··········<tr>333 ··········<tr>
334 ············<td>334 ············<td>
Offset 345, 15 lines modifiedOffset 345, 15 lines modified
  
345 o25·:·Ideal·of·S</code></pre>345 o25·:·Ideal·of·S</code></pre>
346 ············</td>346 ············</td>
347 ··········</tr>347 ··········</tr>
348 ··········<tr>348 ··········<tr>
349 ············<td>349 ············<td>
350 ··············<pre><code·class="language-macaulay2">i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·&quot;F4&quot;);350 ··············<pre><code·class="language-macaulay2">i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·&quot;F4&quot;);
351 ·--·2.92069s·elapsed351 ·--·8.21435s·elapsed
  
352 ··············1······108352 ··············1······108
353 o26·:·Matrix·S··&lt;--·S</code></pre>353 o26·:·Matrix·S··&lt;--·S</code></pre>
354 ············</td>354 ············</td>
355 ··········</tr>355 ··········</tr>
356 ········</table>356 ········</table>
357 ········<div>357 ········<div>
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Offset 93, 30 lines modifiedOffset 93, 30 lines modified
93 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,693 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6
94 i3·:·S·=·ring·I94 i3·:·S·=·ring·I
  
95 o3·=·S95 o3·=·S
  
96 o3·:·PolynomialRing96 o3·:·PolynomialRing
97 i4·:·elapsedTime·minimalBetti·I97 i4·:·elapsedTime·minimalBetti·I
98 ·--·1.87001s·elapsed98 ·--·11.8923s·elapsed
  
99 ············0··1···2···3···4····5···6···7···8··9·1099 ············0··1···2···3···4····5···6···7···8··9·10
100 o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1100 o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1
101 ·········0:·1··.···.···.···.····.···.···.···.··.··.101 ·········0:·1··.···.···.···.····.···.···.···.··.··.
102 ·········1:·.·35·140·189··84····.···.···.···.··.··.102 ·········1:·.·35·140·189··84····.···.···.···.··.··.
103 ·········2:·.··.···.·196·735·1080·735·196···.··.··.103 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
104 ·········3:·.··.···.···.···.····.··84·189·140·35··.104 ·········3:·.··.···.···.···.····.··84·189·140·35··.
105 ·········4:·.··.···.···.···.····.···.···.···.··.··1105 ·········4:·.··.···.···.···.····.···.···.···.··.··1
  
106 o4·:·BettiTally106 o4·:·BettiTally
107 i5·:·I·=·ideal·I_*;107 i5·:·I·=·ideal·I_*;
  
108 o5·:·Ideal·of·S108 o5·:·Ideal·of·S
109 i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true)109 i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true)
110 ·--·1.81656s·elapsed110 ·--·5.03134s·elapsed
  
111 ············0··1···2···3···4····5···6···7···8··9·10111 ············0··1···2···3···4····5···6···7···8··9·10
112 o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1112 o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1
113 ·········0:·1··.···.···.···.····.···.···.···.··.··.113 ·········0:·1··.···.···.···.····.···.···.···.··.··.
114 ·········1:·.·35·140·189··84····.···.···.···.··.··.114 ·········1:·.·35·140·189··84····.···.···.···.··.··.
115 ·········2:·.··.···.·196·735·1080·735·196···.··.··.115 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
116 ·········3:·.··.···.···.···.····.··84·189·140·35··.116 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 126, 15 lines modifiedOffset 126, 15 lines modified
126 i7·:·I·=·ideal·I_*;126 i7·:·I·=·ideal·I_*;
  
127 o7·:·Ideal·of·S127 o7·:·Ideal·of·S
128 i8·:·numTBBThreads·=·1128 i8·:·numTBBThreads·=·1
  
129 o8·=·1129 o8·=·1
130 i9·:·elapsedTime·minimalBetti(I)130 i9·:·elapsedTime·minimalBetti(I)
131 ·--·1.76207s·elapsed131 ·--·6.04471s·elapsed
  
132 ············0··1···2···3···4····5···6···7···8··9·10132 ············0··1···2···3···4····5···6···7···8··9·10
133 o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1133 o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1
134 ·········0:·1··.···.···.···.····.···.···.···.··.··.134 ·········0:·1··.···.···.···.····.···.···.···.··.··.
135 ·········1:·.·35·140·189··84····.···.···.···.··.··.135 ·········1:·.·35·140·189··84····.···.···.···.··.··.
136 ·········2:·.··.···.·196·735·1080·735·196···.··.··.136 ·········2:·.··.···.·196·735·1080·735·196···.··.··.
137 ·········3:·.··.···.···.···.····.··84·189·140·35··.137 ·········3:·.··.···.···.···.····.··84·189·140·35··.
Offset 149, 15 lines modifiedOffset 149, 15 lines modified
149 i11·:·numTBBThreads·=·0149 i11·:·numTBBThreads·=·0
  
150 o11·=·0150 o11·=·0
151 i12·:·I·=·ideal·I_*;151 i12·:·I·=·ideal·I_*;
  
152 o12·:·Ideal·of·S152 o12·:·Ideal·of·S
153 i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)153 i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)
154 ·--·2.08299s·elapsed154 ·--·6.77885s·elapsed
  
155 ·······1······35······241······841······1781······2464······2294······1432155 ·······1······35······241······841······1781······2464······2294······1432
156 576······135······14156 576······135······14
157 o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<-157 o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<-
158 -·S····<--·S····<--·S158 -·S····<--·S····<--·S
  
  
Offset 168, 15 lines modifiedOffset 168, 15 lines modified
168 i14·:·numTBBThreads·=·1168 i14·:·numTBBThreads·=·1
  
169 o14·=·1169 o14·=·1
170 i15·:·I·=·ideal·I_*;170 i15·:·I·=·ideal·I_*;
  
171 o15·:·Ideal·of·S171 o15·:·Ideal·of·S
172 i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)172 i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal)
173 ·--·1.97957s·elapsed173 ·--·7.46347s·elapsed
  
174 ·······1······35······241······841······1781······2464······2294······1432174 ·······1······35······241······841······1781······2464······2294······1432
175 576······135······14175 576······135······14
176 o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<-176 o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<-
177 -·S····<--·S····<--·S177 -·S····<--·S····<--·S
  
  
Offset 195, 37 lines modifiedOffset 195, 37 lines modified
195 o18·=·S195 o18·=·S
  
196 o18·:·PolynomialRing196 o18·:·PolynomialRing
197 i19·:·I·=·ideal·random(S^1,·S^{4:-5});197 i19·:·I·=·ideal·random(S^1,·S^{4:-5});
  
198 o19·:·Ideal·of·S198 o19·:·Ideal·of·S
199 i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");199 i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");
200 ·--·3.10387s·elapsed200 ·--·8.49594s·elapsed
  
201 ··············1······108201 ··············1······108
202 o20·:·Matrix·S··<--·S202 o20·:·Matrix·S··<--·S
203 i21·:·numTBBThreads·=·1203 i21·:·numTBBThreads·=·1
  
204 o21·=·1204 o21·=·1
205 i22·:·I·=·ideal·I_*;205 i22·:·I·=·ideal·I_*;
  
206 o22·:·Ideal·of·S206 o22·:·Ideal·of·S
207 i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");207 i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");
208 ·--·6.09094s·elapsed208 ·--·26.4761s·elapsed
  
209 ··············1······108209 ··············1······108
210 o23·:·Matrix·S··<--·S210 o23·:·Matrix·S··<--·S
211 i24·:·numTBBThreads·=·10211 i24·:·numTBBThreads·=·10
  
212 o24·=·10212 o24·=·10
213 i25·:·I·=·ideal·I_*;213 i25·:·I·=·ideal·I_*;
  
214 o25·:·Ideal·of·S214 o25·:·Ideal·of·S
215 i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");215 i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4");
216 ·--·2.92069s·elapsed216 ·--·8.21435s·elapsed
  
217 ··············1······108217 ··············1······108
218 o26·:·Matrix·S··<--·S218 o26·:·Matrix·S··<--·S
219 For·Gröbner·basis·computation·in·associative·algebras,·ParallelizeByDegree·is219 For·Gröbner·basis·computation·in·associative·algebras,·ParallelizeByDegree·is
220 not·relevant.·In·this·case,·use·numTBBThreads·to·control·the·amount·of220 not·relevant.·In·this·case,·use·numTBBThreads·to·control·the·amount·of
221 parallelism.221 parallelism.
222 i27·:·needsPackage·"AssociativeAlgebras"222 i27·:·needsPackage·"AssociativeAlgebras"
Offset 246, 15 lines modifiedOffset 246, 15 lines modified
246 ···············2·························2·························2246 ···············2·························2·························2
247 o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·)247 o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·)
  
248 ················ZZ248 ················ZZ
249 o30·:·Ideal·of·---<|a,·b,·c|>249 o30·:·Ideal·of·---<|a,·b,·c|>
250 ···············101250 ···············101
251 i31·:·elapsedTime·NCGB(I,·22);251 i31·:·elapsedTime·NCGB(I,·22);
252 ·--·.751013s·elapsed252 ·--·3.2874s·elapsed
  
253 ···············ZZ············1·······ZZ············148253 ···············ZZ············1·······ZZ············148
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Offset 370, 36 lines modifiedOffset 370, 36 lines modified
  
370 o27·=·3</code></pre>370 o27·=·3</code></pre>
371 ············</td>371 ············</td>
372 ··········</tr>372 ··········</tr>
373 ··········<tr>373 ··········<tr>
374 ············<td>374 ············<td>
375 ··············<pre><code·class="language-macaulay2">i28·:·time·poincare·I375 ··············<pre><code·class="language-macaulay2">i28·:·time·poincare·I
376 ·--·used·0.00145017s·(cpu);·7.802e-06s·(thread);·0s·(gc)376 ·--·used·0.00319799s·(cpu);·2.9034e-05s·(thread);·0s·(gc)
  
377 ············3·····6····9377 ············3·····6····9
378 o28·=·1·-·3T··+·3T··-·T378 o28·=·1·-·3T··+·3T··-·T
  
379 o28·:·ZZ[T]</code></pre>379 o28·:·ZZ[T]</code></pre>
380 ············</td>380 ············</td>
381 ··········</tr>381 ··········</tr>
382 ··········<tr>382 ··········<tr>
383 ············<td>383 ············<td>
384 ··············<pre><code·class="language-macaulay2">i29·:·time·gens·gb·I;384 ··············<pre><code·class="language-macaulay2">i29·:·time·gens·gb·I;
  
385 ···--·registering·gb·19·at·0x7f749535a540385 ···--·registering·gb·19·at·0x7f8bad70e540
  
386 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11386 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11
387 ···--·number·of·monomials················=·4186387 ···--·number·of·monomials················=·4186
388 ···--·#reduction·steps·=·38388 ···--·#reduction·steps·=·38
389 ···--·#spairs·done·=·11389 ···--·#spairs·done·=·11
390 ···--·ncalls·=·10390 ···--·ncalls·=·10
391 ···--·nloop·=·29391 ···--·nloop·=·29
392 ···--·nsaved·=·0392 ···--·nsaved·=·0
393 ···--··--·used·0.00903704s·(cpu);·0.0101512s·(thread);·0s·(gc)393 ···--··--·used·0.0101535s·(cpu);·0.0127548s·(thread);·0s·(gc)
  
394 ··············1······11394 ··············1······11
395 o29·:·Matrix·R··&lt;--·R</code></pre>395 o29·:·Matrix·R··&lt;--·R</code></pre>
396 ············</td>396 ············</td>
397 ··········</tr>397 ··········</tr>
398 ········</table>398 ········</table>
399 ········<div>399 ········<div>
Offset 411, 15 lines modifiedOffset 411, 15 lines modified
411 ··············<pre><code·class="language-macaulay2">i30·:·R·=·QQ[a..d];</code></pre>411 ··············<pre><code·class="language-macaulay2">i30·:·R·=·QQ[a..d];</code></pre>
412 ············</td>412 ············</td>
413 ··········</tr>413 ··········</tr>
414 ··········<tr>414 ··········<tr>
415 ············<td>415 ············<td>
416 ··············<pre><code·class="language-macaulay2">i31·:·I·=·ideal·random(R^1,·R^{3:-3});416 ··············<pre><code·class="language-macaulay2">i31·:·I·=·ideal·random(R^1,·R^{3:-3});
  
417 ···--·registering·gb·20·at·0x7f749535a380417 ···--·registering·gb·20·at·0x7f8bad70e380
  
418 ···--·[gb]number·of·(nonminimal)·gb·elements·=·0418 ···--·[gb]number·of·(nonminimal)·gb·elements·=·0
419 ···--·number·of·monomials················=·0419 ···--·number·of·monomials················=·0
420 ···--·#reduction·steps·=·0420 ···--·#reduction·steps·=·0
421 ···--·#spairs·done·=·0421 ···--·#spairs·done·=·0
422 ···--·ncalls·=·0422 ···--·ncalls·=·0
423 ···--·nloop·=·0423 ···--·nloop·=·0
Offset 428, 24 lines modifiedOffset 428, 24 lines modified
428 o31·:·Ideal·of·R</code></pre>428 o31·:·Ideal·of·R</code></pre>
429 ············</td>429 ············</td>
430 ··········</tr>430 ··········</tr>
431 ··········<tr>431 ··········<tr>
432 ············<td>432 ············<td>
433 ··············<pre><code·class="language-macaulay2">i32·:·time·p·=·poincare·I433 ··············<pre><code·class="language-macaulay2">i32·:·time·p·=·poincare·I
  
434 ···--·registering·gb·21·at·0x7f749535a1c0434 ···--·registering·gb·21·at·0x7f8bad70e1c0
  
435 ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11435 ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11
436 ···--·number·of·monomials················=·267436 ···--·number·of·monomials················=·267
437 ···--·#reduction·steps·=·236437 ···--·#reduction·steps·=·236
438 ···--·#spairs·done·=·30438 ···--·#spairs·done·=·30
439 ···--·ncalls·=·10439 ···--·ncalls·=·10
440 ···--·nloop·=·20440 ···--·nloop·=·20
441 ···--·nsaved·=·0441 ···--·nsaved·=·0
442 ···--··--·used·0.00566835s·(cpu);·0.00489106s·(thread);·0s·(gc)442 ···--··--·used·0.00530603s·(cpu);·0.00629818s·(thread);·0s·(gc)
  
443 ············3·····6····9443 ············3·····6····9
444 o32·=·1·-·3T··+·3T··-·T444 o32·=·1·-·3T··+·3T··-·T
  
445 o32·:·ZZ[T]</code></pre>445 o32·:·ZZ[T]</code></pre>
446 ············</td>446 ············</td>
447 ··········</tr>447 ··········</tr>
Offset 510, 27 lines modifiedOffset 510, 27 lines modified
510 o36·=·3</code></pre>510 o36·=·3</code></pre>
511 ············</td>511 ············</td>
512 ··········</tr>512 ··········</tr>
513 ··········<tr>513 ··········<tr>
514 ············<td>514 ············<td>
515 ··············<pre><code·class="language-macaulay2">i37·:·time·gens·gb·J;515 ··············<pre><code·class="language-macaulay2">i37·:·time·gens·gb·J;
  
516 ···--·registering·gb·22·at·0x7f749535a000516 ···--·registering·gb·22·at·0x7f8bad70e000
  
517 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m517 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m
518 ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m518 ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m
519 ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m519 ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m
520 ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39520 ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39
521 ···--·number·of·monomials················=·1051521 ···--·number·of·monomials················=·1051
522 ···--·#reduction·steps·=·284522 ···--·#reduction·steps·=·284
523 ···--·#spairs·done·=·53523 ···--·#spairs·done·=·53
524 ···--·ncalls·=·46524 ···--·ncalls·=·46
525 ···--·nloop·=·54525 ···--·nloop·=·54
526 ···--·nsaved·=·0526 ···--·nsaved·=·0
527 ···--··--·used·0.0464432s·(cpu);·0.0480922s·(thread);·0s·(gc)527 ···--··--·used·0.059633s·(cpu);·0.0564652s·(thread);·0s·(gc)
  
528 ··············1······39528 ··············1······39
529 o37·:·Matrix·S··&lt;--·S</code></pre>529 o37·:·Matrix·S··&lt;--·S</code></pre>
530 ············</td>530 ············</td>
531 ··········</tr>531 ··········</tr>
532 ··········<tr>532 ··········<tr>
533 ············<td>533 ············<td>
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Offset 177, 66 lines modifiedOffset 177, 66 lines modified
177 o26·=·1·-·3T··+·3T··-·T177 o26·=·1·-·3T··+·3T··-·T
  
178 o26·:·ZZ[T]178 o26·:·ZZ[T]
179 i27·:·gbTrace·=·3179 i27·:·gbTrace·=·3
  
180 o27·=·3180 o27·=·3
181 i28·:·time·poincare·I181 i28·:·time·poincare·I
182 ·--·used·0.00145017s·(cpu);·7.802e-06s·(thread);·0s·(gc)182 ·--·used·0.00319799s·(cpu);·2.9034e-05s·(thread);·0s·(gc)
  
183 ············3·····6····9183 ············3·····6····9
184 o28·=·1·-·3T··+·3T··-·T184 o28·=·1·-·3T··+·3T··-·T
  
185 o28·:·ZZ[T]185 o28·:·ZZ[T]
186 i29·:·time·gens·gb·I;186 i29·:·time·gens·gb·I;
  
187 ···--·registering·gb·19·at·0x7f749535a540187 ···--·registering·gb·19·at·0x7f8bad70e540
  
188 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of188 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of
189 (nonminimal)·gb·elements·=·11189 (nonminimal)·gb·elements·=·11
190 ···--·number·of·monomials················=·4186190 ···--·number·of·monomials················=·4186
191 ···--·#reduction·steps·=·38191 ···--·#reduction·steps·=·38
192 ···--·#spairs·done·=·11192 ···--·#spairs·done·=·11
193 ···--·ncalls·=·10193 ···--·ncalls·=·10
194 ···--·nloop·=·29194 ···--·nloop·=·29
195 ···--·nsaved·=·0195 ···--·nsaved·=·0
196 ···--··--·used·0.00903704s·(cpu);·0.0101512s·(thread);·0s·(gc)196 ···--··--·used·0.0101535s·(cpu);·0.0127548s·(thread);·0s·(gc)
  
197 ··············1······11197 ··············1······11
198 o29·:·Matrix·R··<--·R198 o29·:·Matrix·R··<--·R
199 In·this·case,·the·savings·is·minimal,·but·often·it·can·be·dramatic.·Another199 In·this·case,·the·savings·is·minimal,·but·often·it·can·be·dramatic.·Another
200 important·situation·is·to·compute·a·Gröbner·basis·using·a·different·monomial200 important·situation·is·to·compute·a·Gröbner·basis·using·a·different·monomial
201 order.201 order.
202 i30·:·R·=·QQ[a..d];202 i30·:·R·=·QQ[a..d];
203 i31·:·I·=·ideal·random(R^1,·R^{3:-3});203 i31·:·I·=·ideal·random(R^1,·R^{3:-3});
  
204 ···--·registering·gb·20·at·0x7f749535a380204 ···--·registering·gb·20·at·0x7f8bad70e380
  
205 ···--·[gb]number·of·(nonminimal)·gb·elements·=·0205 ···--·[gb]number·of·(nonminimal)·gb·elements·=·0
206 ···--·number·of·monomials················=·0206 ···--·number·of·monomials················=·0
207 ···--·#reduction·steps·=·0207 ···--·#reduction·steps·=·0
208 ···--·#spairs·done·=·0208 ···--·#spairs·done·=·0
209 ···--·ncalls·=·0209 ···--·ncalls·=·0
210 ···--·nloop·=·0210 ···--·nloop·=·0
211 ···--·nsaved·=·0211 ···--·nsaved·=·0
212 ···--212 ···--
213 o31·:·Ideal·of·R213 o31·:·Ideal·of·R
214 i32·:·time·p·=·poincare·I214 i32·:·time·p·=·poincare·I
  
215 ···--·registering·gb·21·at·0x7f749535a1c0215 ···--·registering·gb·21·at·0x7f8bad70e1c0
  
216 ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of216 ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of
217 (nonminimal)·gb·elements·=·11217 (nonminimal)·gb·elements·=·11
218 ···--·number·of·monomials················=·267218 ···--·number·of·monomials················=·267
219 ···--·#reduction·steps·=·236219 ···--·#reduction·steps·=·236
220 ···--·#spairs·done·=·30220 ···--·#spairs·done·=·30
221 ···--·ncalls·=·10221 ···--·ncalls·=·10
222 ···--·nloop·=·20222 ···--·nloop·=·20
223 ···--·nsaved·=·0223 ···--·nsaved·=·0
224 ···--··--·used·0.00566835s·(cpu);·0.00489106s·(thread);·0s·(gc)224 ···--··--·used·0.00530603s·(cpu);·0.00629818s·(thread);·0s·(gc)
  
225 ············3·····6····9225 ············3·····6····9
226 o32·=·1·-·3T··+·3T··-·T226 o32·=·1·-·3T··+·3T··-·T
  
227 o32·:·ZZ[T]227 o32·:·ZZ[T]
228 i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2]228 i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2]
  
Offset 281, 30 lines modifiedOffset 281, 30 lines modified
  
281 o35·:·ZZ[T]281 o35·:·ZZ[T]
282 i36·:·gbTrace·=·3282 i36·:·gbTrace·=·3
  
283 o36·=·3283 o36·=·3
284 i37·:·time·gens·gb·J;284 i37·:·time·gens·gb·J;
  
285 ···--·registering·gb·22·at·0x7f749535a000285 ···--·registering·gb·22·at·0x7f8bad70e000
  
286 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}286 ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}
287 (3,9)m287 (3,9)m
288 ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m288 ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m
289 ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m289 ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m
290 {24}(1,3)m290 {24}(1,3)m
291 ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements291 ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements
292 =·39292 =·39
293 ···--·number·of·monomials················=·1051293 ···--·number·of·monomials················=·1051
294 ···--·#reduction·steps·=·284294 ···--·#reduction·steps·=·284
295 ···--·#spairs·done·=·53295 ···--·#spairs·done·=·53
296 ···--·ncalls·=·46296 ···--·ncalls·=·46
297 ···--·nloop·=·54297 ···--·nloop·=·54
298 ···--·nsaved·=·0298 ···--·nsaved·=·0
299 ···--··--·used·0.0464432s·(cpu);·0.0480922s·(thread);·0s·(gc)299 ···--··--·used·0.059633s·(cpu);·0.0564652s·(thread);·0s·(gc)
  
300 ··············1······39300 ··············1······39
301 o37·:·Matrix·S··<--·S301 o37·:·Matrix·S··<--·S
302 i38·:·selectInSubring(1,·gens·gb·J)302 i38·:·selectInSubring(1,·gens·gb·J)
  
303 o38·=·|·188529931266160087758259645374082357642621166724936033369975727480205303 o38·=·|·188529931266160087758259645374082357642621166724936033369975727480205
304 ······-----------------------------------------------------------------------304 ······-----------------------------------------------------------------------
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Offset 97, 22 lines modifiedOffset 97, 22 lines modified
97 o2·:·File</code></pre>97 o2·:·File</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i3·:·fn·=·temporaryFileName()102 ··············<pre><code·class="language-macaulay2">i3·:·fn·=·temporaryFileName()
  
103 o3·=·/tmp/M2-1083217-0/0</code></pre>103 o3·=·/tmp/M2-997039-0/0</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i4·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·endl·&lt;&lt;·close108 ··············<pre><code·class="language-macaulay2">i4·:·fn·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·endl·&lt;&lt;·close
  
109 o4·=·/tmp/M2-1083217-0/0109 o4·=·/tmp/M2-997039-0/0
  
110 o4·:·File</code></pre>110 o4·:·File</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i5·:·get·fn115 ··············<pre><code·class="language-macaulay2">i5·:·get·fn
Offset 151, 15 lines modifiedOffset 151, 15 lines modified
151 o8·:·File</code></pre>151 o8·:·File</code></pre>
152 ············</td>152 ············</td>
153 ··········</tr>153 ··········</tr>
154 ··········<tr>154 ··········<tr>
155 ············<td>155 ············<td>
156 ··············<pre><code·class="language-macaulay2">i9·:·fn·&lt;&lt;·f·&lt;&lt;·close156 ··············<pre><code·class="language-macaulay2">i9·:·fn·&lt;&lt;·f·&lt;&lt;·close
  
157 o9·=·/tmp/M2-1083217-0/0157 o9·=·/tmp/M2-997039-0/0
  
158 o9·:·File</code></pre>158 o9·:·File</code></pre>
159 ············</td>159 ············</td>
160 ··········</tr>160 ··········</tr>
161 ··········<tr>161 ··········<tr>
162 ············<td>162 ············<td>
163 ··············<pre><code·class="language-macaulay2">i10·:·get·fn163 ··············<pre><code·class="language-macaulay2">i10·:·get·fn
Offset 169, 15 lines modifiedOffset 169, 15 lines modified
169 ······+·1</code></pre>169 ······+·1</code></pre>
170 ············</td>170 ············</td>
171 ··········</tr>171 ··········</tr>
172 ··········<tr>172 ··········<tr>
173 ············<td>173 ············<td>
174 ··············<pre><code·class="language-macaulay2">i11·:·fn·&lt;&lt;·toExternalString·f·&lt;&lt;·close174 ··············<pre><code·class="language-macaulay2">i11·:·fn·&lt;&lt;·toExternalString·f·&lt;&lt;·close
  
175 o11·=·/tmp/M2-1083217-0/0175 o11·=·/tmp/M2-997039-0/0
  
176 o11·:·File</code></pre>176 o11·:·File</code></pre>
177 ············</td>177 ············</td>
178 ··········</tr>178 ··········</tr>
179 ··········<tr>179 ··········<tr>
180 ············<td>180 ············<td>
181 ··············<pre><code·class="language-macaulay2">i12·:·get·fn181 ··············<pre><code·class="language-macaulay2">i12·:·get·fn
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Offset 36, 18 lines modifiedOffset 36, 18 lines modified
36 --·ho·there·--36 --·ho·there·--
  
37 o2·=·stdio37 o2·=·stdio
  
38 o2·:·File38 o2·:·File
39 i3·:·fn·=·temporaryFileName()39 i3·:·fn·=·temporaryFileName()
  
40 o3·=·/tmp/M2-1083217-0/040 o3·=·/tmp/M2-997039-0/0
41 i4·:·fn·<<·"hi·there"·<<·endl·<<·close41 i4·:·fn·<<·"hi·there"·<<·endl·<<·close
  
42 o4·=·/tmp/M2-1083217-0/042 o4·=·/tmp/M2-997039-0/0
  
43 o4·:·File43 o4·:·File
44 i5·:·get·fn44 i5·:·get·fn
  
45 o5·=·hi·there45 o5·=·hi·there
46 i6·:·R·=·QQ[x]46 i6·:·R·=·QQ[x]
  
Offset 66, 25 lines modifiedOffset 66, 25 lines modified
66 ·10······9······8·······7·······6·······5·······4·······3······266 ·10······9······8·······7·······6·······5·······4·······3······2
67 x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·167 x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·1
68 o8·=·stdio68 o8·=·stdio
  
69 o8·:·File69 o8·:·File
70 i9·:·fn·<<·f·<<·close70 i9·:·fn·<<·f·<<·close
  
71 o9·=·/tmp/M2-1083217-0/071 o9·=·/tmp/M2-997039-0/0
  
72 o9·:·File72 o9·:·File
73 i10·:·get·fn73 i10·:·get·fn
  
74 o10·=··10······9······8·······7·······6·······5·······4·······3······274 o10·=··10······9······8·······7·······6·······5·······4·······3······2
75 ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x75 ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x
76 ······+·176 ······+·1
77 i11·:·fn·<<·toExternalString·f·<<·close77 i11·:·fn·<<·toExternalString·f·<<·close
  
78 o11·=·/tmp/M2-1083217-0/078 o11·=·/tmp/M2-997039-0/0
  
79 o11·:·File79 o11·:·File
80 i12·:·get·fn80 i12·:·get·fn
  
81 o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+81 o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+
82 ······182 ······1
83 i13·:·value·get·fn83 i13·:·value·get·fn
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64 ······<div>64 ······<div>
65 ········<h2>Description</h2>65 ········<h2>Description</h2>
66 ········<table·class="examples">66 ········<table·class="examples">
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i1·:·processID()69 ··············<pre><code·class="language-macaulay2">i1·:·processID()
  
70 o1·=·1075204</code></pre>70 o1·=·980911</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ········</table>73 ········</table>
74 ······</div>74 ······</div>
75 ······<div>75 ······<div>
76 ········<h2>See·also</h2>76 ········<h2>See·also</h2>
77 ········<ul>77 ········<ul>
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8 ····*···Usage:8 ····*···Usage:
9 ············processID()9 ············processID()
10 ····*·Outputs:10 ····*·Outputs:
11 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·identifier·of·the·current·Macaulay2·process11 ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·identifier·of·the·current·Macaulay2·process
12 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*12 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
13 i1·:·processID()13 i1·:·processID()
  
14 o1·=·107520414 o1·=·980911
15 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
16 ····*·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·the·process·group·identifier16 ····*·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·the·process·group·identifier
17 ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier17 ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier
18 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*18 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
19 The·object·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.19 The·object·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
20 ===============================================================================20 ===============================================================================
21 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-21 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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91 ········</div>91 ········</div>
92 ········<table·class="examples">92 ········<table·class="examples">
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i2·:·profileSummary95 ··············<pre><code·class="language-macaulay2">i2·:·profileSummary
  
96 o2·=·#run··%time···position·························96 o2·=·#run··%time···position·························
97 ·····1·····91.8····../../m2/matrix1.m2:279:4-282:58·97 ·····1·····92.19···../../m2/matrix1.m2:279:4-282:58·
98 ·····1·····88.55···../../m2/matrix1.m2:281:22-281:4398 ·····1·····89.48···../../m2/matrix1.m2:281:22-281:43
99 ·····1·····44.03···../../m2/matrix1.m2:193:25-193:5299 ·····1·····43.48···../../m2/matrix1.m2:193:25-193:52
100 ·····1·····29.76···../../m2/matrix1.m2:114:5-156:72·100 ·····1·····30.15···../../m2/matrix1.m2:114:5-156:72·
101 ·····1·····28.41···../../m2/matrix1.m2:140:10-155:16101 ·····1·····28.93···../../m2/matrix1.m2:140:10-155:16
102 ·····1·····21.43···../../m2/matrix1.m2:181:4-181:42·102 ·····1·····21.92···../../m2/matrix1.m2:181:4-181:42·
103 ·····1·····19.82···../../m2/set.m2:122:5-122:61·····103 ·····1·····20.36···../../m2/set.m2:122:5-122:61·····
104 ·····1·····18.68···../../m2/matrix1.m2:45:10-49:22··104 ·····1·····20.09···../../m2/matrix1.m2:45:10-49:22··
105 ·····1·····3.22····../../m2/matrix1.m2:112:5-112:29·105 ·····1·····3.32····../../m2/matrix1.m2:112:5-112:29·
106 ·····1·····2.81····../../m2/matrix1.m2:141:13-141:78106 ·····1·····2.45····../../m2/matrix1.m2:141:13-141:78
107 ·····1·····2.07····../../m2/matrix1.m2:96:5-109:11··107 ·····1·····2.09····../../m2/matrix1.m2:96:5-109:11··
108 ·····1·····1.97····../../m2/matrix1.m2:281:7-281:16·108 ·····1·····1.67····../../m2/matrix1.m2:281:7-281:16·
109 ·····1·····1.75····../../m2/modules.m2:278:4-278:52· 
110 ·····1·····1.69····../../m2/matrix1.m2:147:20-147:64109 ·····1·····1.43····../../m2/matrix1.m2:147:20-147:64
111 ·····1·····1.59····../../m2/matrix1.m2:276:4-277:73·110 ·····1·····1.40····../../m2/matrix1.m2:276:4-277:73·
112 ·····1·····1.3·····../../m2/matrix1.m2:111:5-111:91·111 ·····1·····1.22····../../m2/matrix1.m2:111:5-111:91·
113 ·····1·····1.12····../../m2/matrix1.m2:182:4-184:74· 
114 ·····1·····1.04····../../m2/matrix1.m2:98:10-98:46··112 ·····1·····1.06····../../m2/matrix1.m2:98:10-98:46··
 113 ·····1·····1.05····../../m2/matrix1.m2:182:4-184:74·
 114 ·····1·····.86·····../../m2/modules.m2:278:4-278:52·
115 ·····20····.91·····../../m2/matrix1.m2:191:14-192:67115 ·····20····.70·····../../m2/matrix1.m2:191:14-192:67
116 ·····20····.56·····../../m2/matrix1.m2:47:43-47:71··116 ·····1·····.35·····../../m2/matrix1.m2:152:66-152:98
117 ·····1·····.0015s··elapsed·total····················</code></pre>117 ·····1·····.0026s··elapsed·total····················</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i3·:·coverageSummary122 ··············<pre><code·class="language-macaulay2">i3·:·coverageSummary
  
123 o3·=·covered·lines:123 o3·=·covered·lines:
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25 ··············4·······525 ··············4·······5
26 o1·:·Matrix·ZZ··<--·ZZ26 o1·:·Matrix·ZZ··<--·ZZ
27 Afterwards,·running·profileSummary·and·coverageSummary·produces·easy·to·read27 Afterwards,·running·profileSummary·and·coverageSummary·produces·easy·to·read
28 tables·summarizing·the·accumulated·data·so·far·in·different·ways.28 tables·summarizing·the·accumulated·data·so·far·in·different·ways.
29 i2·:·profileSummary29 i2·:·profileSummary
  
30 o2·=·#run··%time···position30 o2·=·#run··%time···position
31 ·····1·····91.8····../../m2/matrix1.m2:279:4-282:5831 ·····1·····92.19···../../m2/matrix1.m2:279:4-282:58
32 ·····1·····88.55···../../m2/matrix1.m2:281:22-281:4332 ·····1·····89.48···../../m2/matrix1.m2:281:22-281:43
33 ·····1·····44.03···../../m2/matrix1.m2:193:25-193:5233 ·····1·····43.48···../../m2/matrix1.m2:193:25-193:52
34 ·····1·····29.76···../../m2/matrix1.m2:114:5-156:7234 ·····1·····30.15···../../m2/matrix1.m2:114:5-156:72
35 ·····1·····28.41···../../m2/matrix1.m2:140:10-155:1635 ·····1·····28.93···../../m2/matrix1.m2:140:10-155:16
36 ·····1·····21.43···../../m2/matrix1.m2:181:4-181:4236 ·····1·····21.92···../../m2/matrix1.m2:181:4-181:42
37 ·····1·····19.82···../../m2/set.m2:122:5-122:6137 ·····1·····20.36···../../m2/set.m2:122:5-122:61
38 ·····1·····18.68···../../m2/matrix1.m2:45:10-49:2238 ·····1·····20.09···../../m2/matrix1.m2:45:10-49:22
39 ·····1·····3.22····../../m2/matrix1.m2:112:5-112:2939 ·····1·····3.32····../../m2/matrix1.m2:112:5-112:29
40 ·····1·····2.81····../../m2/matrix1.m2:141:13-141:7840 ·····1·····2.45····../../m2/matrix1.m2:141:13-141:78
41 ·····1·····2.07····../../m2/matrix1.m2:96:5-109:1141 ·····1·····2.09····../../m2/matrix1.m2:96:5-109:11
42 ·····1·····1.97····../../m2/matrix1.m2:281:7-281:1642 ·····1·····1.67····../../m2/matrix1.m2:281:7-281:16
43 ·····1·····1.75····../../m2/modules.m2:278:4-278:52 
44 ·····1·····1.69····../../m2/matrix1.m2:147:20-147:6443 ·····1·····1.43····../../m2/matrix1.m2:147:20-147:64
45 ·····1·····1.59····../../m2/matrix1.m2:276:4-277:7344 ·····1·····1.40····../../m2/matrix1.m2:276:4-277:73
46 ·····1·····1.3·····../../m2/matrix1.m2:111:5-111:9145 ·····1·····1.22····../../m2/matrix1.m2:111:5-111:91
47 ·····1·····1.12····../../m2/matrix1.m2:182:4-184:74 
48 ·····1·····1.04····../../m2/matrix1.m2:98:10-98:4646 ·····1·····1.06····../../m2/matrix1.m2:98:10-98:46
 47 ·····1·····1.05····../../m2/matrix1.m2:182:4-184:74
 48 ·····1·····.86·····../../m2/modules.m2:278:4-278:52
49 ·····20····.91·····../../m2/matrix1.m2:191:14-192:6749 ·····20····.70·····../../m2/matrix1.m2:191:14-192:67
50 ·····20····.56·····../../m2/matrix1.m2:47:43-47:7150 ·····1·····.35·····../../m2/matrix1.m2:152:66-152:98
51 ·····1·····.0015s··elapsed·total51 ·····1·····.0026s··elapsed·total
52 i3·:·coverageSummary52 i3·:·coverageSummary
  
53 o3·=·covered·lines:53 o3·=·covered·lines:
54 ·····../../m2/lists.m2:145:24-145:3254 ·····../../m2/lists.m2:145:24-145:32
55 ·····../../m2/lists.m2:145:34-145:5855 ·····../../m2/lists.m2:145:34-145:58
56 ·····../../m2/matrix.m2:12:5-12:3556 ·····../../m2/matrix.m2:12:5-12:35
57 ·····../../m2/matrix.m2:13:5-13:4657 ·····../../m2/matrix.m2:13:5-13:46
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Offset 99, 15 lines modifiedOffset 99, 15 lines modified
  
99 o5·:·Sequence</code></pre>99 o5·:·Sequence</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i6·:·time·randomKRationalPoint(I)104 ··············<pre><code·class="language-macaulay2">i6·:·time·randomKRationalPoint(I)
105 ·--·used·0.138948s·(cpu);·0.0717858s·(thread);·0s·(gc)105 ·--·used·0.119735s·(cpu);·0.0842559s·(thread);·0s·(gc)
  
106 o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·)106 o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·)
107 ·············2······3···1·····3···0·····3107 ·············2······3···1·····3···0·····3
  
108 o6·:·Ideal·of·R</code></pre>108 o6·:·Ideal·of·R</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
Offset 131, 15 lines modifiedOffset 131, 15 lines modified
  
131 o9·:·Sequence</code></pre>131 o9·:·Sequence</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i10·:·time·randomKRationalPoint(I)136 ··············<pre><code·class="language-macaulay2">i10·:·time·randomKRationalPoint(I)
137 ·--·used·0.538065s·(cpu);·0.203857s·(thread);·0s·(gc)137 ·--·used·0.677037s·(cpu);·0.278406s·(thread);·0s·(gc)
  
138 o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·)138 o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·)
139 ··············4······5···3······5···2·····5···1······5···0······5139 ··············4······5···3······5···2·····5···1······5···0······5
  
140 o10·:·Ideal·of·R</code></pre>140 o10·:·Ideal·of·R</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
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173 o14·:·Ideal·of·R</code></pre>173 o14·:·Ideal·of·R</code></pre>
174 ············</td>174 ············</td>
175 ··········</tr>175 ··········</tr>
176 ··········<tr>176 ··········<tr>
177 ············<td>177 ············<td>
178 ··············<pre><code·class="language-macaulay2">i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c);178 ··············<pre><code·class="language-macaulay2">i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c);
179 ·····················#select(degs,d->d==1))),f->f>0))179 ·····················#select(degs,d->d==1))),f->f>0))
180 ·--·used·2.87793s·(cpu);·1.4543s·(thread);·0s·(gc)180 ·--·used·3.16003s·(cpu);·1.77636s·(thread);·0s·(gc)
  
181 o15·=·58</code></pre>181 o15·=·58</code></pre>
182 ············</td>182 ············</td>
183 ··········</tr>183 ··········</tr>
184 ········</table>184 ········</table>
185 ······</div>185 ······</div>
186 ······<div>186 ······<div>
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29 o4·:·Ideal·of·R29 o4·:·Ideal·of·R
30 i5·:·codim·I,·degree·I30 i5·:·codim·I,·degree·I
  
31 o5·=·(2,·10)31 o5·=·(2,·10)
  
32 o5·:·Sequence32 o5·:·Sequence
33 i6·:·time·randomKRationalPoint(I)33 i6·:·time·randomKRationalPoint(I)
34 ·--·used·0.138948s·(cpu);·0.0717858s·(thread);·0s·(gc)34 ·--·used·0.119735s·(cpu);·0.0842559s·(thread);·0s·(gc)
  
35 o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·)35 o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·)
36 ·············2······3···1·····3···0·····336 ·············2······3···1·····3···0·····3
  
37 o6·:·Ideal·of·R37 o6·:·Ideal·of·R
38 i7·:·R=kk[x_0..x_5];38 i7·:·R=kk[x_0..x_5];
39 i8·:·I=minors(3,random(R^5,R^{3:-1}));39 i8·:·I=minors(3,random(R^5,R^{3:-1}));
Offset 45, 15 lines modifiedOffset 45, 15 lines modified
45 o8·:·Ideal·of·R45 o8·:·Ideal·of·R
46 i9·:·codim·I,·degree·I46 i9·:·codim·I,·degree·I
  
47 o9·=·(3,·10)47 o9·=·(3,·10)
  
48 o9·:·Sequence48 o9·:·Sequence
49 i10·:·time·randomKRationalPoint(I)49 i10·:·time·randomKRationalPoint(I)
50 ·--·used·0.538065s·(cpu);·0.203857s·(thread);·0s·(gc)50 ·--·used·0.677037s·(cpu);·0.278406s·(thread);·0s·(gc)
  
51 o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·)51 o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·)
52 ··············4······5···3······5···2·····5···1······5···0······552 ··············4······5···3······5···2·····5···1······5···0······5
  
53 o10·:·Ideal·of·R53 o10·:·Ideal·of·R
54 The·claim·that·$63·\%$·of·the·intersections·contain·a·K-rational·point·can·be54 The·claim·that·$63·\%$·of·the·intersections·contain·a·K-rational·point·can·be
55 experimentally·tested:55 experimentally·tested:
Offset 69, 15 lines modifiedOffset 69, 15 lines modified
69 o13·:·RR·(of·precision·53)69 o13·:·RR·(of·precision·53)
70 i14·:·I=ideal·random(n,R);70 i14·:·I=ideal·random(n,R);
  
71 o14·:·Ideal·of·R71 o14·:·Ideal·of·R
72 i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c-72 i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c-
73 >degree·c);73 >degree·c);
74 ·····················#select(degs,d->d==1))),f->f>0))74 ·····················#select(degs,d->d==1))),f->f>0))
75 ·--·used·2.87793s·(cpu);·1.4543s·(thread);·0s·(gc)75 ·--·used·3.16003s·(cpu);·1.77636s·(thread);·0s·(gc)
  
76 o15·=·5876 o15·=·58
77 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mK\x8KR\x8Ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lP\x8Po\x8oi\x8in\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*77 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mK\x8KR\x8Ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lP\x8Po\x8oi\x8in\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*
78 ····*·randomKRationalPoint(Ideal)78 ····*·randomKRationalPoint(Ideal)
79 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*79 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
80 The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.80 The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.
81 ===============================================================================81 ===============================================================================
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68 ······<div>68 ······<div>
69 ········<h2>Description</h2>69 ········<h2>Description</h2>
70 ········<table·class="examples">70 ········<table·class="examples">
71 ··········<tr>71 ··········<tr>
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()73 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()
  
74 o1·=·/tmp/M2-1092406-0/0</code></pre>74 o1·=·/tmp/M2-1048456-0/0</code></pre>
75 ············</td>75 ············</td>
76 ··········</tr>76 ··········</tr>
77 ··········<tr>77 ··········<tr>
78 ············<td>78 ············<td>
79 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir79 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir
  
80 o2·=·/tmp/M2-1092406-0/0</code></pre>80 o2·=·/tmp/M2-1048456-0/0</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·(fn·=·dir·|·&quot;/&quot;·|·&quot;foo&quot;)·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close85 ··············<pre><code·class="language-macaulay2">i3·:·(fn·=·dir·|·&quot;/&quot;·|·&quot;foo&quot;)·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
86 o3·=·/tmp/M2-1092406-0/0/foo86 o3·=·/tmp/M2-1048456-0/0/foo
  
87 o3·:·File</code></pre>87 o3·:·File</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i4·:·readDirectory·dir92 ··············<pre><code·class="language-macaulay2">i4·:·readDirectory·dir
  
93 o4·=·{..,·.,·foo}93 o4·=·{foo,·.,·..}
  
94 o4·:·List</code></pre>94 o4·:·List</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre>99 ··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre>
893 B
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10 ····*·Inputs:10 ····*·Inputs:
11 ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory11 ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory
12 ····*·Outputs:12 ····*·Outputs:
13 ··········o·a·_\x8l_\x8i_\x8s_\x8t,·the·list·of·filenames·stored·in·the·directory13 ··········o·a·_\x8l_\x8i_\x8s_\x8t,·the·list·of·filenames·stored·in·the·directory
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 i1·:·dir·=·temporaryFileName()15 i1·:·dir·=·temporaryFileName()
  
16 o1·=·/tmp/M2-1092406-0/016 o1·=·/tmp/M2-1048456-0/0
17 i2·:·makeDirectory·dir17 i2·:·makeDirectory·dir
  
18 o2·=·/tmp/M2-1092406-0/018 o2·=·/tmp/M2-1048456-0/0
19 i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close19 i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close
  
20 o3·=·/tmp/M2-1092406-0/0/foo20 o3·=·/tmp/M2-1048456-0/0/foo
  
21 o3·:·File21 o3·:·File
22 i4·:·readDirectory·dir22 i4·:·readDirectory·dir
  
23 o4·=·{..,·.,·foo}23 o4·=·{foo,·.,·..}
  
24 o4·:·List24 o4·:·List
25 i5·:·removeFile·fn25 i5·:·removeFile·fn
26 i6·:·removeDirectory·dir26 i6·:·removeDirectory·dir
27 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*27 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
28 ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·remove·a·directory28 ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·remove·a·directory
29 ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file29 ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file
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52 ······<div>52 ······<div>
53 Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have·access·to.··For·example,·it·might·be·a·polynomial·produced·by·another·program.··The·function·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a·single·string.··We·illustrate·this·here·with·a·file·whose·name·is·<span·class="tt">expression</span>.········<p></p>53 Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have·access·to.··For·example,·it·might·be·a·polynomial·produced·by·another·program.··The·function·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a·single·string.··We·illustrate·this·here·with·a·file·whose·name·is·<span·class="tt">expression</span>.········<p></p>
54 First·we·create·the·file·by·writing·the·desired·text·to·it.········<table·class="examples">54 First·we·create·the·file·by·writing·the·desired·text·to·it.········<table·class="examples">
55 ··········<tr>55 ··········<tr>
56 ············<td>56 ············<td>
57 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()57 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
58 o1·=·/tmp/M2-1083684-0/0</code></pre>58 o1·=·/tmp/M2-1004559-0/0</code></pre>
59 ············</td>59 ············</td>
60 ··········</tr>60 ··········</tr>
61 ··········<tr>61 ··········<tr>
62 ············<td>62 ············<td>
63 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3&quot;·&lt;&lt;·endl·&lt;&lt;·close63 ··············<pre><code·class="language-macaulay2">i2·:·fn·&lt;&lt;·&quot;z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3&quot;·&lt;&lt;·endl·&lt;&lt;·close
  
64 o2·=·/tmp/M2-1083684-0/064 o2·=·/tmp/M2-1004559-0/0
  
65 o2·:·File</code></pre>65 o2·:·File</code></pre>
66 ············</td>66 ············</td>
67 ··········</tr>67 ··········</tr>
68 ········</table>68 ········</table>
69 Now·we·get·the·contents·of·the·file,·as·a·single·string.········<table·class="examples">69 Now·we·get·the·contents·of·the·file,·as·a·single·string.········<table·class="examples">
70 ··········<tr>70 ··········<tr>
Offset 116, 15 lines modifiedOffset 116, 15 lines modified
116 Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create·such·a·file.········<table·class="examples">116 Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create·such·a·file.········<table·class="examples">
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i7·:·fn·&lt;&lt;·&quot;sample·=·2^100119 ··············<pre><code·class="language-macaulay2">i7·:·fn·&lt;&lt;·&quot;sample·=·2^100
120 ·····print·sample120 ·····print·sample
121 ·····&quot;·&lt;&lt;·close121 ·····&quot;·&lt;&lt;·close
  
122 o7·=·/tmp/M2-1083684-0/0122 o7·=·/tmp/M2-1004559-0/0
  
123 o7·:·File</code></pre>123 o7·:·File</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ········</table>126 ········</table>
127 Now·verify·that·it·contains·the·desired·text·with·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>.········<table·class="examples">127 Now·verify·that·it·contains·the·desired·text·with·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>.········<table·class="examples">
128 ··········<tr>128 ··········<tr>
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8 Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have8 Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have
9 access·to.·For·example,·it·might·be·a·polynomial·produced·by·another·program.9 access·to.·For·example,·it·might·be·a·polynomial·produced·by·another·program.
10 The·function·_\x8g_\x8e_\x8t·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a10 The·function·_\x8g_\x8e_\x8t·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a
11 single·string.·We·illustrate·this·here·with·a·file·whose·name·is·expression.11 single·string.·We·illustrate·this·here·with·a·file·whose·name·is·expression.
12 First·we·create·the·file·by·writing·the·desired·text·to·it.12 First·we·create·the·file·by·writing·the·desired·text·to·it.
13 i1·:·fn·=·temporaryFileName()13 i1·:·fn·=·temporaryFileName()
  
14 o1·=·/tmp/M2-1083684-0/014 o1·=·/tmp/M2-1004559-0/0
15 i2·:·fn·<<15 i2·:·fn·<<
16 "z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"16 "z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"
17 <<·endl·<<·close17 <<·endl·<<·close
  
18 o2·=·/tmp/M2-1083684-0/018 o2·=·/tmp/M2-1004559-0/0
  
19 o2·:·File19 o2·:·File
20 Now·we·get·the·contents·of·the·file,·as·a·single·string.20 Now·we·get·the·contents·of·the·file,·as·a·single·string.
21 i3·:·get·fn21 i3·:·get·fn
  
22 o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^222 o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2
23 ·····+8*y^323 ·····+8*y^3
Offset 51, 15 lines modifiedOffset 51, 15 lines modified
51 o6·:·Expression·of·class·Product51 o6·:·Expression·of·class·Product
52 Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create52 Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create
53 such·a·file.53 such·a·file.
54 i7·:·fn·<<·"sample·=·2^10054 i7·:·fn·<<·"sample·=·2^100
55 ·····print·sample55 ·····print·sample
56 ·····"·<<·close56 ·····"·<<·close
  
57 o7·=·/tmp/M2-1083684-0/057 o7·=·/tmp/M2-1004559-0/0
  
58 o7·:·File58 o7·:·File
59 Now·verify·that·it·contains·the·desired·text·with·_\x8g_\x8e_\x8t.59 Now·verify·that·it·contains·the·desired·text·with·_\x8g_\x8e_\x8t.
60 i8·:·get·fn60 i8·:·get·fn
  
61 o8·=·sample·=·2^10061 o8·=·sample·=·2^100
62 ·····print·sample62 ·····print·sample
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68 ······<div>68 ······<div>
69 ········<h2>Description</h2>69 ········<h2>Description</h2>
70 ········<table·class="examples">70 ········<table·class="examples">
71 ··········<tr>71 ··········<tr>
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName·()73 ··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName·()
  
74 o1·=·/tmp/M2-1093698-0/0</code></pre>74 o1·=·/tmp/M2-1054229-0/0</code></pre>
75 ············</td>75 ············</td>
76 ··········</tr>76 ··········</tr>
77 ··········<tr>77 ··········<tr>
78 ············<td>78 ············<td>
79 ··············<pre><code·class="language-macaulay2">i2·:·symlinkFile·(&quot;foo&quot;,·p)</code></pre>79 ··············<pre><code·class="language-macaulay2">i2·:·symlinkFile·(&quot;foo&quot;,·p)</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
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11 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·file11 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·file
12 ····*·Outputs:12 ····*·Outputs:
13 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·resolved·path·to·a·symbolic·link,·or·null·if·the·file13 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·resolved·path·to·a·symbolic·link,·or·null·if·the·file
14 ············was·not·a·symbolic·link.14 ············was·not·a·symbolic·link.
15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
16 i1·:·p·=·temporaryFileName·()16 i1·:·p·=·temporaryFileName·()
  
17 o1·=·/tmp/M2-1093698-0/017 o1·=·/tmp/M2-1054229-0/0
18 i2·:·symlinkFile·("foo",·p)18 i2·:·symlinkFile·("foo",·p)
19 i3·:·readlink·p19 i3·:·readlink·p
  
20 o3·=·foo20 o3·=·foo
21 i4·:·removeFile·p21 i4·:·removeFile·p
22 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*22 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
23 ····*·_\x8r_\x8e_\x8a_\x8l_\x8p_\x8a_\x8t_\x8h·--·convert·a·filename·to·one·passing·through·no·symbolic·links23 ····*·_\x8r_\x8e_\x8a_\x8l_\x8p_\x8a_\x8t_\x8h·--·convert·a·filename·to·one·passing·through·no·symbolic·links
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68 ······<div>68 ······<div>
69 ········<h2>Description</h2>69 ········<h2>Description</h2>
70 ········<table·class="examples">70 ········<table·class="examples">
71 ··········<tr>71 ··········<tr>
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i1·:·realpath·&quot;.&quot;73 ··············<pre><code·class="language-macaulay2">i1·:·realpath·&quot;.&quot;
  
74 o1·=·/tmp/M2-1075204-0/86-rundir/</code></pre>74 o1·=·/tmp/M2-980911-0/86-rundir/</code></pre>
75 ············</td>75 ············</td>
76 ··········</tr>76 ··········</tr>
77 ··········<tr>77 ··········<tr>
78 ············<td>78 ············<td>
79 ··············<pre><code·class="language-macaulay2">i2·:·p·=·temporaryFileName()79 ··············<pre><code·class="language-macaulay2">i2·:·p·=·temporaryFileName()
  
80 o2·=·/tmp/M2-1093886-0/0</code></pre>80 o2·=·/tmp/M2-1054831-0/0</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·q·=·temporaryFileName()85 ··············<pre><code·class="language-macaulay2">i3·:·q·=·temporaryFileName()
  
86 o3·=·/tmp/M2-1093886-0/1</code></pre>86 o3·=·/tmp/M2-1054831-0/1</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i4·:·symlinkFile(p,q)</code></pre>91 ··············<pre><code·class="language-macaulay2">i4·:·symlinkFile(p,q)</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i5·:·p·&lt;&lt;·close96 ··············<pre><code·class="language-macaulay2">i5·:·p·&lt;&lt;·close
  
97 o5·=·/tmp/M2-1093886-0/097 o5·=·/tmp/M2-1054831-0/0
  
98 o5·:·File</code></pre>98 o5·:·File</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i6·:·readlink·q103 ··············<pre><code·class="language-macaulay2">i6·:·readlink·q
  
104 o6·=·/tmp/M2-1093886-0/0</code></pre>104 o6·=·/tmp/M2-1054831-0/0</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i7·:·realpath·q109 ··············<pre><code·class="language-macaulay2">i7·:·realpath·q
  
110 o7·=·/tmp/M2-1093886-0/0</code></pre>110 o7·=·/tmp/M2-1054831-0/0</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i8·:·removeFile·p</code></pre>115 ··············<pre><code·class="language-macaulay2">i8·:·removeFile·p</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
Offset 130, 15 lines modifiedOffset 130, 15 lines modified
130 ········</table>130 ········</table>
131 ········<p>The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.</p>131 ········<p>The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.</p>
132 ········<table·class="examples">132 ········<table·class="examples">
133 ··········<tr>133 ··········<tr>
134 ············<td>134 ············<td>
135 ··············<pre><code·class="language-macaulay2">i10·:·realpath·&quot;&quot;135 ··············<pre><code·class="language-macaulay2">i10·:·realpath·&quot;&quot;
  
136 o10·=·/tmp/M2-1075204-0/86-rundir/</code></pre>136 o10·=·/tmp/M2-980911-0/86-rundir/</code></pre>
137 ············</td>137 ············</td>
138 ··········</tr>138 ··········</tr>
139 ········</table>139 ········</table>
140 ······</div>140 ······</div>
141 ······<div>141 ······<div>
142 ········<h2>Caveat</h2>142 ········<h2>Caveat</h2>
143 Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to·the·user.·Terminal·slashes·will·be·dropped.··Warning:·under·most·operating·systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of·the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain·circumstances,·return·a·relative·path·when·given·a·relative·path.······</div>143 Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to·the·user.·Terminal·slashes·will·be·dropped.··Warning:·under·most·operating·systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of·the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain·circumstances,·return·a·relative·path·when·given·a·relative·path.······</div>
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12 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename,·or·path·to·a·file12 ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename,·or·path·to·a·file
13 ····*·Outputs:13 ····*·Outputs:
14 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·pathname·to·fn·passing·through·no·symbolic·links,·and14 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·pathname·to·fn·passing·through·no·symbolic·links,·and
15 ············ending·with·a·slash·if·fn·refers·to·a·directory15 ············ending·with·a·slash·if·fn·refers·to·a·directory
16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
17 i1·:·realpath·"."17 i1·:·realpath·"."
  
18 o1·=·/tmp/M2-1075204-0/86-rundir/18 o1·=·/tmp/M2-980911-0/86-rundir/
19 i2·:·p·=·temporaryFileName()19 i2·:·p·=·temporaryFileName()
  
20 o2·=·/tmp/M2-1093886-0/020 o2·=·/tmp/M2-1054831-0/0
21 i3·:·q·=·temporaryFileName()21 i3·:·q·=·temporaryFileName()
  
22 o3·=·/tmp/M2-1093886-0/122 o3·=·/tmp/M2-1054831-0/1
23 i4·:·symlinkFile(p,q)23 i4·:·symlinkFile(p,q)
24 i5·:·p·<<·close24 i5·:·p·<<·close
  
25 o5·=·/tmp/M2-1093886-0/025 o5·=·/tmp/M2-1054831-0/0
  
26 o5·:·File26 o5·:·File
27 i6·:·readlink·q27 i6·:·readlink·q
  
28 o6·=·/tmp/M2-1093886-0/028 o6·=·/tmp/M2-1054831-0/0
29 i7·:·realpath·q29 i7·:·realpath·q
  
30 o7·=·/tmp/M2-1093886-0/030 o7·=·/tmp/M2-1054831-0/0
31 i8·:·removeFile·p31 i8·:·removeFile·p
32 i9·:·removeFile·q32 i9·:·removeFile·q
33 The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.33 The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.
34 i10·:·realpath·""34 i10·:·realpath·""
  
35 o10·=·/tmp/M2-1075204-0/86-rundir/35 o10·=·/tmp/M2-980911-0/86-rundir/
36 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*36 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
37 Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to37 Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to
38 the·user.·Terminal·slashes·will·be·dropped.·Warning:·under·most·operating38 the·user.·Terminal·slashes·will·be·dropped.·Warning:·under·most·operating
39 systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of39 systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of
40 the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain40 the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain
41 circumstances,·return·a·relative·path·when·given·a·relative·path.41 circumstances,·return·a·relative·path·when·given·a·relative·path.
42 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*42 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
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76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·&quot;--·finalizing·sequence·#&quot;|i|&quot;·--&quot;))</code></pre>77 ··············<pre><code·class="language-macaulay2">i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·&quot;--·finalizing·sequence·#&quot;|i|&quot;·--&quot;))</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·collectGarbage()·82 ··············<pre><code·class="language-macaulay2">i2·:·collectGarbage()·
83 --finalization:·(1)[1]:·--·finalizing·sequence·#2·-- 
84 --finalization:·(2)[7]:·--·finalizing·sequence·#8·-- 
85 --finalization:·(3)[4]:·--·finalizing·sequence·#5·-- 
86 --finalization:·(4)[3]:·--·finalizing·sequence·#4·-- 
87 --finalization:·(5)[0]:·--·finalizing·sequence·#1·-- 
88 --finalization:·(6)[6]:·--·finalizing·sequence·#7·--83 --finalization:·(1)[6]:·--·finalizing·sequence·#7·--
 84 --finalization:·(2)[3]:·--·finalizing·sequence·#4·--
 85 --finalization:·(3)[0]:·--·finalizing·sequence·#1·--
 86 --finalization:·(4)[7]:·--·finalizing·sequence·#8·--
 87 --finalization:·(5)[4]:·--·finalizing·sequence·#5·--
 88 --finalization:·(6)[1]:·--·finalizing·sequence·#2·--
89 --finalization:·(7)[5]:·--·finalizing·sequence·#6·--89 --finalization:·(7)[5]:·--·finalizing·sequence·#6·--
90 --finalization:·(8)[2]:·--·finalizing·sequence·#3·--</code></pre>90 --finalization:·(8)[2]:·--·finalizing·sequence·#3·--</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ········</table>93 ········</table>
94 ······</div>94 ······</div>
95 ······<div>95 ······<div>
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14 ····*·Consequences:14 ····*·Consequences:
15 ··········o·A·finalizer·is·registered·with·the·garbage·collector·to·print·a15 ··········o·A·finalizer·is·registered·with·the·garbage·collector·to·print·a
16 ············string·when·that·object·is·collected·as·garbage16 ············string·when·that·object·is·collected·as·garbage
17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*17 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
18 i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"-18 i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"-
19 -·finalizing·sequence·#"|i|"·--"))19 -·finalizing·sequence·#"|i|"·--"))
20 i2·:·collectGarbage()20 i2·:·collectGarbage()
21 --finalization:·(1)[1]:·--·finalizing·sequence·#2·-- 
22 --finalization:·(2)[7]:·--·finalizing·sequence·#8·-- 
23 --finalization:·(3)[4]:·--·finalizing·sequence·#5·-- 
24 --finalization:·(4)[3]:·--·finalizing·sequence·#4·-- 
25 --finalization:·(5)[0]:·--·finalizing·sequence·#1·-- 
26 --finalization:·(6)[6]:·--·finalizing·sequence·#7·--21 --finalization:·(1)[6]:·--·finalizing·sequence·#7·--
 22 --finalization:·(2)[3]:·--·finalizing·sequence·#4·--
 23 --finalization:·(3)[0]:·--·finalizing·sequence·#1·--
 24 --finalization:·(4)[7]:·--·finalizing·sequence·#8·--
 25 --finalization:·(5)[4]:·--·finalizing·sequence·#5·--
 26 --finalization:·(6)[1]:·--·finalizing·sequence·#2·--
27 --finalization:·(7)[5]:·--·finalizing·sequence·#6·--27 --finalization:·(7)[5]:·--·finalizing·sequence·#6·--
28 --finalization:·(8)[2]:·--·finalizing·sequence·#3·--28 --finalization:·(8)[2]:·--·finalizing·sequence·#3·--
29 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
30 This·function·should·mainly·be·used·for·debugging.·Having·a·large·number·of30 This·function·should·mainly·be·used·for·debugging.·Having·a·large·number·of
31 finalizers·might·degrade·the·performance·of·the·program.·Moreover,·registering31 finalizers·might·degrade·the·performance·of·the·program.·Moreover,·registering
32 two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for32 two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for
33 finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the33 finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the
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71 ······<div>71 ······<div>
72 ········<h2>Description</h2>72 ········<h2>Description</h2>
73 ········<table·class="examples">73 ········<table·class="examples">
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()76 ··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName()
  
77 o1·=·/tmp/M2-1082943-0/0</code></pre>77 o1·=·/tmp/M2-996065-0/0</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir82 ··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir
  
83 o2·=·/tmp/M2-1082943-0/0</code></pre>83 o2·=·/tmp/M2-996065-0/0</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·readDirectory·dir88 ··············<pre><code·class="language-macaulay2">i3·:·readDirectory·dir
  
89 o3·=·{..,·.}89 o3·=·{.,·..}
  
90 o3·:·List</code></pre>90 o3·:·List</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i4·:·removeDirectory·dir</code></pre>95 ··············<pre><code·class="language-macaulay2">i4·:·removeDirectory·dir</code></pre>
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10 ····*·Inputs:10 ····*·Inputs:
11 ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory11 ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory
12 ····*·Consequences:12 ····*·Consequences:
13 ··········o·the·directory·is·removed13 ··········o·the·directory·is·removed
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 i1·:·dir·=·temporaryFileName()15 i1·:·dir·=·temporaryFileName()
  
16 o1·=·/tmp/M2-1082943-0/016 o1·=·/tmp/M2-996065-0/0
17 i2·:·makeDirectory·dir17 i2·:·makeDirectory·dir
  
18 o2·=·/tmp/M2-1082943-0/018 o2·=·/tmp/M2-996065-0/0
19 i3·:·readDirectory·dir19 i3·:·readDirectory·dir
  
20 o3·=·{..,·.}20 o3·=·{.,·..}
  
21 o3·:·List21 o3·:·List
22 i4·:·removeDirectory·dir22 i4·:·removeDirectory·dir
23 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
24 ····*·_\x8r_\x8e_\x8a_\x8d_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·read·the·contents·of·a·directory24 ····*·_\x8r_\x8e_\x8a_\x8d_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·read·the·contents·of·a·directory
25 ····*·_\x8m_\x8a_\x8k_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·make·a·directory25 ····*·_\x8m_\x8a_\x8k_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·make·a·directory
26 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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65 ········<h2>Description</h2>65 ········<h2>Description</h2>
66 ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·external·programs.</p>66 ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·external·programs.</p>
67 ········<table·class="examples">67 ········<table·class="examples">
68 ··········<tr>68 ··········<tr>
69 ············<td>69 ············<td>
70 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()70 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
71 o1·=·/tmp/M2-1076046-0/0</code></pre>71 o1·=·/tmp/M2-982439-0/0</code></pre>
72 ············</td>72 ············</td>
73 ··········</tr>73 ··········</tr>
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i2·:·rootPath·|·fn76 ··············<pre><code·class="language-macaulay2">i2·:·rootPath·|·fn
  
77 o2·=·/tmp/M2-1076046-0/0</code></pre>77 o2·=·/tmp/M2-982439-0/0</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ········</table>80 ········</table>
81 ······</div>81 ······</div>
82 ······<div>82 ······<div>
83 ········<h2>See·also</h2>83 ········<h2>See·also</h2>
84 ········<ul>84 ········<ul>
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11 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·path,·as·seen·by·external·programs,·to·the·root·of11 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·path,·as·seen·by·external·programs,·to·the·root·of
12 ············the·file·system·seen·by·Macaulay212 ············the·file·system·seen·by·Macaulay2
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable14 This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable
15 by·external·programs.15 by·external·programs.
16 i1·:·fn·=·temporaryFileName()16 i1·:·fn·=·temporaryFileName()
  
17 o1·=·/tmp/M2-1076046-0/017 o1·=·/tmp/M2-982439-0/0
18 i2·:·rootPath·|·fn18 i2·:·rootPath·|·fn
  
19 o2·=·/tmp/M2-1076046-0/019 o2·=·/tmp/M2-982439-0/0
20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
21 ····*·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I21 ····*·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I
22 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*22 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
23 The·object·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g.23 The·object·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g.
24 ===============================================================================24 ===============================================================================
25 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-25 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
26 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_system.m2:2025:0.26 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_system.m2:2025:0.
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65 ········<h2>Description</h2>65 ········<h2>Description</h2>
66 ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·an·external·browser.</p>66 ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·an·external·browser.</p>
67 ········<table·class="examples">67 ········<table·class="examples">
68 ··········<tr>68 ··········<tr>
69 ············<td>69 ············<td>
70 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()70 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
71 o1·=·/tmp/M2-1086087-0/0</code></pre>71 o1·=·/tmp/M2-1047499-0/0</code></pre>
72 ············</td>72 ············</td>
73 ··········</tr>73 ··········</tr>
74 ··········<tr>74 ··········<tr>
75 ············<td>75 ············<td>
76 ··············<pre><code·class="language-macaulay2">i2·:·rootURI·|·fn76 ··············<pre><code·class="language-macaulay2">i2·:·rootURI·|·fn
  
77 o2·=·file:///tmp/M2-1086087-0/0</code></pre>77 o2·=·file:///tmp/M2-1047499-0/0</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ········</table>80 ········</table>
81 ······</div>81 ······</div>
82 ······<div>82 ······<div>
83 ········<h2>See·also</h2>83 ········<h2>See·also</h2>
84 ········<ul>84 ········<ul>
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11 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·path,·as·seen·by·an·external·browser,·to·the·root·of11 ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·path,·as·seen·by·an·external·browser,·to·the·root·of
12 ············the·file·system·seen·by·Macaulay212 ············the·file·system·seen·by·Macaulay2
13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*13 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
14 This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable14 This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable
15 by·an·external·browser.15 by·an·external·browser.
16 i1·:·fn·=·temporaryFileName()16 i1·:·fn·=·temporaryFileName()
  
17 o1·=·/tmp/M2-1086087-0/017 o1·=·/tmp/M2-1047499-0/0
18 i2·:·rootURI·|·fn18 i2·:·rootURI·|·fn
  
19 o2·=·file:///tmp/M2-1086087-0/019 o2·=·file:///tmp/M2-1047499-0/0
20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
21 ····*·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h21 ····*·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h
22 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*22 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
23 The·object·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g.23 The·object·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g.
24 ===============================================================================24 ===============================================================================
25 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-25 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
26 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_system.m2:2041:0.26 1.25.06+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_system.m2:2041:0.
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90 o4·:·R-module,·submodule·of·R</code></pre>90 o4·:·R-module,·submodule·of·R</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i5·:·f·=·temporaryFileName()95 ··············<pre><code·class="language-macaulay2">i5·:·f·=·temporaryFileName()
  
96 o5·=·/tmp/M2-1084627-0/0</code></pre>96 o5·=·/tmp/M2-1040535-0/0</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i6·:·f·&lt;&lt;·toString·(p,m,M)·&lt;&lt;·close101 ··············<pre><code·class="language-macaulay2">i6·:·f·&lt;&lt;·toString·(p,m,M)·&lt;&lt;·close
  
102 o6·=·/tmp/M2-1084627-0/0102 o6·=·/tmp/M2-1040535-0/0
  
103 o6·:·File</code></pre>103 o6·:·File</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i7·:·get·f108 ··············<pre><code·class="language-macaulay2">i7·:·get·f
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28 o4·=·image·|·x2·x2-y2·xyz7·|28 o4·=·image·|·x2·x2-y2·xyz7·|
  
29 ·····························129 ·····························1
30 o4·:·R-module,·submodule·of·R30 o4·:·R-module,·submodule·of·R
31 i5·:·f·=·temporaryFileName()31 i5·:·f·=·temporaryFileName()
  
32 o5·=·/tmp/M2-1084627-0/032 o5·=·/tmp/M2-1040535-0/0
33 i6·:·f·<<·toString·(p,m,M)·<<·close33 i6·:·f·<<·toString·(p,m,M)·<<·close
  
34 o6·=·/tmp/M2-1084627-0/034 o6·=·/tmp/M2-1040535-0/0
  
35 o6·:·File35 o6·:·File
36 i7·:·get·f36 i7·:·get·f
  
37 o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2,37 o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2,
38 ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}})38 ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}})
39 i8·:·(p',m',M')·=·value·get·f39 i8·:·(p',m',M')·=·value·get·f
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94 o2·:·Task</code></pre>94 o2·:·Task</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i3·:·schedule·t99 ··············<pre><code·class="language-macaulay2">i3·:·schedule·t
  
100 o3·=·&lt;&lt;task,·created>>100 o3·=·&lt;&lt;task,·result·available,·task·done>>
  
101 o3·:·Task</code></pre>101 o3·:·Task</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i4·:·taskResult·t106 ··············<pre><code·class="language-macaulay2">i4·:·taskResult·t
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32 i2·:·t·=·createTask(f,3)32 i2·:·t·=·createTask(f,3)
  
33 o2·=·<<task,·created>>33 o2·=·<<task,·created>>
  
34 o2·:·Task34 o2·:·Task
35 i3·:·schedule·t35 i3·:·schedule·t
  
36 o3·=·<<task,·created>>36 o3·=·<<task,·result·available,·task·done>>
  
37 o3·:·Task37 o3·:·Task
38 i4·:·taskResult·t38 i4·:·taskResult·t
  
39 o4·=·839 o4·=·8
40 i5·:·u·=·schedule(f,4)40 i5·:·u·=·schedule(f,4)
  
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366 ············<td>366 ············<td>
367 ··············<pre><code·class="language-macaulay2">i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;</code></pre>367 ··············<pre><code·class="language-macaulay2">i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;</code></pre>
368 ············</td>368 ············</td>
369 ··········</tr>369 ··········</tr>
370 ··········<tr>370 ··········<tr>
371 ············<td>371 ············<td>
372 ··············<pre><code·class="language-macaulay2">i30·:·time·X·=·solve(A,B);372 ··············<pre><code·class="language-macaulay2">i30·:·time·X·=·solve(A,B);
373 ·--·used·0.000120261s·(cpu);·0.00011242s·(thread);·0s·(gc)</code></pre>373 ·--·used·0.000573995s·(cpu);·0.00059232s·(thread);·0s·(gc)</code></pre>
374 ············</td>374 ············</td>
375 ··········</tr>375 ··········</tr>
376 ··········<tr>376 ··········<tr>
377 ············<td>377 ············<td>
378 ··············<pre><code·class="language-macaulay2">i31·:·time·X·=·solve(A,B,·MaximalRank=>true);378 ··············<pre><code·class="language-macaulay2">i31·:·time·X·=·solve(A,B,·MaximalRank=>true);
379 ·--·used·7.266e-05s·(cpu);·7.271e-05s·(thread);·0s·(gc)</code></pre>379 ·--·used·0.000120916s·(cpu);·0.000120496s·(thread);·0s·(gc)</code></pre>
380 ············</td>380 ············</td>
381 ··········</tr>381 ··········</tr>
382 ··········<tr>382 ··········<tr>
383 ············<td>383 ············<td>
384 ··············<pre><code·class="language-macaulay2">i32·:·norm(A*X-B)384 ··············<pre><code·class="language-macaulay2">i32·:·norm(A*X-B)
  
385 o32·=·5.111850690840453e-15385 o32·=·5.111850690840453e-15
Offset 411, 21 lines modifiedOffset 411, 21 lines modified
411 ············<td>411 ············<td>
412 ··············<pre><code·class="language-macaulay2">i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;</code></pre>412 ··············<pre><code·class="language-macaulay2">i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;</code></pre>
413 ············</td>413 ············</td>
414 ··········</tr>414 ··········</tr>
415 ··········<tr>415 ··········<tr>
416 ············<td>416 ············<td>
417 ··············<pre><code·class="language-macaulay2">i38·:·time·X·=·solve(A,B);417 ··············<pre><code·class="language-macaulay2">i38·:·time·X·=·solve(A,B);
418 ·--·used·0.306572s·(cpu);·0.140883s·(thread);·0s·(gc)</code></pre>418 ·--·used·0.295576s·(cpu);·0.154725s·(thread);·0s·(gc)</code></pre>
419 ············</td>419 ············</td>
420 ··········</tr>420 ··········</tr>
421 ··········<tr>421 ··········<tr>
422 ············<td>422 ············<td>
423 ··············<pre><code·class="language-macaulay2">i39·:·time·X·=·solve(A,B,·MaximalRank=>true);423 ··············<pre><code·class="language-macaulay2">i39·:·time·X·=·solve(A,B,·MaximalRank=>true);
424 ·--·used·0.106319s·(cpu);·0.106326s·(thread);·0s·(gc)</code></pre>424 ·--·used·0.120689s·(cpu);·0.120669s·(thread);·0s·(gc)</code></pre>
425 ············</td>425 ············</td>
426 ··········</tr>426 ··········</tr>
427 ··········<tr>427 ··········<tr>
428 ············<td>428 ············<td>
429 ··············<pre><code·class="language-macaulay2">i40·:·norm(A*X-B)429 ··············<pre><code·class="language-macaulay2">i40·:·norm(A*X-B)
  
430 o40·=·1.491578274689709814082355885932e-28430 o40·=·1.491578274689709814082355885932e-28
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192 i24·:·printingPrecision·=·4;192 i24·:·printingPrecision·=·4;
193 i25·:·N·=·40193 i25·:·N·=·40
  
194 o25·=·40194 o25·=·40
195 i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;195 i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;
196 i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;196 i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;
197 i30·:·time·X·=·solve(A,B);197 i30·:·time·X·=·solve(A,B);
198 ·--·used·0.000120261s·(cpu);·0.00011242s·(thread);·0s·(gc)198 ·--·used·0.000573995s·(cpu);·0.00059232s·(thread);·0s·(gc)
199 i31·:·time·X·=·solve(A,B,·MaximalRank=>true);199 i31·:·time·X·=·solve(A,B,·MaximalRank=>true);
200 ·--·used·7.266e-05s·(cpu);·7.271e-05s·(thread);·0s·(gc)200 ·--·used·0.000120916s·(cpu);·0.000120496s·(thread);·0s·(gc)
201 i32·:·norm(A*X-B)201 i32·:·norm(A*X-B)
  
202 o32·=·5.111850690840453e-15202 o32·=·5.111850690840453e-15
  
203 o32·:·RR·(of·precision·53)203 o32·:·RR·(of·precision·53)
204 Over·higher·precision·RR·or·CC,·these·routines·will·be·much·slower·than·the204 Over·higher·precision·RR·or·CC,·these·routines·will·be·much·slower·than·the
205 lower·precision·LAPACK·routines.205 lower·precision·LAPACK·routines.
206 i33·:·N·=·100206 i33·:·N·=·100
  
207 o33·=·100207 o33·=·100
208 i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;208 i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;
209 i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;209 i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;
210 i38·:·time·X·=·solve(A,B);210 i38·:·time·X·=·solve(A,B);
211 ·--·used·0.306572s·(cpu);·0.140883s·(thread);·0s·(gc)211 ·--·used·0.295576s·(cpu);·0.154725s·(thread);·0s·(gc)
212 i39·:·time·X·=·solve(A,B,·MaximalRank=>true);212 i39·:·time·X·=·solve(A,B,·MaximalRank=>true);
213 ·--·used·0.106319s·(cpu);·0.106326s·(thread);·0s·(gc)213 ·--·used·0.120689s·(cpu);·0.120669s·(thread);·0s·(gc)
214 i40·:·norm(A*X-B)214 i40·:·norm(A*X-B)
  
215 o40·=·1.491578274689709814082355885932e-28215 o40·=·1.491578274689709814082355885932e-28
  
216 o40·:·RR·(of·precision·100)216 o40·:·RR·(of·precision·100)
217 Giving·the·option·ClosestFit=>true,·in·the·case·when·the·field·is·RR·or·CC,217 Giving·the·option·ClosestFit=>true,·in·the·case·when·the·field·is·RR·or·CC,
218 uses·a·least·squares·algorithm·to·find·a·best·fit·solution.218 uses·a·least·squares·algorithm·to·find·a·best·fit·solution.
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Offset 80, 93 lines modifiedOffset 80, 93 lines modified
80 ······<div>80 ······<div>
81 ········<h2>Description</h2>81 ········<h2>Description</h2>
82 ········<table·class="examples">82 ········<table·class="examples">
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·&quot;/&quot;85 ··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·&quot;/&quot;
  
86 o1·=·/tmp/M2-1083759-0/0/</code></pre>86 o1·=·/tmp/M2-1012869-0/0/</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·&quot;/&quot;91 ··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·&quot;/&quot;
  
92 o2·=·/tmp/M2-1083759-0/1/</code></pre>92 o2·=·/tmp/M2-1012869-0/1/</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|&quot;a/&quot;)97 ··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|&quot;a/&quot;)
  
98 o3·=·/tmp/M2-1083759-0/0/a/</code></pre>98 o3·=·/tmp/M2-1012869-0/0/a/</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|&quot;b/&quot;)103 ··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|&quot;b/&quot;)
  
104 o4·=·/tmp/M2-1083759-0/0/b/</code></pre>104 o4·=·/tmp/M2-1012869-0/0/b/</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|&quot;b/c/&quot;)109 ··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|&quot;b/c/&quot;)
  
110 o5·=·/tmp/M2-1083759-0/0/b/c/</code></pre>110 o5·=·/tmp/M2-1012869-0/0/b/c/</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i6·:·src|&quot;a/f&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close115 ··············<pre><code·class="language-macaulay2">i6·:·src|&quot;a/f&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
116 o6·=·/tmp/M2-1083759-0/0/a/f116 o6·=·/tmp/M2-1012869-0/0/a/f
  
117 o6·:·File</code></pre>117 o6·:·File</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i7·:·src|&quot;a/g&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close122 ··············<pre><code·class="language-macaulay2">i7·:·src|&quot;a/g&quot;·&lt;&lt;·&quot;hi·there&quot;·&lt;&lt;·close
  
123 o7·=·/tmp/M2-1083759-0/0/a/g123 o7·=·/tmp/M2-1012869-0/0/a/g
  
124 o7·:·File</code></pre>124 o7·:·File</code></pre>
125 ············</td>125 ············</td>
126 ··········</tr>126 ··········</tr>
127 ··········<tr>127 ··········<tr>
128 ············<td>128 ············<td>
129 ··············<pre><code·class="language-macaulay2">i8·:·src|&quot;b/c/g&quot;·&lt;&lt;·&quot;ho·there&quot;·&lt;&lt;·close129 ··············<pre><code·class="language-macaulay2">i8·:·src|&quot;b/c/g&quot;·&lt;&lt;·&quot;ho·there&quot;·&lt;&lt;·close
  
130 o8·=·/tmp/M2-1083759-0/0/b/c/g130 o8·=·/tmp/M2-1012869-0/0/b/c/g
  
131 o8·:·File</code></pre>131 o8·:·File</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i9·:·symlinkDirectory(src,dst,Verbose=>true)136 ··············<pre><code·class="language-macaulay2">i9·:·symlinkDirectory(src,dst,Verbose=>true)
137 --symlinking:·../../../0/b/c/g·->·/tmp/M2-1083759-0/1/b/c/g137 --symlinking:·../../../0/b/c/g·->·/tmp/M2-1012869-0/1/b/c/g
138 --symlinking:·../../0/a/f·->·/tmp/M2-1083759-0/1/a/f138 --symlinking:·../../0/a/g·->·/tmp/M2-1012869-0/1/a/g
139 --symlinking:·../../0/a/g·->·/tmp/M2-1083759-0/1/a/g</code></pre>139 --symlinking:·../../0/a/f·->·/tmp/M2-1012869-0/1/a/f</code></pre>
140 ············</td>140 ············</td>
141 ··········</tr>141 ··········</tr>
142 ··········<tr>142 ··········<tr>
143 ············<td>143 ············<td>
144 ··············<pre><code·class="language-macaulay2">i10·:·get·(dst|&quot;b/c/g&quot;)144 ··············<pre><code·class="language-macaulay2">i10·:·get·(dst|&quot;b/c/g&quot;)
  
145 o10·=·ho·there</code></pre>145 o10·=·ho·there</code></pre>
146 ············</td>146 ············</td>
147 ··········</tr>147 ··········</tr>
148 ··········<tr>148 ··········<tr>
149 ············<td>149 ············<td>
150 ··············<pre><code·class="language-macaulay2">i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true)150 ··············<pre><code·class="language-macaulay2">i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true)
151 --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-1083759-0/1/b/c/g151 --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-1012869-0/1/b/c/g
152 --unsymlinking:·../../0/a/f·->·/tmp/M2-1083759-0/1/a/f152 --unsymlinking:·../../0/a/g·->·/tmp/M2-1012869-0/1/a/g
153 --unsymlinking:·../../0/a/g·->·/tmp/M2-1083759-0/1/a/g</code></pre>153 --unsymlinking:·../../0/a/f·->·/tmp/M2-1012869-0/1/a/f</code></pre>
154 ············</td>154 ············</td>
155 ··········</tr>155 ··········</tr>
156 ········</table>156 ········</table>
157 Now·we·remove·the·files·and·directories·we·created.········<table·class="examples">157 Now·we·remove·the·files·and·directories·we·created.········<table·class="examples">
158 ··········<tr>158 ··········<tr>
159 ············<td>159 ············<td>
160 ··············<pre><code·class="language-macaulay2">i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d160 ··············<pre><code·class="language-macaulay2">i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d
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Offset 30, 53 lines modifiedOffset 30, 53 lines modified
30 ··········o·The·directory·tree·rooted·at·src·is·duplicated·by·a·directory·tree30 ··········o·The·directory·tree·rooted·at·src·is·duplicated·by·a·directory·tree
31 ············rooted·at·dst.·The·files·in·the·source·tree·are·represented·by31 ············rooted·at·dst.·The·files·in·the·source·tree·are·represented·by
32 ············relative·symbolic·links·in·the·destination·tree·to·the·original32 ············relative·symbolic·links·in·the·destination·tree·to·the·original
33 ············files·in·the·source·tree.33 ············files·in·the·source·tree.
34 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*34 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
35 i1·:·src·=·temporaryFileName()·|·"/"35 i1·:·src·=·temporaryFileName()·|·"/"
  
36 o1·=·/tmp/M2-1083759-0/0/36 o1·=·/tmp/M2-1012869-0/0/
37 i2·:·dst·=·temporaryFileName()·|·"/"37 i2·:·dst·=·temporaryFileName()·|·"/"
  
38 o2·=·/tmp/M2-1083759-0/1/38 o2·=·/tmp/M2-1012869-0/1/
39 i3·:·makeDirectory·(src|"a/")39 i3·:·makeDirectory·(src|"a/")
  
40 o3·=·/tmp/M2-1083759-0/0/a/40 o3·=·/tmp/M2-1012869-0/0/a/
41 i4·:·makeDirectory·(src|"b/")41 i4·:·makeDirectory·(src|"b/")
  
42 o4·=·/tmp/M2-1083759-0/0/b/42 o4·=·/tmp/M2-1012869-0/0/b/
43 i5·:·makeDirectory·(src|"b/c/")43 i5·:·makeDirectory·(src|"b/c/")
  
44 o5·=·/tmp/M2-1083759-0/0/b/c/44 o5·=·/tmp/M2-1012869-0/0/b/c/
45 i6·:·src|"a/f"·<<·"hi·there"·<<·close45 i6·:·src|"a/f"·<<·"hi·there"·<<·close
  
46 o6·=·/tmp/M2-1083759-0/0/a/f46 o6·=·/tmp/M2-1012869-0/0/a/f
  
47 o6·:·File47 o6·:·File
48 i7·:·src|"a/g"·<<·"hi·there"·<<·close48 i7·:·src|"a/g"·<<·"hi·there"·<<·close
  
49 o7·=·/tmp/M2-1083759-0/0/a/g49 o7·=·/tmp/M2-1012869-0/0/a/g
  
50 o7·:·File50 o7·:·File
51 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close51 i8·:·src|"b/c/g"·<<·"ho·there"·<<·close
  
52 o8·=·/tmp/M2-1083759-0/0/b/c/g52 o8·=·/tmp/M2-1012869-0/0/b/c/g
  
53 o8·:·File53 o8·:·File
54 i9·:·symlinkDirectory(src,dst,Verbose=>true)54 i9·:·symlinkDirectory(src,dst,Verbose=>true)
55 --symlinking:·../../../0/b/c/g·->·/tmp/M2-1083759-0/1/b/c/g55 --symlinking:·../../../0/b/c/g·->·/tmp/M2-1012869-0/1/b/c/g
56 --symlinking:·../../0/a/f·->·/tmp/M2-1083759-0/1/a/f 
57 --symlinking:·../../0/a/g·->·/tmp/M2-1083759-0/1/a/g56 --symlinking:·../../0/a/g·->·/tmp/M2-1012869-0/1/a/g
 57 --symlinking:·../../0/a/f·->·/tmp/M2-1012869-0/1/a/f
58 i10·:·get·(dst|"b/c/g")58 i10·:·get·(dst|"b/c/g")
  
59 o10·=·ho·there59 o10·=·ho·there
60 i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true)60 i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true)
61 --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-1083759-0/1/b/c/g61 --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-1012869-0/1/b/c/g
62 --unsymlinking:·../../0/a/f·->·/tmp/M2-1083759-0/1/a/f 
63 --unsymlinking:·../../0/a/g·->·/tmp/M2-1083759-0/1/a/g62 --unsymlinking:·../../0/a/g·->·/tmp/M2-1012869-0/1/a/g
 63 --unsymlinking:·../../0/a/f·->·/tmp/M2-1012869-0/1/a/f
64 Now·we·remove·the·files·and·directories·we·created.64 Now·we·remove·the·files·and·directories·we·created.
65 i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d65 i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d
  
66 o12·=·rm66 o12·=·rm
  
67 o12·:·FunctionClosure67 o12·:·FunctionClosure
68 i13·:·scan(reverse·findFiles·src,·rm)68 i13·:·scan(reverse·findFiles·src,·rm)
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Offset 72, 15 lines modifiedOffset 72, 15 lines modified
72 ······<div>72 ······<div>
73 ········<h2>Description</h2>73 ········<h2>Description</h2>
74 ········<table·class="examples">74 ········<table·class="examples">
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()77 ··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName()
  
78 o1·=·/tmp/M2-1083870-0/0</code></pre>78 o1·=·/tmp/M2-1018263-0/0</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i2·:·symlinkFile(&quot;qwert&quot;,·fn)</code></pre>83 ··············<pre><code·class="language-macaulay2">i2·:·symlinkFile(&quot;qwert&quot;,·fn)</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
478 B
    
Offset 12, 15 lines modifiedOffset 12, 15 lines modified
12 ··········o·dst,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g12 ··········o·dst,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g
13 ····*·Consequences:13 ····*·Consequences:
14 ··········o·a·symbolic·link·at·the·location·in·the·directory·tree·specified·by14 ··········o·a·symbolic·link·at·the·location·in·the·directory·tree·specified·by
15 ············dst·is·created,·pointing·to·src15 ············dst·is·created,·pointing·to·src
16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
17 i1·:·fn·=·temporaryFileName()17 i1·:·fn·=·temporaryFileName()
  
18 o1·=·/tmp/M2-1083870-0/018 o1·=·/tmp/M2-1018263-0/0
19 i2·:·symlinkFile("qwert",·fn)19 i2·:·symlinkFile("qwert",·fn)
20 i3·:·fileExists·fn20 i3·:·fileExists·fn
  
21 o3·=·false21 o3·=·false
22 i4·:·readlink·fn22 i4·:·readlink·fn
  
23 o4·=·qwert23 o4·=·qwert
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./usr/share/doc/Macaulay2/Macaulay2Doc/html/_temporary__File__Name.html
    
Offset 64, 22 lines modifiedOffset 64, 22 lines modified
64 ······<div>64 ······<div>
65 ········<h2>Description</h2>65 ········<h2>Description</h2>
66 The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no·collision·with·existing·files·will·occur.··The·files·will·be·removed·when·the·program·terminates,·unless·it·terminates·as·the·result·of·an·error.········<table·class="examples">66 The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no·collision·with·existing·files·will·occur.··The·files·will·be·removed·when·the·program·terminates,·unless·it·terminates·as·the·result·of·an·error.········<table·class="examples">
67 ··········<tr>67 ··········<tr>
68 ············<td>68 ············<td>
69 ··············<pre><code·class="language-macaulay2">i1·:·temporaryFileName·()·|·&quot;.tex&quot;69 ··············<pre><code·class="language-macaulay2">i1·:·temporaryFileName·()·|·&quot;.tex&quot;
  
70 o1·=·/tmp/M2-1101176-0/0.tex</code></pre>70 o1·=·/tmp/M2-1060134-0/0.tex</code></pre>
71 ············</td>71 ············</td>
72 ··········</tr>72 ··········</tr>
73 ··········<tr>73 ··········<tr>
74 ············<td>74 ············<td>
75 ··············<pre><code·class="language-macaulay2">i2·:·temporaryFileName·()·|·&quot;.html&quot;75 ··············<pre><code·class="language-macaulay2">i2·:·temporaryFileName·()·|·&quot;.html&quot;
  
76 o2·=·/tmp/M2-1101176-0/1.html</code></pre>76 o2·=·/tmp/M2-1060134-0/1.html</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ········</table>79 ········</table>
80 ········<p>This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a·directory·on·the·same·drive·called·<span·class="tt">/tmp</span>.</p>80 ········<p>This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a·directory·on·the·same·drive·called·<span·class="tt">/tmp</span>.</p>
81 ········<p>If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may·be·necessary·to·concatenate·it·with·<a·href="_root__Path.html">rootPath</a>·or·<a·href="_root__U__R__I.html">rootURI</a>·to·enable·the·external·program·to·find·the·file.</p>81 ········<p>If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may·be·necessary·to·concatenate·it·with·<a·href="_root__Path.html">rootPath</a>·or·<a·href="_root__U__R__I.html">rootURI</a>·to·enable·the·external·program·to·find·the·file.</p>
82 ········<p>The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable·<span·class="tt">TMPDIR</span>,·if·it·has·one.</p>82 ········<p>The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable·<span·class="tt">TMPDIR</span>,·if·it·has·one.</p>
83 ········<p>If·<a·title="fork·the·process"·href="_fork.html">fork</a>·is·used,·then·the·parent·and·child·Macaulay2·processes·will·each·remove·their·own·temporary·files·upon·termination,·with·the·parent·removing·any·files·created·before·<a·title="fork·the·process"·href="_fork.html">fork</a>·was·called.</p>83 ········<p>If·<a·title="fork·the·process"·href="_fork.html">fork</a>·is·used,·then·the·parent·and·child·Macaulay2·processes·will·each·remove·their·own·temporary·files·upon·termination,·with·the·parent·removing·any·files·created·before·<a·title="fork·the·process"·href="_fork.html">fork</a>·was·called.</p>
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11 ··········o·a·unique·temporary·file·name.11 ··········o·a·unique·temporary·file·name.
12 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*12 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
13 The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no13 The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no
14 collision·with·existing·files·will·occur.·The·files·will·be·removed·when·the14 collision·with·existing·files·will·occur.·The·files·will·be·removed·when·the
15 program·terminates,·unless·it·terminates·as·the·result·of·an·error.15 program·terminates,·unless·it·terminates·as·the·result·of·an·error.
16 i1·:·temporaryFileName·()·|·".tex"16 i1·:·temporaryFileName·()·|·".tex"
  
17 o1·=·/tmp/M2-1101176-0/0.tex17 o1·=·/tmp/M2-1060134-0/0.tex
18 i2·:·temporaryFileName·()·|·".html"18 i2·:·temporaryFileName·()·|·".html"
  
19 o2·=·/tmp/M2-1101176-0/1.html19 o2·=·/tmp/M2-1060134-0/1.html
20 This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a20 This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a
21 directory·on·the·same·drive·called·/tmp.21 directory·on·the·same·drive·called·/tmp.
22 If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may22 If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may
23 be·necessary·to·concatenate·it·with·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·or·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·to·enable·the·external23 be·necessary·to·concatenate·it·with·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·or·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·to·enable·the·external
24 program·to·find·the·file.24 program·to·find·the·file.
25 The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable25 The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable
26 TMPDIR,·if·it·has·one.26 TMPDIR,·if·it·has·one.
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59 ······</ul>59 ······</ul>
60 ······<div>60 ······<div>
61 ········<h2>Description</h2>61 ········<h2>Description</h2>
62 <span·class="tt">time·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·cpu·time·used,·and·returns·the·value·of·<span·class="tt">e</span>.··The·time·used·by·the·the·current·thread·and·garbage·collection·during·the·evaluation·of·<span·class="tt">e</span>·is·also·shown.········<table·class="examples">62 <span·class="tt">time·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·cpu·time·used,·and·returns·the·value·of·<span·class="tt">e</span>.··The·time·used·by·the·the·current·thread·and·garbage·collection·during·the·evaluation·of·<span·class="tt">e</span>·is·also·shown.········<table·class="examples">
63 ··········<tr>63 ··········<tr>
64 ············<td>64 ············<td>
65 ··············<pre><code·class="language-macaulay2">i1·:·time·3^3065 ··············<pre><code·class="language-macaulay2">i1·:·time·3^30
66 ·--·used·1.5744e-05s·(cpu);·4.767e-06s·(thread);·0s·(gc)66 ·--·used·1.597e-05s·(cpu);·5.33e-06s·(thread);·0s·(gc)
  
67 o1·=·205891132094649</code></pre>67 o1·=·205891132094649</code></pre>
68 ············</td>68 ············</td>
69 ··········</tr>69 ··········</tr>
70 ········</table>70 ········</table>
71 ······</div>71 ······</div>
72 ······<div>72 ······<div>
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7 ····*···Usage:7 ····*···Usage:
8 ············time·e8 ············time·e
9 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
10 time·e·evaluates·e,·prints·the·amount·of·cpu·time·used,·and·returns·the·value10 time·e·evaluates·e,·prints·the·amount·of·cpu·time·used,·and·returns·the·value
11 of·e.·The·time·used·by·the·the·current·thread·and·garbage·collection·during·the11 of·e.·The·time·used·by·the·the·current·thread·and·garbage·collection·during·the
12 evaluation·of·e·is·also·shown.12 evaluation·of·e·is·also·shown.
13 i1·:·time·3^3013 i1·:·time·3^30
14 ·--·used·1.5744e-05s·(cpu);·4.767e-06s·(thread);·0s·(gc)14 ·--·used·1.597e-05s·(cpu);·5.33e-06s·(thread);·0s·(gc)
  
15 o1·=·20589113209464915 o1·=·205891132094649
16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
17 ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation17 ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation
18 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began18 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began
19 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed19 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed
20 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed20 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed
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./usr/share/doc/Macaulay2/Macaulay2Doc/html/_timing.html
    
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54 <span·class="tt">timing·e</span>·evaluates·<span·class="tt">e</span>·and·returns·a·list·of·type·<a·title="the·class·of·all·timing·results"·href="___Time.html">Time</a>·of·the·form·<span·class="tt">{t,v}</span>,·where·<span·class="tt">t</span>·is·the·number·of·seconds·of·cpu·timing·used,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p>54 <span·class="tt">timing·e</span>·evaluates·<span·class="tt">e</span>·and·returns·a·list·of·type·<a·title="the·class·of·all·timing·results"·href="___Time.html">Time</a>·of·the·form·<span·class="tt">{t,v}</span>,·where·<span·class="tt">t</span>·is·the·number·of·seconds·of·cpu·timing·used,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p>
55 The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples">55 The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples">
56 ··········<tr>56 ··········<tr>
57 ············<td>57 ············<td>
58 ··············<pre><code·class="language-macaulay2">i1·:·timing·3^3058 ··············<pre><code·class="language-macaulay2">i1·:·timing·3^30
  
59 o1·=·20589113209464959 o1·=·205891132094649
60 ·····--·.000012869·seconds60 ·····--·.000013385·seconds
  
61 o1·:·Time</code></pre>61 o1·:·Time</code></pre>
62 ············</td>62 ············</td>
63 ··········</tr>63 ··········</tr>
64 ··········<tr>64 ··········<tr>
65 ············<td>65 ············<td>
66 ··············<pre><code·class="language-macaulay2">i2·:·peek·oo66 ··············<pre><code·class="language-macaulay2">i2·:·peek·oo
  
67 o2·=·Time{.000012869,·205891132094649}</code></pre>67 o2·=·Time{.000013385,·205891132094649}</code></pre>
68 ············</td>68 ············</td>
69 ··········</tr>69 ··········</tr>
70 ········</table>70 ········</table>
71 ······</div>71 ······</div>
72 ······<div>72 ······<div>
73 ········<h2>See·also</h2>73 ········<h2>See·also</h2>
74 ········<ul>74 ········<ul>
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10 is·the·number·of·seconds·of·cpu·timing·used,·and·v·is·the·value·of·the10 is·the·number·of·seconds·of·cpu·timing·used,·and·v·is·the·value·of·the
11 expression.11 expression.
12 The·default·method·for·printing·such·timing·results·is·to·display·the·timing12 The·default·method·for·printing·such·timing·results·is·to·display·the·timing
13 separately·in·a·comment·below·the·computed·value.13 separately·in·a·comment·below·the·computed·value.
14 i1·:·timing·3^3014 i1·:·timing·3^30
  
15 o1·=·20589113209464915 o1·=·205891132094649
16 ·····--·.000012869·seconds16 ·····--·.000013385·seconds
  
17 o1·:·Time17 o1·:·Time
18 i2·:·peek·oo18 i2·:·peek·oo
  
19 o2·=·Time{.000012869,·205891132094649}19 o2·=·Time{.000013385,·205891132094649}
20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
21 ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results21 ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results
22 ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation22 ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation
23 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began23 ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began
24 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed24 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed
25 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed25 ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed
26 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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103 ···············&quot;memtailor·version&quot;·=>·1.0103 ···············&quot;memtailor·version&quot;·=>·1.0
104 ···············&quot;mpfi·version&quot;·=>·1.5.4104 ···············&quot;mpfi·version&quot;·=>·1.5.4
105 ···············&quot;mpfr·version&quot;·=>·4.2.2105 ···············&quot;mpfr·version&quot;·=>·4.2.2
106 ···············&quot;mpsolve·version&quot;·=>·3.2.1106 ···············&quot;mpsolve·version&quot;·=>·3.2.1
107 ···············&quot;mysql·version&quot;·=>·not·present107 ···············&quot;mysql·version&quot;·=>·not·present
108 ···············&quot;normaliz·version&quot;·=>·3.10.4108 ···············&quot;normaliz·version&quot;·=>·3.10.4
109 ···············&quot;ntl·version&quot;·=>·11.5.1109 ···············&quot;ntl·version&quot;·=>·11.5.1
110 ···············&quot;operating·system·release&quot;·=>·6.1.0-37-cloud-amd64110 ···············&quot;operating·system·release&quot;·=>·6.12.22+bpo-amd64
111 ···············&quot;operating·system&quot;·=>·Linux111 ···············&quot;operating·system&quot;·=>·Linux
112 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Offset 70, 15 lines modifiedOffset 70, 15 lines modified
70 ·····|···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2|···1,2,2,2·2,2,2,1····1,2,2,1·2,2,2,2|70 ·····|···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2|···1,2,2,2·2,2,2,1····1,2,2,1·2,2,2,2|
71 ·····+-------------------------------------+-------------------------------------+71 ·····+-------------------------------------+-------------------------------------+
72 ·····|-·p·······p········+·p·······p·······|-·p·······p········+·p·······p·······|72 ·····|-·p·······p········+·p·······p·······|-·p·······p········+·p·······p·······|
73 ·····|···1,1,2,1·1,2,1,1····1,1,1,1·1,2,2,1|···1,1,2,2·1,2,1,2····1,1,1,2·1,2,2,2|73 ·····|···1,1,2,1·1,2,1,1····1,1,1,1·1,2,2,1|···1,1,2,2·1,2,1,2····1,1,1,2·1,2,2,2|
74 ·····+-------------------------------------+-------------------------------------+74 ·····+-------------------------------------+-------------------------------------+
  
75 i8·:·time·netList·primaryDecomposition·J75 i8·:·time·netList·primaryDecomposition·J
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77 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+77 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
78 o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|78 o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|
79 ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|79 ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|
80 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+80 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
81 ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|81 ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|
82 ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|82 ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|
6.53 KB
./usr/share/doc/Macaulay2/Markov/html/index.html
    
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161 ········<div>161 ········<div>
162 ··········<p>This·ideal·has·5·primary·components.··The·first·is·the·one·that·has·statistical·significance.·The·significance·of·the·other·components·is·still·poorly·understood.</p>162 ··········<p>This·ideal·has·5·primary·components.··The·first·is·the·one·that·has·statistical·significance.·The·significance·of·the·other·components·is·still·poorly·understood.</p>
163 ········</div>163 ········</div>
164 ········<table·class="examples">164 ········<table·class="examples">
165 ··········<tr>165 ··········<tr>
166 ············<td>166 ············<td>
167 ··············<pre><code·class="language-macaulay2">i8·:·time·netList·primaryDecomposition·J167 ··············<pre><code·class="language-macaulay2">i8·:·time·netList·primaryDecomposition·J
168 ·--·used·2.59445s·(cpu);·1.3595s·(thread);·0s·(gc)168 ·--·used·3.13921s·(cpu);·1.42131s·(thread);·0s·(gc)
  
169 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+169 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
170 o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|170 o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|
171 ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|171 ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|
172 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+172 ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
173 ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|173 ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································|
174 ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|174 ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································|
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102 1,2,2,2|102 1,2,2,2|
103 ·····+-------------------------------------+-----------------------------------103 ·····+-------------------------------------+-----------------------------------
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105 This·ideal·has·5·primary·components.·The·first·is·the·one·that·has·statistical105 This·ideal·has·5·primary·components.·The·first·is·the·one·that·has·statistical
106 significance.·The·significance·of·the·other·components·is·still·poorly106 significance.·The·significance·of·the·other·components·is·still·poorly
107 understood.107 understood.
108 i8·:·time·netList·primaryDecomposition·J108 i8·:·time·netList·primaryDecomposition·J
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110 ·····+-------------------------------------------------------------------------110 ·····+-------------------------------------------------------------------------
111 -------------------------------------------------------------------------------111 -------------------------------------------------------------------------------
112 -------------------------------------------------------------------------------112 -------------------------------------------------------------------------------
113 -------------------------------------------------------------------------------113 -------------------------------------------------------------------------------
114 -------------------------------------------------------------------------------114 -------------------------------------------------------------------------------
115 -------------------------------------------------------------------------------115 -------------------------------------------------------------------------------
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8 aXNBU01VbmlvbihMaXN0KQ==8 aXNBU01VbmlvbihMaXN0KQ==
9 #:len=2859 #:len=285
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzMywgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzMywgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNBU01VbmlvbixMaXN0KSwiaXNBU01VbmlvbihM11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNBU01VbmlvbixMaXN0KSwiaXNBU01VbmlvbihM
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212 ······|·1·-1·1·|212 ······|·1·-1·1·|
213 ······|·0·1··0·|213 ······|·0·1··0·|
  
214 ···············3·······3214 ···············3·······3
215 o22·:·Matrix·ZZ··<--·ZZ215 o22·:·Matrix·ZZ··<--·ZZ
  
216 i23·:·time·schubertRegularity·B216 i23·:·time·schubertRegularity·B
217 ·--·used·0.0671455s·(cpu);·0.0307526s·(thread);·0s·(gc)217 ·--·used·0.0720768s·(cpu);·0.0266332s·(thread);·0s·(gc)
  
218 o23·=·1218 o23·=·1
  
219 i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B219 i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B
220 ·--·used·0.0104054s·(cpu);·0.0133256s·(thread);·0s·(gc)220 ·--·used·0.0147747s·(cpu);·0.0148573s·(thread);·0s·(gc)
  
221 o24·=·1221 o24·=·1
  
222 i25·:·222 i25·:·
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178 ······z···z···z···,·z···z···z····-·z···z···,·z···z···z····-·z···z···)178 ······z···z···z···,·z···z···z····-·z···z···,·z···z···z····-·z···z···)
179 ·······1,2·1,3·2,4···1,2·1,4·2,2····1,2·2,4···1,2·1,3·2,2····1,2·2,3179 ·······1,2·1,3·2,4···1,2·1,4·2,2····1,2·2,4···1,2·1,3·2,2····1,2·2,3
  
180 o15·:·Ideal·of·QQ[z···..z···]180 o15·:·Ideal·of·QQ[z···..z···]
181 ···················1,1···5,5181 ···················1,1···5,5
  
182 i16·:·time·schubertRegularity·p182 i16·:·time·schubertRegularity·p
183 ·--·used·0.000466041s·(cpu);·0.000275565s·(thread);·0s·(gc)183 ·--·used·0.000968997s·(cpu);·0.00028791s·(thread);·0s·(gc)
  
184 o16·=·5184 o16·=·5
  
185 i17·:·time·regularity·comodule·I185 i17·:·time·regularity·comodule·I
186 ·--·used·0.0132587s·(cpu);·0.0154415s·(thread);·0s·(gc)186 ·--·used·0.0147026s·(cpu);·0.0183301s·(thread);·0s·(gc)
  
187 o17·=·5187 o17·=·5
  
188 i18·:·188 i18·:·
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3 i1·:·w·=·{2,1,4,3}3 i1·:·w·=·{2,1,4,3}
  
4 o1·=·{2,·1,·4,·3}4 o1·=·{2,·1,·4,·3}
  
5 o1·:·List5 o1·:·List
  
6 i2·:·time·grothendieckPolynomial·w6 i2·:·time·grothendieckPolynomial·w
7 ·--·used·0.00402705s·(cpu);·0.0040085s·(thread);·0s·(gc)7 ·--·used·0.00402323s·(cpu);·0.00448698s·(thread);·0s·(gc)
  
8 ······2········2······2···············28 ······2········2······2···············2
9 o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x9 o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x
10 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·310 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3
  
11 o2·:·QQ[x·..x·]11 o2·:·QQ[x·..x·]
12 ·········1···412 ·········1···4
  
13 i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream")13 i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream")
14 ·--·used·0.000622527s·(cpu);·0.00226186s·(thread);·0s·(gc)14 ·--·used·0.000264727s·(cpu);·0.00207068s·(thread);·0s·(gc)
  
15 ······2········2······2···············215 ······2········2······2···············2
16 o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x16 o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x
17 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·317 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3
  
18 o3·:·QQ[x·..x·]18 o3·:·QQ[x·..x·]
19 ·········1···419 ·········1···4
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383 ········<div>383 ········<div>
384 ··········<p>Additionally,·this·package·facilitates·investigating·homological·invariants·of·ASM·ideals·such·as·regularity·(<a·title="compute·the·Castelnuovo-Mumford·regularity·of·the·quotient·by·an·ASM·ideal"·href="_schubert__Regularity.html">schubertRegularity</a>)·and·codimension·(<a·title="compute·the·codimension·(i.e.,·height)·of·a·Schubert·determinantal·ideal·or·ASM·ideal"·href="_schubert__Codim.html">schubertCodim</a>).·efficiently·by·computing·the·associated·invariants·for·their·antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17].·Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and·projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal·initial·ideals·by·[CV20].</p>384 ··········<p>Additionally,·this·package·facilitates·investigating·homological·invariants·of·ASM·ideals·such·as·regularity·(<a·title="compute·the·Castelnuovo-Mumford·regularity·of·the·quotient·by·an·ASM·ideal"·href="_schubert__Regularity.html">schubertRegularity</a>)·and·codimension·(<a·title="compute·the·codimension·(i.e.,·height)·of·a·Schubert·determinantal·ideal·or·ASM·ideal"·href="_schubert__Codim.html">schubertCodim</a>).·efficiently·by·computing·the·associated·invariants·for·their·antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17].·Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and·projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal·initial·ideals·by·[CV20].</p>
385 ········</div>385 ········</div>
386 ········<table·class="examples">386 ········<table·class="examples">
387 ··········<tr>387 ··········<tr>
388 ············<td>388 ············<td>
389 ··············<pre><code·class="language-macaulay2">i23·:·time·schubertRegularity·B389 ··············<pre><code·class="language-macaulay2">i23·:·time·schubertRegularity·B
390 ·--·used·0.0671455s·(cpu);·0.0307526s·(thread);·0s·(gc)390 ·--·used·0.0720768s·(cpu);·0.0266332s·(thread);·0s·(gc)
  
391 o23·=·1</code></pre>391 o23·=·1</code></pre>
392 ············</td>392 ············</td>
393 ··········</tr>393 ··········</tr>
394 ··········<tr>394 ··········<tr>
395 ············<td>395 ············<td>
396 ··············<pre><code·class="language-macaulay2">i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B396 ··············<pre><code·class="language-macaulay2">i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B
397 ·--·used·0.0104054s·(cpu);·0.0133256s·(thread);·0s·(gc)397 ·--·used·0.0147747s·(cpu);·0.0148573s·(thread);·0s·(gc)
  
398 o24·=·1</code></pre>398 o24·=·1</code></pre>
399 ············</td>399 ············</td>
400 ··········</tr>400 ··········</tr>
401 ········</table>401 ········</table>
402 ········<div>402 ········<div>
403 ··········<h2>Functions·for·investigating·ASM·varieties</h2>403 ··········<h2>Functions·for·investigating·ASM·varieties</h2>
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244 ASM·ideals·such·as·regularity·(_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y)·and·codimension244 ASM·ideals·such·as·regularity·(_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y)·and·codimension
245 (_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8C_\x8o_\x8d_\x8i_\x8m).·efficiently·by·computing·the·associated·invariants·for·their245 (_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8C_\x8o_\x8d_\x8i_\x8m).·efficiently·by·computing·the·associated·invariants·for·their
246 antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17].246 antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17].
247 Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and247 Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and
248 projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal248 projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal
249 initial·ideals·by·[CV20].249 initial·ideals·by·[CV20].
250 i23·:·time·schubertRegularity·B250 i23·:·time·schubertRegularity·B
251 ·--·used·0.0671455s·(cpu);·0.0307526s·(thread);·0s·(gc)251 ·--·used·0.0720768s·(cpu);·0.0266332s·(thread);·0s·(gc)
  
252 o23·=·1252 o23·=·1
253 i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B253 i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B
254 ·--·used·0.0104054s·(cpu);·0.0133256s·(thread);·0s·(gc)254 ·--·used·0.0147747s·(cpu);·0.0148573s·(thread);·0s·(gc)
  
255 o24·=·1255 o24·=·1
256 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·A\x8AS\x8SM\x8M·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*256 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·A\x8AS\x8SM\x8M·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*
257 ····*·_\x8i_\x8s_\x8P_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·whether·a·matrix·is·a·partial·alternating·sign257 ····*·_\x8i_\x8s_\x8P_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·whether·a·matrix·is·a·partial·alternating·sign
258 ······matrix258 ······matrix
259 ····*·_\x8p_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8T_\x8o_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·extend·a·partial·alternating·sign·matrix·to·an259 ····*·_\x8p_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8T_\x8o_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·extend·a·partial·alternating·sign·matrix·to·an
260 ······alternating·sign·matrix260 ······alternating·sign·matrix
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315 ········<div>315 ········<div>
316 ··········<p>Finally,·this·package·contains·functions·for·investigating·homological·invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial·algorithms·produced·in·[PSW24]·via·<a·title="compute·the·Castelnuovo-Mumford·regularity·of·the·quotient·by·an·ASM·ideal"·href="_schubert__Regularity.html">schubertRegularity</a><a·title="compute·the·codimension·(i.e.,·height)·of·a·Schubert·determinantal·ideal·or·ASM·ideal"·href="_schubert__Codim.html">schubertCodim</a>.</p>316 ··········<p>Finally,·this·package·contains·functions·for·investigating·homological·invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial·algorithms·produced·in·[PSW24]·via·<a·title="compute·the·Castelnuovo-Mumford·regularity·of·the·quotient·by·an·ASM·ideal"·href="_schubert__Regularity.html">schubertRegularity</a><a·title="compute·the·codimension·(i.e.,·height)·of·a·Schubert·determinantal·ideal·or·ASM·ideal"·href="_schubert__Codim.html">schubertCodim</a>.</p>
317 ········</div>317 ········</div>
318 ········<table·class="examples">318 ········<table·class="examples">
319 ··········<tr>319 ··········<tr>
320 ············<td>320 ············<td>
321 ··············<pre><code·class="language-macaulay2">i16·:·time·schubertRegularity·p321 ··············<pre><code·class="language-macaulay2">i16·:·time·schubertRegularity·p
322 ·--·used·0.000466041s·(cpu);·0.000275565s·(thread);·0s·(gc)322 ·--·used·0.000968997s·(cpu);·0.00028791s·(thread);·0s·(gc)
  
323 o16·=·5</code></pre>323 o16·=·5</code></pre>
324 ············</td>324 ············</td>
325 ··········</tr>325 ··········</tr>
326 ··········<tr>326 ··········<tr>
327 ············<td>327 ············<td>
328 ··············<pre><code·class="language-macaulay2">i17·:·time·regularity·comodule·I328 ··············<pre><code·class="language-macaulay2">i17·:·time·regularity·comodule·I
329 ·--·used·0.0132587s·(cpu);·0.0154415s·(thread);·0s·(gc)329 ·--·used·0.0147026s·(cpu);·0.0183301s·(thread);·0s·(gc)
  
330 o17·=·5</code></pre>330 o17·=·5</code></pre>
331 ············</td>331 ············</td>
332 ··········</tr>332 ··········</tr>
333 ········</table>333 ········</table>
334 ········<div>334 ········<div>
335 ··········<h2>Functions·for·investigating·matrix·Schubert·varieties</h2>335 ··········<h2>Functions·for·investigating·matrix·Schubert·varieties</h2>
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545 o15·:·Ideal·of·QQ[z···..z···]545 o15·:·Ideal·of·QQ[z···..z···]
546 ···················1,1···5,5546 ···················1,1···5,5
547 Finally,·this·package·contains·functions·for·investigating·homological547 Finally,·this·package·contains·functions·for·investigating·homological
548 invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial548 invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial
549 algorithms·produced·in·[PSW24]·via·_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8C_\x8o_\x8d_\x8i_\x8m.549 algorithms·produced·in·[PSW24]·via·_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y_\x8s_\x8c_\x8h_\x8u_\x8b_\x8e_\x8r_\x8t_\x8C_\x8o_\x8d_\x8i_\x8m.
550 i16·:·time·schubertRegularity·p550 i16·:·time·schubertRegularity·p
551 ·--·used·0.000466041s·(cpu);·0.000275565s·(thread);·0s·(gc)551 ·--·used·0.000968997s·(cpu);·0.00028791s·(thread);·0s·(gc)
  
552 o16·=·5552 o16·=·5
553 i17·:·time·regularity·comodule·I553 i17·:·time·regularity·comodule·I
554 ·--·used·0.0132587s·(cpu);·0.0154415s·(thread);·0s·(gc)554 ·--·used·0.0147026s·(cpu);·0.0183301s·(thread);·0s·(gc)
  
555 o17·=·5555 o17·=·5
556 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·m\x8ma\x8at\x8tr\x8ri\x8ix\x8x·S\x8Sc\x8ch\x8hu\x8ub\x8be\x8er\x8rt\x8t·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*556 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·m\x8ma\x8at\x8tr\x8ri\x8ix\x8x·S\x8Sc\x8ch\x8hu\x8ub\x8be\x8er\x8rt\x8t·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*
557 ····*·_\x8a_\x8n_\x8t_\x8i_\x8D_\x8i_\x8a_\x8g_\x8I_\x8n_\x8i_\x8t_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·the·(unique)·antidiagonal·initial·ideal·of557 ····*·_\x8a_\x8n_\x8t_\x8i_\x8D_\x8i_\x8a_\x8g_\x8I_\x8n_\x8i_\x8t_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·the·(unique)·antidiagonal·initial·ideal·of
558 ······an·ASM·ideal558 ······an·ASM·ideal
559 ····*·_\x8r_\x8a_\x8n_\x8k_\x8T_\x8a_\x8b_\x8l_\x8e_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·a·table·of·rank·conditions·that·determines·the559 ····*·_\x8r_\x8a_\x8n_\x8k_\x8T_\x8a_\x8b_\x8l_\x8e_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·a·table·of·rank·conditions·that·determines·the
560 ······corresponding·ASM·or·matrix·Schubert·variety560 ······corresponding·ASM·or·matrix·Schubert·variety
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80 o1·:·List</code></pre>80 o1·:·List</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·time·grothendieckPolynomial·w85 ··············<pre><code·class="language-macaulay2">i2·:·time·grothendieckPolynomial·w
86 ·--·used·0.00402705s·(cpu);·0.0040085s·(thread);·0s·(gc)86 ·--·used·0.00402323s·(cpu);·0.00448698s·(thread);·0s·(gc)
  
87 ······2········2······2···············287 ······2········2······2···············2
88 o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x88 o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x
89 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·389 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3
  
90 o2·:·QQ[x·..x·]90 o2·:·QQ[x·..x·]
91 ·········1···4</code></pre>91 ·········1···4</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i3·:·time·grothendieckPolynomial·(w,Algorithm=>&quot;PipeDream&quot;)96 ··············<pre><code·class="language-macaulay2">i3·:·time·grothendieckPolynomial·(w,Algorithm=>&quot;PipeDream&quot;)
97 ·--·used·0.000622527s·(cpu);·0.00226186s·(thread);·0s·(gc)97 ·--·used·0.000264727s·(cpu);·0.00207068s·(thread);·0s·(gc)
  
98 ······2········2······2···············298 ······2········2······2···············2
99 o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x99 o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x
100 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3100 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3
  
101 o3·:·QQ[x·..x·]101 o3·:·QQ[x·..x·]
102 ·········1···4</code></pre>102 ·········1···4</code></pre>
818 B
html2text {}
    
Offset 19, 24 lines modifiedOffset 19, 24 lines modified
19 PipeDream.19 PipeDream.
20 i1·:·w·=·{2,1,4,3}20 i1·:·w·=·{2,1,4,3}
  
21 o1·=·{2,·1,·4,·3}21 o1·=·{2,·1,·4,·3}
  
22 o1·:·List22 o1·:·List
23 i2·:·time·grothendieckPolynomial·w23 i2·:·time·grothendieckPolynomial·w
24 ·--·used·0.00402705s·(cpu);·0.0040085s·(thread);·0s·(gc)24 ·--·used·0.00402323s·(cpu);·0.00448698s·(thread);·0s·(gc)
  
25 ······2········2······2···············225 ······2········2······2···············2
26 o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x26 o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x
27 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·327 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3
  
28 o2·:·QQ[x·..x·]28 o2·:·QQ[x·..x·]
29 ·········1···429 ·········1···4
30 i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream")30 i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream")
31 ·--·used·0.000622527s·(cpu);·0.00226186s·(thread);·0s·(gc)31 ·--·used·0.000264727s·(cpu);·0.00207068s·(thread);·0s·(gc)
  
32 ······2········2······2···············232 ······2········2······2···············2
33 o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x33 o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x
34 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·334 ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3
  
35 o3·:·QQ[x·..x·]35 o3·:·QQ[x·..x·]
36 ·········1···436 ·········1···4
733 B
./usr/share/doc/Macaulay2/Matroids/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=247 #:len=24
8 ZmxhdHMoTWF0cm9pZCxaWixTdHJpbmcp8 ZmxhdHMoTWF0cm9pZCxaWixTdHJpbmcp
9 #:len=2559 #:len=255
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzOSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzOSwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZmxhdHMsTWF0cm9pZCxaWixTdHJpbmcpLCJmbGF011 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZmxhdHMsTWF0cm9pZCxaWixTdHJpbmcpLCJmbGF0
1.19 KB
./usr/share/doc/Macaulay2/Matroids/example-output/___Matroid.out
    
Offset 51, 20 lines modifiedOffset 51, 20 lines modified
51 i9·:·keys·R10.cache51 i9·:·keys·R10.cache
  
52 o9·=·{groundSet,·rankFunction,·storedRepresentation}52 o9·=·{groundSet,·rankFunction,·storedRepresentation}
  
53 o9·:·List53 o9·:·List
  
54 i10·:·time·isWellDefined·R1054 i10·:·time·isWellDefined·R10
55 ·--·used·0.0474558s·(cpu);·0.0450812s·(thread);·0s·(gc)55 ·--·used·0.04803s·(cpu);·0.0464441s·(thread);·0s·(gc)
  
56 o10·=·true56 o10·=·true
  
57 i11·:·time·fVector·R1057 i11·:·time·fVector·R10
58 ·--·used·0.10002s·(cpu);·0.0558813s·(thread);·0s·(gc)58 ·--·used·0.121427s·(cpu);·0.0533265s·(thread);·0s·(gc)
  
59 o11·=·HashTable{0·=>·1·}59 o11·=·HashTable{0·=>·1·}
60 ················1·=>·1060 ················1·=>·10
61 ················2·=>·4561 ················2·=>·45
62 ················3·=>·7562 ················3·=>·75
63 ················4·=>·3063 ················4·=>·30
64 ················5·=>·164 ················5·=>·1
Offset 76, 15 lines modifiedOffset 76, 15 lines modified
76 o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats,76 o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats,
77 ······-----------------------------------------------------------------------77 ······-----------------------------------------------------------------------
78 ······groundSet,·dual,·storedRepresentation}78 ······groundSet,·dual,·storedRepresentation}
  
79 o12·:·List79 o12·:·List
  
80 i13·:·time·fVector·R1080 i13·:·time·fVector·R10
81 ·--·used·0.000290027s·(cpu);·0.000194382s·(thread);·0s·(gc)81 ·--·used·0.000339667s·(cpu);·0.000192911s·(thread);·0s·(gc)
  
82 o13·=·HashTable{0·=>·1·}82 o13·=·HashTable{0·=>·1·}
83 ················1·=>·1083 ················1·=>·10
84 ················2·=>·4584 ················2·=>·45
85 ················3·=>·7585 ················3·=>·75
86 ················4·=>·3086 ················4·=>·30
87 ················5·=>·187 ················5·=>·1
378 B
./usr/share/doc/Macaulay2/Matroids/example-output/_all__Minors.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 i2·:·U25·=·uniformMatroid(2,5)9 i2·:·U25·=·uniformMatroid(2,5)
  
10 o2·=·a·"matroid"·of·rank·2·on·5·elements10 o2·=·a·"matroid"·of·rank·2·on·5·elements
  
11 o2·:·Matroid11 o2·:·Matroid
  
12 i3·:·elapsedTime·L·=·allMinors(V,·U25);12 i3·:·elapsedTime·L·=·allMinors(V,·U25);
13 ·--·.152401s·elapsed13 ·--·.280283s·elapsed
  
14 i4·:·#L14 i4·:·#L
  
15 o4·=·6415 o4·=·64
  
16 i5·:·netList·L_{0..4}16 i5·:·netList·L_{0..4}
  
430 B
./usr/share/doc/Macaulay2/Matroids/example-output/_get__Isos.out
    
Offset 33, 14 lines modifiedOffset 33, 14 lines modified
33 i6·:·F7·=·specificMatroid·"fano"33 i6·:·F7·=·specificMatroid·"fano"
  
34 o6·=·a·"matroid"·of·rank·3·on·7·elements34 o6·=·a·"matroid"·of·rank·3·on·7·elements
  
35 o6·:·Matroid35 o6·:·Matroid
  
36 i7·:·time·autF7·=·getIsos(F7,·F7);36 i7·:·time·autF7·=·getIsos(F7,·F7);
37 ·--·used·0.0400072s·(cpu);·0.0392326s·(thread);·0s·(gc)37 ·--·used·0.0440005s·(cpu);·0.0409594s·(thread);·0s·(gc)
  
38 i8·:·#autF738 i8·:·#autF7
  
39 o8·=·16839 o8·=·168
  
40 i9·:·40 i9·:·
378 B
./usr/share/doc/Macaulay2/Matroids/example-output/_has__Minor.out
    
Offset 9, 12 lines modifiedOffset 9, 12 lines modified
9 o1·:·Sequence9 o1·:·Sequence
  
10 i2·:·hasMinor(M4,·uniformMatroid(2,4))10 i2·:·hasMinor(M4,·uniformMatroid(2,4))
  
11 o2·=·false11 o2·=·false
  
12 i3·:·time·hasMinor(M6,·M5)12 i3·:·time·hasMinor(M6,·M5)
13 ·--·used·1.26113s·(cpu);·0.974736s·(thread);·0s·(gc)13 ·--·used·1.48269s·(cpu);·1.08417s·(thread);·0s·(gc)
  
14 o3·=·true14 o3·=·true
  
15 i4·:·15 i4·:·
996 B
./usr/share/doc/Macaulay2/Matroids/example-output/_isomorphism_lp__Matroid_cm__Matroid_rp.out
    
Offset 19, 15 lines modifiedOffset 19, 15 lines modified
19 i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7})19 i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7})
  
20 o4·=·a·"matroid"·of·rank·4·on·10·elements20 o4·=·a·"matroid"·of·rank·4·on·10·elements
  
21 o4·:·Matroid21 o4·:·Matroid
  
22 i5·:·time·isomorphism(M5,·minorM6)22 i5·:·time·isomorphism(M5,·minorM6)
23 ·--·used·0.0120024s·(cpu);·0.0117393s·(thread);·0s·(gc)23 ·--·used·0.0113714s·(cpu);·0.0119669s·(thread);·0s·(gc)
  
24 o5·=·HashTable{0·=>·1}24 o5·=·HashTable{0·=>·1}
25 ···············1·=>·025 ···············1·=>·0
26 ···············2·=>·326 ···············2·=>·3
27 ···············3·=>·227 ···············3·=>·2
28 ···············4·=>·628 ···············4·=>·6
29 ···············5·=>·529 ···············5·=>·5
Offset 56, 15 lines modifiedOffset 56, 15 lines modified
56 i7·:·N·=·relabel·M656 i7·:·N·=·relabel·M6
  
57 o7·=·a·"matroid"·of·rank·5·on·15·elements57 o7·=·a·"matroid"·of·rank·5·on·15·elements
  
58 o7·:·Matroid58 o7·:·Matroid
  
59 i8·:·time·phi·=·isomorphism(N,M6)59 i8·:·time·phi·=·isomorphism(N,M6)
60 ·--·used·3.71843s·(cpu);·2.46126s·(thread);·0s·(gc)60 ·--·used·4.21313s·(cpu);·2.52616s·(thread);·0s·(gc)
  
61 o8·=·HashTable{0·=>·11·}61 o8·=·HashTable{0·=>·11·}
62 ···············1·=>·062 ···············1·=>·0
63 ···············2·=>·163 ···············2·=>·1
64 ···············3·=>·664 ···············3·=>·6
65 ···············4·=>·965 ···············4·=>·9
66 ···············5·=>·866 ···············5·=>·8
495 B
./usr/share/doc/Macaulay2/Matroids/example-output/_quick__Isomorphism__Test.out
    
Offset 37, 15 lines modifiedOffset 37, 15 lines modified
37 o7·:·Matroid37 o7·:·Matroid
  
38 i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R)38 i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R)
  
39 o9·=·true39 o9·=·true
  
40 i10·:·time·quickIsomorphismTest(M0,·M1)40 i10·:·time·quickIsomorphismTest(M0,·M1)
41 ·--·used·0.00248899s·(cpu);·0.00041916s·(thread);·0s·(gc)41 ·--·used·0.00137112s·(cpu);·0.00047432s·(thread);·0s·(gc)
  
42 o10·=·false42 o10·=·false
  
43 i11·:·value·oo·===·false43 i11·:·value·oo·===·false
  
44 o11·=·true44 o11·=·true
  
456 B
./usr/share/doc/Macaulay2/Matroids/example-output/_set__Representation.out
    
Offset 35, 15 lines modifiedOffset 35, 15 lines modified
35 i5·:·keys·M.cache35 i5·:·keys·M.cache
  
36 o5·=·{groundSet,·rankFunction,·storedRepresentation}36 o5·=·{groundSet,·rankFunction,·storedRepresentation}
  
37 o5·:·List37 o5·:·List
  
38 i6·:·elapsedTime·fVector·M38 i6·:·elapsedTime·fVector·M
39 ·--·.00992246s·elapsed39 ·--·.0289656s·elapsed
  
40 o6·=·HashTable{0·=>·1·}40 o6·=·HashTable{0·=>·1·}
41 ···············1·=>·641 ···············1·=>·6
42 ···············2·=>·1542 ···············2·=>·15
43 ···············3·=>·2043 ···············3·=>·20
44 ···············4·=>·144 ···············4·=>·1
  
2.4 KB
./usr/share/doc/Macaulay2/Matroids/html/___Matroid.html
    
Offset 148, 23 lines modifiedOffset 148, 23 lines modified
  
148 o9·:·List</code></pre>148 o9·:·List</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
152 ············<td>152 ············<td>
153 ··············<pre><code·class="language-macaulay2">i10·:·time·isWellDefined·R10153 ··············<pre><code·class="language-macaulay2">i10·:·time·isWellDefined·R10
154 ·--·used·0.0474558s·(cpu);·0.0450812s·(thread);·0s·(gc)154 ·--·used·0.04803s·(cpu);·0.0464441s·(thread);·0s·(gc)
  
155 o10·=·true</code></pre>155 o10·=·true</code></pre>
156 ············</td>156 ············</td>
157 ··········</tr>157 ··········</tr>
158 ··········<tr>158 ··········<tr>
159 ············<td>159 ············<td>
160 ··············<pre><code·class="language-macaulay2">i11·:·time·fVector·R10160 ··············<pre><code·class="language-macaulay2">i11·:·time·fVector·R10
161 ·--·used·0.10002s·(cpu);·0.0558813s·(thread);·0s·(gc)161 ·--·used·0.121427s·(cpu);·0.0533265s·(thread);·0s·(gc)
  
162 o11·=·HashTable{0·=>·1·}162 o11·=·HashTable{0·=>·1·}
163 ················1·=>·10163 ················1·=>·10
164 ················2·=>·45164 ················2·=>·45
165 ················3·=>·75165 ················3·=>·75
166 ················4·=>·30166 ················4·=>·30
167 ················5·=>·1167 ················5·=>·1
Offset 182, 15 lines modifiedOffset 182, 15 lines modified
  
182 o12·:·List</code></pre>182 o12·:·List</code></pre>
183 ············</td>183 ············</td>
184 ··········</tr>184 ··········</tr>
185 ··········<tr>185 ··········<tr>
186 ············<td>186 ············<td>
187 ··············<pre><code·class="language-macaulay2">i13·:·time·fVector·R10187 ··············<pre><code·class="language-macaulay2">i13·:·time·fVector·R10
188 ·--·used·0.000290027s·(cpu);·0.000194382s·(thread);·0s·(gc)188 ·--·used·0.000339667s·(cpu);·0.000192911s·(thread);·0s·(gc)
  
189 o13·=·HashTable{0·=>·1·}189 o13·=·HashTable{0·=>·1·}
190 ················1·=>·10190 ················1·=>·10
191 ················2·=>·45191 ················2·=>·45
192 ················3·=>·75192 ················3·=>·75
193 ················4·=>·30193 ················4·=>·30
194 ················5·=>·1194 ················5·=>·1
1.1 KB
html2text {}
    
Offset 71, 19 lines modifiedOffset 71, 19 lines modified
71 o8·:·Matroid71 o8·:·Matroid
72 i9·:·keys·R10.cache72 i9·:·keys·R10.cache
  
73 o9·=·{groundSet,·rankFunction,·storedRepresentation}73 o9·=·{groundSet,·rankFunction,·storedRepresentation}
  
74 o9·:·List74 o9·:·List
75 i10·:·time·isWellDefined·R1075 i10·:·time·isWellDefined·R10
76 ·--·used·0.0474558s·(cpu);·0.0450812s·(thread);·0s·(gc)76 ·--·used·0.04803s·(cpu);·0.0464441s·(thread);·0s·(gc)
  
77 o10·=·true77 o10·=·true
78 i11·:·time·fVector·R1078 i11·:·time·fVector·R10
79 ·--·used·0.10002s·(cpu);·0.0558813s·(thread);·0s·(gc)79 ·--·used·0.121427s·(cpu);·0.0533265s·(thread);·0s·(gc)
  
80 o11·=·HashTable{0·=>·1·}80 o11·=·HashTable{0·=>·1·}
81 ················1·=>·1081 ················1·=>·10
82 ················2·=>·4582 ················2·=>·45
83 ················3·=>·7583 ················3·=>·75
84 ················4·=>·3084 ················4·=>·30
85 ················5·=>·185 ················5·=>·1
Offset 93, 15 lines modifiedOffset 93, 15 lines modified
  
93 o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats,93 o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats,
94 ······-----------------------------------------------------------------------94 ······-----------------------------------------------------------------------
95 ······groundSet,·dual,·storedRepresentation}95 ······groundSet,·dual,·storedRepresentation}
  
96 o12·:·List96 o12·:·List
97 i13·:·time·fVector·R1097 i13·:·time·fVector·R10
98 ·--·used·0.000290027s·(cpu);·0.000194382s·(thread);·0s·(gc)98 ·--·used·0.000339667s·(cpu);·0.000192911s·(thread);·0s·(gc)
  
99 o13·=·HashTable{0·=>·1·}99 o13·=·HashTable{0·=>·1·}
100 ················1·=>·10100 ················1·=>·10
101 ················2·=>·45101 ················2·=>·45
102 ················3·=>·75102 ················3·=>·75
103 ················4·=>·30103 ················4·=>·30
104 ················5·=>·1104 ················5·=>·1
885 B
./usr/share/doc/Macaulay2/Matroids/html/_all__Minors.html
    
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92 o2·:·Matroid</code></pre>92 o2·:·Matroid</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·L·=·allMinors(V,·U25);97 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·L·=·allMinors(V,·U25);
98 ·--·.152401s·elapsed</code></pre>98 ·--·.280283s·elapsed</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i4·:·#L103 ··············<pre><code·class="language-macaulay2">i4·:·#L
  
104 o4·=·64</code></pre>104 o4·=·64</code></pre>
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27 o1·:·Matroid27 o1·:·Matroid
28 i2·:·U25·=·uniformMatroid(2,5)28 i2·:·U25·=·uniformMatroid(2,5)
  
29 o2·=·a·"matroid"·of·rank·2·on·5·elements29 o2·=·a·"matroid"·of·rank·2·on·5·elements
  
30 o2·:·Matroid30 o2·:·Matroid
31 i3·:·elapsedTime·L·=·allMinors(V,·U25);31 i3·:·elapsedTime·L·=·allMinors(V,·U25);
32 ·--·.152401s·elapsed32 ·--·.280283s·elapsed
33 i4·:·#L33 i4·:·#L
  
34 o4·=·6434 o4·=·64
35 i5·:·netList·L_{0..4}35 i5·:·netList·L_{0..4}
  
36 ·····+----------+-------+36 ·····+----------+-------+
37 o5·=·|set·{5,·3}|set·{2}|37 o5·=·|set·{5,·3}|set·{2}|
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135 o6·:·Matroid</code></pre>135 o6·:·Matroid</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ··········<tr>138 ··········<tr>
139 ············<td>139 ············<td>
140 ··············<pre><code·class="language-macaulay2">i7·:·time·autF7·=·getIsos(F7,·F7);140 ··············<pre><code·class="language-macaulay2">i7·:·time·autF7·=·getIsos(F7,·F7);
141 ·--·used·0.0400072s·(cpu);·0.0392326s·(thread);·0s·(gc)</code></pre>141 ·--·used·0.0440005s·(cpu);·0.0409594s·(thread);·0s·(gc)</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ··········<tr>144 ··········<tr>
145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i8·:·#autF7146 ··············<pre><code·class="language-macaulay2">i8·:·#autF7
  
147 o8·=·168</code></pre>147 o8·=·168</code></pre>
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51 symmetric·group·S_7:51 symmetric·group·S_7:
52 i6·:·F7·=·specificMatroid·"fano"52 i6·:·F7·=·specificMatroid·"fano"
  
53 o6·=·a·"matroid"·of·rank·3·on·7·elements53 o6·=·a·"matroid"·of·rank·3·on·7·elements
  
54 o6·:·Matroid54 o6·:·Matroid
55 i7·:·time·autF7·=·getIsos(F7,·F7);55 i7·:·time·autF7·=·getIsos(F7,·F7);
56 ·--·used·0.0400072s·(cpu);·0.0392326s·(thread);·0s·(gc)56 ·--·used·0.0440005s·(cpu);·0.0409594s·(thread);·0s·(gc)
57 i8·:·#autF757 i8·:·#autF7
  
58 o8·=·16858 o8·=·168
59 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*59 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
60 ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between60 ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between
61 ······isomorphic·matroids61 ······isomorphic·matroids
62 ····*·_\x8q_\x8u_\x8i_\x8c_\x8k_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8T_\x8e_\x8s_\x8t·--·quick·checks·for·isomorphism·between·matroids62 ····*·_\x8q_\x8u_\x8i_\x8c_\x8k_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8T_\x8e_\x8s_\x8t·--·quick·checks·for·isomorphism·between·matroids
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96 o2·=·false</code></pre>96 o2·=·false</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i3·:·time·hasMinor(M6,·M5)101 ··············<pre><code·class="language-macaulay2">i3·:·time·hasMinor(M6,·M5)
102 ·--·used·1.26113s·(cpu);·0.974736s·(thread);·0s·(gc)102 ·--·used·1.48269s·(cpu);·1.08417s·(thread);·0s·(gc)
  
103 o3·=·true</code></pre>103 o3·=·true</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ········</table>106 ········</table>
107 ······</div>107 ······</div>
108 ······<div>108 ······<div>
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34 ·····elements,·a·"matroid"·of·rank·5·on·15·elements)34 ·····elements,·a·"matroid"·of·rank·5·on·15·elements)
  
35 o1·:·Sequence35 o1·:·Sequence
36 i2·:·hasMinor(M4,·uniformMatroid(2,4))36 i2·:·hasMinor(M4,·uniformMatroid(2,4))
  
37 o2·=·false37 o2·=·false
38 i3·:·time·hasMinor(M6,·M5)38 i3·:·time·hasMinor(M6,·M5)
39 ·--·used·1.26113s·(cpu);·0.974736s·(thread);·0s·(gc)39 ·--·used·1.48269s·(cpu);·1.08417s·(thread);·0s·(gc)
  
40 o3·=·true40 o3·=·true
41 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*41 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
42 ····*·_\x8m_\x8i_\x8n_\x8o_\x8r·--·minor·of·matroid42 ····*·_\x8m_\x8i_\x8n_\x8o_\x8r·--·minor·of·matroid
43 ····*·_\x8i_\x8s_\x8B_\x8i_\x8n_\x8a_\x8r_\x8y·--·whether·a·matroid·is·representable·over·F_243 ····*·_\x8i_\x8s_\x8B_\x8i_\x8n_\x8a_\x8r_\x8y·--·whether·a·matroid·is·representable·over·F_2
44 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ha\x8as\x8sM\x8Mi\x8in\x8no\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*44 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ha\x8as\x8sM\x8Mi\x8in\x8no\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
45 ····*·hasMinor(Matroid,Matroid)45 ····*·hasMinor(Matroid,Matroid)
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118 o4·:·Matroid</code></pre>118 o4·:·Matroid</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i5·:·time·isomorphism(M5,·minorM6)123 ··············<pre><code·class="language-macaulay2">i5·:·time·isomorphism(M5,·minorM6)
124 ·--·used·0.0120024s·(cpu);·0.0117393s·(thread);·0s·(gc)124 ·--·used·0.0113714s·(cpu);·0.0119669s·(thread);·0s·(gc)
  
125 o5·=·HashTable{0·=>·1}125 o5·=·HashTable{0·=>·1}
126 ···············1·=>·0126 ···············1·=>·0
127 ···············2·=>·3127 ···············2·=>·3
128 ···············3·=>·2128 ···············3·=>·2
129 ···············4·=>·6129 ···············4·=>·6
130 ···············5·=>·5130 ···············5·=>·5
Offset 164, 15 lines modifiedOffset 164, 15 lines modified
  
164 o7·:·Matroid</code></pre>164 o7·:·Matroid</code></pre>
165 ············</td>165 ············</td>
166 ··········</tr>166 ··········</tr>
167 ··········<tr>167 ··········<tr>
168 ············<td>168 ············<td>
169 ··············<pre><code·class="language-macaulay2">i8·:·time·phi·=·isomorphism(N,M6)169 ··············<pre><code·class="language-macaulay2">i8·:·time·phi·=·isomorphism(N,M6)
170 ·--·used·3.71843s·(cpu);·2.46126s·(thread);·0s·(gc)170 ·--·used·4.21313s·(cpu);·2.52616s·(thread);·0s·(gc)
  
171 o8·=·HashTable{0·=>·11·}171 o8·=·HashTable{0·=>·11·}
172 ···············1·=>·0172 ···············1·=>·0
173 ···············2·=>·1173 ···············2·=>·1
174 ···············3·=>·6174 ···············3·=>·6
175 ···············4·=>·9175 ···············4·=>·9
176 ···············5·=>·8176 ···············5·=>·8
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40 o3·:·Sequence40 o3·:·Sequence
41 i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7})41 i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7})
  
42 o4·=·a·"matroid"·of·rank·4·on·10·elements42 o4·=·a·"matroid"·of·rank·4·on·10·elements
  
43 o4·:·Matroid43 o4·:·Matroid
44 i5·:·time·isomorphism(M5,·minorM6)44 i5·:·time·isomorphism(M5,·minorM6)
45 ·--·used·0.0120024s·(cpu);·0.0117393s·(thread);·0s·(gc)45 ·--·used·0.0113714s·(cpu);·0.0119669s·(thread);·0s·(gc)
  
46 o5·=·HashTable{0·=>·1}46 o5·=·HashTable{0·=>·1}
47 ···············1·=>·047 ···············1·=>·0
48 ···············2·=>·348 ···············2·=>·3
49 ···············3·=>·249 ···············3·=>·2
50 ···············4·=>·650 ···············4·=>·6
51 ···············5·=>·551 ···············5·=>·5
Offset 74, 15 lines modifiedOffset 74, 15 lines modified
74 o6·:·HashTable74 o6·:·HashTable
75 i7·:·N·=·relabel·M675 i7·:·N·=·relabel·M6
  
76 o7·=·a·"matroid"·of·rank·5·on·15·elements76 o7·=·a·"matroid"·of·rank·5·on·15·elements
  
77 o7·:·Matroid77 o7·:·Matroid
78 i8·:·time·phi·=·isomorphism(N,M6)78 i8·:·time·phi·=·isomorphism(N,M6)
79 ·--·used·3.71843s·(cpu);·2.46126s·(thread);·0s·(gc)79 ·--·used·4.21313s·(cpu);·2.52616s·(thread);·0s·(gc)
  
80 o8·=·HashTable{0·=>·11·}80 o8·=·HashTable{0·=>·11·}
81 ···············1·=>·081 ···············1·=>·0
82 ···············2·=>·182 ···············2·=>·1
83 ···············3·=>·683 ···············3·=>·6
84 ···············4·=>·984 ···············4·=>·9
85 ···············5·=>·885 ···············5·=>·8
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137 o9·=·true</code></pre>137 o9·=·true</code></pre>
138 ············</td>138 ············</td>
139 ··········</tr>139 ··········</tr>
140 ··········<tr>140 ··········<tr>
141 ············<td>141 ············<td>
142 ··············<pre><code·class="language-macaulay2">i10·:·time·quickIsomorphismTest(M0,·M1)142 ··············<pre><code·class="language-macaulay2">i10·:·time·quickIsomorphismTest(M0,·M1)
143 ·--·used·0.00248899s·(cpu);·0.00041916s·(thread);·0s·(gc)143 ·--·used·0.00137112s·(cpu);·0.00047432s·(thread);·0s·(gc)
  
144 o10·=·false</code></pre>144 o10·=·false</code></pre>
145 ············</td>145 ············</td>
146 ··········</tr>146 ··········</tr>
147 ··········<tr>147 ··········<tr>
148 ············<td>148 ············<td>
149 ··············<pre><code·class="language-macaulay2">i11·:·value·oo·===·false149 ··············<pre><code·class="language-macaulay2">i11·:·value·oo·===·false
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51 o7·=·a·"matroid"·of·rank·7·on·11·elements51 o7·=·a·"matroid"·of·rank·7·on·11·elements
  
52 o7·:·Matroid52 o7·:·Matroid
53 i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R)53 i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R)
  
54 o9·=·true54 o9·=·true
55 i10·:·time·quickIsomorphismTest(M0,·M1)55 i10·:·time·quickIsomorphismTest(M0,·M1)
56 ·--·used·0.00248899s·(cpu);·0.00041916s·(thread);·0s·(gc)56 ·--·used·0.00137112s·(cpu);·0.00047432s·(thread);·0s·(gc)
  
57 o10·=·false57 o10·=·false
58 i11·:·value·oo·===·false58 i11·:·value·oo·===·false
  
59 o11·=·true59 o11·=·true
60 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*60 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
61 ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between61 ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between
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126 o5·:·List</code></pre>126 o5·:·List</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·fVector·M131 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·fVector·M
132 ·--·.00992246s·elapsed132 ·--·.0289656s·elapsed
  
133 o6·=·HashTable{0·=>·1·}133 o6·=·HashTable{0·=>·1·}
134 ···············1·=>·6134 ···············1·=>·6
135 ···············2·=>·15135 ···············2·=>·15
136 ···············3·=>·20136 ···············3·=>·20
137 ···············4·=>·1137 ···············4·=>·1
  
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48 o4·:·Matrix·QQ··<--·QQ48 o4·:·Matrix·QQ··<--·QQ
49 i5·:·keys·M.cache49 i5·:·keys·M.cache
  
50 o5·=·{groundSet,·rankFunction,·storedRepresentation}50 o5·=·{groundSet,·rankFunction,·storedRepresentation}
  
51 o5·:·List51 o5·:·List
52 i6·:·elapsedTime·fVector·M52 i6·:·elapsedTime·fVector·M
53 ·--·.00992246s·elapsed53 ·--·.0289656s·elapsed
  
54 o6·=·HashTable{0·=>·1·}54 o6·=·HashTable{0·=>·1·}
55 ···············1·=>·655 ···············1·=>·6
56 ···············2·=>·1556 ···············2·=>·15
57 ···············3·=>·2057 ···············3·=>·20
58 ···············4·=>·158 ···············4·=>·1
  
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./usr/share/doc/Macaulay2/MinimalPrimes/example-output/___Hybrid.out
    
Offset 5, 16 lines modifiedOffset 5, 16 lines modified
5 i2·:·R·=·ZZ/101[w..z];5 i2·:·R·=·ZZ/101[w..z];
  
6 i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2);6 i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2);
  
7 o3·:·Ideal·of·R7 o3·:·Ideal·of·R
  
8 i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2);8 i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2);
9 ··Strategy:·Linear············(time·.00399932)··#primes·=·0·#prunedViaCodim·=·09 ··Strategy:·Linear············(time·0)·········#primes·=·0·#prunedViaCodim·=·0
10 ··Strategy:·Birational········(time·.00813261)··#primes·=·0·#prunedViaCodim·=·010 ··Strategy:·Birational········(time·.0120825)··#primes·=·0·#prunedViaCodim·=·0
11 ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·011 ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0
12 ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes...12 ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes...
13 ·--··Time·taken·:·.072852513 ·--··Time·taken·:·.0743921
14 ·--·.138779s·elapsed14 ·--·.110911s·elapsed
15 (time·0)·········#primes·=·1·#prunedViaCodim·=·015 (time·0)·········#primes·=·1·#prunedViaCodim·=·0
  
16 i5·:·16 i5·:·
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./usr/share/doc/Macaulay2/MinimalPrimes/example-output/_radical.out
    
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30 ·············2········2···3·····230 ·············2········2···3·····2
31 o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·)31 o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·)
  
32 o5·:·Ideal·of·R32 o5·:·Ideal·of·R
  
33 i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial)33 i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial)
34 ·--·.000445142s·elapsed34 ·--·.000668634s·elapsed
  
35 o6·=·ideal·(a,·b,·c)35 o6·=·ideal·(a,·b,·c)
  
36 o6·:·Ideal·of·R36 o6·:·Ideal·of·R
  
37 i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true)37 i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true)
38 ·--·.133367s·elapsed38 ·--·.0835847s·elapsed
  
39 o7·=·ideal·(c,·b,·a)39 o7·=·ideal·(c,·b,·a)
  
40 o7·:·Ideal·of·R40 o7·:·Ideal·of·R
  
41 i8·:·41 i8·:·
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Offset 29, 22 lines modifiedOffset 29, 22 lines modified
29 o5·=·84029 o5·=·840
  
30 i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·030 i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0
  
31 o6·=·true31 o6·=·true
  
32 i7·:·elapsedTime·radicalContainment(x_0,·I)32 i7·:·elapsedTime·radicalContainment(x_0,·I)
33 ·--·.100965s·elapsed33 ·--·.1814s·elapsed
  
34 o7·=·true34 o7·=·true
  
35 i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar")35 i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar")
36 ·--·.00129191s·elapsed36 ·--·.00175592s·elapsed
  
37 o8·=·true37 o8·=·true
  
38 i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar")38 i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar")
39 ·--·.00502951s·elapsed39 ·--·.00139067s·elapsed
  
40 o9·=·false40 o9·=·false
  
41 i10·:·41 i10·:·
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72 o3·:·Ideal·of·R</code></pre>72 o3·:·Ideal·of·R</code></pre>
73 ············</td>73 ············</td>
74 ··········</tr>74 ··········</tr>
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2);77 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2);
78 ··Strategy:·Linear············(time·.00399932)··#primes·=·0·#prunedViaCodim·=·078 ··Strategy:·Linear············(time·0)·········#primes·=·0·#prunedViaCodim·=·0
79 ··Strategy:·Birational········(time·.00813261)··#primes·=·0·#prunedViaCodim·=·079 ··Strategy:·Birational········(time·.0120825)··#primes·=·0·#prunedViaCodim·=·0
80 ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·080 ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0
81 ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes...81 ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes...
82 ·--··Time·taken·:·.072852582 ·--··Time·taken·:·.0743921
83 ·--·.138779s·elapsed83 ·--·.110911s·elapsed
84 (time·0)·········#primes·=·1·#prunedViaCodim·=·0</code></pre>84 (time·0)·········#primes·=·1·#prunedViaCodim·=·0</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ········</table>87 ········</table>
88 ······</div>88 ······</div>
89 ······<div>89 ······<div>
90 ········<h2>See·also</h2>90 ········<h2>See·also</h2>
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11 i1·:·debug·MinimalPrimes11 i1·:·debug·MinimalPrimes
12 i2·:·R·=·ZZ/101[w..z];12 i2·:·R·=·ZZ/101[w..z];
13 i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2);13 i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2);
  
14 o3·:·Ideal·of·R14 o3·:·Ideal·of·R
15 i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid15 i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid
16 {Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2);16 {Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2);
17 ··Strategy:·Linear············(time·.00399932)··#primes·=·0·#prunedViaCodim·=·017 ··Strategy:·Linear············(time·0)·········#primes·=·0·#prunedViaCodim·=·0
18 ··Strategy:·Birational········(time·.00813261)··#primes·=·0·#prunedViaCodim·=·018 ··Strategy:·Birational········(time·.0120825)··#primes·=·0·#prunedViaCodim·=·0
19 ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·019 ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0
20 ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and20 ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and
21 selecting·minimal·primes...21 selecting·minimal·primes...
22 ·--··Time·taken·:·.072852522 ·--··Time·taken·:·.0743921
23 ·--·.138779s·elapsed23 ·--·.110911s·elapsed
24 (time·0)·········#primes·=·1·#prunedViaCodim·=·024 (time·0)·········#primes·=·1·#prunedViaCodim·=·0
25 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*25 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
26 ····*·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n_\x8(_\x8._\x8._\x8._\x8,_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8=_\x8>_\x8._\x8._\x8._\x8)26 ····*·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n_\x8(_\x8._\x8._\x8._\x8,_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8=_\x8>_\x8._\x8._\x8._\x8)
27 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*27 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
28 The·object·_\x8H_\x8y_\x8b_\x8r_\x8i_\x8d·is·a·_\x8s_\x8e_\x8l_\x8f_\x8·_\x8i_\x8n_\x8i_\x8t_\x8i_\x8a_\x8l_\x8i_\x8z_\x8i_\x8n_\x8g_\x8·_\x8t_\x8y_\x8p_\x8e,·with·ancestor·classes·_\x8L_\x8i_\x8s_\x8t·<28 The·object·_\x8H_\x8y_\x8b_\x8r_\x8i_\x8d·is·a·_\x8s_\x8e_\x8l_\x8f_\x8·_\x8i_\x8n_\x8i_\x8t_\x8i_\x8a_\x8l_\x8i_\x8z_\x8i_\x8n_\x8g_\x8·_\x8t_\x8y_\x8p_\x8e,·with·ancestor·classes·_\x8L_\x8i_\x8s_\x8t·<
29 _\x8V_\x8i_\x8s_\x8i_\x8b_\x8l_\x8e_\x8L_\x8i_\x8s_\x8t·<·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8L_\x8i_\x8s_\x8t·<·_\x8T_\x8h_\x8i_\x8n_\x8g.29 _\x8V_\x8i_\x8s_\x8i_\x8b_\x8l_\x8e_\x8L_\x8i_\x8s_\x8t·<·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8L_\x8i_\x8s_\x8t·<·_\x8T_\x8h_\x8i_\x8n_\x8g.
30 ===============================================================================30 ===============================================================================
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131 o5·:·Ideal·of·R</code></pre>131 o5·:·Ideal·of·R</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial)136 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial)
137 ·--·.000445142s·elapsed137 ·--·.000668634s·elapsed
  
138 o6·=·ideal·(a,·b,·c)138 o6·=·ideal·(a,·b,·c)
  
139 o6·:·Ideal·of·R</code></pre>139 o6·:·Ideal·of·R</code></pre>
140 ············</td>140 ············</td>
141 ··········</tr>141 ··········</tr>
142 ··········<tr>142 ··········<tr>
143 ············<td>143 ············<td>
144 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true)144 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true)
145 ·--·.133367s·elapsed145 ·--·.0835847s·elapsed
  
146 o7·=·ideal·(c,·b,·a)146 o7·=·ideal·(c,·b,·a)
  
147 o7·:·Ideal·of·R</code></pre>147 o7·:·Ideal·of·R</code></pre>
148 ············</td>148 ············</td>
149 ··········</tr>149 ··········</tr>
150 ········</table>150 ········</table>
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62 i5·:·I·=·intersect(ideal(a^2,b^2,c),·ideal(a,b^3,c^2))62 i5·:·I·=·intersect(ideal(a^2,b^2,c),·ideal(a,b^3,c^2))
  
63 ·············2········2···3·····263 ·············2········2···3·····2
64 o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·)64 o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·)
  
65 o5·:·Ideal·of·R65 o5·:·Ideal·of·R
66 i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial)66 i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial)
67 ·--·.000445142s·elapsed67 ·--·.000668634s·elapsed
  
68 o6·=·ideal·(a,·b,·c)68 o6·=·ideal·(a,·b,·c)
  
69 o6·:·Ideal·of·R69 o6·:·Ideal·of·R
70 i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true)70 i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true)
71 ·--·.133367s·elapsed71 ·--·.0835847s·elapsed
  
72 o7·=·ideal·(c,·b,·a)72 o7·=·ideal·(c,·b,·a)
  
73 o7·:·Ideal·of·R73 o7·:·Ideal·of·R
74 For·another·example,·see·_\x8P_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n.74 For·another·example,·see·_\x8P_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n.
75 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*75 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*
76 Eisenbud,·Huneke,·Vasconcelos,·Invent.·Math.·110·207-235·(1992).76 Eisenbud,·Huneke,·Vasconcelos,·Invent.·Math.·110·207-235·(1992).
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125 o6·=·true</code></pre>125 o6·=·true</code></pre>
126 ············</td>126 ············</td>
127 ··········</tr>127 ··········</tr>
128 ··········<tr>128 ··········<tr>
129 ············<td>129 ············<td>
130 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radicalContainment(x_0,·I)130 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radicalContainment(x_0,·I)
131 ·--·.100965s·elapsed131 ·--·.1814s·elapsed
  
132 o7·=·true</code></pre>132 o7·=·true</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·&quot;Kollar&quot;)137 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·&quot;Kollar&quot;)
138 ·--·.00129191s·elapsed138 ·--·.00175592s·elapsed
  
139 o8·=·true</code></pre>139 o8·=·true</code></pre>
140 ············</td>140 ············</td>
141 ··········</tr>141 ··········</tr>
142 ··········<tr>142 ··········<tr>
143 ············<td>143 ············<td>
144 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·&quot;Kollar&quot;)144 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·&quot;Kollar&quot;)
145 ·--·.00502951s·elapsed145 ·--·.00139067s·elapsed
  
146 o9·=·false</code></pre>146 o9·=·false</code></pre>
147 ············</td>147 ············</td>
148 ··········</tr>148 ··········</tr>
149 ········</table>149 ········</table>
150 ······</div>150 ······</div>
151 ······<div>151 ······<div>
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50 i5·:·D·=·product(I_*/degree/sum)50 i5·:·D·=·product(I_*/degree/sum)
  
51 o5·=·84051 o5·=·840
52 i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·052 i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0
  
53 o6·=·true53 o6·=·true
54 i7·:·elapsedTime·radicalContainment(x_0,·I)54 i7·:·elapsedTime·radicalContainment(x_0,·I)
55 ·--·.100965s·elapsed55 ·--·.1814s·elapsed
  
56 o7·=·true56 o7·=·true
57 i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar")57 i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar")
58 ·--·.00129191s·elapsed58 ·--·.00175592s·elapsed
  
59 o8·=·true59 o8·=·true
60 i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar")60 i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar")
61 ·--·.00502951s·elapsed61 ·--·.00139067s·elapsed
  
62 o9·=·false62 o9·=·false
63 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*63 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
64 ····*·_\x8r_\x8a_\x8d_\x8i_\x8c_\x8a_\x8l·--·the·radical·of·an·ideal64 ····*·_\x8r_\x8a_\x8d_\x8i_\x8c_\x8a_\x8l·--·the·radical·of·an·ideal
65 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8ad\x8di\x8ic\x8ca\x8al\x8lC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8nm\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*65 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8ad\x8di\x8ic\x8ca\x8al\x8lC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8nm\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*
66 ····*·radicalContainment(Ideal,Ideal)66 ····*·radicalContainment(Ideal,Ideal)
67 ····*·radicalContainment(RingElement,Ideal)67 ····*·radicalContainment(RingElement,Ideal)
724 B
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747 B
./usr/share/doc/Macaulay2/MixedMultiplicity/dump/rawdocumentation.dump
    
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1.44 KB
./usr/share/doc/Macaulay2/MixedMultiplicity/example-output/_multi__Rees__Ideal.out
    
Offset 57, 29 lines modifiedOffset 57, 29 lines modified
57 i9·:·J·=·ideal·vars·U57 i9·:·J·=·ideal·vars·U
  
58 o9·=·ideal·(a,·b,·c)58 o9·=·ideal·(a,·b,·c)
  
59 o9·:·Ideal·of·U59 o9·:·Ideal·of·U
  
60 i10·:·time·multiReesIdeal·J60 i10·:·time·multiReesIdeal·J
61 ·--·used·0.90596s·(cpu);·0.20951s·(thread);·0s·(gc)61 ·--·used·0.852364s·(cpu);·0.152748s·(thread);·0s·(gc)
  
62 ·············································································62 ·············································································
63 o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,63 o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,
64 ················1······2·····1······2·····1······2·····0······2·····0······2·64 ················1······2·····1······2·····1······2·····0······2·····0······2·
65 ······-----------------------------------------------------------------------65 ······-----------------------------------------------------------------------
66 ····················2·················2···266 ····················2·················2···2
67 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)67 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)
68 ·········0······2···1····0·2···0·1····2···0····1·268 ·········0······2···1····0·2···0·1····2···0····1·2
  
69 o10·:·Ideal·of·U[X·..X·]69 o10·:·Ideal·of·U[X·..X·]
70 ··················0···270 ··················0···2
  
71 i11·:·time·multiReesIdeal·(J,·a)71 i11·:·time·multiReesIdeal·(J,·a)
72 ·--·used·0.179996s·(cpu);·0.0363036s·(thread);·0s·(gc)72 ·--·used·0.184817s·(cpu);·0.0302166s·(thread);·0s·(gc)
  
73 ·············································································73 ·············································································
74 o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,74 o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,
75 ················1······2·····1······2·····1······2·····0······2·····0······2·75 ················1······2·····1······2·····1······2·····0······2·····0······2·
76 ······-----------------------------------------------------------------------76 ······-----------------------------------------------------------------------
77 ····················2·················2···277 ····················2·················2···2
78 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)78 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)
2.78 KB
./usr/share/doc/Macaulay2/MixedMultiplicity/html/_multi__Rees__Ideal.html
    
Offset 173, 15 lines modifiedOffset 173, 15 lines modified
  
173 o9·:·Ideal·of·U</code></pre>173 o9·:·Ideal·of·U</code></pre>
174 ············</td>174 ············</td>
175 ··········</tr>175 ··········</tr>
176 ··········<tr>176 ··········<tr>
177 ············<td>177 ············<td>
178 ··············<pre><code·class="language-macaulay2">i10·:·time·multiReesIdeal·J178 ··············<pre><code·class="language-macaulay2">i10·:·time·multiReesIdeal·J
179 ·--·used·0.90596s·(cpu);·0.20951s·(thread);·0s·(gc)179 ·--·used·0.852364s·(cpu);·0.152748s·(thread);·0s·(gc)
  
180 ·············································································180 ·············································································
181 o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,181 o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,
182 ················1······2·····1······2·····1······2·····0······2·····0······2·182 ················1······2·····1······2·····1······2·····0······2·····0······2·
183 ······-----------------------------------------------------------------------183 ······-----------------------------------------------------------------------
184 ····················2·················2···2184 ····················2·················2···2
185 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)185 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)
Offset 190, 15 lines modifiedOffset 190, 15 lines modified
190 o10·:·Ideal·of·U[X·..X·]190 o10·:·Ideal·of·U[X·..X·]
191 ··················0···2</code></pre>191 ··················0···2</code></pre>
192 ············</td>192 ············</td>
193 ··········</tr>193 ··········</tr>
194 ··········<tr>194 ··········<tr>
195 ············<td>195 ············<td>
196 ··············<pre><code·class="language-macaulay2">i11·:·time·multiReesIdeal·(J,·a)196 ··············<pre><code·class="language-macaulay2">i11·:·time·multiReesIdeal·(J,·a)
197 ·--·used·0.179996s·(cpu);·0.0363036s·(thread);·0s·(gc)197 ·--·used·0.184817s·(cpu);·0.0302166s·(thread);·0s·(gc)
  
198 ·············································································198 ·············································································
199 o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,199 o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,
200 ················1······2·····1······2·····1······2·····0······2·····0······2·200 ················1······2·····1······2·····1······2·····0······2·····0······2·
201 ······-----------------------------------------------------------------------201 ······-----------------------------------------------------------------------
202 ····················2·················2···2202 ····················2·················2···2
203 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)203 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)
1.17 KB
html2text {}
    
Offset 79, 28 lines modifiedOffset 79, 28 lines modified
79 i8·:·U·=·T/minors(2,m);79 i8·:·U·=·T/minors(2,m);
80 i9·:·J·=·ideal·vars·U80 i9·:·J·=·ideal·vars·U
  
81 o9·=·ideal·(a,·b,·c)81 o9·=·ideal·(a,·b,·c)
  
82 o9·:·Ideal·of·U82 o9·:·Ideal·of·U
83 i10·:·time·multiReesIdeal·J83 i10·:·time·multiReesIdeal·J
84 ·--·used·0.90596s·(cpu);·0.20951s·(thread);·0s·(gc)84 ·--·used·0.852364s·(cpu);·0.152748s·(thread);·0s·(gc)
  
  
85 o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,85 o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,
86 ················1······2·····1······2·····1······2·····0······2·····0······286 ················1······2·····1······2·····1······2·····0······2·····0······2
87 ······-----------------------------------------------------------------------87 ······-----------------------------------------------------------------------
88 ····················2·················2···288 ····················2·················2···2
89 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)89 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)
90 ·········0······2···1····0·2···0·1····2···0····1·290 ·········0······2···1····0·2···0·1····2···0····1·2
  
91 o10·:·Ideal·of·U[X·..X·]91 o10·:·Ideal·of·U[X·..X·]
92 ··················0···292 ··················0···2
93 i11·:·time·multiReesIdeal·(J,·a)93 i11·:·time·multiReesIdeal·(J,·a)
94 ·--·used·0.179996s·(cpu);·0.0363036s·(thread);·0s·(gc)94 ·--·used·0.184817s·(cpu);·0.0302166s·(thread);·0s·(gc)
  
  
95 o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,95 o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·,
96 ················1······2·····1······2·····1······2·····0······2·····0······296 ················1······2·····1······2·····1······2·····0······2·····0······2
97 ······-----------------------------------------------------------------------97 ······-----------------------------------------------------------------------
98 ····················2·················2···298 ····················2·················2···2
99 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)99 ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·)
742 B
./usr/share/doc/Macaulay2/ModuleDeformations/dump/rawdocumentation.dump
    
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1.43 KB
./usr/share/doc/Macaulay2/ModuleDeformations/example-output/_deform__M__C__M__Module_lp__Module_rp.out
    
Offset 40, 15 lines modifiedOffset 40, 15 lines modified
  
40 o7·=·image·|·x2·y2·|40 o7·=·image·|·x2·y2·|
  
41 ·····························141 ·····························1
42 o7·:·R-module,·submodule·of·R42 o7·:·R-module,·submodule·of·R
  
43 i8·:·(S,N)·=·time·deformMCMModule·N0·43 i8·:·(S,N)·=·time·deformMCMModule·N0·
44 ·--·used·0.398063s·(cpu);·0.282676s·(thread);·0s·(gc)44 ·--·used·0.414926s·(cpu);·0.292135s·(thread);·0s·(gc)
  
45 o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^345 o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3
46 ··················{8}·|·xxi_4-y+xi_3·······································46 ··················{8}·|·xxi_4-y+xi_3·······································
47 ·····------------------------------------------------------------------------47 ·····------------------------------------------------------------------------
48 ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|)48 ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|)
49 ·····-x2-xxi_2-xi_1···········································|49 ·····-x2-xxi_2-xi_1···········································|
  
Offset 70, 15 lines modifiedOffset 70, 15 lines modified
70 o10·=·cokernel·|·x2·y2··|70 o10·=·cokernel·|·x2·y2··|
71 ···············|·-y·-x2·|71 ···············|·-y·-x2·|
  
72 ·····························272 ·····························2
73 o10·:·R-module,·quotient·of·R73 o10·:·R-module,·quotient·of·R
  
74 i11·:·(S',N')·=·time·deformMCMModule·N0'74 i11·:·(S',N')·=·time·deformMCMModule·N0'
75 ·--·used·0.521768s·(cpu);·0.41052s·(thread);·0s·(gc)75 ·--·used·0.638973s·(cpu);·0.473377s·(thread);·0s·(gc)
  
76 o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_176 o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1
77 ····················|·xxi_4-y+xi_3·······································77 ····················|·xxi_4-y+xi_3·······································
78 ······-----------------------------------------------------------------------78 ······-----------------------------------------------------------------------
79 ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|)79 ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|)
80 ······-x2-xxi_2-xi_1·····························|80 ······-x2-xxi_2-xi_1·····························|
  
2.8 KB
./usr/share/doc/Macaulay2/ModuleDeformations/html/_deform__M__C__M__Module_lp__Module_rp.html
    
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145 ·····························1145 ·····························1
146 o7·:·R-module,·submodule·of·R</code></pre>146 o7·:·R-module,·submodule·of·R</code></pre>
147 ············</td>147 ············</td>
148 ··········</tr>148 ··········</tr>
149 ··········<tr>149 ··········<tr>
150 ············<td>150 ············<td>
151 ··············<pre><code·class="language-macaulay2">i8·:·(S,N)·=·time·deformMCMModule·N0·151 ··············<pre><code·class="language-macaulay2">i8·:·(S,N)·=·time·deformMCMModule·N0·
152 ·--·used·0.398063s·(cpu);·0.282676s·(thread);·0s·(gc)152 ·--·used·0.414926s·(cpu);·0.292135s·(thread);·0s·(gc)
  
153 o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3153 o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3
154 ··················{8}·|·xxi_4-y+xi_3·······································154 ··················{8}·|·xxi_4-y+xi_3·······································
155 ·····------------------------------------------------------------------------155 ·····------------------------------------------------------------------------
156 ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|)156 ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|)
157 ·····-x2-xxi_2-xi_1···········································|157 ·····-x2-xxi_2-xi_1···········································|
  
Offset 186, 15 lines modifiedOffset 186, 15 lines modified
186 ·····························2186 ·····························2
187 o10·:·R-module,·quotient·of·R</code></pre>187 o10·:·R-module,·quotient·of·R</code></pre>
188 ············</td>188 ············</td>
189 ··········</tr>189 ··········</tr>
190 ··········<tr>190 ··········<tr>
191 ············<td>191 ············<td>
192 ··············<pre><code·class="language-macaulay2">i11·:·(S',N')·=·time·deformMCMModule·N0'192 ··············<pre><code·class="language-macaulay2">i11·:·(S',N')·=·time·deformMCMModule·N0'
193 ·--·used·0.521768s·(cpu);·0.41052s·(thread);·0s·(gc)193 ·--·used·0.638973s·(cpu);·0.473377s·(thread);·0s·(gc)
  
194 o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1194 o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1
195 ····················|·xxi_4-y+xi_3·······································195 ····················|·xxi_4-y+xi_3·······································
196 ······-----------------------------------------------------------------------196 ······-----------------------------------------------------------------------
197 ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|)197 ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|)
198 ······-x2-xxi_2-xi_1·····························|198 ······-x2-xxi_2-xi_1·····························|
  
1.21 KB
html2text {}
    
Offset 70, 15 lines modifiedOffset 70, 15 lines modified
70 i7·:·N0·=·module·ideal·(x^2,y^2)70 i7·:·N0·=·module·ideal·(x^2,y^2)
  
71 o7·=·image·|·x2·y2·|71 o7·=·image·|·x2·y2·|
  
72 ·····························172 ·····························1
73 o7·:·R-module,·submodule·of·R73 o7·:·R-module,·submodule·of·R
74 i8·:·(S,N)·=·time·deformMCMModule·N074 i8·:·(S,N)·=·time·deformMCMModule·N0
75 ·--·used·0.398063s·(cpu);·0.282676s·(thread);·0s·(gc)75 ·--·used·0.414926s·(cpu);·0.292135s·(thread);·0s·(gc)
  
76 o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^376 o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3
77 ··················{8}·|·xxi_4-y+xi_377 ··················{8}·|·xxi_4-y+xi_3
78 ·····------------------------------------------------------------------------78 ·····------------------------------------------------------------------------
79 ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|)79 ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|)
80 ·····-x2-xxi_2-xi_1···········································|80 ·····-x2-xxi_2-xi_1···········································|
  
Offset 103, 15 lines modifiedOffset 103, 15 lines modified
  
103 o10·=·cokernel·|·x2·y2··|103 o10·=·cokernel·|·x2·y2··|
104 ···············|·-y·-x2·|104 ···············|·-y·-x2·|
  
105 ·····························2105 ·····························2
106 o10·:·R-module,·quotient·of·R106 o10·:·R-module,·quotient·of·R
107 i11·:·(S',N')·=·time·deformMCMModule·N0'107 i11·:·(S',N')·=·time·deformMCMModule·N0'
108 ·--·used·0.521768s·(cpu);·0.41052s·(thread);·0s·(gc)108 ·--·used·0.638973s·(cpu);·0.473377s·(thread);·0s·(gc)
  
109 o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1109 o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1
110 ····················|·xxi_4-y+xi_3110 ····················|·xxi_4-y+xi_3
111 ······-----------------------------------------------------------------------111 ······-----------------------------------------------------------------------
112 ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|)112 ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|)
113 ······-x2-xxi_2-xi_1·····························|113 ······-x2-xxi_2-xi_1·····························|
  
779 B
./usr/share/doc/Macaulay2/MonodromySolver/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=467 #:len=46
8 c3BhcnNlTW9ub2Ryb215U29sdmUoLi4uLE51bWJlck9mUmVwZWF0cz0+Li4uKQ==8 c3BhcnNlTW9ub2Ryb215U29sdmUoLi4uLE51bWJlck9mUmVwZWF0cz0+Li4uKQ==
9 #:len=3459 #:len=345
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tzcGFyc2VNb25vZHJvbXlTb2x2ZSxOdW1iZXJPZlJl11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tzcGFyc2VNb25vZHJvbXlTb2x2ZSxOdW1iZXJPZlJl
1.15 KB
./usr/share/doc/Macaulay2/MonodromySolver/example-output/_dynamic__Flower__Solve.out
    
Offset 3, 27 lines modifiedOffset 3, 27 lines modified
3 i1·:·R·=·CC[a,b,c,d][x,y];3 i1·:·R·=·CC[a,b,c,d][x,y];
  
4 i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};4 i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};
  
5 i3·:·(p0,·x0)·=·createSeedPair·polys;5 i3·:·(p0,·x0)·=·createSeedPair·polys;
  
6 i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0})6 i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0})
7 ·--·.00272893s·elapsed7 ·--·.00287299s·elapsed
8 ·--·.00730117s·elapsed 
9 ·--·.000329827s·elapsed 
10 ·--·.00255376s·elapsed 
11 ·--·.0146902s·elapsed8 ·--·.018689s·elapsed
12 ·--·.000303599s·elapsed9 ·--·.000404799s·elapsed
13 ·--·.00561597s·elapsed 
14 ·--·.00286168s·elapsed10 ·--·.0186731s·elapsed
 11 ·--·.0188651s·elapsed
15 ·--·.000255155s·elapsed12 ·--·.000256801s·elapsed
 13 ·--·.0187656s·elapsed
16 ·--·.00253974s·elapsed14 ·--·.00265803s·elapsed
 15 ·--·.000226875s·elapsed
17 ·--·.00257069s·elapsed16 ·--·.00933203s·elapsed
 17 ·--·.0197389s·elapsed
18 ·--·.000234044s·elapsed18 ·--·.000422362s·elapsed
19 --backup·directory·created:·/tmp/M2-1237418-0/119 --backup·directory·created:·/tmp/M2-1280505-0/1
20 ··H01:·120 ··H01:·1
21 ··H10:·121 ··H10:·1
22 number·of·paths·tracked:·222 number·of·paths·tracked:·2
23 found·1·points·in·the·fiber·so·far23 found·1·points·in·the·fiber·so·far
24 ··H01:·124 ··H01:·1
25 ··H10:·125 ··H10:·1
26 number·of·paths·tracked:·426 number·of·paths·tracked:·4
13.7 KB
./usr/share/doc/Macaulay2/MonodromySolver/example-output/_monodromy__Group.out
    
Offset 15, 128 lines modifiedOffset 15, 128 lines modified
  
15 i7·:·dLoss·=·diff(varMatrix,·gateMatrix{{loss}});15 i7·:·dLoss·=·diff(varMatrix,·gateMatrix{{loss}});
  
16 i8·:·G·=·gateSystem(paramMatrix,varMatrix,transpose·dLoss);16 i8·:·G·=·gateSystem(paramMatrix,varMatrix,transpose·dLoss);
  
17 i9·:·monodromyGroup(G,"msOptions"·=>·{NumberOfEdges=>10})17 i9·:·monodromyGroup(G,"msOptions"·=>·{NumberOfEdges=>10})
  
18 o9·=·{{1,·6,·3,·19,·16,·2,·0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,18 o9·=·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,
19 ·····------------------------------------------------------------------------19 ·····------------------------------------------------------------------------
20 ·····7},·{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,·0,·3,·19,20 ·····20},·{2,·0,·9,·3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·18,
21 ·····------------------------------------------------------------------------21 ·····------------------------------------------------------------------------
22 ·····20,·18},·{11,·10,·8,·13,·6,·20,·9,·18,·12,·4,·14,·19,·2,·5,·1,·16,·7,·0,22 ·····19,·20},·{0,·1,·2,·3,·4,·11,·6,·5,·8,·9,·10,·7,·12,·13,·14,·15,·16,·17,
23 ·····------------------------------------------------------------------------23 ·····------------------------------------------------------------------------
24 ·····3,·15,·17},·{13,·10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,24 ·····18,·19,·20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,
25 ·····------------------------------------------------------------------------25 ·····------------------------------------------------------------------------
26 ·····3,·19,·20,·18},·{15,·9,·0,·7,·10,·8,·14,·12,·13,·1,·4,·2,·16,·17,·6,·11,26 ·····16,·18,·9,·4,·6},·{3,·1,·12,·4,·0,·11,·13,·5,·2,·16,·10,·7,·8,·15,·14,
27 ·····------------------------------------------------------------------------27 ·····------------------------------------------------------------------------
28 ·····3,·5,·19,·20,·18},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,28 ·····6,·17,·9,·18,·19,·20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,
29 ·····------------------------------------------------------------------------29 ·····------------------------------------------------------------------------
30 ·····18,·1,·19,·5,·7,·11},·{10,·9,·7,·0,·12,·17,·2,·3,·11,·8,·4,·15,·5,·14,30 ·····14,·20,·16,·18,·9,·4,·6},·{1,·7,·12,·19,·16,·4,·0,·6,·2,·13,·11,·9,·8,
31 ·····------------------------------------------------------------------------31 ·····------------------------------------------------------------------------
32 ·····6,·13,·1,·16,·19,·20,·18},·{16,·6,·3,·19,·10,·2,·14,·8,·15,·1,·9,·12,32 ·····10,·5,·20,·14,·18,·3,·15,·17},·{1,·16,·12,·19,·11,·15,·5,·17,·2,·7,·0,
33 ·····------------------------------------------------------------------------33 ·····------------------------------------------------------------------------
34 ·····17,·0,·4,·20,·13,·18,·11,·5,·7},·{3,·1,·6,·19,·0,·2,·13,·8,·9,·16,·10,34 ·····3,·8,·10,·13,·20,·14,·18,·9,·4,·6},·{2,·0,·1,·3,·6,·5,·9,·7,·10,·4,·13,
35 ·····------------------------------------------------------------------------35 ·····------------------------------------------------------------------------
36 ·····12,·4,·15,·14,·20,·17,·18,·11,·5,·7},·{15,·1,·0,·7,·4,·8,·6,·12,·13,·9,36 ·····11,·14,·8,·16,·15,·12,·17,·18,·19,·20},·{3,·16,·12,·4,·10,·11,·14,·5,·2,
37 ·····------------------------------------------------------------------------37 ·····------------------------------------------------------------------------
38 ·····10,·2,·16,·17,·14,·11,·3,·5,·19,·20,·18},·{10,·0,·5,·2,·6,·19,·9,·20,·7,38 ·····1,·0,·7,·8,·15,·13,·6,·17,·9,·18,·19,·20},·{12,·1,·7,·17,·16,·9,·0,·4,
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
40 ·····4,·13,·18,·11,·14,·16,·8,·1,·12,·17,·3,·15},·{13,·10,·8,·15,·6,·7,·9,40 ·····11,·13,·10,·6,·5,·2,·14,·3,·8,·15,·20,·18,·19},·{0,·1,·3,·19,·12,·11,·2,
41 ·····------------------------------------------------------------------------41 ·····------------------------------------------------------------------------
42 ·····11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},·{1,·6,·3,·19,·16,·2,42 ·····5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{17,·16,·14,·9,·8,·7,
43 ·····------------------------------------------------------------------------43 ·····------------------------------------------------------------------------
44 ·····0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},·{3,·1,·6,·5,·16,44 ·····12,·11,·1,·2,·0,·5,·10,·3,·13,·4,·15,·6,·20,·18,·19},·{1,·16,·12,·19,
45 ·····------------------------------------------------------------------------45 ·····------------------------------------------------------------------------
46 ·····2,·0,·8,·9,·13,·10,·12,·4,·15,·14,·7,·17,·11,·18,·19,·20},·{11,·10,·12,46 ·····11,·15,·5,·17,·2,·7,·0,·3,·8,·10,·13,·20,·14,·18,·9,·4,·6},·{0,·1,·2,·3,
47 ·····------------------------------------------------------------------------47 ·····------------------------------------------------------------------------
48 ·····13,·6,·20,·9,·18,·2,·4,·14,·19,·8,·5,·1,·16,·7,·0,·3,·15,·17},·{16,·6,48 ·····4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{2,·0,·9,
49 ·····------------------------------------------------------------------------49 ·····------------------------------------------------------------------------
50 ·····3,·19,·10,·2,·14,·8,·15,·1,·9,·12,·17,·0,·4,·20,·13,·18,·11,·5,·7},·{1,50 ·····3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·18,·19,·20},·{0,·9,
51 ·····------------------------------------------------------------------------51 ·····------------------------------------------------------------------------
52 ·····6,·3,·19,·16,·2,·0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},52 ·····2,·3,·10,·5,·14,·7,·8,·1,·4,·11,·12,·13,·6,·15,·16,·17,·18,·19,·20},
53 ·····------------------------------------------------------------------------53 ·····------------------------------------------------------------------------
54 ·····{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,·0,·3,·19,·20,54 ·····{16,·14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,·13,·20,·6,·9,
55 ·····------------------------------------------------------------------------55 ·····------------------------------------------------------------------------
56 ·····18},·{6,·10,·12,·13,·11,·20,·5,·18,·2,·7,·14,·19,·8,·9,·1,·16,·4,·0,·3,56 ·····4},·{2,·1,·0,·3,·4,·5,·6,·7,·13,·9,·10,·11,·16,·8,·14,·15,·12,·17,·18,
57 ·····------------------------------------------------------------------------57 ·····------------------------------------------------------------------------
58 ·····15,·17},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,58 ·····19,·20},·{12,·16,·14,·19,·4,·3,·6,·15,·1,·9,·0,·17,·10,·2,·13,·20,·8,
59 ·····------------------------------------------------------------------------59 ·····------------------------------------------------------------------------
60 ·····18,·19,·20},·{3,·6,·1,·19,·16,·2,·0,·8,·10,·13,·9,·12,·14,·15,·4,·20,60 ·····18,·7,·11,·5},·{0,·1,·7,·17,·12,·18,·2,·19,·11,·8,·10,·20,·5,·13,·14,·3,
61 ·····------------------------------------------------------------------------61 ·····------------------------------------------------------------------------
62 ·····17,·18,·11,·5,·7},·{0,·1,·6,·20,·7,·15,·11,·17,·9,·5,·10,·3,·4,·13,·14,62 ·····16,·15,·6,·9,·4},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,
63 ·····------------------------------------------------------------------------63 ·····------------------------------------------------------------------------
64 ·····18,·16,·19,·2,·8,·12},·{13,·10,·19,·2,·6,·5,·9,·7,·20,·4,·14,·11,·18,64 ·····18,·16,·19,·15,·17,·3},·{12,·16,·7,·17,·10,·9,·14,·4,·11,·1,·0,·6,·5,·2,
65 ·····------------------------------------------------------------------------65 ·····------------------------------------------------------------------------
66 ·····16,·1,·8,·0,·12,·17,·3,·15},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,66 ·····13,·3,·8,·15,·20,·18,·19},·{0,·1,·2,·3,·9,·11,·4,·5,·8,·6,·10,·7,·12,
67 ·····------------------------------------------------------------------------67 ·····------------------------------------------------------------------------
68 ·····13,·14,·18,·16,·19,·15,·17,·3},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,68 ·····13,·14,·15,·16,·17,·18,·19,·20},·{16,·7,·12,·19,·9,·1,·4,·10,·2,·6,·11,
69 ·····------------------------------------------------------------------------69 ·····------------------------------------------------------------------------
70 ·····12,·13,·14,·15,·16,·17,·18,·19,·20},·{7,·10,·8,·13,·6,·20,·9,·18,·12,·4,70 ·····14,·8,·0,·5,·20,·13,·18,·3,·15,·17},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,
71 ·····------------------------------------------------------------------------71 ·····------------------------------------------------------------------------
72 ·····14,·19,·2,·11,·1,·16,·5,·0,·3,·15,·17},·{7,·1,·9,·0,·12,·17,·2,·3,·4,·8,72 ·····11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{12,·16,·3,·19,·10,·11,·14,·5,
73 ·····------------------------------------------------------------------------73 ·····------------------------------------------------------------------------
74 ·····10,·15,·6,·11,·14,·13,·5,·16,·19,·20,·18},·{1,·6,·3,·19,·16,·2,·0,·8,74 ·····15,·1,·0,·7,·17,·2,·13,·20,·8,·18,·9,·4,·6},·{0,·9,·2,·3,·10,·5,·14,·7,
75 ·····------------------------------------------------------------------------75 ·····------------------------------------------------------------------------
76 ·····15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},·{0,·1,·15,·20,·4,·8,·6,76 ·····8,·1,·4,·11,·12,·13,·6,·15,·16,·17,·18,·19,·20},·{0,·1,·2,·3,·4,·5,·6,
77 ·····------------------------------------------------------------------------77 ·····------------------------------------------------------------------------
78 ·····12,·17,·9,·10,·2,·3,·13,·14,·18,·16,·19,·5,·7,·11},·{6,·10,·12,·13,·11,78 ·····7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{12,·1,·3,·19,·0,
79 ·····------------------------------------------------------------------------79 ·····------------------------------------------------------------------------
80 ·····20,·5,·18,·2,·7,·14,·19,·8,·9,·1,·16,·4,·0,·3,·15,·17},·{0,·1,·2,·3,·4,80 ·····11,·13,·5,·15,·16,·10,·7,·17,·2,·14,·20,·8,·18,·9,·4,·6},·{0,·1,·3,·19,
81 ·····------------------------------------------------------------------------81 ·····------------------------------------------------------------------------
82 ·····5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{0,·9,·15,82 ·····12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{4,·1,·2,
83 ·····------------------------------------------------------------------------83 ·····------------------------------------------------------------------------
84 ·····20,·10,·8,·14,·12,·17,·1,·4,·2,·3,·13,·6,·18,·16,·19,·5,·7,·11},·{13,84 ·····3,·0,·5,·13,·7,·8,·16,·10,·11,·12,·6,·14,·15,·9,·17,·18,·19,·20},·{0,·1,
85 ·····------------------------------------------------------------------------85 ·····------------------------------------------------------------------------
86 ·····10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},86 ·····3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{0,
87 ·····------------------------------------------------------------------------87 ·····------------------------------------------------------------------------
88 ·····{16,·6,·3,·19,·1,·2,·10,·8,·15,·14,·9,·12,·17,·0,·4,·20,·13,·18,·11,·5,88 ·····1,·7,·17,·12,·18,·2,·19,·11,·8,·10,·20,·5,·13,·14,·3,·16,·15,·6,·9,·4},
89 ·····------------------------------------------------------------------------89 ·····------------------------------------------------------------------------
90 ·····7},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,·18,·1,·19,·5,90 ·····{0,·14,·12,·19,·11,·15,·5,·17,·2,·7,·1,·3,·8,·13,·10,·20,·16,·18,·9,·4,
91 ·····------------------------------------------------------------------------91 ·····------------------------------------------------------------------------
92 ·····7,·11},·{13,·10,·19,·2,·6,·5,·9,·7,·20,·4,·14,·11,·18,·16,·1,·8,·0,·12,92 ·····6},·{2,·0,·9,·3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·20,
93 ·····------------------------------------------------------------------------93 ·····------------------------------------------------------------------------
94 ·····17,·3,·15},·{16,·1,·3,·19,·9,·2,·4,·8,·15,·6,·10,·12,·17,·0,·14,·20,·13,94 ·····18,·19},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,
95 ·····------------------------------------------------------------------------95 ·····------------------------------------------------------------------------
96 ·····18,·11,·5,·7},·{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,96 ·····18,·9,·4,·6},·{16,·14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,
97 ·····------------------------------------------------------------------------97 ·····------------------------------------------------------------------------
98 ·····0,·3,·18,·19,·20},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,98 ·····13,·20,·6,·9,·4},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,
99 ·····------------------------------------------------------------------------99 ·····------------------------------------------------------------------------
100 ·····18,·1,·19,·5,·7,·11},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,100 ·····18,·16,·19,·15,·17,·3},·{3,·16,·14,·4,·5,·2,·7,·8,·1,·11,·0,·12,·10,·15,
101 ·····------------------------------------------------------------------------101 ·····------------------------------------------------------------------------
102 ·····15,·16,·17,·18,·19,·20},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,102 ·····13,·6,·17,·9,·18,·19,·20},·{12,·16,·14,·19,·4,·7,·6,·11,·1,·9,·0,·5,·10,
103 ·····------------------------------------------------------------------------103 ·····------------------------------------------------------------------------
104 ·····14,·18,·16,·19,·15,·17,·3},·{19,·14,·4,·16,·2,·3,·8,·15,·6,·12,·1,·17,104 ·····2,·13,·20,·8,·18,·3,·15,·17},·{16,·1,·7,·17,·12,·18,·2,·19,·11,·8,·10,
105 ·····------------------------------------------------------------------------105 ·····------------------------------------------------------------------------
106 ·····9,·20,·10,·0,·18,·13,·11,·5,·7},·{0,·1,·6,·20,·7,·2,·11,·8,·9,·5,·10,106 ·····20,·5,·0,·14,·3,·13,·15,·6,·9,·4},·{0,·1,·3,·19,·12,·5,·2,·7,·15,·8,·10,
107 ·····------------------------------------------------------------------------107 ·····------------------------------------------------------------------------
108 ·····12,·4,·13,·14,·18,·16,·19,·15,·17,·3},·{13,·1,·19,·2,·6,·5,·9,·7,·20,·4,108 ·····11,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{12,·16,·7,·17,·10,·9,·14,·4,·11,
109 ·····------------------------------------------------------------------------109 ·····------------------------------------------------------------------------
110 ·····10,·11,·18,·16,·14,·8,·0,·12,·17,·3,·15},·{3,·1,·2,·19,·4,·16,·6,·0,·8,110 ·····1,·0,·6,·5,·2,·13,·3,·8,·15,·18,·19,·20},·{12,·16,·14,·17,·4,·7,·6,·11,
111 ·····------------------------------------------------------------------------111 ·····------------------------------------------------------------------------
112 ·····9,·10,·13,·12,·15,·14,·20,·17,·18,·11,·5,·7},·{0,·1,·2,·3,·4,·5,·6,·7,112 ·····1,·9,·0,·5,·10,·2,·13,·3,·8,·15,·20,·18,·19},·{0,·1,·3,·19,·12,·11,·2,
113 ·····------------------------------------------------------------------------113 ·····------------------------------------------------------------------------
114 ·····8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·19,·20,·18},·{0,·1,·6,·3,·7,·2,114 ·····5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{0,·1,·2,·20,·6,·5,
115 ·····------------------------------------------------------------------------115 ·····------------------------------------------------------------------------
116 ·····11,·8,·9,·5,·10,·12,·4,·13,·14,·15,·16,·17,·18,·19,·20},·{13,·10,·8,·15,116 ·····9,·7,·8,·4,·10,·11,·12,·13,·14,·18,·16,·19,·15,·17,·3},·{4,·16,·14,·3,
117 ·····------------------------------------------------------------------------117 ·····------------------------------------------------------------------------
118 ·····6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},·{0,·1,·2,118 ·····5,·2,·7,·8,·1,·11,·0,·12,·10,·6,·13,·15,·9,·17,·18,·19,·20},·{12,·16,·7,
119 ·····------------------------------------------------------------------------119 ·····------------------------------------------------------------------------
120 ·····20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,·14,·18,·16,·19,·15,·17,·3},·{16,120 ·····17,·10,·9,·14,·4,·11,·1,·0,·6,·5,·2,·13,·3,·8,·15,·20,·18,·19},·{0,·11,
121 ·····------------------------------------------------------------------------121 ·····------------------------------------------------------------------------
122 ·····14,·4,·19,·2,·3,·8,·15,·6,·12,·1,·17,·9,·0,·10,·20,·13,·18,·11,·5,·7},122 ·····2,·3,·10,·4,·14,·6,·8,·1,·5,·9,·12,·13,·7,·15,·16,·17,·18,·19,·20},·{16,
123 ·····------------------------------------------------------------------------123 ·····------------------------------------------------------------------------
124 ·····{6,·10,·7,·13,·2,·20,·8,·18,·11,·12,·14,·19,·5,·9,·1,·16,·4,·0,·3,·15,124 ·····14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,·13,·20,·6,·9,·4},
125 ·····------------------------------------------------------------------------125 ·····------------------------------------------------------------------------
126 ·····17},·{13,·10,·8,·15,·4,·7,·6,·11,·12,·9,·14,·5,·2,·16,·1,·17,·0,·3,·19,126 ·····{2,·0,·11,·3,·10,·4,·14,·6,·5,·1,·13,·9,·7,·8,·16,·15,·12,·17,·18,·19,
127 ·····------------------------------------------------------------------------127 ·····------------------------------------------------------------------------
128 ·····20,·18},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,·18,·1,128 ·····20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,
129 ·····------------------------------------------------------------------------129 ·····------------------------------------------------------------------------
130 ·····19,·5,·7,·11},·{13,·10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,130 ·····9,·4,·6},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,
131 ·····------------------------------------------------------------------------131 ·····------------------------------------------------------------------------
132 ·····0,·3,·19,·20,·18},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,·14,132 ·····18,·9,·4,·6},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,·18,
133 ·····------------------------------------------------------------------------133 ·····------------------------------------------------------------------------
134 ·····18,·16,·19,·15,·17,·3}}134 ·····16,·19,·15,·17,·3}}
  
135 o9·:·List135 o9·:·List
  
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Offset 96, 27 lines modifiedOffset 96, 27 lines modified
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i3·:·(p0,·x0)·=·createSeedPair·polys;</code></pre>97 ··············<pre><code·class="language-macaulay2">i3·:·(p0,·x0)·=·createSeedPair·polys;</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0})102 ··············<pre><code·class="language-macaulay2">i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0})
103 ·--·.00272893s·elapsed103 ·--·.00287299s·elapsed
104 ·--·.00730117s·elapsed 
105 ·--·.000329827s·elapsed 
106 ·--·.00255376s·elapsed 
107 ·--·.0146902s·elapsed104 ·--·.018689s·elapsed
108 ·--·.000303599s·elapsed105 ·--·.000404799s·elapsed
109 ·--·.00561597s·elapsed 
110 ·--·.00286168s·elapsed106 ·--·.0186731s·elapsed
 107 ·--·.0188651s·elapsed
111 ·--·.000255155s·elapsed108 ·--·.000256801s·elapsed
 109 ·--·.0187656s·elapsed
112 ·--·.00253974s·elapsed110 ·--·.00265803s·elapsed
 111 ·--·.000226875s·elapsed
113 ·--·.00257069s·elapsed112 ·--·.00933203s·elapsed
 113 ·--·.0197389s·elapsed
114 ·--·.000234044s·elapsed114 ·--·.000422362s·elapsed
115 --backup·directory·created:·/tmp/M2-1237418-0/1115 --backup·directory·created:·/tmp/M2-1280505-0/1
116 ··H01:·1116 ··H01:·1
117 ··H10:·1117 ··H10:·1
118 number·of·paths·tracked:·2118 number·of·paths·tracked:·2
119 found·1·points·in·the·fiber·so·far119 found·1·points·in·the·fiber·so·far
120 ··H01:·1120 ··H01:·1
121 ··H10:·1121 ··H10:·1
122 number·of·paths·tracked:·4122 number·of·paths·tracked:·4
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html2text {}
    
Offset 22, 27 lines modifiedOffset 22, 27 lines modified
22 ··········o·npaths,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,22 ··········o·npaths,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,
23 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
24 Output·is·verbose.·For·other·dynamic·strategies,·see·_\x8M_\x8o_\x8n_\x8o_\x8d_\x8r_\x8o_\x8m_\x8y_\x8S_\x8o_\x8l_\x8v_\x8e_\x8r_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.24 Output·is·verbose.·For·other·dynamic·strategies,·see·_\x8M_\x8o_\x8n_\x8o_\x8d_\x8r_\x8o_\x8m_\x8y_\x8S_\x8o_\x8l_\x8v_\x8e_\x8r_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
25 i1·:·R·=·CC[a,b,c,d][x,y];25 i1·:·R·=·CC[a,b,c,d][x,y];
26 i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};26 i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};
27 i3·:·(p0,·x0)·=·createSeedPair·polys;27 i3·:·(p0,·x0)·=·createSeedPair·polys;
28 i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0})28 i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0})
29 ·--·.00272893s·elapsed29 ·--·.00287299s·elapsed
30 ·--·.00730117s·elapsed 
31 ·--·.000329827s·elapsed 
32 ·--·.00255376s·elapsed 
33 ·--·.0146902s·elapsed30 ·--·.018689s·elapsed
34 ·--·.000303599s·elapsed31 ·--·.000404799s·elapsed
35 ·--·.00561597s·elapsed 
36 ·--·.00286168s·elapsed32 ·--·.0186731s·elapsed
 33 ·--·.0188651s·elapsed
37 ·--·.000255155s·elapsed34 ·--·.000256801s·elapsed
 35 ·--·.0187656s·elapsed
38 ·--·.00253974s·elapsed36 ·--·.00265803s·elapsed
 37 ·--·.000226875s·elapsed
39 ·--·.00257069s·elapsed38 ·--·.00933203s·elapsed
 39 ·--·.0197389s·elapsed
40 ·--·.000234044s·elapsed40 ·--·.000422362s·elapsed
41 --backup·directory·created:·/tmp/M2-1237418-0/141 --backup·directory·created:·/tmp/M2-1280505-0/1
42 ··H01:·142 ··H01:·1
43 ··H10:·143 ··H10:·1
44 number·of·paths·tracked:·244 number·of·paths·tracked:·2
45 found·1·points·in·the·fiber·so·far45 found·1·points·in·the·fiber·so·far
46 ··H01:·146 ··H01:·1
47 ··H10:·147 ··H10:·1
48 number·of·paths·tracked:·448 number·of·paths·tracked:·4
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./usr/share/doc/Macaulay2/MonodromySolver/html/_monodromy__Group.html
    
Offset 118, 131 lines modifiedOffset 118, 131 lines modified
118 ··············<pre><code·class="language-macaulay2">i8·:·G·=·gateSystem(paramMatrix,varMatrix,transpose·dLoss);</code></pre>118 ··············<pre><code·class="language-macaulay2">i8·:·G·=·gateSystem(paramMatrix,varMatrix,transpose·dLoss);</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i9·:·monodromyGroup(G,&quot;msOptions&quot;·=>·{NumberOfEdges=>10})123 ··············<pre><code·class="language-macaulay2">i9·:·monodromyGroup(G,&quot;msOptions&quot;·=>·{NumberOfEdges=>10})
  
124 o9·=·{{1,·6,·3,·19,·16,·2,·0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,124 o9·=·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,
125 ·····------------------------------------------------------------------------125 ·····------------------------------------------------------------------------
126 ·····7},·{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,·0,·3,·19,126 ·····20},·{2,·0,·9,·3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·18,
127 ·····------------------------------------------------------------------------127 ·····------------------------------------------------------------------------
128 ·····20,·18},·{11,·10,·8,·13,·6,·20,·9,·18,·12,·4,·14,·19,·2,·5,·1,·16,·7,·0,128 ·····19,·20},·{0,·1,·2,·3,·4,·11,·6,·5,·8,·9,·10,·7,·12,·13,·14,·15,·16,·17,
129 ·····------------------------------------------------------------------------129 ·····------------------------------------------------------------------------
130 ·····3,·15,·17},·{13,·10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,130 ·····18,·19,·20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,
131 ·····------------------------------------------------------------------------131 ·····------------------------------------------------------------------------
132 ·····3,·19,·20,·18},·{15,·9,·0,·7,·10,·8,·14,·12,·13,·1,·4,·2,·16,·17,·6,·11,132 ·····16,·18,·9,·4,·6},·{3,·1,·12,·4,·0,·11,·13,·5,·2,·16,·10,·7,·8,·15,·14,
133 ·····------------------------------------------------------------------------133 ·····------------------------------------------------------------------------
134 ·····3,·5,·19,·20,·18},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,134 ·····6,·17,·9,·18,·19,·20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,
135 ·····------------------------------------------------------------------------135 ·····------------------------------------------------------------------------
136 ·····18,·1,·19,·5,·7,·11},·{10,·9,·7,·0,·12,·17,·2,·3,·11,·8,·4,·15,·5,·14,136 ·····14,·20,·16,·18,·9,·4,·6},·{1,·7,·12,·19,·16,·4,·0,·6,·2,·13,·11,·9,·8,
137 ·····------------------------------------------------------------------------137 ·····------------------------------------------------------------------------
138 ·····6,·13,·1,·16,·19,·20,·18},·{16,·6,·3,·19,·10,·2,·14,·8,·15,·1,·9,·12,138 ·····10,·5,·20,·14,·18,·3,·15,·17},·{1,·16,·12,·19,·11,·15,·5,·17,·2,·7,·0,
139 ·····------------------------------------------------------------------------139 ·····------------------------------------------------------------------------
140 ·····17,·0,·4,·20,·13,·18,·11,·5,·7},·{3,·1,·6,·19,·0,·2,·13,·8,·9,·16,·10,140 ·····3,·8,·10,·13,·20,·14,·18,·9,·4,·6},·{2,·0,·1,·3,·6,·5,·9,·7,·10,·4,·13,
141 ·····------------------------------------------------------------------------141 ·····------------------------------------------------------------------------
142 ·····12,·4,·15,·14,·20,·17,·18,·11,·5,·7},·{15,·1,·0,·7,·4,·8,·6,·12,·13,·9,142 ·····11,·14,·8,·16,·15,·12,·17,·18,·19,·20},·{3,·16,·12,·4,·10,·11,·14,·5,·2,
143 ·····------------------------------------------------------------------------143 ·····------------------------------------------------------------------------
144 ·····10,·2,·16,·17,·14,·11,·3,·5,·19,·20,·18},·{10,·0,·5,·2,·6,·19,·9,·20,·7,144 ·····1,·0,·7,·8,·15,·13,·6,·17,·9,·18,·19,·20},·{12,·1,·7,·17,·16,·9,·0,·4,
145 ·····------------------------------------------------------------------------145 ·····------------------------------------------------------------------------
146 ·····4,·13,·18,·11,·14,·16,·8,·1,·12,·17,·3,·15},·{13,·10,·8,·15,·6,·7,·9,146 ·····11,·13,·10,·6,·5,·2,·14,·3,·8,·15,·20,·18,·19},·{0,·1,·3,·19,·12,·11,·2,
147 ·····------------------------------------------------------------------------147 ·····------------------------------------------------------------------------
148 ·····11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},·{1,·6,·3,·19,·16,·2,148 ·····5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{17,·16,·14,·9,·8,·7,
149 ·····------------------------------------------------------------------------149 ·····------------------------------------------------------------------------
150 ·····0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},·{3,·1,·6,·5,·16,150 ·····12,·11,·1,·2,·0,·5,·10,·3,·13,·4,·15,·6,·20,·18,·19},·{1,·16,·12,·19,
151 ·····------------------------------------------------------------------------151 ·····------------------------------------------------------------------------
152 ·····2,·0,·8,·9,·13,·10,·12,·4,·15,·14,·7,·17,·11,·18,·19,·20},·{11,·10,·12,152 ·····11,·15,·5,·17,·2,·7,·0,·3,·8,·10,·13,·20,·14,·18,·9,·4,·6},·{0,·1,·2,·3,
153 ·····------------------------------------------------------------------------153 ·····------------------------------------------------------------------------
154 ·····13,·6,·20,·9,·18,·2,·4,·14,·19,·8,·5,·1,·16,·7,·0,·3,·15,·17},·{16,·6,154 ·····4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{2,·0,·9,
155 ·····------------------------------------------------------------------------155 ·····------------------------------------------------------------------------
156 ·····3,·19,·10,·2,·14,·8,·15,·1,·9,·12,·17,·0,·4,·20,·13,·18,·11,·5,·7},·{1,156 ·····3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·18,·19,·20},·{0,·9,
157 ·····------------------------------------------------------------------------157 ·····------------------------------------------------------------------------
158 ·····6,·3,·19,·16,·2,·0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},158 ·····2,·3,·10,·5,·14,·7,·8,·1,·4,·11,·12,·13,·6,·15,·16,·17,·18,·19,·20},
159 ·····------------------------------------------------------------------------159 ·····------------------------------------------------------------------------
160 ·····{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,·0,·3,·19,·20,160 ·····{16,·14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,·13,·20,·6,·9,
161 ·····------------------------------------------------------------------------161 ·····------------------------------------------------------------------------
162 ·····18},·{6,·10,·12,·13,·11,·20,·5,·18,·2,·7,·14,·19,·8,·9,·1,·16,·4,·0,·3,162 ·····4},·{2,·1,·0,·3,·4,·5,·6,·7,·13,·9,·10,·11,·16,·8,·14,·15,·12,·17,·18,
163 ·····------------------------------------------------------------------------163 ·····------------------------------------------------------------------------
164 ·····15,·17},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,164 ·····19,·20},·{12,·16,·14,·19,·4,·3,·6,·15,·1,·9,·0,·17,·10,·2,·13,·20,·8,
165 ·····------------------------------------------------------------------------165 ·····------------------------------------------------------------------------
166 ·····18,·19,·20},·{3,·6,·1,·19,·16,·2,·0,·8,·10,·13,·9,·12,·14,·15,·4,·20,166 ·····18,·7,·11,·5},·{0,·1,·7,·17,·12,·18,·2,·19,·11,·8,·10,·20,·5,·13,·14,·3,
167 ·····------------------------------------------------------------------------167 ·····------------------------------------------------------------------------
168 ·····17,·18,·11,·5,·7},·{0,·1,·6,·20,·7,·15,·11,·17,·9,·5,·10,·3,·4,·13,·14,168 ·····16,·15,·6,·9,·4},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,
169 ·····------------------------------------------------------------------------169 ·····------------------------------------------------------------------------
170 ·····18,·16,·19,·2,·8,·12},·{13,·10,·19,·2,·6,·5,·9,·7,·20,·4,·14,·11,·18,170 ·····18,·16,·19,·15,·17,·3},·{12,·16,·7,·17,·10,·9,·14,·4,·11,·1,·0,·6,·5,·2,
171 ·····------------------------------------------------------------------------171 ·····------------------------------------------------------------------------
172 ·····16,·1,·8,·0,·12,·17,·3,·15},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,172 ·····13,·3,·8,·15,·20,·18,·19},·{0,·1,·2,·3,·9,·11,·4,·5,·8,·6,·10,·7,·12,
173 ·····------------------------------------------------------------------------173 ·····------------------------------------------------------------------------
174 ·····13,·14,·18,·16,·19,·15,·17,·3},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,174 ·····13,·14,·15,·16,·17,·18,·19,·20},·{16,·7,·12,·19,·9,·1,·4,·10,·2,·6,·11,
175 ·····------------------------------------------------------------------------175 ·····------------------------------------------------------------------------
176 ·····12,·13,·14,·15,·16,·17,·18,·19,·20},·{7,·10,·8,·13,·6,·20,·9,·18,·12,·4,176 ·····14,·8,·0,·5,·20,·13,·18,·3,·15,·17},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,
177 ·····------------------------------------------------------------------------177 ·····------------------------------------------------------------------------
178 ·····14,·19,·2,·11,·1,·16,·5,·0,·3,·15,·17},·{7,·1,·9,·0,·12,·17,·2,·3,·4,·8,178 ·····11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{12,·16,·3,·19,·10,·11,·14,·5,
179 ·····------------------------------------------------------------------------179 ·····------------------------------------------------------------------------
180 ·····10,·15,·6,·11,·14,·13,·5,·16,·19,·20,·18},·{1,·6,·3,·19,·16,·2,·0,·8,180 ·····15,·1,·0,·7,·17,·2,·13,·20,·8,·18,·9,·4,·6},·{0,·9,·2,·3,·10,·5,·14,·7,
181 ·····------------------------------------------------------------------------181 ·····------------------------------------------------------------------------
182 ·····15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},·{0,·1,·15,·20,·4,·8,·6,182 ·····8,·1,·4,·11,·12,·13,·6,·15,·16,·17,·18,·19,·20},·{0,·1,·2,·3,·4,·5,·6,
183 ·····------------------------------------------------------------------------183 ·····------------------------------------------------------------------------
184 ·····12,·17,·9,·10,·2,·3,·13,·14,·18,·16,·19,·5,·7,·11},·{6,·10,·12,·13,·11,184 ·····7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{12,·1,·3,·19,·0,
185 ·····------------------------------------------------------------------------185 ·····------------------------------------------------------------------------
186 ·····20,·5,·18,·2,·7,·14,·19,·8,·9,·1,·16,·4,·0,·3,·15,·17},·{0,·1,·2,·3,·4,186 ·····11,·13,·5,·15,·16,·10,·7,·17,·2,·14,·20,·8,·18,·9,·4,·6},·{0,·1,·3,·19,
187 ·····------------------------------------------------------------------------187 ·····------------------------------------------------------------------------
188 ·····5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{0,·9,·15,188 ·····12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{4,·1,·2,
189 ·····------------------------------------------------------------------------189 ·····------------------------------------------------------------------------
190 ·····20,·10,·8,·14,·12,·17,·1,·4,·2,·3,·13,·6,·18,·16,·19,·5,·7,·11},·{13,190 ·····3,·0,·5,·13,·7,·8,·16,·10,·11,·12,·6,·14,·15,·9,·17,·18,·19,·20},·{0,·1,
191 ·····------------------------------------------------------------------------191 ·····------------------------------------------------------------------------
192 ·····10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},192 ·····3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{0,
193 ·····------------------------------------------------------------------------193 ·····------------------------------------------------------------------------
194 ·····{16,·6,·3,·19,·1,·2,·10,·8,·15,·14,·9,·12,·17,·0,·4,·20,·13,·18,·11,·5,194 ·····1,·7,·17,·12,·18,·2,·19,·11,·8,·10,·20,·5,·13,·14,·3,·16,·15,·6,·9,·4},
195 ·····------------------------------------------------------------------------195 ·····------------------------------------------------------------------------
196 ·····7},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,·18,·1,·19,·5,196 ·····{0,·14,·12,·19,·11,·15,·5,·17,·2,·7,·1,·3,·8,·13,·10,·20,·16,·18,·9,·4,
197 ·····------------------------------------------------------------------------197 ·····------------------------------------------------------------------------
198 ·····7,·11},·{13,·10,·19,·2,·6,·5,·9,·7,·20,·4,·14,·11,·18,·16,·1,·8,·0,·12,198 ·····6},·{2,·0,·9,·3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·20,
199 ·····------------------------------------------------------------------------199 ·····------------------------------------------------------------------------
200 ·····17,·3,·15},·{16,·1,·3,·19,·9,·2,·4,·8,·15,·6,·10,·12,·17,·0,·14,·20,·13,200 ·····18,·19},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,
201 ·····------------------------------------------------------------------------201 ·····------------------------------------------------------------------------
202 ·····18,·11,·5,·7},·{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,202 ·····18,·9,·4,·6},·{16,·14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,
203 ·····------------------------------------------------------------------------203 ·····------------------------------------------------------------------------
204 ·····0,·3,·18,·19,·20},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,204 ·····13,·20,·6,·9,·4},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,
205 ·····------------------------------------------------------------------------205 ·····------------------------------------------------------------------------
206 ·····18,·1,·19,·5,·7,·11},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,206 ·····18,·16,·19,·15,·17,·3},·{3,·16,·14,·4,·5,·2,·7,·8,·1,·11,·0,·12,·10,·15,
207 ·····------------------------------------------------------------------------207 ·····------------------------------------------------------------------------
208 ·····15,·16,·17,·18,·19,·20},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,208 ·····13,·6,·17,·9,·18,·19,·20},·{12,·16,·14,·19,·4,·7,·6,·11,·1,·9,·0,·5,·10,
209 ·····------------------------------------------------------------------------209 ·····------------------------------------------------------------------------
210 ·····14,·18,·16,·19,·15,·17,·3},·{19,·14,·4,·16,·2,·3,·8,·15,·6,·12,·1,·17,210 ·····2,·13,·20,·8,·18,·3,·15,·17},·{16,·1,·7,·17,·12,·18,·2,·19,·11,·8,·10,
211 ·····------------------------------------------------------------------------211 ·····------------------------------------------------------------------------
212 ·····9,·20,·10,·0,·18,·13,·11,·5,·7},·{0,·1,·6,·20,·7,·2,·11,·8,·9,·5,·10,212 ·····20,·5,·0,·14,·3,·13,·15,·6,·9,·4},·{0,·1,·3,·19,·12,·5,·2,·7,·15,·8,·10,
213 ·····------------------------------------------------------------------------213 ·····------------------------------------------------------------------------
214 ·····12,·4,·13,·14,·18,·16,·19,·15,·17,·3},·{13,·1,·19,·2,·6,·5,·9,·7,·20,·4,214 ·····11,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{12,·16,·7,·17,·10,·9,·14,·4,·11,
215 ·····------------------------------------------------------------------------215 ·····------------------------------------------------------------------------
216 ·····10,·11,·18,·16,·14,·8,·0,·12,·17,·3,·15},·{3,·1,·2,·19,·4,·16,·6,·0,·8,216 ·····1,·0,·6,·5,·2,·13,·3,·8,·15,·18,·19,·20},·{12,·16,·14,·17,·4,·7,·6,·11,
217 ·····------------------------------------------------------------------------217 ·····------------------------------------------------------------------------
218 ·····9,·10,·13,·12,·15,·14,·20,·17,·18,·11,·5,·7},·{0,·1,·2,·3,·4,·5,·6,·7,218 ·····1,·9,·0,·5,·10,·2,·13,·3,·8,·15,·20,·18,·19},·{0,·1,·3,·19,·12,·11,·2,
219 ·····------------------------------------------------------------------------219 ·····------------------------------------------------------------------------
220 ·····8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·19,·20,·18},·{0,·1,·6,·3,·7,·2,220 ·····5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{0,·1,·2,·20,·6,·5,
221 ·····------------------------------------------------------------------------221 ·····------------------------------------------------------------------------
222 ·····11,·8,·9,·5,·10,·12,·4,·13,·14,·15,·16,·17,·18,·19,·20},·{13,·10,·8,·15,222 ·····9,·7,·8,·4,·10,·11,·12,·13,·14,·18,·16,·19,·15,·17,·3},·{4,·16,·14,·3,
223 ·····------------------------------------------------------------------------223 ·····------------------------------------------------------------------------
224 ·····6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},·{0,·1,·2,224 ·····5,·2,·7,·8,·1,·11,·0,·12,·10,·6,·13,·15,·9,·17,·18,·19,·20},·{12,·16,·7,
225 ·····------------------------------------------------------------------------225 ·····------------------------------------------------------------------------
226 ·····20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,·14,·18,·16,·19,·15,·17,·3},·{16,226 ·····17,·10,·9,·14,·4,·11,·1,·0,·6,·5,·2,·13,·3,·8,·15,·20,·18,·19},·{0,·11,
227 ·····------------------------------------------------------------------------227 ·····------------------------------------------------------------------------
228 ·····14,·4,·19,·2,·3,·8,·15,·6,·12,·1,·17,·9,·0,·10,·20,·13,·18,·11,·5,·7},228 ·····2,·3,·10,·4,·14,·6,·8,·1,·5,·9,·12,·13,·7,·15,·16,·17,·18,·19,·20},·{16,
229 ·····------------------------------------------------------------------------229 ·····------------------------------------------------------------------------
230 ·····{6,·10,·7,·13,·2,·20,·8,·18,·11,·12,·14,·19,·5,·9,·1,·16,·4,·0,·3,·15,230 ·····14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,·13,·20,·6,·9,·4},
231 ·····------------------------------------------------------------------------231 ·····------------------------------------------------------------------------
232 ·····17},·{13,·10,·8,·15,·4,·7,·6,·11,·12,·9,·14,·5,·2,·16,·1,·17,·0,·3,·19,232 ·····{2,·0,·11,·3,·10,·4,·14,·6,·5,·1,·13,·9,·7,·8,·16,·15,·12,·17,·18,·19,
233 ·····------------------------------------------------------------------------233 ·····------------------------------------------------------------------------
234 ·····20,·18},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,·18,·1,234 ·····20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,
235 ·····------------------------------------------------------------------------235 ·····------------------------------------------------------------------------
236 ·····19,·5,·7,·11},·{13,·10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,236 ·····9,·4,·6},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,
237 ·····------------------------------------------------------------------------237 ·····------------------------------------------------------------------------
238 ·····0,·3,·19,·20,·18},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,·14,238 ·····18,·9,·4,·6},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,·18,
239 ·····------------------------------------------------------------------------239 ·····------------------------------------------------------------------------
240 ·····18,·16,·19,·15,·17,·3}}240 ·····16,·19,·15,·17,·3}}
  
241 o9·:·List</code></pre>241 o9·:·List</code></pre>
242 ············</td>242 ············</td>
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Offset 32, 131 lines modifiedOffset 32, 131 lines modified
32 i4·:·varMatrix·=·gateMatrix{{t_1,t_2}};32 i4·:·varMatrix·=·gateMatrix{{t_1,t_2}};
33 i5·:·phi·=·transpose·gateMatrix{{t_1^3,·t_1^2*t_2,·t_1*t_2^2,·t_2^3}};33 i5·:·phi·=·transpose·gateMatrix{{t_1^3,·t_1^2*t_2,·t_1*t_2^2,·t_2^3}};
34 i6·:·loss·=·sum·for·i·from·0·to·3·list·(u_i·-·phi_(i,0))^2;34 i6·:·loss·=·sum·for·i·from·0·to·3·list·(u_i·-·phi_(i,0))^2;
35 i7·:·dLoss·=·diff(varMatrix,·gateMatrix{{loss}});35 i7·:·dLoss·=·diff(varMatrix,·gateMatrix{{loss}});
36 i8·:·G·=·gateSystem(paramMatrix,varMatrix,transpose·dLoss);36 i8·:·G·=·gateSystem(paramMatrix,varMatrix,transpose·dLoss);
37 i9·:·monodromyGroup(G,"msOptions"·=>·{NumberOfEdges=>10})37 i9·:·monodromyGroup(G,"msOptions"·=>·{NumberOfEdges=>10})
  
38 o9·=·{{1,·6,·3,·19,·16,·2,·0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,38 o9·=·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
40 ·····7},·{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,·0,·3,·19,40 ·····20},·{2,·0,·9,·3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·18,
41 ·····------------------------------------------------------------------------41 ·····------------------------------------------------------------------------
42 ·····20,·18},·{11,·10,·8,·13,·6,·20,·9,·18,·12,·4,·14,·19,·2,·5,·1,·16,·7,·0,42 ·····19,·20},·{0,·1,·2,·3,·4,·11,·6,·5,·8,·9,·10,·7,·12,·13,·14,·15,·16,·17,
43 ·····------------------------------------------------------------------------43 ·····------------------------------------------------------------------------
44 ·····3,·15,·17},·{13,·10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,44 ·····18,·19,·20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,
45 ·····------------------------------------------------------------------------45 ·····------------------------------------------------------------------------
46 ·····3,·19,·20,·18},·{15,·9,·0,·7,·10,·8,·14,·12,·13,·1,·4,·2,·16,·17,·6,·11,46 ·····16,·18,·9,·4,·6},·{3,·1,·12,·4,·0,·11,·13,·5,·2,·16,·10,·7,·8,·15,·14,
47 ·····------------------------------------------------------------------------47 ·····------------------------------------------------------------------------
48 ·····3,·5,·19,·20,·18},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,48 ·····6,·17,·9,·18,·19,·20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,
49 ·····------------------------------------------------------------------------49 ·····------------------------------------------------------------------------
50 ·····18,·1,·19,·5,·7,·11},·{10,·9,·7,·0,·12,·17,·2,·3,·11,·8,·4,·15,·5,·14,50 ·····14,·20,·16,·18,·9,·4,·6},·{1,·7,·12,·19,·16,·4,·0,·6,·2,·13,·11,·9,·8,
51 ·····------------------------------------------------------------------------51 ·····------------------------------------------------------------------------
52 ·····6,·13,·1,·16,·19,·20,·18},·{16,·6,·3,·19,·10,·2,·14,·8,·15,·1,·9,·12,52 ·····10,·5,·20,·14,·18,·3,·15,·17},·{1,·16,·12,·19,·11,·15,·5,·17,·2,·7,·0,
53 ·····------------------------------------------------------------------------53 ·····------------------------------------------------------------------------
54 ·····17,·0,·4,·20,·13,·18,·11,·5,·7},·{3,·1,·6,·19,·0,·2,·13,·8,·9,·16,·10,54 ·····3,·8,·10,·13,·20,·14,·18,·9,·4,·6},·{2,·0,·1,·3,·6,·5,·9,·7,·10,·4,·13,
55 ·····------------------------------------------------------------------------55 ·····------------------------------------------------------------------------
56 ·····12,·4,·15,·14,·20,·17,·18,·11,·5,·7},·{15,·1,·0,·7,·4,·8,·6,·12,·13,·9,56 ·····11,·14,·8,·16,·15,·12,·17,·18,·19,·20},·{3,·16,·12,·4,·10,·11,·14,·5,·2,
57 ·····------------------------------------------------------------------------57 ·····------------------------------------------------------------------------
58 ·····10,·2,·16,·17,·14,·11,·3,·5,·19,·20,·18},·{10,·0,·5,·2,·6,·19,·9,·20,·7,58 ·····1,·0,·7,·8,·15,·13,·6,·17,·9,·18,·19,·20},·{12,·1,·7,·17,·16,·9,·0,·4,
59 ·····------------------------------------------------------------------------59 ·····------------------------------------------------------------------------
60 ·····4,·13,·18,·11,·14,·16,·8,·1,·12,·17,·3,·15},·{13,·10,·8,·15,·6,·7,·9,60 ·····11,·13,·10,·6,·5,·2,·14,·3,·8,·15,·20,·18,·19},·{0,·1,·3,·19,·12,·11,·2,
61 ·····------------------------------------------------------------------------61 ·····------------------------------------------------------------------------
62 ·····11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},·{1,·6,·3,·19,·16,·2,62 ·····5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{17,·16,·14,·9,·8,·7,
63 ·····------------------------------------------------------------------------63 ·····------------------------------------------------------------------------
64 ·····0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},·{3,·1,·6,·5,·16,64 ·····12,·11,·1,·2,·0,·5,·10,·3,·13,·4,·15,·6,·20,·18,·19},·{1,·16,·12,·19,
65 ·····------------------------------------------------------------------------65 ·····------------------------------------------------------------------------
66 ·····2,·0,·8,·9,·13,·10,·12,·4,·15,·14,·7,·17,·11,·18,·19,·20},·{11,·10,·12,66 ·····11,·15,·5,·17,·2,·7,·0,·3,·8,·10,·13,·20,·14,·18,·9,·4,·6},·{0,·1,·2,·3,
67 ·····------------------------------------------------------------------------67 ·····------------------------------------------------------------------------
68 ·····13,·6,·20,·9,·18,·2,·4,·14,·19,·8,·5,·1,·16,·7,·0,·3,·15,·17},·{16,·6,68 ·····4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{2,·0,·9,
69 ·····------------------------------------------------------------------------69 ·····------------------------------------------------------------------------
70 ·····3,·19,·10,·2,·14,·8,·15,·1,·9,·12,·17,·0,·4,·20,·13,·18,·11,·5,·7},·{1,70 ·····3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·18,·19,·20},·{0,·9,
71 ·····------------------------------------------------------------------------71 ·····------------------------------------------------------------------------
72 ·····6,·3,·19,·16,·2,·0,·8,·15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},72 ·····2,·3,·10,·5,·14,·7,·8,·1,·4,·11,·12,·13,·6,·15,·16,·17,·18,·19,·20},
73 ·····------------------------------------------------------------------------73 ·····------------------------------------------------------------------------
74 ·····{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,·0,·3,·19,·20,74 ·····{16,·14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,·13,·20,·6,·9,
75 ·····------------------------------------------------------------------------75 ·····------------------------------------------------------------------------
76 ·····18},·{6,·10,·12,·13,·11,·20,·5,·18,·2,·7,·14,·19,·8,·9,·1,·16,·4,·0,·3,76 ·····4},·{2,·1,·0,·3,·4,·5,·6,·7,·13,·9,·10,·11,·16,·8,·14,·15,·12,·17,·18,
77 ·····------------------------------------------------------------------------77 ·····------------------------------------------------------------------------
78 ·····15,·17},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,78 ·····19,·20},·{12,·16,·14,·19,·4,·3,·6,·15,·1,·9,·0,·17,·10,·2,·13,·20,·8,
79 ·····------------------------------------------------------------------------79 ·····------------------------------------------------------------------------
80 ·····18,·19,·20},·{3,·6,·1,·19,·16,·2,·0,·8,·10,·13,·9,·12,·14,·15,·4,·20,80 ·····18,·7,·11,·5},·{0,·1,·7,·17,·12,·18,·2,·19,·11,·8,·10,·20,·5,·13,·14,·3,
81 ·····------------------------------------------------------------------------81 ·····------------------------------------------------------------------------
82 ·····17,·18,·11,·5,·7},·{0,·1,·6,·20,·7,·15,·11,·17,·9,·5,·10,·3,·4,·13,·14,82 ·····16,·15,·6,·9,·4},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,
83 ·····------------------------------------------------------------------------83 ·····------------------------------------------------------------------------
84 ·····18,·16,·19,·2,·8,·12},·{13,·10,·19,·2,·6,·5,·9,·7,·20,·4,·14,·11,·18,84 ·····18,·16,·19,·15,·17,·3},·{12,·16,·7,·17,·10,·9,·14,·4,·11,·1,·0,·6,·5,·2,
85 ·····------------------------------------------------------------------------85 ·····------------------------------------------------------------------------
86 ·····16,·1,·8,·0,·12,·17,·3,·15},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,86 ·····13,·3,·8,·15,·20,·18,·19},·{0,·1,·2,·3,·9,·11,·4,·5,·8,·6,·10,·7,·12,
87 ·····------------------------------------------------------------------------87 ·····------------------------------------------------------------------------
88 ·····13,·14,·18,·16,·19,·15,·17,·3},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,88 ·····13,·14,·15,·16,·17,·18,·19,·20},·{16,·7,·12,·19,·9,·1,·4,·10,·2,·6,·11,
89 ·····------------------------------------------------------------------------89 ·····------------------------------------------------------------------------
90 ·····12,·13,·14,·15,·16,·17,·18,·19,·20},·{7,·10,·8,·13,·6,·20,·9,·18,·12,·4,90 ·····14,·8,·0,·5,·20,·13,·18,·3,·15,·17},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,
91 ·····------------------------------------------------------------------------91 ·····------------------------------------------------------------------------
92 ·····14,·19,·2,·11,·1,·16,·5,·0,·3,·15,·17},·{7,·1,·9,·0,·12,·17,·2,·3,·4,·8,92 ·····11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{12,·16,·3,·19,·10,·11,·14,·5,
93 ·····------------------------------------------------------------------------93 ·····------------------------------------------------------------------------
94 ·····10,·15,·6,·11,·14,·13,·5,·16,·19,·20,·18},·{1,·6,·3,·19,·16,·2,·0,·8,94 ·····15,·1,·0,·7,·17,·2,·13,·20,·8,·18,·9,·4,·6},·{0,·9,·2,·3,·10,·5,·14,·7,
95 ·····------------------------------------------------------------------------95 ·····------------------------------------------------------------------------
96 ·····15,·13,·9,·12,·17,·10,·4,·20,·14,·18,·11,·5,·7},·{0,·1,·15,·20,·4,·8,·6,96 ·····8,·1,·4,·11,·12,·13,·6,·15,·16,·17,·18,·19,·20},·{0,·1,·2,·3,·4,·5,·6,
97 ·····------------------------------------------------------------------------97 ·····------------------------------------------------------------------------
98 ·····12,·17,·9,·10,·2,·3,·13,·14,·18,·16,·19,·5,·7,·11},·{6,·10,·12,·13,·11,98 ·····7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{12,·1,·3,·19,·0,
99 ·····------------------------------------------------------------------------99 ·····------------------------------------------------------------------------
100 ·····20,·5,·18,·2,·7,·14,·19,·8,·9,·1,·16,·4,·0,·3,·15,·17},·{0,·1,·2,·3,·4,100 ·····11,·13,·5,·15,·16,·10,·7,·17,·2,·14,·20,·8,·18,·9,·4,·6},·{0,·1,·3,·19,
101 ·····------------------------------------------------------------------------101 ·····------------------------------------------------------------------------
102 ·····5,·6,·7,·8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·18,·19,·20},·{0,·9,·15,102 ·····12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{4,·1,·2,
103 ·····------------------------------------------------------------------------103 ·····------------------------------------------------------------------------
104 ·····20,·10,·8,·14,·12,·17,·1,·4,·2,·3,·13,·6,·18,·16,·19,·5,·7,·11},·{13,104 ·····3,·0,·5,·13,·7,·8,·16,·10,·11,·12,·6,·14,·15,·9,·17,·18,·19,·20},·{0,·1,
105 ·····------------------------------------------------------------------------105 ·····------------------------------------------------------------------------
106 ·····10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},106 ·····3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{0,
107 ·····------------------------------------------------------------------------107 ·····------------------------------------------------------------------------
108 ·····{16,·6,·3,·19,·1,·2,·10,·8,·15,·14,·9,·12,·17,·0,·4,·20,·13,·18,·11,·5,108 ·····1,·7,·17,·12,·18,·2,·19,·11,·8,·10,·20,·5,·13,·14,·3,·16,·15,·6,·9,·4},
109 ·····------------------------------------------------------------------------109 ·····------------------------------------------------------------------------
110 ·····7},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,·18,·1,·19,·5,110 ·····{0,·14,·12,·19,·11,·15,·5,·17,·2,·7,·1,·3,·8,·13,·10,·20,·16,·18,·9,·4,
111 ·····------------------------------------------------------------------------111 ·····------------------------------------------------------------------------
112 ·····7,·11},·{13,·10,·19,·2,·6,·5,·9,·7,·20,·4,·14,·11,·18,·16,·1,·8,·0,·12,112 ·····6},·{2,·0,·9,·3,·10,·5,·14,·7,·4,·1,·13,·11,·6,·8,·16,·15,·12,·17,·20,
113 ·····------------------------------------------------------------------------113 ·····------------------------------------------------------------------------
114 ·····17,·3,·15},·{16,·1,·3,·19,·9,·2,·4,·8,·15,·6,·10,·12,·17,·0,·14,·20,·13,114 ·····18,·19},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,
115 ·····------------------------------------------------------------------------115 ·····------------------------------------------------------------------------
116 ·····18,·11,·5,·7},·{13,·10,·5,·15,·4,·12,·6,·2,·7,·9,·14,·8,·11,·16,·1,·17,116 ·····18,·9,·4,·6},·{16,·14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,
117 ·····------------------------------------------------------------------------117 ·····------------------------------------------------------------------------
118 ·····0,·3,·18,·19,·20},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,118 ·····13,·20,·6,·9,·4},·{0,·1,·2,·20,·6,·5,·9,·7,·8,·4,·10,·11,·12,·13,·14,
119 ·····------------------------------------------------------------------------119 ·····------------------------------------------------------------------------
120 ·····18,·1,·19,·5,·7,·11},·{0,·1,·2,·3,·4,·5,·6,·7,·8,·9,·10,·11,·12,·13,·14,120 ·····18,·16,·19,·15,·17,·3},·{3,·16,·14,·4,·5,·2,·7,·8,·1,·11,·0,·12,·10,·15,
121 ·····------------------------------------------------------------------------121 ·····------------------------------------------------------------------------
122 ·····15,·16,·17,·18,·19,·20},·{0,·1,·2,·20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,122 ·····13,·6,·17,·9,·18,·19,·20},·{12,·16,·14,·19,·4,·7,·6,·11,·1,·9,·0,·5,·10,
123 ·····------------------------------------------------------------------------123 ·····------------------------------------------------------------------------
124 ·····14,·18,·16,·19,·15,·17,·3},·{19,·14,·4,·16,·2,·3,·8,·15,·6,·12,·1,·17,124 ·····2,·13,·20,·8,·18,·3,·15,·17},·{16,·1,·7,·17,·12,·18,·2,·19,·11,·8,·10,
125 ·····------------------------------------------------------------------------125 ·····------------------------------------------------------------------------
126 ·····9,·20,·10,·0,·18,·13,·11,·5,·7},·{0,·1,·6,·20,·7,·2,·11,·8,·9,·5,·10,126 ·····20,·5,·0,·14,·3,·13,·15,·6,·9,·4},·{0,·1,·3,·19,·12,·5,·2,·7,·15,·8,·10,
127 ·····------------------------------------------------------------------------127 ·····------------------------------------------------------------------------
128 ·····12,·4,·13,·14,·18,·16,·19,·15,·17,·3},·{13,·1,·19,·2,·6,·5,·9,·7,·20,·4,128 ·····11,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{12,·16,·7,·17,·10,·9,·14,·4,·11,
129 ·····------------------------------------------------------------------------129 ·····------------------------------------------------------------------------
130 ·····10,·11,·18,·16,·14,·8,·0,·12,·17,·3,·15},·{3,·1,·2,·19,·4,·16,·6,·0,·8,130 ·····1,·0,·6,·5,·2,·13,·3,·8,·15,·18,·19,·20},·{12,·16,·14,·17,·4,·7,·6,·11,
131 ·····------------------------------------------------------------------------131 ·····------------------------------------------------------------------------
132 ·····9,·10,·13,·12,·15,·14,·20,·17,·18,·11,·5,·7},·{0,·1,·2,·3,·4,·5,·6,·7,132 ·····1,·9,·0,·5,·10,·2,·13,·3,·8,·15,·20,·18,·19},·{0,·1,·3,·19,·12,·11,·2,
133 ·····------------------------------------------------------------------------133 ·····------------------------------------------------------------------------
134 ·····8,·9,·10,·11,·12,·13,·14,·15,·16,·17,·19,·20,·18},·{0,·1,·6,·3,·7,·2,134 ·····5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,·9,·4,·6},·{0,·1,·2,·20,·6,·5,
135 ·····------------------------------------------------------------------------135 ·····------------------------------------------------------------------------
136 ·····11,·8,·9,·5,·10,·12,·4,·13,·14,·15,·16,·17,·18,·19,·20},·{13,·10,·8,·15,136 ·····9,·7,·8,·4,·10,·11,·12,·13,·14,·18,·16,·19,·15,·17,·3},·{4,·16,·14,·3,
137 ·····------------------------------------------------------------------------137 ·····------------------------------------------------------------------------
138 ·····6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,·0,·3,·19,·20,·18},·{0,·1,·2,138 ·····5,·2,·7,·8,·1,·11,·0,·12,·10,·6,·13,·15,·9,·17,·18,·19,·20},·{12,·16,·7,
139 ·····------------------------------------------------------------------------139 ·····------------------------------------------------------------------------
140 ·····20,·4,·7,·6,·11,·8,·9,·10,·5,·12,·13,·14,·18,·16,·19,·15,·17,·3},·{16,140 ·····17,·10,·9,·14,·4,·11,·1,·0,·6,·5,·2,·13,·3,·8,·15,·20,·18,·19},·{0,·11,
141 ·····------------------------------------------------------------------------141 ·····------------------------------------------------------------------------
142 ·····14,·4,·19,·2,·3,·8,·15,·6,·12,·1,·17,·9,·0,·10,·20,·13,·18,·11,·5,·7},142 ·····2,·3,·10,·4,·14,·6,·8,·1,·5,·9,·12,·13,·7,·15,·16,·17,·18,·19,·20},·{16,
143 ·····------------------------------------------------------------------------143 ·····------------------------------------------------------------------------
144 ·····{6,·10,·7,·13,·2,·20,·8,·18,·11,·12,·14,·19,·5,·9,·1,·16,·4,·0,·3,·15,144 ·····14,·17,·18,·8,·7,·12,·11,·3,·2,·1,·5,·15,·0,·10,·19,·13,·20,·6,·9,·4},
145 ·····------------------------------------------------------------------------145 ·····------------------------------------------------------------------------
146 ·····17},·{13,·10,·8,·15,·4,·7,·6,·11,·12,·9,·14,·5,·2,·16,·1,·17,·0,·3,·19,146 ·····{2,·0,·11,·3,·10,·4,·14,·6,·5,·1,·13,·9,·7,·8,·16,·15,·12,·17,·18,·19,
147 ·····------------------------------------------------------------------------147 ·····------------------------------------------------------------------------
148 ·····20,·18},·{10,·9,·15,·20,·0,·8,·13,·12,·17,·16,·4,·2,·3,·14,·6,·18,·1,148 ·····20},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,·18,
149 ·····------------------------------------------------------------------------149 ·····------------------------------------------------------------------------
150 ·····19,·5,·7,·11},·{13,·10,·8,·15,·6,·7,·9,·11,·12,·4,·14,·5,·2,·16,·1,·17,150 ·····9,·4,·6},·{0,·1,·3,·19,·12,·11,·2,·5,·15,·8,·10,·7,·17,·13,·14,·20,·16,
151 ·····------------------------------------------------------------------------151 ·····------------------------------------------------------------------------
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153 ·····------------------------------------------------------------------------153 ·····------------------------------------------------------------------------
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3.14 KB
./usr/share/doc/Macaulay2/Msolve/example-output/___Msolve.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 i2·:·I·=·ideal(x,·y,·z)9 i2·:·I·=·ideal(x,·y,·z)
  
10 o2·=·ideal·(x,·y,·z)10 o2·=·ideal·(x,·y,·z)
  
11 o2·:·Ideal·of·R11 o2·:·Ideal·of·R
  
12 i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6)12 i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6)
13 ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-1381459-0/0-in.ms·-o·/tmp/M2-1381459-0/0-out.ms13 ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-1442734-0/0-in.ms·-o·/tmp/M2-1442734-0/0-out.ms
  
14 ---------------·INPUT·DATA·---------------14 ---------------·INPUT·DATA·---------------
15 #variables·······················315 #variables·······················3
16 #equations·······················316 #equations·······················3
17 #invalid·equations···············017 #invalid·equations···············0
18 field·characteristic·············018 field·characteristic·············0
19 homogeneous·input?···············119 homogeneous·input?···············1
Offset 45, 24 lines modifiedOffset 45, 24 lines modified
45 time(rd)··time·of·the·current·f4·round·in·seconds·given45 time(rd)··time·of·the·current·f4·round·in·seconds·given
46 ··········for·real·and·cpu·time46 ··········for·real·and·cpu·time
47 --------------------------------------------------------47 --------------------------------------------------------
  
48 deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu)48 deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu)
49 ------------------------------------------------------------------------------------------------------49 ------------------------------------------------------------------------------------------------------
50 ------------------------------------------------------------------------------------------------------50 ------------------------------------------------------------------------------------------------------
51 reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.05·|·0.15·········51 reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.07·|·0.13·········
52 ------------------------------------------------------------------------------------------------------52 ------------------------------------------------------------------------------------------------------
  
53 ----------------·TIMINGS·----------------53 ----------------·TIMINGS·----------------
54 overall(elapsed)········0.09·sec54 overall(elapsed)········0.13·sec
55 overall(cpu)············0.27·sec55 overall(cpu)············0.24·sec
56 select··················0.00·sec···0.0%56 select··················0.00·sec···0.0%
57 symbolic·prep.··········0.00·sec···0.0%57 symbolic·prep.··········0.00·sec···0.0%
58 update··················0.04·sec··47.0%58 update··················0.06·sec··47.1%
59 convert·················0.05·sec··52.9%59 convert·················0.07·sec··52.8%
60 linear·algebra··········0.00·sec···0.0%60 linear·algebra··········0.00·sec···0.0%
61 reduce·gb···············0.00·sec···0.0%61 reduce·gb···············0.00·sec···0.0%
62 -----------------------------------------62 -----------------------------------------
  
63 ----------·COMPUTATIONAL·DATA·-----------63 ----------·COMPUTATIONAL·DATA·-----------
64 size·of·basis·····················364 size·of·basis·····················3
65 #terms·in·basis···················365 #terms·in·basis···················3
Offset 79, 25 lines modifiedOffset 79, 25 lines modified
  
79 ----------·COMPUTATIONAL·DATA·-----------79 ----------·COMPUTATIONAL·DATA·-----------
80 [3]80 [3]
81 #polynomials·to·lift··············381 #polynomials·to·lift··············3
82 -----------------------------------------82 -----------------------------------------
  
83 ----------------·TIMINGS·----------------83 ----------------·TIMINGS·----------------
84 multi-mod·overall(elapsed)······0.10·sec84 multi-mod·overall(elapsed)······0.18·sec
85 learning·phase··················0.00·Gops/sec85 learning·phase··················0.00·Gops/sec
86 application·phase···············0.00·Gops/sec86 application·phase···············0.00·Gops/sec
87 -----------------------------------------87 -----------------------------------------
  
88 multi-modular·steps88 multi-modular·steps
89 ------------------------------------------------------------------------------------------------------89 ------------------------------------------------------------------------------------------------------
90 {1}{2}<100.00%>90 {1}{2}<100.00%>
  
91 ------------------------------------------------------------------------------------91 ------------------------------------------------------------------------------------
92 msolve·overall·time···········0.37·sec·(elapsed)·/··1.19·sec·(cpu)92 msolve·overall·time···········0.83·sec·(elapsed)·/··1.11·sec·(cpu)
93 ------------------------------------------------------------------------------------93 ------------------------------------------------------------------------------------
94 ·94 ·
95 ------------------------------------------------------------------------------------------------------95 ------------------------------------------------------------------------------------------------------
  
  
96 ----------·COMPUTATIONAL·DATA·-----------96 ----------·COMPUTATIONAL·DATA·-----------
97 Max·coeff.·bitsize················197 Max·coeff.·bitsize················1
7.48 KB
./usr/share/doc/Macaulay2/Msolve/example-output/_msolve__Real__Solutions.out
    
Offset 11, 107 lines modifiedOffset 11, 111 lines modified
11 ·············2·······211 ·············2·······2
12 o2·=·ideal·(x··-·x,·y··-·5)12 o2·=·ideal·(x··-·x,·y··-·5)
  
13 o2·:·Ideal·of·R13 o2·:·Ideal·of·R
  
14 i3·:·rationalIntervalSols·=·msolveRealSolutions·I14 i3·:·rationalIntervalSols·=·msolveRealSolutions·I
  
15 ······························7971549723·····················15 ········8589934591··8589934593······9603838835····4801919417······8589934591·
 16 o3·=·{{{----------,·----------},·{-·----------,·-·----------}},·{{----------,
 17 ········8589934592··8589934592······4294967296····2147483648······8589934592·
16 o3·=·{{{-·--------------------------------------------------,18 ·····------------------------------------------------------------------------
17 ··········23384026197294446691258957323460528314494920687616·19 ·····8589934593····4801919417··9603838835·······
 20 ·····----------},·{----------,·----------}},·{{-
 21 ·····8589934592····2147483648··4294967296·······
18 ·····------------------------------------------------------------------------22 ·····------------------------------------------------------------------------
19 ·························780945615························4801919417· 
20 ·····-------------------------------------------------},·{----------, 
21 ·····5846006549323611672814739330865132078623730171904····2147483648· 
22 ·····------------------------------------------------------------------------ 
23 ·····9603838835······8589934591··8589934593····4801919417··9603838835······· 
24 ·····----------}},·{{----------,·----------},·{----------,·----------}},·{{- 
25 ·····4294967296······8589934592··8589934592····2147483648··4294967296······· 
26 ·····------------------------------------------------------------------------ 
27 ·························7473697071····················23 ·························2205335583····················
28 ·····-------------------------------------------------,24 ·····-------------------------------------------------,
29 ·····1461501637330902918203684832716283019655932542976·25 ·····5846006549323611672814739330865132078623730171904·
30 ·····------------------------------------------------------------------------26 ·····------------------------------------------------------------------------
31 ························487006717·························9603838835···27 ·························15106293·························9603838835···
32 ·····-----------------------------------------------},·{-·----------,·-28 ·····-----------------------------------------------},·{-·----------,·-
33 ·····45671926166590716193865151022383844364247891968······4294967296···29 ·····91343852333181432387730302044767688728495783936······4294967296···
 30 ·····------------------------------------------------------------------------
 31 ·····4801919417·····························952552029·····················
 32 ·····----------}},·{{-·--------------------------------------------------,
 33 ·····2147483648········11692013098647223345629478661730264157247460343808·
 34 ·····------------------------------------------------------------------------
 35 ·························2796080021·······················4801919417·
 36 ·····-------------------------------------------------},·{----------,
 37 ·····5846006549323611672814739330865132078623730171904····2147483648·
34 ·····------------------------------------------------------------------------38 ·····------------------------------------------------------------------------
35 ·····4801919417······8589934591··8589934593······9603838835····4801919417 
36 ·····----------}},·{{----------,·----------},·{-·----------,·-·----------}}} 
37 ·····2147483648······8589934592··8589934592······4294967296····214748364839 ·····9603838835
 40 ·····----------}}}
 41 ·····4294967296
  
38 o3·:·List42 o3·:·List
  
39 i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ)43 i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ)
  
40 ··········19207677669····································34030073············ 
41 o4·=·{{1,·-----------},·{-·-------------------------------------------------- 
42 ···········8589934592······3369993333393829974333376885877453834204643052817544 ············19207677669·····
 45 o4·=·{{1,·-·-----------},·{-
 46 ·············8589934592·····
43 ·····------------------------------------------------------------------------47 ·····------------------------------------------------------------------------
44 ························19207677669·········19207677669·····48 ·························472762529························19207677669······
45 ·····-----------------,·-----------},·{1,·-·-----------},·{-49 ·····-------------------------------------------------,·-·-----------},·{1,
46 ·····71560137951281152···8589934592··········8589934592·····50 ·····5846006549323611672814739330865132078623730171904·····8589934592······
47 ·····------------------------------------------------------------------------51 ·····------------------------------------------------------------------------
48 ··································14420230677································ 
49 ·····---------------------------------------------------------------------,·- 
50 ·····215679573337205118357336120696157045389097155380324579848828881993728···52 ·····19207677669··························2406089371·····················
 53 ·····-----------},·{-·--------------------------------------------------,
 54 ······8589934592······23384026197294446691258957323460528314494920687616·
51 ·····------------------------------------------------------------------------55 ·····------------------------------------------------------------------------
52 ·····1920767766956 ·····19207677669
53 ·····-----------}}57 ·····-----------}}
54 ······858993459258 ······8589934592
  
55 o4·:·List59 o4·:·List
  
56 i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi)60 i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi)
  
57 o5·=·{{[1,1],·[-2.23607,-2.23607]},·{[-4.97327e-39,3.47765e-39],61 o5·=·{{[-1.50965e-40,4.18899e-41],·[2.23607,2.23607]},·{[1,1],
58 ·····------------------------------------------------------------------------62 ·····------------------------------------------------------------------------
59 ·····[-2.23607,-2.23607]},·{[1,1],·[2.23607,2.23607]},63 ·····[2.23607,2.23607]},·{[-5.48246e-39,4.24367e-39],·[-2.23607,-2.23607]},
60 ·····------------------------------------------------------------------------64 ·····------------------------------------------------------------------------
61 ·····{[-8.55099e-42,1.1637e-41],·[2.23607,2.23607]}}65 ·····{[1,1],·[-2.23607,-2.23607]}}
  
62 o5·:·List66 o5·:·List
  
63 i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10)67 i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10)
  
64 o6·=·{{[.999512,1.00049],·[-2.23633,-2.23535]},·{[-3.03344e-39,2.39131e-39],68 o6·=·{{[-4.12004e-40,2.43041e-40],·[2.23535,2.23633]},
65 ·····------------------------------------------------------------------------69 ·····------------------------------------------------------------------------
66 ·····[-2.23633,-2.23535]},·{[.999512,1.00049],·[2.23535,2.23633]},70 ·····{[-1.34367e-42,2.10808e-43],·[-2.23633,-2.23535]},·{[.999512,1.00049],
67 ·····------------------------------------------------------------------------71 ·····------------------------------------------------------------------------
68 ·····{[-8.77101e-41,1.41072e-40],·[2.23535,2.23633]}}72 ·····[2.23535,2.23633]},·{[.999512,1.00049],·[-2.23633,-2.23535]}}
  
69 o6·:·List73 o6·:·List
  
70 i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR)74 i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR)
  
71 o7·=·{{1,·-2.23607},·{1.11773e-39,·-2.23607},·{1,·2.23607},·{-2.45047e-44,75 o7·=·{{1,·2.23607},·{1,·-2.23607},·{5.27699e-40,·2.23607},·{-6.0982e-43,
72 ·····------------------------------------------------------------------------76 ·····------------------------------------------------------------------------
73 ·····2.23607}}77 ·····-2.23607}}
  
74 o7·:·List78 o7·:·List
  
75 i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10)79 i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10)
  
76 o8·=·{{-5.84285e-41,·-2.23584},·{1,·-2.23584},·{-1.63295e-39,·2.23584},·{1,80 o8·=·{{-7.65894e-41,·-2.23584},·{1,·-2.23584},·{5.65004e-41,·2.23584},·{1,
77 ·····------------------------------------------------------------------------81 ·····------------------------------------------------------------------------
78 ·····2.23584}}82 ·····2.23584}}
  
79 o8·:·List83 o8·:·List
  
80 i9·:·I·=·ideal·{(x-1)*x^3,·(y^2-5)^2}84 i9·:·I·=·ideal·{(x-1)*x^3,·(y^2-5)^2}
  
81 ·············4····3···4······285 ·············4····3···4······2
82 o9·=·ideal·(x··-·x·,·y··-·10y··+·25)86 o9·=·ideal·(x··-·x·,·y··-·10y··+·25)
  
83 o9·:·Ideal·of·R87 o9·:·Ideal·of·R
  
84 i10·:·floatApproxSols·=·msolveRealSolutions(I,·RRi)88 i10·:·floatApproxSols·=·msolveRealSolutions(I,·RRi)
  
85 o10·=·{{[-3.33715e-58,1.00764e-58],·[-2.23607,-2.23607]},·{[1,1],89 o10·=·{{[-2.43646e-42,4.37337e-42],·[2.23607,2.23607]},·{[1,1],
86 ······-----------------------------------------------------------------------90 ······-----------------------------------------------------------------------
87 ······[-2.23607,-2.23607]},·{[-3.02213e-39,2.06306e-39],·[2.23607,2.23607]},91 ······[2.23607,2.23607]},·{[-1.8498e-40,2.4706e-40],·[-2.23607,-2.23607]},
88 ······-----------------------------------------------------------------------92 ······-----------------------------------------------------------------------
89 ······{[1,1],·[2.23607,2.23607]}}93 ······{[1,1],·[-2.23607,-2.23607]}}
  
90 o10·:·List94 o10·:·List
  
91 i11·:·95 i11·:·
16.0 KB
./usr/share/doc/Macaulay2/Msolve/html/_msolve__Real__Solutions.html
    
Offset 100, 106 lines modifiedOffset 100, 110 lines modified
100 o2·:·Ideal·of·R</code></pre>100 o2·:·Ideal·of·R</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i3·:·rationalIntervalSols·=·msolveRealSolutions·I105 ··············<pre><code·class="language-macaulay2">i3·:·rationalIntervalSols·=·msolveRealSolutions·I
  
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116 ·····4294967296······8589934592··8589934592····2147483648··4294967296······· 
117 ·····------------------------------------------------------------------------ 
118 ·························7473697071····················114 ·························2205335583····················
119 ·····-------------------------------------------------,115 ·····-------------------------------------------------,
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125 ·····------------------------------------------------------------------------129 ·····------------------------------------------------------------------------
126 ·····4801919417······8589934591··8589934593······9603838835····4801919417 
127 ·····----------}},·{{----------,·----------},·{-·----------,·-·----------}}} 
128 ·····2147483648······8589934592··8589934592······4294967296····2147483648130 ·····9603838835
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 132 ·····4294967296
  
129 o3·:·List</code></pre>133 o3·:·List</code></pre>
130 ············</td>134 ············</td>
131 ··········</tr>135 ··········</tr>
132 ··········<tr>136 ··········<tr>
133 ············<td>137 ············<td>
134 ··············<pre><code·class="language-macaulay2">i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ)138 ··············<pre><code·class="language-macaulay2">i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ)
  
135 ··········19207677669····································34030073············ 
136 o4·=·{{1,·-----------},·{-·-------------------------------------------------- 
137 ···········8589934592······33699933333938299743333768858774538342046430528175139 ············19207677669·····
 140 o4·=·{{1,·-·-----------},·{-
 141 ·············8589934592·····
138 ·····------------------------------------------------------------------------142 ·····------------------------------------------------------------------------
139 ························19207677669·········19207677669·····143 ·························472762529························19207677669······
140 ·····-----------------,·-----------},·{1,·-·-----------},·{-144 ·····-------------------------------------------------,·-·-----------},·{1,
141 ·····71560137951281152···8589934592··········8589934592·····145 ·····5846006549323611672814739330865132078623730171904·····8589934592······
142 ·····------------------------------------------------------------------------146 ·····------------------------------------------------------------------------
143 ··································14420230677································ 
144 ·····---------------------------------------------------------------------,·- 
145 ·····215679573337205118357336120696157045389097155380324579848828881993728···147 ·····19207677669··························2406089371·····················
 148 ·····-----------},·{-·--------------------------------------------------,
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146 ·····------------------------------------------------------------------------150 ·····------------------------------------------------------------------------
147 ·····19207677669151 ·····19207677669
148 ·····-----------}}152 ·····-----------}}
149 ······8589934592153 ······8589934592
  
150 o4·:·List</code></pre>154 o4·:·List</code></pre>
151 ············</td>155 ············</td>
152 ··········</tr>156 ··········</tr>
153 ··········<tr>157 ··········<tr>
154 ············<td>158 ············<td>
155 ··············<pre><code·class="language-macaulay2">i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi)159 ··············<pre><code·class="language-macaulay2">i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi)
  
156 o5·=·{{[1,1],·[-2.23607,-2.23607]},·{[-4.97327e-39,3.47765e-39],160 o5·=·{{[-1.50965e-40,4.18899e-41],·[2.23607,2.23607]},·{[1,1],
157 ·····------------------------------------------------------------------------161 ·····------------------------------------------------------------------------
158 ·····[-2.23607,-2.23607]},·{[1,1],·[2.23607,2.23607]},162 ·····[2.23607,2.23607]},·{[-5.48246e-39,4.24367e-39],·[-2.23607,-2.23607]},
159 ·····------------------------------------------------------------------------163 ·····------------------------------------------------------------------------
160 ·····{[-8.55099e-42,1.1637e-41],·[2.23607,2.23607]}}164 ·····{[1,1],·[-2.23607,-2.23607]}}
  
161 o5·:·List</code></pre>165 o5·:·List</code></pre>
162 ············</td>166 ············</td>
163 ··········</tr>167 ··········</tr>
164 ··········<tr>168 ··········<tr>
165 ············<td>169 ············<td>
166 ··············<pre><code·class="language-macaulay2">i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10)170 ··············<pre><code·class="language-macaulay2">i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10)
  
167 o6·=·{{[.999512,1.00049],·[-2.23633,-2.23535]},·{[-3.03344e-39,2.39131e-39],171 o6·=·{{[-4.12004e-40,2.43041e-40],·[2.23535,2.23633]},
168 ·····------------------------------------------------------------------------172 ·····------------------------------------------------------------------------
169 ·····[-2.23633,-2.23535]},·{[.999512,1.00049],·[2.23535,2.23633]},173 ·····{[-1.34367e-42,2.10808e-43],·[-2.23633,-2.23535]},·{[.999512,1.00049],
170 ·····------------------------------------------------------------------------174 ·····------------------------------------------------------------------------
171 ·····{[-8.77101e-41,1.41072e-40],·[2.23535,2.23633]}}175 ·····[2.23535,2.23633]},·{[.999512,1.00049],·[-2.23633,-2.23535]}}
  
172 o6·:·List</code></pre>176 o6·:·List</code></pre>
173 ············</td>177 ············</td>
174 ··········</tr>178 ··········</tr>
175 ··········<tr>179 ··········<tr>
176 ············<td>180 ············<td>
177 ··············<pre><code·class="language-macaulay2">i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR)181 ··············<pre><code·class="language-macaulay2">i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR)
  
178 o7·=·{{1,·-2.23607},·{1.11773e-39,·-2.23607},·{1,·2.23607},·{-2.45047e-44,182 o7·=·{{1,·2.23607},·{1,·-2.23607},·{5.27699e-40,·2.23607},·{-6.0982e-43,
179 ·····------------------------------------------------------------------------183 ·····------------------------------------------------------------------------
180 ·····2.23607}}184 ·····-2.23607}}
  
181 o7·:·List</code></pre>185 o7·:·List</code></pre>
182 ············</td>186 ············</td>
183 ··········</tr>187 ··········</tr>
184 ··········<tr>188 ··········<tr>
185 ············<td>189 ············<td>
186 ··············<pre><code·class="language-macaulay2">i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10)190 ··············<pre><code·class="language-macaulay2">i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10)
  
187 o8·=·{{-5.84285e-41,·-2.23584},·{1,·-2.23584},·{-1.63295e-39,·2.23584},·{1,191 o8·=·{{-7.65894e-41,·-2.23584},·{1,·-2.23584},·{5.65004e-41,·2.23584},·{1,
188 ·····------------------------------------------------------------------------192 ·····------------------------------------------------------------------------
189 ·····2.23584}}193 ·····2.23584}}
  
190 o8·:·List</code></pre>194 o8·:·List</code></pre>
191 ············</td>195 ············</td>
192 ··········</tr>196 ··········</tr>
193 ········</table>197 ········</table>
Offset 217, 19 lines modifiedOffset 221, 19 lines modified
217 o9·:·Ideal·of·R</code></pre>221 o9·:·Ideal·of·R</code></pre>
218 ············</td>222 ············</td>
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Offset 43, 86 lines modifiedOffset 43, 90 lines modified
  
43 ·············2·······243 ·············2·······2
44 o2·=·ideal·(x··-·x,·y··-·5)44 o2·=·ideal·(x··-·x,·y··-·5)
  
45 o2·:·Ideal·of·R45 o2·:·Ideal·of·R
46 i3·:·rationalIntervalSols·=·msolveRealSolutions·I46 i3·:·rationalIntervalSols·=·msolveRealSolutions·I
  
47 ······························797154972347 ········8589934591··8589934593······9603838835····4801919417······8589934591
 48 o3·=·{{{----------,·----------},·{-·----------,·-·----------}},·{{----------,
 49 ········8589934592··8589934592······4294967296····2147483648······8589934592
48 o3·=·{{{-·--------------------------------------------------,50 ·····------------------------------------------------------------------------
49 ··········2338402619729444669125895732346052831449492068761651 ·····8589934593····4801919417··9603838835
 52 ·····----------},·{----------,·----------}},·{{-
 53 ·····8589934592····2147483648··4294967296
50 ·····------------------------------------------------------------------------54 ·····------------------------------------------------------------------------
 55 ·························2205335583
51 ·························780945615························4801919417 
52 ·····-------------------------------------------------},·{----------, 
53 ·····5846006549323611672814739330865132078623730171904····2147483648 
54 ·····------------------------------------------------------------------------ 
55 ·····9603838835······8589934591··8589934593····4801919417··9603838835 
56 ·····----------}},·{{----------,·----------},·{----------,·----------}},·{{- 
57 ·····4294967296······8589934592··8589934592····2147483648··4294967296 
58 ·····------------------------------------------------------------------------ 
59 ·························7473697071 
60 ·····-------------------------------------------------,56 ·····-------------------------------------------------,
61 ·····146150163733090291820368483271628301965593254297657 ·····5846006549323611672814739330865132078623730171904
62 ·····------------------------------------------------------------------------58 ·····------------------------------------------------------------------------
63 ························487006717·························960383883559 ·························15106293·························9603838835
64 ·····-----------------------------------------------},·{-·----------,·-60 ·····-----------------------------------------------},·{-·----------,·-
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 62 ·····------------------------------------------------------------------------
 63 ·····4801919417·····························952552029
 64 ·····----------}},·{{-·--------------------------------------------------,
 65 ·····2147483648········11692013098647223345629478661730264157247460343808
 66 ·····------------------------------------------------------------------------
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 68 ·····-------------------------------------------------},·{----------,
 69 ·····5846006549323611672814739330865132078623730171904····2147483648
66 ·····------------------------------------------------------------------------70 ·····------------------------------------------------------------------------
67 ·····4801919417······8589934591··8589934593······9603838835····4801919417 
68 ·····----------}},·{{----------,·----------},·{-·----------,·-·----------}}} 
69 ·····2147483648······8589934592··8589934592······4294967296····214748364871 ·····9603838835
 72 ·····----------}}}
 73 ·····4294967296
  
70 o3·:·List74 o3·:·List
71 i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ)75 i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ)
  
72 ··········19207677669····································34030073 
73 o4·=·{{1,·-----------},·{-·-------------------------------------------------- 
74 ···········8589934592······3369993333393829974333376885877453834204643052817576 ············19207677669
 77 o4·=·{{1,·-·-----------},·{-
 78 ·············8589934592
75 ·····------------------------------------------------------------------------79 ·····------------------------------------------------------------------------
76 ························19207677669·········1920767766980 ·························472762529························19207677669
77 ·····-----------------,·-----------},·{1,·-·-----------},·{-81 ·····-------------------------------------------------,·-·-----------},·{1,
78 ·····71560137951281152···8589934592··········858993459282 ·····5846006549323611672814739330865132078623730171904·····8589934592
79 ·····------------------------------------------------------------------------83 ·····------------------------------------------------------------------------
80 ··································14420230677 
81 ·····---------------------------------------------------------------------,·- 
82 ·····21567957333720511835733612069615704538909715538032457984882888199372884 ·····19207677669··························2406089371
 85 ·····-----------},·{-·--------------------------------------------------,
 86 ······8589934592······23384026197294446691258957323460528314494920687616
83 ·····------------------------------------------------------------------------87 ·····------------------------------------------------------------------------
84 ·····1920767766988 ·····19207677669
85 ·····-----------}}89 ·····-----------}}
86 ······858993459290 ······8589934592
  
87 o4·:·List91 o4·:·List
88 i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi)92 i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi)
  
89 o5·=·{{[1,1],·[-2.23607,-2.23607]},·{[-4.97327e-39,3.47765e-39],93 o5·=·{{[-1.50965e-40,4.18899e-41],·[2.23607,2.23607]},·{[1,1],
90 ·····------------------------------------------------------------------------94 ·····------------------------------------------------------------------------
91 ·····[-2.23607,-2.23607]},·{[1,1],·[2.23607,2.23607]},95 ·····[2.23607,2.23607]},·{[-5.48246e-39,4.24367e-39],·[-2.23607,-2.23607]},
92 ·····------------------------------------------------------------------------96 ·····------------------------------------------------------------------------
93 ·····{[-8.55099e-42,1.1637e-41],·[2.23607,2.23607]}}97 ·····{[1,1],·[-2.23607,-2.23607]}}
  
94 o5·:·List98 o5·:·List
95 i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10)99 i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10)
  
96 o6·=·{{[.999512,1.00049],·[-2.23633,-2.23535]},·{[-3.03344e-39,2.39131e-39],100 o6·=·{{[-4.12004e-40,2.43041e-40],·[2.23535,2.23633]},
97 ·····------------------------------------------------------------------------101 ·····------------------------------------------------------------------------
98 ·····[-2.23633,-2.23535]},·{[.999512,1.00049],·[2.23535,2.23633]},102 ·····{[-1.34367e-42,2.10808e-43],·[-2.23633,-2.23535]},·{[.999512,1.00049],
99 ·····------------------------------------------------------------------------103 ·····------------------------------------------------------------------------
100 ·····{[-8.77101e-41,1.41072e-40],·[2.23535,2.23633]}}104 ·····[2.23535,2.23633]},·{[.999512,1.00049],·[-2.23633,-2.23535]}}
  
101 o6·:·List105 o6·:·List
102 i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR)106 i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR)
  
103 o7·=·{{1,·-2.23607},·{1.11773e-39,·-2.23607},·{1,·2.23607},·{-2.45047e-44,107 o7·=·{{1,·2.23607},·{1,·-2.23607},·{5.27699e-40,·2.23607},·{-6.0982e-43,
104 ·····------------------------------------------------------------------------108 ·····------------------------------------------------------------------------
105 ·····2.23607}}109 ·····-2.23607}}
  
106 o7·:·List110 o7·:·List
107 i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10)111 i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10)
  
108 o8·=·{{-5.84285e-41,·-2.23584},·{1,·-2.23584},·{-1.63295e-39,·2.23584},·{1,112 o8·=·{{-7.65894e-41,·-2.23584},·{1,·-2.23584},·{5.65004e-41,·2.23584},·{1,
109 ·····------------------------------------------------------------------------113 ·····------------------------------------------------------------------------
110 ·····2.23584}}114 ·····2.23584}}
  
111 o8·:·List115 o8·:·List
112 Note·in·cases·where·solutions·have·multiplicity·this·is·not·reflected·in·the116 Note·in·cases·where·solutions·have·multiplicity·this·is·not·reflected·in·the
113 output.·While·the·solver·does·not·return·multiplicities,·it·reliably·outputs117 output.·While·the·solver·does·not·return·multiplicities,·it·reliably·outputs
114 the·verified·isolating·intervals·for·multiple·solutions.118 the·verified·isolating·intervals·for·multiple·solutions.
Offset 130, 19 lines modifiedOffset 134, 19 lines modified
  
130 ·············4····3···4······2134 ·············4····3···4······2
131 o9·=·ideal·(x··-·x·,·y··-·10y··+·25)135 o9·=·ideal·(x··-·x·,·y··-·10y··+·25)
  
132 o9·:·Ideal·of·R136 o9·:·Ideal·of·R
133 i10·:·floatApproxSols·=·msolveRealSolutions(I,·RRi)137 i10·:·floatApproxSols·=·msolveRealSolutions(I,·RRi)
  
134 o10·=·{{[-3.33715e-58,1.00764e-58],·[-2.23607,-2.23607]},·{[1,1],138 o10·=·{{[-2.43646e-42,4.37337e-42],·[2.23607,2.23607]},·{[1,1],
135 ······-----------------------------------------------------------------------139 ······-----------------------------------------------------------------------
136 ······[-2.23607,-2.23607]},·{[-3.02213e-39,2.06306e-39],·[2.23607,2.23607]},140 ······[2.23607,2.23607]},·{[-1.8498e-40,2.4706e-40],·[-2.23607,-2.23607]},
137 ······-----------------------------------------------------------------------141 ······-----------------------------------------------------------------------
138 ······{[1,1],·[2.23607,2.23607]}}142 ······{[1,1],·[-2.23607,-2.23607]}}
  
139 o10·:·List143 o10·:·List
140 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8ms\x8so\x8ol\x8lv\x8ve\x8eR\x8Re\x8ea\x8al\x8lS\x8So\x8ol\x8lu\x8ut\x8ti\x8io\x8on\x8ns\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*144 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8ms\x8so\x8ol\x8lv\x8ve\x8eR\x8Re\x8ea\x8al\x8lS\x8So\x8ol\x8lu\x8ut\x8ti\x8io\x8on\x8ns\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
141 ····*·msolveRealSolutions(Ideal)145 ····*·msolveRealSolutions(Ideal)
142 ····*·msolveRealSolutions(Ideal,Ring)146 ····*·msolveRealSolutions(Ideal,Ring)
143 ····*·msolveRealSolutions(Ideal,RingFamily)147 ····*·msolveRealSolutions(Ideal,RingFamily)
144 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*148 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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Offset 78, 15 lines modifiedOffset 78, 15 lines modified
  
78 o2·:·Ideal·of·R</code></pre>78 o2·:·Ideal·of·R</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6)83 ··············<pre><code·class="language-macaulay2">i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6)
84 ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-1381459-0/0-in.ms·-o·/tmp/M2-1381459-0/0-out.ms84 ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-1442734-0/0-in.ms·-o·/tmp/M2-1442734-0/0-out.ms
  
85 ---------------·INPUT·DATA·---------------85 ---------------·INPUT·DATA·---------------
86 #variables·······················386 #variables·······················3
87 #equations·······················387 #equations·······················3
88 #invalid·equations···············088 #invalid·equations···············0
89 field·characteristic·············089 field·characteristic·············0
90 homogeneous·input?···············190 homogeneous·input?···············1
Offset 114, 24 lines modifiedOffset 114, 24 lines modified
114 time(rd)··time·of·the·current·f4·round·in·seconds·given114 time(rd)··time·of·the·current·f4·round·in·seconds·given
115 ··········for·real·and·cpu·time115 ··········for·real·and·cpu·time
116 --------------------------------------------------------116 --------------------------------------------------------
  
117 deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu)117 deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu)
118 ------------------------------------------------------------------------------------------------------118 ------------------------------------------------------------------------------------------------------
119 ------------------------------------------------------------------------------------------------------119 ------------------------------------------------------------------------------------------------------
120 reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.05·|·0.15·········120 reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.07·|·0.13·········
121 ------------------------------------------------------------------------------------------------------121 ------------------------------------------------------------------------------------------------------
  
122 ----------------·TIMINGS·----------------122 ----------------·TIMINGS·----------------
123 overall(elapsed)········0.09·sec123 overall(elapsed)········0.13·sec
124 overall(cpu)············0.27·sec124 overall(cpu)············0.24·sec
125 select··················0.00·sec···0.0%125 select··················0.00·sec···0.0%
126 symbolic·prep.··········0.00·sec···0.0%126 symbolic·prep.··········0.00·sec···0.0%
127 update··················0.04·sec··47.0%127 update··················0.06·sec··47.1%
128 convert·················0.05·sec··52.9%128 convert·················0.07·sec··52.8%
129 linear·algebra··········0.00·sec···0.0%129 linear·algebra··········0.00·sec···0.0%
130 reduce·gb···············0.00·sec···0.0%130 reduce·gb···············0.00·sec···0.0%
131 -----------------------------------------131 -----------------------------------------
  
132 ----------·COMPUTATIONAL·DATA·-----------132 ----------·COMPUTATIONAL·DATA·-----------
133 size·of·basis·····················3133 size·of·basis·····················3
134 #terms·in·basis···················3134 #terms·in·basis···················3
Offset 148, 25 lines modifiedOffset 148, 25 lines modified
  
148 ----------·COMPUTATIONAL·DATA·-----------148 ----------·COMPUTATIONAL·DATA·-----------
149 [3]149 [3]
150 #polynomials·to·lift··············3150 #polynomials·to·lift··············3
151 -----------------------------------------151 -----------------------------------------
  
152 ----------------·TIMINGS·----------------152 ----------------·TIMINGS·----------------
153 multi-mod·overall(elapsed)······0.10·sec153 multi-mod·overall(elapsed)······0.18·sec
154 learning·phase··················0.00·Gops/sec154 learning·phase··················0.00·Gops/sec
155 application·phase···············0.00·Gops/sec155 application·phase···············0.00·Gops/sec
156 -----------------------------------------156 -----------------------------------------
  
157 multi-modular·steps157 multi-modular·steps
158 ------------------------------------------------------------------------------------------------------158 ------------------------------------------------------------------------------------------------------
159 {1}{2}&lt;100.00%>159 {1}{2}&lt;100.00%>
  
160 ------------------------------------------------------------------------------------160 ------------------------------------------------------------------------------------
161 msolve·overall·time···········0.37·sec·(elapsed)·/··1.19·sec·(cpu)161 msolve·overall·time···········0.83·sec·(elapsed)·/··1.11·sec·(cpu)
162 ------------------------------------------------------------------------------------162 ------------------------------------------------------------------------------------
163 ·163 ·
164 ------------------------------------------------------------------------------------------------------164 ------------------------------------------------------------------------------------------------------
  
  
165 ----------·COMPUTATIONAL·DATA·-----------165 ----------·COMPUTATIONAL·DATA·-----------
166 Max·coeff.·bitsize················1166 Max·coeff.·bitsize················1
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Offset 31, 16 lines modifiedOffset 31, 16 lines modified
31 o1·:·PolynomialRing31 o1·:·PolynomialRing
32 i2·:·I·=·ideal(x,·y,·z)32 i2·:·I·=·ideal(x,·y,·z)
  
33 o2·=·ideal·(x,·y,·z)33 o2·=·ideal·(x,·y,·z)
  
34 o2·:·Ideal·of·R34 o2·:·Ideal·of·R
35 i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6)35 i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6)
36 ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-1381459-0/0-in.ms·-o·/36 ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-1442734-0/0-in.ms·-o·/
37 tmp/M2-1381459-0/0-out.ms37 tmp/M2-1442734-0/0-out.ms
  
38 ---------------·INPUT·DATA·---------------38 ---------------·INPUT·DATA·---------------
39 #variables·······················339 #variables·······················3
40 #equations·······················340 #equations·······················3
41 #invalid·equations···············041 #invalid·equations···············0
42 field·characteristic·············042 field·characteristic·············0
43 homogeneous·input?···············143 homogeneous·input?···············1
Offset 72, 25 lines modifiedOffset 72, 25 lines modified
72 deg·····sel···pairs········mat··········density············new·data72 deg·····sel···pairs········mat··········density············new·data
73 time(rd)·in·sec·(real|cpu)73 time(rd)·in·sec·(real|cpu)
74 -------------------------------------------------------------------------------74 -------------------------------------------------------------------------------
75 -----------------------75 -----------------------
76 -------------------------------------------------------------------------------76 -------------------------------------------------------------------------------
77 -----------------------77 -----------------------
78 reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero78 reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero
79 0.05·|·0.1579 0.07·|·0.13
80 -------------------------------------------------------------------------------80 -------------------------------------------------------------------------------
81 -----------------------81 -----------------------
  
82 ----------------·TIMINGS·----------------82 ----------------·TIMINGS·----------------
83 overall(elapsed)········0.09·sec83 overall(elapsed)········0.13·sec
84 overall(cpu)············0.27·sec84 overall(cpu)············0.24·sec
85 select··················0.00·sec···0.0%85 select··················0.00·sec···0.0%
86 symbolic·prep.··········0.00·sec···0.0%86 symbolic·prep.··········0.00·sec···0.0%
87 update··················0.04·sec··47.0%87 update··················0.06·sec··47.1%
88 convert·················0.05·sec··52.9%88 convert·················0.07·sec··52.8%
89 linear·algebra··········0.00·sec···0.0%89 linear·algebra··········0.00·sec···0.0%
90 reduce·gb···············0.00·sec···0.0%90 reduce·gb···············0.00·sec···0.0%
91 -----------------------------------------91 -----------------------------------------
  
92 ----------·COMPUTATIONAL·DATA·-----------92 ----------·COMPUTATIONAL·DATA·-----------
93 size·of·basis·····················393 size·of·basis·····················3
94 #terms·in·basis···················394 #terms·in·basis···················3
Offset 107, 27 lines modifiedOffset 107, 27 lines modified
  
107 ----------·COMPUTATIONAL·DATA·-----------107 ----------·COMPUTATIONAL·DATA·-----------
108 [3]108 [3]
109 #polynomials·to·lift··············3109 #polynomials·to·lift··············3
110 -----------------------------------------110 -----------------------------------------
  
111 ----------------·TIMINGS·----------------111 ----------------·TIMINGS·----------------
112 multi-mod·overall(elapsed)······0.10·sec112 multi-mod·overall(elapsed)······0.18·sec
113 learning·phase··················0.00·Gops/sec113 learning·phase··················0.00·Gops/sec
114 application·phase···············0.00·Gops/sec114 application·phase···············0.00·Gops/sec
115 -----------------------------------------115 -----------------------------------------
  
116 multi-modular·steps116 multi-modular·steps
117 -------------------------------------------------------------------------------117 -------------------------------------------------------------------------------
118 -----------------------118 -----------------------
119 {1}{2}<100.00%>119 {1}{2}<100.00%>
  
120 -------------------------------------------------------------------------------120 -------------------------------------------------------------------------------
121 -----121 -----
122 msolve·overall·time···········0.37·sec·(elapsed)·/··1.19·sec·(cpu)122 msolve·overall·time···········0.83·sec·(elapsed)·/··1.11·sec·(cpu)
123 -------------------------------------------------------------------------------123 -------------------------------------------------------------------------------
124 -----124 -----
  
125 -------------------------------------------------------------------------------125 -------------------------------------------------------------------------------
126 -----------------------126 -----------------------
  
  
753 B
./usr/share/doc/Macaulay2/MultiGradedRationalMap/dump/rawdocumentation.dump
    
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750 B
./usr/share/doc/Macaulay2/MultigradedBGG/dump/rawdocumentation.dump
    
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774 B
./usr/share/doc/Macaulay2/MultigradedImplicitization/dump/rawdocumentation.dump
    
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750 B
./usr/share/doc/Macaulay2/MultigradedImplicitization/example-output/_components__Of__Kernel.out
    
Offset 20, 16 lines modifiedOffset 20, 16 lines modified
20 o4·=·map·(S,·R,·{t·s·,·t·s·,·t·s·,·t·s·,·t·s·,·t·s·})20 o4·=·map·(S,·R,·{t·s·,·t·s·,·t·s·,·t·s·,·t·s·,·t·s·})
21 ··················1·1···1·2···1·3···2·1···2·2···2·321 ··················1·1···1·2···1·3···2·1···2·2···2·3
  
22 o4·:·RingMap·S·<--·R22 o4·:·RingMap·S·<--·R
  
23 i5·:·peek·componentsOfKernel(2,·F)23 i5·:·peek·componentsOfKernel(2,·F)
24 warning:·computation·begun·over·finite·field.·resulting·polynomials·may·not·lie·in·the·ideal24 warning:·computation·begun·over·finite·field.·resulting·polynomials·may·not·lie·in·the·ideal
25 ·--·.00185862s·elapsed25 ·--·.0101801s·elapsed
26 ·--·.00805996s·elapsed26 ·--·.0412833s·elapsed
27 computing·total·degree:·127 computing·total·degree:·1
28 number·of·monomials·=·628 number·of·monomials·=·6
29 number·of·distinct·multidegrees·=·629 number·of·distinct·multidegrees·=·6
30 computing·total·degree:·230 computing·total·degree:·2
31 number·of·monomials·=·2131 number·of·monomials·=·21
32 number·of·distinct·multidegrees·=·1832 number·of·distinct·multidegrees·=·18
  
1.31 KB
./usr/share/doc/Macaulay2/MultigradedImplicitization/html/_components__Of__Kernel.html
    
Offset 114, 16 lines modifiedOffset 114, 16 lines modified
114 o4·:·RingMap·S·&lt;--·R</code></pre>114 o4·:·RingMap·S·&lt;--·R</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i5·:·peek·componentsOfKernel(2,·F)119 ··············<pre><code·class="language-macaulay2">i5·:·peek·componentsOfKernel(2,·F)
120 warning:·computation·begun·over·finite·field.·resulting·polynomials·may·not·lie·in·the·ideal120 warning:·computation·begun·over·finite·field.·resulting·polynomials·may·not·lie·in·the·ideal
121 ·--·.00185862s·elapsed121 ·--·.0101801s·elapsed
122 ·--·.00805996s·elapsed122 ·--·.0412833s·elapsed
123 computing·total·degree:·1123 computing·total·degree:·1
124 number·of·monomials·=·6124 number·of·monomials·=·6
125 number·of·distinct·multidegrees·=·6125 number·of·distinct·multidegrees·=·6
126 computing·total·degree:·2126 computing·total·degree:·2
127 number·of·monomials·=·21127 number·of·monomials·=·21
128 number·of·distinct·multidegrees·=·18128 number·of·distinct·multidegrees·=·18
  
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48 o4·=·map·(S,·R,·{t·s·,·t·s·,·t·s·,·t·s·,·t·s·,·t·s·})48 o4·=·map·(S,·R,·{t·s·,·t·s·,·t·s·,·t·s·,·t·s·,·t·s·})
49 ··················1·1···1·2···1·3···2·1···2·2···2·349 ··················1·1···1·2···1·3···2·1···2·2···2·3
  
50 o4·:·RingMap·S·<--·R50 o4·:·RingMap·S·<--·R
51 i5·:·peek·componentsOfKernel(2,·F)51 i5·:·peek·componentsOfKernel(2,·F)
52 warning:·computation·begun·over·finite·field.·resulting·polynomials·may·not·lie52 warning:·computation·begun·over·finite·field.·resulting·polynomials·may·not·lie
53 in·the·ideal53 in·the·ideal
54 ·--·.00185862s·elapsed54 ·--·.0101801s·elapsed
55 ·--·.00805996s·elapsed55 ·--·.0412833s·elapsed
56 computing·total·degree:·156 computing·total·degree:·1
57 number·of·monomials·=·657 number·of·monomials·=·6
58 number·of·distinct·multidegrees·=·658 number·of·distinct·multidegrees·=·6
59 computing·total·degree:·259 computing·total·degree:·2
60 number·of·monomials·=·2160 number·of·monomials·=·21
61 number·of·distinct·multidegrees·=·1861 number·of·distinct·multidegrees·=·18
  
741 B
./usr/share/doc/Macaulay2/MultiplicitySequence/dump/rawdocumentation.dump
    
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572 B
./usr/share/doc/Macaulay2/MultiplicitySequence/example-output/_j__Mult.out
    
Offset 9, 25 lines modifiedOffset 9, 25 lines modified
9 i2·:·I·=·ideal"xy,yz,zx"9 i2·:·I·=·ideal"xy,yz,zx"
  
10 o2·=·ideal·(x*y,·y*z,·x*z)10 o2·=·ideal·(x*y,·y*z,·x*z)
  
11 o2·:·Ideal·of·R11 o2·:·Ideal·of·R
  
12 i3·:·elapsedTime·jMult·I12 i3·:·elapsedTime·jMult·I
13 ·--·.0597996s·elapsed13 ·--·.107333s·elapsed
  
14 o3·=·214 o3·=·2
  
15 i4·:·elapsedTime·monjMult·I15 i4·:·elapsedTime·monjMult·I
16 ·--·.150827s·elapsed16 ·--·.293612s·elapsed
  
17 o4·=·217 o4·=·2
  
18 i5·:·elapsedTime·multiplicitySequence·I18 i5·:·elapsedTime·multiplicitySequence·I
19 ·--·.885177s·elapsed19 ·--·1.17212s·elapsed
  
20 o5·=·HashTable{2·=>·3}20 o5·=·HashTable{2·=>·3}
21 ···············3·=>·221 ···············3·=>·2
  
22 o5·:·HashTable22 o5·:·HashTable
  
23 i6·:·23 i6·:·
371 B
./usr/share/doc/Macaulay2/MultiplicitySequence/example-output/_mon__Analytic__Spread.out
    
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10 ·············2········310 ·············2········3
11 o2·=·ideal·(x·,·x*y,·y·)11 o2·=·ideal·(x·,·x*y,·y·)
  
12 o2·:·Ideal·of·R12 o2·:·Ideal·of·R
  
13 i3·:·elapsedTime·monAnalyticSpread·I13 i3·:·elapsedTime·monAnalyticSpread·I
14 ·--·.269797s·elapsed14 ·--·.336662s·elapsed
  
15 o3·=·215 o3·=·2
  
16 i4·:·16 i4·:·
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./usr/share/doc/Macaulay2/MultiplicitySequence/example-output/_monj__Mult.out
    
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13 ·····------------------------------------------------------------------------13 ·····------------------------------------------------------------------------
14 ······10·11···8·12···9·11···10·10···11·9···12·814 ······10·11···8·12···9·11···10·10···11·9···12·8
15 ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·)15 ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·)
  
16 o2·:·Ideal·of·R16 o2·:·Ideal·of·R
  
17 i3·:·elapsedTime·monjMult·I17 i3·:·elapsedTime·monjMult·I
18 ·--·.26519s·elapsed18 ·--·.572626s·elapsed
  
19 o3·=·19219 o3·=·192
  
20 i4·:·elapsedTime·jMult·I20 i4·:·elapsedTime·jMult·I
21 ·--·1.55413s·elapsed21 ·--·3.41914s·elapsed
  
22 o4·=·19222 o4·=·192
  
23 i5·:·23 i5·:·
1.52 KB
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88 o2·:·Ideal·of·R</code></pre>88 o2·:·Ideal·of·R</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·jMult·I93 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·jMult·I
94 ·--·.0597996s·elapsed94 ·--·.107333s·elapsed
  
95 o3·=·2</code></pre>95 o3·=·2</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·monjMult·I100 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·monjMult·I
101 ·--·.150827s·elapsed101 ·--·.293612s·elapsed
  
102 o4·=·2</code></pre>102 o4·=·2</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·multiplicitySequence·I107 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·multiplicitySequence·I
108 ·--·.885177s·elapsed108 ·--·1.17212s·elapsed
  
109 o5·=·HashTable{2·=>·3}109 o5·=·HashTable{2·=>·3}
110 ···············3·=>·2110 ···············3·=>·2
  
111 o5·:·HashTable</code></pre>111 o5·:·HashTable</code></pre>
112 ············</td>112 ············</td>
113 ··········</tr>113 ··········</tr>
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20 o1·:·PolynomialRing20 o1·:·PolynomialRing
21 i2·:·I·=·ideal"xy,yz,zx"21 i2·:·I·=·ideal"xy,yz,zx"
  
22 o2·=·ideal·(x*y,·y*z,·x*z)22 o2·=·ideal·(x*y,·y*z,·x*z)
  
23 o2·:·Ideal·of·R23 o2·:·Ideal·of·R
24 i3·:·elapsedTime·jMult·I24 i3·:·elapsedTime·jMult·I
25 ·--·.0597996s·elapsed25 ·--·.107333s·elapsed
  
26 o3·=·226 o3·=·2
27 i4·:·elapsedTime·monjMult·I27 i4·:·elapsedTime·monjMult·I
28 ·--·.150827s·elapsed28 ·--·.293612s·elapsed
  
29 o4·=·229 o4·=·2
30 i5·:·elapsedTime·multiplicitySequence·I30 i5·:·elapsedTime·multiplicitySequence·I
31 ·--·.885177s·elapsed31 ·--·1.17212s·elapsed
  
32 o5·=·HashTable{2·=>·3}32 o5·=·HashTable{2·=>·3}
33 ···············3·=>·233 ···············3·=>·2
  
34 o5·:·HashTable34 o5·:·HashTable
35 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*35 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
36 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal36 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal
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89 o2·:·Ideal·of·R</code></pre>89 o2·:·Ideal·of·R</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monAnalyticSpread·I94 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monAnalyticSpread·I
95 ·--·.269797s·elapsed95 ·--·.336662s·elapsed
  
96 o3·=·2</code></pre>96 o3·=·2</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ········</table>99 ········</table>
100 ······</div>100 ······</div>
101 ······<div>101 ······<div>
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22 i2·:·I·=·ideal"x2,xy,y3"22 i2·:·I·=·ideal"x2,xy,y3"
  
23 ·············2········323 ·············2········3
24 o2·=·ideal·(x·,·x*y,·y·)24 o2·=·ideal·(x·,·x*y,·y·)
  
25 o2·:·Ideal·of·R25 o2·:·Ideal·of·R
26 i3·:·elapsedTime·monAnalyticSpread·I26 i3·:·elapsedTime·monAnalyticSpread·I
27 ·--·.269797s·elapsed27 ·--·.336662s·elapsed
  
28 o3·=·228 o3·=·2
29 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
30 ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal30 ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal
31 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mo\x8on\x8nA\x8An\x8na\x8al\x8ly\x8yt\x8ti\x8ic\x8cS\x8Sp\x8pr\x8re\x8ea\x8ad\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*31 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mo\x8on\x8nA\x8An\x8na\x8al\x8ly\x8yt\x8ti\x8ic\x8cS\x8Sp\x8pr\x8re\x8ea\x8ad\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
32 ····*·monAnalyticSpread(Ideal)32 ····*·monAnalyticSpread(Ideal)
33 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*33 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
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92 o2·:·Ideal·of·R</code></pre>92 o2·:·Ideal·of·R</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monjMult·I97 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monjMult·I
98 ·--·.26519s·elapsed98 ·--·.572626s·elapsed
  
99 o3·=·192</code></pre>99 o3·=·192</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jMult·I104 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jMult·I
105 ·--·1.55413s·elapsed105 ·--·3.41914s·elapsed
  
106 o4·=·192</code></pre>106 o4·=·192</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ········</table>109 ········</table>
110 ······</div>110 ······</div>
111 ······<div>111 ······<div>
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24 o2·=·ideal·(x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,24 o2·=·ideal·(x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,
25 ·····------------------------------------------------------------------------25 ·····------------------------------------------------------------------------
26 ······10·11···8·12···9·11···10·10···11·9···12·826 ······10·11···8·12···9·11···10·10···11·9···12·8
27 ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·)27 ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·)
  
28 o2·:·Ideal·of·R28 o2·:·Ideal·of·R
29 i3·:·elapsedTime·monjMult·I29 i3·:·elapsedTime·monjMult·I
30 ·--·.26519s·elapsed30 ·--·.572626s·elapsed
  
31 o3·=·19231 o3·=·192
32 i4·:·elapsedTime·jMult·I32 i4·:·elapsedTime·jMult·I
33 ·--·1.55413s·elapsed33 ·--·3.41914s·elapsed
  
34 o4·=·19234 o4·=·192
35 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*35 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
36 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal36 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal
37 ····*·_\x8j_\x8M_\x8u_\x8l_\x8t·--·the·j-multiplicity·of·an·ideal37 ····*·_\x8j_\x8M_\x8u_\x8l_\x8t·--·the·j-multiplicity·of·an·ideal
38 ····*·_\x8m_\x8o_\x8n_\x8R_\x8e_\x8d_\x8u_\x8c_\x8t_\x8i_\x8o_\x8n·--·the·minimal·monomial·reduction·of·a·monomial·ideal38 ····*·_\x8m_\x8o_\x8n_\x8R_\x8e_\x8d_\x8u_\x8c_\x8t_\x8i_\x8o_\x8n·--·the·minimal·monomial·reduction·of·a·monomial·ideal
39 ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal39 ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobG9nQ2Fub25pY2FsVGhyZXNob2xkLENlbnRyYWxB11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobG9nQ2Fub25pY2FsVGhyZXNob2xkLENlbnRyYWxB
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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749 B
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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13 o4·:·ProjectiveVariety,·curve·in·PP^813 o4·:·ProjectiveVariety,·curve·in·PP^8
  
14 i5·:·?·X14 i5·:·?·X
  
15 o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·15 o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·
  
16 i6·:·time·f·=·X·===>·Y;16 i6·:·time·f·=·X·===>·Y;
17 ·--·used·3.53608s·(cpu);·1.55292s·(thread);·0s·(gc)17 ·--·used·3.89343s·(cpu);·1.7934s·(thread);·0s·(gc)
  
18 o6·:·MultirationalMap·(automorphism·of·PP^8)18 o6·:·MultirationalMap·(automorphism·of·PP^8)
  
19 i7·:·f·X19 i7·:·f·X
  
20 o7·=·Y20 o7·=·Y
  
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38 o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^838 o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8
  
39 i10·:·W·=·random({{2},{1}},Y);39 i10·:·W·=·random({{2},{1}},Y);
  
40 o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^840 o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8
  
41 i11·:·time·g·=·V·===>·W;41 i11·:·time·g·=·V·===>·W;
42 ·--·used·5.53863s·(cpu);·1.869s·(thread);·0s·(gc)42 ·--·used·5.92392s·(cpu);·2.14528s·(thread);·0s·(gc)
  
43 o11·:·MultirationalMap·(automorphism·of·PP^8)43 o11·:·MultirationalMap·(automorphism·of·PP^8)
  
44 i12·:·g||W44 i12·:·g||W
  
45 o12·=·multi-rational·map·consisting·of·one·single·rational·map45 o12·=·multi-rational·map·consisting·of·one·single·rational·map
46 ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·2·hypersurfaces·of·degrees·1^1·2^1·46 ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·2·hypersurfaces·of·degrees·1^1·2^1·
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129 o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9129 o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9
  
130 i16·:·?·Z130 i16·:·?·Z
  
131 o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2131 o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2
  
132 i17·:·time·h·=·Z·===>·GG_K(1,4)132 i17·:·time·h·=·Z·===>·GG_K(1,4)
133 ·--·used·6.15904s·(cpu);·3.76456s·(thread);·0s·(gc)133 ·--·used·6.47522s·(cpu);·3.88016s·(thread);·0s·(gc)
  
134 o17·=·h134 o17·=·h
  
135 o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)135 o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)
  
136 i18·:·h·||·GG_K(1,4)136 i18·:·h·||·GG_K(1,4)
  
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./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/___Multirational__Map_sp^_st_st_sp__Multiprojective__Variety.out
    
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7 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)7 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)
  
8 i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi));8 i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi));
  
9 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^49 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4
  
10 i4·:·time·X·=·Phi^*·Y;10 i4·:·time·X·=·Phi^*·Y;
11 ·--·used·3.50881s·(cpu);·2.92836s·(thread);·0s·(gc)11 ·--·used·3.99873s·(cpu);·3.23998s·(thread);·0s·(gc)
  
12 o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)12 o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)
  
13 i5·:·dim·X,·degree·X,·degrees·X13 i5·:·dim·X,·degree·X,·degrees·X
  
14 o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1),14 o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1),
15 ·····------------------------------------------------------------------------15 ·····------------------------------------------------------------------------
1.13 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/___Multirational__Map_sp__Multiprojective__Variety.out
    
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11 o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^7·x·PP^7)11 o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^7·x·PP^7)
  
12 i4·:·Z·=·source·Phi;12 i4·:·Z·=·source·Phi;
  
13 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^713 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7
  
14 i5·:·time·Phi·Z;14 i5·:·time·Phi·Z;
15 ·--·used·0.360574s·(cpu);·0.103132s·(thread);·0s·(gc)15 ·--·used·0.294659s·(cpu);·0.114851s·(thread);·0s·(gc)
  
16 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^716 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7
  
17 i6·:·dim·oo,·degree·oo,·degrees·oo17 i6·:·dim·oo,·degree·oo,·degrees·oo
  
18 o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)})18 o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)})
  
19 o6·:·Sequence19 o6·:·Sequence
  
20 i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z)20 i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z)
21 ·--·used·1.63541s·(cpu);·1.04326s·(thread);·0s·(gc)21 ·--·used·2.02818s·(cpu);·1.17572s·(thread);·0s·(gc)
  
22 o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3·22 o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3·
  
23 o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^723 o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7
  
24 i8·:·dim·oo,·degree·oo,·degrees·oo24 i8·:·dim·oo,·degree·oo,·degrees·oo
  
1.07 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_degree_lp__Multirational__Map_cm__Option_rp.out
    
Offset 11, 22 lines modifiedOffset 11, 22 lines modified
11 o3·=·multi-rational·map·consisting·of·one·single·rational·map11 o3·=·multi-rational·map·consisting·of·one·single·rational·map
12 ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of12 ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of
13 ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·213 ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2
14 ·····------------------------------------------------------------------------14 ·····------------------------------------------------------------------------
15 ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^115 ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1
  
16 i4·:·time·degree(Phi,Strategy=>"random·point")16 i4·:·time·degree(Phi,Strategy=>"random·point")
17 ·--·used·2.93997s·(cpu);·1.99497s·(thread);·0s·(gc)17 ·--·used·3.85446s·(cpu);·2.11782s·(thread);·0s·(gc)
  
18 o4·=·218 o4·=·2
  
19 i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree")19 i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree")
20 ·--·used·0.279191s·(cpu);·0.229555s·(thread);·0s·(gc)20 ·--·used·0.281775s·(cpu);·0.232056s·(thread);·0s·(gc)
  
21 o5·=·221 o5·=·2
  
22 i6·:·time·degree·Phi22 i6·:·time·degree·Phi
23 ·--·used·0.181398s·(cpu);·0.182456s·(thread);·0s·(gc)23 ·--·used·0.278486s·(cpu);·0.231241s·(thread);·0s·(gc)
  
24 o6·=·224 o6·=·2
  
25 i7·:·25 i7·:·
670 B
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_degree_lp__Multirational__Map_rp.out
    
Offset 3, 12 lines modifiedOffset 3, 12 lines modified
3 i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2};3 i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2};
  
4 i2·:·Phi·=·last·graph·rationalMap·{f,g};4 i2·:·Phi·=·last·graph·rationalMap·{f,g};
  
5 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)5 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)
  
6 i3·:·time·degree·Phi6 i3·:·time·degree·Phi
7 ·--·used·0.637757s·(cpu);·0.32408s·(thread);·0s·(gc)7 ·--·used·0.638345s·(cpu);·0.34008s·(thread);·0s·(gc)
  
8 o3·=·18 o3·=·1
  
9 i4·:·9 i4·:·
2.66 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_describe_lp__Multirational__Map_rp.out
    
Offset 1, 52 lines modifiedOffset 1, 52 lines modified
1 --·-*-·M2-comint·-*-·hash:·115337213248520721611 --·-*-·M2-comint·-*-·hash:·11533721324852072161
  
2 i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4);2 i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4);
  
3 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)3 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)
  
4 i2·:·time·?·Phi4 i2·:·time·?·Phi
5 ·--·used·0.00182462s·(cpu);·0.000129435s·(thread);·0s·(gc)5 ·--·used·0.00205399s·(cpu);·0.000158266s·(thread);·0s·(gc)
  
6 o2·=·multi-rational·map·consisting·of·2·rational·maps6 o2·=·multi-rational·map·consisting·of·2·rational·maps
7 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·97 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9
8 ·····target·variety:·PP^4·x·PP^58 ·····target·variety:·PP^4·x·PP^5
9 ·····------------------------------------------------------------------------9 ·····------------------------------------------------------------------------
10 ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^810 ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8
  
11 i3·:·image·Phi;11 i3·:·image·Phi;
  
12 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^512 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5
  
13 i4·:·time·?·Phi13 i4·:·time·?·Phi
14 ·--·used·0.00338759s·(cpu);·0.000233021s·(thread);·0s·(gc)14 ·--·used·2.2382e-05s·(cpu);·0.00027188s·(thread);·0s·(gc)
  
15 o4·=·multi-rational·map·consisting·of·2·rational·maps15 o4·=·multi-rational·map·consisting·of·2·rational·maps
16 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·16 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
17 ·····target·variety:·PP^4·x·PP^517 ·····target·variety:·PP^4·x·PP^5
18 ·····dominance:·false18 ·····dominance:·false
19 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·19 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
  
20 i5·:·time·describe·Phi20 i5·:·time·describe·Phi
21 ·--·used·0.980811s·(cpu);·0.801706s·(thread);·0s·(gc)21 ·--·used·1.14347s·(cpu);·0.892664s·(thread);·0s·(gc)
  
22 o5·=·multi-rational·map·consisting·of·2·rational·maps22 o5·=·multi-rational·map·consisting·of·2·rational·maps
23 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·23 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
24 ·····target·variety:·PP^4·x·PP^524 ·····target·variety:·PP^4·x·PP^5
25 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^525 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5
26 ·····dominance:·false26 ·····dominance:·false
27 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·27 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
28 ·····multidegree:·{51,·51,·51,·51,·51}28 ·····multidegree:·{51,·51,·51,·51,·51}
29 ·····degree:·129 ·····degree:·1
30 ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)]30 ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)]
31 ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)]31 ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)]
32 ·····coefficient·ring:·ZZ/6552132 ·····coefficient·ring:·ZZ/65521
  
33 i6·:·time·?·Phi33 i6·:·time·?·Phi
34 ·--·used·0.000396647s·(cpu);·0.000394103s·(thread);·0s·(gc)34 ·--·used·0.000120365s·(cpu);·0.000394941s·(thread);·0s·(gc)
  
35 o6·=·multi-rational·map·consisting·of·2·rational·maps35 o6·=·multi-rational·map·consisting·of·2·rational·maps
36 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·36 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
37 ·····target·variety:·PP^4·x·PP^537 ·····target·variety:·PP^4·x·PP^5
38 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^538 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5
39 ·····dominance:·false39 ·····dominance:·false
40 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·40 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
1.47 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_graph_lp__Multirational__Map_rp.out
    
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3 i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true)3 i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true)
  
4 o1·=·Phi4 o1·=·Phi
  
5 o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)5 o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)
  
6 i2·:·time·(Phi1,Phi2)·=·graph·Phi6 i2·:·time·(Phi1,Phi2)·=·graph·Phi
7 ·--·used·0.326284s·(cpu);·0.0700423s·(thread);·0s·(gc)7 ·--·used·0.293922s·(cpu);·0.0574203s·(thread);·0s·(gc)
  
8 o2·=·(Phi1,·Phi2)8 o2·=·(Phi1,·Phi2)
  
9 o2·:·Sequence9 o2·:·Sequence
  
10 i3·:·Phi1;10 i3·:·Phi1;
  
11 o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4)11 o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4)
  
12 i4·:·Phi2;12 i4·:·Phi2;
  
13 o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)13 o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)
  
14 i5·:·time·(Phi21,Phi22)·=·graph·Phi214 i5·:·time·(Phi21,Phi22)·=·graph·Phi2
15 ·--·used·0.221098s·(cpu);·0.042252s·(thread);·0s·(gc)15 ·--·used·0.251043s·(cpu);·0.0546244s·(thread);·0s·(gc)
  
16 o5·=·(Phi21,·Phi22)16 o5·=·(Phi21,·Phi22)
  
17 o5·:·Sequence17 o5·:·Sequence
  
18 i6·:·Phi21;18 i6·:·Phi21;
  
19 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)19 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)
  
20 i7·:·Phi22;20 i7·:·Phi22;
  
21 o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)21 o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)
  
22 i8·:·time·(Phi211,Phi212)·=·graph·Phi2122 i8·:·time·(Phi211,Phi212)·=·graph·Phi21
23 ·--·used·0.374103s·(cpu);·0.132385s·(thread);·0s·(gc)23 ·--·used·0.433531s·(cpu);·0.173915s·(thread);·0s·(gc)
  
24 o8·=·(Phi211,·Phi212)24 o8·=·(Phi211,·Phi212)
  
25 o8·:·Sequence25 o8·:·Sequence
  
26 i9·:·Phi211;26 i9·:·Phi211;
  
1000 B
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_image_lp__Multirational__Map_rp.out
    
Offset 11, 25 lines modifiedOffset 11, 25 lines modified
11 o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)11 o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)
  
12 i4·:·Phi·=·rationalMap·{f,g};12 i4·:·Phi·=·rationalMap·{f,g};
  
13 o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)13 o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)
  
14 i5·:·time·Z·=·image·Phi;14 i5·:·time·Z·=·image·Phi;
15 ·--·used·0.277154s·(cpu);·0.117854s·(thread);·0s·(gc)15 ·--·used·0.324497s·(cpu);·0.128013s·(thread);·0s·(gc)
  
16 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^416 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4
  
17 i6·:·dim·Z,·degree·Z,·degrees·Z17 i6·:·dim·Z,·degree·Z,·degrees·Z
  
18 o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)})18 o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)})
  
19 o6·:·Sequence19 o6·:·Sequence
  
20 i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4");20 i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4");
21 ·--·used·7.51151s·(cpu);·2.34826s·(thread);·0s·(gc)21 ·--·used·8.32727s·(cpu);·2.58615s·(thread);·0s·(gc)
  
22 o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^422 o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4
  
23 i8·:·assert(Z·==·Z')23 i8·:·assert(Z·==·Z')
  
24 i9·:·24 i9·:·
1.02 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_inverse2.out
    
Offset 4, 25 lines modifiedOffset 4, 25 lines modified
  
4 i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational·normal·curve·of·degree·64 i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational·normal·curve·of·degree·6
5 ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2));5 ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2));
  
6 o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))6 o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))
  
7 i3·:·time·Psi·=·inverse2·Phi;7 i3·:·time·Psi·=·inverse2·Phi;
8 ·--·used·0.605001s·(cpu);·0.302001s·(thread);·0s·(gc)8 ·--·used·0.576582s·(cpu);·0.29168s·(thread);·0s·(gc)
  
9 o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)9 o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)
  
10 i4·:·assert(Phi·*·Psi·==·1)10 i4·:·assert(Phi·*·Psi·==·1)
  
11 i5·:·Phi'·=·Phi·||·Phi;11 i5·:·Phi'·=·Phi·||·Phi;
  
12 o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))12 o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))
  
13 i6·:·time·Psi'·=·inverse2·Phi';13 i6·:·time·Psi'·=·inverse2·Phi';
14 ·--·used·1.19344s·(cpu);·0.83645s·(thread);·0s·(gc)14 ·--·used·1.27758s·(cpu);·0.905749s·(thread);·0s·(gc)
  
15 o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)15 o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)
  
16 i7·:·assert(Phi'·*·Psi'·==·1)16 i7·:·assert(Phi'·*·Psi'·==·1)
  
17 i8·:·17 i8·:·
1.51 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_inverse_lp__Multirational__Map_rp.out
    
Offset 7, 33 lines modifiedOffset 7, 33 lines modified
  
7 i2·:·--·we·see·Phi·as·a·dominant·map7 i2·:·--·we·see·Phi·as·a·dominant·map
8 ·····Phi·=·rationalMap(Phi,image·Phi);8 ·····Phi·=·rationalMap(Phi,image·Phi);
  
9 o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)9 o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)
  
10 i3·:·time·inverse·Phi;10 i3·:·time·inverse·Phi;
11 ·--·used·0.31778s·(cpu);·0.0727678s·(thread);·0s·(gc)11 ·--·used·0.307053s·(cpu);·0.0770788s·(thread);·0s·(gc)
  
12 o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)12 o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)
  
13 i4·:·Psi·=·last·graph·Phi;13 i4·:·Psi·=·last·graph·Phi;
  
14 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)14 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)
  
15 i5·:·time·inverse·Psi;15 i5·:·time·inverse·Psi;
16 ·--·used·0.595157s·(cpu);·0.123909s·(thread);·0s·(gc)16 ·--·used·0.591947s·(cpu);·0.138383s·(thread);·0s·(gc)
  
17 o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)17 o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)
  
18 i6·:·Eta·=·first·graph·Psi;18 i6·:·Eta·=·first·graph·Psi;
  
19 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)19 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)
  
20 i7·:·time·inverse·Eta;20 i7·:·time·inverse·Eta;
21 ·--·used·0.862919s·(cpu);·0.296744s·(thread);·0s·(gc)21 ·--·used·0.983512s·(cpu);·0.397828s·(thread);·0s·(gc)
  
22 o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)22 o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)
  
23 i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)23 i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)
  
24 i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1)24 i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1)
  
1.17 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_is__Isomorphism_lp__Multirational__Map_rp.out
    
Offset 6, 32 lines modifiedOffset 6, 32 lines modified
6 o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2)6 o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2)
  
7 i3·:·Phi·=·rationalMap·{f,f};7 i3·:·Phi·=·rationalMap·{f,f};
  
8 o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)8 o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)
  
9 i4·:·time·isIsomorphism·Phi9 i4·:·time·isIsomorphism·Phi
10 ·--·used·0.000403758s·(cpu);·6.009e-06s·(thread);·0s·(gc)10 ·--·used·0.00291045s·(cpu);·8.326e-06s·(thread);·0s·(gc)
  
11 o4·=·false11 o4·=·false
  
12 i5·:·Psi·=·first·graph·Phi;12 i5·:·Psi·=·first·graph·Phi;
  
13 o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)13 o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)
  
14 i6·:·time·isIsomorphism·Psi14 i6·:·time·isIsomorphism·Psi
15 ·--·used·0.753016s·(cpu);·0.215353s·(thread);·0s·(gc)15 ·--·used·0.762507s·(cpu);·0.228863s·(thread);·0s·(gc)
  
16 o6·=·false16 o6·=·false
  
17 i7·:·Eta·=·first·graph·Psi;17 i7·:·Eta·=·first·graph·Psi;
  
18 o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)18 o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)
  
19 i8·:·time·isIsomorphism·Eta19 i8·:·time·isIsomorphism·Eta
20 ·--·used·1.65491s·(cpu);·0.746739s·(thread);·0s·(gc)20 ·--·used·1.87751s·(cpu);·0.849471s·(thread);·0s·(gc)
  
21 o8·=·true21 o8·=·true
  
22 i9·:·assert(o8·and·(not·o6)·and·(not·o4))22 i9·:·assert(o8·and·(not·o6)·and·(not·o4))
  
23 i10·:·23 i10·:·
1.1 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_is__Morphism_lp__Multirational__Map_rp.out
    
Offset 3, 24 lines modifiedOffset 3, 24 lines modified
3 i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2-a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2});3 i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2-a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2});
  
4 i2·:·Phi·=·rationalMap·{f,g};4 i2·:·Phi·=·rationalMap·{f,g};
  
5 o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)5 o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)
  
6 i3·:·time·isMorphism·Phi6 i3·:·time·isMorphism·Phi
7 ·--·used·0.298026s·(cpu);·0.198458s·(thread);·0s·(gc)7 ·--·used·0.327156s·(cpu);·0.209736s·(thread);·0s·(gc)
  
8 o3·=·false8 o3·=·false
  
9 i4·:·time·Psi·=·first·graph·Phi;9 i4·:·time·Psi·=·first·graph·Phi;
10 ·--·used·0.338977s·(cpu);·0.104163s·(thread);·0s·(gc)10 ·--·used·0.374814s·(cpu);·0.0905049s·(thread);·0s·(gc)
  
11 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)11 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)
  
12 i5·:·time·isMorphism·Psi12 i5·:·time·isMorphism·Psi
13 ·--·used·2.9027s·(cpu);·2.49449s·(thread);·0s·(gc)13 ·--·used·3.03797s·(cpu);·2.57755s·(thread);·0s·(gc)
  
14 o5·=·true14 o5·=·true
  
15 i6·:·assert((not·o3)·and·o5)15 i6·:·assert((not·o3)·and·o5)
  
16 i7·:·16 i7·:·
968 B
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_linearly__Normal__Embedding.out
    
Offset 3, 24 lines modifiedOffset 3, 24 lines modified
3 i1·:·K·=·ZZ/333331;3 i1·:·K·=·ZZ/333331;
  
4 i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·74 i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7
  
5 o2·:·ProjectiveVariety,·curve·in·PP^75 o2·:·ProjectiveVariety,·curve·in·PP^7
  
6 i3·:·time·f·=·linearlyNormalEmbedding·X;6 i3·:·time·f·=·linearlyNormalEmbedding·X;
7 ·--·used·0.00836101s·(cpu);·0.00902196s·(thread);·0s·(gc)7 ·--·used·0.0119464s·(cpu);·0.0103894s·(thread);·0s·(gc)
  
8 o3·:·MultirationalMap·(automorphism·of·X)8 o3·:·MultirationalMap·(automorphism·of·X)
  
9 i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^39 i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^3
  
10 o4·:·ProjectiveVariety,·curve·in·PP^310 o4·:·ProjectiveVariety,·curve·in·PP^3
  
11 i5·:·time·g·=·linearlyNormalEmbedding·Y;11 i5·:·time·g·=·linearlyNormalEmbedding·Y;
12 ·--·used·0.36771s·(cpu);·0.332505s·(thread);·0s·(gc)12 ·--·used·0.419817s·(cpu);·0.365869s·(thread);·0s·(gc)
  
13 o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)13 o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)
  
14 i6·:·assert(isIsomorphism·g)14 i6·:·assert(isIsomorphism·g)
  
15 i7·:·describe·g15 i7·:·describe·g
  
752 B
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_multidegree_lp__Multirational__Map_rp.out
    
Offset 3, 15 lines modifiedOffset 3, 15 lines modified
3 i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2};3 i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2};
  
4 i2·:·Phi·=·last·graph·rationalMap·{f,g};4 i2·:·Phi·=·last·graph·rationalMap·{f,g};
  
5 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)5 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)
  
6 i3·:·time·multidegree·Phi6 i3·:·time·multidegree·Phi
7 ·--·used·0.605515s·(cpu);·0.32402s·(thread);·0s·(gc)7 ·--·used·0.672585s·(cpu);·0.325083s·(thread);·0s·(gc)
  
8 o3·=·{66,·46,·31,·20}8 o3·=·{66,·46,·31,·20}
  
9 o3·:·List9 o3·:·List
  
10 i4·:·(degree·source·Phi,degree·image·Phi)10 i4·:·(degree·source·Phi,degree·image·Phi)
  
1.24 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_multidegree_lp__Z__Z_cm__Multirational__Map_rp.out
    
Offset 1, 21 lines modifiedOffset 1, 21 lines modified
1 --·-*-·M2-comint·-*-·hash:·161997332192100812141 --·-*-·M2-comint·-*-·hash:·16199733219210081214
  
2 i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4);2 i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4);
  
3 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)3 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)
  
4 i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi)4 i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi)
5 ·--·used·0.00137308s·(cpu);·0.00112143s·(thread);·0s·(gc)5 ·--·used·0.00161832s·(cpu);·0.00142918s·(thread);·0s·(gc)
6 ·--·used·0.173207s·(cpu);·0.125968s·(thread);·0s·(gc)6 ·--·used·0.174177s·(cpu);·0.128396s·(thread);·0s·(gc)
7 ·--·used·0.196544s·(cpu);·0.151621s·(thread);·0s·(gc) 
8 ·--·used·0.174714s·(cpu);·0.125714s·(thread);·0s·(gc)7 ·--·used·0.184877s·(cpu);·0.142434s·(thread);·0s·(gc)
 8 ·--·used·0.168329s·(cpu);·0.120877s·(thread);·0s·(gc)
9 ·--·used·0.147903s·(cpu);·0.100526s·(thread);·0s·(gc)9 ·--·used·0.175593s·(cpu);·0.114917s·(thread);·0s·(gc)
  
10 o2·=·{51,·28,·14,·6,·2}10 o2·=·{51,·28,·14,·6,·2}
  
11 o2·:·List11 o2·:·List
  
12 i3·:·time·assert(oo·==·multidegree·Phi)12 i3·:·time·assert(oo·==·multidegree·Phi)
13 ·--·used·0.292374s·(cpu);·0.079935s·(thread);·0s·(gc)13 ·--·used·0.303852s·(cpu);·0.0897984s·(thread);·0s·(gc)
  
14 i4·:·14 i4·:·
1.04 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_point_lp__Multiprojective__Variety_rp.out
    
Offset 3, 26 lines modifiedOffset 3, 26 lines modified
3 i1·:·K·=·ZZ/1000003;3 i1·:·K·=·ZZ/1000003;
  
4 i2·:·X·=·PP_K^({1,1,2},{3,2,3});4 i2·:·X·=·PP_K^({1,1,2},{3,2,3});
  
5 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^95 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9
  
6 i3·:·time·p·:=·point·X6 i3·:·time·p·:=·point·X
7 ·--·used·0.249919s·(cpu);·0.0321772s·(thread);·0s·(gc)7 ·--·used·0.18054s·(cpu);·0.0395397s·(thread);·0s·(gc)
  
8 o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1])8 o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1])
  
9 o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^99 o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9
  
10 i4·:·Y·=·random({2,1,2},X);10 i4·:·Y·=·random({2,1,2},X);
  
11 o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^911 o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9
  
12 i5·:·time·q·=·point·Y12 i5·:·time·q·=·point·Y
13 ·--·used·1.23577s·(cpu);·0.747615s·(thread);·0s·(gc)13 ·--·used·1.37418s·(cpu);·0.779439s·(thread);·0s·(gc)
  
14 o5·=·q14 o5·=·q
  
15 o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^915 o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9
  
16 i6·:·assert(isSubset(p,X)·and·isSubset(q,Y))16 i6·:·assert(isSubset(p,X)·and·isSubset(q,Y))
  
697 B
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_segre_lp__Multirational__Map_rp.out
    
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15 o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)15 o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)
  
16 i5·:·Phi·=·rationalMap·{f,g,h};16 i5·:·Phi·=·rationalMap·{f,g,h};
  
17 o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)17 o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)
  
18 i6·:·time·segre·Phi;18 i6·:·time·segre·Phi;
19 ·--·used·4.05061s·(cpu);·0.750041s·(thread);·0s·(gc)19 ·--·used·3.88011s·(cpu);·0.8594s·(thread);·0s·(gc)
  
20 o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)20 o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)
  
21 i7·:·describe·segre·Phi21 i7·:·describe·segre·Phi
  
22 o7·=·rational·map·defined·by·forms·of·degree·622 o7·=·rational·map·defined·by·forms·of·degree·6
23 ·····source·variety:·PP^423 ·····source·variety:·PP^4
939 B
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/example-output/_show_lp__Multirational__Map_rp.out
    
Offset 3, 15 lines modifiedOffset 3, 15 lines modified
3 i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3)3 i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3)
  
4 o1·=·Phi4 o1·=·Phi
  
5 o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2)5 o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2)
  
6 i2·:·time·describe·Phi6 i2·:·time·describe·Phi
7 ·--·used·0.251286s·(cpu);·0.155829s·(thread);·0s·(gc)7 ·--·used·0.246161s·(cpu);·0.133396s·(thread);·0s·(gc)
  
8 o2·=·multi-rational·map·consisting·of·3·rational·maps8 o2·=·multi-rational·map·consisting·of·3·rational·maps
9 ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1)9 ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1)
10 ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2·10 ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2·
11 ·····base·locus:·empty·subscheme·of·PP^3·x·PP^211 ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2
12 ·····dominance:·true12 ·····dominance:·true
13 ·····multidegree:·{10,·14,·19,·25}13 ·····multidegree:·{10,·14,·19,·25}
3.31 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/html/___Embedded__Projective__Variety_sp_eq_eq_eq_gt_sp__Embedded__Projective__Variety.html
    
Offset 103, 15 lines modifiedOffset 103, 15 lines modified
  
103 o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·</code></pre>103 o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i6·:·time·f·=·X·===>·Y;108 ··············<pre><code·class="language-macaulay2">i6·:·time·f·=·X·===>·Y;
109 ·--·used·3.53608s·(cpu);·1.55292s·(thread);·0s·(gc)109 ·--·used·3.89343s·(cpu);·1.7934s·(thread);·0s·(gc)
  
110 o6·:·MultirationalMap·(automorphism·of·PP^8)</code></pre>110 o6·:·MultirationalMap·(automorphism·of·PP^8)</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i7·:·f·X115 ··············<pre><code·class="language-macaulay2">i7·:·f·X
Offset 143, 15 lines modifiedOffset 143, 15 lines modified
  
143 o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8</code></pre>143 o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8</code></pre>
144 ············</td>144 ············</td>
145 ··········</tr>145 ··········</tr>
146 ··········<tr>146 ··········<tr>
147 ············<td>147 ············<td>
148 ··············<pre><code·class="language-macaulay2">i11·:·time·g·=·V·===>·W;148 ··············<pre><code·class="language-macaulay2">i11·:·time·g·=·V·===>·W;
149 ·--·used·5.53863s·(cpu);·1.869s·(thread);·0s·(gc)149 ·--·used·5.92392s·(cpu);·2.14528s·(thread);·0s·(gc)
  
150 o11·:·MultirationalMap·(automorphism·of·PP^8)</code></pre>150 o11·:·MultirationalMap·(automorphism·of·PP^8)</code></pre>
151 ············</td>151 ············</td>
152 ··········</tr>152 ··········</tr>
153 ··········<tr>153 ··········<tr>
154 ············<td>154 ············<td>
155 ··············<pre><code·class="language-macaulay2">i12·:·g||W155 ··············<pre><code·class="language-macaulay2">i12·:·g||W
Offset 252, 15 lines modifiedOffset 252, 15 lines modified
  
252 o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2</code></pre>252 o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2</code></pre>
253 ············</td>253 ············</td>
254 ··········</tr>254 ··········</tr>
255 ··········<tr>255 ··········<tr>
256 ············<td>256 ············<td>
257 ··············<pre><code·class="language-macaulay2">i17·:·time·h·=·Z·===>·GG_K(1,4)257 ··············<pre><code·class="language-macaulay2">i17·:·time·h·=·Z·===>·GG_K(1,4)
258 ·--·used·6.15904s·(cpu);·3.76456s·(thread);·0s·(gc)258 ·--·used·6.47522s·(cpu);·3.88016s·(thread);·0s·(gc)
  
259 o17·=·h259 o17·=·h
  
260 o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)</code></pre>260 o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)</code></pre>
261 ············</td>261 ············</td>
262 ··········</tr>262 ··········</tr>
263 ··········<tr>263 ··········<tr>
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33 take(N,-2));33 take(N,-2));
  
34 o4·:·ProjectiveVariety,·curve·in·PP^834 o4·:·ProjectiveVariety,·curve·in·PP^8
35 i5·:·?·X35 i5·:·?·X
  
36 o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^1536 o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15
37 i6·:·time·f·=·X·===>·Y;37 i6·:·time·f·=·X·===>·Y;
38 ·--·used·3.53608s·(cpu);·1.55292s·(thread);·0s·(gc)38 ·--·used·3.89343s·(cpu);·1.7934s·(thread);·0s·(gc)
  
39 o6·:·MultirationalMap·(automorphism·of·PP^8)39 o6·:·MultirationalMap·(automorphism·of·PP^8)
40 i7·:·f·X40 i7·:·f·X
  
41 o7·=·Y41 o7·=·Y
  
42 o7·:·ProjectiveVariety,·curve·in·PP^842 o7·:·ProjectiveVariety,·curve·in·PP^8
Offset 53, 15 lines modifiedOffset 53, 15 lines modified
53 i9·:·V·=·random({{2},{1}},X);53 i9·:·V·=·random({{2},{1}},X);
  
54 o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^854 o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8
55 i10·:·W·=·random({{2},{1}},Y);55 i10·:·W·=·random({{2},{1}},Y);
  
56 o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^856 o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8
57 i11·:·time·g·=·V·===>·W;57 i11·:·time·g·=·V·===>·W;
58 ·--·used·5.53863s·(cpu);·1.869s·(thread);·0s·(gc)58 ·--·used·5.92392s·(cpu);·2.14528s·(thread);·0s·(gc)
  
59 o11·:·MultirationalMap·(automorphism·of·PP^8)59 o11·:·MultirationalMap·(automorphism·of·PP^8)
60 i12·:·g||W60 i12·:·g||W
  
61 o12·=·multi-rational·map·consisting·of·one·single·rational·map61 o12·=·multi-rational·map·consisting·of·one·single·rational·map
62 ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·262 ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·2
63 hypersurfaces·of·degrees·1^1·2^163 hypersurfaces·of·degrees·1^1·2^1
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144 i15·:·Z·=·projectiveVariety·pfaffians(4,A);144 i15·:·Z·=·projectiveVariety·pfaffians(4,A);
  
145 o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9145 o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9
146 i16·:·?·Z146 i16·:·?·Z
  
147 o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2147 o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2
148 i17·:·time·h·=·Z·===>·GG_K(1,4)148 i17·:·time·h·=·Z·===>·GG_K(1,4)
149 ·--·used·6.15904s·(cpu);·3.76456s·(thread);·0s·(gc)149 ·--·used·6.47522s·(cpu);·3.88016s·(thread);·0s·(gc)
  
150 o17·=·h150 o17·=·h
  
151 o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)151 o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)
152 i18·:·h·||·GG_K(1,4)152 i18·:·h·||·GG_K(1,4)
  
153 o18·=·multi-rational·map·consisting·of·one·single·rational·map153 o18·=·multi-rational·map·consisting·of·one·single·rational·map
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89 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4</code></pre>89 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i4·:·time·X·=·Phi^*·Y;94 ··············<pre><code·class="language-macaulay2">i4·:·time·X·=·Phi^*·Y;
95 ·--·used·3.50881s·(cpu);·2.92836s·(thread);·0s·(gc)95 ·--·used·3.99873s·(cpu);·3.23998s·(thread);·0s·(gc)
  
96 o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)</code></pre>96 o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i5·:·dim·X,·degree·X,·degrees·X101 ··············<pre><code·class="language-macaulay2">i5·:·dim·X,·degree·X,·degrees·X
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26 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to26 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to
27 PP^2·x·PP^4)27 PP^2·x·PP^4)
28 i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random(28 i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random(
29 {1,1},ring·target·Phi));29 {1,1},ring·target·Phi));
  
30 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^430 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4
31 i4·:·time·X·=·Phi^*·Y;31 i4·:·time·X·=·Phi^*·Y;
32 ·--·used·3.50881s·(cpu);·2.92836s·(thread);·0s·(gc)32 ·--·used·3.99873s·(cpu);·3.23998s·(thread);·0s·(gc)
  
33 o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension33 o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension
34 2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-34 2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-
35 degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)35 degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)
36 i5·:·dim·X,·degree·X,·degrees·X36 i5·:·dim·X,·degree·X,·degrees·X
  
37 o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1),37 o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1),
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95 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7</code></pre>95 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i5·:·time·Phi·Z;100 ··············<pre><code·class="language-macaulay2">i5·:·time·Phi·Z;
101 ·--·used·0.360574s·(cpu);·0.103132s·(thread);·0s·(gc)101 ·--·used·0.294659s·(cpu);·0.114851s·(thread);·0s·(gc)
  
102 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7</code></pre>102 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i6·:·dim·oo,·degree·oo,·degrees·oo107 ··············<pre><code·class="language-macaulay2">i6·:·dim·oo,·degree·oo,·degrees·oo
Offset 112, 15 lines modifiedOffset 112, 15 lines modified
  
112 o6·:·Sequence</code></pre>112 o6·:·Sequence</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z)117 ··············<pre><code·class="language-macaulay2">i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z)
118 ·--·used·1.63541s·(cpu);·1.04326s·(thread);·0s·(gc)118 ·--·used·2.02818s·(cpu);·1.17572s·(thread);·0s·(gc)
  
119 o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3·119 o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3·
  
120 o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7</code></pre>120 o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7</code></pre>
121 ············</td>121 ············</td>
122 ··········</tr>122 ··········</tr>
123 ··········<tr>123 ··········<tr>
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25 o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x25 o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x
26 PP^7·to·PP^7·x·PP^7)26 PP^7·to·PP^7·x·PP^7)
27 i4·:·Z·=·source·Phi;27 i4·:·Z·=·source·Phi;
  
28 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^728 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7
29 i5·:·time·Phi·Z;29 i5·:·time·Phi·Z;
30 ·--·used·0.360574s·(cpu);·0.103132s·(thread);·0s·(gc)30 ·--·used·0.294659s·(cpu);·0.114851s·(thread);·0s·(gc)
  
31 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^731 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7
32 i6·:·dim·oo,·degree·oo,·degrees·oo32 i6·:·dim·oo,·degree·oo,·degrees·oo
  
33 o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)})33 o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)})
  
34 o6·:·Sequence34 o6·:·Sequence
35 i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z)35 i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z)
36 ·--·used·1.63541s·(cpu);·1.04326s·(thread);·0s·(gc)36 ·--·used·2.02818s·(cpu);·1.17572s·(thread);·0s·(gc)
  
37 o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of37 o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of
38 multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^338 multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3
  
39 o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^739 o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7
40 i8·:·dim·oo,·degree·oo,·degrees·oo40 i8·:·dim·oo,·degree·oo,·degrees·oo
  
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93 ·····------------------------------------------------------------------------93 ·····------------------------------------------------------------------------
94 ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1</code></pre>94 ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i4·:·time·degree(Phi,Strategy=>&quot;random·point&quot;)99 ··············<pre><code·class="language-macaulay2">i4·:·time·degree(Phi,Strategy=>&quot;random·point&quot;)
100 ·--·used·2.93997s·(cpu);·1.99497s·(thread);·0s·(gc)100 ·--·used·3.85446s·(cpu);·2.11782s·(thread);·0s·(gc)
  
101 o4·=·2</code></pre>101 o4·=·2</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i5·:·time·degree(Phi,Strategy=>&quot;0-th·projective·degree&quot;)106 ··············<pre><code·class="language-macaulay2">i5·:·time·degree(Phi,Strategy=>&quot;0-th·projective·degree&quot;)
107 ·--·used·0.279191s·(cpu);·0.229555s·(thread);·0s·(gc)107 ·--·used·0.281775s·(cpu);·0.232056s·(thread);·0s·(gc)
  
108 o5·=·2</code></pre>108 o5·=·2</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i6·:·time·degree·Phi113 ··············<pre><code·class="language-macaulay2">i6·:·time·degree·Phi
114 ·--·used·0.181398s·(cpu);·0.182456s·(thread);·0s·(gc)114 ·--·used·0.278486s·(cpu);·0.231241s·(thread);·0s·(gc)
  
115 o6·=·2</code></pre>115 o6·=·2</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ········</table>118 ········</table>
119 ········<p>Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the·strategy·used.</p>119 ········<p>Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the·strategy·used.</p>
120 ······</div>120 ······</div>
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27 o3·=·multi-rational·map·consisting·of·one·single·rational·map27 o3·=·multi-rational·map·consisting·of·one·single·rational·map
28 ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of28 ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of
29 ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·229 ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2
30 ·····------------------------------------------------------------------------30 ·····------------------------------------------------------------------------
31 ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^131 ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1
32 i4·:·time·degree(Phi,Strategy=>"random·point")32 i4·:·time·degree(Phi,Strategy=>"random·point")
33 ·--·used·2.93997s·(cpu);·1.99497s·(thread);·0s·(gc)33 ·--·used·3.85446s·(cpu);·2.11782s·(thread);·0s·(gc)
  
34 o4·=·234 o4·=·2
35 i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree")35 i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree")
36 ·--·used·0.279191s·(cpu);·0.229555s·(thread);·0s·(gc)36 ·--·used·0.281775s·(cpu);·0.232056s·(thread);·0s·(gc)
  
37 o5·=·237 o5·=·2
38 i6·:·time·degree·Phi38 i6·:·time·degree·Phi
39 ·--·used·0.181398s·(cpu);·0.182456s·(thread);·0s·(gc)39 ·--·used·0.278486s·(cpu);·0.231241s·(thread);·0s·(gc)
  
40 o6·=·240 o6·=·2
41 Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the41 Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the
42 strategy·used.42 strategy·used.
43 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*43 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
44 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·multi-rational·map44 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·multi-rational·map
45 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map45 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map
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81 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre>81 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i3·:·time·degree·Phi86 ··············<pre><code·class="language-macaulay2">i3·:·time·degree·Phi
87 ·--·used·0.637757s·(cpu);·0.32408s·(thread);·0s·(gc)87 ·--·used·0.638345s·(cpu);·0.34008s·(thread);·0s·(gc)
  
88 o3·=·1</code></pre>88 o3·=·1</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ········</table>91 ········</table>
92 ······</div>92 ······</div>
93 ······<div>93 ······<div>
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18 x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,18 x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,
19 x_3^2};19 x_3^2};
20 i2·:·Phi·=·last·graph·rationalMap·{f,g};20 i2·:·Phi·=·last·graph·rationalMap·{f,g};
  
21 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to21 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to
22 PP^2·x·PP^4)22 PP^2·x·PP^4)
23 i3·:·time·degree·Phi23 i3·:·time·degree·Phi
24 ·--·used·0.637757s·(cpu);·0.32408s·(thread);·0s·(gc)24 ·--·used·0.638345s·(cpu);·0.34008s·(thread);·0s·(gc)
  
25 o3·=·125 o3·=·1
26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
27 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8,_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8)·--·degree·of·a·multi-rational·map·using·a27 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8,_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8)·--·degree·of·a·multi-rational·map·using·a
28 ······probabilistic·approach28 ······probabilistic·approach
29 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map29 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map
30 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational30 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational
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77 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)</code></pre>77 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·time·?·Phi82 ··············<pre><code·class="language-macaulay2">i2·:·time·?·Phi
83 ·--·used·0.00182462s·(cpu);·0.000129435s·(thread);·0s·(gc)83 ·--·used·0.00205399s·(cpu);·0.000158266s·(thread);·0s·(gc)
  
84 o2·=·multi-rational·map·consisting·of·2·rational·maps84 o2·=·multi-rational·map·consisting·of·2·rational·maps
85 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·985 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9
86 ·····target·variety:·PP^4·x·PP^586 ·····target·variety:·PP^4·x·PP^5
87 ·····------------------------------------------------------------------------87 ·····------------------------------------------------------------------------
88 ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8</code></pre>88 ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8</code></pre>
89 ············</td>89 ············</td>
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96 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5</code></pre>96 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·time·?·Phi101 ··············<pre><code·class="language-macaulay2">i4·:·time·?·Phi
102 ·--·used·0.00338759s·(cpu);·0.000233021s·(thread);·0s·(gc)102 ·--·used·2.2382e-05s·(cpu);·0.00027188s·(thread);·0s·(gc)
  
103 o4·=·multi-rational·map·consisting·of·2·rational·maps103 o4·=·multi-rational·map·consisting·of·2·rational·maps
104 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·104 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
105 ·····target·variety:·PP^4·x·PP^5105 ·····target·variety:·PP^4·x·PP^5
106 ·····dominance:·false106 ·····dominance:·false
107 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·</code></pre>107 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i5·:·time·describe·Phi112 ··············<pre><code·class="language-macaulay2">i5·:·time·describe·Phi
113 ·--·used·0.980811s·(cpu);·0.801706s·(thread);·0s·(gc)113 ·--·used·1.14347s·(cpu);·0.892664s·(thread);·0s·(gc)
  
114 o5·=·multi-rational·map·consisting·of·2·rational·maps114 o5·=·multi-rational·map·consisting·of·2·rational·maps
115 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·115 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
116 ·····target·variety:·PP^4·x·PP^5116 ·····target·variety:·PP^4·x·PP^5
117 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5117 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5
118 ·····dominance:·false118 ·····dominance:·false
119 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·119 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
Offset 126, 15 lines modifiedOffset 126, 15 lines modified
126 ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)]126 ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)]
127 ·····coefficient·ring:·ZZ/65521</code></pre>127 ·····coefficient·ring:·ZZ/65521</code></pre>
128 ············</td>128 ············</td>
129 ··········</tr>129 ··········</tr>
130 ··········<tr>130 ··········<tr>
131 ············<td>131 ············<td>
132 ··············<pre><code·class="language-macaulay2">i6·:·time·?·Phi132 ··············<pre><code·class="language-macaulay2">i6·:·time·?·Phi
133 ·--·used·0.000396647s·(cpu);·0.000394103s·(thread);·0s·(gc)133 ·--·used·0.000120365s·(cpu);·0.000394941s·(thread);·0s·(gc)
  
134 o6·=·multi-rational·map·consisting·of·2·rational·maps134 o6·=·multi-rational·map·consisting·of·2·rational·maps
135 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·135 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
136 ·····target·variety:·PP^4·x·PP^5136 ·····target·variety:·PP^4·x·PP^5
137 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5137 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5
138 ·····dominance:·false138 ·····dominance:·false
139 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·139 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·
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16 ?·Phi·is·a·lite·version·of·describe·Phi.·The·latter·has·a·different·behavior16 ?·Phi·is·a·lite·version·of·describe·Phi.·The·latter·has·a·different·behavior
17 than·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8),·since·it·performs·computations.17 than·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8),·since·it·performs·computations.
18 i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4);18 i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4);
  
19 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x19 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x
20 PP^5·to·PP^4·x·PP^5)20 PP^5·to·PP^4·x·PP^5)
21 i2·:·time·?·Phi21 i2·:·time·?·Phi
22 ·--·used·0.00182462s·(cpu);·0.000129435s·(thread);·0s·(gc)22 ·--·used·0.00205399s·(cpu);·0.000158266s·(thread);·0s·(gc)
  
23 o2·=·multi-rational·map·consisting·of·2·rational·maps23 o2·=·multi-rational·map·consisting·of·2·rational·maps
24 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·924 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9
25 ·····target·variety:·PP^4·x·PP^525 ·····target·variety:·PP^4·x·PP^5
26 ·····------------------------------------------------------------------------26 ·····------------------------------------------------------------------------
27 ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^827 ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8
28 i3·:·image·Phi;28 i3·:·image·Phi;
  
29 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^529 o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5
30 i4·:·time·?·Phi30 i4·:·time·?·Phi
31 ·--·used·0.00338759s·(cpu);·0.000233021s·(thread);·0s·(gc)31 ·--·used·2.2382e-05s·(cpu);·0.00027188s·(thread);·0s·(gc)
  
32 o4·=·multi-rational·map·consisting·of·2·rational·maps32 o4·=·multi-rational·map·consisting·of·2·rational·maps
33 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·933 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9
34 hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^834 hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8
35 ·····target·variety:·PP^4·x·PP^535 ·····target·variety:·PP^4·x·PP^5
36 ·····dominance:·false36 ·····dominance:·false
37 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces37 ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces
38 of·multi-degrees·(0,2)^1·(1,1)^838 of·multi-degrees·(0,2)^1·(1,1)^8
39 i5·:·time·describe·Phi39 i5·:·time·describe·Phi
40 ·--·used·0.980811s·(cpu);·0.801706s·(thread);·0s·(gc)40 ·--·used·1.14347s·(cpu);·0.892664s·(thread);·0s·(gc)
  
41 o5·=·multi-rational·map·consisting·of·2·rational·maps41 o5·=·multi-rational·map·consisting·of·2·rational·maps
42 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·942 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9
43 hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^843 hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8
44 ·····target·variety:·PP^4·x·PP^544 ·····target·variety:·PP^4·x·PP^5
45 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^545 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5
46 ·····dominance:·false46 ·····dominance:·false
Offset 53, 15 lines modifiedOffset 53, 15 lines modified
53 of·multi-degrees·(0,2)^1·(1,1)^853 of·multi-degrees·(0,2)^1·(1,1)^8
54 ·····multidegree:·{51,·51,·51,·51,·51}54 ·····multidegree:·{51,·51,·51,·51,·51}
55 ·····degree:·155 ·····degree:·1
56 ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)]56 ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)]
57 ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)]57 ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)]
58 ·····coefficient·ring:·ZZ/6552158 ·····coefficient·ring:·ZZ/65521
59 i6·:·time·?·Phi59 i6·:·time·?·Phi
60 ·--·used·0.000396647s·(cpu);·0.000394103s·(thread);·0s·(gc)60 ·--·used·0.000120365s·(cpu);·0.000394941s·(thread);·0s·(gc)
  
61 o6·=·multi-rational·map·consisting·of·2·rational·maps61 o6·=·multi-rational·map·consisting·of·2·rational·maps
62 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·962 ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9
63 hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^863 hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8
64 ·····target·variety:·PP^4·x·PP^564 ·····target·variety:·PP^4·x·PP^5
65 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^565 ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5
66 ·····dominance:·false66 ·····dominance:·false
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83 o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>83 o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i2·:·time·(Phi1,Phi2)·=·graph·Phi88 ··············<pre><code·class="language-macaulay2">i2·:·time·(Phi1,Phi2)·=·graph·Phi
89 ·--·used·0.326284s·(cpu);·0.0700423s·(thread);·0s·(gc)89 ·--·used·0.293922s·(cpu);·0.0574203s·(thread);·0s·(gc)
  
90 o2·=·(Phi1,·Phi2)90 o2·=·(Phi1,·Phi2)
  
91 o2·:·Sequence</code></pre>91 o2·:·Sequence</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
Offset 107, 15 lines modifiedOffset 107, 15 lines modified
  
107 o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre>107 o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i5·:·time·(Phi21,Phi22)·=·graph·Phi2112 ··············<pre><code·class="language-macaulay2">i5·:·time·(Phi21,Phi22)·=·graph·Phi2
113 ·--·used·0.221098s·(cpu);·0.042252s·(thread);·0s·(gc)113 ·--·used·0.251043s·(cpu);·0.0546244s·(thread);·0s·(gc)
  
114 o5·=·(Phi21,·Phi22)114 o5·=·(Phi21,·Phi22)
  
115 o5·:·Sequence</code></pre>115 o5·:·Sequence</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ··········<tr>118 ··········<tr>
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131 o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)</code></pre>131 o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)</code></pre>
132 ············</td>132 ············</td>
133 ··········</tr>133 ··········</tr>
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i8·:·time·(Phi211,Phi212)·=·graph·Phi21136 ··············<pre><code·class="language-macaulay2">i8·:·time·(Phi211,Phi212)·=·graph·Phi21
137 ·--·used·0.374103s·(cpu);·0.132385s·(thread);·0s·(gc)137 ·--·used·0.433531s·(cpu);·0.173915s·(thread);·0s·(gc)
  
138 o8·=·(Phi211,·Phi212)138 o8·=·(Phi211,·Phi212)
  
139 o8·:·Sequence</code></pre>139 o8·:·Sequence</code></pre>
140 ············</td>140 ············</td>
141 ··········</tr>141 ··········</tr>
142 ··········<tr>142 ··········<tr>
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19 Phi)^-1·*·(last·graph·Phi)·==·Phi·are·always·satisfied.19 Phi)^-1·*·(last·graph·Phi)·==·Phi·are·always·satisfied.
20 i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true)20 i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true)
  
21 o1·=·Phi21 o1·=·Phi
  
22 o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)22 o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)
23 i2·:·time·(Phi1,Phi2)·=·graph·Phi23 i2·:·time·(Phi1,Phi2)·=·graph·Phi
24 ·--·used·0.326284s·(cpu);·0.0700423s·(thread);·0s·(gc)24 ·--·used·0.293922s·(cpu);·0.0574203s·(thread);·0s·(gc)
  
25 o2·=·(Phi1,·Phi2)25 o2·=·(Phi1,·Phi2)
  
26 o2·:·Sequence26 o2·:·Sequence
27 i3·:·Phi1;27 i3·:·Phi1;
  
28 o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x28 o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x
29 PP^5·to·PP^4)29 PP^5·to·PP^4)
30 i4·:·Phi2;30 i4·:·Phi2;
  
31 o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of31 o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of
32 PP^4·x·PP^5·to·hypersurface·in·PP^5)32 PP^4·x·PP^5·to·hypersurface·in·PP^5)
33 i5·:·time·(Phi21,Phi22)·=·graph·Phi233 i5·:·time·(Phi21,Phi22)·=·graph·Phi2
34 ·--·used·0.221098s·(cpu);·0.042252s·(thread);·0s·(gc)34 ·--·used·0.251043s·(cpu);·0.0546244s·(thread);·0s·(gc)
  
35 o5·=·(Phi21,·Phi22)35 o5·=·(Phi21,·Phi22)
  
36 o5·:·Sequence36 o5·:·Sequence
37 i6·:·Phi21;37 i6·:·Phi21;
  
38 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x38 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x
39 PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)39 PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)
40 i7·:·Phi22;40 i7·:·Phi22;
  
41 o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of41 o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of
42 PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)42 PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)
43 i8·:·time·(Phi211,Phi212)·=·graph·Phi2143 i8·:·time·(Phi211,Phi212)·=·graph·Phi21
44 ·--·used·0.374103s·(cpu);·0.132385s·(thread);·0s·(gc)44 ·--·used·0.433531s·(cpu);·0.173915s·(thread);·0s·(gc)
  
45 o8·=·(Phi211,·Phi212)45 o8·=·(Phi211,·Phi212)
  
46 o8·:·Sequence46 o8·:·Sequence
47 i9·:·Phi211;47 i9·:·Phi211;
  
48 o9·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x48 o9·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x
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95 o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)</code></pre>95 o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i5·:·time·Z·=·image·Phi;100 ··············<pre><code·class="language-macaulay2">i5·:·time·Z·=·image·Phi;
101 ·--·used·0.277154s·(cpu);·0.117854s·(thread);·0s·(gc)101 ·--·used·0.324497s·(cpu);·0.128013s·(thread);·0s·(gc)
  
102 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre>102 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i6·:·dim·Z,·degree·Z,·degrees·Z107 ··············<pre><code·class="language-macaulay2">i6·:·dim·Z,·degree·Z,·degrees·Z
Offset 115, 15 lines modifiedOffset 115, 15 lines modified
115 ··········</tr>115 ··········</tr>
116 ········</table>116 ········</table>
117 ········<p>Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as·follows:</p>117 ········<p>Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as·follows:</p>
118 ········<table·class="examples">118 ········<table·class="examples">
119 ··········<tr>119 ··········<tr>
120 ············<td>120 ············<td>
121 ··············<pre><code·class="language-macaulay2">i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,&quot;F4&quot;);121 ··············<pre><code·class="language-macaulay2">i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,&quot;F4&quot;);
122 ·--·used·7.51151s·(cpu);·2.34826s·(thread);·0s·(gc)122 ·--·used·8.32727s·(cpu);·2.58615s·(thread);·0s·(gc)
  
123 o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre>123 o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i8·:·assert(Z·==·Z')</code></pre>128 ··············<pre><code·class="language-macaulay2">i8·:·assert(Z·==·Z')</code></pre>
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23 3*x_2^2+2*x_1*x_3+x_0*x_4,·2*x_1*x_2-2*x_0*x_3,·-x_1^2+x_0*x_2};23 3*x_2^2+2*x_1*x_3+x_0*x_4,·2*x_1*x_2-2*x_0*x_3,·-x_1^2+x_0*x_2};
  
24 o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)24 o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)
25 i4·:·Phi·=·rationalMap·{f,g};25 i4·:·Phi·=·rationalMap·{f,g};
  
26 o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)26 o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)
27 i5·:·time·Z·=·image·Phi;27 i5·:·time·Z·=·image·Phi;
28 ·--·used·0.277154s·(cpu);·0.117854s·(thread);·0s·(gc)28 ·--·used·0.324497s·(cpu);·0.128013s·(thread);·0s·(gc)
  
29 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^429 o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4
30 i6·:·dim·Z,·degree·Z,·degrees·Z30 i6·:·dim·Z,·degree·Z,·degrees·Z
  
31 o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)})31 o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)})
  
32 o6·:·Sequence32 o6·:·Sequence
33 Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as33 Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as
34 follows:34 follows:
35 i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4");35 i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4");
36 ·--·used·7.51151s·(cpu);·2.34826s·(thread);·0s·(gc)36 ·--·used·8.32727s·(cpu);·2.58615s·(thread);·0s·(gc)
  
37 o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^437 o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4
38 i8·:·assert(Z·==·Z')38 i8·:·assert(Z·==·Z')
39 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
40 ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·direct·image·via·a·multi-40 ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·direct·image·via·a·multi-
41 ······rational·map41 ······rational·map
42 ····*·_\x8i_\x8m_\x8a_\x8g_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·closure·of·the·image·of·a·rational·map42 ····*·_\x8i_\x8m_\x8a_\x8g_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·closure·of·the·image·of·a·rational·map
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Offset 83, 15 lines modifiedOffset 83, 15 lines modified
  
83 o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))</code></pre>83 o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·time·Psi·=·inverse2·Phi;88 ··············<pre><code·class="language-macaulay2">i3·:·time·Psi·=·inverse2·Phi;
89 ·--·used·0.605001s·(cpu);·0.302001s·(thread);·0s·(gc)89 ·--·used·0.576582s·(cpu);·0.29168s·(thread);·0s·(gc)
  
90 o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)</code></pre>90 o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i4·:·assert(Phi·*·Psi·==·1)</code></pre>95 ··············<pre><code·class="language-macaulay2">i4·:·assert(Phi·*·Psi·==·1)</code></pre>
Offset 103, 15 lines modifiedOffset 103, 15 lines modified
  
103 o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))</code></pre>103 o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i6·:·time·Psi'·=·inverse2·Phi';108 ··············<pre><code·class="language-macaulay2">i6·:·time·Psi'·=·inverse2·Phi';
109 ·--·used·1.19344s·(cpu);·0.83645s·(thread);·0s·(gc)109 ·--·used·1.27758s·(cpu);·0.905749s·(thread);·0s·(gc)
  
110 o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)</code></pre>110 o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i7·:·assert(Phi'·*·Psi'·==·1)</code></pre>115 ··············<pre><code·class="language-macaulay2">i7·:·assert(Phi'·*·Psi'·==·1)</code></pre>
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Offset 24, 23 lines modifiedOffset 24, 23 lines modified
24 i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational24 i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational
25 normal·curve·of·degree·625 normal·curve·of·degree·6
26 ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal26 ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal
27 PP_K([6],2));27 PP_K([6],2));
  
28 o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))28 o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))
29 i3·:·time·Psi·=·inverse2·Phi;29 i3·:·time·Psi·=·inverse2·Phi;
30 ·--·used·0.605001s·(cpu);·0.302001s·(thread);·0s·(gc)30 ·--·used·0.576582s·(cpu);·0.29168s·(thread);·0s·(gc)
  
31 o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)31 o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)
32 i4·:·assert(Phi·*·Psi·==·1)32 i4·:·assert(Phi·*·Psi·==·1)
33 i5·:·Phi'·=·Phi·||·Phi;33 i5·:·Phi'·=·Phi·||·Phi;
  
34 o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))34 o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))
35 i6·:·time·Psi'·=·inverse2·Phi';35 i6·:·time·Psi'·=·inverse2·Phi';
36 ·--·used·1.19344s·(cpu);·0.83645s·(thread);·0s·(gc)36 ·--·used·1.27758s·(cpu);·0.905749s·(thread);·0s·(gc)
  
37 o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)37 o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)
38 i7·:·assert(Phi'·*·Psi'·==·1)38 i7·:·assert(Phi'·*·Psi'·==·1)
39 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
40 ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map40 ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map
41 ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8<_\x8=_\x8=_\x8>_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·equality·of·multi-rational·maps41 ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8<_\x8=_\x8=_\x8>_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·equality·of·multi-rational·maps
42 ······with·checks·on·internal·data42 ······with·checks·on·internal·data
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88 o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>88 o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i3·:·time·inverse·Phi;93 ··············<pre><code·class="language-macaulay2">i3·:·time·inverse·Phi;
94 ·--·used·0.31778s·(cpu);·0.0727678s·(thread);·0s·(gc)94 ·--·used·0.307053s·(cpu);·0.0770788s·(thread);·0s·(gc)
  
95 o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre>95 o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i4·:·Psi·=·last·graph·Phi;100 ··············<pre><code·class="language-macaulay2">i4·:·Psi·=·last·graph·Phi;
  
101 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre>101 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i5·:·time·inverse·Psi;106 ··············<pre><code·class="language-macaulay2">i5·:·time·inverse·Psi;
107 ·--·used·0.595157s·(cpu);·0.123909s·(thread);·0s·(gc)107 ·--·used·0.591947s·(cpu);·0.138383s·(thread);·0s·(gc)
  
108 o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre>108 o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i6·:·Eta·=·first·graph·Psi;113 ··············<pre><code·class="language-macaulay2">i6·:·Eta·=·first·graph·Psi;
  
114 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre>114 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i7·:·time·inverse·Eta;119 ··············<pre><code·class="language-macaulay2">i7·:·time·inverse·Eta;
120 ·--·used·0.862919s·(cpu);·0.296744s·(thread);·0s·(gc)120 ·--·used·0.983512s·(cpu);·0.397828s·(thread);·0s·(gc)
  
121 o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)</code></pre>121 o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)</code></pre>
122 ············</td>122 ············</td>
123 ··········</tr>123 ··········</tr>
124 ··········<tr>124 ··········<tr>
125 ············<td>125 ············<td>
126 ··············<pre><code·class="language-macaulay2">i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)</code></pre>126 ··············<pre><code·class="language-macaulay2">i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)</code></pre>
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Offset 24, 32 lines modifiedOffset 24, 32 lines modified
  
24 o1·:·MultirationalMap·(rational·map·from·PP^4·to·PP^5)24 o1·:·MultirationalMap·(rational·map·from·PP^4·to·PP^5)
25 i2·:·--·we·see·Phi·as·a·dominant·map25 i2·:·--·we·see·Phi·as·a·dominant·map
26 ·····Phi·=·rationalMap(Phi,image·Phi);26 ·····Phi·=·rationalMap(Phi,image·Phi);
  
27 o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)27 o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)
28 i3·:·time·inverse·Phi;28 i3·:·time·inverse·Phi;
29 ·--·used·0.31778s·(cpu);·0.0727678s·(thread);·0s·(gc)29 ·--·used·0.307053s·(cpu);·0.0770788s·(thread);·0s·(gc)
  
30 o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)30 o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)
31 i4·:·Psi·=·last·graph·Phi;31 i4·:·Psi·=·last·graph·Phi;
  
32 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x32 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x
33 PP^5·to·hypersurface·in·PP^5)33 PP^5·to·hypersurface·in·PP^5)
34 i5·:·time·inverse·Psi;34 i5·:·time·inverse·Psi;
35 ·--·used·0.595157s·(cpu);·0.123909s·(thread);·0s·(gc)35 ·--·used·0.591947s·(cpu);·0.138383s·(thread);·0s·(gc)
  
36 o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-36 o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-
37 dimensional·subvariety·of·PP^4·x·PP^5)37 dimensional·subvariety·of·PP^4·x·PP^5)
38 i6·:·Eta·=·first·graph·Psi;38 i6·:·Eta·=·first·graph·Psi;
  
39 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x39 o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x
40 PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)40 PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)
41 i7·:·time·inverse·Eta;41 i7·:·time·inverse·Eta;
42 ·--·used·0.862919s·(cpu);·0.296744s·(thread);·0s·(gc)42 ·--·used·0.983512s·(cpu);·0.397828s·(thread);·0s·(gc)
  
43 o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x43 o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x
44 PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)44 PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)
45 i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)45 i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)
46 i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1)46 i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1)
47 i10·:·assert(Eta·*·Eta^-1·==·1·and·Eta^-1·*·Eta·==·1)47 i10·:·assert(Eta·*·Eta^-1·==·1·and·Eta^-1·*·Eta·==·1)
48 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*48 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*
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Offset 83, 45 lines modifiedOffset 83, 45 lines modified
  
83 o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)</code></pre>83 o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i4·:·time·isIsomorphism·Phi88 ··············<pre><code·class="language-macaulay2">i4·:·time·isIsomorphism·Phi
89 ·--·used·0.000403758s·(cpu);·6.009e-06s·(thread);·0s·(gc)89 ·--·used·0.00291045s·(cpu);·8.326e-06s·(thread);·0s·(gc)
  
90 o4·=·false</code></pre>90 o4·=·false</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i5·:·Psi·=·first·graph·Phi;95 ··············<pre><code·class="language-macaulay2">i5·:·Psi·=·first·graph·Phi;
  
96 o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)</code></pre>96 o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i6·:·time·isIsomorphism·Psi101 ··············<pre><code·class="language-macaulay2">i6·:·time·isIsomorphism·Psi
102 ·--·used·0.753016s·(cpu);·0.215353s·(thread);·0s·(gc)102 ·--·used·0.762507s·(cpu);·0.228863s·(thread);·0s·(gc)
  
103 o6·=·false</code></pre>103 o6·=·false</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i7·:·Eta·=·first·graph·Psi;108 ··············<pre><code·class="language-macaulay2">i7·:·Eta·=·first·graph·Psi;
  
109 o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre>109 o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i8·:·time·isIsomorphism·Eta114 ··············<pre><code·class="language-macaulay2">i8·:·time·isIsomorphism·Eta
115 ·--·used·1.65491s·(cpu);·0.746739s·(thread);·0s·(gc)115 ·--·used·1.87751s·(cpu);·0.849471s·(thread);·0s·(gc)
  
116 o8·=·true</code></pre>116 o8·=·true</code></pre>
117 ············</td>117 ············</td>
118 ··········</tr>118 ··········</tr>
119 ··········<tr>119 ··········<tr>
120 ············<td>120 ············<td>
121 ··············<pre><code·class="language-macaulay2">i9·:·assert(o8·and·(not·o6)·and·(not·o4))</code></pre>121 ··············<pre><code·class="language-macaulay2">i9·:·assert(o8·and·(not·o6)·and·(not·o4))</code></pre>
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17 ·····ZZ/33331[a..d];·f·=·rationalMap·{c^2-b*d,b*c-a*d,b^2-a*c};17 ·····ZZ/33331[a..d];·f·=·rationalMap·{c^2-b*d,b*c-a*d,b^2-a*c};
  
18 o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2)18 o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2)
19 i3·:·Phi·=·rationalMap·{f,f};19 i3·:·Phi·=·rationalMap·{f,f};
  
20 o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)20 o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)
21 i4·:·time·isIsomorphism·Phi21 i4·:·time·isIsomorphism·Phi
22 ·--·used·0.000403758s·(cpu);·6.009e-06s·(thread);·0s·(gc)22 ·--·used·0.00291045s·(cpu);·8.326e-06s·(thread);·0s·(gc)
  
23 o4·=·false23 o4·=·false
24 i5·:·Psi·=·first·graph·Phi;24 i5·:·Psi·=·first·graph·Phi;
  
25 o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to25 o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to
26 PP^3)26 PP^3)
27 i6·:·time·isIsomorphism·Psi27 i6·:·time·isIsomorphism·Psi
28 ·--·used·0.753016s·(cpu);·0.215353s·(thread);·0s·(gc)28 ·--·used·0.762507s·(cpu);·0.228863s·(thread);·0s·(gc)
  
29 o6·=·false29 o6·=·false
30 i7·:·Eta·=·first·graph·Psi;30 i7·:·Eta·=·first·graph·Psi;
  
31 o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x31 o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x
32 PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)32 PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)
33 i8·:·time·isIsomorphism·Eta33 i8·:·time·isIsomorphism·Eta
34 ·--·used·1.65491s·(cpu);·0.746739s·(thread);·0s·(gc)34 ·--·used·1.87751s·(cpu);·0.849471s·(thread);·0s·(gc)
  
35 o8·=·true35 o8·=·true
36 i9·:·assert(o8·and·(not·o6)·and·(not·o4))36 i9·:·assert(o8·and·(not·o6)·and·(not·o4))
37 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*37 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
38 ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map38 ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map
39 ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·multi-rational·map·is·a39 ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·multi-rational·map·is·a
40 ······morphism40 ······morphism
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Offset 80, 31 lines modifiedOffset 80, 31 lines modified
  
80 o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)</code></pre>80 o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·time·isMorphism·Phi85 ··············<pre><code·class="language-macaulay2">i3·:·time·isMorphism·Phi
86 ·--·used·0.298026s·(cpu);·0.198458s·(thread);·0s·(gc)86 ·--·used·0.327156s·(cpu);·0.209736s·(thread);·0s·(gc)
  
87 o3·=·false</code></pre>87 o3·=·false</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i4·:·time·Psi·=·first·graph·Phi;92 ··············<pre><code·class="language-macaulay2">i4·:·time·Psi·=·first·graph·Phi;
93 ·--·used·0.338977s·(cpu);·0.104163s·(thread);·0s·(gc)93 ·--·used·0.374814s·(cpu);·0.0905049s·(thread);·0s·(gc)
  
94 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)</code></pre>94 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i5·:·time·isMorphism·Psi99 ··············<pre><code·class="language-macaulay2">i5·:·time·isMorphism·Psi
100 ·--·used·2.9027s·(cpu);·2.49449s·(thread);·0s·(gc)100 ·--·used·3.03797s·(cpu);·2.57755s·(thread);·0s·(gc)
  
101 o5·=·true</code></pre>101 o5·=·true</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i6·:·assert((not·o3)·and·o5)</code></pre>106 ··············<pre><code·class="language-macaulay2">i6·:·assert((not·o3)·and·o5)</code></pre>
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17 i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2-17 i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2-
18 a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2});18 a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2});
19 i2·:·Phi·=·rationalMap·{f,g};19 i2·:·Phi·=·rationalMap·{f,g};
  
20 o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x20 o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x
21 PP^7·to·PP^4·x·PP^2)21 PP^7·to·PP^4·x·PP^2)
22 i3·:·time·isMorphism·Phi22 i3·:·time·isMorphism·Phi
23 ·--·used·0.298026s·(cpu);·0.198458s·(thread);·0s·(gc)23 ·--·used·0.327156s·(cpu);·0.209736s·(thread);·0s·(gc)
  
24 o3·=·false24 o3·=·false
25 i4·:·time·Psi·=·first·graph·Phi;25 i4·:·time·Psi·=·first·graph·Phi;
26 ·--·used·0.338977s·(cpu);·0.104163s·(thread);·0s·(gc)26 ·--·used·0.374814s·(cpu);·0.0905049s·(thread);·0s·(gc)
  
27 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x27 o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x
28 PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)28 PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)
29 i5·:·time·isMorphism·Psi29 i5·:·time·isMorphism·Psi
30 ·--·used·2.9027s·(cpu);·2.49449s·(thread);·0s·(gc)30 ·--·used·3.03797s·(cpu);·2.57755s·(thread);·0s·(gc)
  
31 o5·=·true31 o5·=·true
32 i6·:·assert((not·o3)·and·o5)32 i6·:·assert((not·o3)·and·o5)
33 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*33 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
34 ····*·_\x8i_\x8s_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·birational·map·is·an34 ····*·_\x8i_\x8s_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·birational·map·is·an
35 ······isomorphism35 ······isomorphism
36 ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·rational·map·is·a·morphism36 ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·rational·map·is·a·morphism
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79 o2·:·ProjectiveVariety,·curve·in·PP^7</code></pre>79 o2·:·ProjectiveVariety,·curve·in·PP^7</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i3·:·time·f·=·linearlyNormalEmbedding·X;84 ··············<pre><code·class="language-macaulay2">i3·:·time·f·=·linearlyNormalEmbedding·X;
85 ·--·used·0.00836101s·(cpu);·0.00902196s·(thread);·0s·(gc)85 ·--·used·0.0119464s·(cpu);·0.0103894s·(thread);·0s·(gc)
  
86 o3·:·MultirationalMap·(automorphism·of·X)</code></pre>86 o3·:·MultirationalMap·(automorphism·of·X)</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^391 ··············<pre><code·class="language-macaulay2">i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^3
  
92 o4·:·ProjectiveVariety,·curve·in·PP^3</code></pre>92 o4·:·ProjectiveVariety,·curve·in·PP^3</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i5·:·time·g·=·linearlyNormalEmbedding·Y;97 ··············<pre><code·class="language-macaulay2">i5·:·time·g·=·linearlyNormalEmbedding·Y;
98 ·--·used·0.36771s·(cpu);·0.332505s·(thread);·0s·(gc)98 ·--·used·0.419817s·(cpu);·0.365869s·(thread);·0s·(gc)
  
99 o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)</code></pre>99 o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i6·:·assert(isIsomorphism·g)</code></pre>104 ··············<pre><code·class="language-macaulay2">i6·:·assert(isIsomorphism·g)</code></pre>
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13 ············is·a·linear·projection13 ············is·a·linear·projection
14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 i1·:·K·=·ZZ/333331;15 i1·:·K·=·ZZ/333331;
16 i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·716 i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7
  
17 o2·:·ProjectiveVariety,·curve·in·PP^717 o2·:·ProjectiveVariety,·curve·in·PP^7
18 i3·:·time·f·=·linearlyNormalEmbedding·X;18 i3·:·time·f·=·linearlyNormalEmbedding·X;
19 ·--·used·0.00836101s·(cpu);·0.00902196s·(thread);·0s·(gc)19 ·--·used·0.0119464s·(cpu);·0.0103894s·(thread);·0s·(gc)
  
20 o3·:·MultirationalMap·(automorphism·of·X)20 o3·:·MultirationalMap·(automorphism·of·X)
21 i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an21 i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an
22 isomorphic·projection·of·X·in·PP^322 isomorphic·projection·of·X·in·PP^3
  
23 o4·:·ProjectiveVariety,·curve·in·PP^323 o4·:·ProjectiveVariety,·curve·in·PP^3
24 i5·:·time·g·=·linearlyNormalEmbedding·Y;24 i5·:·time·g·=·linearlyNormalEmbedding·Y;
25 ·--·used·0.36771s·(cpu);·0.332505s·(thread);·0s·(gc)25 ·--·used·0.419817s·(cpu);·0.365869s·(thread);·0s·(gc)
  
26 o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)26 o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)
27 i6·:·assert(isIsomorphism·g)27 i6·:·assert(isIsomorphism·g)
28 i7·:·describe·g28 i7·:·describe·g
  
29 o7·=·multi-rational·map·consisting·of·one·single·rational·map29 o7·=·multi-rational·map·consisting·of·one·single·rational·map
30 ·····source·variety:·curve·in·PP^3·cut·out·by·6·hypersurfaces·of·degree·430 ·····source·variety:·curve·in·PP^3·cut·out·by·6·hypersurfaces·of·degree·4
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Offset 81, 15 lines modifiedOffset 81, 15 lines modified
  
81 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre>81 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i3·:·time·multidegree·Phi86 ··············<pre><code·class="language-macaulay2">i3·:·time·multidegree·Phi
87 ·--·used·0.605515s·(cpu);·0.32402s·(thread);·0s·(gc)87 ·--·used·0.672585s·(cpu);·0.325083s·(thread);·0s·(gc)
  
88 o3·=·{66,·46,·31,·20}88 o3·=·{66,·46,·31,·20}
  
89 o3·:·List</code></pre>89 o3·:·List</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
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19 x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,19 x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,
20 x_3^2};20 x_3^2};
21 i2·:·Phi·=·last·graph·rationalMap·{f,g};21 i2·:·Phi·=·last·graph·rationalMap·{f,g};
  
22 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to22 o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to
23 PP^2·x·PP^4)23 PP^2·x·PP^4)
24 i3·:·time·multidegree·Phi24 i3·:·time·multidegree·Phi
25 ·--·used·0.605515s·(cpu);·0.32402s·(thread);·0s·(gc)25 ·--·used·0.672585s·(cpu);·0.325083s·(thread);·0s·(gc)
  
26 o3·=·{66,·46,·31,·20}26 o3·=·{66,·46,·31,·20}
  
27 o3·:·List27 o3·:·List
28 i4·:·(degree·source·Phi,degree·image·Phi)28 i4·:·(degree·source·Phi,degree·image·Phi)
  
29 o4·=·(66,·20)29 o4·=·(66,·20)
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./usr/share/doc/Macaulay2/MultiprojectiveVarieties/html/_multidegree_lp__Z__Z_cm__Multirational__Map_rp.html
    
Offset 77, 29 lines modifiedOffset 77, 29 lines modified
  
77 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)</code></pre>77 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi)82 ··············<pre><code·class="language-macaulay2">i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi)
83 ·--·used·0.00137308s·(cpu);·0.00112143s·(thread);·0s·(gc)83 ·--·used·0.00161832s·(cpu);·0.00142918s·(thread);·0s·(gc)
84 ·--·used·0.173207s·(cpu);·0.125968s·(thread);·0s·(gc)84 ·--·used·0.174177s·(cpu);·0.128396s·(thread);·0s·(gc)
85 ·--·used·0.196544s·(cpu);·0.151621s·(thread);·0s·(gc) 
86 ·--·used·0.174714s·(cpu);·0.125714s·(thread);·0s·(gc)85 ·--·used·0.184877s·(cpu);·0.142434s·(thread);·0s·(gc)
 86 ·--·used·0.168329s·(cpu);·0.120877s·(thread);·0s·(gc)
87 ·--·used·0.147903s·(cpu);·0.100526s·(thread);·0s·(gc)87 ·--·used·0.175593s·(cpu);·0.114917s·(thread);·0s·(gc)
  
88 o2·=·{51,·28,·14,·6,·2}88 o2·=·{51,·28,·14,·6,·2}
  
89 o2·:·List</code></pre>89 o2·:·List</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·time·assert(oo·==·multidegree·Phi)94 ··············<pre><code·class="language-macaulay2">i3·:·time·assert(oo·==·multidegree·Phi)
95 ·--·used·0.292374s·(cpu);·0.079935s·(thread);·0s·(gc)</code></pre>95 ·--·used·0.303852s·(cpu);·0.0897984s·(thread);·0s·(gc)</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ········</table>98 ········</table>
99 ······</div>99 ······</div>
100 ······<div>100 ······<div>
101 ········<h2>References</h2>101 ········<h2>References</h2>
102 ArXiv·preprint:·<a·href="https://arxiv.org/abs/2101.04503">Computations·with·rational·maps·between·multi-projective·varieties</a>.······</div>102 ArXiv·preprint:·<a·href="https://arxiv.org/abs/2101.04503">Computations·with·rational·maps·between·multi-projective·varieties</a>.······</div>
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17 This·is·calculated·by·means·of·the·inverse·image·of·an·appropriate·random17 This·is·calculated·by·means·of·the·inverse·image·of·an·appropriate·random
18 subvariety·of·the·target.18 subvariety·of·the·target.
19 i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4);19 i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4);
  
20 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x20 o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x
21 PP^5·to·PP^5)21 PP^5·to·PP^5)
22 i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi)22 i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi)
23 ·--·used·0.00137308s·(cpu);·0.00112143s·(thread);·0s·(gc)23 ·--·used·0.00161832s·(cpu);·0.00142918s·(thread);·0s·(gc)
24 ·--·used·0.173207s·(cpu);·0.125968s·(thread);·0s·(gc)24 ·--·used·0.174177s·(cpu);·0.128396s·(thread);·0s·(gc)
25 ·--·used·0.196544s·(cpu);·0.151621s·(thread);·0s·(gc) 
26 ·--·used·0.174714s·(cpu);·0.125714s·(thread);·0s·(gc)25 ·--·used·0.184877s·(cpu);·0.142434s·(thread);·0s·(gc)
 26 ·--·used·0.168329s·(cpu);·0.120877s·(thread);·0s·(gc)
27 ·--·used·0.147903s·(cpu);·0.100526s·(thread);·0s·(gc)27 ·--·used·0.175593s·(cpu);·0.114917s·(thread);·0s·(gc)
  
28 o2·=·{51,·28,·14,·6,·2}28 o2·=·{51,·28,·14,·6,·2}
  
29 o2·:·List29 o2·:·List
30 i3·:·time·assert(oo·==·multidegree·Phi)30 i3·:·time·assert(oo·==·multidegree·Phi)
31 ·--·used·0.292374s·(cpu);·0.079935s·(thread);·0s·(gc)31 ·--·used·0.303852s·(cpu);·0.0897984s·(thread);·0s·(gc)
32 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*32 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*
33 ArXiv·preprint:·_\x8C_\x8o_\x8m_\x8p_\x8u_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p_\x8s_\x8·_\x8b_\x8e_\x8t_\x8w_\x8e_\x8e_\x8n_\x8·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e33 ArXiv·preprint:·_\x8C_\x8o_\x8m_\x8p_\x8u_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p_\x8s_\x8·_\x8b_\x8e_\x8t_\x8w_\x8e_\x8e_\x8n_\x8·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e
34 _\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s.34 _\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s.
35 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*35 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
36 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational36 ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational
37 ······map37 ······map
38 ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·rational·map38 ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·rational·map
2.4 KB
./usr/share/doc/Macaulay2/MultiprojectiveVarieties/html/_point_lp__Multiprojective__Variety_rp.html
    
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80 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9</code></pre>80 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·time·p·:=·point·X85 ··············<pre><code·class="language-macaulay2">i3·:·time·p·:=·point·X
86 ·--·used·0.249919s·(cpu);·0.0321772s·(thread);·0s·(gc)86 ·--·used·0.18054s·(cpu);·0.0395397s·(thread);·0s·(gc)
  
87 o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1])87 o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1])
  
88 o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre>88 o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
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97 o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9</code></pre>97 o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i5·:·time·q·=·point·Y102 ··············<pre><code·class="language-macaulay2">i5·:·time·q·=·point·Y
103 ·--·used·1.23577s·(cpu);·0.747615s·(thread);·0s·(gc)103 ·--·used·1.37418s·(cpu);·0.779439s·(thread);·0s·(gc)
  
104 o5·=·q104 o5·=·q
  
105 o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre>105 o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ··········<tr>108 ··········<tr>
1.11 KB
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14 ··········o·a·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y,·a·random·rational·point·on·$X$14 ··········o·a·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y,·a·random·rational·point·on·$X$
15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
16 i1·:·K·=·ZZ/1000003;16 i1·:·K·=·ZZ/1000003;
17 i2·:·X·=·PP_K^({1,1,2},{3,2,3});17 i2·:·X·=·PP_K^({1,1,2},{3,2,3});
  
18 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^918 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9
19 i3·:·time·p·:=·point·X19 i3·:·time·p·:=·point·X
20 ·--·used·0.249919s·(cpu);·0.0321772s·(thread);·0s·(gc)20 ·--·used·0.18054s·(cpu);·0.0395397s·(thread);·0s·(gc)
  
21 o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],21 o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],
22 [3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1])22 [3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1])
  
23 o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^923 o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9
24 i4·:·Y·=·random({2,1,2},X);24 i4·:·Y·=·random({2,1,2},X);
  
25 o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^925 o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9
26 i5·:·time·q·=·point·Y26 i5·:·time·q·=·point·Y
27 ·--·used·1.23577s·(cpu);·0.747615s·(thread);·0s·(gc)27 ·--·used·1.37418s·(cpu);·0.779439s·(thread);·0s·(gc)
  
28 o5·=·q28 o5·=·q
  
29 o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^929 o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9
30 i6·:·assert(isSubset(p,X)·and·isSubset(q,Y))30 i6·:·assert(isSubset(p,X)·and·isSubset(q,Y))
31 The·list·of·homogeneous·coordinates·can·be·obtained·with·the·operator·|-.31 The·list·of·homogeneous·coordinates·can·be·obtained·with·the·operator·|-.
32 i7·:·|-·p32 i7·:·|-·p
1.29 KB
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101 o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)</code></pre>101 o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i6·:·time·segre·Phi;106 ··············<pre><code·class="language-macaulay2">i6·:·time·segre·Phi;
107 ·--·used·4.05061s·(cpu);·0.750041s·(thread);·0s·(gc)107 ·--·used·3.88011s·(cpu);·0.8594s·(thread);·0s·(gc)
  
108 o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)</code></pre>108 o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i7·:·describe·segre·Phi113 ··············<pre><code·class="language-macaulay2">i7·:·describe·segre·Phi
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29 o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)29 o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4)
30 i5·:·Phi·=·rationalMap·{f,g,h};30 i5·:·Phi·=·rationalMap·{f,g,h};
  
31 o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x31 o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x
32 PP^4)32 PP^4)
33 i6·:·time·segre·Phi;33 i6·:·time·segre·Phi;
34 ·--·used·4.05061s·(cpu);·0.750041s·(thread);·0s·(gc)34 ·--·used·3.88011s·(cpu);·0.8594s·(thread);·0s·(gc)
  
35 o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)35 o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)
36 i7·:·describe·segre·Phi36 i7·:·describe·segre·Phi
  
37 o7·=·rational·map·defined·by·forms·of·degree·637 o7·=·rational·map·defined·by·forms·of·degree·6
38 ·····source·variety:·PP^438 ·····source·variety:·PP^4
39 ·····target·variety:·PP^14939 ·····target·variety:·PP^149
1.63 KB
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77 o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre>77 o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·time·describe·Phi82 ··············<pre><code·class="language-macaulay2">i2·:·time·describe·Phi
83 ·--·used·0.251286s·(cpu);·0.155829s·(thread);·0s·(gc)83 ·--·used·0.246161s·(cpu);·0.133396s·(thread);·0s·(gc)
  
84 o2·=·multi-rational·map·consisting·of·3·rational·maps84 o2·=·multi-rational·map·consisting·of·3·rational·maps
85 ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1)85 ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1)
86 ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2·86 ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2·
87 ·····base·locus:·empty·subscheme·of·PP^3·x·PP^287 ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2
88 ·····dominance:·true88 ·····dominance:·true
89 ·····multidegree:·{10,·14,·19,·25}89 ·····multidegree:·{10,·14,·19,·25}
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15 i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3)15 i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3)
  
16 o1·=·Phi16 o1·=·Phi
  
17 o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to17 o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to
18 threefold·in·PP^3·x·PP^2·x·PP^2)18 threefold·in·PP^3·x·PP^2·x·PP^2)
19 i2·:·time·describe·Phi19 i2·:·time·describe·Phi
20 ·--·used·0.251286s·(cpu);·0.155829s·(thread);·0s·(gc)20 ·--·used·0.246161s·(cpu);·0.133396s·(thread);·0s·(gc)
  
21 o2·=·multi-rational·map·consisting·of·3·rational·maps21 o2·=·multi-rational·map·consisting·of·3·rational·maps
22 ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of22 ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of
23 multi-degree·(1,1)23 multi-degree·(1,1)
24 ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces24 ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces
25 of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^225 of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2
26 ·····base·locus:·empty·subscheme·of·PP^3·x·PP^226 ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2
712 B
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8 Z2VuZXJhdGVSYW5kb21HcmFwaHMoWlosWlosWlop8 Z2VuZXJhdGVSYW5kb21HcmFwaHMoWlosWlosWlop
9 #:len=2759 #:len=275
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTExMSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTExMSwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2VuZXJhdGVSYW5kb21HcmFwaHMsWlosWlosWlop11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2VuZXJhdGVSYW5kb21HcmFwaHMsWlosWlosWlop
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26 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true};26 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true};
  
27 i8·:·prob·=·n·->·log(n)/n;27 i8·:·prob·=·n·->·log(n)/n;
  
28 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))28 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))
  
29 o9·=·(69,·81,·90,·96,·88,·94,·98,·97,·97,·94,·93,·97,·97,·98,·100,·96,·98,29 o9·=·(73,·81,·87,·95,·94,·97,·98,·96,·96,·95,·92,·99,·99,·97,·97,·96,·98,·99,
30 ·····------------------------------------------------------------------------30 ·····------------------------------------------------------------------------
31 ·····99,·98,·97,·99,·98,·97,·99,·97,·99,·98,·96,·97)31 ·····96,·98,·96,·95,·98,·98,·98,·97,·95,·98,·100)
  
32 o9·:·Sequence32 o9·:·Sequence
  
33 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))33 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))
  
34 o10·=·(16,·9,·3,·5,·2,·4,·1,·2,·2,·1,·2,·2,·2,·2,·1,·0,·2,·2,·2,·0,·0,·0,·0,34 o10·=·(19,·8,·6,·5,·2,·5,·1,·1,·0,·1,·2,·1,·1,·0,·1,·0,·0,·0,·1,·1,·0,·2,·0,
35 ······-----------------------------------------------------------------------35 ······-----------------------------------------------------------------------
36 ······2,·1,·0,·1,·1,·0)36 ······1,·0,·0,·0,·0,·1)
  
37 o10·:·Sequence37 o10·:·Sequence
  
38 i11·:·38 i11·:·
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Offset 4, 15 lines modifiedOffset 4, 15 lines modified
  
4 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}4 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
5 o1·:·List5 o1·:·List
  
6 i2·:·generateRandomGraphs(5,·5)6 i2·:·generateRandomGraphs(5,·5)
  
7 o2·=·{DRc,·Dr{,·Djg,·Dxw,·DW{}7 o2·=·{D]K,·D{C,·DUk,·DCo,·Djs}
  
8 o2·:·List8 o2·:·List
  
9 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)9 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
  
10 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}10 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
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Offset 1, 21 lines modifiedOffset 1, 21 lines modified
1 --·-*-·M2-comint·-*-·hash:·17298311710600676751 --·-*-·M2-comint·-*-·hash:·1729831171060067675
  
2 i1·:·R·=·QQ[a..e];2 i1·:·R·=·QQ[a..e];
  
3 i2·:·generateRandomRegularGraphs(R,·3,·2)3 i2·:·generateRandomRegularGraphs(R,·3,·2)
  
4 o2·=·{Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}},4 o2·=·{Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}},
5 ············"ring"·=>·R··········································5 ············"ring"·=>·R··········································
6 ············"vertices"·=>·{a,·b,·c,·d,·e}························6 ············"vertices"·=>·{a,·b,·c,·d,·e}························
7 ·····------------------------------------------------------------------------7 ·····------------------------------------------------------------------------
8 ·····Graph{"edges"·=>·{{a,·c},·{b,·d},·{c,·d},·{a,·e},·{b,·e}}},8 ·····Graph{"edges"·=>·{{b,·c},·{a,·d},·{c,·d},·{a,·e},·{b,·e}}},
9 ···········"ring"·=>·R··········································9 ···········"ring"·=>·R··········································
10 ···········"vertices"·=>·{a,·b,·c,·d,·e}························10 ···········"vertices"·=>·{a,·b,·c,·d,·e}························
11 ·····------------------------------------------------------------------------11 ·····------------------------------------------------------------------------
12 ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}}12 ·····Graph{"edges"·=>·{{a,·c},·{b,·c},·{b,·d},·{a,·e},·{d,·e}}}}
13 ···········"ring"·=>·R13 ···········"ring"·=>·R
14 ···········"vertices"·=>·{a,·b,·c,·d,·e}14 ···········"vertices"·=>·{a,·b,·c,·d,·e}
  
15 o2·:·List15 o2·:·List
  
16 i3·:·16 i3·:·
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Offset 13, 13 lines modifiedOffset 13, 13 lines modified
13 i3·:·graphComplement·"Dhc"13 i3·:·graphComplement·"Dhc"
  
14 o3·=·DUW14 o3·=·DUW
  
15 i4·:·G·=·generateBipartiteGraphs·7;15 i4·:·G·=·generateBipartiteGraphs·7;
  
16 i5·:·time·graphComplement·G;16 i5·:·time·graphComplement·G;
17 ·--·used·0.000505481s·(cpu);·0.000380343s·(thread);·0s·(gc)17 ·--·used·0.000795532s·(cpu);·0.000815941s·(thread);·0s·(gc)
  
18 i6·:·time·(graphComplement·\·G);18 i6·:·time·(graphComplement·\·G);
19 ·--·used·0.0544651s·(cpu);·0.0531322s·(thread);·0s·(gc)19 ·--·used·0.0755693s·(cpu);·0.0732034s·(thread);·0s·(gc)
  
20 i7·:·20 i7·:·
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117 ··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre>117 ··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))122 ··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))
  
123 o9·=·(69,·81,·90,·96,·88,·94,·98,·97,·97,·94,·93,·97,·97,·98,·100,·96,·98,123 o9·=·(73,·81,·87,·95,·94,·97,·98,·96,·96,·95,·92,·99,·99,·97,·97,·96,·98,·99,
124 ·····------------------------------------------------------------------------124 ·····------------------------------------------------------------------------
125 ·····99,·98,·97,·99,·98,·97,·99,·97,·99,·98,·96,·97)125 ·····96,·98,·96,·95,·98,·98,·98,·97,·95,·98,·100)
  
126 o9·:·Sequence</code></pre>126 o9·:·Sequence</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))131 ··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))
  
132 o10·=·(16,·9,·3,·5,·2,·4,·1,·2,·2,·1,·2,·2,·2,·2,·1,·0,·2,·2,·2,·0,·0,·0,·0,132 o10·=·(19,·8,·6,·5,·2,·5,·1,·1,·0,·1,·2,·1,·1,·0,·1,·0,·0,·0,·1,·1,·0,·2,·0,
133 ······-----------------------------------------------------------------------133 ······-----------------------------------------------------------------------
134 ······2,·1,·0,·1,·1,·0)134 ······1,·0,·0,·0,·0,·1)
  
135 o10·:·Sequence</code></pre>135 o10·:·Sequence</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ········</table>138 ········</table>
139 ······</div>139 ······</div>
140 ······<div>140 ······<div>
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38 connected,·at·least·as·$n$·tends·to·infinity.38 connected,·at·least·as·$n$·tends·to·infinity.
39 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>39 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>
40 true};40 true};
41 i8·:·prob·=·n·->·log(n)/n;41 i8·:·prob·=·n·->·log(n)/n;
42 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),42 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),
43 connected))43 connected))
  
44 o9·=·(69,·81,·90,·96,·88,·94,·98,·97,·97,·94,·93,·97,·97,·98,·100,·96,·98,44 o9·=·(73,·81,·87,·95,·94,·97,·98,·96,·96,·95,·92,·99,·99,·97,·97,·96,·98,·99,
45 ·····------------------------------------------------------------------------45 ·····------------------------------------------------------------------------
46 ·····99,·98,·97,·99,·98,·97,·99,·97,·99,·98,·96,·97)46 ·····96,·98,·96,·95,·98,·98,·98,·97,·95,·98,·100)
  
47 o9·:·Sequence47 o9·:·Sequence
48 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),48 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),
49 connected))49 connected))
  
50 o10·=·(16,·9,·3,·5,·2,·4,·1,·2,·2,·1,·2,·2,·2,·2,·1,·0,·2,·2,·2,·0,·0,·0,·0,50 o10·=·(19,·8,·6,·5,·2,·5,·1,·1,·0,·1,·2,·1,·1,·0,·1,·0,·0,·0,·1,·1,·0,·2,·0,
51 ······-----------------------------------------------------------------------51 ······-----------------------------------------------------------------------
52 ······2,·1,·0,·1,·1,·0)52 ······1,·0,·0,·0,·0,·1)
  
53 o10·:·Sequence53 o10·:·Sequence
54 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*54 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
55 ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with55 ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with
56 ······filterGraphs·and·countGraphs56 ······filterGraphs·and·countGraphs
57 ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given57 ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given
58 ······properties58 ······properties
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100 o1·:·List</code></pre>100 o1·:·List</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5)105 ··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5)
  
106 o2·=·{DRc,·Dr{,·Djg,·Dxw,·DW{}106 o2·=·{D]K,·D{C,·DUk,·DCo,·Djs}
  
107 o2·:·List</code></pre>107 o2·:·List</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)112 ··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
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37 i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)37 i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
  
38 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}38 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
39 o1·:·List39 o1·:·List
40 i2·:·generateRandomGraphs(5,·5)40 i2·:·generateRandomGraphs(5,·5)
  
41 o2·=·{DRc,·Dr{,·Djg,·Dxw,·DW{}41 o2·=·{D]K,·D{C,·DUk,·DCo,·Djs}
  
42 o2·:·List42 o2·:·List
43 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)43 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
  
44 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}44 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
45 o3·:·List45 o3·:·List
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./usr/share/doc/Macaulay2/Nauty/html/_generate__Random__Regular__Graphs.html
    
Offset 87, 23 lines modifiedOffset 87, 23 lines modified
87 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[a..e];</code></pre>87 ··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[a..e];</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i2·:·generateRandomRegularGraphs(R,·3,·2)92 ··············<pre><code·class="language-macaulay2">i2·:·generateRandomRegularGraphs(R,·3,·2)
  
93 o2·=·{Graph{&quot;edges&quot;·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}},93 o2·=·{Graph{&quot;edges&quot;·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}},
94 ············&quot;ring&quot;·=>·R··········································94 ············&quot;ring&quot;·=>·R··········································
95 ············&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}························95 ············&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}························
96 ·····------------------------------------------------------------------------96 ·····------------------------------------------------------------------------
97 ·····Graph{&quot;edges&quot;·=>·{{a,·c},·{b,·d},·{c,·d},·{a,·e},·{b,·e}}},97 ·····Graph{&quot;edges&quot;·=>·{{b,·c},·{a,·d},·{c,·d},·{a,·e},·{b,·e}}},
98 ···········&quot;ring&quot;·=>·R··········································98 ···········&quot;ring&quot;·=>·R··········································
99 ···········&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}························99 ···········&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}························
100 ·····------------------------------------------------------------------------100 ·····------------------------------------------------------------------------
101 ·····Graph{&quot;edges&quot;·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}}101 ·····Graph{&quot;edges&quot;·=>·{{a,·c},·{b,·c},·{b,·d},·{a,·e},·{d,·e}}}}
102 ···········&quot;ring&quot;·=>·R102 ···········&quot;ring&quot;·=>·R
103 ···········&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}103 ···········&quot;vertices&quot;·=>·{a,·b,·c,·d,·e}
  
104 o2·:·List</code></pre>104 o2·:·List</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ········</table>107 ········</table>
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24 vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.24 vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.
25 If·a·_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8R_\x8i_\x8n_\x8g·$R$·is·supplied·instead,·then·the·number·of·vertices·is·the25 If·a·_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8R_\x8i_\x8n_\x8g·$R$·is·supplied·instead,·then·the·number·of·vertices·is·the
26 number·of·generators.·Moreover,·the·nauty-based·strings·are·automatically26 number·of·generators.·Moreover,·the·nauty-based·strings·are·automatically
27 converted·to·instances·of·the·class·_\x8G_\x8r_\x8a_\x8p_\x8h·in·$R$.27 converted·to·instances·of·the·class·_\x8G_\x8r_\x8a_\x8p_\x8h·in·$R$.
28 i1·:·R·=·QQ[a..e];28 i1·:·R·=·QQ[a..e];
29 i2·:·generateRandomRegularGraphs(R,·3,·2)29 i2·:·generateRandomRegularGraphs(R,·3,·2)
  
30 o2·=·{Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}},30 o2·=·{Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}},
31 ············"ring"·=>·R31 ············"ring"·=>·R
32 ············"vertices"·=>·{a,·b,·c,·d,·e}32 ············"vertices"·=>·{a,·b,·c,·d,·e}
33 ·····------------------------------------------------------------------------33 ·····------------------------------------------------------------------------
34 ·····Graph{"edges"·=>·{{a,·c},·{b,·d},·{c,·d},·{a,·e},·{b,·e}}},34 ·····Graph{"edges"·=>·{{b,·c},·{a,·d},·{c,·d},·{a,·e},·{b,·e}}},
35 ···········"ring"·=>·R35 ···········"ring"·=>·R
36 ···········"vertices"·=>·{a,·b,·c,·d,·e}36 ···········"vertices"·=>·{a,·b,·c,·d,·e}
37 ·····------------------------------------------------------------------------37 ·····------------------------------------------------------------------------
38 ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}}38 ·····Graph{"edges"·=>·{{a,·c},·{b,·c},·{b,·d},·{a,·e},·{d,·e}}}}
39 ···········"ring"·=>·R39 ···········"ring"·=>·R
40 ···········"vertices"·=>·{a,·b,·c,·d,·e}40 ···········"vertices"·=>·{a,·b,·c,·d,·e}
  
41 o2·:·List41 o2·:·List
42 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*42 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
43 The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with43 The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with
44 zero·vertices.44 zero·vertices.
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./usr/share/doc/Macaulay2/Nauty/html/_graph__Complement.html
    
Offset 116, 21 lines modifiedOffset 116, 21 lines modified
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i4·:·G·=·generateBipartiteGraphs·7;</code></pre>117 ··············<pre><code·class="language-macaulay2">i4·:·G·=·generateBipartiteGraphs·7;</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i5·:·time·graphComplement·G;122 ··············<pre><code·class="language-macaulay2">i5·:·time·graphComplement·G;
123 ·--·used·0.000505481s·(cpu);·0.000380343s·(thread);·0s·(gc)</code></pre>123 ·--·used·0.000795532s·(cpu);·0.000815941s·(thread);·0s·(gc)</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i6·:·time·(graphComplement·\·G);128 ··············<pre><code·class="language-macaulay2">i6·:·time·(graphComplement·\·G);
129 ·--·used·0.0544651s·(cpu);·0.0531322s·(thread);·0s·(gc)</code></pre>129 ·--·used·0.0755693s·(cpu);·0.0732034s·(thread);·0s·(gc)</code></pre>
130 ············</td>130 ············</td>
131 ··········</tr>131 ··········</tr>
132 ········</table>132 ········</table>
133 ······</div>133 ······</div>
134 ······<div>134 ······<div>
135 ········<h2>See·also</h2>135 ········<h2>See·also</h2>
136 ········<ul>136 ········<ul>
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Offset 41, 17 lines modifiedOffset 41, 17 lines modified
  
41 o3·=·DUW41 o3·=·DUW
42 Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input42 Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input
43 format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in43 format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in
44 Graph6·or·Sparse6·format.44 Graph6·or·Sparse6·format.
45 i4·:·G·=·generateBipartiteGraphs·7;45 i4·:·G·=·generateBipartiteGraphs·7;
46 i5·:·time·graphComplement·G;46 i5·:·time·graphComplement·G;
47 ·--·used·0.000505481s·(cpu);·0.000380343s·(thread);·0s·(gc)47 ·--·used·0.000795532s·(cpu);·0.000815941s·(thread);·0s·(gc)
48 i6·:·time·(graphComplement·\·G);48 i6·:·time·(graphComplement·\·G);
49 ·--·used·0.0544651s·(cpu);·0.0531322s·(thread);·0s·(gc)49 ·--·used·0.0755693s·(cpu);·0.0732034s·(thread);·0s·(gc)
50 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*50 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
51 ····*·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8G_\x8r_\x8a_\x8p_\x8h·--·returns·the·complement·of·a·graph·or·hypergraph51 ····*·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8G_\x8r_\x8a_\x8p_\x8h·--·returns·the·complement·of·a·graph·or·hypergraph
52 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*52 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*
53 ····*·graphComplement(Graph)53 ····*·graphComplement(Graph)
54 ····*·graphComplement(List)54 ····*·graphComplement(List)
55 ····*·graphComplement(String)55 ····*·graphComplement(String)
56 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*56 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
751 B
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=317 #:len=31
8 YWRkRWRnZXMoLi4uLE5vTmV3NUN5Y2xlcz0+Li4uKQ==8 YWRkRWRnZXMoLi4uLE5vTmV3NUN5Y2xlcz0+Li4uKQ==
9 #:len=2619 #:len=261
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTkxLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTkxLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1thZGRFZGdlcyxOb05ldzVDeWNsZXNdLCJhZGRFZGdl11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1thZGRFZGdlcyxOb05ldzVDeWNsZXNdLCJhZGRFZGdl
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./usr/share/doc/Macaulay2/NautyGraphs/example-output/___Example_co_sp__Generating_spand_spfiltering_spgraphs.out
    
Offset 26, 22 lines modifiedOffset 26, 22 lines modified
  
26 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true};26 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true};
  
27 i8·:·prob·=·n·->·log(n)/n;27 i8·:·prob·=·n·->·log(n)/n;
  
28 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))28 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))
  
29 o9·=·(70,·85,·88,·94,·98,·98,·96,·98,·96,·96,·100,·96,·98,·99,·97,·98,·97,29 o9·=·(74,·87,·86,·94,·95,·94,·97,·97,·96,·98,·98,·98,·97,·99,·98,·100,·99,
30 ·····------------------------------------------------------------------------30 ·····------------------------------------------------------------------------
31 ·····97,·97,·97,·97,·97,·98,·100,·100,·96,·98,·96,·97)31 ·····99,·99,·94,·100,·99,·96,·97,·98,·96,·98,·100,·99)
  
32 o9·:·Sequence32 o9·:·Sequence
  
33 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))33 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))
  
34 o10·=·(18,·6,·5,·3,·2,·4,·4,·3,·1,·1,·1,·1,·1,·0,·0,·2,·1,·0,·0,·1,·0,·0,·0,34 o10·=·(20,·15,·5,·7,·1,·1,·0,·2,·3,·4,·1,·1,·0,·0,·2,·2,·0,·0,·0,·0,·0,·0,·2,
35 ······-----------------------------------------------------------------------35 ······-----------------------------------------------------------------------
36 ······0,·0,·0,·0,·1,·1)36 ······1,·0,·0,·0,·0,·0)
  
37 o10·:·Sequence37 o10·:·Sequence
  
38 i11·:·38 i11·:·
436 B
./usr/share/doc/Macaulay2/NautyGraphs/example-output/_generate__Random__Graphs.out
    
Offset 4, 15 lines modifiedOffset 4, 15 lines modified
  
4 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}4 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
5 o1·:·List5 o1·:·List
  
6 i2·:·generateRandomGraphs(5,·5)6 i2·:·generateRandomGraphs(5,·5)
  
7 o2·=·{Dhw,·Dgc,·DKo,·Dpw,·DAC}7 o2·=·{Dtk,·DRS,·Dno,·DP[,·D_g}
  
8 o2·:·List8 o2·:·List
  
9 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)9 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
  
10 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}10 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
353 B
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Offset 1, 9 lines modifiedOffset 1, 9 lines modified
1 --·-*-·M2-comint·-*-·hash:·13312873922681 --·-*-·M2-comint·-*-·hash:·1331287392268
  
2 i1·:·generateRandomRegularGraphs(5,·3,·2)2 i1·:·generateRandomRegularGraphs(5,·3,·2)
  
3 o1·=·{DLo,·DdW,·DqK}3 o1·=·{DdW,·DpS,·D[S}
  
4 o1·:·List4 o1·:·List
  
5 i2·:·5 i2·:·
560 B
./usr/share/doc/Macaulay2/NautyGraphs/example-output/_graph__Complement.out
    
Offset 13, 13 lines modifiedOffset 13, 13 lines modified
13 ···········4·=>·{2,·1}13 ···········4·=>·{2,·1}
  
14 o2·:·Graph14 o2·:·Graph
  
15 i3·:·G·=·generateBipartiteGraphs·7;15 i3·:·G·=·generateBipartiteGraphs·7;
  
16 i4·:·time·graphComplement·G;16 i4·:·time·graphComplement·G;
17 ·--·used·0.000799884s·(cpu);·0.000598421s·(thread);·0s·(gc)17 ·--·used·0.000951685s·(cpu);·0.000752111s·(thread);·0s·(gc)
  
18 i5·:·time·(graphComplement·\·G);18 i5·:·time·(graphComplement·\·G);
19 ·--·used·0.0566896s·(cpu);·0.0553318s·(thread);·0s·(gc)19 ·--·used·0.0731809s·(cpu);·0.0710135s·(thread);·0s·(gc)
  
20 i6·:·20 i6·:·
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117 ··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre>117 ··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))122 ··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected))
  
123 o9·=·(70,·85,·88,·94,·98,·98,·96,·98,·96,·96,·100,·96,·98,·99,·97,·98,·97,123 o9·=·(74,·87,·86,·94,·95,·94,·97,·97,·96,·98,·98,·98,·97,·99,·98,·100,·99,
124 ·····------------------------------------------------------------------------124 ·····------------------------------------------------------------------------
125 ·····97,·97,·97,·97,·97,·98,·100,·100,·96,·98,·96,·97)125 ·····99,·99,·94,·100,·99,·96,·97,·98,·96,·98,·100,·99)
  
126 o9·:·Sequence</code></pre>126 o9·:·Sequence</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))131 ··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected))
  
132 o10·=·(18,·6,·5,·3,·2,·4,·4,·3,·1,·1,·1,·1,·1,·0,·0,·2,·1,·0,·0,·1,·0,·0,·0,132 o10·=·(20,·15,·5,·7,·1,·1,·0,·2,·3,·4,·1,·1,·0,·0,·2,·2,·0,·0,·0,·0,·0,·0,·2,
133 ······-----------------------------------------------------------------------133 ······-----------------------------------------------------------------------
134 ······0,·0,·0,·0,·1,·1)134 ······1,·0,·0,·0,·0,·0)
  
135 o10·:·Sequence</code></pre>135 o10·:·Sequence</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ········</table>138 ········</table>
139 ······</div>139 ······</div>
140 ······<div>140 ······<div>
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38 connected,·at·least·as·$n$·tends·to·infinity.38 connected,·at·least·as·$n$·tends·to·infinity.
39 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>39 i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>
40 true};40 true};
41 i8·:·prob·=·n·->·log(n)/n;41 i8·:·prob·=·n·->·log(n)/n;
42 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),42 i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),
43 connected))43 connected))
  
44 o9·=·(70,·85,·88,·94,·98,·98,·96,·98,·96,·96,·100,·96,·98,·99,·97,·98,·97,44 o9·=·(74,·87,·86,·94,·95,·94,·97,·97,·96,·98,·98,·98,·97,·99,·98,·100,·99,
45 ·····------------------------------------------------------------------------45 ·····------------------------------------------------------------------------
46 ·····97,·97,·97,·97,·97,·98,·100,·100,·96,·98,·96,·97)46 ·····99,·99,·94,·100,·99,·96,·97,·98,·96,·98,·100,·99)
  
47 o9·:·Sequence47 o9·:·Sequence
48 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),48 i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),
49 connected))49 connected))
  
50 o10·=·(18,·6,·5,·3,·2,·4,·4,·3,·1,·1,·1,·1,·1,·0,·0,·2,·1,·0,·0,·1,·0,·0,·0,50 o10·=·(20,·15,·5,·7,·1,·1,·0,·2,·3,·4,·1,·1,·0,·0,·2,·2,·0,·0,·0,·0,·0,·0,·2,
51 ······-----------------------------------------------------------------------51 ······-----------------------------------------------------------------------
52 ······0,·0,·0,·0,·1,·1)52 ······1,·0,·0,·0,·0,·0)
  
53 o10·:·Sequence53 o10·:·Sequence
54 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*54 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
55 ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with55 ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with
56 ······filterGraphs·and·countGraphs56 ······filterGraphs·and·countGraphs
57 ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given57 ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given
58 ······properties58 ······properties
974 B
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Offset 93, 15 lines modifiedOffset 93, 15 lines modified
93 o1·:·List</code></pre>93 o1·:·List</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5)98 ··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5)
  
99 o2·=·{Dhw,·Dgc,·DKo,·Dpw,·DAC}99 o2·=·{Dtk,·DRS,·Dno,·DP[,·D_g}
  
100 o2·:·List</code></pre>100 o2·:·List</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)105 ··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
360 B
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30 i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)30 i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
  
31 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}31 o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
32 o1·:·List32 o1·:·List
33 i2·:·generateRandomGraphs(5,·5)33 i2·:·generateRandomGraphs(5,·5)
  
34 o2·=·{Dhw,·Dgc,·DKo,·Dpw,·DAC}34 o2·=·{Dtk,·DRS,·Dno,·DP[,·D_g}
  
35 o2·:·List35 o2·:·List
36 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)36 i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159)
  
37 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}37 o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K}
  
38 o3·:·List38 o3·:·List
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./usr/share/doc/Macaulay2/NautyGraphs/html/_generate__Random__Regular__Graphs.html
    
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77 ··········<p>This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of·vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.</p>77 ··········<p>This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of·vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.</p>
78 ········</div>78 ········</div>
79 ········<table·class="examples">79 ········<table·class="examples">
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i1·:·generateRandomRegularGraphs(5,·3,·2)82 ··············<pre><code·class="language-macaulay2">i1·:·generateRandomRegularGraphs(5,·3,·2)
  
83 o1·=·{DLo,·DdW,·DqK}83 o1·=·{DdW,·DpS,·D[S}
  
84 o1·:·List</code></pre>84 o1·:·List</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ········</table>87 ········</table>
88 ······</div>88 ······</div>
89 ······<div>89 ······<div>
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18 ····*·Outputs:18 ····*·Outputs:
19 ··········o·G,·a·_\x8l_\x8i_\x8s_\x8t,·the·randomly·generated·regular·graphs19 ··········o·G,·a·_\x8l_\x8i_\x8s_\x8t,·the·randomly·generated·regular·graphs
20 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
21 This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of21 This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of
22 vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.22 vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.
23 i1·:·generateRandomRegularGraphs(5,·3,·2)23 i1·:·generateRandomRegularGraphs(5,·3,·2)
  
24 o1·=·{DLo,·DdW,·DqK}24 o1·=·{DdW,·DpS,·D[S}
  
25 o1·:·List25 o1·:·List
26 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
27 The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with27 The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with
28 zero·vertices.28 zero·vertices.
29 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
30 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8e_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·generates·random·graphs·on·a·given·number·of30 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8e_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·generates·random·graphs·on·a·given·number·of
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110 ············<td>110 ············<td>
111 ··············<pre><code·class="language-macaulay2">i3·:·G·=·generateBipartiteGraphs·7;</code></pre>111 ··············<pre><code·class="language-macaulay2">i3·:·G·=·generateBipartiteGraphs·7;</code></pre>
112 ············</td>112 ············</td>
113 ··········</tr>113 ··········</tr>
114 ··········<tr>114 ··········<tr>
115 ············<td>115 ············<td>
116 ··············<pre><code·class="language-macaulay2">i4·:·time·graphComplement·G;116 ··············<pre><code·class="language-macaulay2">i4·:·time·graphComplement·G;
117 ·--·used·0.000799884s·(cpu);·0.000598421s·(thread);·0s·(gc)</code></pre>117 ·--·used·0.000951685s·(cpu);·0.000752111s·(thread);·0s·(gc)</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i5·:·time·(graphComplement·\·G);122 ··············<pre><code·class="language-macaulay2">i5·:·time·(graphComplement·\·G);
123 ·--·used·0.0566896s·(cpu);·0.0553318s·(thread);·0s·(gc)</code></pre>123 ·--·used·0.0731809s·(cpu);·0.0710135s·(thread);·0s·(gc)</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ········</table>126 ········</table>
127 ······</div>127 ······</div>
128 ······<div>128 ······<div>
129 ········<div·class="waystouse">129 ········<div·class="waystouse">
130 ··········<h2>Ways·to·use·<span·class="tt">graphComplement</span>:</h2>130 ··········<h2>Ways·to·use·<span·class="tt">graphComplement</span>:</h2>
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38 o2·:·Graph38 o2·:·Graph
39 Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input39 Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input
40 format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in40 format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in
41 Graph6·or·Sparse6·format.41 Graph6·or·Sparse6·format.
42 i3·:·G·=·generateBipartiteGraphs·7;42 i3·:·G·=·generateBipartiteGraphs·7;
43 i4·:·time·graphComplement·G;43 i4·:·time·graphComplement·G;
44 ·--·used·0.000799884s·(cpu);·0.000598421s·(thread);·0s·(gc)44 ·--·used·0.000951685s·(cpu);·0.000752111s·(thread);·0s·(gc)
45 i5·:·time·(graphComplement·\·G);45 i5·:·time·(graphComplement·\·G);
46 ·--·used·0.0566896s·(cpu);·0.0553318s·(thread);·0s·(gc)46 ·--·used·0.0731809s·(cpu);·0.0710135s·(thread);·0s·(gc)
47 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*47 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8*
48 ····*·graphComplement(Graph)48 ····*·graphComplement(Graph)
49 ····*·graphComplement(List)49 ····*·graphComplement(List)
50 ····*·graphComplement(String)50 ····*·graphComplement(String)
51 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*51 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
52 The·object·_\x8g_\x8r_\x8a_\x8p_\x8h_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.52 The·object·_\x8g_\x8r_\x8a_\x8p_\x8h_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
53 ===============================================================================53 ===============================================================================
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47 o4·:·Ideal·of·R47 o4·:·Ideal·of·R
  
48 i5·:·isPrimary·Q48 i5·:·isPrimary·Q
  
49 o5·=·true49 o5·=·true
  
50 i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot")50 i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot")
51 ·--·.0728466s·elapsed51 ·--·.179197s·elapsed
  
52 o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·|52 o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·|
53 ·····------------------------------------------------------------------------53 ·····------------------------------------------------------------------------
54 ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|}54 ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|}
  
55 o6·:·List55 o6·:·List
  
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120 o5·=·true</code></pre>120 o5·=·true</code></pre>
121 ············</td>121 ············</td>
122 ··········</tr>122 ··········</tr>
123 ··········<tr>123 ··········<tr>
124 ············<td>124 ············<td>
125 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·&quot;PunctualQuot&quot;)125 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·&quot;PunctualQuot&quot;)
126 ·--·.0728466s·elapsed126 ·--·.179197s·elapsed
  
127 o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·|127 o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·|
128 ·····------------------------------------------------------------------------128 ·····------------------------------------------------------------------------
129 ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|}129 ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|}
  
130 o6·:·List</code></pre>130 o6·:·List</code></pre>
131 ············</td>131 ············</td>
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51 ·······1·2·3····2·351 ·······1·2·3····2·3
  
52 o4·:·Ideal·of·R52 o4·:·Ideal·of·R
53 i5·:·isPrimary·Q53 i5·:·isPrimary·Q
  
54 o5·=·true54 o5·=·true
55 i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot")55 i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot")
56 ·--·.0728466s·elapsed56 ·--·.179197s·elapsed
  
57 o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·|57 o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·|
58 ·····------------------------------------------------------------------------58 ·····------------------------------------------------------------------------
59 ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|}59 ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|}
  
60 o6·:·List60 o6·:·List
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./usr/share/doc/Macaulay2/NormalToricVarieties/example-output/___Chow_spring.out
    
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78 i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1)78 i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1)
  
79 o13·=·{1,·2,·3,·3,·2,·1}79 o13·=·{1,·2,·3,·3,·2,·1}
  
80 o13·:·List80 o13·:·List
  
81 i14·:·Y·=·time·smoothFanoToricVariety(5,100);81 i14·:·Y·=·time·smoothFanoToricVariety(5,100);
82 ·--·used·0.167225s·(cpu);·0.167931s·(thread);·0s·(gc)82 ·--·used·0.20316s·(cpu);·0.202777s·(thread);·0s·(gc)
  
83 i15·:·A2·=·intersectionRing·Y;83 i15·:·A2·=·intersectionRing·Y;
  
84 i16·:·assert·(#·rays·Y·===·numgens·A2)84 i16·:·assert·(#·rays·Y·===·numgens·A2)
  
85 i17·:·ideal·A285 i17·:·ideal·A2
  
Offset 110, 19 lines modifiedOffset 110, 19 lines modified
110 ········2·················2···2·······················2···2·····························2·············2······················2·····3······2110 ········2·················2···2·······················2···2·····························2·············2······················2·····3······2
111 ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t·t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··)111 ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t·t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··)
112 ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10····9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10112 ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10····9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10
  
113 o18·:·QuotientRing113 o18·:·QuotientRing
  
114 i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2)114 i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2)
115 ·--·used·0.00379324s·(cpu);·0.00125573s·(thread);·0s·(gc)115 ·--·used·0.00386596s·(cpu);·0.00168535s·(thread);·0s·(gc)
 116 ·--·used·2.5518e-05s·(cpu);·0.000102692s·(thread);·0s·(gc)
 117 ·--·used·1.1382e-05s·(cpu);·8.1182e-05s·(thread);·0s·(gc)
 118 ·--·used·9.698e-06s·(cpu);·8.4719e-05s·(thread);·0s·(gc)
116 ·--·used·2.686e-05s·(cpu);·7.9039e-05s·(thread);·0s·(gc)119 ·--·used·1.056e-05s·(cpu);·9.0319e-05s·(thread);·0s·(gc)
117 ·--·used·6.119e-06s·(cpu);·5.1648e-05s·(thread);·0s·(gc) 
118 ·--·used·5.448e-06s·(cpu);·5.276e-05s·(thread);·0s·(gc) 
119 ·--·used·5.548e-06s·(cpu);·5.2068e-05s·(thread);·0s·(gc) 
120 ·--·used·5.068e-06s·(cpu);·5.2068e-05s·(thread);·0s·(gc)120 ·--·used·9.267e-06s·(cpu);·0.000120116s·(thread);·0s·(gc)
  
121 o19·=·{1,·6,·13,·13,·6,·1}121 o19·=·{1,·6,·13,·13,·6,·1}
  
122 o19·:·List122 o19·:·List
  
123 i20·:·123 i20·:·
930 B
./usr/share/doc/Macaulay2/NormalToricVarieties/example-output/_is__Well__Defined_lp__Normal__Toric__Variety_rp.out
    
Offset 1, 29 lines modifiedOffset 1, 29 lines modified
1 --·-*-·M2-comint·-*-·hash:·164083857648436956321 --·-*-·M2-comint·-*-·hash:·16408385764843695632
  
2 i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1))2 i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1))
  
3 i2·:·setRandomSeed·(currentTime·());3 i2·:·setRandomSeed·(currentTime·());
4 ·--·setting·random·seed·to·17492079234 ·--·setting·random·seed·to·1783630474
  
5 i3·:·a·=·sort·apply·(3,·i·->·random·(7))5 i3·:·a·=·sort·apply·(3,·i·->·random·(7))
  
6 o3·=·{3,·4,·4}6 o3·=·{3,·4,·6}
  
7 o3·:·List7 o3·:·List
  
8 i4·:·assert·isWellDefined·kleinschmidt·(4,a)8 i4·:·assert·isWellDefined·kleinschmidt·(4,a)
  
9 i5·:·q·=·sort·apply·(5,·j·->·random·(1,9));9 i5·:·q·=·sort·apply·(5,·j·->·random·(1,9));
  
10 i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9));10 i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9));
  
11 i7·:·q11 i7·:·q
  
12 o7·=·{2,·4,·7,·7,·8}12 o7·=·{4,·4,·5,·5,·6}
  
13 o7·:·List13 o7·:·List
  
14 i8·:·assert·isWellDefined·weightedProjectiveSpace·q14 i8·:·assert·isWellDefined·weightedProjectiveSpace·q
  
15 i9·:·X·=·new·MutableHashTable;15 i9·:·X·=·new·MutableHashTable;
  
1.82 KB
./usr/share/doc/Macaulay2/NormalToricVarieties/example-output/_monomials_lp__Toric__Divisor_rp.out
    
Offset 6, 61 lines modifiedOffset 6, 61 lines modified
  
6 o2·=·5*PP26 o2·=·5*PP2
7 ··········07 ··········0
  
8 o2·:·ToricDivisor·on·PP28 o2·:·ToricDivisor·on·PP2
  
9 i3·:·M1·=·elapsedTime·monomials·D19 i3·:·M1·=·elapsedTime·monomials·D1
10 ·--·.225018s·elapsed10 ·--·.536582s·elapsed
  
11 ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4···11 ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4···
12 o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·,12 o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·,
13 ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2·13 ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2·
14 ·····------------------------------------------------------------------------14 ·····------------------------------------------------------------------------
15 ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····515 ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5
16 ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·}16 ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·}
17 ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···017 ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0
  
18 o3·:·List18 o3·:·List
  
19 i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1))19 i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1))
20 ·--·.0011225s·elapsed20 ·--·.00126481s·elapsed
  
21 i5·:·FF2·=·hirzebruchSurface·2;21 i5·:·FF2·=·hirzebruchSurface·2;
  
22 i6·:·D2·=·2*FF2_0·+·3·*·FF2_122 i6·:·D2·=·2*FF2_0·+·3·*·FF2_1
  
23 o6·=·2*FF2··+·3*FF223 o6·=·2*FF2··+·3*FF2
24 ··········0········124 ··········0········1
  
25 o6·:·ToricDivisor·on·FF225 o6·:·ToricDivisor·on·FF2
  
26 i7·:·M2·=·elapsedTime·monomials·D226 i7·:·M2·=·elapsedTime·monomials·D2
27 ·--·.337739s·elapsed27 ·--·.57286s·elapsed
  
28 ·······2·····3·2·····3·····2·328 ·······2·····3·2·····3·····2·3
29 o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·}29 o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·}
30 ·······1·3···1·2···0·1·2···0·130 ·······1·3···1·2···0·1·2···0·1
  
31 o7·:·List31 o7·:·List
  
32 i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2))32 i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2))
33 ·--·.00107011s·elapsed33 ·--·.00172497s·elapsed
  
34 i9·:·X·=·kleinschmidt·(5,·{1,2,3});34 i9·:·X·=·kleinschmidt·(5,·{1,2,3});
  
35 i10·:·D3·=·3*X_0·+·5*X_135 i10·:·D3·=·3*X_0·+·5*X_1
  
36 o10·=·3*X··+·5*X36 o10·=·3*X··+·5*X
37 ·········0······137 ·········0······1
  
38 o10·:·ToricDivisor·on·X38 o10·:·ToricDivisor·on·X
  
39 i11·:·m3·=·elapsedTime·#·monomials·D339 i11·:·m3·=·elapsedTime·#·monomials·D3
40 ·--·34.0465s·elapsed40 ·--·74.766s·elapsed
  
41 o11·=·790941 o11·=·7909
  
42 i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3))42 i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3))
43 ·--·.0223298s·elapsed43 ·--·.0965507s·elapsed
  
44 i13·:·44 i13·:·
904 B
./usr/share/doc/Macaulay2/NormalToricVarieties/example-output/_normal__Toric__Variety_lp__Fan_rp.out
    
Offset 24, 19 lines modifiedOffset 24, 19 lines modified
24 o3·:·List24 o3·:·List
  
25 i4·:·X·=·normalToricVariety·F;25 i4·:·X·=·normalToricVariety·F;
  
26 i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F)26 i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F)
  
27 i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}})27 i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}})
28 ·--·used·0.00166827s·(cpu);·1.8158e-05s·(thread);·0s·(gc)28 ·--·used·4.7639e-05s·(cpu);·3.0838e-05s·(thread);·0s·(gc)
  
29 o6·=·X129 o6·=·X1
  
30 o6·:·NormalToricVariety30 o6·:·NormalToricVariety
  
31 i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}};31 i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}};
32 ·--·used·0.113356s·(cpu);·0.0652s·(thread);·0s·(gc)32 ·--·used·0.115753s·(cpu);·0.0622265s·(thread);·0s·(gc)
  
33 i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)33 i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)
  
34 i9·:·34 i9·:·
744 B
./usr/share/doc/Macaulay2/NormalToricVarieties/example-output/_normal__Toric__Variety_lp__Polyhedron_rp.out
    
Offset 88, 15 lines modifiedOffset 88, 15 lines modified
88 o18·=·|·0·1·0·|88 o18·=·|·0·1·0·|
89 ······|·0·0·1·|89 ······|·0·0·1·|
  
90 ···············2·······390 ···············2·······3
91 o18·:·Matrix·ZZ··<--·ZZ91 o18·:·Matrix·ZZ··<--·ZZ
  
92 i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix);92 i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix);
93 ·--·used·0.0191267s·(cpu);·0.0200144s·(thread);·0s·(gc)93 ·--·used·0.0239109s·(cpu);·0.0228231s·(thread);·0s·(gc)
  
94 i20·:·X2·=·time·normalToricVariety·vertMatrix;94 i20·:·X2·=·time·normalToricVariety·vertMatrix;
95 ·--·used·0.00178574s·(cpu);·0.00205128s·(thread);·0s·(gc)95 ·--·used·0.00212713s·(cpu);·0.00232491s·(thread);·0s·(gc)
  
96 i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)96 i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)
  
97 i22·:·97 i22·:·
3.7 KB
./usr/share/doc/Macaulay2/NormalToricVarieties/html/___Chow_spring.html
    
Offset 207, 15 lines modifiedOffset 207, 15 lines modified
207 ········<div>207 ········<div>
208 ··········<p>We·end·with·a·slightly·larger·example.</p>208 ··········<p>We·end·with·a·slightly·larger·example.</p>
209 ········</div>209 ········</div>
210 ········<table·class="examples">210 ········<table·class="examples">
211 ··········<tr>211 ··········<tr>
212 ············<td>212 ············<td>
213 ··············<pre><code·class="language-macaulay2">i14·:·Y·=·time·smoothFanoToricVariety(5,100);213 ··············<pre><code·class="language-macaulay2">i14·:·Y·=·time·smoothFanoToricVariety(5,100);
214 ·--·used·0.167225s·(cpu);·0.167931s·(thread);·0s·(gc)</code></pre>214 ·--·used·0.20316s·(cpu);·0.202777s·(thread);·0s·(gc)</code></pre>
215 ············</td>215 ············</td>
216 ··········</tr>216 ··········</tr>
217 ··········<tr>217 ··········<tr>
218 ············<td>218 ············<td>
219 ··············<pre><code·class="language-macaulay2">i15·:·A2·=·intersectionRing·Y;</code></pre>219 ··············<pre><code·class="language-macaulay2">i15·:·A2·=·intersectionRing·Y;</code></pre>
220 ············</td>220 ············</td>
221 ··········</tr>221 ··········</tr>
Offset 254, 20 lines modifiedOffset 254, 20 lines modified
  
254 o18·:·QuotientRing</code></pre>254 o18·:·QuotientRing</code></pre>
255 ············</td>255 ············</td>
256 ··········</tr>256 ··········</tr>
257 ··········<tr>257 ··········<tr>
258 ············<td>258 ············<td>
259 ··············<pre><code·class="language-macaulay2">i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2)259 ··············<pre><code·class="language-macaulay2">i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2)
260 ·--·used·0.00379324s·(cpu);·0.00125573s·(thread);·0s·(gc)260 ·--·used·0.00386596s·(cpu);·0.00168535s·(thread);·0s·(gc)
 261 ·--·used·2.5518e-05s·(cpu);·0.000102692s·(thread);·0s·(gc)
 262 ·--·used·1.1382e-05s·(cpu);·8.1182e-05s·(thread);·0s·(gc)
 263 ·--·used·9.698e-06s·(cpu);·8.4719e-05s·(thread);·0s·(gc)
261 ·--·used·2.686e-05s·(cpu);·7.9039e-05s·(thread);·0s·(gc)264 ·--·used·1.056e-05s·(cpu);·9.0319e-05s·(thread);·0s·(gc)
262 ·--·used·6.119e-06s·(cpu);·5.1648e-05s·(thread);·0s·(gc) 
263 ·--·used·5.448e-06s·(cpu);·5.276e-05s·(thread);·0s·(gc) 
264 ·--·used·5.548e-06s·(cpu);·5.2068e-05s·(thread);·0s·(gc) 
265 ·--·used·5.068e-06s·(cpu);·5.2068e-05s·(thread);·0s·(gc)265 ·--·used·9.267e-06s·(cpu);·0.000120116s·(thread);·0s·(gc)
  
266 o19·=·{1,·6,·13,·13,·6,·1}266 o19·=·{1,·6,·13,·13,·6,·1}
  
267 o19·:·List</code></pre>267 o19·:·List</code></pre>
268 ············</td>268 ············</td>
269 ··········</tr>269 ··········</tr>
270 ········</table>270 ········</table>
1.94 KB
html2text {}
    
Offset 96, 15 lines modifiedOffset 96, 15 lines modified
96 i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1)96 i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1)
  
97 o13·=·{1,·2,·3,·3,·2,·1}97 o13·=·{1,·2,·3,·3,·2,·1}
  
98 o13·:·List98 o13·:·List
99 We·end·with·a·slightly·larger·example.99 We·end·with·a·slightly·larger·example.
100 i14·:·Y·=·time·smoothFanoToricVariety(5,100);100 i14·:·Y·=·time·smoothFanoToricVariety(5,100);
101 ·--·used·0.167225s·(cpu);·0.167931s·(thread);·0s·(gc)101 ·--·used·0.20316s·(cpu);·0.202777s·(thread);·0s·(gc)
102 i15·:·A2·=·intersectionRing·Y;102 i15·:·A2·=·intersectionRing·Y;
103 i16·:·assert·(#·rays·Y·===·numgens·A2)103 i16·:·assert·(#·rays·Y·===·numgens·A2)
104 i17·:·ideal·A2104 i17·:·ideal·A2
  
105 o17·=·ideal·(t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·t··,105 o17·=·ideal·(t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·t··,
106 ··············2·3···2·5···4·5···3·6···4·6···1·7···7·9···8·9···0·1·10106 ··············2·3···2·5···4·5···3·6···4·6···1·7···7·9···8·9···0·1·10
107 ······-----------------------------------------------------------------------107 ······-----------------------------------------------------------------------
Offset 129, 20 lines modifiedOffset 129, 20 lines modified
129 ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t129 ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t
130 t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··)130 t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··)
131 ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10131 ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10
132 9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10132 9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10
  
133 o18·:·QuotientRing133 o18·:·QuotientRing
134 i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2)134 i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2)
135 ·--·used·0.00379324s·(cpu);·0.00125573s·(thread);·0s·(gc)135 ·--·used·0.00386596s·(cpu);·0.00168535s·(thread);·0s·(gc)
 136 ·--·used·2.5518e-05s·(cpu);·0.000102692s·(thread);·0s·(gc)
 137 ·--·used·1.1382e-05s·(cpu);·8.1182e-05s·(thread);·0s·(gc)
 138 ·--·used·9.698e-06s·(cpu);·8.4719e-05s·(thread);·0s·(gc)
136 ·--·used·2.686e-05s·(cpu);·7.9039e-05s·(thread);·0s·(gc)139 ·--·used·1.056e-05s·(cpu);·9.0319e-05s·(thread);·0s·(gc)
137 ·--·used·6.119e-06s·(cpu);·5.1648e-05s·(thread);·0s·(gc) 
138 ·--·used·5.448e-06s·(cpu);·5.276e-05s·(thread);·0s·(gc) 
139 ·--·used·5.548e-06s·(cpu);·5.2068e-05s·(thread);·0s·(gc) 
140 ·--·used·5.068e-06s·(cpu);·5.2068e-05s·(thread);·0s·(gc)140 ·--·used·9.267e-06s·(cpu);·0.000120116s·(thread);·0s·(gc)
  
141 o19·=·{1,·6,·13,·13,·6,·1}141 o19·=·{1,·6,·13,·13,·6,·1}
  
142 o19·:·List142 o19·:·List
143 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*143 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
144 ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8s_\x8h_\x8e_\x8a_\x8v_\x8e_\x8s·--·information·about·coherent·sheaves·and·total144 ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8s_\x8h_\x8e_\x8a_\x8v_\x8e_\x8s·--·information·about·coherent·sheaves·and·total
145 ······coordinate·rings·(a.k.a.·Cox·rings)145 ······coordinate·rings·(a.k.a.·Cox·rings)
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Offset 93, 22 lines modifiedOffset 93, 22 lines modified
93 ········<div>93 ········<div>
94 ··········<p>The·second·examples·show·that·a·randomly·selected·Kleinschmidt·toric·variety·and·a·weighted·projective·space·are·also·well-defined.</p>94 ··········<p>The·second·examples·show·that·a·randomly·selected·Kleinschmidt·toric·variety·and·a·weighted·projective·space·are·also·well-defined.</p>
95 ········</div>95 ········</div>
96 ········<table·class="examples">96 ········<table·class="examples">
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i2·:·setRandomSeed·(currentTime·());99 ··············<pre><code·class="language-macaulay2">i2·:·setRandomSeed·(currentTime·());
100 ·--·setting·random·seed·to·1749207923</code></pre>100 ·--·setting·random·seed·to·1783630474</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i3·:·a·=·sort·apply·(3,·i·->·random·(7))105 ··············<pre><code·class="language-macaulay2">i3·:·a·=·sort·apply·(3,·i·->·random·(7))
  
106 o3·=·{3,·4,·4}106 o3·=·{3,·4,·6}
  
107 o3·:·List</code></pre>107 o3·:·List</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i4·:·assert·isWellDefined·kleinschmidt·(4,a)</code></pre>112 ··············<pre><code·class="language-macaulay2">i4·:·assert·isWellDefined·kleinschmidt·(4,a)</code></pre>
Offset 126, 15 lines modifiedOffset 126, 15 lines modified
126 ··············<pre><code·class="language-macaulay2">i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9));</code></pre>126 ··············<pre><code·class="language-macaulay2">i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9));</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i7·:·q131 ··············<pre><code·class="language-macaulay2">i7·:·q
  
132 o7·=·{2,·4,·7,·7,·8}132 o7·=·{4,·4,·5,·5,·6}
  
133 o7·:·List</code></pre>133 o7·:·List</code></pre>
134 ············</td>134 ············</td>
135 ··········</tr>135 ··········</tr>
136 ··········<tr>136 ··········<tr>
137 ············<td>137 ············<td>
138 ··············<pre><code·class="language-macaulay2">i8·:·assert·isWellDefined·weightedProjectiveSpace·q</code></pre>138 ··············<pre><code·class="language-macaulay2">i8·:·assert·isWellDefined·weightedProjectiveSpace·q</code></pre>
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Offset 28, 27 lines modifiedOffset 28, 27 lines modified
28 ····*·the·intersection·of·the·cones·associated·to·two·elements·of·coneList·is·a28 ····*·the·intersection·of·the·cones·associated·to·two·elements·of·coneList·is·a
29 ······face·of·each·cone.29 ······face·of·each·cone.
30 The·first·examples·illustrate·that·small·projective·spaces·are·well-defined.30 The·first·examples·illustrate·that·small·projective·spaces·are·well-defined.
31 i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1))31 i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1))
32 The·second·examples·show·that·a·randomly·selected·Kleinschmidt·toric·variety32 The·second·examples·show·that·a·randomly·selected·Kleinschmidt·toric·variety
33 and·a·weighted·projective·space·are·also·well-defined.33 and·a·weighted·projective·space·are·also·well-defined.
34 i2·:·setRandomSeed·(currentTime·());34 i2·:·setRandomSeed·(currentTime·());
35 ·--·setting·random·seed·to·174920792335 ·--·setting·random·seed·to·1783630474
36 i3·:·a·=·sort·apply·(3,·i·->·random·(7))36 i3·:·a·=·sort·apply·(3,·i·->·random·(7))
  
37 o3·=·{3,·4,·4}37 o3·=·{3,·4,·6}
  
38 o3·:·List38 o3·:·List
39 i4·:·assert·isWellDefined·kleinschmidt·(4,a)39 i4·:·assert·isWellDefined·kleinschmidt·(4,a)
40 i5·:·q·=·sort·apply·(5,·j·->·random·(1,9));40 i5·:·q·=·sort·apply·(5,·j·->·random·(1,9));
41 i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j41 i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j
42 ->·random·(1,9));42 ->·random·(1,9));
43 i7·:·q43 i7·:·q
  
44 o7·=·{2,·4,·7,·7,·8}44 o7·=·{4,·4,·5,·5,·6}
  
45 o7·:·List45 o7·:·List
46 i8·:·assert·isWellDefined·weightedProjectiveSpace·q46 i8·:·assert·isWellDefined·weightedProjectiveSpace·q
47 The·next·ten·examples·illustrate·various·ways·that·two·lists·can·fail·to·define47 The·next·ten·examples·illustrate·various·ways·that·two·lists·can·fail·to·define
48 a·normal·toric·variety.·By·making·the·current·debugging·level·greater·than·one,48 a·normal·toric·variety.·By·making·the·current·debugging·level·greater·than·one,
49 one·gets·some·addition·information·about·the·nature·of·the·failure.49 one·gets·some·addition·information·about·the·nature·of·the·failure.
50 i9·:·X·=·new·MutableHashTable;50 i9·:·X·=·new·MutableHashTable;
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Offset 96, 15 lines modifiedOffset 96, 15 lines modified
  
96 o2·:·ToricDivisor·on·PP2</code></pre>96 o2·:·ToricDivisor·on·PP2</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i3·:·M1·=·elapsedTime·monomials·D1101 ··············<pre><code·class="language-macaulay2">i3·:·M1·=·elapsedTime·monomials·D1
102 ·--·.225018s·elapsed102 ·--·.536582s·elapsed
  
103 ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4···103 ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4···
104 o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·,104 o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·,
105 ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2·105 ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2·
106 ·····------------------------------------------------------------------------106 ·····------------------------------------------------------------------------
107 ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5107 ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5
108 ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·}108 ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·}
Offset 112, 15 lines modifiedOffset 112, 15 lines modified
  
112 o3·:·List</code></pre>112 o3·:·List</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1))117 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1))
118 ·--·.0011225s·elapsed</code></pre>118 ·--·.00126481s·elapsed</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ········</table>121 ········</table>
122 ········<div>122 ········<div>
123 ··········<p>Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.</p>123 ··········<p>Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.</p>
124 ········</div>124 ········</div>
125 ········<table·class="examples">125 ········<table·class="examples">
Offset 138, 27 lines modifiedOffset 138, 27 lines modified
  
138 o6·:·ToricDivisor·on·FF2</code></pre>138 o6·:·ToricDivisor·on·FF2</code></pre>
139 ············</td>139 ············</td>
140 ··········</tr>140 ··········</tr>
141 ··········<tr>141 ··········<tr>
142 ············<td>142 ············<td>
143 ··············<pre><code·class="language-macaulay2">i7·:·M2·=·elapsedTime·monomials·D2143 ··············<pre><code·class="language-macaulay2">i7·:·M2·=·elapsedTime·monomials·D2
144 ·--·.337739s·elapsed144 ·--·.57286s·elapsed
  
145 ·······2·····3·2·····3·····2·3145 ·······2·····3·2·····3·····2·3
146 o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·}146 o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·}
147 ·······1·3···1·2···0·1·2···0·1147 ·······1·3···1·2···0·1·2···0·1
  
148 o7·:·List</code></pre>148 o7·:·List</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
152 ············<td>152 ············<td>
153 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2))153 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2))
154 ·--·.00107011s·elapsed</code></pre>154 ·--·.00172497s·elapsed</code></pre>
155 ············</td>155 ············</td>
156 ··········</tr>156 ··········</tr>
157 ··········<tr>157 ··········<tr>
158 ············<td>158 ············<td>
159 ··············<pre><code·class="language-macaulay2">i9·:·X·=·kleinschmidt·(5,·{1,2,3});</code></pre>159 ··············<pre><code·class="language-macaulay2">i9·:·X·=·kleinschmidt·(5,·{1,2,3});</code></pre>
160 ············</td>160 ············</td>
161 ··········</tr>161 ··········</tr>
Offset 171, 23 lines modifiedOffset 171, 23 lines modified
  
171 o10·:·ToricDivisor·on·X</code></pre>171 o10·:·ToricDivisor·on·X</code></pre>
172 ············</td>172 ············</td>
173 ··········</tr>173 ··········</tr>
174 ··········<tr>174 ··········<tr>
175 ············<td>175 ············<td>
176 ··············<pre><code·class="language-macaulay2">i11·:·m3·=·elapsedTime·#·monomials·D3176 ··············<pre><code·class="language-macaulay2">i11·:·m3·=·elapsedTime·#·monomials·D3
177 ·--·34.0465s·elapsed177 ·--·74.766s·elapsed
  
178 o11·=·7909</code></pre>178 o11·=·7909</code></pre>
179 ············</td>179 ············</td>
180 ··········</tr>180 ··········</tr>
181 ··········<tr>181 ··········<tr>
182 ············<td>182 ············<td>
183 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3))183 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3))
184 ·--·.0223298s·elapsed</code></pre>184 ·--·.0965507s·elapsed</code></pre>
185 ············</td>185 ············</td>
186 ··········</tr>186 ··········</tr>
187 ········</table>187 ········</table>
188 ········<div>188 ········<div>
189 ··········<p>By·exploiting·<a·title="computes·the·lattice·points·of·a·polytope"·href="../../Polyhedra/html/_lattice__Points.html">latticePoints</a>,·this·method·function·avoids·using·the·<a·title="basis·or·generating·set·of·all·or·part·of·a·ring,·ideal·or·module"·href="../../Macaulay2Doc/html/_basis.html">basis</a>·function.</p>189 ··········<p>By·exploiting·<a·title="computes·the·lattice·points·of·a·polytope"·href="../../Polyhedra/html/_lattice__Points.html">latticePoints</a>,·this·method·function·avoids·using·the·<a·title="basis·or·generating·set·of·all·or·part·of·a·ring,·ideal·or·module"·href="../../Macaulay2Doc/html/_basis.html">basis</a>·function.</p>
190 ········</div>190 ········</div>
191 ······</div>191 ······</div>
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Offset 27, 61 lines modifiedOffset 27, 61 lines modified
27 i2·:·D1·=·5*PP2_027 i2·:·D1·=·5*PP2_0
  
28 o2·=·5*PP228 o2·=·5*PP2
29 ··········029 ··········0
  
30 o2·:·ToricDivisor·on·PP230 o2·:·ToricDivisor·on·PP2
31 i3·:·M1·=·elapsedTime·monomials·D131 i3·:·M1·=·elapsedTime·monomials·D1
32 ·--·.225018s·elapsed32 ·--·.536582s·elapsed
  
33 ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···433 ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4
34 o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·,34 o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·,
35 ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·235 ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2
36 ·····------------------------------------------------------------------------36 ·····------------------------------------------------------------------------
37 ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····537 ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5
38 ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·}38 ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·}
39 ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···039 ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0
  
40 o3·:·List40 o3·:·List
41 i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring41 i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring
42 variety·D1))42 variety·D1))
43 ·--·.0011225s·elapsed43 ·--·.00126481s·elapsed
44 Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.44 Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.
45 i5·:·FF2·=·hirzebruchSurface·2;45 i5·:·FF2·=·hirzebruchSurface·2;
46 i6·:·D2·=·2*FF2_0·+·3·*·FF2_146 i6·:·D2·=·2*FF2_0·+·3·*·FF2_1
  
47 o6·=·2*FF2··+·3*FF247 o6·=·2*FF2··+·3*FF2
48 ··········0········148 ··········0········1
  
49 o6·:·ToricDivisor·on·FF249 o6·:·ToricDivisor·on·FF2
50 i7·:·M2·=·elapsedTime·monomials·D250 i7·:·M2·=·elapsedTime·monomials·D2
51 ·--·.337739s·elapsed51 ·--·.57286s·elapsed
  
52 ·······2·····3·2·····3·····2·352 ·······2·····3·2·····3·····2·3
53 o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·}53 o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·}
54 ·······1·3···1·2···0·1·2···0·154 ·······1·3···1·2···0·1·2···0·1
  
55 o7·:·List55 o7·:·List
56 i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring56 i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring
57 variety·D2))57 variety·D2))
58 ·--·.00107011s·elapsed58 ·--·.00172497s·elapsed
59 i9·:·X·=·kleinschmidt·(5,·{1,2,3});59 i9·:·X·=·kleinschmidt·(5,·{1,2,3});
60 i10·:·D3·=·3*X_0·+·5*X_160 i10·:·D3·=·3*X_0·+·5*X_1
  
61 o10·=·3*X··+·5*X61 o10·=·3*X··+·5*X
62 ·········0······162 ·········0······1
  
63 o10·:·ToricDivisor·on·X63 o10·:·ToricDivisor·on·X
64 i11·:·m3·=·elapsedTime·#·monomials·D364 i11·:·m3·=·elapsedTime·#·monomials·D3
65 ·--·34.0465s·elapsed65 ·--·74.766s·elapsed
  
66 o11·=·790966 o11·=·7909
67 i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety67 i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety
68 D3))68 D3))
69 ·--·.0223298s·elapsed69 ·--·.0965507s·elapsed
70 By·exploiting·_\x8l_\x8a_\x8t_\x8t_\x8i_\x8c_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s,·this·method·function·avoids·using·the·_\x8b_\x8a_\x8s_\x8i_\x8s70 By·exploiting·_\x8l_\x8a_\x8t_\x8t_\x8i_\x8c_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s,·this·method·function·avoids·using·the·_\x8b_\x8a_\x8s_\x8i_\x8s
71 function.71 function.
72 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*72 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
73 ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8d_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8s·--·information·about·toric·divisors·and·their73 ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8d_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8s·--·information·about·toric·divisors·and·their
74 ······related·groups74 ······related·groups
75 ····*·_\x8r_\x8i_\x8n_\x8g_\x8(_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·make·the·total·coordinate·ring·(a.k.a.·Cox75 ····*·_\x8r_\x8i_\x8n_\x8g_\x8(_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·make·the·total·coordinate·ring·(a.k.a.·Cox
76 ······ring)76 ······ring)
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125 ········<div>125 ········<div>
126 ··········<p>The·recommended·method·for·creating·a·<a·title="the·class·of·all·normal·toric·varieties"·href="___Normal__Toric__Variety.html">NormalToricVariety</a>·from·a·fan·is·<a·title="make·a·normal·toric·variety"·href="_normal__Toric__Variety_lp__List_cm__List_rp.html">normalToricVariety(List,List)</a>.··In·fact,·this·package·avoids·using·objects·from·the·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·package·whenever·possible.···Here·is·a·trivial·example,·namely·projective·2-space,·illustrating·the·substantial·increase·in·time·resulting·from·the·use·of·a·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·fan.</p>126 ··········<p>The·recommended·method·for·creating·a·<a·title="the·class·of·all·normal·toric·varieties"·href="___Normal__Toric__Variety.html">NormalToricVariety</a>·from·a·fan·is·<a·title="make·a·normal·toric·variety"·href="_normal__Toric__Variety_lp__List_cm__List_rp.html">normalToricVariety(List,List)</a>.··In·fact,·this·package·avoids·using·objects·from·the·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·package·whenever·possible.···Here·is·a·trivial·example,·namely·projective·2-space,·illustrating·the·substantial·increase·in·time·resulting·from·the·use·of·a·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·fan.</p>
127 ········</div>127 ········</div>
128 ········<table·class="examples">128 ········<table·class="examples">
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}})131 ··············<pre><code·class="language-macaulay2">i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}})
132 ·--·used·0.00166827s·(cpu);·1.8158e-05s·(thread);·0s·(gc)132 ·--·used·4.7639e-05s·(cpu);·3.0838e-05s·(thread);·0s·(gc)
  
133 o6·=·X1133 o6·=·X1
  
134 o6·:·NormalToricVariety</code></pre>134 o6·:·NormalToricVariety</code></pre>
135 ············</td>135 ············</td>
136 ··········</tr>136 ··········</tr>
137 ··········<tr>137 ··········<tr>
138 ············<td>138 ············<td>
139 ··············<pre><code·class="language-macaulay2">i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}};139 ··············<pre><code·class="language-macaulay2">i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}};
140 ·--·used·0.113356s·(cpu);·0.0652s·(thread);·0s·(gc)</code></pre>140 ·--·used·0.115753s·(cpu);·0.0622265s·(thread);·0s·(gc)</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
143 ··········<tr>143 ··········<tr>
144 ············<td>144 ············<td>
145 ··············<pre><code·class="language-macaulay2">i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)</code></pre>145 ··············<pre><code·class="language-macaulay2">i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)</code></pre>
146 ············</td>146 ············</td>
147 ··········</tr>147 ··········</tr>
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48 i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F)48 i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F)
49 The·recommended·method·for·creating·a·_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·from·a·fan·is49 The·recommended·method·for·creating·a·_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·from·a·fan·is
50 _\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8L_\x8i_\x8s_\x8t_\x8,_\x8L_\x8i_\x8s_\x8t_\x8).·In·fact,·this·package·avoids·using·objects·from50 _\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8L_\x8i_\x8s_\x8t_\x8,_\x8L_\x8i_\x8s_\x8t_\x8).·In·fact,·this·package·avoids·using·objects·from
51 the·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·package·whenever·possible.·Here·is·a·trivial·example,·namely51 the·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·package·whenever·possible.·Here·is·a·trivial·example,·namely
52 projective·2-space,·illustrating·the·substantial·increase·in·time·resulting52 projective·2-space,·illustrating·the·substantial·increase·in·time·resulting
53 from·the·use·of·a·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·fan.53 from·the·use·of·a·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·fan.
54 i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}})54 i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}})
55 ·--·used·0.00166827s·(cpu);·1.8158e-05s·(thread);·0s·(gc)55 ·--·used·4.7639e-05s·(cpu);·3.0838e-05s·(thread);·0s·(gc)
  
56 o6·=·X156 o6·=·X1
  
57 o6·:·NormalToricVariety57 o6·:·NormalToricVariety
58 i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull58 i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull
59 matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}};59 matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}};
60 ·--·used·0.113356s·(cpu);·0.0652s·(thread);·0s·(gc)60 ·--·used·0.115753s·(cpu);·0.0622265s·(thread);·0s·(gc)
61 i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)61 i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)
62 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*62 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
63 ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors63 ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors
64 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·make·a·normal·toric·variety64 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·make·a·normal·toric·variety
65 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*65 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
66 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8F_\x8a_\x8n_\x8)·--·make·a·normal·toric·variety·from·a·'Polyhedra'66 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8F_\x8a_\x8n_\x8)·--·make·a·normal·toric·variety·from·a·'Polyhedra'
67 ······fan67 ······fan
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233 ···············2·······3233 ···············2·······3
234 o18·:·Matrix·ZZ··&lt;--·ZZ</code></pre>234 o18·:·Matrix·ZZ··&lt;--·ZZ</code></pre>
235 ············</td>235 ············</td>
236 ··········</tr>236 ··········</tr>
237 ··········<tr>237 ··········<tr>
238 ············<td>238 ············<td>
239 ··············<pre><code·class="language-macaulay2">i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix);239 ··············<pre><code·class="language-macaulay2">i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix);
240 ·--·used·0.0191267s·(cpu);·0.0200144s·(thread);·0s·(gc)</code></pre>240 ·--·used·0.0239109s·(cpu);·0.0228231s·(thread);·0s·(gc)</code></pre>
241 ············</td>241 ············</td>
242 ··········</tr>242 ··········</tr>
243 ··········<tr>243 ··········<tr>
244 ············<td>244 ············<td>
245 ··············<pre><code·class="language-macaulay2">i20·:·X2·=·time·normalToricVariety·vertMatrix;245 ··············<pre><code·class="language-macaulay2">i20·:·X2·=·time·normalToricVariety·vertMatrix;
246 ·--·used·0.00178574s·(cpu);·0.00205128s·(thread);·0s·(gc)</code></pre>246 ·--·used·0.00212713s·(cpu);·0.00232491s·(thread);·0s·(gc)</code></pre>
247 ············</td>247 ············</td>
248 ··········</tr>248 ··········</tr>
249 ··········<tr>249 ··········<tr>
250 ············<td>250 ············<td>
251 ··············<pre><code·class="language-macaulay2">i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)</code></pre>251 ··············<pre><code·class="language-macaulay2">i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)</code></pre>
252 ············</td>252 ············</td>
253 ··········</tr>253 ··········</tr>
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102 o18·=·|·0·1·0·|102 o18·=·|·0·1·0·|
103 ······|·0·0·1·|103 ······|·0·0·1·|
  
104 ···············2·······3104 ···············2·······3
105 o18·:·Matrix·ZZ··<--·ZZ105 o18·:·Matrix·ZZ··<--·ZZ
106 i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix);106 i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix);
107 ·--·used·0.0191267s·(cpu);·0.0200144s·(thread);·0s·(gc)107 ·--·used·0.0239109s·(cpu);·0.0228231s·(thread);·0s·(gc)
108 i20·:·X2·=·time·normalToricVariety·vertMatrix;108 i20·:·X2·=·time·normalToricVariety·vertMatrix;
109 ·--·used·0.00178574s·(cpu);·0.00205128s·(thread);·0s·(gc)109 ·--·used·0.00212713s·(cpu);·0.00232491s·(thread);·0s·(gc)
110 i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)110 i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)
111 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*111 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
112 ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors112 ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors
113 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·make·a·normal·toric·variety·from·a·polytope113 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·make·a·normal·toric·variety·from·a·polytope
114 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*114 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
115 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8o_\x8n_\x8)·--·make·a·normal·toric·variety·from·a115 ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8o_\x8n_\x8)·--·make·a·normal·toric·variety·from·a
116 ······'Polyhedra'·polyhedron116 ······'Polyhedra'·polyhedron
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25 o4·=·true25 o4·=·true
  
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37 o5·:·NumericalInterpolationTable37 o5·:·NumericalInterpolationTable
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1.53 KB
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27 o3·:·NumericalInterpolationTable27 o3·:·NumericalInterpolationTable
  
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31 i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true)31 i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true)
32 Creating·interpolation·matrix·...32 Creating·interpolation·matrix·...
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34 Performing·normalization·preconditioning·...34 Performing·normalization·preconditioning·...
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38 o7·=·a·"numerical·interpolation·table",·indicating38 o7·=·a·"numerical·interpolation·table",·indicating
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40 o7·:·NumericalInterpolationTable40 o7·:·NumericalInterpolationTable
  
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31 o5·:·Ideal·of·R31 o5·:·Ideal·of·R
  
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114 Computing·numerical·kernel·...114 Computing·numerical·kernel·...
115 ·····--·used·0·seconds115 ·····--·used·0·seconds
  
116 o5·=·a·&quot;numerical·interpolation·table&quot;,·indicating116 o5·=·a·&quot;numerical·interpolation·table&quot;,·indicating
117 ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3117 ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3
  
118 o5·:·NumericalInterpolationTable</code></pre>118 o5·:·NumericalInterpolationTable</code></pre>
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35 ==·035 ==·0
36 --·warning:·experimental·computation·over·inexact·field·begun36 --·warning:·experimental·computation·over·inexact·field·begun
37 --··········results·not·reliable·(one·warning·given·per·session)37 --··········results·not·reliable·(one·warning·given·per·session)
  
38 o4·=·true38 o4·=·true
39 i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true)39 i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true)
40 Sampling·image·points·...40 Sampling·image·points·...
41 ·····--·used·.0595964·seconds41 ·····--·used·.0644741·seconds
42 Creating·interpolation·matrix·...42 Creating·interpolation·matrix·...
43 ·····--·used·.00297505·seconds43 ·····--·used·.00803833·seconds
44 Performing·normalization·preconditioning·...44 Performing·normalization·preconditioning·...
45 ·····--·used·.00398358·seconds45 ·····--·used·.00219362·seconds
46 Computing·numerical·kernel·...46 Computing·numerical·kernel·...
47 ·····--·used·0·seconds47 ·····--·used·0·seconds
  
48 o5·=·a·"numerical·interpolation·table",·indicating48 o5·=·a·"numerical·interpolation·table",·indicating
49 ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·349 ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3
  
50 o5·:·NumericalInterpolationTable50 o5·:·NumericalInterpolationTable
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104 o2·:·Matrix·R··&lt;--·R</code></pre>104 o2·:·Matrix·R··&lt;--·R</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true)109 ··············<pre><code·class="language-macaulay2">i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true)
110 Sampling·image·points·...110 Sampling·image·points·...
111 ·····--·used·0·seconds111 ·····--·used·.0033548·seconds
112 Creating·interpolation·matrix·...112 Creating·interpolation·matrix·...
113 ·····--·used·0·seconds113 ·····--·used·.00397767·seconds
114 Performing·normalization·preconditioning·...114 Performing·normalization·preconditioning·...
115 ·····--·used·0·seconds115 ·····--·used·0·seconds
116 Computing·numerical·kernel·...116 Computing·numerical·kernel·...
117 ·····--·used·.00400115·seconds117 ·····--·used·0·seconds
  
118 o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·|118 o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·|
  
119 ··························1···················3119 ··························1···················3
120 o3·:·Matrix·(CC··[y·..y·])··&lt;--·(CC··[y·..y·])120 o3·:·Matrix·(CC··[y·..y·])··&lt;--·(CC··[y·..y·])
121 ···············53··0···3···········53··0···3</code></pre>121 ···············53··0···3···········53··0···3</code></pre>
122 ············</td>122 ············</td>
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40 o2·=·|·s3·s2t·st2·t3·|40 o2·=·|·s3·s2t·st2·t3·|
  
41 ·············1······441 ·············1······4
42 o2·:·Matrix·R··<--·R42 o2·:·Matrix·R··<--·R
43 i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true)43 i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true)
44 Sampling·image·points·...44 Sampling·image·points·...
45 ·····--·used·0·seconds45 ·····--·used·.0033548·seconds
46 Creating·interpolation·matrix·...46 Creating·interpolation·matrix·...
47 ·····--·used·0·seconds47 ·····--·used·.00397767·seconds
48 Performing·normalization·preconditioning·...48 Performing·normalization·preconditioning·...
49 ·····--·used·0·seconds49 ·····--·used·0·seconds
50 Computing·numerical·kernel·...50 Computing·numerical·kernel·...
51 ·····--·used·.00400115·seconds51 ·····--·used·0·seconds
  
52 o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·|52 o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·|
  
53 ··························1···················353 ··························1···················3
54 o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·])54 o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·])
55 ···············53··0···3···········53··0···355 ···············53··0···3···········53··0···3
56 Here·is·how·to·do·the·same·computation·symbolically.56 Here·is·how·to·do·the·same·computation·symbolically.
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109 o2·:·Matrix·R··&lt;--·R</code></pre>109 o2·:·Matrix·R··&lt;--·R</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i3·:·numericalHilbertFunction(F,·ideal·0_R,·4)114 ··············<pre><code·class="language-macaulay2">i3·:·numericalHilbertFunction(F,·ideal·0_R,·4)
115 Sampling·image·points·...115 Sampling·image·points·...
116 ·····--·used·.00949317·seconds116 ·····--·used·.0133699·seconds
117 Creating·interpolation·matrix·...117 Creating·interpolation·matrix·...
118 ·····--·used·.00835372·seconds118 ·····--·used·.0107967·seconds
119 Performing·normalization·preconditioning·...119 Performing·normalization·preconditioning·...
120 ·····--·used·.00338085·seconds120 ·····--·used·.00774066·seconds
121 Computing·numerical·kernel·...121 Computing·numerical·kernel·...
122 ·····--·used·.00396718·seconds122 ·····--·used·0·seconds
  
123 o3·=·a·&quot;numerical·interpolation·table&quot;,·indicating123 o3·=·a·&quot;numerical·interpolation·table&quot;,·indicating
124 ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22124 ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22
  
125 o3·:·NumericalInterpolationTable</code></pre>125 o3·:·NumericalInterpolationTable</code></pre>
126 ············</td>126 ············</td>
127 ··········</tr>127 ··········</tr>
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149 ··············<pre><code·class="language-macaulay2">i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);</code></pre>149 ··············<pre><code·class="language-macaulay2">i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);</code></pre>
150 ············</td>150 ············</td>
151 ··········</tr>151 ··········</tr>
152 ··········<tr>152 ··········<tr>
153 ············<td>153 ············<td>
154 ··············<pre><code·class="language-macaulay2">i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true)154 ··············<pre><code·class="language-macaulay2">i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true)
155 Creating·interpolation·matrix·...155 Creating·interpolation·matrix·...
156 ·····--·used·.0571857·seconds156 ·····--·used·.0524567·seconds
157 Performing·normalization·preconditioning·...157 Performing·normalization·preconditioning·...
158 ·····--·used·.00800386·seconds158 ·····--·used·.00397913·seconds
159 Computing·numerical·kernel·...159 Computing·numerical·kernel·...
160 ·····--·used·0·seconds160 ·····--·used·.00407357·seconds
  
161 o7·=·a·&quot;numerical·interpolation·table&quot;,·indicating161 o7·=·a·&quot;numerical·interpolation·table&quot;,·indicating
162 ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1162 ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1
  
163 o7·:·NumericalInterpolationTable</code></pre>163 o7·:·NumericalInterpolationTable</code></pre>
164 ············</td>164 ············</td>
165 ··········</tr>165 ··········</tr>
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59 o2·=·|·s3·s2t·st2·t3·|59 o2·=·|·s3·s2t·st2·t3·|
  
60 ·············1······460 ·············1······4
61 o2·:·Matrix·R··<--·R61 o2·:·Matrix·R··<--·R
62 i3·:·numericalHilbertFunction(F,·ideal·0_R,·4)62 i3·:·numericalHilbertFunction(F,·ideal·0_R,·4)
63 Sampling·image·points·...63 Sampling·image·points·...
64 ·····--·used·.00949317·seconds64 ·····--·used·.0133699·seconds
65 Creating·interpolation·matrix·...65 Creating·interpolation·matrix·...
66 ·····--·used·.00835372·seconds66 ·····--·used·.0107967·seconds
67 Performing·normalization·preconditioning·...67 Performing·normalization·preconditioning·...
68 ·····--·used·.00338085·seconds68 ·····--·used·.00774066·seconds
69 Computing·numerical·kernel·...69 Computing·numerical·kernel·...
70 ·····--·used·.00396718·seconds70 ·····--·used·0·seconds
  
71 o3·=·a·"numerical·interpolation·table",·indicating71 o3·=·a·"numerical·interpolation·table",·indicating
72 ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·2272 ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22
  
73 o3·:·NumericalInterpolationTable73 o3·:·NumericalInterpolationTable
74 The·following·example·computes·the·dimension·of·Pl&uuml;cker·quadrics·in·the74 The·following·example·computes·the·dimension·of·Pl&uuml;cker·quadrics·in·the
75 defining·ideal·of·the·Grassmannian·$Gr(2,4)$·of·$P^1$'s·in·$P^3$,·in·the75 defining·ideal·of·the·Grassmannian·$Gr(2,4)$·of·$P^1$'s·in·$P^3$,·in·the
76 ambient·space·$P^5$.76 ambient·space·$P^5$.
77 i4·:·R·=·CC[x_(1,1)..x_(2,4)];77 i4·:·R·=·CC[x_(1,1)..x_(2,4)];
78 i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*;78 i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*;
79 i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);79 i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);
80 i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true)80 i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true)
81 Creating·interpolation·matrix·...81 Creating·interpolation·matrix·...
82 ·····--·used·.0571857·seconds82 ·····--·used·.0524567·seconds
83 Performing·normalization·preconditioning·...83 Performing·normalization·preconditioning·...
84 ·····--·used·.00800386·seconds84 ·····--·used·.00397913·seconds
85 Computing·numerical·kernel·...85 Computing·numerical·kernel·...
86 ·····--·used·0·seconds86 ·····--·used·.00407357·seconds
  
87 o7·=·a·"numerical·interpolation·table",·indicating87 o7·=·a·"numerical·interpolation·table",·indicating
88 ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·188 ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1
  
89 o7·:·NumericalInterpolationTable89 o7·:·NumericalInterpolationTable
90 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*90 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
91 ····*·_\x8N_\x8u_\x8m_\x8e_\x8r_\x8i_\x8c_\x8a_\x8l_\x8I_\x8n_\x8t_\x8e_\x8r_\x8p_\x8o_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8T_\x8a_\x8b_\x8l_\x8e·--·the·class·of·all91 ····*·_\x8N_\x8u_\x8m_\x8e_\x8r_\x8i_\x8c_\x8a_\x8l_\x8I_\x8n_\x8t_\x8e_\x8r_\x8p_\x8o_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8T_\x8a_\x8b_\x8l_\x8e·--·the·class·of·all
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142 ·············1······70142 ·············1······70
143 o8·:·Matrix·R··&lt;--·R</code></pre>143 o8·:·Matrix·R··&lt;--·R</code></pre>
144 ············</td>144 ············</td>
145 ··········</tr>145 ··········</tr>
146 ··········<tr>146 ··········<tr>
147 ············<td>147 ············<td>
148 ··············<pre><code·class="language-macaulay2">i9·:·time·numericalImageDim(F,·ideal·0_R)148 ··············<pre><code·class="language-macaulay2">i9·:·time·numericalImageDim(F,·ideal·0_R)
149 ·--·used·0.0538093s·(cpu);·0.0547888s·(thread);·0s·(gc)149 ·--·used·0.0554439s·(cpu);·0.0555157s·(thread);·0s·(gc)
  
150 o9·=·69</code></pre>150 o9·=·69</code></pre>
151 ············</td>151 ············</td>
152 ··········</tr>152 ··········</tr>
153 ········</table>153 ········</table>
154 ······</div>154 ······</div>
155 ······<div>155 ······<div>
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45 i8·:·F·=·sum(1..14,·i·->·basis(4,·R,·Variables=>toList(a_(i,1)..a_(i,5))));45 i8·:·F·=·sum(1..14,·i·->·basis(4,·R,·Variables=>toList(a_(i,1)..a_(i,5))));
46 --·warning:·experimental·computation·over·inexact·field·begun46 --·warning:·experimental·computation·over·inexact·field·begun
47 --··········results·not·reliable·(one·warning·given·per·session)47 --··········results·not·reliable·(one·warning·given·per·session)
  
48 ·············1······7048 ·············1······70
49 o8·:·Matrix·R··<--·R49 o8·:·Matrix·R··<--·R
50 i9·:·time·numericalImageDim(F,·ideal·0_R)50 i9·:·time·numericalImageDim(F,·ideal·0_R)
51 ·--·used·0.0538093s·(cpu);·0.0547888s·(thread);·0s·(gc)51 ·--·used·0.0554439s·(cpu);·0.0555157s·(thread);·0s·(gc)
  
52 o9·=·6952 o9·=·69
53 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·n\x8nu\x8um\x8me\x8er\x8ri\x8ic\x8ca\x8al\x8lI\x8Im\x8ma\x8ag\x8ge\x8eD\x8Di\x8im\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8*53 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·n\x8nu\x8um\x8me\x8er\x8ri\x8ic\x8ca\x8al\x8lI\x8Im\x8ma\x8ag\x8ge\x8eD\x8Di\x8im\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8*
54 ····*·numericalImageDim(List,Ideal)54 ····*·numericalImageDim(List,Ideal)
55 ····*·numericalImageDim(List,Ideal,Point)55 ····*·numericalImageDim(List,Ideal,Point)
56 ····*·numericalImageDim(Matrix,Ideal)56 ····*·numericalImageDim(Matrix,Ideal)
57 ····*·numericalImageDim(Matrix,Ideal,Point)57 ····*·numericalImageDim(Matrix,Ideal,Point)
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132 o6·:·Ideal·of·R</code></pre>132 o6·:·Ideal·of·R</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100)137 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100)
138 ·--·.503857s·elapsed138 ·--·1.24839s·elapsed
  
139 o7·=·p139 o7·=·p
  
140 o7·:·Point</code></pre>140 o7·:·Point</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
143 ··········<tr>143 ··········<tr>
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49 i5·:·I2·=·ideal·apply(entries·transpose·A,·row·->·sum(row,·v·->·v^2)·-·1);49 i5·:·I2·=·ideal·apply(entries·transpose·A,·row·->·sum(row,·v·->·v^2)·-·1);
  
50 o5·:·Ideal·of·R50 o5·:·Ideal·of·R
51 i6·:·I·=·I1·+·I2;51 i6·:·I·=·I1·+·I2;
  
52 o6·:·Ideal·of·R52 o6·:·Ideal·of·R
53 i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100)53 i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100)
54 ·--·.503857s·elapsed54 ·--·1.24839s·elapsed
  
55 o7·=·p55 o7·=·p
  
56 o7·:·Point56 o7·:·Point
57 i8·:·matrix·pack(5,·p#Coordinates)57 i8·:·matrix·pack(5,·p#Coordinates)
  
58 o8·=·|·.722359··.289465··-.295808··.591752··-.454678·|58 o8·=·|·.722359··.289465··-.295808··.591752··-.454678·|
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775 B
./usr/share/doc/Macaulay2/NumericalSemigroups/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
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1.77 KB
./usr/share/doc/Macaulay2/NumericalSemigroups/example-output/___Lab__Book__Protocol.out
    
Offset 14, 35 lines modifiedOffset 14, 35 lines modified
  
14 i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a14 i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a
  
15 o5·=·215 o5·=·2
  
16 i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true))16 i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true))
17 unfolding17 unfolding
18 ·--·.135763s·elapsed18 ·--·.366067s·elapsed
19 flatteningRelations19 flatteningRelations
20 ·--·.128706s·elapsed20 ·--·.157959s·elapsed
21 next·gb21 next·gb
22 ·--·.000563632s·elapsed22 ·--·.000742792s·elapsed
23 true23 true
24 unfolding24 unfolding
25 ·--·.100671s·elapsed25 ·--·.266595s·elapsed
26 flatteningRelations26 flatteningRelations
27 ·--·.11401s·elapsed27 ·--·.248024s·elapsed
28 next·gb28 next·gb
29 ·--·.000431301s·elapsed29 ·--·.000636323s·elapsed
30 true30 true
31 ·--·1.41187s·elapsed31 ·--·2.4495s·elapsed
  
32 o6·=·{}32 o6·=·{}
  
33 o6·:·List33 o6·:·List
  
34 i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0))34 i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0))
35 ·--·1.24269s·elapsed35 ·--·2.55405s·elapsed
  
36 o7·=·{}36 o7·=·{}
  
37 o7·:·List37 o7·:·List
  
38 i8·:·LL7b=={}38 i8·:·LL7b=={}
  
Offset 75, 22 lines modifiedOffset 75, 22 lines modified
  
75 o10·:·Sequence75 o10·:·Sequence
  
76 i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true)76 i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true)
77 (13,·1)77 (13,·1)
78 {5,·8,·11,·12}78 {5,·8,·11,·12}
79 unfolding79 unfolding
80 ·--·.19375s·elapsed80 ·--·.516032s·elapsed
81 flatteningRelations81 flatteningRelations
82 ·--·.110392s·elapsed82 ·--·.290405s·elapsed
83 next·gb83 next·gb
84 ·--·.000674258s·elapsed84 ·--·.00100319s·elapsed
85 true85 true
86 ·--·.607305s·elapsed86 ·--·1.50429s·elapsed
87 (5,·8,··all·semigroups·are·smoothable)·--·.652941s·elapsed87 (5,·8,··all·semigroups·are·smoothable)·--·1.58951s·elapsed
  
  
88 o11·=·{}88 o11·=·{}
  
89 o11·:·List89 o11·:·List
  
90 i12·:·L={6,8,9,11}90 i12·:·L={6,8,9,11}
Offset 100, 22 lines modifiedOffset 100, 22 lines modified
100 o12·:·List100 o12·:·List
  
101 i13·:·genus·L101 i13·:·genus·L
  
102 o13·=·8102 o13·=·8
  
103 i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true)103 i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true)
104 ·--·.0508446s·elapsed104 ·--·.201539s·elapsed
105 6105 6
106 false106 false
107 5107 5
108 false108 false
109 4109 4
110 decompose110 decompose
111 ·--·.240413s·elapsed111 ·--·.986497s·elapsed
112 number·of·components:·2112 number·of·components:·2
113 support·c,·codim·c:·{(1,·1),·(16,·3)}113 support·c,·codim·c:·{(1,·1),·(16,·3)}
114 {0,·-1}114 {0,·-1}
  
115 o14·=·true115 o14·=·true
  
116 i15·:·116 i15·:·
611 B
./usr/share/doc/Macaulay2/NumericalSemigroups/example-output/_heuristic__Smoothness.out
    
Offset 10, 15 lines modifiedOffset 10, 15 lines modified
10 ·--·setting·random·seed·to·164481453440449127431341128518604198809956756390578037482408606251655943810 ·--·setting·random·seed·to·1644814534404491274313411285186041988099567563905780374824086062516559438
  
11 i4·:·elapsedTime·tally·apply(10,i->·(11 i4·:·elapsedTime·tally·apply(10,i->·(
12 ·············c=minors(2,random(S^2,S^{3:-2}));12 ·············c=minors(2,random(S^2,S^{3:-2}));
13 ·············c=sub(c,x_0=>1);13 ·············c=sub(c,x_0=>1);
14 ·············R=kk[support·c];c=sub(c,R);14 ·············R=kk[support·c];c=sub(c,R);
15 ·············heuristicSmoothness·c))15 ·············heuristicSmoothness·c))
16 ·--·2.15519s·elapsed16 ·--·5.79753s·elapsed
  
17 o4·=·Tally{false·=>·6}17 o4·=·Tally{false·=>·6}
18 ···········true·=>·418 ···········true·=>·4
  
19 o4·:·Tally19 o4·:·Tally
  
20 i5·:·20 i5·:·
464 B
./usr/share/doc/Macaulay2/NumericalSemigroups/example-output/_is__Smoothable__Semigroup.out
    
Offset 7, 17 lines modifiedOffset 7, 17 lines modified
7 o1·:·List7 o1·:·List
  
8 i2·:·genus·L8 i2·:·genus·L
  
9 o2·=·89 o2·=·8
  
10 i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0)10 i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0)
11 ·--·1.8799s·elapsed11 ·--·1.95732s·elapsed
  
12 o3·=·false12 o3·=·false
  
13 i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0)13 i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0)
14 ·--·7.47251s·elapsed14 ·--·6.97864s·elapsed
  
15 o4·=·true15 o4·=·true
  
16 i5·:·16 i5·:·
356 B
./usr/share/doc/Macaulay2/NumericalSemigroups/example-output/_is__Weierstrass__Semigroup.out
    
Offset 7, 12 lines modifiedOffset 7, 12 lines modified
7 o1·:·List7 o1·:·List
  
8 i2·:·genus·L8 i2·:·genus·L
  
9 o2·=·89 o2·=·8
  
10 i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15)10 i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15)
11 ·--·6.16473s·elapsed11 ·--·7.12663s·elapsed
  
12 o3·=·true12 o3·=·true
  
13 i4·:·13 i4·:·
1.95 KB
./usr/share/doc/Macaulay2/NumericalSemigroups/example-output/_non__Weierstrass__Semigroups.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·68609965328516315561 --·-*-·M2-comint·-*-·hash:·6860996532851631556
  
2 i1·:·elapsedTime·nonWeierstrassSemigroups(6,7)2 i1·:·elapsedTime·nonWeierstrassSemigroups(6,7)
3 (6,·7,··all·semigroups·are·smoothable)·--·1.56007s·elapsed3 (6,·7,··all·semigroups·are·smoothable)·--·3.37527s·elapsed
  
  
4 o1·=·{}4 o1·=·{}
  
5 o1·:·List5 o1·:·List
  
6 i2·:·LLdifficult={{6,·8,·9,·11}}6 i2·:·LLdifficult={{6,·8,·9,·11}}
Offset 14, 61 lines modifiedOffset 14, 61 lines modified
  
14 o2·:·List14 o2·:·List
  
15 i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true)15 i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true)
16 (17,·5)16 (17,·5)
17 {6,·7,·8,·17}17 {6,·7,·8,·17}
18 unfolding18 unfolding
19 ·--·.383948s·elapsed19 ·--·1.22298s·elapsed
20 flatteningRelations20 flatteningRelations
21 ·--·.19233s·elapsed21 ·--·.415793s·elapsed
22 next·gb22 next·gb
23 ·--·.00127309s·elapsed23 ·--·.0016185s·elapsed
24 true24 true
25 ·--·.952286s·elapsed25 ·--·2.46891s·elapsed
26 {6,·7,·9,·17}26 {6,·7,·9,·17}
27 unfolding27 unfolding
28 ·--·.298426s·elapsed28 ·--·.822646s·elapsed
29 flatteningRelations29 flatteningRelations
30 ·--·.183205s·elapsed30 ·--·.508234s·elapsed
31 next·gb31 next·gb
32 ·--·.0018451s·elapsed32 ·--·.0101984s·elapsed
33 decompose33 decompose
34 ·--·.116035s·elapsed34 ·--·.344565s·elapsed
35 number·of·components:·235 number·of·components:·2
36 support·c,·codim·c:·{(2,·2),·(5,·2)}36 support·c,·codim·c:·{(2,·2),·(5,·2)}
37 {0,·-1}37 {0,·-1}
38 ·--·2.56119s·elapsed38 ·--·6.45395s·elapsed
39 {6,·8,·9,·10}39 {6,·8,·9,·10}
40 unfolding40 unfolding
41 ·--·.178728s·elapsed41 ·--·.317501s·elapsed
42 flatteningRelations42 flatteningRelations
43 ·--·.119241s·elapsed43 ·--·.346679s·elapsed
44 next·gb44 next·gb
45 ·--·.000342488s·elapsed45 ·--·.000534763s·elapsed
46 true46 true
47 ·--·.681551s·elapsed47 ·--·1.87851s·elapsed
48 {6,·8,·10,·11,·13}48 {6,·8,·10,·11,·13}
49 unfolding49 unfolding
50 ·--·.438175s·elapsed50 ·--·1.54586s·elapsed
51 flatteningRelations51 flatteningRelations
52 ·--·.14481s·elapsed52 ·--·.704984s·elapsed
53 next·gb53 next·gb
54 ·--·.0150665s·elapsed54 ·--·.0116644s·elapsed
55 decompose55 decompose
56 ·--·.754905s·elapsed56 ·--·2.51517s·elapsed
57 number·of·components:·157 number·of·components:·1
58 support·c,·codim·c:·{(5,·1)}58 support·c,·codim·c:·{(5,·1)}
59 {-1}59 {-1}
 60 ·--·7.62765s·elapsed
60 ·--·2.4931s·elapsed61 ·--·18.4292s·elapsed
61 ·--·6.68824s·elapsed 
62 062 0
  
63 ·--·.000003596s·elapsed63 ·--·.000003637s·elapsed
64 ·--·6.79533s·elapsed64 ·--·18.6024s·elapsed
65 {}65 {}
  
66 o3·=·{{6,·8,·9,·11}}66 o3·=·{{6,·8,·9,·11}}
  
67 o3·:·List67 o3·:·List
  
68 i4·:·68 i4·:·
4.17 KB
./usr/share/doc/Macaulay2/NumericalSemigroups/html/___Lab__Book__Protocol.html
    
Offset 96, 38 lines modifiedOffset 96, 38 lines modified
96 o5·=·2</code></pre>96 o5·=·2</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true))101 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true))
102 unfolding102 unfolding
103 ·--·.135763s·elapsed103 ·--·.366067s·elapsed
104 flatteningRelations104 flatteningRelations
105 ·--·.128706s·elapsed105 ·--·.157959s·elapsed
106 next·gb106 next·gb
107 ·--·.000563632s·elapsed107 ·--·.000742792s·elapsed
108 true108 true
109 unfolding109 unfolding
110 ·--·.100671s·elapsed110 ·--·.266595s·elapsed
111 flatteningRelations111 flatteningRelations
112 ·--·.11401s·elapsed112 ·--·.248024s·elapsed
113 next·gb113 next·gb
114 ·--·.000431301s·elapsed114 ·--·.000636323s·elapsed
115 true115 true
116 ·--·1.41187s·elapsed116 ·--·2.4495s·elapsed
  
117 o6·=·{}117 o6·=·{}
  
118 o6·:·List</code></pre>118 o6·:·List</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0))123 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0))
124 ·--·1.24269s·elapsed124 ·--·2.55405s·elapsed
  
125 o7·=·{}125 o7·=·{}
  
126 o7·:·List</code></pre>126 o7·:·List</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
Offset 184, 22 lines modifiedOffset 184, 22 lines modified
184 ··········</tr>184 ··········</tr>
185 ··········<tr>185 ··········<tr>
186 ············<td>186 ············<td>
187 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true)187 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true)
188 (13,·1)188 (13,·1)
189 {5,·8,·11,·12}189 {5,·8,·11,·12}
190 unfolding190 unfolding
191 ·--·.19375s·elapsed191 ·--·.516032s·elapsed
192 flatteningRelations192 flatteningRelations
193 ·--·.110392s·elapsed193 ·--·.290405s·elapsed
194 next·gb194 next·gb
195 ·--·.000674258s·elapsed195 ·--·.00100319s·elapsed
196 true196 true
197 ·--·.607305s·elapsed197 ·--·1.50429s·elapsed
198 (5,·8,··all·semigroups·are·smoothable)·--·.652941s·elapsed198 (5,·8,··all·semigroups·are·smoothable)·--·1.58951s·elapsed
  
  
199 o11·=·{}199 o11·=·{}
  
200 o11·:·List</code></pre>200 o11·:·List</code></pre>
201 ············</td>201 ············</td>
202 ··········</tr>202 ··········</tr>
Offset 223, 22 lines modifiedOffset 223, 22 lines modified
  
223 o13·=·8</code></pre>223 o13·=·8</code></pre>
224 ············</td>224 ············</td>
225 ··········</tr>225 ··········</tr>
226 ··········<tr>226 ··········<tr>
227 ············<td>227 ············<td>
228 ··············<pre><code·class="language-macaulay2">i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true)228 ··············<pre><code·class="language-macaulay2">i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true)
229 ·--·.0508446s·elapsed229 ·--·.201539s·elapsed
230 6230 6
231 false231 false
232 5232 5
233 false233 false
234 4234 4
235 decompose235 decompose
236 ·--·.240413s·elapsed236 ·--·.986497s·elapsed
237 number·of·components:·2237 number·of·components:·2
238 support·c,·codim·c:·{(1,·1),·(16,·3)}238 support·c,·codim·c:·{(1,·1),·(16,·3)}
239 {0,·-1}239 {0,·-1}
  
240 o14·=·true</code></pre>240 o14·=·true</code></pre>
241 ············</td>241 ············</td>
242 ··········</tr>242 ··········</tr>
1.92 KB
html2text {}
    
Offset 26, 34 lines modifiedOffset 26, 34 lines modified
26 o3·=·3926 o3·=·39
27 i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a27 i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a
  
28 o5·=·228 o5·=·2
29 i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup29 i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup
30 (L,0.25,0,Verbose=>true))30 (L,0.25,0,Verbose=>true))
31 unfolding31 unfolding
32 ·--·.135763s·elapsed32 ·--·.366067s·elapsed
33 flatteningRelations33 flatteningRelations
34 ·--·.128706s·elapsed34 ·--·.157959s·elapsed
35 next·gb35 next·gb
36 ·--·.000563632s·elapsed36 ·--·.000742792s·elapsed
37 true37 true
38 unfolding38 unfolding
39 ·--·.100671s·elapsed39 ·--·.266595s·elapsed
40 flatteningRelations40 flatteningRelations
41 ·--·.11401s·elapsed41 ·--·.248024s·elapsed
42 next·gb42 next·gb
43 ·--·.000431301s·elapsed43 ·--·.000636323s·elapsed
44 true44 true
45 ·--·1.41187s·elapsed45 ·--·2.4495s·elapsed
  
46 o6·=·{}46 o6·=·{}
  
47 o6·:·List47 o6·:·List
48 i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0))48 i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0))
49 ·--·1.24269s·elapsed49 ·--·2.55405s·elapsed
  
50 o7·=·{}50 o7·=·{}
  
51 o7·:·List51 o7·:·List
52 i8·:·LL7b=={}52 i8·:·LL7b=={}
  
53 o8·=·true53 o8·=·true
Offset 92, 22 lines modifiedOffset 92, 22 lines modified
92 o10·=·(5,·8)92 o10·=·(5,·8)
  
93 o10·:·Sequence93 o10·:·Sequence
94 i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true)94 i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true)
95 (13,·1)95 (13,·1)
96 {5,·8,·11,·12}96 {5,·8,·11,·12}
97 unfolding97 unfolding
98 ·--·.19375s·elapsed98 ·--·.516032s·elapsed
99 flatteningRelations99 flatteningRelations
100 ·--·.110392s·elapsed100 ·--·.290405s·elapsed
101 next·gb101 next·gb
102 ·--·.000674258s·elapsed102 ·--·.00100319s·elapsed
103 true103 true
104 ·--·.607305s·elapsed104 ·--·1.50429s·elapsed
105 (5,·8,··all·semigroups·are·smoothable)·--·.652941s·elapsed105 (5,·8,··all·semigroups·are·smoothable)·--·1.58951s·elapsed
  
  
106 o11·=·{}106 o11·=·{}
  
107 o11·:·List107 o11·:·List
108 In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further108 In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further
109 information.·The·first·line,·(13,1),·indicates·that·there·13·semigroups·of109 information.·The·first·line,·(13,1),·indicates·that·there·13·semigroups·of
Offset 120, 22 lines modifiedOffset 120, 22 lines modified
120 o12·=·{6,·8,·9,·11}120 o12·=·{6,·8,·9,·11}
  
121 o12·:·List121 o12·:·List
122 i13·:·genus·L122 i13·:·genus·L
  
123 o13·=·8123 o13·=·8
124 i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true)124 i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true)
125 ·--·.0508446s·elapsed125 ·--·.201539s·elapsed
126 6126 6
127 false127 false
128 5128 5
129 false129 false
130 4130 4
131 decompose131 decompose
132 ·--·.240413s·elapsed132 ·--·.986497s·elapsed
133 number·of·components:·2133 number·of·components:·2
134 support·c,·codim·c:·{(1,·1),·(16,·3)}134 support·c,·codim·c:·{(1,·1),·(16,·3)}
135 {0,·-1}135 {0,·-1}
  
136 o14·=·true136 o14·=·true
137 The·first·integer,·6,·tells·that·in·this·attempt·deformation·parameters·of137 The·first·integer,·6,·tells·that·in·this·attempt·deformation·parameters·of
138 degree·>=·6·were·used·and·no·smooth·fiber·was·found.·Finally·with·all138 degree·>=·6·were·used·and·no·smooth·fiber·was·found.·Finally·with·all
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94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·tally·apply(10,i->·(96 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·tally·apply(10,i->·(
97 ·············c=minors(2,random(S^2,S^{3:-2}));97 ·············c=minors(2,random(S^2,S^{3:-2}));
98 ·············c=sub(c,x_0=>1);98 ·············c=sub(c,x_0=>1);
99 ·············R=kk[support·c];c=sub(c,R);99 ·············R=kk[support·c];c=sub(c,R);
100 ·············heuristicSmoothness·c))100 ·············heuristicSmoothness·c))
101 ·--·2.15519s·elapsed101 ·--·5.79753s·elapsed
  
102 o4·=·Tally{false·=>·6}102 o4·=·Tally{false·=>·6}
103 ···········true·=>·4103 ···········true·=>·4
  
104 o4·:·Tally</code></pre>104 o4·:·Tally</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
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27 ·--·setting·random·seed·to27 ·--·setting·random·seed·to
28 164481453440449127431341128518604198809956756390578037482408606251655943828 1644814534404491274313411285186041988099567563905780374824086062516559438
29 i4·:·elapsedTime·tally·apply(10,i->·(29 i4·:·elapsedTime·tally·apply(10,i->·(
30 ·············c=minors(2,random(S^2,S^{3:-2}));30 ·············c=minors(2,random(S^2,S^{3:-2}));
31 ·············c=sub(c,x_0=>1);31 ·············c=sub(c,x_0=>1);
32 ·············R=kk[support·c];c=sub(c,R);32 ·············R=kk[support·c];c=sub(c,R);
33 ·············heuristicSmoothness·c))33 ·············heuristicSmoothness·c))
34 ·--·2.15519s·elapsed34 ·--·5.79753s·elapsed
  
35 o4·=·Tally{false·=>·6}35 o4·=·Tally{false·=>·6}
36 ···········true·=>·436 ···········true·=>·4
  
37 o4·:·Tally37 o4·:·Tally
38 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8cS\x8Sm\x8mo\x8oo\x8ot\x8th\x8hn\x8ne\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*38 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8cS\x8Sm\x8mo\x8oo\x8ot\x8th\x8hn\x8ne\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
39 ····*·heuristicSmoothness(Ideal)39 ····*·heuristicSmoothness(Ideal)
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Offset 95, 23 lines modifiedOffset 95, 23 lines modified
  
95 o2·=·8</code></pre>95 o2·=·8</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0)100 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0)
101 ·--·1.8799s·elapsed101 ·--·1.95732s·elapsed
  
102 o3·=·false</code></pre>102 o3·=·false</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0)107 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0)
108 ·--·7.47251s·elapsed108 ·--·6.97864s·elapsed
  
109 o4·=·true</code></pre>109 o4·=·true</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ········</table>112 ········</table>
113 ······</div>113 ······</div>
114 ······<div>114 ······<div>
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29 o1·=·{6,·8,·9,·11}29 o1·=·{6,·8,·9,·11}
  
30 o1·:·List30 o1·:·List
31 i2·:·genus·L31 i2·:·genus·L
  
32 o2·=·832 o2·=·8
33 i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0)33 i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0)
34 ·--·1.8799s·elapsed34 ·--·1.95732s·elapsed
  
35 o3·=·false35 o3·=·false
36 i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0)36 i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0)
37 ·--·7.47251s·elapsed37 ·--·6.97864s·elapsed
  
38 o4·=·true38 o4·=·true
39 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
40 ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal40 ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal
41 ······with·positive·degree·parameters41 ······with·positive·degree·parameters
42 ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding42 ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding
43 ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of43 ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of
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Offset 94, 15 lines modifiedOffset 94, 15 lines modified
  
94 o2·=·8</code></pre>94 o2·=·8</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15)99 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15)
100 ·--·6.16473s·elapsed100 ·--·7.12663s·elapsed
  
101 o3·=·true</code></pre>101 o3·=·true</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ········</table>104 ········</table>
105 ······</div>105 ······</div>
106 ······<div>106 ······<div>
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29 o1·=·{6,·8,·9,·11}29 o1·=·{6,·8,·9,·11}
  
30 o1·:·List30 o1·:·List
31 i2·:·genus·L31 i2·:·genus·L
  
32 o2·=·832 o2·=·8
33 i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15)33 i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15)
34 ·--·6.16473s·elapsed34 ·--·7.12663s·elapsed
  
35 o3·=·true35 o3·=·true
36 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*36 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
37 ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal37 ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal
38 ······with·positive·degree·parameters38 ······with·positive·degree·parameters
39 ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding39 ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding
40 ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of40 ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of
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78 ········<div>78 ········<div>
79 ··········<p>We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no·smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In·this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is·particular·heavy·are·excluded.</p>79 ··········<p>We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no·smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In·this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is·particular·heavy·are·excluded.</p>
80 ········</div>80 ········</div>
81 ········<table·class="examples">81 ········<table·class="examples">
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nonWeierstrassSemigroups(6,7)84 ··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nonWeierstrassSemigroups(6,7)
85 (6,·7,··all·semigroups·are·smoothable)·--·1.56007s·elapsed85 (6,·7,··all·semigroups·are·smoothable)·--·3.37527s·elapsed
  
  
86 o1·=·{}86 o1·=·{}
  
87 o1·:·List</code></pre>87 o1·:·List</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
Offset 101, 61 lines modifiedOffset 101, 61 lines modified
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true)104 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true)
105 (17,·5)105 (17,·5)
106 {6,·7,·8,·17}106 {6,·7,·8,·17}
107 unfolding107 unfolding
108 ·--·.383948s·elapsed108 ·--·1.22298s·elapsed
109 flatteningRelations109 flatteningRelations
110 ·--·.19233s·elapsed110 ·--·.415793s·elapsed
111 next·gb111 next·gb
112 ·--·.00127309s·elapsed112 ·--·.0016185s·elapsed
113 true113 true
114 ·--·.952286s·elapsed114 ·--·2.46891s·elapsed
115 {6,·7,·9,·17}115 {6,·7,·9,·17}
116 unfolding116 unfolding
117 ·--·.298426s·elapsed117 ·--·.822646s·elapsed
118 flatteningRelations118 flatteningRelations
119 ·--·.183205s·elapsed119 ·--·.508234s·elapsed
120 next·gb120 next·gb
121 ·--·.0018451s·elapsed121 ·--·.0101984s·elapsed
122 decompose122 decompose
123 ·--·.116035s·elapsed123 ·--·.344565s·elapsed
124 number·of·components:·2124 number·of·components:·2
125 support·c,·codim·c:·{(2,·2),·(5,·2)}125 support·c,·codim·c:·{(2,·2),·(5,·2)}
126 {0,·-1}126 {0,·-1}
127 ·--·2.56119s·elapsed127 ·--·6.45395s·elapsed
128 {6,·8,·9,·10}128 {6,·8,·9,·10}
129 unfolding129 unfolding
130 ·--·.178728s·elapsed130 ·--·.317501s·elapsed
131 flatteningRelations131 flatteningRelations
132 ·--·.119241s·elapsed132 ·--·.346679s·elapsed
133 next·gb133 next·gb
134 ·--·.000342488s·elapsed134 ·--·.000534763s·elapsed
135 true135 true
136 ·--·.681551s·elapsed136 ·--·1.87851s·elapsed
137 {6,·8,·10,·11,·13}137 {6,·8,·10,·11,·13}
138 unfolding138 unfolding
139 ·--·.438175s·elapsed139 ·--·1.54586s·elapsed
140 flatteningRelations140 flatteningRelations
141 ·--·.14481s·elapsed141 ·--·.704984s·elapsed
142 next·gb142 next·gb
143 ·--·.0150665s·elapsed143 ·--·.0116644s·elapsed
144 decompose144 decompose
145 ·--·.754905s·elapsed145 ·--·2.51517s·elapsed
146 number·of·components:·1146 number·of·components:·1
147 support·c,·codim·c:·{(5,·1)}147 support·c,·codim·c:·{(5,·1)}
148 {-1}148 {-1}
 149 ·--·7.62765s·elapsed
149 ·--·2.4931s·elapsed150 ·--·18.4292s·elapsed
150 ·--·6.68824s·elapsed 
151 0151 0
  
152 ·--·.000003596s·elapsed152 ·--·.000003637s·elapsed
153 ·--·6.79533s·elapsed153 ·--·18.6024s·elapsed
154 {}154 {}
  
155 o3·=·{{6,·8,·9,·11}}155 o3·=·{{6,·8,·9,·11}}
  
156 o3·:·List</code></pre>156 o3·:·List</code></pre>
157 ············</td>157 ············</td>
158 ··········</tr>158 ··········</tr>
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21 ············LLdifficult21 ············LLdifficult
22 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*22 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
23 We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no23 We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no
24 smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In24 smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In
25 this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is25 this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is
26 particular·heavy·are·excluded.26 particular·heavy·are·excluded.
27 i1·:·elapsedTime·nonWeierstrassSemigroups(6,7)27 i1·:·elapsedTime·nonWeierstrassSemigroups(6,7)
28 (6,·7,··all·semigroups·are·smoothable)·--·1.56007s·elapsed28 (6,·7,··all·semigroups·are·smoothable)·--·3.37527s·elapsed
  
  
29 o1·=·{}29 o1·=·{}
  
30 o1·:·List30 o1·:·List
31 i2·:·LLdifficult={{6,·8,·9,·11}}31 i2·:·LLdifficult={{6,·8,·9,·11}}
  
32 o2·=·{{6,·8,·9,·11}}32 o2·=·{{6,·8,·9,·11}}
  
33 o2·:·List33 o2·:·List
34 i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true)34 i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true)
35 (17,·5)35 (17,·5)
36 {6,·7,·8,·17}36 {6,·7,·8,·17}
37 unfolding37 unfolding
38 ·--·.383948s·elapsed38 ·--·1.22298s·elapsed
39 flatteningRelations39 flatteningRelations
40 ·--·.19233s·elapsed40 ·--·.415793s·elapsed
41 next·gb41 next·gb
42 ·--·.00127309s·elapsed42 ·--·.0016185s·elapsed
43 true43 true
44 ·--·.952286s·elapsed44 ·--·2.46891s·elapsed
45 {6,·7,·9,·17}45 {6,·7,·9,·17}
46 unfolding46 unfolding
47 ·--·.298426s·elapsed47 ·--·.822646s·elapsed
48 flatteningRelations48 flatteningRelations
49 ·--·.183205s·elapsed49 ·--·.508234s·elapsed
50 next·gb50 next·gb
51 ·--·.0018451s·elapsed51 ·--·.0101984s·elapsed
52 decompose52 decompose
53 ·--·.116035s·elapsed53 ·--·.344565s·elapsed
54 number·of·components:·254 number·of·components:·2
55 support·c,·codim·c:·{(2,·2),·(5,·2)}55 support·c,·codim·c:·{(2,·2),·(5,·2)}
56 {0,·-1}56 {0,·-1}
57 ·--·2.56119s·elapsed57 ·--·6.45395s·elapsed
58 {6,·8,·9,·10}58 {6,·8,·9,·10}
59 unfolding59 unfolding
60 ·--·.178728s·elapsed60 ·--·.317501s·elapsed
61 flatteningRelations61 flatteningRelations
62 ·--·.119241s·elapsed62 ·--·.346679s·elapsed
63 next·gb63 next·gb
64 ·--·.000342488s·elapsed64 ·--·.000534763s·elapsed
65 true65 true
66 ·--·.681551s·elapsed66 ·--·1.87851s·elapsed
67 {6,·8,·10,·11,·13}67 {6,·8,·10,·11,·13}
68 unfolding68 unfolding
69 ·--·.438175s·elapsed69 ·--·1.54586s·elapsed
70 flatteningRelations70 flatteningRelations
71 ·--·.14481s·elapsed71 ·--·.704984s·elapsed
72 next·gb72 next·gb
73 ·--·.0150665s·elapsed73 ·--·.0116644s·elapsed
74 decompose74 decompose
75 ·--·.754905s·elapsed75 ·--·2.51517s·elapsed
76 number·of·components:·176 number·of·components:·1
77 support·c,·codim·c:·{(5,·1)}77 support·c,·codim·c:·{(5,·1)}
78 {-1}78 {-1}
 79 ·--·7.62765s·elapsed
79 ·--·2.4931s·elapsed80 ·--·18.4292s·elapsed
80 ·--·6.68824s·elapsed 
81 081 0
  
82 ·--·.000003596s·elapsed82 ·--·.000003637s·elapsed
83 ·--·6.79533s·elapsed83 ·--·18.6024s·elapsed
84 {}84 {}
  
85 o3·=·{{6,·8,·9,·11}}85 o3·=·{{6,·8,·9,·11}}
  
86 o3·:·List86 o3·:·List
87 In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further87 In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further
88 information.·The·first·line,·(17,5),·indicates·that·there·17·semigroups·of88 information.·The·first·line,·(17,5),·indicates·that·there·17·semigroups·of
756 B
./usr/share/doc/Macaulay2/OIGroebnerBases/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=297 #:len=29
8 dG9TdHJpbmcoUG9seW5vbWlhbE9JQWxnZWJyYSk=8 dG9TdHJpbmcoUG9seW5vbWlhbE9JQWxnZWJyYSk=
9 #:len=10449 #:len=1044
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheSBhIHBvbHlub21pYWwgT0kt10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheSBhIHBvbHlub21pYWwgT0kt
11 YWxnZWJyYSBpbiBjb25kZW5zZWQgZm9ybSIsICJsaW5lbnVtIiA9PiAxNTE2LCBJbnB1dHMgPT4g11 YWxnZWJyYSBpbiBjb25kZW5zZWQgZm9ybSIsICJsaW5lbnVtIiA9PiAxNTE2LCBJbnB1dHMgPT4g
566 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/___O__I__Resolution.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·C·=·oiRes({b},·1)8 i5·:·time·C·=·oiRes({b},·1)
9 ·--·used·0.109504s·(cpu);·0.0835769s·(thread);·0s·(gc)9 ·--·used·0.120323s·(cpu);·0.0829441s·(thread);·0s·(gc)
  
10 o5·=·0:·(e0,·{2},·{-2})10 o5·=·0:·(e0,·{2},·{-2})
11 ·····1:·(e1,·{4,·4},·{-4,·-4})11 ·····1:·(e1,·{4,·4},·{-4,·-4})
  
12 o5·:·OIResolution12 o5·:·OIResolution
  
13 i6·:·C.dd_013 i6·:·C.dd_0
649 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/___O__I__Resolution_sp_us_sp__Z__Z.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·C·=·oiRes({b},·1);8 i5·:·time·C·=·oiRes({b},·1);
9 ·--·used·0.113233s·(cpu);·0.0784591s·(thread);·0s·(gc)9 ·--·used·0.135898s·(cpu);·0.0974228s·(thread);·0s·(gc)
  
10 i6·:·C_010 i6·:·C_0
  
11 o6·=·Basis·symbol:·e011 o6·=·Basis·symbol:·e0
12 ·····Basis·element·widths:·{2}12 ·····Basis·element·widths:·{2}
13 ·····Degree·shifts:·{-2}13 ·····Degree·shifts:·{-2}
14 ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)14 ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)
620 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/___Top__Nonminimal.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)8 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)
9 ·--·used·0.269704s·(cpu);·0.207854s·(thread);·0s·(gc)9 ·--·used·0.26618s·(cpu);·0.203506s·(thread);·0s·(gc)
  
10 o5·=·0:·(e0,·{2},·{-2})10 o5·=·0:·(e0,·{2},·{-2})
11 ·····1:·(e1,·{4},·{-4})11 ·····1:·(e1,·{4},·{-4})
12 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})12 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
13 o5·:·OIResolution13 o5·:·OIResolution
  
666 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_describe__Full.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·C·=·oiRes({b},·1);8 i5·:·time·C·=·oiRes({b},·1);
9 ·--·used·0.113727s·(cpu);·0.0843757s·(thread);·0s·(gc)9 ·--·used·0.121019s·(cpu);·0.0830597s·(thread);·0s·(gc)
  
10 i6·:·describeFull·C10 i6·:·describeFull·C
  
11 o6·=·0:·Module:·Basis·symbol:·e011 o6·=·0:·Module:·Basis·symbol:·e0
12 ················Basis·element·widths:·{2}12 ················Basis·element·widths:·{2}
13 ················Degree·shifts:·{-2}13 ················Degree·shifts:·{-2}
14 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)14 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)
697 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_describe_lp__O__I__Resolution_rp.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·C·=·oiRes({b},·1);8 i5·:·time·C·=·oiRes({b},·1);
9 ·--·used·0.109861s·(cpu);·0.0852836s·(thread);·0s·(gc)9 ·--·used·0.155737s·(cpu);·0.117164s·(thread);·0s·(gc)
  
10 i6·:·describe·C10 i6·:·describe·C
  
11 o6·=·0:·Module:·Basis·symbol:·e011 o6·=·0:·Module:·Basis·symbol:·e0
12 ················Basis·element·widths:·{2}12 ················Basis·element·widths:·{2}
13 ················Degree·shifts:·{-2}13 ················Degree·shifts:·{-2}
14 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)14 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)
1.21 KB
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_get__Schreyer__Map.out
    
Offset 16, 22 lines modifiedOffset 16, 22 lines modified
16 ·····x···x···x···e·······}16 ·····x···x···x···e·······}
17 ······2,3·2,1·1,2·3,{1},217 ······2,3·2,1·1,2·3,{1},2
  
18 o5·:·List18 o5·:·List
  
19 i6·:·G'·=·oiSyz(G,·d)19 i6·:·G'·=·oiSyz(G,·d)
  
20 o6·=·{x···d··············-·x···d··············-·x···d·············,20 o6·=·{x···d···········-·x···d···········+·1d·············,·x···d·············
21 ·······1,2·4,{1,·3,·4},2····1,1·4,{2,·3,·4},2····1,3·4,{1,·2,·4},2·21 ·······1,2·3,{1,·3},1····1,1·3,{2,·3},1·····3,{1,·2,·3},2···1,2·4,{1,·3,·4},2
22 ·····------------------------------------------------------------------------22 ·····------------------------------------------------------------------------
23 ·····x···d···········-·x···d···········+·1d·············,·x···d·············23 ·····-·x···d··············-·x···d·············,·x···d··············-
24 ······1,2·3,{1,·3},1····1,1·3,{2,·3},1·····3,{1,·2,·3},2···2,4·4,{1,·2,·3},224 ········1,1·4,{2,·3,·4},2····1,3·4,{1,·2,·4},2···2,4·4,{1,·2,·3},2··
25 ·····------------------------------------------------------------------------25 ·····------------------------------------------------------------------------
26 ·····-·x···d·············}26 ·····x···d·············}
27 ········2,3·4,{1,·2,·4},227 ······2,3·4,{1,·2,·4},2
  
28 o6·:·List28 o6·:·List
  
29 i7·:·H·=·getFreeOIModule·G'#029 i7·:·H·=·getFreeOIModule·G'#0
  
30 o7·=·Basis·symbol:·d30 o7·=·Basis·symbol:·d
31 ·····Basis·element·widths:·{2,·3}31 ·····Basis·element·widths:·{2,·3}
613 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_is__Complex.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true)8 i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true)
9 ·--·used·0.275746s·(cpu);·0.217538s·(thread);·0s·(gc)9 ·--·used·0.311667s·(cpu);·0.230991s·(thread);·0s·(gc)
  
10 o5·=·0:·(e0,·{2},·{-2})10 o5·=·0:·(e0,·{2},·{-2})
11 ·····1:·(e1,·{4},·{-4})11 ·····1:·(e1,·{4},·{-4})
12 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})12 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
13 o5·:·OIResolution13 o5·:·OIResolution
  
789 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_is__O__I__G__B.out
    
Offset 15, 15 lines modifiedOffset 15, 15 lines modified
15 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);15 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);
  
16 i10·:·isOIGB·{b1,·b2}16 i10·:·isOIGB·{b1,·b2}
  
17 o10·=·false17 o10·=·false
  
18 i11·:·time·B·=·oiGB·{b1,·b2}18 i11·:·time·B·=·oiGB·{b1,·b2}
19 ·--·used·0.0199702s·(cpu);·0.0205353s·(thread);·0s·(gc)19 ·--·used·0.0234776s·(cpu);·0.0243159s·(thread);·0s·(gc)
  
20 o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,20 o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
21 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·21 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·
22 ······-----------------------------------------------------------------------22 ······-----------------------------------------------------------------------
23 ······x···x···x···e···········-·x···x···x···e··········}23 ······x···x···x···e···········-·x···x···x···e··········}
24 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},324 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
864 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_minimize__O__I__G__B.out
    
Offset 11, 15 lines modifiedOffset 11, 15 lines modified
11 i5·:·installGeneratorsInWidth(F,·3);11 i5·:·installGeneratorsInWidth(F,·3);
  
12 i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);12 i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);
  
13 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);13 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);
  
14 i10·:·time·B·=·oiGB·{b1,·b2}14 i10·:·time·B·=·oiGB·{b1,·b2}
15 ·--·used·0.0240041s·(cpu);·0.0220337s·(thread);·0s·(gc)15 ·--·used·0.0239965s·(cpu);·0.0249364s·(thread);·0s·(gc)
  
16 o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,16 o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
17 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·17 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·
18 ······-----------------------------------------------------------------------18 ······-----------------------------------------------------------------------
19 ······x···x···x···e···········-·x···x···x···e··········}19 ······x···x···x···e···········-·x···x···x···e··········}
20 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},320 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
572 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_net_lp__O__I__Resolution_rp.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·C·=·oiRes({b},·1);8 i5·:·time·C·=·oiRes({b},·1);
9 ·--·used·0.110693s·(cpu);·0.0838183s·(thread);·0s·(gc)9 ·--·used·0.129261s·(cpu);·0.0946426s·(thread);·0s·(gc)
  
10 i6·:·net·C10 i6·:·net·C
  
11 o6·=·0:·(e0,·{2},·{-2})11 o6·=·0:·(e0,·{2},·{-2})
12 ·····1:·(e1,·{4,·4},·{-4,·-4})12 ·····1:·(e1,·{4,·4},·{-4,·-4})
  
13 i7·:·13 i7·:·
828 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_oi__G__B.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 i4·:·installGeneratorsInWidth(F,·2);9 i4·:·installGeneratorsInWidth(F,·2);
  
10 i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);10 i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);
  
11 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);11 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);
  
12 i9·:·time·oiGB·{b1,·b2}12 i9·:·time·oiGB·{b1,·b2}
13 ·--·used·0.026015s·(cpu);·0.0247683s·(thread);·0s·(gc)13 ·--·used·0.0225874s·(cpu);·0.0248167s·(thread);·0s·(gc)
  
14 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,14 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
15 ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·15 ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·
16 ·····------------------------------------------------------------------------16 ·····------------------------------------------------------------------------
17 ·····x···x···x···e···········-·x···x···x···e··········}17 ·····x···x···x···e···········-·x···x···x···e··········}
18 ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},318 ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
601 B
./usr/share/doc/Macaulay2/OIGroebnerBases/example-output/_oi__Res.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);5 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
  
6 i3·:·installGeneratorsInWidth(F,·2);6 i3·:·installGeneratorsInWidth(F,·2);
  
7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);7 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
  
8 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)8 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)
9 ·--·used·0.280569s·(cpu);·0.218551s·(thread);·0s·(gc)9 ·--·used·0.293913s·(cpu);·0.217175s·(thread);·0s·(gc)
  
10 o5·=·0:·(e0,·{2},·{-2})10 o5·=·0:·(e0,·{2},·{-2})
11 ·····1:·(e1,·{4},·{-4})11 ·····1:·(e1,·{4},·{-4})
12 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})12 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
13 o5·:·OIResolution13 o5·:·OIResolution
  
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9 i4·:·installGeneratorsInWidth(F,·2);9 i4·:·installGeneratorsInWidth(F,·2);
  
10 i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2);10 i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2);
  
11 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);11 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);
  
12 i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal)12 i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal)
13 ·--·used·0.146197s·(cpu);·0.115413s·(thread);·0s·(gc)13 ·--·used·0.152396s·(cpu);·0.111711s·(thread);·0s·(gc)
  
14 ·······································································14 ·······································································
15 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······,15 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······,
16 ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2·16 ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2·
17 ·····------------------------------------------------------------------------17 ·····------------------------------------------------------------------------
18 ······2··················218 ······2··················2
19 ·····x···x···e········-·x···x···e·······}19 ·····x···x···e········-·x···x···e·······}
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13 ·································413 ·································4
14 o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·214 o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2
15 ··········2,2···2,1···1,2···1,115 ··········2,2···2,1···1,2···1,1
  
16 i5·:·terms·f16 i5·:·terms·f
  
17 o5·=·{x···e·······,·-x···e·······,·x···e·······,·-x···e·······}17 o5·=·{-x···e·······,·x···e·······,·-x···e·······,·x···e·······}
18 ·······1,1·2,{1},1····1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},218 ········1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},2···1,1·2,{1},1
  
19 o5·:·List19 o5·:·List
  
20 i6·:·20 i6·:·
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74 ············<td>74 ············<td>
75 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>75 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1)80 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1)
81 ·--·used·0.109504s·(cpu);·0.0835769s·(thread);·0s·(gc)81 ·--·used·0.120323s·(cpu);·0.0829441s·(thread);·0s·(gc)
  
82 o5·=·0:·(e0,·{2},·{-2})82 o5·=·0:·(e0,·{2},·{-2})
83 ·····1:·(e1,·{4,·4},·{-4,·-4})83 ·····1:·(e1,·{4,·4},·{-4,·-4})
  
84 o5·:·OIResolution</code></pre>84 o5·:·OIResolution</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
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11 complex,·use·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x.·To·get·the·$n$th·differential·in·an·OI-resolution·C,11 complex,·use·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x.·To·get·the·$n$th·differential·in·an·OI-resolution·C,
12 use·C.dd_n.12 use·C.dd_n.
13 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);13 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
14 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);14 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
15 i3·:·installGeneratorsInWidth(F,·2);15 i3·:·installGeneratorsInWidth(F,·2);
16 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);16 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
17 i5·:·time·C·=·oiRes({b},·1)17 i5·:·time·C·=·oiRes({b},·1)
18 ·--·used·0.109504s·(cpu);·0.0835769s·(thread);·0s·(gc)18 ·--·used·0.120323s·(cpu);·0.0829441s·(thread);·0s·(gc)
  
19 o5·=·0:·(e0,·{2},·{-2})19 o5·=·0:·(e0,·{2},·{-2})
20 ·····1:·(e1,·{4,·4},·{-4,·-4})20 ·····1:·(e1,·{4,·4},·{-4,·-4})
  
21 o5·:·OIResolution21 o5·:·OIResolution
22 i6·:·C.dd_022 i6·:·C.dd_0
  
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92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>93 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);98 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);
99 ·--·used·0.113233s·(cpu);·0.0784591s·(thread);·0s·(gc)</code></pre>99 ·--·used·0.135898s·(cpu);·0.0974228s·(thread);·0s·(gc)</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i6·:·C_0104 ··············<pre><code·class="language-macaulay2">i6·:·C_0
  
105 o6·=·Basis·symbol:·e0105 o6·=·Basis·symbol:·e0
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16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
17 Returns·the·free·OI-module·of·$C$·in·homological·degree·$n$.17 Returns·the·free·OI-module·of·$C$·in·homological·degree·$n$.
18 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);18 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
19 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);19 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
20 i3·:·installGeneratorsInWidth(F,·2);20 i3·:·installGeneratorsInWidth(F,·2);
21 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);21 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
22 i5·:·time·C·=·oiRes({b},·1);22 i5·:·time·C·=·oiRes({b},·1);
23 ·--·used·0.113233s·(cpu);·0.0784591s·(thread);·0s·(gc)23 ·--·used·0.135898s·(cpu);·0.0974228s·(thread);·0s·(gc)
24 i6·:·C_024 i6·:·C_0
  
25 o6·=·Basis·symbol:·e025 o6·=·Basis·symbol:·e0
26 ·····Basis·element·widths:·{2}26 ·····Basis·element·widths:·{2}
27 ·····Degree·shifts:·{-2}27 ·····Degree·shifts:·{-2}
28 ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)28 ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)
29 ·····Monomial·order:·Lex29 ·····Monomial·order:·Lex
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74 ············<td>74 ············<td>
75 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>75 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
76 ············</td>76 ············</td>
77 ··········</tr>77 ··········</tr>
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)80 ··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)
81 ·--·used·0.269704s·(cpu);·0.207854s·(thread);·0s·(gc)81 ·--·used·0.26618s·(cpu);·0.203506s·(thread);·0s·(gc)
  
82 o5·=·0:·(e0,·{2},·{-2})82 o5·=·0:·(e0,·{2},·{-2})
83 ·····1:·(e1,·{4},·{-4})83 ·····1:·(e1,·{4},·{-4})
84 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})84 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
85 o5·:·OIResolution</code></pre>85 o5·:·OIResolution</code></pre>
86 ············</td>86 ············</td>
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11 homological·degree·$n-1$·to·be·minimized.·Therefore,·use·TopNonminimal·=>·true11 homological·degree·$n-1$·to·be·minimized.·Therefore,·use·TopNonminimal·=>·true
12 for·no·minimization·of·the·basis·in·degree·$n-1$.12 for·no·minimization·of·the·basis·in·degree·$n-1$.
13 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);13 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
14 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);14 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
15 i3·:·installGeneratorsInWidth(F,·2);15 i3·:·installGeneratorsInWidth(F,·2);
16 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);16 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
17 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)17 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)
18 ·--·used·0.269704s·(cpu);·0.207854s·(thread);·0s·(gc)18 ·--·used·0.26618s·(cpu);·0.203506s·(thread);·0s·(gc)
  
19 o5·=·0:·(e0,·{2},·{-2})19 o5·=·0:·(e0,·{2},·{-2})
20 ·····1:·(e1,·{4},·{-4})20 ·····1:·(e1,·{4},·{-4})
21 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})21 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
22 o5·:·OIResolution22 o5·:·OIResolution
23 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·T\x8To\x8op\x8pN\x8No\x8on\x8nm\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·T\x8To\x8op\x8pN\x8No\x8on\x8nm\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*
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90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>91 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);96 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);
97 ·--·used·0.113727s·(cpu);·0.0843757s·(thread);·0s·(gc)</code></pre>97 ·--·used·0.121019s·(cpu);·0.0830597s·(thread);·0s·(gc)</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i6·:·describeFull·C102 ··············<pre><code·class="language-macaulay2">i6·:·describeFull·C
  
103 o6·=·0:·Module:·Basis·symbol:·e0103 o6·=·0:·Module:·Basis·symbol:·e0
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14 Displays·the·free·OI-modules·and·describes·the·differentials·of·an·OI-14 Displays·the·free·OI-modules·and·describes·the·differentials·of·an·OI-
15 resolution.15 resolution.
16 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);16 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
17 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);17 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
18 i3·:·installGeneratorsInWidth(F,·2);18 i3·:·installGeneratorsInWidth(F,·2);
19 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);19 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
20 i5·:·time·C·=·oiRes({b},·1);20 i5·:·time·C·=·oiRes({b},·1);
21 ·--·used·0.113727s·(cpu);·0.0843757s·(thread);·0s·(gc)21 ·--·used·0.121019s·(cpu);·0.0830597s·(thread);·0s·(gc)
22 i6·:·describeFull·C22 i6·:·describeFull·C
  
23 o6·=·0:·Module:·Basis·symbol:·e023 o6·=·0:·Module:·Basis·symbol:·e0
24 ················Basis·element·widths:·{2}24 ················Basis·element·widths:·{2}
25 ················Degree·shifts:·{-2}25 ················Degree·shifts:·{-2}
26 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)26 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)
27 ················Monomial·order:·Lex27 ················Monomial·order:·Lex
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91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>92 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);97 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);
98 ·--·used·0.109861s·(cpu);·0.0852836s·(thread);·0s·(gc)</code></pre>98 ·--·used·0.155737s·(cpu);·0.117164s·(thread);·0s·(gc)</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i6·:·describe·C103 ··············<pre><code·class="language-macaulay2">i6·:·describe·C
  
104 o6·=·0:·Module:·Basis·symbol:·e0104 o6·=·0:·Module:·Basis·symbol:·e0
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14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*14 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
15 Displays·the·free·OI-modules·and·differentials·of·an·OI-resolution.15 Displays·the·free·OI-modules·and·differentials·of·an·OI-resolution.
16 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);16 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
17 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);17 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
18 i3·:·installGeneratorsInWidth(F,·2);18 i3·:·installGeneratorsInWidth(F,·2);
19 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);19 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
20 i5·:·time·C·=·oiRes({b},·1);20 i5·:·time·C·=·oiRes({b},·1);
21 ·--·used·0.109861s·(cpu);·0.0852836s·(thread);·0s·(gc)21 ·--·used·0.155737s·(cpu);·0.117164s·(thread);·0s·(gc)
22 i6·:·describe·C22 i6·:·describe·C
  
23 o6·=·0:·Module:·Basis·symbol:·e023 o6·=·0:·Module:·Basis·symbol:·e0
24 ················Basis·element·widths:·{2}24 ················Basis·element·widths:·{2}
25 ················Degree·shifts:·{-2}25 ················Degree·shifts:·{-2}
26 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)26 ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp)
27 ················Monomial·order:·Lex27 ················Monomial·order:·Lex
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104 o5·:·List</code></pre>104 o5·:·List</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i6·:·G'·=·oiSyz(G,·d)109 ··············<pre><code·class="language-macaulay2">i6·:·G'·=·oiSyz(G,·d)
  
110 o6·=·{x···d··············-·x···d··············-·x···d·············,110 o6·=·{x···d···········-·x···d···········+·1d·············,·x···d·············
111 ·······1,2·4,{1,·3,·4},2····1,1·4,{2,·3,·4},2····1,3·4,{1,·2,·4},2·111 ·······1,2·3,{1,·3},1····1,1·3,{2,·3},1·····3,{1,·2,·3},2···1,2·4,{1,·3,·4},2
112 ·····------------------------------------------------------------------------112 ·····------------------------------------------------------------------------
113 ·····x···d···········-·x···d···········+·1d·············,·x···d·············113 ·····-·x···d··············-·x···d·············,·x···d··············-
114 ······1,2·3,{1,·3},1····1,1·3,{2,·3},1·····3,{1,·2,·3},2···2,4·4,{1,·2,·3},2114 ········1,1·4,{2,·3,·4},2····1,3·4,{1,·2,·4},2···2,4·4,{1,·2,·3},2··
115 ·····------------------------------------------------------------------------115 ·····------------------------------------------------------------------------
116 ·····-·x···d·············}116 ·····x···d·············}
117 ········2,3·4,{1,·2,·4},2117 ······2,3·4,{1,·2,·4},2
  
118 o6·:·List</code></pre>118 o6·:·List</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i7·:·H·=·getFreeOIModule·G'#0123 ··············<pre><code·class="language-macaulay2">i7·:·H·=·getFreeOIModule·G'#0
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28 ·····------------------------------------------------------------------------28 ·····------------------------------------------------------------------------
29 ·····x···x···x···e·······}29 ·····x···x···x···e·······}
30 ······2,3·2,1·1,2·3,{1},230 ······2,3·2,1·1,2·3,{1},2
  
31 o5·:·List31 o5·:·List
32 i6·:·G'·=·oiSyz(G,·d)32 i6·:·G'·=·oiSyz(G,·d)
  
33 o6·=·{x···d··············-·x···d··············-·x···d·············,33 o6·=·{x···d···········-·x···d···········+·1d·············,·x···d
34 ·······1,2·4,{1,·3,·4},2····1,1·4,{2,·3,·4},2····1,3·4,{1,·2,·4},234 ·······1,2·3,{1,·3},1····1,1·3,{2,·3},1·····3,{1,·2,·3},2···1,2·4,{1,·3,·4},2
35 ·····------------------------------------------------------------------------35 ·····------------------------------------------------------------------------
36 ·····x···d···········-·x···d···········+·1d·············,·x···d36 ·····-·x···d··············-·x···d·············,·x···d··············-
37 ······1,2·3,{1,·3},1····1,1·3,{2,·3},1·····3,{1,·2,·3},2···2,4·4,{1,·2,·3},237 ········1,1·4,{2,·3,·4},2····1,3·4,{1,·2,·4},2···2,4·4,{1,·2,·3},2
38 ·····------------------------------------------------------------------------38 ·····------------------------------------------------------------------------
39 ·····-·x···d·············}39 ·····x···d·············}
40 ········2,3·4,{1,·2,·4},240 ······2,3·4,{1,·2,·4},2
  
41 o6·:·List41 o6·:·List
42 i7·:·H·=·getFreeOIModule·G'#042 i7·:·H·=·getFreeOIModule·G'#0
  
43 o7·=·Basis·symbol:·d43 o7·=·Basis·symbol:·d
44 ·····Basis·element·widths:·{2,·3}44 ·····Basis·element·widths:·{2,·3}
45 ·····Degree·shifts:·{-2,·-3}45 ·····Degree·shifts:·{-2,·-3}
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94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>95 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true)100 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true)
101 ·--·used·0.275746s·(cpu);·0.217538s·(thread);·0s·(gc)101 ·--·used·0.311667s·(cpu);·0.230991s·(thread);·0s·(gc)
  
102 o5·=·0:·(e0,·{2},·{-2})102 o5·=·0:·(e0,·{2},·{-2})
103 ·····1:·(e1,·{4},·{-4})103 ·····1:·(e1,·{4},·{-4})
104 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})104 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
105 o5·:·OIResolution</code></pre>105 o5·:·OIResolution</code></pre>
106 ············</td>106 ············</td>
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17 option·must·be·either·true·or·false,·depending·on·whether·one·wants·debug17 option·must·be·either·true·or·false,·depending·on·whether·one·wants·debug
18 information·printed.18 information·printed.
19 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);19 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
20 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);20 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
21 i3·:·installGeneratorsInWidth(F,·2);21 i3·:·installGeneratorsInWidth(F,·2);
22 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);22 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
23 i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true)23 i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true)
24 ·--·used·0.275746s·(cpu);·0.217538s·(thread);·0s·(gc)24 ·--·used·0.311667s·(cpu);·0.230991s·(thread);·0s·(gc)
  
25 o5·=·0:·(e0,·{2},·{-2})25 o5·=·0:·(e0,·{2},·{-2})
26 ·····1:·(e1,·{4},·{-4})26 ·····1:·(e1,·{4},·{-4})
27 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})27 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
28 o5·:·OIResolution28 o5·:·OIResolution
29 i6·:·isComplex·C29 i6·:·isComplex·C
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116 o10·=·false</code></pre>116 o10·=·false</code></pre>
117 ············</td>117 ············</td>
118 ··········</tr>118 ··········</tr>
119 ··········<tr>119 ··········<tr>
120 ············<td>120 ············<td>
121 ··············<pre><code·class="language-macaulay2">i11·:·time·B·=·oiGB·{b1,·b2}121 ··············<pre><code·class="language-macaulay2">i11·:·time·B·=·oiGB·{b1,·b2}
122 ·--·used·0.0199702s·(cpu);·0.0205353s·(thread);·0s·(gc)122 ·--·used·0.0234776s·(cpu);·0.0243159s·(thread);·0s·(gc)
  
123 o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,123 o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
124 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·124 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·
125 ······-----------------------------------------------------------------------125 ······-----------------------------------------------------------------------
126 ······x···x···x···e···········-·x···x···x···e··········}126 ······x···x···x···e···········-·x···x···x···e··········}
127 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3127 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
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24 i5·:·installGeneratorsInWidth(F,·3);24 i5·:·installGeneratorsInWidth(F,·3);
25 i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);25 i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);
26 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);26 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);
27 i10·:·isOIGB·{b1,·b2}27 i10·:·isOIGB·{b1,·b2}
  
28 o10·=·false28 o10·=·false
29 i11·:·time·B·=·oiGB·{b1,·b2}29 i11·:·time·B·=·oiGB·{b1,·b2}
30 ·--·used·0.0199702s·(cpu);·0.0205353s·(thread);·0s·(gc)30 ·--·used·0.0234776s·(cpu);·0.0243159s·(thread);·0s·(gc)
  
31 o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,31 o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
32 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},332 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3
33 ······-----------------------------------------------------------------------33 ······-----------------------------------------------------------------------
34 ······x···x···x···e···········-·x···x···x···e··········}34 ······x···x···x···e···········-·x···x···x···e··········}
35 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},335 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
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109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre>110 ··············<pre><code·class="language-macaulay2">i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i10·:·time·B·=·oiGB·{b1,·b2}115 ··············<pre><code·class="language-macaulay2">i10·:·time·B·=·oiGB·{b1,·b2}
116 ·--·used·0.0240041s·(cpu);·0.0220337s·(thread);·0s·(gc)116 ·--·used·0.0239965s·(cpu);·0.0249364s·(thread);·0s·(gc)
  
117 o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,117 o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
118 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·118 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·
119 ······-----------------------------------------------------------------------119 ······-----------------------------------------------------------------------
120 ······x···x···x···e···········-·x···x···x···e··········}120 ······x···x···x···e···········-·x···x···x···e··········}
121 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3121 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
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21 i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P);21 i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P);
22 i3·:·installGeneratorsInWidth(F,·1);22 i3·:·installGeneratorsInWidth(F,·1);
23 i4·:·installGeneratorsInWidth(F,·2);23 i4·:·installGeneratorsInWidth(F,·2);
24 i5·:·installGeneratorsInWidth(F,·3);24 i5·:·installGeneratorsInWidth(F,·3);
25 i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);25 i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);
26 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);26 i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);
27 i10·:·time·B·=·oiGB·{b1,·b2}27 i10·:·time·B·=·oiGB·{b1,·b2}
28 ·--·used·0.0240041s·(cpu);·0.0220337s·(thread);·0s·(gc)28 ·--·used·0.0239965s·(cpu);·0.0249364s·(thread);·0s·(gc)
  
29 o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,29 o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
30 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},330 ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3
31 ······-----------------------------------------------------------------------31 ······-----------------------------------------------------------------------
32 ······x···x···x···e···········-·x···x···x···e··········}32 ······x···x···x···e···········-·x···x···x···e··········}
33 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},333 ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
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91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>92 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);97 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1);
98 ·--·used·0.110693s·(cpu);·0.0838183s·(thread);·0s·(gc)</code></pre>98 ·--·used·0.129261s·(cpu);·0.0946426s·(thread);·0s·(gc)</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i6·:·net·C103 ··············<pre><code·class="language-macaulay2">i6·:·net·C
  
104 o6·=·0:·(e0,·{2},·{-2})104 o6·=·0:·(e0,·{2},·{-2})
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15 Displays·the·basis·element·widths·and·degree·shifts·of·the·free·OI-modules·in15 Displays·the·basis·element·widths·and·degree·shifts·of·the·free·OI-modules·in
16 an·OI-resolution.16 an·OI-resolution.
17 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);17 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
18 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);18 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
19 i3·:·installGeneratorsInWidth(F,·2);19 i3·:·installGeneratorsInWidth(F,·2);
20 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);20 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
21 i5·:·time·C·=·oiRes({b},·1);21 i5·:·time·C·=·oiRes({b},·1);
22 ·--·used·0.110693s·(cpu);·0.0838183s·(thread);·0s·(gc)22 ·--·used·0.129261s·(cpu);·0.0946426s·(thread);·0s·(gc)
23 i6·:·net·C23 i6·:·net·C
  
24 o6·=·0:·(e0,·{2},·{-2})24 o6·=·0:·(e0,·{2},·{-2})
25 ·····1:·(e1,·{4,·4},·{-4,·-4})25 ·····1:·(e1,·{4,·4},·{-4,·-4})
26 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
27 ····*·_\x8n_\x8e_\x8t_\x8(_\x8O_\x8I_\x8R_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n_\x8)·--·display·an·OI-resolution27 ····*·_\x8n_\x8e_\x8t_\x8(_\x8O_\x8I_\x8R_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n_\x8)·--·display·an·OI-resolution
28 ===============================================================================28 ===============================================================================
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111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre>112 ··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i9·:·time·oiGB·{b1,·b2}117 ··············<pre><code·class="language-macaulay2">i9·:·time·oiGB·{b1,·b2}
118 ·--·used·0.026015s·(cpu);·0.0247683s·(thread);·0s·(gc)118 ·--·used·0.0225874s·(cpu);·0.0248167s·(thread);·0s·(gc)
  
119 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,119 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
120 ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·120 ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3·
121 ·····------------------------------------------------------------------------121 ·····------------------------------------------------------------------------
122 ·····x···x···x···e···········-·x···x···x···e··········}122 ·····x···x···x···e···········-·x···x···x···e··········}
123 ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3123 ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
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28 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);28 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
29 i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P);29 i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P);
30 i3·:·installGeneratorsInWidth(F,·1);30 i3·:·installGeneratorsInWidth(F,·1);
31 i4·:·installGeneratorsInWidth(F,·2);31 i4·:·installGeneratorsInWidth(F,·2);
32 i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);32 i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);
33 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);33 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);
34 i9·:·time·oiGB·{b1,·b2}34 i9·:·time·oiGB·{b1,·b2}
35 ·--·used·0.026015s·(cpu);·0.0247683s·(thread);·0s·(gc)35 ·--·used·0.0225874s·(cpu);·0.0248167s·(thread);·0s·(gc)
  
36 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,36 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········,
37 ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},337 ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3
38 ·····------------------------------------------------------------------------38 ·····------------------------------------------------------------------------
39 ·····x···x···x···e···········-·x···x···x···e··········}39 ·····x···x···x···e···········-·x···x···x···e··········}
40 ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},340 ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3
  
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106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>107 ··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)112 ··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)
113 ·--·used·0.280569s·(cpu);·0.218551s·(thread);·0s·(gc)113 ·--·used·0.293913s·(cpu);·0.217175s·(thread);·0s·(gc)
  
114 o5·=·0:·(e0,·{2},·{-2})114 o5·=·0:·(e0,·{2},·{-2})
115 ·····1:·(e1,·{4},·{-4})115 ·····1:·(e1,·{4},·{-4})
116 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})116 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
117 o5·:·OIResolution</code></pre>117 o5·:·OIResolution</code></pre>
118 ············</td>118 ············</td>
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33 Therefore,·use·TopNonminimal·=>·true·for·no·minimization·of·the·basis·in·degree33 Therefore,·use·TopNonminimal·=>·true·for·no·minimization·of·the·basis·in·degree
34 $n-1$.34 $n-1$.
35 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);35 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
36 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);36 i2·:·F·=·makeFreeOIModule(e,·{1,1},·P);
37 i3·:·installGeneratorsInWidth(F,·2);37 i3·:·installGeneratorsInWidth(F,·2);
38 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);38 i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);
39 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)39 i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true)
40 ·--·used·0.280569s·(cpu);·0.218551s·(thread);·0s·(gc)40 ·--·used·0.293913s·(cpu);·0.217175s·(thread);·0s·(gc)
  
41 o5·=·0:·(e0,·{2},·{-2})41 o5·=·0:·(e0,·{2},·{-2})
42 ·····1:·(e1,·{4},·{-4})42 ·····1:·(e1,·{4},·{-4})
43 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})43 ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5})
  
44 o5·:·OIResolution44 o5·:·OIResolution
45 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·o\x8oi\x8iR\x8Re\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*45 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·o\x8oi\x8iR\x8Re\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
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104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);</code></pre>105 ··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ··········<tr>108 ··········<tr>
109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal)110 ··············<pre><code·class="language-macaulay2">i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal)
111 ·--·used·0.146197s·(cpu);·0.115413s·(thread);·0s·(gc)111 ·--·used·0.152396s·(cpu);·0.111711s·(thread);·0s·(gc)
  
112 ·······································································112 ·······································································
113 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······,113 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······,
114 ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2·114 ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2·
115 ·····------------------------------------------------------------------------115 ·····------------------------------------------------------------------------
116 ······2··················2116 ······2··················2
117 ·····x···x···e········-·x···x···e·······}117 ·····x···x···e········-·x···x···e·······}
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20 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);20 i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ);
21 i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P);21 i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P);
22 i3·:·installGeneratorsInWidth(F,·1);22 i3·:·installGeneratorsInWidth(F,·1);
23 i4·:·installGeneratorsInWidth(F,·2);23 i4·:·installGeneratorsInWidth(F,·2);
24 i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2);24 i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2);
25 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);25 i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);
26 i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal)26 i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal)
27 ·--·used·0.146197s·(cpu);·0.115413s·(thread);·0s·(gc)27 ·--·used·0.152396s·(cpu);·0.111711s·(thread);·0s·(gc)
  
  
28 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······,28 o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······,
29 ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},229 ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2
30 ·····------------------------------------------------------------------------30 ·····------------------------------------------------------------------------
31 ······2··················231 ······2··················2
32 ·····x···x···e········-·x···x···e·······}32 ·····x···x···e········-·x···x···e·······}
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99 ··········2,2···2,1···1,2···1,1</code></pre>99 ··········2,2···2,1···1,2···1,1</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i5·:·terms·f104 ··············<pre><code·class="language-macaulay2">i5·:·terms·f
  
105 o5·=·{x···e·······,·-x···e·······,·x···e·······,·-x···e·······}105 o5·=·{-x···e·······,·x···e·······,·-x···e·······,·x···e·······}
106 ·······1,1·2,{1},1····1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},2106 ········1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},2···1,1·2,{1},1
  
107 o5·:·List</code></pre>107 o5·:·List</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ········</table>110 ········</table>
111 ······</div>111 ······</div>
112 ······<div>112 ······<div>
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24 ·······1,2·2,{2},1····1,1·2,{1},1····2,2·2,{2},2····2,1·2,{1},224 ·······1,2·2,{2},1····1,1·2,{1},1····2,2·2,{2},2····2,1·2,{1},2
  
25 ·································425 ·································4
26 o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·226 o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2
27 ··········2,2···2,1···1,2···1,127 ··········2,2···2,1···1,2···1,1
28 i5·:·terms·f28 i5·:·terms·f
  
29 o5·=·{x···e·······,·-x···e·······,·x···e·······,·-x···e·······}29 o5·=·{-x···e·······,·x···e·······,·-x···e·······,·x···e·······}
30 ·······1,1·2,{1},1····1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},230 ········1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},2···1,1·2,{1},1
  
31 o5·:·List31 o5·:·List
32 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*32 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
33 The·list·of·terms·need·not·be·in·order.·To·find·the·lead·term·of·an·element,33 The·list·of·terms·need·not·be·in·order.·To·find·the·lead·term·of·an·element,
34 see·_\x8l_\x8e_\x8a_\x8d_\x8T_\x8e_\x8r_\x8m_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8).34 see·_\x8l_\x8e_\x8a_\x8d_\x8T_\x8e_\x8r_\x8m_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8).
35 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*35 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
36 ····*·_\x8t_\x8e_\x8r_\x8m_\x8s_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8)·--·get·the·terms·of·an·element·of·a·free·OI-module36 ····*·_\x8t_\x8e_\x8r_\x8m_\x8s_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8)·--·get·the·terms·of·an·element·of·a·free·OI-module
747 B
./usr/share/doc/Macaulay2/OldChainComplexes/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=207 #:len=20
8 Z3JhZGVkTW9kdWxlKE1vZHVsZSk=8 Z3JhZGVkTW9kdWxlKE1vZHVsZSk=
9 #:len=2949 #:len=294
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODEsIHN5bWJvbCBEb2N1bWVudFRhZyA910 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODEsIHN5bWJvbCBEb2N1bWVudFRhZyA9
11 PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KGdyYWRlZE1vZHVsZSxNb2R1bGUpLCJncmFkZWRNb2R111 PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KGdyYWRlZE1vZHVsZSxNb2R1bGUpLCJncmFkZWRNb2R1
1.26 KB
./usr/share/doc/Macaulay2/OldChainComplexes/example-output/___Fast__Nonminimal.out
    
Offset 9, 25 lines modifiedOffset 9, 25 lines modified
9 i2·:·S·=·ring·I9 i2·:·S·=·ring·I
  
10 o2·=·S10 o2·=·S
  
11 o2·:·PolynomialRing11 o2·:·PolynomialRing
  
12 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)12 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)
13 ·--·2.27405s·elapsed13 ·--·3.75418s·elapsed
  
14 ······1······35······241······841······1781······2464······2294······1432······576······135······1414 ······1······35······241······841······1781······2464······2294······1432······576······135······14
15 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·015 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0
16 ·········································································································16 ·········································································································
17 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······1117 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11
  
18 o3·:·ChainComplex18 o3·:·ChainComplex
  
19 i4·:·elapsedTime·C1·=·res·ideal(I_*)19 i4·:·elapsedTime·C1·=·res·ideal(I_*)
20 ·--·1.21671s·elapsed20 ·--·3.08925s·elapsed
  
21 ······1······35······140······385······819······1080······819······385······140······35······121 ······1······35······140······385······819······1080······819······385······140······35······1
22 o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·022 o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·0
23 ····································································································23 ····································································································
24 ·····0······1·······2········3········4········5·········6········7········8········9·······10·····1124 ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11
  
25 o4·:·ChainComplex25 o4·:·ChainComplex
813 B
./usr/share/doc/Macaulay2/OldChainComplexes/example-output/_betti_lp..._cm__Minimize_eq_gt..._rp.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 i2·:·S·=·ring·I9 i2·:·S·=·ring·I
  
10 o2·=·S10 o2·=·S
  
11 o2·:·PolynomialRing11 o2·:·PolynomialRing
  
12 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)12 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)
13 ·--·2.15083s·elapsed13 ·--·5.56982s·elapsed
  
14 ······1······35······241······841······1781······2464······2294······1432······576······135······1414 ······1······35······241······841······1781······2464······2294······1432······576······135······14
15 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·015 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0
16 ·········································································································16 ·········································································································
17 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······1117 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11
  
18 o3·:·ChainComplex18 o3·:·ChainComplex
1.24 KB
./usr/share/doc/Macaulay2/OldChainComplexes/example-output/_computing_spresolutions.out
    
Offset 36, 19 lines modifiedOffset 36, 28 lines modified
36 ··········<<·res·M·<<·endl·<<·endl;36 ··········<<·res·M·<<·endl·<<·endl;
37 ··········break;37 ··········break;
38 ··········)·else·(38 ··········)·else·(
39 ··········<<·"--·computation·interrupted"·<<·endl;39 ··········<<·"--·computation·interrupted"·<<·endl;
40 ··········status·M.cache.resolution;40 ··········status·M.cache.resolution;
41 ··········<<·"--·continuing·the·computation"·<<·endl;41 ··········<<·"--·continuing·the·computation"·<<·endl;
42 ··········))42 ··········))
 43 ·--·used·0.266535s·(cpu);·0.262817s·(thread);·0s·(gc)
 44 ·--·used·0.359742s·(cpu);·0.312892s·(thread);·0s·(gc)
 45 ·--·used·0.396689s·(cpu);·0.313416s·(thread);·0s·(gc)
43 ·--·used·0.92044s·(cpu);·0.840668s·(thread);·0s·(gc)46 ·--·used·0.382042s·(cpu);·0.383186s·(thread);·0s·(gc)
44 ·--·used·0.75468s·(cpu);·0.70378s·(thread);·0s·(gc)47 ·--·used·0.415713s·(cpu);·0.336383s·(thread);·0s·(gc)
45 --·computation·started:·48 --·computation·started:·
46 --·computation·interrupted49 --·computation·interrupted
47 --·continuing·the·computation50 --·continuing·the·computation
 51 --·computation·interrupted
 52 --·continuing·the·computation
 53 --·computation·interrupted
 54 --·continuing·the·computation
 55 --·computation·interrupted
 56 --·continuing·the·computation
48 --·computation·complete57 --·computation·complete
49 ·4······11······89······122······4058 ·4······11······89······122······40
50 R··<--·R···<--·R···<--·R····<--·R···<--·059 R··<--·R···<--·R···<--·R····<--·R···<--·0
51 ·········································60 ·········································
52 0······1·······2·······3········4·······561 0······1·······2·······3········4·······5
  
  
2.4 KB
./usr/share/doc/Macaulay2/OldChainComplexes/html/___Fast__Nonminimal.html
    
Offset 89, 28 lines modifiedOffset 89, 28 lines modified
  
89 o2·:·PolynomialRing</code></pre>89 o2·:·PolynomialRing</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)94 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)
95 ·--·2.27405s·elapsed95 ·--·3.75418s·elapsed
  
96 ······1······35······241······841······1781······2464······2294······1432······576······135······1496 ······1······35······241······841······1781······2464······2294······1432······576······135······14
97 o3·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S···&lt;--·097 o3·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S···&lt;--·0
98 ·········································································································98 ·········································································································
99 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······1199 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11
  
100 o3·:·ChainComplex</code></pre>100 o3·:·ChainComplex</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C1·=·res·ideal(I_*)105 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C1·=·res·ideal(I_*)
106 ·--·1.21671s·elapsed106 ·--·3.08925s·elapsed
  
107 ······1······35······140······385······819······1080······819······385······140······35······1107 ······1······35······140······385······819······1080······819······385······140······35······1
108 o4·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S····&lt;--·S···&lt;--·S··&lt;--·0108 o4·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S····&lt;--·S···&lt;--·S··&lt;--·0
109 ····································································································109 ····································································································
110 ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11110 ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11
  
111 o4·:·ChainComplex</code></pre>111 o4·:·ChainComplex</code></pre>
867 B
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29 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,629 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6
30 i2·:·S·=·ring·I30 i2·:·S·=·ring·I
  
31 o2·=·S31 o2·=·S
  
32 o2·:·PolynomialRing32 o2·:·PolynomialRing
33 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)33 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)
34 ·--·2.27405s·elapsed34 ·--·3.75418s·elapsed
  
35 ······1······35······241······841······1781······2464······2294······143235 ······1······35······241······841······1781······2464······2294······1432
36 576······135······1436 576······135······14
37 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S37 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S
38 <--·S····<--·S···<--·038 <--·S····<--·S···<--·0
  
  
39 ·····0······1·······2········3········4·········5·········6·········7·········839 ·····0······1·······2········3········4·········5·········6·········7·········8
40 9········10······1140 9········10······11
  
41 o3·:·ChainComplex41 o3·:·ChainComplex
42 i4·:·elapsedTime·C1·=·res·ideal(I_*)42 i4·:·elapsedTime·C1·=·res·ideal(I_*)
43 ·--·1.21671s·elapsed43 ·--·3.08925s·elapsed
  
44 ······1······35······140······385······819······1080······819······385······14044 ······1······35······140······385······819······1080······819······385······140
45 35······145 35······1
46 o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S46 o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S
47 <--·S···<--·S··<--·047 <--·S···<--·S··<--·0
  
  
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./usr/share/doc/Macaulay2/OldChainComplexes/html/_betti_lp..._cm__Minimize_eq_gt..._rp.html
    
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88 o2·:·PolynomialRing</code></pre>88 o2·:·PolynomialRing</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)93 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)
94 ·--·2.15083s·elapsed94 ·--·5.56982s·elapsed
  
95 ······1······35······241······841······1781······2464······2294······1432······576······135······1495 ······1······35······241······841······1781······2464······2294······1432······576······135······14
96 o3·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S···&lt;--·096 o3·=·S··&lt;--·S···&lt;--·S····&lt;--·S····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S·····&lt;--·S····&lt;--·S····&lt;--·S···&lt;--·0
97 ·········································································································97 ·········································································································
98 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······1198 ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11
  
99 o3·:·ChainComplex</code></pre>99 o3·:·ChainComplex</code></pre>
464 B
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26 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,626 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6
27 i2·:·S·=·ring·I27 i2·:·S·=·ring·I
  
28 o2·=·S28 o2·=·S
  
29 o2·:·PolynomialRing29 o2·:·PolynomialRing
30 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)30 i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true)
31 ·--·2.15083s·elapsed31 ·--·5.56982s·elapsed
  
32 ······1······35······241······841······1781······2464······2294······143232 ······1······35······241······841······1781······2464······2294······1432
33 576······135······1433 576······135······14
34 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S34 o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S
35 <--·S····<--·S···<--·035 <--·S····<--·S···<--·0
  
  
2.53 KB
./usr/share/doc/Macaulay2/OldChainComplexes/html/_computing_spresolutions.html
    
Offset 112, 19 lines modifiedOffset 112, 28 lines modified
112 ··········&lt;&lt;·res·M·&lt;&lt;·endl·&lt;&lt;·endl;112 ··········&lt;&lt;·res·M·&lt;&lt;·endl·&lt;&lt;·endl;
113 ··········break;113 ··········break;
114 ··········)·else·(114 ··········)·else·(
115 ··········&lt;&lt;·&quot;--·computation·interrupted&quot;·&lt;&lt;·endl;115 ··········&lt;&lt;·&quot;--·computation·interrupted&quot;·&lt;&lt;·endl;
116 ··········status·M.cache.resolution;116 ··········status·M.cache.resolution;
117 ··········&lt;&lt;·&quot;--·continuing·the·computation&quot;·&lt;&lt;·endl;117 ··········&lt;&lt;·&quot;--·continuing·the·computation&quot;·&lt;&lt;·endl;
118 ··········))118 ··········))
 119 ·--·used·0.266535s·(cpu);·0.262817s·(thread);·0s·(gc)
 120 ·--·used·0.359742s·(cpu);·0.312892s·(thread);·0s·(gc)
 121 ·--·used·0.396689s·(cpu);·0.313416s·(thread);·0s·(gc)
119 ·--·used·0.92044s·(cpu);·0.840668s·(thread);·0s·(gc)122 ·--·used·0.382042s·(cpu);·0.383186s·(thread);·0s·(gc)
120 ·--·used·0.75468s·(cpu);·0.70378s·(thread);·0s·(gc)123 ·--·used·0.415713s·(cpu);·0.336383s·(thread);·0s·(gc)
121 --·computation·started:·124 --·computation·started:·
122 --·computation·interrupted125 --·computation·interrupted
123 --·continuing·the·computation126 --·continuing·the·computation
 127 --·computation·interrupted
 128 --·continuing·the·computation
 129 --·computation·interrupted
 130 --·continuing·the·computation
 131 --·computation·interrupted
 132 --·continuing·the·computation
124 --·computation·complete133 --·computation·complete
125 ·4······11······89······122······40134 ·4······11······89······122······40
126 R··&lt;--·R···&lt;--·R···&lt;--·R····&lt;--·R···&lt;--·0135 R··&lt;--·R···&lt;--·R···&lt;--·R····&lt;--·R···&lt;--·0
127 ·········································136 ·········································
128 0······1·······2·······3········4·······5</code></pre>137 0······1·······2·······3········4·······5</code></pre>
129 ············</td>138 ············</td>
130 ··········</tr>139 ··········</tr>
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50 ··········<<·res·M·<<·endl·<<·endl;50 ··········<<·res·M·<<·endl·<<·endl;
51 ··········break;51 ··········break;
52 ··········)·else·(52 ··········)·else·(
53 ··········<<·"--·computation·interrupted"·<<·endl;53 ··········<<·"--·computation·interrupted"·<<·endl;
54 ··········status·M.cache.resolution;54 ··········status·M.cache.resolution;
55 ··········<<·"--·continuing·the·computation"·<<·endl;55 ··········<<·"--·continuing·the·computation"·<<·endl;
56 ··········))56 ··········))
 57 ·--·used·0.266535s·(cpu);·0.262817s·(thread);·0s·(gc)
 58 ·--·used·0.359742s·(cpu);·0.312892s·(thread);·0s·(gc)
 59 ·--·used·0.396689s·(cpu);·0.313416s·(thread);·0s·(gc)
57 ·--·used·0.92044s·(cpu);·0.840668s·(thread);·0s·(gc)60 ·--·used·0.382042s·(cpu);·0.383186s·(thread);·0s·(gc)
58 ·--·used·0.75468s·(cpu);·0.70378s·(thread);·0s·(gc)61 ·--·used·0.415713s·(cpu);·0.336383s·(thread);·0s·(gc)
59 --·computation·started:62 --·computation·started:
60 --·computation·interrupted63 --·computation·interrupted
61 --·continuing·the·computation64 --·continuing·the·computation
 65 --·computation·interrupted
 66 --·continuing·the·computation
 67 --·computation·interrupted
 68 --·continuing·the·computation
 69 --·computation·interrupted
 70 --·continuing·the·computation
62 --·computation·complete71 --·computation·complete
63 ·4······11······89······122······4072 ·4······11······89······122······40
64 R··<--·R···<--·R···<--·R····<--·R···<--·073 R··<--·R···<--·R···<--·R····<--·R···<--·0
  
65 0······1·······2·······3········4·······574 0······1·······2·······3········4·······5
66 If·the·user·has·a·chain·complex·in·hand·that·is·known·to·be·a·projective75 If·the·user·has·a·chain·complex·in·hand·that·is·known·to·be·a·projective
67 resolution·of·M,·then·it·can·be·installed·with·M.cache.resolution·=·C.76 resolution·of·M,·then·it·can·be·installed·with·M.cache.resolution·=·C.
721 B
./usr/share/doc/Macaulay2/OldPolyhedra/dump/rawdocumentation.dump
    
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760 B
./usr/share/doc/Macaulay2/OldToricVectorBundles/dump/rawdocumentation.dump
    
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474 B
./usr/share/doc/Macaulay2/OldToricVectorBundles/example-output/_projective__Space__Fan.out
    
Offset 7, 13 lines modifiedOffset 7, 13 lines modified
7 ······number·of·rays·=>·37 ······number·of·rays·=>·3
8 ······top·dimension·of·the·cones·=>·28 ······top·dimension·of·the·cones·=>·2
  
9 o1·:·Fan9 o1·:·Fan
  
10 i2·:·apply(maxCones·F,·rays)10 i2·:·apply(maxCones·F,·rays)
  
11 o2·=·{|·1·-1·|,·|·1·0·|,·|·-1·0·|} 
12 ······|·0·-1·|··|·0·1·|··|·-1·1·|11 o2·=·{|·1·0·|,·|·-1·0·|,·|·1·-1·|}
 12 ······|·0·1·|··|·-1·1·|··|·0·-1·|
  
13 o2·:·List13 o2·:·List
  
14 i3·:·14 i3·:·
1.31 KB
./usr/share/doc/Macaulay2/OldToricVectorBundles/html/_projective__Space__Fan.html
    
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81 o1·:·Fan</code></pre>81 o1·:·Fan</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i2·:·apply(maxCones·F,·rays)86 ··············<pre><code·class="language-macaulay2">i2·:·apply(maxCones·F,·rays)
  
87 o2·=·{|·1·-1·|,·|·1·0·|,·|·-1·0·|} 
88 ······|·0·-1·|··|·0·1·|··|·-1·1·|87 o2·=·{|·1·0·|,·|·-1·0·|,·|·1·-1·|}
 88 ······|·0·1·|··|·-1·1·|··|·0·-1·|
  
89 o2·:·List</code></pre>89 o2·:·List</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ········</table>92 ········</table>
93 ······</div>93 ······</div>
94 ······<div>94 ······<div>
736 B
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18 ······number·of·generating·cones·=>·318 ······number·of·generating·cones·=>·3
19 ······number·of·rays·=>·319 ······number·of·rays·=>·3
20 ······top·dimension·of·the·cones·=>·220 ······top·dimension·of·the·cones·=>·2
  
21 o1·:·Fan21 o1·:·Fan
22 i2·:·apply(maxCones·F,·rays)22 i2·:·apply(maxCones·F,·rays)
  
23 o2·=·{|·1·-1·|,·|·1·0·|,·|·-1·0·|} 
24 ······|·0·-1·|··|·0·1·|··|·-1·1·|23 o2·=·{|·1·0·|,·|·-1·0·|,·|·1·-1·|}
 24 ······|·0·1·|··|·-1·1·|··|·0·-1·|
  
25 o2·:·List25 o2·:·List
26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*26 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
27 ····*·_\x8F_\x8a_\x8n·--·the·class·of·all·fans27 ····*·_\x8F_\x8a_\x8n·--·the·class·of·all·fans
28 ····*·_\x8h_\x8i_\x8r_\x8z_\x8e_\x8b_\x8r_\x8u_\x8c_\x8h_\x8F_\x8a_\x8n·--·the·fan·of·the·n-th·Hirzebruch·surface28 ····*·_\x8h_\x8i_\x8r_\x8z_\x8e_\x8b_\x8r_\x8u_\x8c_\x8h_\x8F_\x8a_\x8n·--·the·fan·of·the·n-th·Hirzebruch·surface
29 ····*·_\x8p_\x8p_\x81_\x8P_\x8r_\x8o_\x8d_\x8u_\x8c_\x8t_\x8F_\x8a_\x8n·--·the·fan·of·n·products·of·PP^129 ····*·_\x8p_\x8p_\x81_\x8P_\x8r_\x8o_\x8d_\x8u_\x8c_\x8t_\x8F_\x8a_\x8n·--·the·fan·of·n·products·of·PP^1
30 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pr\x8ro\x8oj\x8je\x8ec\x8ct\x8ti\x8iv\x8ve\x8eS\x8Sp\x8pa\x8ac\x8ce\x8eF\x8Fa\x8an\x8n:\x8:·*\x8**\x8**\x8**\x8**\x8*30 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pr\x8ro\x8oj\x8je\x8ec\x8ct\x8ti\x8iv\x8ve\x8eS\x8Sp\x8pa\x8ac\x8ce\x8eF\x8Fa\x8an\x8n:\x8:·*\x8**\x8**\x8**\x8**\x8*
716 B
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751 B
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4.24 KB
./usr/share/doc/Macaulay2/Oscillators/example-output/___Checking_spthe_spcodimension_spand_spirreducible_spdecomposition_spof_spthe_sp__I__G_spideal.out
    
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182 o15·=·4182 o15·=·4
  
183 i16·:·for·G·in·Gs·list·(183 i16·:·for·G·in·Gs·list·(
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185 ··········elapsedTime·comps·:=·decompose·IG;185 ··········elapsedTime·comps·:=·decompose·IG;
186 ··········{comps/codim,·comps/degree}186 ··········{comps/codim,·comps/degree}
187 ··········);187 ··········);
188 ·--·.850561s·elapsed 
189 ·--·.672463s·elapsed 
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191 ·--·.517266s·elapsed 
192 ·--·.599794s·elapsed 
193 ·--·.62642s·elapsed 
194 ·--·1.35892s·elapsed189 ·--·1.04109s·elapsed
195 ·--·1.12385s·elapsed190 ·--·1.47165s·elapsed
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 195 ·--·1.47437s·elapsed
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196 ·--·1.11318s·elapsed197 ·--·1.15583s·elapsed
197 ·--·.908933s·elapsed 
198 ·--·.624111s·elapsed198 ·--·.728054s·elapsed
  
199 i17·:·netList·oo199 i17·:·netList·oo
  
200 ······+---------------+---------------+200 ······+---------------+---------------+
201 o17·=·|{3,·4,·4}······|{2,·3,·5}······|201 o17·=·|{3,·4,·4}······|{2,·3,·5}······|
202 ······+---------------+---------------+202 ······+---------------+---------------+
203 ······|{3,·4,·4}······|{2,·3,·5}······|203 ······|{3,·4,·4}······|{2,·3,·5}······|
Offset 242, 75 lines modifiedOffset 242, 75 lines modified
242 o22·=·15242 o22·=·15
  
243 i23·:·allcomps·=·for·G·in·Gs·list·(243 i23·:·allcomps·=·for·G·in·Gs·list·(
244 ··········IG·=·oscQuadrics(G,·R);244 ··········IG·=·oscQuadrics(G,·R);
245 ··········elapsedTime·comps·:=·decompose·IG;245 ··········elapsedTime·comps·:=·decompose·IG;
246 ··········{comps/codim,·comps/degree}246 ··········{comps/codim,·comps/degree}
247 ··········);247 ··········);
248 ·--·.748348s·elapsed248 ·--·1.43895s·elapsed
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 285 ·--·1.87367s·elapsed
 286 ·--·2.44172s·elapsed
 287 ·--·1.5063s·elapsed
 288 ·--·1.47397s·elapsed
 289 ·--·2.32976s·elapsed
 290 ·--·2.83499s·elapsed
 291 ·--·3.31741s·elapsed
 292 ·--·2.47836s·elapsed
 293 ·--·1.9358s·elapsed
 294 ·--·2.00411s·elapsed
 295 ·--·2.62136s·elapsed
 296 ·--·2.28741s·elapsed
 297 ·--·2.52702s·elapsed
251 ·--·2.62883s·elapsed298 ·--·2.65288s·elapsed
252 ·--·1.29166s·elapsed 
253 ·--·1.86117s·elapsed 
254 ·--·2.15933s·elapsed 
255 ·--·2.02516s·elapsed 
256 ·--·1.22886s·elapsed 
257 ·--·1.00474s·elapsed 
258 ·--·.444663s·elapsed 
259 ·--·.583647s·elapsed 
260 ·--·.504881s·elapsed 
261 ·--·.699276s·elapsed 
262 ·--·.916662s·elapsed 
263 ·--·1.10234s·elapsed 
264 ·--·.846727s·elapsed 
265 ·--·.80879s·elapsed 
266 ·--·1.07314s·elapsed 
267 ·--·1.16764s·elapsed 
268 ·--·1.58771s·elapsed 
269 ·--·1.68781s·elapsed 
270 ·--·2.08282s·elapsed 
271 ·--·2.46889s·elapsed 
272 ·--·1.02719s·elapsed 
273 ·--·1.45656s·elapsed 
274 ·--·2.79411s·elapsed 
275 ·--·1.4512s·elapsed299 ·--·1.65502s·elapsed
276 ·--·.990204s·elapsed 
277 ·--·1.64138s·elapsed 
278 ·--·2.20034s·elapsed 
279 ·--·1.89725s·elapsed 
280 ·--·1.06631s·elapsed 
281 ·--·1.98299s·elapsed 
282 ·--·1.53379s·elapsed 
283 ·--·2.19289s·elapsed 
284 ·--·1.71743s·elapsed 
285 ·--·2.39891s·elapsed 
286 ·--·2.55446s·elapsed 
287 ·--·1.4703s·elapsed300 ·--·1.47074s·elapsed
288 ·--·1.32323s·elapsed301 ·--·1.92486s·elapsed
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984 B
./usr/share/doc/Macaulay2/Oscillators/example-output/___Example_sp4.2_co_spa_sp__K5_spand_sppentagon_spglued_spalong_span_spedge.out
    
Offset 41, 16 lines modifiedOffset 41, 16 lines modified
41 ·····.954}}41 ·····.954}}
  
42 o5·:·List42 o5·:·List
  
43 i6·:·elapsedTime·stablesolsPent·=·showExoticSolutions·Pent43 i6·:·elapsedTime·stablesolsPent·=·showExoticSolutions·Pent
44 --·warning:·experimental·computation·over·inexact·field·begun44 --·warning:·experimental·computation·over·inexact·field·begun
45 --··········results·not·reliable·(one·warning·given·per·session)45 --··········results·not·reliable·(one·warning·given·per·session)
46 ·--·1.58s·elapsed46 ·--·1.95s·elapsed
47 ·--·1.74s·elapsed47 ·--·2.17s·elapsed
48 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--48 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--
49 ················································1·=>·{0,·2}49 ················································1·=>·{0,·2}
50 ················································2·=>·{1,·3}50 ················································2·=>·{1,·3}
51 ················································3·=>·{2,·4}51 ················································3·=>·{2,·4}
52 ················································4·=>·{0,·3}52 ················································4·=>·{0,·3}
53 +----+-----+-----+----+-----+-----+-----+-----+53 +----+-----+-----+----+-----+-----+-----+-----+
54 |.309|-.809|-.809|.309|.951·|.588·|-.588|-.951|54 |.309|-.809|-.809|.309|.951·|.588·|-.588|-.951|
1.5 KB
./usr/share/doc/Macaulay2/Oscillators/example-output/___S__C__T_spgraphs_spwith_spexotic_spsolutions.out
    
Offset 45, 25 lines modifiedOffset 45, 25 lines modified
45 i5·:·printingPrecision·=·345 i5·:·printingPrecision·=·3
  
46 o5·=·346 o5·=·3
  
47 i6·:·for·G·in·Gs·list·showExoticSolutions·G;47 i6·:·for·G·in·Gs·list·showExoticSolutions·G;
48 --·warning:·experimental·computation·over·inexact·field·begun48 --·warning:·experimental·computation·over·inexact·field·begun
49 --··········results·not·reliable·(one·warning·given·per·session)49 --··········results·not·reliable·(one·warning·given·per·session)
50 ·--·1.32s·elapsed 
51 ·--·1.12s·elapsed 
52 ·--·1.2s·elapsed50 ·--·1.25s·elapsed
53 ·--·1.78s·elapsed51 ·--·1.48s·elapsed
54 ·--·1.88s·elapsed52 ·--·1.38s·elapsed
55 ·--·1.88s·elapsed53 ·--·1.3s·elapsed
56 ·--·3.11s·elapsed 
57 ·--·2.63s·elapsed54 ·--·2.56s·elapsed
58 ·--·2.04s·elapsed 
59 ·--·2.39s·elapsed55 ·--·2.69s·elapsed
 56 ·--·3.33s·elapsed
 57 ·--·1.62s·elapsed
 58 ·--·2.31s·elapsed
 59 ·--·3.09s·elapsed
60 ·--·2.45s·elapsed60 ·--·2.44s·elapsed
61 warning:·some·solutions·are·not·regular:·{37,·38,·40,·41,·42,·43,·44,·45,·46,·48,·50,·52,·53,·54,·55,·59,·60,·64,·65,·68,·69,·70,·71,·72,·73,·75,·76,·77,·78,·79,·81,·83,·85,·86,·87,·88,·89}61 warning:·some·solutions·are·not·regular:·{37,·38,·40,·41,·42,·43,·44,·45,·46,·48,·50,·52,·53,·54,·55,·59,·60,·64,·65,·68,·69,·70,·71,·72,·73,·75,·76,·77,·78,·79,·81,·83,·85,·86,·87,·88,·89}
62 warning:·some·solutions·are·not·regular:·{43,·44,·47,·49,·50,·51,·52,·53,·55,·57,·59,·61,·62,·63,·64,·65,·66,·68,·72,·74,·76,·77,·78,·79,·80,·84,·85,·87,·88,·89,·90,·91,·97}62 warning:·some·solutions·are·not·regular:·{43,·44,·47,·49,·50,·51,·52,·53,·55,·57,·59,·61,·62,·63,·64,·65,·66,·68,·72,·74,·76,·77,·78,·79,·80,·84,·85,·87,·88,·89,·90,·91,·97}
63 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{2,·3}}·--63 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{2,·3}}·--
64 ················································1·=>·{3,·4}64 ················································1·=>·{3,·4}
65 ················································2·=>·{0,·4}65 ················································2·=>·{0,·4}
66 ················································3·=>·{0,·1}66 ················································3·=>·{0,·1}
67 ················································4·=>·{2,·1}67 ················································4·=>·{2,·1}
664 B
./usr/share/doc/Macaulay2/Oscillators/example-output/_get__Linearly__Stable__Solutions.out
    
Offset 1, 15 lines modifiedOffset 1, 15 lines modified
1 --·-*-·M2-comint·-*-·hash:·17293281293469698411 --·-*-·M2-comint·-*-·hash:·1729328129346969841
  
2 i1·:·G·=·graph({0,1,2,3},·{{0,1},{1,2},{2,3},{0,3}});2 i1·:·G·=·graph({0,1,2,3},·{{0,1},{1,2},{2,3},{0,3}});
  
3 i2·:·getLinearlyStableSolutions(G)3 i2·:·getLinearlyStableSolutions(G)
4 --·warning:·experimental·computation·over·inexact·field·begun4 --·warning:·experimental·computation·over·inexact·field·begun
5 --··········results·not·reliable·(one·warning·given·per·session)5 --··········results·not·reliable·(one·warning·given·per·session)
6 ·--·.400525s·elapsed6 ·--·.494423s·elapsed
7 warning:·some·solutions·are·not·regular:·{4,·5,·7,·9,·10,·12,·13,·14,·15,·16,·17,·18,·19,·20,·21}7 warning:·some·solutions·are·not·regular:·{4,·5,·7,·9,·10,·12,·13,·14,·15,·16,·17,·18,·19,·20,·21}
  
8 o2·=·{{1,·1,·1,·0,·0,·0}}8 o2·=·{{1,·1,·1,·0,·0,·0}}
  
9 o2·:·List9 o2·:·List
  
10 i3·:·10 i3·:·
1.09 KB
./usr/share/doc/Macaulay2/Oscillators/example-output/_show__Exotic__Solutions.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 ···········4·=>·{0,·3}9 ···········4·=>·{0,·3}
  
10 o1·:·Graph10 o1·:·Graph
  
11 i2·:·showExoticSolutions·G11 i2·:·showExoticSolutions·G
12 --·warning:·experimental·computation·over·inexact·field·begun12 --·warning:·experimental·computation·over·inexact·field·begun
13 --··········results·not·reliable·(one·warning·given·per·session)13 --··········results·not·reliable·(one·warning·given·per·session)
14 ·--·1.19586s·elapsed14 ·--·1.09354s·elapsed
15 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--15 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--
16 ················································1·=>·{0,·2}16 ················································1·=>·{0,·2}
17 ················································2·=>·{1,·3}17 ················································2·=>·{1,·3}
18 ················································3·=>·{2,·4}18 ················································3·=>·{2,·4}
19 ················································4·=>·{0,·3}19 ················································4·=>·{0,·3}
20 +-------+--------+--------+-------+--------+--------+--------+--------+20 +-------+--------+--------+-------+--------+--------+--------+--------+
21 |.309017|-.809017|-.809017|.309017|.951057·|.587785·|-.587785|-.951057|21 |.309017|-.809017|-.809017|.309017|.951057·|.587785·|-.587785|-.951057|
Offset 50, 14 lines modifiedOffset 50, 14 lines modified
50 ···········2·=>·{1,·3,·4}50 ···········2·=>·{1,·3,·4}
51 ···········3·=>·{2,·4}51 ···········3·=>·{2,·4}
52 ···········4·=>·{0,·2,·3}52 ···········4·=>·{0,·2,·3}
  
53 o3·:·Graph53 o3·:·Graph
  
54 i4·:·showExoticSolutions·G54 i4·:·showExoticSolutions·G
55 ·--·1.40819s·elapsed55 ·--·2.51322s·elapsed
  
56 o4·=·{{1,·1,·1,·1,·0,·0,·0,·0}}56 o4·=·{{1,·1,·1,·1,·0,·0,·0,·0}}
  
57 o4·:·List57 o4·:·List
  
58 i5·:·58 i5·:·
8.44 KB
./usr/share/doc/Macaulay2/Oscillators/html/___Checking_spthe_spcodimension_spand_spirreducible_spdecomposition_spof_spthe_sp__I__G_spideal.html
    
Offset 295, 25 lines modifiedOffset 295, 25 lines modified
295 ··········<tr>295 ··········<tr>
296 ············<td>296 ············<td>
297 ··············<pre><code·class="language-macaulay2">i16·:·for·G·in·Gs·list·(297 ··············<pre><code·class="language-macaulay2">i16·:·for·G·in·Gs·list·(
298 ··········IG·=·oscQuadrics(G,·R);298 ··········IG·=·oscQuadrics(G,·R);
299 ··········elapsedTime·comps·:=·decompose·IG;299 ··········elapsedTime·comps·:=·decompose·IG;
300 ··········{comps/codim,·comps/degree}300 ··········{comps/codim,·comps/degree}
301 ··········);301 ··········);
302 ·--·.850561s·elapsed 
303 ·--·.672463s·elapsed 
304 ·--·1.03111s·elapsed302 ·--·1.00432s·elapsed
305 ·--·.517266s·elapsed 
306 ·--·.599794s·elapsed 
307 ·--·.62642s·elapsed 
308 ·--·1.35892s·elapsed303 ·--·1.04109s·elapsed
309 ·--·1.12385s·elapsed304 ·--·1.47165s·elapsed
 305 ·--·.670675s·elapsed
 306 ·--·.581795s·elapsed
 307 ·--·.787456s·elapsed
 308 ·--·1.26959s·elapsed
 309 ·--·1.47437s·elapsed
 310 ·--·1.44251s·elapsed
310 ·--·1.11318s·elapsed311 ·--·1.15583s·elapsed
311 ·--·.908933s·elapsed 
312 ·--·.624111s·elapsed</code></pre>312 ·--·.728054s·elapsed</code></pre>
313 ············</td>313 ············</td>
314 ··········</tr>314 ··········</tr>
315 ··········<tr>315 ··········<tr>
316 ············<td>316 ············<td>
317 ··············<pre><code·class="language-macaulay2">i17·:·netList·oo317 ··············<pre><code·class="language-macaulay2">i17·:·netList·oo
  
318 ······+---------------+---------------+318 ······+---------------+---------------+
Offset 380, 75 lines modifiedOffset 380, 75 lines modified
380 ··········<tr>380 ··········<tr>
381 ············<td>381 ············<td>
382 ··············<pre><code·class="language-macaulay2">i23·:·allcomps·=·for·G·in·Gs·list·(382 ··············<pre><code·class="language-macaulay2">i23·:·allcomps·=·for·G·in·Gs·list·(
383 ··········IG·=·oscQuadrics(G,·R);383 ··········IG·=·oscQuadrics(G,·R);
384 ··········elapsedTime·comps·:=·decompose·IG;384 ··········elapsedTime·comps·:=·decompose·IG;
385 ··········{comps/codim,·comps/degree}385 ··········{comps/codim,·comps/degree}
386 ··········);386 ··········);
387 ·--·.748348s·elapsed387 ·--·1.43895s·elapsed
388 ·--·1.02351s·elapsed388 ·--·1.8355s·elapsed
 389 ·--·2.97236s·elapsed
 390 ·--·3.03012s·elapsed
 391 ·--·1.75278s·elapsed
 392 ·--·2.29717s·elapsed
 393 ·--·2.36417s·elapsed
 394 ·--·2.41553s·elapsed
 395 ·--·1.61803s·elapsed
 396 ·--·1.67575s·elapsed
 397 ·--·.738311s·elapsed
 398 ·--·1.28289s·elapsed
 399 ·--·1.31437s·elapsed
 400 ·--·1.45899s·elapsed
 401 ·--·1.99364s·elapsed
389 ·--·2.04633s·elapsed402 ·--·2.41637s·elapsed
 403 ·--·2.07293s·elapsed
 404 ·--·2.02884s·elapsed
 405 ·--·2.85907s·elapsed
 406 ·--·2.33118s·elapsed
 407 ·--·1.66412s·elapsed
 408 ·--·2.11513s·elapsed
 409 ·--·2.6471s·elapsed
 410 ·--·2.8118s·elapsed
 411 ·--·1.14673s·elapsed
 412 ·--·1.4133s·elapsed
 413 ·--·3.11933s·elapsed
 414 ·--·1.52453s·elapsed
 415 ·--·1.35823s·elapsed
 416 ·--·2.47741s·elapsed
 417 ·--·2.34183s·elapsed
 418 ·--·1.95295s·elapsed
 419 ·--·1.33409s·elapsed
 420 ·--·2.04954s·elapsed
 421 ·--·1.37113s·elapsed
 422 ·--·2.3776s·elapsed
 423 ·--·1.68497s·elapsed
 424 ·--·1.87367s·elapsed
 425 ·--·2.44172s·elapsed
 426 ·--·1.5063s·elapsed
 427 ·--·1.47397s·elapsed
 428 ·--·2.32976s·elapsed
 429 ·--·2.83499s·elapsed
 430 ·--·3.31741s·elapsed
 431 ·--·2.47836s·elapsed
 432 ·--·1.9358s·elapsed
 433 ·--·2.00411s·elapsed
 434 ·--·2.62136s·elapsed
 435 ·--·2.28741s·elapsed
 436 ·--·2.52702s·elapsed
390 ·--·2.62883s·elapsed437 ·--·2.65288s·elapsed
391 ·--·1.29166s·elapsed 
392 ·--·1.86117s·elapsed 
393 ·--·2.15933s·elapsed 
394 ·--·2.02516s·elapsed 
395 ·--·1.22886s·elapsed 
396 ·--·1.00474s·elapsed 
397 ·--·.444663s·elapsed 
398 ·--·.583647s·elapsed 
399 ·--·.504881s·elapsed 
400 ·--·.699276s·elapsed 
401 ·--·.916662s·elapsed 
402 ·--·1.10234s·elapsed 
403 ·--·.846727s·elapsed 
404 ·--·.80879s·elapsed 
405 ·--·1.07314s·elapsed 
406 ·--·1.16764s·elapsed 
407 ·--·1.58771s·elapsed 
408 ·--·1.68781s·elapsed 
409 ·--·2.08282s·elapsed 
410 ·--·2.46889s·elapsed 
411 ·--·1.02719s·elapsed 
412 ·--·1.45656s·elapsed 
413 ·--·2.79411s·elapsed 
414 ·--·1.4512s·elapsed438 ·--·1.65502s·elapsed
415 ·--·.990204s·elapsed 
416 ·--·1.64138s·elapsed 
417 ·--·2.20034s·elapsed 
418 ·--·1.89725s·elapsed 
419 ·--·1.06631s·elapsed 
420 ·--·1.98299s·elapsed 
421 ·--·1.53379s·elapsed 
422 ·--·2.19289s·elapsed 
423 ·--·1.71743s·elapsed 
424 ·--·2.39891s·elapsed 
425 ·--·2.55446s·elapsed 
426 ·--·1.4703s·elapsed439 ·--·1.47074s·elapsed
427 ·--·1.32323s·elapsed440 ·--·1.92486s·elapsed
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html2text {}
    
Offset 180, 25 lines modifiedOffset 180, 25 lines modified
  
180 o15·=·4180 o15·=·4
181 i16·:·for·G·in·Gs·list·(181 i16·:·for·G·in·Gs·list·(
182 ··········IG·=·oscQuadrics(G,·R);182 ··········IG·=·oscQuadrics(G,·R);
183 ··········elapsedTime·comps·:=·decompose·IG;183 ··········elapsedTime·comps·:=·decompose·IG;
184 ··········{comps/codim,·comps/degree}184 ··········{comps/codim,·comps/degree}
185 ··········);185 ··········);
186 ·--·.850561s·elapsed 
187 ·--·.672463s·elapsed 
188 ·--·1.03111s·elapsed186 ·--·1.00432s·elapsed
189 ·--·.517266s·elapsed 
190 ·--·.599794s·elapsed 
191 ·--·.62642s·elapsed 
192 ·--·1.35892s·elapsed187 ·--·1.04109s·elapsed
193 ·--·1.12385s·elapsed188 ·--·1.47165s·elapsed
 189 ·--·.670675s·elapsed
 190 ·--·.581795s·elapsed
 191 ·--·.787456s·elapsed
 192 ·--·1.26959s·elapsed
 193 ·--·1.47437s·elapsed
 194 ·--·1.44251s·elapsed
194 ·--·1.11318s·elapsed195 ·--·1.15583s·elapsed
195 ·--·.908933s·elapsed 
196 ·--·.624111s·elapsed196 ·--·.728054s·elapsed
197 i17·:·netList·oo197 i17·:·netList·oo
  
198 ······+---------------+---------------+198 ······+---------------+---------------+
199 o17·=·|{3,·4,·4}······|{2,·3,·5}······|199 o17·=·|{3,·4,·4}······|{2,·3,·5}······|
200 ······+---------------+---------------+200 ······+---------------+---------------+
201 ······|{3,·4,·4}······|{2,·3,·5}······|201 ······|{3,·4,·4}······|{2,·3,·5}······|
202 ······+---------------+---------------+202 ······+---------------+---------------+
Offset 233, 75 lines modifiedOffset 233, 75 lines modified
  
233 o22·=·15233 o22·=·15
234 i23·:·allcomps·=·for·G·in·Gs·list·(234 i23·:·allcomps·=·for·G·in·Gs·list·(
235 ··········IG·=·oscQuadrics(G,·R);235 ··········IG·=·oscQuadrics(G,·R);
236 ··········elapsedTime·comps·:=·decompose·IG;236 ··········elapsedTime·comps·:=·decompose·IG;
237 ··········{comps/codim,·comps/degree}237 ··········{comps/codim,·comps/degree}
238 ··········);238 ··········);
239 ·--·.748348s·elapsed239 ·--·1.43895s·elapsed
240 ·--·1.02351s·elapsed240 ·--·1.8355s·elapsed
 241 ·--·2.97236s·elapsed
 242 ·--·3.03012s·elapsed
 243 ·--·1.75278s·elapsed
 244 ·--·2.29717s·elapsed
 245 ·--·2.36417s·elapsed
 246 ·--·2.41553s·elapsed
 247 ·--·1.61803s·elapsed
 248 ·--·1.67575s·elapsed
 249 ·--·.738311s·elapsed
 250 ·--·1.28289s·elapsed
 251 ·--·1.31437s·elapsed
 252 ·--·1.45899s·elapsed
 253 ·--·1.99364s·elapsed
241 ·--·2.04633s·elapsed254 ·--·2.41637s·elapsed
 255 ·--·2.07293s·elapsed
 256 ·--·2.02884s·elapsed
 257 ·--·2.85907s·elapsed
 258 ·--·2.33118s·elapsed
 259 ·--·1.66412s·elapsed
 260 ·--·2.11513s·elapsed
 261 ·--·2.6471s·elapsed
 262 ·--·2.8118s·elapsed
 263 ·--·1.14673s·elapsed
 264 ·--·1.4133s·elapsed
 265 ·--·3.11933s·elapsed
 266 ·--·1.52453s·elapsed
 267 ·--·1.35823s·elapsed
 268 ·--·2.47741s·elapsed
 269 ·--·2.34183s·elapsed
 270 ·--·1.95295s·elapsed
 271 ·--·1.33409s·elapsed
 272 ·--·2.04954s·elapsed
 273 ·--·1.37113s·elapsed
 274 ·--·2.3776s·elapsed
 275 ·--·1.68497s·elapsed
 276 ·--·1.87367s·elapsed
 277 ·--·2.44172s·elapsed
 278 ·--·1.5063s·elapsed
 279 ·--·1.47397s·elapsed
 280 ·--·2.32976s·elapsed
 281 ·--·2.83499s·elapsed
 282 ·--·3.31741s·elapsed
 283 ·--·2.47836s·elapsed
 284 ·--·1.9358s·elapsed
 285 ·--·2.00411s·elapsed
 286 ·--·2.62136s·elapsed
 287 ·--·2.28741s·elapsed
 288 ·--·2.52702s·elapsed
242 ·--·2.62883s·elapsed289 ·--·2.65288s·elapsed
243 ·--·1.29166s·elapsed 
244 ·--·1.86117s·elapsed 
245 ·--·2.15933s·elapsed 
246 ·--·2.02516s·elapsed 
247 ·--·1.22886s·elapsed 
248 ·--·1.00474s·elapsed 
249 ·--·.444663s·elapsed 
250 ·--·.583647s·elapsed 
251 ·--·.504881s·elapsed 
252 ·--·.699276s·elapsed 
253 ·--·.916662s·elapsed 
254 ·--·1.10234s·elapsed 
255 ·--·.846727s·elapsed 
256 ·--·.80879s·elapsed 
257 ·--·1.07314s·elapsed 
258 ·--·1.16764s·elapsed 
259 ·--·1.58771s·elapsed 
260 ·--·1.68781s·elapsed 
261 ·--·2.08282s·elapsed 
262 ·--·2.46889s·elapsed 
263 ·--·1.02719s·elapsed 
264 ·--·1.45656s·elapsed 
265 ·--·2.79411s·elapsed 
266 ·--·1.4512s·elapsed290 ·--·1.65502s·elapsed
267 ·--·.990204s·elapsed 
268 ·--·1.64138s·elapsed 
269 ·--·2.20034s·elapsed 
270 ·--·1.89725s·elapsed 
271 ·--·1.06631s·elapsed 
272 ·--·1.98299s·elapsed 
273 ·--·1.53379s·elapsed 
274 ·--·2.19289s·elapsed 
275 ·--·1.71743s·elapsed 
276 ·--·2.39891s·elapsed 
277 ·--·2.55446s·elapsed 
278 ·--·1.4703s·elapsed291 ·--·1.47074s·elapsed
279 ·--·1.32323s·elapsed292 ·--·1.92486s·elapsed
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112 ············</td>112 ············</td>
113 ··········</tr>113 ··········</tr>
114 ··········<tr>114 ··········<tr>
115 ············<td>115 ············<td>
116 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·stablesolsPent·=·showExoticSolutions·Pent116 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·stablesolsPent·=·showExoticSolutions·Pent
117 --·warning:·experimental·computation·over·inexact·field·begun117 --·warning:·experimental·computation·over·inexact·field·begun
118 --··········results·not·reliable·(one·warning·given·per·session)118 --··········results·not·reliable·(one·warning·given·per·session)
119 ·--·1.58s·elapsed119 ·--·1.95s·elapsed
120 ·--·1.74s·elapsed120 ·--·2.17s·elapsed
121 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--121 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--
122 ················································1·=>·{0,·2}122 ················································1·=>·{0,·2}
123 ················································2·=>·{1,·3}123 ················································2·=>·{1,·3}
124 ················································3·=>·{2,·4}124 ················································3·=>·{2,·4}
125 ················································4·=>·{0,·3}125 ················································4·=>·{0,·3}
126 +----+-----+-----+----+-----+-----+-----+-----+126 +----+-----+-----+----+-----+-----+-----+-----+
127 |.309|-.809|-.809|.309|.951·|.588·|-.588|-.951|127 |.309|-.809|-.809|.309|.951·|.588·|-.588|-.951|
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45 ·····------------------------------------------------------------------------45 ·····------------------------------------------------------------------------
46 ·····.954}}46 ·····.954}}
  
47 o5·:·List47 o5·:·List
48 i6·:·elapsedTime·stablesolsPent·=·showExoticSolutions·Pent48 i6·:·elapsedTime·stablesolsPent·=·showExoticSolutions·Pent
49 --·warning:·experimental·computation·over·inexact·field·begun49 --·warning:·experimental·computation·over·inexact·field·begun
50 --··········results·not·reliable·(one·warning·given·per·session)50 --··········results·not·reliable·(one·warning·given·per·session)
51 ·--·1.58s·elapsed51 ·--·1.95s·elapsed
52 ·--·1.74s·elapsed52 ·--·2.17s·elapsed
53 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--53 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--
54 ················································1·=>·{0,·2}54 ················································1·=>·{0,·2}
55 ················································2·=>·{1,·3}55 ················································2·=>·{1,·3}
56 ················································3·=>·{2,·4}56 ················································3·=>·{2,·4}
57 ················································4·=>·{0,·3}57 ················································4·=>·{0,·3}
58 +----+-----+-----+----+-----+-----+-----+-----+58 +----+-----+-----+----+-----+-----+-----+-----+
59 |.309|-.809|-.809|.309|.951·|.588·|-.588|-.951|59 |.309|-.809|-.809|.309|.951·|.588·|-.588|-.951|
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116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ··········<tr>118 ··········<tr>
119 ············<td>119 ············<td>
120 ··············<pre><code·class="language-macaulay2">i6·:·for·G·in·Gs·list·showExoticSolutions·G;120 ··············<pre><code·class="language-macaulay2">i6·:·for·G·in·Gs·list·showExoticSolutions·G;
121 --·warning:·experimental·computation·over·inexact·field·begun121 --·warning:·experimental·computation·over·inexact·field·begun
122 --··········results·not·reliable·(one·warning·given·per·session)122 --··········results·not·reliable·(one·warning·given·per·session)
123 ·--·1.32s·elapsed 
124 ·--·1.12s·elapsed 
125 ·--·1.2s·elapsed123 ·--·1.25s·elapsed
126 ·--·1.78s·elapsed124 ·--·1.48s·elapsed
127 ·--·1.88s·elapsed125 ·--·1.38s·elapsed
128 ·--·1.88s·elapsed126 ·--·1.3s·elapsed
129 ·--·3.11s·elapsed 
130 ·--·2.63s·elapsed127 ·--·2.56s·elapsed
131 ·--·2.04s·elapsed 
132 ·--·2.39s·elapsed128 ·--·2.69s·elapsed
 129 ·--·3.33s·elapsed
 130 ·--·1.62s·elapsed
 131 ·--·2.31s·elapsed
 132 ·--·3.09s·elapsed
133 ·--·2.45s·elapsed133 ·--·2.44s·elapsed
134 warning:·some·solutions·are·not·regular:·{37,·38,·40,·41,·42,·43,·44,·45,·46,·48,·50,·52,·53,·54,·55,·59,·60,·64,·65,·68,·69,·70,·71,·72,·73,·75,·76,·77,·78,·79,·81,·83,·85,·86,·87,·88,·89}134 warning:·some·solutions·are·not·regular:·{37,·38,·40,·41,·42,·43,·44,·45,·46,·48,·50,·52,·53,·54,·55,·59,·60,·64,·65,·68,·69,·70,·71,·72,·73,·75,·76,·77,·78,·79,·81,·83,·85,·86,·87,·88,·89}
135 warning:·some·solutions·are·not·regular:·{43,·44,·47,·49,·50,·51,·52,·53,·55,·57,·59,·61,·62,·63,·64,·65,·66,·68,·72,·74,·76,·77,·78,·79,·80,·84,·85,·87,·88,·89,·90,·91,·97}135 warning:·some·solutions·are·not·regular:·{43,·44,·47,·49,·50,·51,·52,·53,·55,·57,·59,·61,·62,·63,·64,·65,·66,·68,·72,·74,·76,·77,·78,·79,·80,·84,·85,·87,·88,·89,·90,·91,·97}
136 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{2,·3}}·--136 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{2,·3}}·--
137 ················································1·=>·{3,·4}137 ················································1·=>·{3,·4}
138 ················································2·=>·{0,·4}138 ················································2·=>·{0,·4}
139 ················································3·=>·{0,·1}139 ················································3·=>·{0,·1}
140 ················································4·=>·{2,·1}140 ················································4·=>·{2,·1}
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47 o4·:·List47 o4·:·List
48 i5·:·printingPrecision·=·348 i5·:·printingPrecision·=·3
  
49 o5·=·349 o5·=·3
50 i6·:·for·G·in·Gs·list·showExoticSolutions·G;50 i6·:·for·G·in·Gs·list·showExoticSolutions·G;
51 --·warning:·experimental·computation·over·inexact·field·begun51 --·warning:·experimental·computation·over·inexact·field·begun
52 --··········results·not·reliable·(one·warning·given·per·session)52 --··········results·not·reliable·(one·warning·given·per·session)
53 ·--·1.32s·elapsed 
54 ·--·1.12s·elapsed 
55 ·--·1.2s·elapsed53 ·--·1.25s·elapsed
56 ·--·1.78s·elapsed54 ·--·1.48s·elapsed
57 ·--·1.88s·elapsed55 ·--·1.38s·elapsed
58 ·--·1.88s·elapsed56 ·--·1.3s·elapsed
59 ·--·3.11s·elapsed 
60 ·--·2.63s·elapsed57 ·--·2.56s·elapsed
61 ·--·2.04s·elapsed 
62 ·--·2.39s·elapsed58 ·--·2.69s·elapsed
 59 ·--·3.33s·elapsed
 60 ·--·1.62s·elapsed
 61 ·--·2.31s·elapsed
 62 ·--·3.09s·elapsed
63 ·--·2.45s·elapsed63 ·--·2.44s·elapsed
64 warning:·some·solutions·are·not·regular:·{37,·38,·40,·41,·42,·43,·44,·45,·46,64 warning:·some·solutions·are·not·regular:·{37,·38,·40,·41,·42,·43,·44,·45,·46,
65 48,·50,·52,·53,·54,·55,·59,·60,·64,·65,·68,·69,·70,·71,·72,·73,·75,·76,·77,·78,65 48,·50,·52,·53,·54,·55,·59,·60,·64,·65,·68,·69,·70,·71,·72,·73,·75,·76,·77,·78,
66 79,·81,·83,·85,·86,·87,·88,·89}66 79,·81,·83,·85,·86,·87,·88,·89}
67 warning:·some·solutions·are·not·regular:·{43,·44,·47,·49,·50,·51,·52,·53,·55,67 warning:·some·solutions·are·not·regular:·{43,·44,·47,·49,·50,·51,·52,·53,·55,
68 57,·59,·61,·62,·63,·64,·65,·66,·68,·72,·74,·76,·77,·78,·79,·80,·84,·85,·87,·88,68 57,·59,·61,·62,·63,·64,·65,·66,·68,·72,·74,·76,·77,·78,·79,·80,·84,·85,·87,·88,
69 89,·90,·91,·97}69 89,·90,·91,·97}
70 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{2,·3}}·--70 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{2,·3}}·--
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77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i2·:·getLinearlyStableSolutions(G)81 ··············<pre><code·class="language-macaulay2">i2·:·getLinearlyStableSolutions(G)
82 --·warning:·experimental·computation·over·inexact·field·begun82 --·warning:·experimental·computation·over·inexact·field·begun
83 --··········results·not·reliable·(one·warning·given·per·session)83 --··········results·not·reliable·(one·warning·given·per·session)
84 ·--·.400525s·elapsed84 ·--·.494423s·elapsed
85 warning:·some·solutions·are·not·regular:·{4,·5,·7,·9,·10,·12,·13,·14,·15,·16,·17,·18,·19,·20,·21}85 warning:·some·solutions·are·not·regular:·{4,·5,·7,·9,·10,·12,·13,·14,·15,·16,·17,·18,·19,·20,·21}
  
86 o2·=·{{1,·1,·1,·0,·0,·0}}86 o2·=·{{1,·1,·1,·0,·0,·0}}
  
87 o2·:·List</code></pre>87 o2·:·List</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
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19 of·each·oscillator·is·given·by·the·Kuramoto·model.·The·linear·stability·of·a19 of·each·oscillator·is·given·by·the·Kuramoto·model.·The·linear·stability·of·a
20 solution·is·determined·by·the·eigenvalues·of·the·Jacobian·matrix·of·the·system20 solution·is·determined·by·the·eigenvalues·of·the·Jacobian·matrix·of·the·system
21 evaluated·at·the·solution.21 evaluated·at·the·solution.
22 i1·:·G·=·graph({0,1,2,3},·{{0,1},{1,2},{2,3},{0,3}});22 i1·:·G·=·graph({0,1,2,3},·{{0,1},{1,2},{2,3},{0,3}});
23 i2·:·getLinearlyStableSolutions(G)23 i2·:·getLinearlyStableSolutions(G)
24 --·warning:·experimental·computation·over·inexact·field·begun24 --·warning:·experimental·computation·over·inexact·field·begun
25 --··········results·not·reliable·(one·warning·given·per·session)25 --··········results·not·reliable·(one·warning·given·per·session)
26 ·--·.400525s·elapsed26 ·--·.494423s·elapsed
27 warning:·some·solutions·are·not·regular:·{4,·5,·7,·9,·10,·12,·13,·14,·15,·16,27 warning:·some·solutions·are·not·regular:·{4,·5,·7,·9,·10,·12,·13,·14,·15,·16,
28 17,·18,·19,·20,·21}28 17,·18,·19,·20,·21}
  
29 o2·=·{{1,·1,·1,·0,·0,·0}}29 o2·=·{{1,·1,·1,·0,·0,·0}}
  
30 o2·:·List30 o2·:·List
31 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*31 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
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95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i2·:·showExoticSolutions·G99 ··············<pre><code·class="language-macaulay2">i2·:·showExoticSolutions·G
100 --·warning:·experimental·computation·over·inexact·field·begun100 --·warning:·experimental·computation·over·inexact·field·begun
101 --··········results·not·reliable·(one·warning·given·per·session)101 --··········results·not·reliable·(one·warning·given·per·session)
102 ·--·1.19586s·elapsed102 ·--·1.09354s·elapsed
103 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--103 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--
104 ················································1·=>·{0,·2}104 ················································1·=>·{0,·2}
105 ················································2·=>·{1,·3}105 ················································2·=>·{1,·3}
106 ················································3·=>·{2,·4}106 ················································3·=>·{2,·4}
107 ················································4·=>·{0,·3}107 ················································4·=>·{0,·3}
108 +-------+--------+--------+-------+--------+--------+--------+--------+108 +-------+--------+--------+-------+--------+--------+--------+--------+
109 |.309017|-.809017|-.809017|.309017|.951057·|.587785·|-.587785|-.951057|109 |.309017|-.809017|-.809017|.309017|.951057·|.587785·|-.587785|-.951057|
Offset 147, 15 lines modifiedOffset 147, 15 lines modified
  
147 o3·:·Graph</code></pre>147 o3·:·Graph</code></pre>
148 ············</td>148 ············</td>
149 ··········</tr>149 ··········</tr>
150 ··········<tr>150 ··········<tr>
151 ············<td>151 ············<td>
152 ··············<pre><code·class="language-macaulay2">i4·:·showExoticSolutions·G152 ··············<pre><code·class="language-macaulay2">i4·:·showExoticSolutions·G
153 ·--·1.40819s·elapsed153 ·--·2.51322s·elapsed
  
154 o4·=·{{1,·1,·1,·1,·0,·0,·0,·0}}154 o4·=·{{1,·1,·1,·1,·0,·0,·0,·0}}
  
155 o4·:·List</code></pre>155 o4·:·List</code></pre>
156 ············</td>156 ············</td>
157 ··········</tr>157 ··········</tr>
158 ········</table>158 ········</table>
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36 ···········3·=>·{2,·4}36 ···········3·=>·{2,·4}
37 ···········4·=>·{0,·3}37 ···········4·=>·{0,·3}
  
38 o1·:·Graph38 o1·:·Graph
39 i2·:·showExoticSolutions·G39 i2·:·showExoticSolutions·G
40 --·warning:·experimental·computation·over·inexact·field·begun40 --·warning:·experimental·computation·over·inexact·field·begun
41 --··········results·not·reliable·(one·warning·given·per·session)41 --··········results·not·reliable·(one·warning·given·per·session)
42 ·--·1.19586s·elapsed42 ·--·1.09354s·elapsed
43 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--43 --·found·extra·exotic·solutions·for·graph·Graph{0·=>·{1,·4}}·--
44 ················································1·=>·{0,·2}44 ················································1·=>·{0,·2}
45 ················································2·=>·{1,·3}45 ················································2·=>·{1,·3}
46 ················································3·=>·{2,·4}46 ················································3·=>·{2,·4}
47 ················································4·=>·{0,·3}47 ················································4·=>·{0,·3}
48 +-------+--------+--------+-------+--------+--------+--------+--------+48 +-------+--------+--------+-------+--------+--------+--------+--------+
49 |.309017|-.809017|-.809017|.309017|.951057·|.587785·|-.587785|-.951057|49 |.309017|-.809017|-.809017|.309017|.951057·|.587785·|-.587785|-.951057|
Offset 78, 15 lines modifiedOffset 78, 15 lines modified
78 ···········1·=>·{0,·2}78 ···········1·=>·{0,·2}
79 ···········2·=>·{1,·3,·4}79 ···········2·=>·{1,·3,·4}
80 ···········3·=>·{2,·4}80 ···········3·=>·{2,·4}
81 ···········4·=>·{0,·2,·3}81 ···········4·=>·{0,·2,·3}
  
82 o3·:·Graph82 o3·:·Graph
83 i4·:·showExoticSolutions·G83 i4·:·showExoticSolutions·G
84 ·--·1.40819s·elapsed84 ·--·2.51322s·elapsed
  
85 o4·=·{{1,·1,·1,·1,·0,·0,·0,·0}}85 o4·=·{{1,·1,·1,·1,·0,·0,·0,·0}}
  
86 o4·:·List86 o4·:·List
87 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*87 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
88 ····*·_\x8g_\x8e_\x8t_\x8L_\x8i_\x8n_\x8e_\x8a_\x8r_\x8l_\x8y_\x8S_\x8t_\x8a_\x8b_\x8l_\x8e_\x8S_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·linearly·stable·solutions·for·the88 ····*·_\x8g_\x8e_\x8t_\x8L_\x8i_\x8n_\x8e_\x8a_\x8r_\x8l_\x8y_\x8S_\x8t_\x8a_\x8b_\x8l_\x8e_\x8S_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·linearly·stable·solutions·for·the
89 ······Kuramoto·oscillator·system·associated·to·a·graph89 ······Kuramoto·oscillator·system·associated·to·a·graph
747 B
./usr/share/doc/Macaulay2/PHCpack/dump/rawdocumentation.dump
    
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9 #:len=5959 #:len=595
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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735 B
./usr/share/doc/Macaulay2/PackageTemplate/dump/rawdocumentation.dump
    
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2 #:version=1.12 #:version=1.1
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6 #·End·of·header6 #·End·of·header
7 #:len=147 #:len=14
8 c2Vjb25kRnVuY3Rpb24=8 c2Vjb25kRnVuY3Rpb24=
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11 LCBEZXNjcmlwdGlvbiA9PiAoIlRoaXMgZnVuY3Rpb24gaXMgcHJvdmlkZWQgYnkgdGhlIHBhY2th11 LCBEZXNjcmlwdGlvbiA9PiAoIlRoaXMgZnVuY3Rpb24gaXMgcHJvdmlkZWQgYnkgdGhlIHBhY2th
740 B
./usr/share/doc/Macaulay2/Parametrization/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=167 #:len=16
8 cGFyYW1ldHJpemVDb25pYw==8 cGFyYW1ldHJpemVDb25pYw==
9 #:len=19049 #:len=1904
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3B0aW9uIHdoZXRoZXIgdG8gcmF0aW9u10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3B0aW9uIHdoZXRoZXIgdG8gcmF0aW9u
11 YWxseSBwYXJhbWV0cml6ZSBjb25pY3MuIiwgImxpbmVudW0iID0+IDE2NzYsICJmaWxlbmFtZSIg11 YWxseSBwYXJhbWV0cml6ZSBjb25pY3MuIiwgImxpbmVudW0iID0+IDE2NzYsICJmaWxlbmFtZSIg
715 B
./usr/share/doc/Macaulay2/Parsing/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=127 #:len=12
8 Y2hhckFuYWx5emVy8 Y2hhckFuYWx5emVy
9 #:len=7529 #:len=752
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBsZXhpY2FsIGFuYWx5emVyIHRoYXQg10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBsZXhpY2FsIGFuYWx5emVyIHRoYXQg
11 cHJvdmlkZXMgY2hhcmFjdGVycyBmcm9tIGEgc3RyaW5nIG9uZSBhdCBhIHRpbWUiLCAibGluZW5111 cHJvdmlkZXMgY2hhcmFjdGVycyBmcm9tIGEgc3RyaW5nIG9uZSBhdCBhIHRpbWUiLCAibGluZW51
759 B
./usr/share/doc/Macaulay2/PencilsOfQuadrics/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=307 #:len=30
8 cmFuZG9tRXh0ZW5zaW9uKE1hdHJpeCxNYXRyaXgp8 cmFuZG9tRXh0ZW5zaW9uKE1hdHJpeCxNYXRyaXgp
9 #:len=3019 #:len=301
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzE5NSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzE5NSwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmFuZG9tRXh0ZW5zaW9uLE1hdHJpeCxNYXRyaXgp11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmFuZG9tRXh0ZW5zaW9uLE1hdHJpeCxNYXRyaXgp
1.35 KB
./usr/share/doc/Macaulay2/PencilsOfQuadrics/example-output/___Lab__Book__Protocol.out
    
Offset 41, 15 lines modifiedOffset 41, 15 lines modified
41 i3·:·g=341 i3·:·g=3
  
42 o3·=·342 o3·=·3
  
43 i4·:·kk=·ZZ/101;43 i4·:·kk=·ZZ/101;
  
44 i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g);44 i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g);
45 ·--·1.47926s·elapsed45 ·--·2.7899s·elapsed
  
46 i6·:·M=cliffordModule(Mu1,Mu2,R)46 i6·:·M=cliffordModule(Mu1,Mu2,R)
  
47 o6·=·CliffordModule{...6...}47 o6·=·CliffordModule{...6...}
  
48 o6·:·CliffordModule48 o6·:·CliffordModule
  
Offset 67, 30 lines modifiedOffset 67, 30 lines modified
67 ··········m12=randomExtension(m1.yAction,m2.yAction);67 ··········m12=randomExtension(m1.yAction,m2.yAction);
68 ··········V·=·vectorBundleOnE·m12;68 ··········V·=·vectorBundleOnE·m12;
69 ··········Ul=tensorProduct(Mor,V);69 ··········Ul=tensorProduct(Mor,V);
70 ··········Ul1=tensorProduct(Mor1,V);70 ··········Ul1=tensorProduct(Mor1,V);
71 ··········d0=unique·degrees·target·Ul.yAction;71 ··········d0=unique·degrees·target·Ul.yAction;
72 ··········d1=unique·degrees·target·Ul1.yAction;72 ··········d1=unique·degrees·target·Ul1.yAction;
73 ··········#d1·>=3·or·#d0·>=3)·do·();73 ··········#d1·>=3·or·#d0·>=3)·do·();
74 ·--·.431474s·elapsed74 ·--·1.19124s·elapsed
  
75 i12·:·betti·Ul.yAction,·betti·Ul1.yAction75 i12·:·betti·Ul.yAction,·betti·Ul1.yAction
  
76 ···············0··1··········0··176 ···············0··1··········0··1
77 o12·=·(total:·32·32,·total:·32·32)77 o12·=·(total:·32·32,·total:·32·32)
78 ··········-4:·16··.·····-2:·32··.78 ··········-4:·16··.·····-2:·32··.
79 ··········-3:·16··.·····-1:··.··.79 ··········-3:·16··.·····-1:··.··.
80 ··········-2:··.··.······0:··.··.80 ··········-2:··.··.······0:··.··.
81 ··········-1:··.·16······1:··.·3281 ··········-1:··.·16······1:··.·32
82 ···········0:··.·1682 ···········0:··.·16
  
83 o12·:·Sequence83 o12·:·Sequence
  
84 i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators84 i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators
85 ·--·25.9412s·elapsed85 ·--·34.8478s·elapsed
  
86 i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S));86 i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S));
  
87 ··············32······3287 ··············32······32
88 o14·:·Matrix·S···<--·S88 o14·:·Matrix·S···<--·S
  
89 i15·:·r=289 i15·:·r=2
721 B
./usr/share/doc/Macaulay2/PencilsOfQuadrics/example-output/_search__Ulrich.out
    
Offset 46, 30 lines modifiedOffset 46, 30 lines modified
46 i11·:·M=cliffordModule(Mu1,Mu2,R)46 i11·:·M=cliffordModule(Mu1,Mu2,R)
  
47 o11·=·CliffordModule{...6...}47 o11·=·CliffordModule{...6...}
  
48 o11·:·CliffordModule48 o11·:·CliffordModule
  
49 i12·:·elapsedTime·Ulr·=·searchUlrich(M,S);49 i12·:·elapsedTime·Ulr·=·searchUlrich(M,S);
50 ·--·.732068s·elapsed50 ·--·1.72442s·elapsed
  
51 i13·:·betti·freeResolution·Ulr51 i13·:·betti·freeResolution·Ulr
  
52 ·············0··1·252 ·············0··1·2
53 o13·=·total:·8·16·853 o13·=·total:·8·16·8
54 ··········0:·8·16·854 ··········0:·8·16·8
  
55 o13·:·BettiTally55 o13·:·BettiTally
  
56 i14·:·ann·Ulr·==·ideal·qs56 i14·:·ann·Ulr·==·ideal·qs
  
57 o14·=·true57 o14·=·true
  
58 i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3);58 i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3);
59 ·--·2.37398s·elapsed59 ·--·3.21688s·elapsed
  
60 i16·:·betti·freeResolution·Ulr360 i16·:·betti·freeResolution·Ulr3
  
61 ··············0··1··261 ··············0··1··2
62 o16·=·total:·12·24·1262 o16·=·total:·12·24·12
63 ··········0:·12·24·1263 ··········0:·12·24·12
  
3.2 KB
./usr/share/doc/Macaulay2/PencilsOfQuadrics/html/___Lab__Book__Protocol.html
    
Offset 128, 15 lines modifiedOffset 128, 15 lines modified
128 ············<td>128 ············<td>
129 ··············<pre><code·class="language-macaulay2">i4·:·kk=·ZZ/101;</code></pre>129 ··············<pre><code·class="language-macaulay2">i4·:·kk=·ZZ/101;</code></pre>
130 ············</td>130 ············</td>
131 ··········</tr>131 ··········</tr>
132 ··········<tr>132 ··········<tr>
133 ············<td>133 ············<td>
134 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g);134 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g);
135 ·--·1.47926s·elapsed</code></pre>135 ·--·2.7899s·elapsed</code></pre>
136 ············</td>136 ············</td>
137 ··········</tr>137 ··········</tr>
138 ··········<tr>138 ··········<tr>
139 ············<td>139 ············<td>
140 ··············<pre><code·class="language-macaulay2">i6·:·M=cliffordModule(Mu1,Mu2,R)140 ··············<pre><code·class="language-macaulay2">i6·:·M=cliffordModule(Mu1,Mu2,R)
  
141 o6·=·CliffordModule{...6...}141 o6·=·CliffordModule{...6...}
Offset 172, 15 lines modifiedOffset 172, 15 lines modified
172 ··········m12=randomExtension(m1.yAction,m2.yAction);172 ··········m12=randomExtension(m1.yAction,m2.yAction);
173 ··········V·=·vectorBundleOnE·m12;173 ··········V·=·vectorBundleOnE·m12;
174 ··········Ul=tensorProduct(Mor,V);174 ··········Ul=tensorProduct(Mor,V);
175 ··········Ul1=tensorProduct(Mor1,V);175 ··········Ul1=tensorProduct(Mor1,V);
176 ··········d0=unique·degrees·target·Ul.yAction;176 ··········d0=unique·degrees·target·Ul.yAction;
177 ··········d1=unique·degrees·target·Ul1.yAction;177 ··········d1=unique·degrees·target·Ul1.yAction;
178 ··········#d1·>=3·or·#d0·>=3)·do·();178 ··········#d1·>=3·or·#d0·>=3)·do·();
179 ·--·.431474s·elapsed</code></pre>179 ·--·1.19124s·elapsed</code></pre>
180 ············</td>180 ············</td>
181 ··········</tr>181 ··········</tr>
182 ··········<tr>182 ··········<tr>
183 ············<td>183 ············<td>
184 ··············<pre><code·class="language-macaulay2">i12·:·betti·Ul.yAction,·betti·Ul1.yAction184 ··············<pre><code·class="language-macaulay2">i12·:·betti·Ul.yAction,·betti·Ul1.yAction
  
185 ···············0··1··········0··1185 ···············0··1··········0··1
Offset 193, 15 lines modifiedOffset 193, 15 lines modified
  
193 o12·:·Sequence</code></pre>193 o12·:·Sequence</code></pre>
194 ············</td>194 ············</td>
195 ··········</tr>195 ··········</tr>
196 ··········<tr>196 ··········<tr>
197 ············<td>197 ············<td>
198 ··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators198 ··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators
199 ·--·25.9412s·elapsed</code></pre>199 ·--·34.8478s·elapsed</code></pre>
200 ············</td>200 ············</td>
201 ··········</tr>201 ··········</tr>
202 ··········<tr>202 ··········<tr>
203 ············<td>203 ············<td>
204 ··············<pre><code·class="language-macaulay2">i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S));204 ··············<pre><code·class="language-macaulay2">i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S));
  
205 ··············32······32205 ··············32······32
1.37 KB
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Offset 55, 15 lines modifiedOffset 55, 15 lines modified
55 ············--·will·give·an·Ulrich·bundle,·with·betti·table55 ············--·will·give·an·Ulrich·bundle,·with·betti·table
56 ············--·16·32·1656 ············--·16·32·16
57 i3·:·g=357 i3·:·g=3
  
58 o3·=·358 o3·=·3
59 i4·:·kk=·ZZ/101;59 i4·:·kk=·ZZ/101;
60 i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g);60 i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g);
61 ·--·1.47926s·elapsed61 ·--·2.7899s·elapsed
62 i6·:·M=cliffordModule(Mu1,Mu2,R)62 i6·:·M=cliffordModule(Mu1,Mu2,R)
  
63 o6·=·CliffordModule{...6...}63 o6·=·CliffordModule{...6...}
  
64 o6·:·CliffordModule64 o6·:·CliffordModule
65 i7·:·Mor·=·vectorBundleOnE·M.evenCenter;65 i7·:·Mor·=·vectorBundleOnE·M.evenCenter;
66 i8·:·Mor1=·vectorBundleOnE·M.oddCenter;66 i8·:·Mor1=·vectorBundleOnE·M.oddCenter;
Offset 75, 29 lines modifiedOffset 75, 29 lines modified
75 ··········m12=randomExtension(m1.yAction,m2.yAction);75 ··········m12=randomExtension(m1.yAction,m2.yAction);
76 ··········V·=·vectorBundleOnE·m12;76 ··········V·=·vectorBundleOnE·m12;
77 ··········Ul=tensorProduct(Mor,V);77 ··········Ul=tensorProduct(Mor,V);
78 ··········Ul1=tensorProduct(Mor1,V);78 ··········Ul1=tensorProduct(Mor1,V);
79 ··········d0=unique·degrees·target·Ul.yAction;79 ··········d0=unique·degrees·target·Ul.yAction;
80 ··········d1=unique·degrees·target·Ul1.yAction;80 ··········d1=unique·degrees·target·Ul1.yAction;
81 ··········#d1·>=3·or·#d0·>=3)·do·();81 ··········#d1·>=3·or·#d0·>=3)·do·();
82 ·--·.431474s·elapsed82 ·--·1.19124s·elapsed
83 i12·:·betti·Ul.yAction,·betti·Ul1.yAction83 i12·:·betti·Ul.yAction,·betti·Ul1.yAction
  
84 ···············0··1··········0··184 ···············0··1··········0··1
85 o12·=·(total:·32·32,·total:·32·32)85 o12·=·(total:·32·32,·total:·32·32)
86 ··········-4:·16··.·····-2:·32··.86 ··········-4:·16··.·····-2:·32··.
87 ··········-3:·16··.·····-1:··.··.87 ··········-3:·16··.·····-1:··.··.
88 ··········-2:··.··.······0:··.··.88 ··········-2:··.··.······0:··.··.
89 ··········-1:··.·16······1:··.·3289 ··········-1:··.·16······1:··.·32
90 ···········0:··.·1690 ···········0:··.·16
  
91 o12·:·Sequence91 o12·:·Sequence
92 i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the92 i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the
93 actions·of·generators93 actions·of·generators
94 ·--·25.9412s·elapsed94 ·--·34.8478s·elapsed
95 i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S));95 i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S));
  
96 ··············32······3296 ··············32······32
97 o14·:·Matrix·S···<--·S97 o14·:·Matrix·S···<--·S
98 i15·:·r=298 i15·:·r=2
  
99 o15·=·299 o15·=·2
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./usr/share/doc/Macaulay2/PencilsOfQuadrics/html/_search__Ulrich.html
    
Offset 161, 15 lines modifiedOffset 161, 15 lines modified
  
161 o11·:·CliffordModule</code></pre>161 o11·:·CliffordModule</code></pre>
162 ············</td>162 ············</td>
163 ··········</tr>163 ··········</tr>
164 ··········<tr>164 ··········<tr>
165 ············<td>165 ············<td>
166 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·Ulr·=·searchUlrich(M,S);166 ··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·Ulr·=·searchUlrich(M,S);
167 ·--·.732068s·elapsed</code></pre>167 ·--·1.72442s·elapsed</code></pre>
168 ············</td>168 ············</td>
169 ··········</tr>169 ··········</tr>
170 ··········<tr>170 ··········<tr>
171 ············<td>171 ············<td>
172 ··············<pre><code·class="language-macaulay2">i13·:·betti·freeResolution·Ulr172 ··············<pre><code·class="language-macaulay2">i13·:·betti·freeResolution·Ulr
  
173 ·············0··1·2173 ·············0··1·2
Offset 185, 15 lines modifiedOffset 185, 15 lines modified
  
185 o14·=·true</code></pre>185 o14·=·true</code></pre>
186 ············</td>186 ············</td>
187 ··········</tr>187 ··········</tr>
188 ··········<tr>188 ··········<tr>
189 ············<td>189 ············<td>
190 ··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3);190 ··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3);
191 ·--·2.37398s·elapsed</code></pre>191 ·--·3.21688s·elapsed</code></pre>
192 ············</td>192 ············</td>
193 ··········</tr>193 ··········</tr>
194 ··········<tr>194 ··········<tr>
195 ············<td>195 ············<td>
196 ··············<pre><code·class="language-macaulay2">i16·:·betti·freeResolution·Ulr3196 ··············<pre><code·class="language-macaulay2">i16·:·betti·freeResolution·Ulr3
  
197 ··············0··1··2197 ··············0··1··2
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Offset 64, 27 lines modifiedOffset 64, 27 lines modified
64 o10·:·Matrix·S··<--·S64 o10·:·Matrix·S··<--·S
65 i11·:·M=cliffordModule(Mu1,Mu2,R)65 i11·:·M=cliffordModule(Mu1,Mu2,R)
  
66 o11·=·CliffordModule{...6...}66 o11·=·CliffordModule{...6...}
  
67 o11·:·CliffordModule67 o11·:·CliffordModule
68 i12·:·elapsedTime·Ulr·=·searchUlrich(M,S);68 i12·:·elapsedTime·Ulr·=·searchUlrich(M,S);
69 ·--·.732068s·elapsed69 ·--·1.72442s·elapsed
70 i13·:·betti·freeResolution·Ulr70 i13·:·betti·freeResolution·Ulr
  
71 ·············0··1·271 ·············0··1·2
72 o13·=·total:·8·16·872 o13·=·total:·8·16·8
73 ··········0:·8·16·873 ··········0:·8·16·8
  
74 o13·:·BettiTally74 o13·:·BettiTally
75 i14·:·ann·Ulr·==·ideal·qs75 i14·:·ann·Ulr·==·ideal·qs
  
76 o14·=·true76 o14·=·true
77 i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3);77 i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3);
78 ·--·2.37398s·elapsed78 ·--·3.21688s·elapsed
79 i16·:·betti·freeResolution·Ulr379 i16·:·betti·freeResolution·Ulr3
  
80 ··············0··1··280 ··············0··1··2
81 o16·=·total:·12·24·1281 o16·=·total:·12·24·12
82 ··········0:·12·24·1282 ··········0:·12·24·12
  
83 o16·:·BettiTally83 o16·:·BettiTally
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./usr/share/doc/Macaulay2/Permanents/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=57 #:len=5
8 cnlzZXI=8 cnlzZXI=
9 #:len=21079 #:len=2107
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBwZXJtYW5lbnQgdXNpbmcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBwZXJtYW5lbnQgdXNpbmcg
11 UnlzZXIncyBmb3JtdWxhIiwgImxpbmVudW0iID0+IDQ0NCwgSW5wdXRzID0+IHtTUEFOe1RUeyJN11 UnlzZXIncyBmb3JtdWxhIiwgImxpbmVudW0iID0+IDQ0NCwgSW5wdXRzID0+IHtTUEFOe1RUeyJN
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./usr/share/doc/Macaulay2/Permutations/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=217 #:len=21
8 ZGVzY2VudHMoUGVybXV0YXRpb24p8 ZGVzY2VudHMoUGVybXV0YXRpb24p
9 #:len=2769 #:len=276
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg3LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg3LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhkZXNjZW50cyxQZXJtdXRhdGlvbiksImRlc2NlbnRz11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhkZXNjZW50cyxQZXJtdXRhdGlvbiksImRlc2NlbnRz
740 B
./usr/share/doc/Macaulay2/PhylogeneticTrees/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=157 #:len=15
8 cGh5bG9Ub3JpY1F1YWRz8 cGh5bG9Ub3JpY1F1YWRz
9 #:len=28489 #:len=2848
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSB0aGUgcXVhZHJhdGljIGlu10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSB0aGUgcXVhZHJhdGljIGlu
11 dmFyaWFudHMgb2YgYSBncm91cC1iYXNlZCBwaHlsb2dlbmV0aWMgbW9kZWwiLCAibGluZW51bSIg11 dmFyaWFudHMgb2YgYSBncm91cC1iYXNlZCBwaHlsb2dlbmV0aWMgbW9kZWwiLCAibGluZW51bSIg
739 B
./usr/share/doc/Macaulay2/PieriMaps/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=257 #:len=25
8 c3RhbmRhcmRUYWJsZWF1eChaWixMaXN0KQ==8 c3RhbmRhcmRUYWJsZWF1eChaWixMaXN0KQ==
9 #:len=2689 #:len=268
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTA0LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTA0LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzdGFuZGFyZFRhYmxlYXV4LFpaLExpc3QpLCJzdGFu11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzdGFuZGFyZFRhYmxlYXV4LFpaLExpc3QpLCJzdGFu
765 B
./usr/share/doc/Macaulay2/PlaneCurveLinearSeries/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=277 #:len=27
8 YWRkaXRpb24oSWRlYWwsSWRlYWwsSWRlYWwp8 YWRkaXRpb24oSWRlYWwsSWRlYWwsSWRlYWwp
9 #:len=2959 #:len=295
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU5LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU5LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGRpdGlvbixJZGVhbCxJZGVhbCxJZGVhbCksImFk11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGRpdGlvbixJZGVhbCxJZGVhbCxJZGVhbCksImFk
729 B
./usr/share/doc/Macaulay2/Points/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=247 #:len=24
8 cmFuZG9tUG9pbnRzTWF0KFJpbmcsWlop8 cmFuZG9tUG9pbnRzTWF0KFJpbmcsWlop
9 #:len=2559 #:len=255
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODc0LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODc0LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyYW5kb21Qb2ludHNNYXQsUmluZyxaWiksInJhbmRv11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyYW5kb21Qb2ludHNNYXQsUmluZyxaWiksInJhbmRv
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./usr/share/doc/Macaulay2/Points/example-output/_affine__Fat__Points.out
    
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66 i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3}66 i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3}
  
67 o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3}67 o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3}
  
68 o9·:·List68 o9·:·List
  
69 i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R);69 i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R);
70 ·--·2.30885s·elapsed70 ·--·3.83126s·elapsed
  
71 i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R);71 i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R);
72 ·--·3.77783s·elapsed72 ·--·7.2075s·elapsed
  
73 i12·:·G==H73 i12·:·G==H
  
74 o12·=·true74 o12·=·true
  
75 i13·:·75 i13·:·
1.58 KB
./usr/share/doc/Macaulay2/Points/html/_affine__Fat__Points.html
    
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177 o9·:·List</code></pre>177 o9·:·List</code></pre>
178 ············</td>178 ············</td>
179 ··········</tr>179 ··········</tr>
180 ··········<tr>180 ··········<tr>
181 ············<td>181 ············<td>
182 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R);182 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R);
183 ·--·2.30885s·elapsed</code></pre>183 ·--·3.83126s·elapsed</code></pre>
184 ············</td>184 ············</td>
185 ··········</tr>185 ··········</tr>
186 ··········<tr>186 ··········<tr>
187 ············<td>187 ············<td>
188 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R);188 ··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R);
189 ·--·3.77783s·elapsed</code></pre>189 ·--·7.2075s·elapsed</code></pre>
190 ············</td>190 ············</td>
191 ··········</tr>191 ··········</tr>
192 ··········<tr>192 ··········<tr>
193 ············<td>193 ············<td>
194 ··············<pre><code·class="language-macaulay2">i12·:·G==H194 ··············<pre><code·class="language-macaulay2">i12·:·G==H
  
195 o12·=·true</code></pre>195 o12·=·true</code></pre>
781 B
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81 o8·:·Matrix·K··<--·K81 o8·:·Matrix·K··<--·K
82 i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3}82 i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3}
  
83 o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3}83 o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3}
  
84 o9·:·List84 o9·:·List
85 i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R);85 i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R);
86 ·--·2.30885s·elapsed86 ·--·3.83126s·elapsed
87 i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R);87 i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R);
88 ·--·3.77783s·elapsed88 ·--·7.2075s·elapsed
89 i12·:·G==H89 i12·:·G==H
  
90 o12·=·true90 o12·=·true
91 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*91 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
92 For·reduced·points,·this·function·may·be·a·bit·slower·than·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s.92 For·reduced·points,·this·function·may·be·a·bit·slower·than·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s.
93 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*93 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
94 ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8F_\x8a_\x8t_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s_\x8B_\x8y_\x8I_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8,_\x8L_\x8i_\x8s_\x8t_\x8,_\x8R_\x8i_\x8n_\x8g_\x8)·--·computes·ideal·of·fat94 ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8F_\x8a_\x8t_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s_\x8B_\x8y_\x8I_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8,_\x8L_\x8i_\x8s_\x8t_\x8,_\x8R_\x8i_\x8n_\x8g_\x8)·--·computes·ideal·of·fat
715 B
./usr/share/doc/Macaulay2/Polyhedra/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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7 #:len=87 #:len=8
8 bWF4Q29uZXM=8 bWF4Q29uZXM=
9 #:len=11859 #:len=1185
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11 Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gODQzLCBJbnB1dHMgPT4ge1NQQU57VFR7IkYi11 Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gODQzLCBJbnB1dHMgPT4ge1NQQU57VFR7IkYi
712 B
./usr/share/doc/Macaulay2/Polymake/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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6 #·End·of·header6 #·End·of·header
7 #:len=87 #:len=8
8 UG9seW1ha2U=8 UG9seW1ha2U=
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZvciBpbnRlcmZhY2lu10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZvciBpbnRlcmZhY2lu
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739 B
./usr/share/doc/Macaulay2/PolyominoIdeals/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=167 #:len=16
8 cG9seW9JZGVhbChMaXN0KQ==8 cG9seW9JZGVhbChMaXN0KQ==
9 #:len=2569 #:len=256
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwb2x5b0lkZWFsLExpc3QpLCJwb2x5b0lkZWFsKExp11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwb2x5b0lkZWFsLExpc3QpLCJwb2x5b0lkZWFsKExp
722 B
./usr/share/doc/Macaulay2/Posets/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=177 #:len=17
8 bWF4aW1hbEFudGljaGFpbnM=8 bWF4aW1hbEFudGljaGFpbnM=
9 #:len=11279 #:len=1127
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYWxsIG1heGltYWwgYW5010 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYWxsIG1heGltYWwgYW50
11 aWNoYWlucyBvZiBhIHBvc2V0IiwgImxpbmVudW0iID0+IDQ4NzUsIElucHV0cyA9PiB7U1BBTntU11 aWNoYWlucyBvZiBhIHBvc2V0IiwgImxpbmVudW0iID0+IDQ4NzUsIElucHV0cyA9PiB7U1BBTntU
949 B
./usr/share/doc/Macaulay2/Posets/example-output/___Precompute.out
    
Offset 31, 27 lines modifiedOffset 31, 27 lines modified
31 o5·=·CacheTable{name·=>·P}31 o5·=·CacheTable{name·=>·P}
  
32 i6·:·C·==·P32 i6·:·C·==·P
  
33 o6·=·true33 o6·=·true
  
34 i7·:·time·isDistributive·C34 i7·:·time·isDistributive·C
35 ·--·used·0.00132875s·(cpu);·5.077e-06s·(thread);·0s·(gc)35 ·--·used·0.00189373s·(cpu);·5.34e-06s·(thread);·0s·(gc)
  
36 o7·=·true36 o7·=·true
  
37 i8·:·time·isDistributive·P37 i8·:·time·isDistributive·P
38 ·--·used·4.70143s·(cpu);·3.21962s·(thread);·0s·(gc)38 ·--·used·5.12731s·(cpu);·3.37642s·(thread);·0s·(gc)
  
39 o8·=·true39 o8·=·true
  
40 i9·:·C'·=·dual·C;40 i9·:·C'·=·dual·C;
  
41 i10·:·time·isDistributive·C'41 i10·:·time·isDistributive·C'
42 ·--·used·0.000207623s·(cpu);·4.116e-06s·(thread);·0s·(gc)42 ·--·used·0.000242023s·(cpu);·2.4856e-05s·(thread);·0s·(gc)
  
43 o10·=·true43 o10·=·true
  
44 i11·:·peek·C'.cache44 i11·:·peek·C'.cache
  
45 o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}······································}45 o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}······································}
46 ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4},·{6,·5},·{7,·6},·{8,·7},·{9,·8}}46 ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4},·{6,·5},·{7,·6},·{8,·7},·{9,·8}}
731 B
./usr/share/doc/Macaulay2/Posets/example-output/_greene__Kleitman__Partition.out
    
Offset 7, 22 lines modifiedOffset 7, 22 lines modified
7 o2·=·Partition{4,·2}7 o2·=·Partition{4,·2}
  
8 o2·:·Partition8 o2·:·Partition
  
9 i3·:·D·=·dominanceLattice·6;9 i3·:·D·=·dominanceLattice·6;
  
10 i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains")10 i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains")
11 ·--·used·0.294633s·(cpu);·0.197251s·(thread);·0s·(gc)11 ·--·used·0.39228s·(cpu);·0.267371s·(thread);·0s·(gc)
  
12 o4·=·Partition{9,·2}12 o4·=·Partition{9,·2}
  
13 o4·:·Partition13 o4·:·Partition
  
14 i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains")14 i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains")
15 ·--·used·0.000122995s·(cpu);·7.261e-06s·(thread);·0s·(gc)15 ·--·used·0.000200166s·(cpu);·2.17e-05s·(thread);·0s·(gc)
  
16 o5·=·Partition{9,·2}16 o5·=·Partition{9,·2}
  
17 o5·:·Partition17 o5·:·Partition
  
18 i6·:·greeneKleitmanPartition·chain·1018 i6·:·greeneKleitmanPartition·chain·10
  
2.37 KB
./usr/share/doc/Macaulay2/Posets/html/___Precompute.html
    
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107 o6·=·true</code></pre>107 o6·=·true</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i7·:·time·isDistributive·C112 ··············<pre><code·class="language-macaulay2">i7·:·time·isDistributive·C
113 ·--·used·0.00132875s·(cpu);·5.077e-06s·(thread);·0s·(gc)113 ·--·used·0.00189373s·(cpu);·5.34e-06s·(thread);·0s·(gc)
  
114 o7·=·true</code></pre>114 o7·=·true</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i8·:·time·isDistributive·P119 ··············<pre><code·class="language-macaulay2">i8·:·time·isDistributive·P
120 ·--·used·4.70143s·(cpu);·3.21962s·(thread);·0s·(gc)120 ·--·used·5.12731s·(cpu);·3.37642s·(thread);·0s·(gc)
  
121 o8·=·true</code></pre>121 o8·=·true</code></pre>
122 ············</td>122 ············</td>
123 ··········</tr>123 ··········</tr>
124 ········</table>124 ········</table>
125 ········<div>125 ········<div>
126 ··········<p>We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive·lattice.··Other·information·is·copied·when·possible.</p>126 ··········<p>We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive·lattice.··Other·information·is·copied·when·possible.</p>
Offset 133, 15 lines modifiedOffset 133, 15 lines modified
133 ············<td>133 ············<td>
134 ··············<pre><code·class="language-macaulay2">i9·:·C'·=·dual·C;</code></pre>134 ··············<pre><code·class="language-macaulay2">i9·:·C'·=·dual·C;</code></pre>
135 ············</td>135 ············</td>
136 ··········</tr>136 ··········</tr>
137 ··········<tr>137 ··········<tr>
138 ············<td>138 ············<td>
139 ··············<pre><code·class="language-macaulay2">i10·:·time·isDistributive·C'139 ··············<pre><code·class="language-macaulay2">i10·:·time·isDistributive·C'
140 ·--·used·0.000207623s·(cpu);·4.116e-06s·(thread);·0s·(gc)140 ·--·used·0.000242023s·(cpu);·2.4856e-05s·(thread);·0s·(gc)
  
141 o10·=·true</code></pre>141 o10·=·true</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ··········<tr>144 ··········<tr>
145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i11·:·peek·C'.cache146 ··············<pre><code·class="language-macaulay2">i11·:·peek·C'.cache
915 B
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41 i5·:·peek·P.cache41 i5·:·peek·P.cache
  
42 o5·=·CacheTable{name·=>·P}42 o5·=·CacheTable{name·=>·P}
43 i6·:·C·==·P43 i6·:·C·==·P
  
44 o6·=·true44 o6·=·true
45 i7·:·time·isDistributive·C45 i7·:·time·isDistributive·C
46 ·--·used·0.00132875s·(cpu);·5.077e-06s·(thread);·0s·(gc)46 ·--·used·0.00189373s·(cpu);·5.34e-06s·(thread);·0s·(gc)
  
47 o7·=·true47 o7·=·true
48 i8·:·time·isDistributive·P48 i8·:·time·isDistributive·P
49 ·--·used·4.70143s·(cpu);·3.21962s·(thread);·0s·(gc)49 ·--·used·5.12731s·(cpu);·3.37642s·(thread);·0s·(gc)
  
50 o8·=·true50 o8·=·true
51 We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive51 We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive
52 lattice.·Other·information·is·copied·when·possible.52 lattice.·Other·information·is·copied·when·possible.
53 i9·:·C'·=·dual·C;53 i9·:·C'·=·dual·C;
54 i10·:·time·isDistributive·C'54 i10·:·time·isDistributive·C'
55 ·--·used·0.000207623s·(cpu);·4.116e-06s·(thread);·0s·(gc)55 ·--·used·0.000242023s·(cpu);·2.4856e-05s·(thread);·0s·(gc)
  
56 o10·=·true56 o10·=·true
57 i11·:·peek·C'.cache57 i11·:·peek·C'.cache
  
58 o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}58 o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}
59 }59 }
60 ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4},60 ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4},
1.92 KB
./usr/share/doc/Macaulay2/Posets/html/_greene__Kleitman__Partition.html
    
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100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i3·:·D·=·dominanceLattice·6;</code></pre>101 ··············<pre><code·class="language-macaulay2">i3·:·D·=·dominanceLattice·6;</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·&quot;antichains&quot;)106 ··············<pre><code·class="language-macaulay2">i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·&quot;antichains&quot;)
107 ·--·used·0.294633s·(cpu);·0.197251s·(thread);·0s·(gc)107 ·--·used·0.39228s·(cpu);·0.267371s·(thread);·0s·(gc)
  
108 o4·=·Partition{9,·2}108 o4·=·Partition{9,·2}
  
109 o4·:·Partition</code></pre>109 o4·:·Partition</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·&quot;chains&quot;)114 ··············<pre><code·class="language-macaulay2">i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·&quot;chains&quot;)
115 ·--·used·0.000122995s·(cpu);·7.261e-06s·(thread);·0s·(gc)115 ·--·used·0.000200166s·(cpu);·2.17e-05s·(thread);·0s·(gc)
  
116 o5·=·Partition{9,·2}116 o5·=·Partition{9,·2}
  
117 o5·:·Partition</code></pre>117 o5·:·Partition</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ········</table>120 ········</table>
907 B
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28 o2·:·Partition28 o2·:·Partition
29 The·conjugate·of·$l$·has·the·same·property,·but·with·chains·replaced·by29 The·conjugate·of·$l$·has·the·same·property,·but·with·chains·replaced·by
30 _\x8a_\x8n_\x8t_\x8i_\x8c_\x8h_\x8a_\x8i_\x8n_\x8s.·Because·of·this,·it·is·often·better·to·count·via·antichains·instead30 _\x8a_\x8n_\x8t_\x8i_\x8c_\x8h_\x8a_\x8i_\x8n_\x8s.·Because·of·this,·it·is·often·better·to·count·via·antichains·instead
31 of·chains.·This·can·be·done·by·passing·"antichains"·as·the·Strategy.31 of·chains.·This·can·be·done·by·passing·"antichains"·as·the·Strategy.
32 i3·:·D·=·dominanceLattice·6;32 i3·:·D·=·dominanceLattice·6;
33 i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains")33 i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains")
34 ·--·used·0.294633s·(cpu);·0.197251s·(thread);·0s·(gc)34 ·--·used·0.39228s·(cpu);·0.267371s·(thread);·0s·(gc)
  
35 o4·=·Partition{9,·2}35 o4·=·Partition{9,·2}
  
36 o4·:·Partition36 o4·:·Partition
37 i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains")37 i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains")
38 ·--·used·0.000122995s·(cpu);·7.261e-06s·(thread);·0s·(gc)38 ·--·used·0.000200166s·(cpu);·2.17e-05s·(thread);·0s·(gc)
  
39 o5·=·Partition{9,·2}39 o5·=·Partition{9,·2}
  
40 o5·:·Partition40 o5·:·Partition
41 The·Greene-Kleitman·partition·of·the·$n$·_\x8c_\x8h_\x8a_\x8i_\x8n·is·the·partition·of·$n$·with·$1$41 The·Greene-Kleitman·partition·of·the·$n$·_\x8c_\x8h_\x8a_\x8i_\x8n·is·the·partition·of·$n$·with·$1$
42 part.42 part.
43 i6·:·greeneKleitmanPartition·chain·1043 i6·:·greeneKleitmanPartition·chain·10
758 B
./usr/share/doc/Macaulay2/PositivityToricBundles/dump/rawdocumentation.dump
    
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773 B
./usr/share/doc/Macaulay2/PrimaryDecomposition/dump/rawdocumentation.dump
    
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1.81 KB
./usr/share/doc/Macaulay2/PrimaryDecomposition/example-output/_kernel__Of__Localization.out
    
Offset 24, 35 lines modifiedOffset 24, 35 lines modified
24 ··············|·0············0·············0············x_1^3-x_0x_2^2·0··············|24 ··············|·0············0·············0············x_1^3-x_0x_2^2·0··············|
25 ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·|25 ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·|
  
26 ····························326 ····························3
27 o3·:·R-module,·quotient·of·R27 o3·:·R-module,·quotient·of·R
  
28 i4·:·elapsedTime·kernelOfLocalization(M,·I1)28 i4·:·elapsedTime·kernelOfLocalization(M,·I1)
29 ·--·.175277s·elapsed29 ·--·.393048s·elapsed
  
30 o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)30 o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)
31 ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|31 ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|
32 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|32 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|
  
33 ·······························333 ·······························3
34 o4·:·R-module,·subquotient·of·R34 o4·:·R-module,·subquotient·of·R
  
35 i5·:·elapsedTime·kernelOfLocalization(M,·I2)35 i5·:·elapsedTime·kernelOfLocalization(M,·I2)
36 ·--·.0162986s·elapsed36 ·--·.0456281s·elapsed
  
37 o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)37 o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)
38 ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|38 ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|
39 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|39 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|
  
40 ·······························340 ·······························3
41 o5·:·R-module,·subquotient·of·R41 o5·:·R-module,·subquotient·of·R
  
42 i6·:·elapsedTime·kernelOfLocalization(M,·I3)42 i6·:·elapsedTime·kernelOfLocalization(M,·I3)
43 ·--·.0537158s·elapsed43 ·--·.110952s·elapsed
  
44 o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)44 o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)
45 ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|45 ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|
46 ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|46 ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|
  
47 ·······························347 ·······························3
48 o6·:·R-module,·subquotient·of·R48 o6·:·R-module,·subquotient·of·R
933 B
./usr/share/doc/Macaulay2/PrimaryDecomposition/example-output/_reg__Seq__In__Ideal.out
    
Offset 13, 15 lines modifiedOffset 13, 15 lines modified
13 ·····------------------------------------------------------------------------13 ·····------------------------------------------------------------------------
14 ·····x·x·)14 ·····x·x·)
15 ······0·415 ······0·4
  
16 o2·:·Ideal·of·R16 o2·:·Ideal·of·R
  
17 i3·:·elapsedTime·regSeqInIdeal·I17 i3·:·elapsedTime·regSeqInIdeal·I
18 ·--·.0682009s·elapsed18 ·--·.172462s·elapsed
  
19 o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·)19 o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·)
20 ·············2·7···3·6····0·7···2·5····0·7···1·4····0·720 ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7
  
21 o3·:·Ideal·of·R21 o3·:·Ideal·of·R
  
22 i4·:·R·=·QQ[h,l,s,x,y,z]22 i4·:·R·=·QQ[h,l,s,x,y,z]
Offset 41, 15 lines modifiedOffset 41, 15 lines modified
41 o5·:·Ideal·of·R41 o5·:·Ideal·of·R
  
42 i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·342 i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3
  
43 o6·=·true43 o6·=·true
  
44 i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1)44 i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1)
45 ·--·.00689182s·elapsed45 ·--·.0150305s·elapsed
  
46 ···················2················3····2·····2····8····3····2·····246 ···················2················3····2·····2····8····3····2·····2
47 o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x)47 o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x)
  
48 o7·:·Ideal·of·R48 o7·:·Ideal·of·R
  
49 i8·:·49 i8·:·
3.46 KB
./usr/share/doc/Macaulay2/PrimaryDecomposition/html/_kernel__Of__Localization.html
    
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107 ····························3107 ····························3
108 o3·:·R-module,·quotient·of·R</code></pre>108 o3·:·R-module,·quotient·of·R</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·kernelOfLocalization(M,·I1)113 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·kernelOfLocalization(M,·I1)
114 ·--·.175277s·elapsed114 ·--·.393048s·elapsed
  
115 o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)115 o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)
116 ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|116 ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|
117 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|117 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|
  
118 ·······························3118 ·······························3
119 o4·:·R-module,·subquotient·of·R</code></pre>119 o4·:·R-module,·subquotient·of·R</code></pre>
120 ············</td>120 ············</td>
121 ··········</tr>121 ··········</tr>
122 ··········<tr>122 ··········<tr>
123 ············<td>123 ············<td>
124 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·kernelOfLocalization(M,·I2)124 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·kernelOfLocalization(M,·I2)
125 ·--·.0162986s·elapsed125 ·--·.0456281s·elapsed
  
126 o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)126 o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)
127 ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|127 ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|
128 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|128 ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|
  
129 ·······························3129 ·······························3
130 o5·:·R-module,·subquotient·of·R</code></pre>130 o5·:·R-module,·subquotient·of·R</code></pre>
131 ············</td>131 ············</td>
132 ··········</tr>132 ··········</tr>
133 ··········<tr>133 ··········<tr>
134 ············<td>134 ············<td>
135 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·kernelOfLocalization(M,·I3)135 ··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·kernelOfLocalization(M,·I3)
136 ·--·.0537158s·elapsed136 ·--·.110952s·elapsed
  
137 o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)137 o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|)
138 ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|138 ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············|
139 ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|139 ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·|
  
140 ·······························3140 ·······························3
141 o6·:·R-module,·subquotient·of·R</code></pre>141 o6·:·R-module,·subquotient·of·R</code></pre>
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41 |41 |
42 ··············|·0············0·············0············0··············x_1^5-42 ··············|·0············0·············0············0··············x_1^5-
43 x_0x_2^4·|43 x_0x_2^4·|
  
44 ····························344 ····························3
45 o3·:·R-module,·quotient·of·R45 o3·:·R-module,·quotient·of·R
46 i4·:·elapsedTime·kernelOfLocalization(M,·I1)46 i4·:·elapsedTime·kernelOfLocalization(M,·I1)
47 ·--·.175277s·elapsed47 ·--·.393048s·elapsed
  
48 o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·048 o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0
49 0··············|)49 0··············|)
50 ··················|·1·0·|··|·0············0·············0············x_1^3-50 ··················|·1·0·|··|·0············0·············0············x_1^3-
51 x_0x_2^2·0··············|51 x_0x_2^2·0··············|
52 ··················|·0·1·|··|·0············0·············0············052 ··················|·0·1·|··|·0············0·············0············0
53 x_1^5-x_0x_2^4·|53 x_1^5-x_0x_2^4·|
  
54 ·······························354 ·······························3
55 o4·:·R-module,·subquotient·of·R55 o4·:·R-module,·subquotient·of·R
56 i5·:·elapsedTime·kernelOfLocalization(M,·I2)56 i5·:·elapsedTime·kernelOfLocalization(M,·I2)
57 ·--·.0162986s·elapsed57 ·--·.0456281s·elapsed
  
58 o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·058 o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0
59 0··············|)59 0··············|)
60 ··················|·0·0·|··|·0············0·············0············x_1^3-60 ··················|·0·0·|··|·0············0·············0············x_1^3-
61 x_0x_2^2·0··············|61 x_0x_2^2·0··············|
62 ··················|·0·1·|··|·0············0·············0············062 ··················|·0·1·|··|·0············0·············0············0
63 x_1^5-x_0x_2^4·|63 x_1^5-x_0x_2^4·|
  
64 ·······························364 ·······························3
65 o5·:·R-module,·subquotient·of·R65 o5·:·R-module,·subquotient·of·R
66 i6·:·elapsedTime·kernelOfLocalization(M,·I3)66 i6·:·elapsedTime·kernelOfLocalization(M,·I3)
67 ·--·.0537158s·elapsed67 ·--·.110952s·elapsed
  
68 o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·068 o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0
69 0··············|)69 0··············|)
70 ··················|·0·1·|··|·0············0·············0············x_1^3-70 ··················|·0·1·|··|·0············0·············0············x_1^3-
71 x_0x_2^2·0··············|71 x_0x_2^2·0··············|
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73 x_1^5-x_0x_2^4·|73 x_1^5-x_0x_2^4·|
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103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
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108 ·--·.0682009s·elapsed108 ·--·.172462s·elapsed
  
109 o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·)109 o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·)
110 ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7110 ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7
  
111 o3·:·Ideal·of·R</code></pre>111 o3·:·Ideal·of·R</code></pre>
112 ············</td>112 ············</td>
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153 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1)153 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1)
154 ·--·.00689182s·elapsed154 ·--·.0150305s·elapsed
  
155 ···················2················3····2·····2····8····3····2·····2155 ···················2················3····2·····2····8····3····2·····2
156 o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x)156 o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x)
  
157 o7·:·Ideal·of·R</code></pre>157 o7·:·Ideal·of·R</code></pre>
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42 ·····x·x·)42 ·····x·x·)
43 ······0·443 ······0·4
  
44 o2·:·Ideal·of·R44 o2·:·Ideal·of·R
45 i3·:·elapsedTime·regSeqInIdeal·I45 i3·:·elapsedTime·regSeqInIdeal·I
46 ·--·.0682009s·elapsed46 ·--·.172462s·elapsed
  
47 o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·)47 o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·)
48 ·············2·7···3·6····0·7···2·5····0·7···1·4····0·748 ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7
  
49 o3·:·Ideal·of·R49 o3·:·Ideal·of·R
50 If·I·is·the·unit·ideal,·then·an·ideal·of·variables·of·the·ring·is·returned.50 If·I·is·the·unit·ideal,·then·an·ideal·of·variables·of·the·ring·is·returned.
51 If·the·codimension·of·I·is·already·known,·then·one·can·specify·this,·along·with51 If·the·codimension·of·I·is·already·known,·then·one·can·specify·this,·along·with
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72 i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·372 i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3
  
73 o6·=·true73 o6·=·true
74 i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1)74 i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1)
75 ·--·.00689182s·elapsed75 ·--·.0150305s·elapsed
  
76 ···················2················3····2·····2····8····3····2·····276 ···················2················3····2·····2····8····3····2·····2
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78 o7·:·Ideal·of·R78 o7·:·Ideal·of·R
79 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*79 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
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22 o2·:·PythonObject·of·class·range_iterator22 o2·:·PythonObject·of·class·range_iterator
23 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
24 ····*·_\x8n_\x8e_\x8x_\x8t_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·retrieve·the·next·item·from·a·python·iterator24 ····*·_\x8n_\x8e_\x8x_\x8t_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·retrieve·the·next·item·from·a·python·iterator
25 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*25 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
26 ····*·_\x8i_\x8t_\x8e_\x8r_\x8a_\x8t_\x8o_\x8r_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·get·iterator·of·iterable·python·object26 ····*·_\x8i_\x8t_\x8e_\x8r_\x8a_\x8t_\x8o_\x8r_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·get·iterator·of·iterable·python·object
27 ===============================================================================27 ===============================================================================
1000 B
./usr/share/doc/Macaulay2/Python/html/_next_lp__Python__Object_rp.html
    
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77 o1·:·PythonObject·of·class·range</code></pre>77 o1·:·PythonObject·of·class·range</code></pre>
78 ············</td>78 ············</td>
79 ··········</tr>79 ··········</tr>
80 ··········<tr>80 ··········<tr>
81 ············<td>81 ············<td>
82 ··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x82 ··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x
  
83 o2·=·&lt;range_iterator·object·at·0x7f6b389af810>83 o2·=·&lt;range_iterator·object·at·0x7f8c0a593780>
  
84 o2·:·PythonObject·of·class·range_iterator</code></pre>84 o2·:·PythonObject·of·class·range_iterator</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i3·:·next·i89 ··············<pre><code·class="language-macaulay2">i3·:·next·i
354 B
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16 i1·:·x·=·pythonValue·"range(3)"16 i1·:·x·=·pythonValue·"range(3)"
  
17 o1·=·range(0,·3)17 o1·=·range(0,·3)
  
18 o1·:·PythonObject·of·class·range18 o1·:·PythonObject·of·class·range
19 i2·:·i·=·iterator·x19 i2·:·i·=·iterator·x
  
20 o2·=·<range_iterator·object·at·0x7f6b389af810>20 o2·=·<range_iterator·object·at·0x7f8c0a593780>
  
21 o2·:·PythonObject·of·class·range_iterator21 o2·:·PythonObject·of·class·range_iterator
22 i3·:·next·i22 i3·:·next·i
  
23 o3·=·023 o3·=·0
  
24 o3·:·PythonObject·of·class·int24 o3·:·PythonObject·of·class·int
1.07 KB
./usr/share/doc/Macaulay2/Python/html/_to__Python.html
    
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181 o12·:·FunctionClosure</code></pre>181 o12·:·FunctionClosure</code></pre>
182 ············</td>182 ············</td>
183 ··········</tr>183 ··········</tr>
184 ··········<tr>184 ··········<tr>
185 ············<td>185 ············<td>
186 ··············<pre><code·class="language-macaulay2">i13·:·pysqrt·=·toPython·m2sqrt186 ··············<pre><code·class="language-macaulay2">i13·:·pysqrt·=·toPython·m2sqrt
  
187 o13·=·&lt;built-in·method·m2sqrt·of·PyCapsule·object·at·0x7fefdfa32700>187 o13·=·&lt;built-in·method·m2sqrt·of·PyCapsule·object·at·0x7fe58e65e750>
  
188 o13·:·PythonObject·of·class·builtin_function_or_method</code></pre>188 o13·:·PythonObject·of·class·builtin_function_or_method</code></pre>
189 ············</td>189 ············</td>
190 ··········</tr>190 ··········</tr>
191 ··········<tr>191 ··········<tr>
192 ············<td>192 ············<td>
193 ··············<pre><code·class="language-macaulay2">i14·:·pysqrt·2193 ··············<pre><code·class="language-macaulay2">i14·:·pysqrt·2
419 B
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Offset 72, 15 lines modifiedOffset 72, 15 lines modified
72 ··········sqrt·x)72 ··········sqrt·x)
  
73 o12·=·m2sqrt73 o12·=·m2sqrt
  
74 o12·:·FunctionClosure74 o12·:·FunctionClosure
75 i13·:·pysqrt·=·toPython·m2sqrt75 i13·:·pysqrt·=·toPython·m2sqrt
  
76 o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7fefdfa32700>76 o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7fe58e65e750>
  
77 o13·:·PythonObject·of·class·builtin_function_or_method77 o13·:·PythonObject·of·class·builtin_function_or_method
78 i14·:·pysqrt·278 i14·:·pysqrt·2
79 calling·Macaulay2·code·from·Python!79 calling·Macaulay2·code·from·Python!
  
80 o14·=·1.414213562373095180 o14·=·1.4142135623730951
  
718 B
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7 #:len=127 #:len=12
8 bWluaW1pemF0aW9u8 bWluaW1pemF0aW9u
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765 B
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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8 aGlnaGVyRGVwdGhUYWJsZQ==8 aGlnaGVyRGVwdGhUYWJsZQ==
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11 LUVyaWsgUm9vcycgZXhhbXBsZXMgb2YgcXVhZHJhdGljIGlkZWFscyB3aXRoIHBvc2l0aXZlIGRl11 LUVyaWsgUm9vcycgZXhhbXBsZXMgb2YgcXVhZHJhdGljIGlkZWFscyB3aXRoIHBvc2l0aXZlIGRl
746 B
./usr/share/doc/Macaulay2/Quasidegrees/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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6 #·End·of·header6 #·End·of·header
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8 cXVhc2lkZWdyZWVzTG9jYWxDb2hvbW9sb2d58 cXVhc2lkZWdyZWVzTG9jYWxDb2hvbW9sb2d5
9 #:len=38819 #:len=3881
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgcXVhc2lkZWdyZWUg10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgcXVhc2lkZWdyZWUg
11 c2V0cyBvZiBsb2NhbCBjb2hvbW9sb2d5IG1vZHVsZXMiLCAibGluZW51bSIgPT4gNzcyLCBJbnB111 c2V0cyBvZiBsb2NhbCBjb2hvbW9sb2d5IG1vZHVsZXMiLCAibGluZW51bSIgPT4gNzcyLCBJbnB1
728 B
./usr/share/doc/Macaulay2/QuaternaryQuartics/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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7 #:len=47 #:len=4
8 W1FRXQ==8 W1FRXQ==
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUXVhdGVybmFyeSBRdWFydGljIEZvcm1z10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUXVhdGVybmFyeSBRdWFydGljIEZvcm1z
11 IGFuZCBHb3JlbnN0ZWluIHJpbmdzIChLYXB1c3RrYSwgS2FwdXN0a2EsIFJhbmVzdGFkLCBTY2hl11 IGFuZCBHb3JlbnN0ZWluIHJpbmdzIChLYXB1c3RrYSwgS2FwdXN0a2EsIFJhbmVzdGFkLCBTY2hl
26.2 KB
./usr/share/doc/Macaulay2/QuaternaryQuartics/example-output/___Hilbert_spscheme_spof_sp6_sppoints_spin_spprojective_sp3-space.out
    
Offset 180, 15 lines modifiedOffset 180, 15 lines modified
180 i21·:·L·=·trim·groebnerStratum·F;180 i21·:·L·=·trim·groebnerStratum·F;
  
181 o21·:·Ideal·of·T181 o21·:·Ideal·of·T
  
182 i22·:·assert(dim·L·==·18)182 i22·:·assert(dim·L·==·18)
  
183 i23·:·elapsedTime·isPrime·L183 i23·:·elapsedTime·isPrime·L
184 ·--·3.48423s·elapsed184 ·--·5.99366s·elapsed
  
185 o23·=·true185 o23·=·true
  
186 i24·:·I·=·pointsIdeal·randomPoints(S,·6)186 i24·:·I·=·pointsIdeal·randomPoints(S,·6)
  
187 ·····························2······························2···2··········187 ·····························2······························2···2··········
188 o24·=·ideal·(a*c·-·7b*c·-·49c··+·40a*d·-·42b*d·+·12c*d·+·28d·,·b··-·36b*c·-188 o24·=·ideal·(a*c·-·7b*c·-·49c··+·40a*d·-·42b*d·+·12c*d·+·28d·,·b··-·36b*c·-
Offset 302, 15 lines modifiedOffset 302, 15 lines modified
302 o38·=·true302 o38·=·true
  
303 i39·:·L441·=·trim(L·+·ideal·M1);303 i39·:·L441·=·trim(L·+·ideal·M1);
  
304 o39·:·Ideal·of·T304 o39·:·Ideal·of·T
  
305 i40·:·elapsedTime·compsL441·=·decompose·L441;305 i40·:·elapsedTime·compsL441·=·decompose·L441;
306 ·--·1.98893s·elapsed306 ·--·2.79803s·elapsed
  
307 i41·:·#compsL441307 i41·:·#compsL441
  
308 o41·=·2308 o41·=·2
  
309 i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16.309 i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16.
  
Offset 320, 37 lines modifiedOffset 320, 37 lines modified
  
320 i43·:·compsL441/dim·==·{16,·14}320 i43·:·compsL441/dim·==·{16,·14}
  
321 o43·=·true321 o43·=·true
  
322 i44·:·pta·=·randomPointOnRationalVariety·compsL441_0322 i44·:·pta·=·randomPointOnRationalVariety·compsL441_0
  
323 o44·=·|·-49·11·-25·17·44·-16·-27·40·-34·20·-19·29·41·19·-40·42·-13·5·17·39·31323 o44·=·|·-40·-4·-40·44·-22·-50·-30·13·-1·-16·45·-23·29·19·14·23·-21·19·14·29·6
324 ······-----------------------------------------------------------------------324 ······-----------------------------------------------------------------------
325 ······10·45·26·43·49·-32·-29·19·-50·15·18·37·-10·34·-28·|325 ······10·-32·18·-22·37·34·15·5·-10·-29·26·49·-50·45·-28·|
  
326 ···············1·······36326 ···············1·······36
327 o44·:·Matrix·kk··<--·kk327 o44·:·Matrix·kk··<--·kk
  
328 i45·:·Fa·=·sub(F,·(vars·S)·|·pta)328 i45·:·Fa·=·sub(F,·(vars·S)·|·pta)
  
329 ··············2··············2······························2···············329 ··············2··············2······························2···············
330 o45·=·ideal·(a··-·40b*c·+·20c··+·29a*d·-·16b*d·-·25c*d·-·49d·,·a*b·+·43b*c·+330 o45·=·ideal·(a··+·14b*c·-·16c··-·23a*d·-·50b*d·-·40c*d·-·40d·,·a*b·-·22b*c·+
331 ······-----------------------------------------------------------------------331 ······-----------------------------------------------------------------------
332 ·········2······························2···2··············2················332 ·········2··························2···2··············2··················
333 ······17c··+·31a*d·+·41b*d·-·34c*d·+·11d·,·b··+·34b*c·-·29c··+·37a*d·+·10b*d333 ······14c··+·6a*d·+·29b*d·-·c*d·-·4d·,·b··+·45b*c·+·15c··+·49a*d·+·10b*d·+
334 ······-----------------------------------------------------------------------334 ······-----------------------------------------------------------------------
335 ···················2···················2······························2·····2335 ·················2···················2·····························2·····2··
336 ······+·42c*d·-·27d·,·a*c·+·18b*c·+·49c··+·19a*d·+·39b*d·+·19c*d·+·44d·,·b*c·336 ······23c*d·-·30d·,·a*c·+·26b*c·+·37c··+·5a*d·+·29b*d·+·19c*d·-·22d·,·b*c··-
337 ······-----------------------------------------------------------------------337 ······-----------------------------------------------------------------------
338 ·····················2·········2········2········2······3···3············338 ···················2·········2········2········2······3···3················2·
339 ······-·50b*c*d·+·45c·d·-·32a*d··-·13b*d··-·19c*d··+·17d·,·c··-·28b*c*d·+339 ······10b*c*d·-·32c·d·+·34a*d··-·21b*d··+·45c*d··+·44d·,·c··-·28b*c*d·-·29c·d
340 ······-----------------------------------------------------------------------340 ······-----------------------------------------------------------------------
341 ·········2·········2········2·······2······3341 ·············2········2········2······3
342 ······15c·d·-·10a*d··+·26b*d··+·5c*d··+·40d·)342 ······-·50a*d··+·18b*d··+·19c*d··+·13d·)
  
343 o45·:·Ideal·of·S343 o45·:·Ideal·of·S
  
344 i46·:·betti·res·Fa344 i46·:·betti·res·Fa
  
345 ·············0·1·2·3345 ·············0·1·2·3
346 o46·=·total:·1·6·8·3346 o46·=·total:·1·6·8·3
Offset 358, 81 lines modifiedOffset 358, 84 lines modified
358 ··········1:·.·4·4·1358 ··········1:·.·4·4·1
359 ··········2:·.·2·4·2359 ··········2:·.·2·4·2
  
360 o46·:·BettiTally360 o46·:·BettiTally
  
361 i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point361 i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point
  
362 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+362 ······+------------------------------------------------------------------------------------------------------------+
363 o47·=·|ideal·(c·+·19d,·b·-·10d,·a·+·6d)···································································································································|363 o47·=·|ideal·(c·+·5d,·b·-·33d,·a·-·21d)············································································|
364 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+364 ······+------------------------------------------------------------------------------------------------------------+
365 ······|····························2··············2······················2···3················2········2········2······3·····2················2·········2········2······3·| 
366 ······|ideal·(a·+·18b·+·49c·-·3d,·b··+·34b*c·-·29c··-·50b*d·+·47c*d·-·17d·,·c··-·28b*c*d·+·15c·d·+·4b*d··-·10c*d··+·10d·,·b*c··-·50b*c*d·+·45c·d·-·43b*d··+·34c*d··+·22d·)|365 ······|······································2··············2······················································|
 366 ······|ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,·c··+·49c*d·+·42d·)·····················································|
367 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+367 ······+------------------------------------------------------------------------------------------------------------+
 368 ······|·····························2······················2···························2···2·····················2·|
 369 ······|ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+·27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)|
 370 ······+------------------------------------------------------------------------------------------------------------+
  
368 i48·:·CFa·=·minimalPrimes·Fa371 i48·:·CFa·=·minimalPrimes·Fa
  
369 ·····································································2··372 ·············································································
370 o48·=·{ideal·(c·+·19d,·b·-·10d,·a·+·6d),·ideal·(a·+·18b·+·49c·-·3d,·b··+373 o48·=·{ideal·(c·+·5d,·b·-·33d,·a·-·21d),·ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,
371 ······-----------------------------------------------------------------------374 ······-----------------------------------------------------------------------
372 ·················2······················2···3················2········2··375 ·······2··············2································2··················
373 ······34b*c·-·29c··-·50b*d·+·47c*d·-·17d·,·c··-·28b*c*d·+·15c·d·+·4b*d··-376 ······c··+·49c*d·+·42d·),·ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+
374 ······-----------------------------------------------------------------------377 ······-----------------------------------------------------------------------
375 ···········2······3·····2················2·········2········2······3 
376 ······10c*d··+·10d·,·b*c··-·50b*c*d·+·45c·d·-·43b*d··+·34c*d··+·22d·)}378 ·········2···························2···2·····················2
 379 ······27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)}
  
377 o48·:·List380 o48·:·List
  
378 i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane.381 i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane.
  
379 o49·=·a·+·18b·+·49c·-·3d382 o49·=·b·+·45c·+·49d
  
380 o49·:·S383 o49·:·S
  
381 i50·:·CFa/degree384 i50·:·CFa/degree
  
382 o50·=·{1,·5}385 o50·=·{1,·2,·3}
  
383 o50·:·List386 o50·:·List
  
384 i51·:·CFa/(I·->·lin·%·I·==·0)·--·so·5·points·on·the·plane.387 i51·:·CFa/(I·->·lin·%·I·==·0)·--·so·5·points·on·the·plane.
  
385 o51·=·{false,·true}388 o51·=·{false,·true,·false}
  
386 o51·:·List389 o51·:·List
  
387 i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of·the·5·points390 i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of·the·5·points
  
388 o52·=·5391 o52·=·2
  
389 i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1392 i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1
  
390 o53·=·|·27·12·-34·9·-19·-43·-32·27·40·45·-13·29·-41·-13·22·-49·-4·-4·9·-23·43393 o53·=·|·31·42·28·25·19·3·43·-7·-3·-42·-29·-29·14·2·50·5·36·-13·-42·47·13·31
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./usr/share/doc/Macaulay2/QuaternaryQuartics/html/___Hilbert_spscheme_spof_sp6_sppoints_spin_spprojective_sp3-space.html
    
Offset 344, 15 lines modifiedOffset 344, 15 lines modified
344 ············<td>344 ············<td>
345 ··············<pre><code·class="language-macaulay2">i22·:·assert(dim·L·==·18)</code></pre>345 ··············<pre><code·class="language-macaulay2">i22·:·assert(dim·L·==·18)</code></pre>
346 ············</td>346 ············</td>
347 ··········</tr>347 ··········</tr>
348 ··········<tr>348 ··········<tr>
349 ············<td>349 ············<td>
350 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·L350 ··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·L
351 ·--·3.48423s·elapsed351 ·--·5.99366s·elapsed
  
352 o23·=·true</code></pre>352 o23·=·true</code></pre>
353 ············</td>353 ············</td>
354 ··········</tr>354 ··········</tr>
355 ········</table>355 ········</table>
356 ········<div>356 ········<div>
357 ··········<h2>The·Schreyer·resolution·and·minimal·Betti·numbers</h2>357 ··········<h2>The·Schreyer·resolution·and·minimal·Betti·numbers</h2>
Offset 556, 15 lines modifiedOffset 556, 15 lines modified
  
556 o39·:·Ideal·of·T</code></pre>556 o39·:·Ideal·of·T</code></pre>
557 ············</td>557 ············</td>
558 ··········</tr>558 ··········</tr>
559 ··········<tr>559 ··········<tr>
560 ············<td>560 ············<td>
561 ··············<pre><code·class="language-macaulay2">i40·:·elapsedTime·compsL441·=·decompose·L441;561 ··············<pre><code·class="language-macaulay2">i40·:·elapsedTime·compsL441·=·decompose·L441;
562 ·--·1.98893s·elapsed</code></pre>562 ·--·2.79803s·elapsed</code></pre>
563 ············</td>563 ············</td>
564 ··········</tr>564 ··········</tr>
565 ··········<tr>565 ··········<tr>
566 ············<td>566 ············<td>
567 ··············<pre><code·class="language-macaulay2">i41·:·#compsL441567 ··············<pre><code·class="language-macaulay2">i41·:·#compsL441
  
568 o41·=·2</code></pre>568 o41·=·2</code></pre>
Offset 591, 40 lines modifiedOffset 591, 40 lines modified
591 ··········<p>Both·components·are·rational,·and·here·are·random·points,·one·on·each·component:</p>591 ··········<p>Both·components·are·rational,·and·here·are·random·points,·one·on·each·component:</p>
592 ········</div>592 ········</div>
593 ········<table·class="examples">593 ········<table·class="examples">
594 ··········<tr>594 ··········<tr>
595 ············<td>595 ············<td>
596 ··············<pre><code·class="language-macaulay2">i44·:·pta·=·randomPointOnRationalVariety·compsL441_0596 ··············<pre><code·class="language-macaulay2">i44·:·pta·=·randomPointOnRationalVariety·compsL441_0
  
597 o44·=·|·-49·11·-25·17·44·-16·-27·40·-34·20·-19·29·41·19·-40·42·-13·5·17·39·31597 o44·=·|·-40·-4·-40·44·-22·-50·-30·13·-1·-16·45·-23·29·19·14·23·-21·19·14·29·6
598 ······-----------------------------------------------------------------------598 ······-----------------------------------------------------------------------
599 ······10·45·26·43·49·-32·-29·19·-50·15·18·37·-10·34·-28·|599 ······10·-32·18·-22·37·34·15·5·-10·-29·26·49·-50·45·-28·|
  
600 ···············1·······36600 ···············1·······36
601 o44·:·Matrix·kk··&lt;--·kk</code></pre>601 o44·:·Matrix·kk··&lt;--·kk</code></pre>
602 ············</td>602 ············</td>
603 ··········</tr>603 ··········</tr>
604 ··········<tr>604 ··········<tr>
605 ············<td>605 ············<td>
606 ··············<pre><code·class="language-macaulay2">i45·:·Fa·=·sub(F,·(vars·S)·|·pta)606 ··············<pre><code·class="language-macaulay2">i45·:·Fa·=·sub(F,·(vars·S)·|·pta)
  
607 ··············2··············2······························2···············607 ··············2··············2······························2···············
608 o45·=·ideal·(a··-·40b*c·+·20c··+·29a*d·-·16b*d·-·25c*d·-·49d·,·a*b·+·43b*c·+608 o45·=·ideal·(a··+·14b*c·-·16c··-·23a*d·-·50b*d·-·40c*d·-·40d·,·a*b·-·22b*c·+
609 ······-----------------------------------------------------------------------609 ······-----------------------------------------------------------------------
610 ·········2······························2···2··············2················610 ·········2··························2···2··············2··················
611 ······17c··+·31a*d·+·41b*d·-·34c*d·+·11d·,·b··+·34b*c·-·29c··+·37a*d·+·10b*d611 ······14c··+·6a*d·+·29b*d·-·c*d·-·4d·,·b··+·45b*c·+·15c··+·49a*d·+·10b*d·+
612 ······-----------------------------------------------------------------------612 ······-----------------------------------------------------------------------
613 ···················2···················2······························2·····2613 ·················2···················2·····························2·····2··
614 ······+·42c*d·-·27d·,·a*c·+·18b*c·+·49c··+·19a*d·+·39b*d·+·19c*d·+·44d·,·b*c·614 ······23c*d·-·30d·,·a*c·+·26b*c·+·37c··+·5a*d·+·29b*d·+·19c*d·-·22d·,·b*c··-
615 ······-----------------------------------------------------------------------615 ······-----------------------------------------------------------------------
616 ·····················2·········2········2········2······3···3············616 ···················2·········2········2········2······3···3················2·
617 ······-·50b*c*d·+·45c·d·-·32a*d··-·13b*d··-·19c*d··+·17d·,·c··-·28b*c*d·+617 ······10b*c*d·-·32c·d·+·34a*d··-·21b*d··+·45c*d··+·44d·,·c··-·28b*c*d·-·29c·d
618 ······-----------------------------------------------------------------------618 ······-----------------------------------------------------------------------
619 ·········2·········2········2·······2······3619 ·············2········2········2······3
620 ······15c·d·-·10a*d··+·26b*d··+·5c*d··+·40d·)620 ······-·50a*d··+·18b*d··+·19c*d··+·13d·)
  
621 o45·:·Ideal·of·S</code></pre>621 o45·:·Ideal·of·S</code></pre>
622 ············</td>622 ············</td>
623 ··········</tr>623 ··········</tr>
624 ··········<tr>624 ··········<tr>
625 ············<td>625 ············<td>
626 ··············<pre><code·class="language-macaulay2">i46·:·betti·res·Fa626 ··············<pre><code·class="language-macaulay2">i46·:·betti·res·Fa
Offset 638, 104 lines modifiedOffset 638, 107 lines modified
638 o46·:·BettiTally</code></pre>638 o46·:·BettiTally</code></pre>
639 ············</td>639 ············</td>
640 ··········</tr>640 ··········</tr>
641 ··········<tr>641 ··········<tr>
642 ············<td>642 ············<td>
643 ··············<pre><code·class="language-macaulay2">i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point643 ··············<pre><code·class="language-macaulay2">i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point
  
644 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+644 ······+------------------------------------------------------------------------------------------------------------+
645 o47·=·|ideal·(c·+·19d,·b·-·10d,·a·+·6d)···································································································································|645 o47·=·|ideal·(c·+·5d,·b·-·33d,·a·-·21d)············································································|
646 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+646 ······+------------------------------------------------------------------------------------------------------------+
647 ······|····························2··············2······················2···3················2········2········2······3·····2················2·········2········2······3·| 
648 ······|ideal·(a·+·18b·+·49c·-·3d,·b··+·34b*c·-·29c··-·50b*d·+·47c*d·-·17d·,·c··-·28b*c*d·+·15c·d·+·4b*d··-·10c*d··+·10d·,·b*c··-·50b*c*d·+·45c·d·-·43b*d··+·34c*d··+·22d·)|647 ······|······································2··············2······················································|
 648 ······|ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,·c··+·49c*d·+·42d·)·····················································|
 649 ······+------------------------------------------------------------------------------------------------------------+
 650 ······|·····························2······················2···························2···2·····················2·|
 651 ······|ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+·27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)|
649 ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+</code></pre>652 ······+------------------------------------------------------------------------------------------------------------+</code></pre>
650 ············</td>653 ············</td>
651 ··········</tr>654 ··········</tr>
652 ··········<tr>655 ··········<tr>
653 ············<td>656 ············<td>
654 ··············<pre><code·class="language-macaulay2">i48·:·CFa·=·minimalPrimes·Fa657 ··············<pre><code·class="language-macaulay2">i48·:·CFa·=·minimalPrimes·Fa
  
655 ·····································································2··658 ·············································································
656 o48·=·{ideal·(c·+·19d,·b·-·10d,·a·+·6d),·ideal·(a·+·18b·+·49c·-·3d,·b··+659 o48·=·{ideal·(c·+·5d,·b·-·33d,·a·-·21d),·ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,
657 ······-----------------------------------------------------------------------660 ······-----------------------------------------------------------------------
658 ·················2······················2···3················2········2··661 ·······2··············2································2··················
659 ······34b*c·-·29c··-·50b*d·+·47c*d·-·17d·,·c··-·28b*c*d·+·15c·d·+·4b*d··-662 ······c··+·49c*d·+·42d·),·ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+
660 ······-----------------------------------------------------------------------663 ······-----------------------------------------------------------------------
661 ···········2······3·····2················2·········2········2······3 
662 ······10c*d··+·10d·,·b*c··-·50b*c*d·+·45c·d·-·43b*d··+·34c*d··+·22d·)}664 ·········2···························2···2·····················2
 665 ······27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)}
  
663 o48·:·List</code></pre>666 o48·:·List</code></pre>
664 ············</td>667 ············</td>
665 ··········</tr>668 ··········</tr>
666 ··········<tr>669 ··········<tr>
667 ············<td>670 ············<td>
668 ··············<pre><code·class="language-macaulay2">i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane.671 ··············<pre><code·class="language-macaulay2">i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane.
  
669 o49·=·a·+·18b·+·49c·-·3d672 o49·=·b·+·45c·+·49d
  
670 o49·:·S</code></pre>673 o49·:·S</code></pre>
671 ············</td>674 ············</td>
672 ··········</tr>675 ··········</tr>
673 ··········<tr>676 ··········<tr>
674 ············<td>677 ············<td>
675 ··············<pre><code·class="language-macaulay2">i50·:·CFa/degree678 ··············<pre><code·class="language-macaulay2">i50·:·CFa/degree
  
676 o50·=·{1,·5}679 o50·=·{1,·2,·3}
  
677 o50·:·List</code></pre>680 o50·:·List</code></pre>
678 ············</td>681 ············</td>
679 ··········</tr>682 ··········</tr>
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251 ······|······31·········33········32·······34········35········36····|251 ······|······31·········33········32·······34········35········36····|
252 ······+--------------------------------------------------------------+252 ······+--------------------------------------------------------------+
253 i21·:·L·=·trim·groebnerStratum·F;253 i21·:·L·=·trim·groebnerStratum·F;
  
254 o21·:·Ideal·of·T254 o21·:·Ideal·of·T
255 i22·:·assert(dim·L·==·18)255 i22·:·assert(dim·L·==·18)
256 i23·:·elapsedTime·isPrime·L256 i23·:·elapsedTime·isPrime·L
257 ·--·3.48423s·elapsed257 ·--·5.99366s·elapsed
  
258 o23·=·true258 o23·=·true
259 *\x8**\x8**\x8**\x8**\x8*·T\x8Th\x8he\x8e·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·r\x8re\x8es\x8so\x8ol\x8lu\x8ut\x8ti\x8io\x8on\x8n·a\x8an\x8nd\x8d·m\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l·B\x8Be\x8et\x8tt\x8ti\x8i·n\x8nu\x8um\x8mb\x8be\x8er\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8*259 *\x8**\x8**\x8**\x8**\x8*·T\x8Th\x8he\x8e·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·r\x8re\x8es\x8so\x8ol\x8lu\x8ut\x8ti\x8io\x8on\x8n·a\x8an\x8nd\x8d·m\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l·B\x8Be\x8et\x8tt\x8ti\x8i·n\x8nu\x8um\x8mb\x8be\x8er\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8*
260 Schreyer's·construction·of·a·nonminimal·free·resolution·starts·with·a·Groebner260 Schreyer's·construction·of·a·nonminimal·free·resolution·starts·with·a·Groebner
261 basis.·First,·one·constructs·the·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·f\x8fr\x8ra\x8am\x8me\x8e·(see·La·Scala,·Stillman).·This261 basis.·First,·one·constructs·the·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·f\x8fr\x8ra\x8am\x8me\x8e·(see·La·Scala,·Stillman).·This
262 is·determined·solely·from·the·initial·ideal·$J$·and·its·minimal·generators·(but262 is·determined·solely·from·the·initial·ideal·$J$·and·its·minimal·generators·(but
263 depends·on·some·choices·of·ordering,·but·otherwise·is·combinatorial).·This263 depends·on·some·choices·of·ordering,·but·otherwise·is·combinatorial).·This
Offset 415, 15 lines modifiedOffset 415, 15 lines modified
415 We·now·compute·the·locus·in·$V(L)$·where·the·Betti·diagram·has·no·cancellation.415 We·now·compute·the·locus·in·$V(L)$·where·the·Betti·diagram·has·no·cancellation.
416 This·is·a·closed·subscheme·of·$V(L)$,·which·is·a·closed·subscheme·of·the416 This·is·a·closed·subscheme·of·$V(L)$,·which·is·a·closed·subscheme·of·the
417 Hilbert·scheme.·Notice·that·there·are·two·components.417 Hilbert·scheme.·Notice·that·there·are·two·components.
418 i39·:·L441·=·trim(L·+·ideal·M1);418 i39·:·L441·=·trim(L·+·ideal·M1);
  
419 o39·:·Ideal·of·T419 o39·:·Ideal·of·T
420 i40·:·elapsedTime·compsL441·=·decompose·L441;420 i40·:·elapsedTime·compsL441·=·decompose·L441;
421 ·--·1.98893s·elapsed421 ·--·2.79803s·elapsed
422 i41·:·#compsL441422 i41·:·#compsL441
  
423 o41·=·2423 o41·=·2
424 i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16.424 i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16.
  
425 o42·=·{16,·14}425 o42·=·{16,·14}
  
Offset 431, 36 lines modifiedOffset 431, 36 lines modified
431 i43·:·compsL441/dim·==·{16,·14}431 i43·:·compsL441/dim·==·{16,·14}
  
432 o43·=·true432 o43·=·true
433 Both·components·are·rational,·and·here·are·random·points,·one·on·each433 Both·components·are·rational,·and·here·are·random·points,·one·on·each
434 component:434 component:
435 i44·:·pta·=·randomPointOnRationalVariety·compsL441_0435 i44·:·pta·=·randomPointOnRationalVariety·compsL441_0
  
436 o44·=·|·-49·11·-25·17·44·-16·-27·40·-34·20·-19·29·41·19·-40·42·-13·5·17·39·31436 o44·=·|·-40·-4·-40·44·-22·-50·-30·13·-1·-16·45·-23·29·19·14·23·-21·19·14·29·6
437 ······-----------------------------------------------------------------------437 ······-----------------------------------------------------------------------
438 ······10·45·26·43·49·-32·-29·19·-50·15·18·37·-10·34·-28·|438 ······10·-32·18·-22·37·34·15·5·-10·-29·26·49·-50·45·-28·|
  
439 ···············1·······36439 ···············1·······36
440 o44·:·Matrix·kk··<--·kk440 o44·:·Matrix·kk··<--·kk
441 i45·:·Fa·=·sub(F,·(vars·S)·|·pta)441 i45·:·Fa·=·sub(F,·(vars·S)·|·pta)
  
442 ··············2··············2······························2442 ··············2··············2······························2
443 o45·=·ideal·(a··-·40b*c·+·20c··+·29a*d·-·16b*d·-·25c*d·-·49d·,·a*b·+·43b*c·+443 o45·=·ideal·(a··+·14b*c·-·16c··-·23a*d·-·50b*d·-·40c*d·-·40d·,·a*b·-·22b*c·+
444 ······-----------------------------------------------------------------------444 ······-----------------------------------------------------------------------
445 ·········2······························2···2··············2445 ·········2··························2···2··············2
446 ······17c··+·31a*d·+·41b*d·-·34c*d·+·11d·,·b··+·34b*c·-·29c··+·37a*d·+·10b*d446 ······14c··+·6a*d·+·29b*d·-·c*d·-·4d·,·b··+·45b*c·+·15c··+·49a*d·+·10b*d·+
447 ······-----------------------------------------------------------------------447 ······-----------------------------------------------------------------------
448 ···················2···················2······························2·····2448 ·················2···················2·····························2·····2
449 ······+·42c*d·-·27d·,·a*c·+·18b*c·+·49c··+·19a*d·+·39b*d·+·19c*d·+·44d·,·b*c449 ······23c*d·-·30d·,·a*c·+·26b*c·+·37c··+·5a*d·+·29b*d·+·19c*d·-·22d·,·b*c··-
450 ······-----------------------------------------------------------------------450 ······-----------------------------------------------------------------------
451 ·····················2·········2········2········2······3···3451 ···················2·········2········2········2······3···3················2
452 ······-·50b*c*d·+·45c·d·-·32a*d··-·13b*d··-·19c*d··+·17d·,·c··-·28b*c*d·+452 ······10b*c*d·-·32c·d·+·34a*d··-·21b*d··+·45c*d··+·44d·,·c··-·28b*c*d·-·29c·d
453 ······-----------------------------------------------------------------------453 ······-----------------------------------------------------------------------
454 ·········2·········2········2·······2······3454 ·············2········2········2······3
455 ······15c·d·-·10a*d··+·26b*d··+·5c*d··+·40d·)455 ······-·50a*d··+·18b*d··+·19c*d··+·13d·)
  
456 o45·:·Ideal·of·S456 o45·:·Ideal·of·S
457 i46·:·betti·res·Fa457 i46·:·betti·res·Fa
  
458 ·············0·1·2·3458 ·············0·1·2·3
459 o46·=·total:·1·6·8·3459 o46·=·total:·1·6·8·3
460 ··········0:·1·.·.·.460 ··········0:·1·.·.·.
Offset 468, 172 lines modifiedOffset 468, 256 lines modified
468 ··········2:·.·2·4·2468 ··········2:·.·2·4·2
  
469 o46·:·BettiTally469 o46·:·BettiTally
470 i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another470 i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another
471 point471 point
  
472 ······+------------------------------------------------------------------------472 ······+------------------------------------------------------------------------
 473 ------------------------------------+
473 ------------------------------------------------------------------------------- 
474 ------------+ 
475 o47·=·|ideal·(c·+·19d,·b·-·10d,·a·+·6d)474 o47·=·|ideal·(c·+·5d,·b·-·33d,·a·-·21d)
476 |475 |
477 ······+------------------------------------------------------------------------476 ······+------------------------------------------------------------------------
 477 ------------------------------------+
478 ------------------------------------------------------------------------------- 
479 ------------+ 
480 ······|····························2··············2······················2···3 
481 2········2········2······3·····2················2·········2········2······3·|478 ······|······································2··············2
482 ······|ideal·(a·+·18b·+·49c·-·3d,·b··+·34b*c·-·29c··-·50b*d·+·47c*d·-·17d·,·c 
483 -·28b*c*d·+·15c·d·+·4b*d··-·10c*d··+·10d·,·b*c··-·50b*c*d·+·45c·d·-·43b*d··+ 
484 34c*d··+·22d·)|479 |
 480 ······|ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,·c··+·49c*d·+·42d·)
 481 |
485 ······+------------------------------------------------------------------------482 ······+------------------------------------------------------------------------
 483 ------------------------------------+
 484 ······|·····························2······················2
 485 2···2·····················2·|
 486 ······|ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+·27d·,·b*c·-·30b*d·+
 487 16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)|
486 -------------------------------------------------------------------------------488 ······+------------------------------------------------------------------------
487 ------------+489 ------------------------------------+
488 i48·:·CFa·=·minimalPrimes·Fa490 i48·:·CFa·=·minimalPrimes·Fa
  
489 ·····································································2 
490 o48·=·{ideal·(c·+·19d,·b·-·10d,·a·+·6d),·ideal·(a·+·18b·+·49c·-·3d,·b··+ 
 491 o48·=·{ideal·(c·+·5d,·b·-·33d,·a·-·21d),·ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,
491 ······-----------------------------------------------------------------------492 ······-----------------------------------------------------------------------
492 ·················2······················2···3················2········2493 ·······2··············2································2
493 ······34b*c·-·29c··-·50b*d·+·47c*d·-·17d·,·c··-·28b*c*d·+·15c·d·+·4b*d··-494 ······c··+·49c*d·+·42d·),·ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+
494 ······-----------------------------------------------------------------------495 ······-----------------------------------------------------------------------
495 ···········2······3·····2················2·········2········2······3 
496 ······10c*d··+·10d·,·b*c··-·50b*c*d·+·45c·d·-·43b*d··+·34c*d··+·22d·)}496 ·········2···························2···2·····················2
 497 ······27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)}
  
497 o48·:·List498 o48·:·List
498 i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane.499 i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane.
  
499 o49·=·a·+·18b·+·49c·-·3d500 o49·=·b·+·45c·+·49d
  
500 o49·:·S501 o49·:·S
501 i50·:·CFa/degree502 i50·:·CFa/degree
  
502 o50·=·{1,·5}503 o50·=·{1,·2,·3}
  
503 o50·:·List504 o50·:·List
504 i51·:·CFa/(I·->·lin·%·I·==·0)·--·so·5·points·on·the·plane.505 i51·:·CFa/(I·->·lin·%·I·==·0)·--·so·5·points·on·the·plane.
  
505 o51·=·{false,·true}506 o51·=·{false,·true,·false}
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723 B
./usr/share/doc/Macaulay2/QuillenSuslin/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYSBsb2NhbCBzb2x1dGlv10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYSBsb2NhbCBzb2x1dGlv
11 biB0byB0aGUgdW5pbW9kdWxhciByb3cgcHJvYmxlbSBvdmVyIGEgbG9jYWxpemF0aW9uIGF0IGEg11 biB0byB0aGUgdW5pbW9kdWxhciByb3cgcHJvYmxlbSBvdmVyIGEgbG9jYWxpemF0aW9uIGF0IGEg
733 B
./usr/share/doc/Macaulay2/RInterface/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=197 #:len=19
8 bmV3IFJPYmplY3QgZnJvbSBDQw==8 bmV3IFJPYmplY3QgZnJvbSBDQw==
9 #:len=2519 #:len=251
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMyLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMyLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhOZXdGcm9tTWV0aG9kLFJPYmplY3QsQ0MpLCJuZXcg11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhOZXdGcm9tTWV0aG9kLFJPYmplY3QsQ0MpLCJuZXcg
755 B
./usr/share/doc/Macaulay2/RandomCanonicalCurves/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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6 #·End·of·header6 #·End·of·header
7 #:len=207 #:len=20
8 cmFuZG9tQ2Fub25pY2FsQ3VydmU=8 cmFuZG9tQ2Fub25pY2FsQ3VydmU=
9 #:len=2189 #:len=218
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11 dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7InJhbmRvbUNh11 dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7InJhbmRvbUNh
497 B
./usr/share/doc/Macaulay2/RandomCanonicalCurves/example-output/_canonical__Curve.out
    
Offset 6, 15 lines modifiedOffset 6, 15 lines modified
6 i2·:·g=14;6 i2·:·g=14;
  
7 i3·:·FF=ZZ/10007;7 i3·:·FF=ZZ/10007;
  
8 i4·:·R=FF[x_0..x_(g-1)];8 i4·:·R=FF[x_0..x_(g-1)];
  
9 i5·:·time·betti(I=(random·canonicalCurve)(g,R))9 i5·:·time·betti(I=(random·canonicalCurve)(g,R))
10 ·--·used·5.77629s·(cpu);·4.40231s·(thread);·0s·(gc)10 ·--·used·6.32319s·(cpu);·4.64363s·(thread);·0s·(gc)
  
11 ············0··111 ············0··1
12 o5·=·total:·1·6612 o5·=·total:·1·66
13 ·········0:·1··.13 ·········0:·1··.
14 ·········1:·.·6614 ·········1:·.·66
  
15 o5·:·BettiTally15 o5·:·BettiTally
1.12 KB
./usr/share/doc/Macaulay2/RandomCanonicalCurves/html/_canonical__Curve.html
    
Offset 92, 15 lines modifiedOffset 92, 15 lines modified
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·R=FF[x_0..x_(g-1)];</code></pre>93 ··············<pre><code·class="language-macaulay2">i4·:·R=FF[x_0..x_(g-1)];</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i5·:·time·betti(I=(random·canonicalCurve)(g,R))98 ··············<pre><code·class="language-macaulay2">i5·:·time·betti(I=(random·canonicalCurve)(g,R))
99 ·--·used·5.77629s·(cpu);·4.40231s·(thread);·0s·(gc)99 ·--·used·6.32319s·(cpu);·4.64363s·(thread);·0s·(gc)
  
100 ············0··1100 ············0··1
101 o5·=·total:·1·66101 o5·=·total:·1·66
102 ·········0:·1··.102 ·········0:·1··.
103 ·········1:·.·66103 ·········1:·.·66
  
104 o5·:·BettiTally</code></pre>104 o5·:·BettiTally</code></pre>
484 B
html2text {}
    
Offset 17, 15 lines modifiedOffset 17, 15 lines modified
17 unirationality·of·$M_g$·by·Severi,·Sernesi,·Chang-Ran·and·Verra.17 unirationality·of·$M_g$·by·Severi,·Sernesi,·Chang-Ran·and·Verra.
18 i1·:·setRandomSeed·"alpha";18 i1·:·setRandomSeed·"alpha";
19 ·--·setting·random·seed·to·1020628451819 ·--·setting·random·seed·to·10206284518
20 i2·:·g=14;20 i2·:·g=14;
21 i3·:·FF=ZZ/10007;21 i3·:·FF=ZZ/10007;
22 i4·:·R=FF[x_0..x_(g-1)];22 i4·:·R=FF[x_0..x_(g-1)];
23 i5·:·time·betti(I=(random·canonicalCurve)(g,R))23 i5·:·time·betti(I=(random·canonicalCurve)(g,R))
24 ·--·used·5.77629s·(cpu);·4.40231s·(thread);·0s·(gc)24 ·--·used·6.32319s·(cpu);·4.64363s·(thread);·0s·(gc)
  
25 ············0··125 ············0··1
26 o5·=·total:·1·6626 o5·=·total:·1·66
27 ·········0:·1··.27 ·········0:·1··.
28 ·········1:·.·6628 ·········1:·.·66
  
29 o5·:·BettiTally29 o5·:·BettiTally
751 B
./usr/share/doc/Macaulay2/RandomComplexes/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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1.62 KB
./usr/share/doc/Macaulay2/RandomComplexes/example-output/_test__Time__For__L__L__Lon__Syzygies.out
    
Offset 7, 42 lines modifiedOffset 7, 42 lines modified
  
7 o2·=·(10,·20)7 o2·=·(10,·20)
  
8 o2·:·Sequence8 o2·:·Sequence
  
9 i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11)9 i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11)
  
10 o3·=·({5,·2.91596e52,·9},·.00402662,·0)10 o3·=·({5,·2.91596e52,·9},·.00325742,·.00189569)
  
11 o3·:·Sequence11 o3·:·Sequence
  
12 i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)12 i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
  
13 o4·=·({50,·2.30853e454,·98},·.00398482,·.0319493)13 o4·=·({50,·2.30853e454,·98},·.00387398,·.0312424)
  
14 o4·:·Sequence14 o4·:·Sequence
  
15 i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})15 i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
  
16 o5·=·{{.00397726,·.0119902},·{.00526477,·.00533589},·{.00547969,·.00576887},16 o5·=·{{.00378133,·.0096551},·{.00275465,·.00319102},·{.00713067,·.00401062},
17 ·····------------------------------------------------------------------------17 ·····------------------------------------------------------------------------
18 ·····{.002566,·.00799695},·{.00400098,·.0159961},·{.00800651,·.0120027},18 ·····{.00903241,·.00957532},·{.00514034,·.0127987},·{.0075741,·.0150905},
19 ·····------------------------------------------------------------------------19 ·····------------------------------------------------------------------------
20 ·····{.00478571,·.00594504},·{.00510137,·.00601424},·{.00439059,·.00343678},20 ·····{.00487892,·.00693439},·{.00731596,·.00675704},·{.00597151,·.00187682},
21 ·····------------------------------------------------------------------------21 ·····------------------------------------------------------------------------
22 ·····{.00400003,·.00799544}}22 ·····{.00896122,·.00794756}}
  
23 o5·:·List23 o5·:·List
  
24 i6·:·1/10*sum(L,t->t_0)24 i6·:·1/10*sum(L,t->t_0)
  
25 o6·=·.00475729059999996425 o6·=·.006254110499999887
  
26 o6·:·RR·(of·precision·53)26 o6·:·RR·(of·precision·53)
  
27 i7·:·1/10*sum(L,t->t_1)27 i7·:·1/10*sum(L,t->t_1)
  
28 o7·=·.00824822839999996928 o7·=·.007783717299999981
  
29 o7·:·RR·(of·precision·53)29 o7·:·RR·(of·precision·53)
  
30 i8·:·30 i8·:·
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./usr/share/doc/Macaulay2/RandomComplexes/html/_test__Time__For__L__L__Lon__Syzygies.html
    
Offset 93, 57 lines modifiedOffset 93, 57 lines modified
93 o2·:·Sequence</code></pre>93 o2·:·Sequence</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11)98 ··············<pre><code·class="language-macaulay2">i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11)
  
99 o3·=·({5,·2.91596e52,·9},·.00402662,·0)99 o3·=·({5,·2.91596e52,·9},·.00325742,·.00189569)
  
100 o3·:·Sequence</code></pre>100 o3·:·Sequence</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)105 ··············<pre><code·class="language-macaulay2">i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
  
106 o4·=·({50,·2.30853e454,·98},·.00398482,·.0319493)106 o4·=·({50,·2.30853e454,·98},·.00387398,·.0312424)
  
107 o4·:·Sequence</code></pre>107 o4·:·Sequence</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})112 ··············<pre><code·class="language-macaulay2">i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
  
113 o5·=·{{.00397726,·.0119902},·{.00526477,·.00533589},·{.00547969,·.00576887},113 o5·=·{{.00378133,·.0096551},·{.00275465,·.00319102},·{.00713067,·.00401062},
114 ·····------------------------------------------------------------------------114 ·····------------------------------------------------------------------------
115 ·····{.002566,·.00799695},·{.00400098,·.0159961},·{.00800651,·.0120027},115 ·····{.00903241,·.00957532},·{.00514034,·.0127987},·{.0075741,·.0150905},
116 ·····------------------------------------------------------------------------116 ·····------------------------------------------------------------------------
117 ·····{.00478571,·.00594504},·{.00510137,·.00601424},·{.00439059,·.00343678},117 ·····{.00487892,·.00693439},·{.00731596,·.00675704},·{.00597151,·.00187682},
118 ·····------------------------------------------------------------------------118 ·····------------------------------------------------------------------------
119 ·····{.00400003,·.00799544}}119 ·····{.00896122,·.00794756}}
  
120 o5·:·List</code></pre>120 o5·:·List</code></pre>
121 ············</td>121 ············</td>
122 ··········</tr>122 ··········</tr>
123 ··········<tr>123 ··········<tr>
124 ············<td>124 ············<td>
125 ··············<pre><code·class="language-macaulay2">i6·:·1/10*sum(L,t->t_0)125 ··············<pre><code·class="language-macaulay2">i6·:·1/10*sum(L,t->t_0)
  
126 o6·=·.004757290599999964126 o6·=·.006254110499999887
  
127 o6·:·RR·(of·precision·53)</code></pre>127 o6·:·RR·(of·precision·53)</code></pre>
128 ············</td>128 ············</td>
129 ··········</tr>129 ··········</tr>
130 ··········<tr>130 ··········<tr>
131 ············<td>131 ············<td>
132 ··············<pre><code·class="language-macaulay2">i7·:·1/10*sum(L,t->t_1)132 ··············<pre><code·class="language-macaulay2">i7·:·1/10*sum(L,t->t_1)
  
133 o7·=·.008248228399999969133 o7·=·.007783717299999981
  
134 o7·:·RR·(of·precision·53)</code></pre>134 o7·:·RR·(of·precision·53)</code></pre>
135 ············</td>135 ············</td>
136 ··········</tr>136 ··········</tr>
137 ········</table>137 ········</table>
138 ······</div>138 ······</div>
139 ······<div>139 ······<div>
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Offset 25, 41 lines modifiedOffset 25, 41 lines modified
25 i2·:·r=10,n=2025 i2·:·r=10,n=20
  
26 o2·=·(10,·20)26 o2·=·(10,·20)
  
27 o2·:·Sequence27 o2·:·Sequence
28 i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11)28 i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11)
  
29 o3·=·({5,·2.91596e52,·9},·.00402662,·0)29 o3·=·({5,·2.91596e52,·9},·.00325742,·.00189569)
  
30 o3·:·Sequence30 o3·:·Sequence
31 i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)31 i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
  
32 o4·=·({50,·2.30853e454,·98},·.00398482,·.0319493)32 o4·=·({50,·2.30853e454,·98},·.00387398,·.0312424)
  
33 o4·:·Sequence33 o4·:·Sequence
34 i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})34 i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
  
35 o5·=·{{.00397726,·.0119902},·{.00526477,·.00533589},·{.00547969,·.00576887},35 o5·=·{{.00378133,·.0096551},·{.00275465,·.00319102},·{.00713067,·.00401062},
36 ·····------------------------------------------------------------------------36 ·····------------------------------------------------------------------------
37 ·····{.002566,·.00799695},·{.00400098,·.0159961},·{.00800651,·.0120027},37 ·····{.00903241,·.00957532},·{.00514034,·.0127987},·{.0075741,·.0150905},
38 ·····------------------------------------------------------------------------38 ·····------------------------------------------------------------------------
39 ·····{.00478571,·.00594504},·{.00510137,·.00601424},·{.00439059,·.00343678},39 ·····{.00487892,·.00693439},·{.00731596,·.00675704},·{.00597151,·.00187682},
40 ·····------------------------------------------------------------------------40 ·····------------------------------------------------------------------------
41 ·····{.00400003,·.00799544}}41 ·····{.00896122,·.00794756}}
  
42 o5·:·List42 o5·:·List
43 i6·:·1/10*sum(L,t->t_0)43 i6·:·1/10*sum(L,t->t_0)
  
44 o6·=·.00475729059999996444 o6·=·.006254110499999887
  
45 o6·:·RR·(of·precision·53)45 o6·:·RR·(of·precision·53)
46 i7·:·1/10*sum(L,t->t_1)46 i7·:·1/10*sum(L,t->t_1)
  
47 o7·=·.00824822839999996947 o7·=·.007783717299999981
  
48 o7·:·RR·(of·precision·53)48 o7·:·RR·(of·precision·53)
49 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8te\x8es\x8st\x8tT\x8Ti\x8im\x8me\x8eF\x8Fo\x8or\x8rL\x8LL\x8LL\x8Lo\x8on\x8nS\x8Sy\x8yz\x8zy\x8yg\x8gi\x8ie\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*49 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8te\x8es\x8st\x8tT\x8Ti\x8im\x8me\x8eF\x8Fo\x8or\x8rL\x8LL\x8LL\x8Lo\x8on\x8nS\x8Sy\x8yz\x8zy\x8yg\x8gi\x8ie\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
50 ····*·testTimeForLLLonSyzygies(ZZ,ZZ)50 ····*·testTimeForLLLonSyzygies(ZZ,ZZ)
51 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*51 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
52 The·object·_\x8t_\x8e_\x8s_\x8t_\x8T_\x8i_\x8m_\x8e_\x8F_\x8o_\x8r_\x8L_\x8L_\x8L_\x8o_\x8n_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.52 The·object·_\x8t_\x8e_\x8s_\x8t_\x8T_\x8i_\x8m_\x8e_\x8F_\x8o_\x8r_\x8L_\x8L_\x8L_\x8o_\x8n_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
53 ===============================================================================53 ===============================================================================
725 B
./usr/share/doc/Macaulay2/RandomCurves/dump/rawdocumentation.dump
    
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7 #:len=127 #:len=12
8 UmFuZG9tQ3VydmVz8 UmFuZG9tQ3VydmVz
9 #:len=7759 #:len=775
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmFuZG9tIGN1cnZlcyIsIERlc2NyaXB010 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmFuZG9tIGN1cnZlcyIsIERlc2NyaXB0
11 aW9uID0+IDE6KERJVntQQVJBe1RFWHsiVGhpcyBwYWNrYWdlIGxvYWRzIHRoZSAifSxUT3tuZXcg11 aW9uID0+IDE6KERJVntQQVJBe1RFWHsiVGhpcyBwYWNrYWdlIGxvYWRzIHRoZSAifSxUT3tuZXcg
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./usr/share/doc/Macaulay2/RandomCurvesOverVerySmallFiniteFields/dump/rawdocumentation.dump
    
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTI4Mywgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTI4Mywgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc21vb3RoQ2Fub25pY2FsQ3VydmVHZW51czE1LFBy11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc21vb3RoQ2Fub25pY2FsQ3VydmVHZW51czE1LFBy
557 B
./usr/share/doc/Macaulay2/RandomCurvesOverVerySmallFiniteFields/example-output/_smooth__Canonical__Curve.out
    
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1 --·-*-·M2-comint·-*-·hash:·115495276897903451521 --·-*-·M2-comint·-*-·hash:·11549527689790345152
  
2 i1·:·time·ICan·=·smoothCanonicalCurve(11,5);2 i1·:·time·ICan·=·smoothCanonicalCurve(11,5);
3 ·--·used·1.37708s·(cpu);·0.931475s·(thread);·0s·(gc)3 ·--·used·1.49016s·(cpu);·1.05274s·(thread);·0s·(gc)
  
4 ··············ZZ4 ··············ZZ
5 o1·:·Ideal·of·--[t·..t··]5 o1·:·Ideal·of·--[t·..t··]
6 ···············5··0···106 ···············5··0···10
  
7 i2·:·(dim·ICan,·genus·ICan,·degree·ICan)7 i2·:·(dim·ICan,·genus·ICan,·degree·ICan)
  
1.48 KB
./usr/share/doc/Macaulay2/RandomCurvesOverVerySmallFiniteFields/html/_smooth__Canonical__Curve.html
    
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82 ··········<p>If·the·option·<span·class="tt">Printing</span>·is·set·to·<span·class="tt">true</span>·then·printings·about·the·current·step·in·the·construction·are·displayed.</p>82 ··········<p>If·the·option·<span·class="tt">Printing</span>·is·set·to·<span·class="tt">true</span>·then·printings·about·the·current·step·in·the·construction·are·displayed.</p>
83 ··········<p></p>83 ··········<p></p>
84 ········</div>84 ········</div>
85 ········<table·class="examples">85 ········<table·class="examples">
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i1·:·time·ICan·=·smoothCanonicalCurve(11,5);88 ··············<pre><code·class="language-macaulay2">i1·:·time·ICan·=·smoothCanonicalCurve(11,5);
89 ·--·used·1.37708s·(cpu);·0.931475s·(thread);·0s·(gc)89 ·--·used·1.49016s·(cpu);·1.05274s·(thread);·0s·(gc)
  
90 ··············ZZ90 ··············ZZ
91 o1·:·Ideal·of·--[t·..t··]91 o1·:·Ideal·of·--[t·..t··]
92 ···············5··0···10</code></pre>92 ···············5··0···10</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
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29 For·g<=10·the·curves·are·constructed·via·plane·models.29 For·g<=10·the·curves·are·constructed·via·plane·models.
30 For·g<=13·the·curves·are·constructed·via·space·models.30 For·g<=13·the·curves·are·constructed·via·space·models.
31 For·g=14·the·curves·are·constructed·by·Verra's·method.31 For·g=14·the·curves·are·constructed·by·Verra's·method.
32 For·g=15·the·curves·are·constructed·via·matrix·factorizations.32 For·g=15·the·curves·are·constructed·via·matrix·factorizations.
33 If·the·option·Printing·is·set·to·true·then·printings·about·the·current·step·in33 If·the·option·Printing·is·set·to·true·then·printings·about·the·current·step·in
34 the·construction·are·displayed.34 the·construction·are·displayed.
35 i1·:·time·ICan·=·smoothCanonicalCurve(11,5);35 i1·:·time·ICan·=·smoothCanonicalCurve(11,5);
36 ·--·used·1.37708s·(cpu);·0.931475s·(thread);·0s·(gc)36 ·--·used·1.49016s·(cpu);·1.05274s·(thread);·0s·(gc)
  
37 ··············ZZ37 ··············ZZ
38 o1·:·Ideal·of·--[t·..t··]38 o1·:·Ideal·of·--[t·..t··]
39 ···············5··0···1039 ···············5··0···10
40 i2·:·(dim·ICan,·genus·ICan,·degree·ICan)40 i2·:·(dim·ICan,·genus·ICan,·degree·ICan)
  
41 o2·=·(2,·11,·20)41 o2·=·(2,·11,·20)
752 B
./usr/share/doc/Macaulay2/RandomGenus14Curves/dump/rawdocumentation.dump
    
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7 #:len=217 #:len=21
8 Y2Fub25pY2FsQ3VydmVHZW51czE08 Y2Fub25pY2FsQ3VydmVHZW51czE0
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566 B
./usr/share/doc/Macaulay2/RandomGenus14Curves/example-output/_random__Curve__Genus14__Degree18in__P6.out
    
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4 ·--·setting·random·seed·to·102062845184 ·--·setting·random·seed·to·10206284518
  
5 i2·:·FF=ZZ/10007;5 i2·:·FF=ZZ/10007;
  
6 i3·:·S=FF[x_0..x_6];6 i3·:·S=FF[x_0..x_6];
  
7 i4·:·time·I=randomCurveGenus14Degree18inP6(S);7 i4·:·time·I=randomCurveGenus14Degree18inP6(S);
8 ·--·used·1.27037s·(cpu);·1.11062s·(thread);·0s·(gc)8 ·--·used·1.44523s·(cpu);·1.22148s·(thread);·0s·(gc)
  
9 o4·:·Ideal·of·S9 o4·:·Ideal·of·S
  
10 i5·:·betti·res·I10 i5·:·betti·res·I
  
11 ············0··1··2··3··4·511 ············0··1··2··3··4·5
12 o5·=·total:·1·13·45·56·25·212 o5·=·total:·1·13·45·56·25·2
1.32 KB
./usr/share/doc/Macaulay2/RandomGenus14Curves/html/_random__Curve__Genus14__Degree18in__P6.html
    
Offset 93, 15 lines modifiedOffset 93, 15 lines modified
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i3·:·S=FF[x_0..x_6];</code></pre>94 ··············<pre><code·class="language-macaulay2">i3·:·S=FF[x_0..x_6];</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i4·:·time·I=randomCurveGenus14Degree18inP6(S);99 ··············<pre><code·class="language-macaulay2">i4·:·time·I=randomCurveGenus14Degree18inP6(S);
100 ·--·used·1.27037s·(cpu);·1.11062s·(thread);·0s·(gc)100 ·--·used·1.44523s·(cpu);·1.22148s·(thread);·0s·(gc)
  
101 o4·:·Ideal·of·S</code></pre>101 o4·:·Ideal·of·S</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i5·:·betti·res·I106 ··············<pre><code·class="language-macaulay2">i5·:·betti·res·I
588 B
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Offset 28, 15 lines modifiedOffset 28, 15 lines modified
28 fields·of·the·chosen·finite·characteristic·10007,·for·fields·of·characteristic28 fields·of·the·chosen·finite·characteristic·10007,·for·fields·of·characteristic
29 0·by·semi-continuity,·and,·hence,·for·all·but·finitely·many·primes·$p$.29 0·by·semi-continuity,·and,·hence,·for·all·but·finitely·many·primes·$p$.
30 i1·:·setRandomSeed("alpha");30 i1·:·setRandomSeed("alpha");
31 ·--·setting·random·seed·to·1020628451831 ·--·setting·random·seed·to·10206284518
32 i2·:·FF=ZZ/10007;32 i2·:·FF=ZZ/10007;
33 i3·:·S=FF[x_0..x_6];33 i3·:·S=FF[x_0..x_6];
34 i4·:·time·I=randomCurveGenus14Degree18inP6(S);34 i4·:·time·I=randomCurveGenus14Degree18inP6(S);
35 ·--·used·1.27037s·(cpu);·1.11062s·(thread);·0s·(gc)35 ·--·used·1.44523s·(cpu);·1.22148s·(thread);·0s·(gc)
  
36 o4·:·Ideal·of·S36 o4·:·Ideal·of·S
37 i5·:·betti·res·I37 i5·:·betti·res·I
  
38 ············0··1··2··3··4·538 ············0··1··2··3··4·5
39 o5·=·total:·1·13·45·56·25·239 o5·=·total:·1·13·45·56·25·2
40 ·········0:·1··.··.··.··.·.40 ·········0:·1··.··.··.··.·.
746 B
./usr/share/doc/Macaulay2/RandomIdeals/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=257 #:len=25
8 cmFuZG9tU2hlbGxhYmxlSWRlYWxDaGFpbg==8 cmFuZG9tU2hlbGxhYmxlSWRlYWxDaGFpbg==
9 #:len=17999 #:len=1799
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUHJvZHVjZXMgYSBjaGFpbiBvZiBpZGVh10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUHJvZHVjZXMgYSBjaGFpbiBvZiBpZGVh
11 bHMgZnJvbSBhIHJhbmRvbSBzaGVsbGluZyIsICJsaW5lbnVtIiA9PiA3NjAsIElucHV0cyA9PiB711 bHMgZnJvbSBhIHJhbmRvbSBzaGVsbGluZyIsICJsaW5lbnVtIiA9PiA3NjAsIElucHV0cyA9PiB7
833 B
./usr/share/doc/Macaulay2/RandomIdeals/example-output/___Random__Ideals.out
    
Offset 1, 23 lines modifiedOffset 1, 23 lines modified
1 --·-*-·M2-comint·-*-·hash:·95428017424294951611 --·-*-·M2-comint·-*-·hash:·9542801742429495161
  
2 i1·:·setRandomSeed(currentTime())2 i1·:·setRandomSeed(currentTime())
3 ·--·setting·random·seed·to·17492079923 ·--·setting·random·seed·to·1783630615
  
4 o1·=·17492079924 o1·=·1783630615
  
5 i2·:·kk=ZZ/101;5 i2·:·kk=ZZ/101;
  
6 i3·:·S=kk[vars(0..5)];6 i3·:·S=kk[vars(0..5)];
  
7 i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S)7 i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S)
8 ·--·used·1.41518s·(cpu);·1.17948s·(thread);·0s·(gc)8 ·--·used·1.65596s·(cpu);·1.36494s·(thread);·0s·(gc)
  
9 o4·=·Tally{4·=>·46·}9 o4·=·Tally{4·=>·41·}
10 ···········5·=>·21910 ···········5·=>·208
11 ···········6·=>·17911 ···········6·=>·182
12 ···········7·=>·4812 ···········7·=>·58
13 ···········8·=>·813 ···········8·=>·11
  
14 o4·:·Tally14 o4·:·Tally
  
15 i5·:·15 i5·:·
550 B
./usr/share/doc/Macaulay2/RandomIdeals/example-output/_random__Monomial.out
    
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1 --·-*-·M2-comint·-*-·hash:·59594655671978210461 --·-*-·M2-comint·-*-·hash:·5959465567197821046
  
2 i1·:·setRandomSeed(currentTime())2 i1·:·setRandomSeed(currentTime())
3 ·--·setting·random·seed·to·17492080323 ·--·setting·random·seed·to·1783630704
  
4 o1·=·17492080324 o1·=·1783630704
  
5 i2·:·kk=ZZ/1015 i2·:·kk=ZZ/101
  
6 o2·=·kk6 o2·=·kk
  
7 o2·:·QuotientRing7 o2·:·QuotientRing
  
Offset 16, 12 lines modifiedOffset 16, 12 lines modified
16 o3·=·S16 o3·=·S
  
17 o3·:·PolynomialRing17 o3·:·PolynomialRing
  
18 i4·:·randomMonomial(3,S)18 i4·:·randomMonomial(3,S)
  
19 ········219 ········2
20 o4·=·a*c20 o4·=·b*c
  
21 o4·:·S21 o4·:·S
  
22 i5·:·22 i5·:·
803 B
./usr/share/doc/Macaulay2/RandomIdeals/example-output/_random__Square__Free__Monomial__Ideal.out
    
Offset 1, 13 lines modifiedOffset 1, 13 lines modified
1 --·-*-·M2-comint·-*-·hash:·88763405620218654471 --·-*-·M2-comint·-*-·hash:·8876340562021865447
  
2 i1·:·setRandomSeed(currentTime())2 i1·:·setRandomSeed(currentTime())
3 ·--·setting·random·seed·to·17492080873 ·--·setting·random·seed·to·1783630827
  
4 o1·=·17492080874 o1·=·1783630827
  
5 i2·:·kk=ZZ/1015 i2·:·kk=ZZ/101
  
6 o2·=·kk6 o2·=·kk
  
7 o2·:·QuotientRing7 o2·:·QuotientRing
  
Offset 22, 18 lines modifiedOffset 22, 18 lines modified
22 o4·=·{3,·5,·7}22 o4·=·{3,·5,·7}
  
23 o4·:·List23 o4·:·List
  
24 i5·:·randomSquareFreeMonomialIdeal(L,·S)24 i5·:·randomSquareFreeMonomialIdeal(L,·S)
25 low·degree·gens·generated·everything25 low·degree·gens·generated·everything
  
26 o5·=·ideal(a*c*d)26 o5·=·ideal(a*c*e)
  
27 o5·:·Ideal·of·S27 o5·:·Ideal·of·S
  
28 i6·:·randomSquareFreeMonomialIdeal(5:2,·S)28 i6·:·randomSquareFreeMonomialIdeal(5:2,·S)
  
29 o6·=·ideal·(c*d,·b*d,·b*e,·a*c,·a*b)29 o6·=·ideal·(c*e,·a*b,·a*c,·d*e,·b*c)
  
30 o6·:·Ideal·of·S30 o6·:·Ideal·of·S
  
31 i7·:·31 i7·:·
1.22 KB
./usr/share/doc/Macaulay2/RandomIdeals/example-output/_random__Square__Free__Step.out
    
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1 --·-*-·M2-comint·-*-·hash:·105049112135082813151 --·-*-·M2-comint·-*-·hash:·10504911213508281315
  
2 i1·:·setRandomSeed(currentTime())2 i1·:·setRandomSeed(currentTime())
3 ·--·setting·random·seed·to·17492080733 ·--·setting·random·seed·to·1783630796
  
4 o1·=·17492080734 o1·=·1783630796
  
5 i2·:·S=ZZ/2[vars(0..3)]5 i2·:·S=ZZ/2[vars(0..3)]
  
6 o2·=·S6 o2·=·S
  
7 o2·:·PolynomialRing7 o2·:·PolynomialRing
  
Offset 15, 17 lines modifiedOffset 15, 17 lines modified
  
15 o3·=·monomialIdeal·(a*b,·a*d,·b*c*d)15 o3·=·monomialIdeal·(a*b,·a*d,·b*c*d)
  
16 o3·:·MonomialIdeal·of·S16 o3·:·MonomialIdeal·of·S
  
17 i4·:·randomSquareFreeStep·J17 i4·:·randomSquareFreeStep·J
  
18 o4·=·{monomialIdeal·(a*b*c,·a*d,·b*c*d),·{a*b*c,·a*d,·b*c*d},·{c*d,·b*d,·b*c,18 o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*c*d),·{a*b,·a*c,·a*d,·b*c*d},·{c*d,
19 ·····------------------------------------------------------------------------19 ·····------------------------------------------------------------------------
20 ·····a*c,·a*b}}20 ·····b*d,·b*c,·a}}
  
21 o4·:·List21 o4·:·List
  
22 i5·:·setRandomSeed(1)22 i5·:·setRandomSeed(1)
23 ·--·setting·random·seed·to·123 ·--·setting·random·seed·to·1
  
24 o5·=·124 o5·=·1
Offset 39, 15 lines modifiedOffset 39, 15 lines modified
39 i7·:·J·=·monomialIdeal·0_S39 i7·:·J·=·monomialIdeal·0_S
  
40 o7·=·monomialIdeal·()40 o7·=·monomialIdeal·()
  
41 o7·:·MonomialIdeal·of·S41 o7·:·MonomialIdeal·of·S
  
42 i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01));42 i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01));
43 ·--·used·3.1428s·(cpu);·2.24822s·(thread);·0s·(gc)43 ·--·used·3.94523s·(cpu);·2.78185s·(thread);·0s·(gc)
  
44 i9·:·#T44 i9·:·#T
  
45 o9·=·16845 o9·=·168
  
46 i10·:·T46 i10·:·T
  
2.03 KB
./usr/share/doc/Macaulay2/RandomIdeals/html/_random__Monomial.html
    
Offset 71, 17 lines modifiedOffset 71, 17 lines modified
71 ········<div>71 ········<div>
72 ··········<p>Chooses·a·random·monomial.</p>72 ··········<p>Chooses·a·random·monomial.</p>
73 ········</div>73 ········</div>
74 ········<table·class="examples">74 ········<table·class="examples">
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())77 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())
78 ·--·setting·random·seed·to·174920803278 ·--·setting·random·seed·to·1783630704
  
79 o1·=·1749208032</code></pre>79 o1·=·1783630704</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/10184 ··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101
  
85 o2·=·kk85 o2·=·kk
Offset 99, 15 lines modifiedOffset 99, 15 lines modified
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i4·:·randomMonomial(3,S)103 ··············<pre><code·class="language-macaulay2">i4·:·randomMonomial(3,S)
  
104 ········2104 ········2
105 o4·=·a*c105 o4·=·b*c
  
106 o4·:·S</code></pre>106 o4·:·S</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ········</table>109 ········</table>
110 ······</div>110 ······</div>
111 ······<div>111 ······<div>
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Offset 11, 31 lines modifiedOffset 11, 31 lines modified
11 ··········o·d,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·non-negative11 ··········o·d,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·non-negative
12 ··········o·S,·a·_\x8r_\x8i_\x8n_\x8g,·polynomial·ring12 ··········o·S,·a·_\x8r_\x8i_\x8n_\x8g,·polynomial·ring
13 ····*·Outputs:13 ····*·Outputs:
14 ··········o·m,·a·_\x8r_\x8i_\x8n_\x8g_\x8·_\x8e_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t,·monomial·of·S14 ··········o·m,·a·_\x8r_\x8i_\x8n_\x8g_\x8·_\x8e_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t,·monomial·of·S
15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
16 Chooses·a·random·monomial.16 Chooses·a·random·monomial.
17 i1·:·setRandomSeed(currentTime())17 i1·:·setRandomSeed(currentTime())
18 ·--·setting·random·seed·to·174920803218 ·--·setting·random·seed·to·1783630704
  
19 o1·=·174920803219 o1·=·1783630704
20 i2·:·kk=ZZ/10120 i2·:·kk=ZZ/101
  
21 o2·=·kk21 o2·=·kk
  
22 o2·:·QuotientRing22 o2·:·QuotientRing
23 i3·:·S=kk[a,b,c]23 i3·:·S=kk[a,b,c]
  
24 o3·=·S24 o3·=·S
  
25 o3·:·PolynomialRing25 o3·:·PolynomialRing
26 i4·:·randomMonomial(3,S)26 i4·:·randomMonomial(3,S)
  
27 ········227 ········2
28 o4·=·a*c28 o4·=·b*c
  
29 o4·:·S29 o4·:·S
30 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*30 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
31 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·monomial·ideal·with·given·degree·generators31 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·monomial·ideal·with·given·degree·generators
32 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8q_\x8u_\x8a_\x8r_\x8e_\x8F_\x8r_\x8e_\x8e_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·square-free·monomial·ideal·with32 ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8q_\x8u_\x8a_\x8r_\x8e_\x8F_\x8r_\x8e_\x8e_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·square-free·monomial·ideal·with
33 ······given·degree·generators33 ······given·degree·generators
34 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*34 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*
2.63 KB
./usr/share/doc/Macaulay2/RandomIdeals/html/_random__Square__Free__Monomial__Ideal.html
    
Offset 71, 17 lines modifiedOffset 71, 17 lines modified
71 ········<div>71 ········<div>
72 ··········<p>Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees·specified·by·the·list·or·sequence·L.</p>72 ··········<p>Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees·specified·by·the·list·or·sequence·L.</p>
73 ········</div>73 ········</div>
74 ········<table·class="examples">74 ········<table·class="examples">
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())77 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())
78 ·--·setting·random·seed·to·174920808778 ·--·setting·random·seed·to·1783630827
  
79 o1·=·1749208087</code></pre>79 o1·=·1783630827</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/10184 ··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101
  
85 o2·=·kk85 o2·=·kk
Offset 108, 24 lines modifiedOffset 108, 24 lines modified
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i5·:·randomSquareFreeMonomialIdeal(L,·S)112 ··············<pre><code·class="language-macaulay2">i5·:·randomSquareFreeMonomialIdeal(L,·S)
113 low·degree·gens·generated·everything113 low·degree·gens·generated·everything
  
114 o5·=·ideal(a*c*d)114 o5·=·ideal(a*c*e)
  
115 o5·:·Ideal·of·S</code></pre>115 o5·:·Ideal·of·S</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ··········<tr>118 ··········<tr>
119 ············<td>119 ············<td>
120 ··············<pre><code·class="language-macaulay2">i6·:·randomSquareFreeMonomialIdeal(5:2,·S)120 ··············<pre><code·class="language-macaulay2">i6·:·randomSquareFreeMonomialIdeal(5:2,·S)
  
121 o6·=·ideal·(c*d,·b*d,·b*e,·a*c,·a*b)121 o6·=·ideal·(c*e,·a*b,·a*c,·d*e,·b*c)
  
122 o6·:·Ideal·of·S</code></pre>122 o6·:·Ideal·of·S</code></pre>
123 ············</td>123 ············</td>
124 ··········</tr>124 ··········</tr>
125 ········</table>125 ········</table>
126 ······</div>126 ······</div>
127 ······<div>127 ······<div>
1.21 KB
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Offset 13, 17 lines modifiedOffset 13, 17 lines modified
13 ····*·Outputs:13 ····*·Outputs:
14 ··········o·I,·an·_\x8i_\x8d_\x8e_\x8a_\x8l,·square-free·monomial·ideal·with·generators·of14 ··········o·I,·an·_\x8i_\x8d_\x8e_\x8a_\x8l,·square-free·monomial·ideal·with·generators·of
15 ············specified·degrees15 ············specified·degrees
16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
17 Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees17 Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees
18 specified·by·the·list·or·sequence·L.18 specified·by·the·list·or·sequence·L.
19 i1·:·setRandomSeed(currentTime())19 i1·:·setRandomSeed(currentTime())
20 ·--·setting·random·seed·to·174920808720 ·--·setting·random·seed·to·1783630827
  
21 o1·=·174920808721 o1·=·1783630827
22 i2·:·kk=ZZ/10122 i2·:·kk=ZZ/101
  
23 o2·=·kk23 o2·=·kk
  
24 o2·:·QuotientRing24 o2·:·QuotientRing
25 i3·:·S=kk[a..e]25 i3·:·S=kk[a..e]
  
Offset 34, 20 lines modifiedOffset 34, 20 lines modified
  
34 o4·=·{3,·5,·7}34 o4·=·{3,·5,·7}
  
35 o4·:·List35 o4·:·List
36 i5·:·randomSquareFreeMonomialIdeal(L,·S)36 i5·:·randomSquareFreeMonomialIdeal(L,·S)
37 low·degree·gens·generated·everything37 low·degree·gens·generated·everything
  
38 o5·=·ideal(a*c*d)38 o5·=·ideal(a*c*e)
  
39 o5·:·Ideal·of·S39 o5·:·Ideal·of·S
40 i6·:·randomSquareFreeMonomialIdeal(5:2,·S)40 i6·:·randomSquareFreeMonomialIdeal(5:2,·S)
  
41 o6·=·ideal·(c*d,·b*d,·b*e,·a*c,·a*b)41 o6·=·ideal·(c*e,·a*b,·a*c,·d*e,·b*c)
  
42 o6·:·Ideal·of·S42 o6·:·Ideal·of·S
43 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*43 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
44 The·ideal·is·constructed·degree·by·degree,·starting·from·the·lowest·degree44 The·ideal·is·constructed·degree·by·degree,·starting·from·the·lowest·degree
45 specified.·If·there·are·not·enough·monomials·of·the·next·specified·degree·that45 specified.·If·there·are·not·enough·monomials·of·the·next·specified·degree·that
46 are·not·already·in·the·ideal,·the·function·prints·a·warning·and·returns·an46 are·not·already·in·the·ideal,·the·function·prints·a·warning·and·returns·an
47 ideal·containing·all·the·generators·of·that·degree.47 ideal·containing·all·the·generators·of·that·degree.
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Offset 79, 17 lines modifiedOffset 79, 17 lines modified
79 ··········<p>With·probability·p·the·routine·takes·the·Alexander·dual·of·I;·the·default·value·of·p·is·.05,·and·it·can·be·set·with·the·option·AlexanderProbility.</p>79 ··········<p>With·probability·p·the·routine·takes·the·Alexander·dual·of·I;·the·default·value·of·p·is·.05,·and·it·can·be·set·with·the·option·AlexanderProbility.</p>
80 ··········<p>Otherwise·uses·the·Metropolis·algorithm·to·produce·a·random·walk·on·the·space·of·square-free·ideals.·Note·that·there·are·a·LOT·of·square-free·ideals;·these·are·the·Dedekind·numbers,·and·the·sequence·(with·1,2,3,4,5,6,7,8·variables)·begins·3,6,20,168,7581,·7828354,·2414682040998,·56130437228687557907788.·(see·the·Online·Encyclopedia·of·Integer·Sequences·for·more·information).·Given·I·in·a·polynomial·ring·S,·we·make·a·list·ISocgens·of·the·square-free·minimal·monomial·generators·of·the·socle·of·S/(squares+I)·and·a·list·of·minimal·generators·Igens·of·I.·A·candidate·&quot;next&quot;·ideal·J·is·formed·as·follows:·We·choose·randomly·from·the·union·of·these·lists;·if·a·socle·element·is·chosen,·it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square-free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is·then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the·similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random·RR·&lt;·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1].</p>80 ··········<p>Otherwise·uses·the·Metropolis·algorithm·to·produce·a·random·walk·on·the·space·of·square-free·ideals.·Note·that·there·are·a·LOT·of·square-free·ideals;·these·are·the·Dedekind·numbers,·and·the·sequence·(with·1,2,3,4,5,6,7,8·variables)·begins·3,6,20,168,7581,·7828354,·2414682040998,·56130437228687557907788.·(see·the·Online·Encyclopedia·of·Integer·Sequences·for·more·information).·Given·I·in·a·polynomial·ring·S,·we·make·a·list·ISocgens·of·the·square-free·minimal·monomial·generators·of·the·socle·of·S/(squares+I)·and·a·list·of·minimal·generators·Igens·of·I.·A·candidate·&quot;next&quot;·ideal·J·is·formed·as·follows:·We·choose·randomly·from·the·union·of·these·lists;·if·a·socle·element·is·chosen,·it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square-free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is·then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the·similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random·RR·&lt;·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1].</p>
81 ········</div>81 ········</div>
82 ········<table·class="examples">82 ········<table·class="examples">
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())85 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())
86 ·--·setting·random·seed·to·174920807386 ·--·setting·random·seed·to·1783630796
  
87 o1·=·1749208073</code></pre>87 o1·=·1783630796</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i2·:·S=ZZ/2[vars(0..3)]92 ··············<pre><code·class="language-macaulay2">i2·:·S=ZZ/2[vars(0..3)]
  
93 o2·=·S93 o2·=·S
Offset 106, 17 lines modifiedOffset 106, 17 lines modified
106 o3·:·MonomialIdeal·of·S</code></pre>106 o3·:·MonomialIdeal·of·S</code></pre>
107 ············</td>107 ············</td>
108 ··········</tr>108 ··········</tr>
109 ··········<tr>109 ··········<tr>
110 ············<td>110 ············<td>
111 ··············<pre><code·class="language-macaulay2">i4·:·randomSquareFreeStep·J111 ··············<pre><code·class="language-macaulay2">i4·:·randomSquareFreeStep·J
  
112 o4·=·{monomialIdeal·(a*b*c,·a*d,·b*c*d),·{a*b*c,·a*d,·b*c*d},·{c*d,·b*d,·b*c,112 o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*c*d),·{a*b,·a*c,·a*d,·b*c*d},·{c*d,
113 ·····------------------------------------------------------------------------113 ·····------------------------------------------------------------------------
114 ·····a*c,·a*b}}114 ·····b*d,·b*c,·a}}
  
115 o4·:·List</code></pre>115 o4·:·List</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ········</table>118 ········</table>
119 ········<div>119 ········<div>
120 ··········<p>With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less·than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·1000·takes·about·2·seconds.</p>120 ··········<p>With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less·than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·1000·takes·about·2·seconds.</p>
Offset 147, 15 lines modifiedOffset 147, 15 lines modified
  
147 o7·:·MonomialIdeal·of·S</code></pre>147 o7·:·MonomialIdeal·of·S</code></pre>
148 ············</td>148 ············</td>
149 ··········</tr>149 ··········</tr>
150 ··········<tr>150 ··········<tr>
151 ············<td>151 ············<td>
152 ··············<pre><code·class="language-macaulay2">i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01));152 ··············<pre><code·class="language-macaulay2">i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01));
153 ·--·used·3.1428s·(cpu);·2.24822s·(thread);·0s·(gc)</code></pre>153 ·--·used·3.94523s·(cpu);·2.78185s·(thread);·0s·(gc)</code></pre>
154 ············</td>154 ············</td>
155 ··········</tr>155 ··········</tr>
156 ··········<tr>156 ··········<tr>
157 ············<td>157 ············<td>
158 ··············<pre><code·class="language-macaulay2">i9·:·#T158 ··············<pre><code·class="language-macaulay2">i9·:·#T
  
159 o9·=·168</code></pre>159 o9·=·168</code></pre>
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Offset 35, 32 lines modifiedOffset 35, 32 lines modified
35 choose·randomly·from·the·union·of·these·lists;·if·a·socle·element·is·chosen,35 choose·randomly·from·the·union·of·these·lists;·if·a·socle·element·is·chosen,
36 it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square-36 it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square-
37 free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is37 free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is
38 then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the38 then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the
39 similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random39 similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random
40 RR·<·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1].40 RR·<·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1].
41 i1·:·setRandomSeed(currentTime())41 i1·:·setRandomSeed(currentTime())
42 ·--·setting·random·seed·to·174920807342 ·--·setting·random·seed·to·1783630796
  
43 o1·=·174920807343 o1·=·1783630796
44 i2·:·S=ZZ/2[vars(0..3)]44 i2·:·S=ZZ/2[vars(0..3)]
  
45 o2·=·S45 o2·=·S
  
46 o2·:·PolynomialRing46 o2·:·PolynomialRing
47 i3·:·J·=·monomialIdeal"ab,ad,·bcd"47 i3·:·J·=·monomialIdeal"ab,ad,·bcd"
  
48 o3·=·monomialIdeal·(a*b,·a*d,·b*c*d)48 o3·=·monomialIdeal·(a*b,·a*d,·b*c*d)
  
49 o3·:·MonomialIdeal·of·S49 o3·:·MonomialIdeal·of·S
50 i4·:·randomSquareFreeStep·J50 i4·:·randomSquareFreeStep·J
  
51 o4·=·{monomialIdeal·(a*b*c,·a*d,·b*c*d),·{a*b*c,·a*d,·b*c*d},·{c*d,·b*d,·b*c,51 o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*c*d),·{a*b,·a*c,·a*d,·b*c*d},·{c*d,
52 ·····------------------------------------------------------------------------52 ·····------------------------------------------------------------------------
53 ·····a*c,·a*b}}53 ·····b*d,·b*c,·a}}
  
54 o4·:·List54 o4·:·List
55 With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less55 With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less
56 than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·100056 than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·1000
57 takes·about·2·seconds.57 takes·about·2·seconds.
58 i5·:·setRandomSeed(1)58 i5·:·setRandomSeed(1)
59 ·--·setting·random·seed·to·159 ·--·setting·random·seed·to·1
Offset 74, 15 lines modifiedOffset 74, 15 lines modified
74 i7·:·J·=·monomialIdeal·0_S74 i7·:·J·=·monomialIdeal·0_S
  
75 o7·=·monomialIdeal·()75 o7·=·monomialIdeal·()
  
76 o7·:·MonomialIdeal·of·S76 o7·:·MonomialIdeal·of·S
77 i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs77 i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs
78 (J,AlexanderProbability·=>·.01));78 (J,AlexanderProbability·=>·.01));
79 ·--·used·3.1428s·(cpu);·2.24822s·(thread);·0s·(gc)79 ·--·used·3.94523s·(cpu);·2.78185s·(thread);·0s·(gc)
80 i9·:·#T80 i9·:·#T
  
81 o9·=·16881 o9·=·168
82 i10·:·T82 i10·:·T
  
83 o10·=·Tally{monomialIdeal·()·=>·45····························}83 o10·=·Tally{monomialIdeal·()·=>·45····························}
84 ············monomialIdeal·(a*b*c,·a*b*d)·=>·3384 ············monomialIdeal·(a*b*c,·a*b*d)·=>·33
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./usr/share/doc/Macaulay2/RandomIdeals/html/index.html
    
Offset 54, 17 lines modifiedOffset 54, 17 lines modified
54 ········<div>54 ········<div>
55 ··········<p>This·package·can·be·used·to·make·experiments,·trying·many·ideals,·perhaps·over·small·fields.·For·example...what·would·you·expect·the·regularities·of·&quot;typical&quot;·monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a·bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a·second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done·conveniently.</p>55 ··········<p>This·package·can·be·used·to·make·experiments,·trying·many·ideals,·perhaps·over·small·fields.·For·example...what·would·you·expect·the·regularities·of·&quot;typical&quot;·monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a·bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a·second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done·conveniently.</p>
56 ········</div>56 ········</div>
57 ········<table·class="examples">57 ········<table·class="examples">
58 ··········<tr>58 ··········<tr>
59 ············<td>59 ············<td>
60 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())60 ··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime())
61 ·--·setting·random·seed·to·174920799261 ·--·setting·random·seed·to·1783630615
  
62 o1·=·1749207992</code></pre>62 o1·=·1783630615</code></pre>
63 ············</td>63 ············</td>
64 ··········</tr>64 ··········</tr>
65 ··········<tr>65 ··········<tr>
66 ············<td>66 ············<td>
67 ··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101;</code></pre>67 ··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101;</code></pre>
68 ············</td>68 ············</td>
69 ··········</tr>69 ··········</tr>
Offset 72, 21 lines modifiedOffset 72, 21 lines modified
72 ············<td>72 ············<td>
73 ··············<pre><code·class="language-macaulay2">i3·:·S=kk[vars(0..5)];</code></pre>73 ··············<pre><code·class="language-macaulay2">i3·:·S=kk[vars(0..5)];</code></pre>
74 ············</td>74 ············</td>
75 ··········</tr>75 ··········</tr>
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S)78 ··············<pre><code·class="language-macaulay2">i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S)
79 ·--·used·1.41518s·(cpu);·1.17948s·(thread);·0s·(gc)79 ·--·used·1.65596s·(cpu);·1.36494s·(thread);·0s·(gc)
  
80 o4·=·Tally{4·=>·46·}80 o4·=·Tally{4·=>·41·}
81 ···········5·=>·21981 ···········5·=>·208
82 ···········6·=>·17982 ···········6·=>·182
83 ···········7·=>·4883 ···········7·=>·58
84 ···········8·=>·884 ···········8·=>·11
  
85 o4·:·Tally</code></pre>85 o4·:·Tally</code></pre>
86 ············</td>86 ············</td>
87 ··········</tr>87 ··········</tr>
88 ········</table>88 ········</table>
89 ········<div>89 ········<div>
90 ··········<p>How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial·ideals?·We·invite·the·reader·to·experiment,·replacing·&quot;randomMonomialIdeal&quot;·above·with·&quot;randomBinomialIdeal&quot;·or·&quot;randomPureBinomialIdeal&quot;,·or·taking·larger·numbers·of·examples.·Click·the·link·&quot;Finding·Extreme·Examples&quot;·below·to·see·some·other,·more·elaborate·ways·to·search.</p>90 ··········<p>How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial·ideals?·We·invite·the·reader·to·experiment,·replacing·&quot;randomMonomialIdeal&quot;·above·with·&quot;randomBinomialIdeal&quot;·or·&quot;randomPureBinomialIdeal&quot;,·or·taking·larger·numbers·of·examples.·Click·the·link·&quot;Finding·Extreme·Examples&quot;·below·to·see·some·other,·more·elaborate·ways·to·search.</p>
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Offset 9, 27 lines modifiedOffset 9, 27 lines modified
9 This·package·can·be·used·to·make·experiments,·trying·many·ideals,·perhaps·over9 This·package·can·be·used·to·make·experiments,·trying·many·ideals,·perhaps·over
10 small·fields.·For·example...what·would·you·expect·the·regularities·of·"typical"10 small·fields.·For·example...what·would·you·expect·the·regularities·of·"typical"
11 monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a11 monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a
12 bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a12 bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a
13 second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done13 second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done
14 conveniently.14 conveniently.
15 i1·:·setRandomSeed(currentTime())15 i1·:·setRandomSeed(currentTime())
16 ·--·setting·random·seed·to·174920799216 ·--·setting·random·seed·to·1783630615
  
17 o1·=·174920799217 o1·=·1783630615
18 i2·:·kk=ZZ/101;18 i2·:·kk=ZZ/101;
19 i3·:·S=kk[vars(0..5)];19 i3·:·S=kk[vars(0..5)];
20 i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S)20 i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S)
21 ·--·used·1.41518s·(cpu);·1.17948s·(thread);·0s·(gc)21 ·--·used·1.65596s·(cpu);·1.36494s·(thread);·0s·(gc)
  
22 o4·=·Tally{4·=>·46·}22 o4·=·Tally{4·=>·41·}
23 ···········5·=>·21923 ···········5·=>·208
24 ···········6·=>·17924 ···········6·=>·182
25 ···········7·=>·4825 ···········7·=>·58
26 ···········8·=>·826 ···········8·=>·11
  
27 o4·:·Tally27 o4·:·Tally
28 How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial28 How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial
29 ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal"29 ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal"
30 above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger30 above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger
31 numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see31 numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see
32 some·other,·more·elaborate·ways·to·search.32 some·other,·more·elaborate·ways·to·search.
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7 #:len=127 #:len=12
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11 IHRoZSBpbmRleGVkIHZhcmlhYmxlIG5hbWUgZm9yIHRoZSBwb2x5bm9taWFsIHJpbmciLCAibGlu11 IHRoZSBpbmRleGVkIHZhcmlhYmxlIG5hbWUgZm9yIHRoZSBwb2x5bm9taWFsIHJpbmciLCAibGlu
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6 #·End·of·header6 #·End·of·header
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11 ZSBjb25zdHJ1Y3Rpb24gb2YgYSByYW5kb20gb2JqZWN0IiwgImxpbmVudW0iID0+IDI2MiwgImZp11 ZSBjb25zdHJ1Y3Rpb24gb2YgYSByYW5kb20gb2JqZWN0IiwgImxpbmVudW0iID0+IDI2MiwgImZp
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2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=497 #:len=49
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9 #:len=3829 #:len=382
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc2LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc2LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV0ZUxpbmVhclN5c3RlbU9uTm9kYWxQbGFu11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV0ZUxpbmVhclN5c3RlbU9uTm9kYWxQbGFu
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=467 #:len=46
8 ZmluZEFOb25aZXJvTWlub3IoLi4uLFBvaW50Q2hlY2tBdHRlbXB0cz0+Li4uKQ==8 ZmluZEFOb25aZXJvTWlub3IoLi4uLFBvaW50Q2hlY2tBdHRlbXB0cz0+Li4uKQ==
9 #:len=3159 #:len=315
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg5MCwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg5MCwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbZmluZEFOb25aZXJvTWlub3IsUG9pbnRDaGVja0F011 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbZmluZEFOb25aZXJvTWlub3IsUG9pbnRDaGVja0F0
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./usr/share/doc/Macaulay2/RandomPoints/example-output/_dim__Via__Bezout.out
    
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5 i2·:·S=kk[y_0..y_8];5 i2·:·S=kk[y_0..y_8];
  
6 i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2;6 i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2;
  
7 o3·:·Ideal·of·S7 o3·:·Ideal·of·S
  
8 i4·:·elapsedTime·dimViaBezout(I)8 i4·:·elapsedTime·dimViaBezout(I)
9 ·--·1.05597s·elapsed9 ·--·2.59449s·elapsed
  
10 o4·=·410 o4·=·4
  
11 i5·:·elapsedTime·dim·I11 i5·:·elapsedTime·dim·I
12 ·--·3.02738s·elapsed12 ·--·12.0898s·elapsed
  
13 o5·=·413 o5·=·4
  
14 i6·:·14 i6·:·
444 B
./usr/share/doc/Macaulay2/RandomPoints/example-output/_extend__Ideal__By__Non__Zero__Minor.out
    
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35 i8·:·i·=·0;35 i8·:·i·=·0;
  
36 i9·:·J·=·I;36 i9·:·J·=·I;
  
37 o9·:·Ideal·of·T37 o9·:·Ideal·of·T
  
38 i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·);38 i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·);
39 ·--·1.65638s·elapsed39 ·--·4.07353s·elapsed
  
40 i11·:·dim·J40 i11·:·dim·J
  
41 o11·=·141 o11·=·1
  
42 i12·:·i42 i12·:·i
  
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./usr/share/doc/Macaulay2/RandomPoints/example-output/_random__Points.out
    
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27 i6·:·S=ZZ/103[y_0..y_30];27 i6·:·S=ZZ/103[y_0..y_30];
  
28 i7·:·I=minors(2,random(S^3,S^{3:-1}));28 i7·:·I=minors(2,random(S^3,S^{3:-1}));
  
29 o7·:·Ideal·of·S29 o7·:·Ideal·of·S
  
30 i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable)30 i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable)
31 ·--·2.64297s·elapsed31 ·--·6.10006s·elapsed
  
32 o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0,32 o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0,
33 ·····------------------------------------------------------------------------33 ·····------------------------------------------------------------------------
34 ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}}34 ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}}
  
35 o8·:·List35 o8·:·List
  
36 i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose)36 i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose)
37 ·--·1.792s·elapsed37 ·--·4.67273s·elapsed
  
38 o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16,38 o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16,
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
40 ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}}40 ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}}
  
41 o9·:·List41 o9·:·List
  
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./usr/share/doc/Macaulay2/RandomPoints/html/_dim__Via__Bezout.html
    
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95 o3·:·Ideal·of·S</code></pre>95 o3·:·Ideal·of·S</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·dimViaBezout(I)100 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·dimViaBezout(I)
101 ·--·1.05597s·elapsed101 ·--·2.59449s·elapsed
  
102 o4·=·4</code></pre>102 o4·=·4</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·dim·I107 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·dim·I
108 ·--·3.02738s·elapsed108 ·--·12.0898s·elapsed
  
109 o5·=·4</code></pre>109 o5·=·4</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ········</table>112 ········</table>
113 ········<div>113 ········<div>
114 ··········<p>The·user·may·set·the·<span·class="tt">MinimumFieldSize</span>·to·ensure·that·the·field·being·worked·over·is·big·enough.··For·instance,·there·are·relatively·few·linear·spaces·over·a·field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided.··If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on·ambient·ring.</p>114 ··········<p>The·user·may·set·the·<span·class="tt">MinimumFieldSize</span>·to·ensure·that·the·field·being·worked·over·is·big·enough.··For·instance,·there·are·relatively·few·linear·spaces·over·a·field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided.··If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on·ambient·ring.</p>
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32 examples,·the·built·in·dim·function·is·much·faster.32 examples,·the·built·in·dim·function·is·much·faster.
33 i1·:·kk=ZZ/101;33 i1·:·kk=ZZ/101;
34 i2·:·S=kk[y_0..y_8];34 i2·:·S=kk[y_0..y_8];
35 i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2;35 i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2;
  
36 o3·:·Ideal·of·S36 o3·:·Ideal·of·S
37 i4·:·elapsedTime·dimViaBezout(I)37 i4·:·elapsedTime·dimViaBezout(I)
38 ·--·1.05597s·elapsed38 ·--·2.59449s·elapsed
  
39 o4·=·439 o4·=·4
40 i5·:·elapsedTime·dim·I40 i5·:·elapsedTime·dim·I
41 ·--·3.02738s·elapsed41 ·--·12.0898s·elapsed
  
42 o5·=·442 o5·=·4
43 The·user·may·set·the·MinimumFieldSize·to·ensure·that·the·field·being·worked43 The·user·may·set·the·MinimumFieldSize·to·ensure·that·the·field·being·worked
44 over·is·big·enough.·For·instance,·there·are·relatively·few·linear·spaces·over·a44 over·is·big·enough.·For·instance,·there·are·relatively·few·linear·spaces·over·a
45 field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided.45 field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided.
46 If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on46 If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on
47 ambient·ring.47 ambient·ring.
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155 o9·:·Ideal·of·T</code></pre>155 o9·:·Ideal·of·T</code></pre>
156 ············</td>156 ············</td>
157 ··········</tr>157 ··········</tr>
158 ··········<tr>158 ··········<tr>
159 ············<td>159 ············<td>
160 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime(while·(i·&lt;·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·);160 ··············<pre><code·class="language-macaulay2">i10·:·elapsedTime(while·(i·&lt;·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·);
161 ·--·1.65638s·elapsed</code></pre>161 ·--·4.07353s·elapsed</code></pre>
162 ············</td>162 ············</td>
163 ··········</tr>163 ··········</tr>
164 ··········<tr>164 ··········<tr>
165 ············<td>165 ············<td>
166 ··············<pre><code·class="language-macaulay2">i11·:·dim·J166 ··············<pre><code·class="language-macaulay2">i11·:·dim·J
  
167 o11·=·1</code></pre>167 o11·=·1</code></pre>
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79 o7·:·Matrix·T··<--·T79 o7·:·Matrix·T··<--·T
80 i8·:·i·=·0;80 i8·:·i·=·0;
81 i9·:·J·=·I;81 i9·:·J·=·I;
  
82 o9·:·Ideal·of·T82 o9·:·Ideal·of·T
83 i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=83 i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=
84 extendIdealByNonZeroMinor(4,·M,·J))·);84 extendIdealByNonZeroMinor(4,·M,·J))·);
85 ·--·1.65638s·elapsed85 ·--·4.07353s·elapsed
86 i11·:·dim·J86 i11·:·dim·J
  
87 o11·=·187 o11·=·1
88 i12·:·i88 i12·:·i
  
89 o12·=·489 o12·=·4
90 In·this·particular·example,·there·tend·to·be·about·5·associated·primes·when90 In·this·particular·example,·there·tend·to·be·about·5·associated·primes·when
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144 o7·:·Ideal·of·S</code></pre>144 o7·:·Ideal·of·S</code></pre>
145 ············</td>145 ············</td>
146 ··········</tr>146 ··········</tr>
147 ··········<tr>147 ··········<tr>
148 ············<td>148 ············<td>
149 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable)149 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable)
150 ·--·2.64297s·elapsed150 ·--·6.10006s·elapsed
  
151 o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0,151 o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0,
152 ·····------------------------------------------------------------------------152 ·····------------------------------------------------------------------------
153 ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}}153 ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}}
  
154 o8·:·List</code></pre>154 o8·:·List</code></pre>
155 ············</td>155 ············</td>
156 ··········</tr>156 ··········</tr>
157 ··········<tr>157 ··········<tr>
158 ············<td>158 ············<td>
159 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose)159 ··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose)
160 ·--·1.792s·elapsed160 ·--·4.67273s·elapsed
  
161 o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16,161 o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16,
162 ·····------------------------------------------------------------------------162 ·····------------------------------------------------------------------------
163 ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}}163 ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}}
  
164 o9·:·List</code></pre>164 o9·:·List</code></pre>
165 ············</td>165 ············</td>
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66 first·in·rings·with·more·variables.66 first·in·rings·with·more·variables.
67 i6·:·S=ZZ/103[y_0..y_30];67 i6·:·S=ZZ/103[y_0..y_30];
68 i7·:·I=minors(2,random(S^3,S^{3:-1}));68 i7·:·I=minors(2,random(S^3,S^{3:-1}));
  
69 o7·:·Ideal·of·S69 o7·:·Ideal·of·S
70 i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,70 i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,
71 DecompositionStrategy=>MultiplicationTable)71 DecompositionStrategy=>MultiplicationTable)
72 ·--·2.64297s·elapsed72 ·--·6.10006s·elapsed
  
73 o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0,73 o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0,
74 ·····------------------------------------------------------------------------74 ·····------------------------------------------------------------------------
75 ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}}75 ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}}
  
76 o8·:·List76 o8·:·List
77 i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,77 i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,
78 DecompositionStrategy=>Decompose)78 DecompositionStrategy=>Decompose)
79 ·--·1.792s·elapsed79 ·--·4.67273s·elapsed
  
80 o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16,80 o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16,
81 ·····------------------------------------------------------------------------81 ·····------------------------------------------------------------------------
82 ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}}82 ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}}
  
83 o9·:·List83 o9·:·List
84 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mP\x8Po\x8oi\x8in\x8nt\x8ts\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*84 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mP\x8Po\x8oi\x8in\x8nt\x8ts\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
772 B
./usr/share/doc/Macaulay2/RandomSpaceCurves/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=387 #:len=38
8 a25vd25VbmlyYXRpb25hbENvbXBvbmVudE9mU3BhY2VDdXJ2ZXM=8 a25vd25VbmlyYXRpb25hbENvbXBvbmVudE9mU3BhY2VDdXJ2ZXM=
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11 IHVuaXJhdGlvbmFsIGNvbnN0cnVjdGlvbiBmb3IgYSBjb21wb25lbnQgb2YgdGhlIEhpbGJlcnQg11 IHVuaXJhdGlvbmFsIGNvbnN0cnVjdGlvbiBmb3IgYSBjb21wb25lbnQgb2YgdGhlIEhpbGJlcnQg
773 B
./usr/share/doc/Macaulay2/RationalMaps/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
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11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaXNCaXJhdGlvbmFsT250b0ltYWdlLEFzc3VtZURv11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaXNCaXJhdGlvbmFsT250b0ltYWdlLEFzc3VtZURv
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./usr/share/doc/Macaulay2/RationalMaps/example-output/_inverse__Of__Map.out
    
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49 i12·:·Q=QQ[x,y,z,t,u];49 i12·:·Q=QQ[x,y,z,t,u];
  
50 i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}});50 i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}});
  
51 o13·:·RingMap·Q·<--·Q51 o13·:·RingMap·Q·<--·Q
  
52 i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0)52 i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0)
53 ·--·used·2.53794s·(cpu);·0.559042s·(thread);·0s·(gc)53 ·--·used·2.41164s·(cpu);·0.56543s·(thread);·0s·(gc)
  
54 ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····12454 ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····124
55 o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u}55 o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u}
  
56 o14·:·RationalMapping56 o14·:·RationalMapping
  
57 i15·:·R=QQ[x,y,z,t]/(z-2*t);57 i15·:·R=QQ[x,y,z,t]/(z-2*t);
4.33 KB
./usr/share/doc/Macaulay2/RationalMaps/html/_inverse__Of__Map.html
    
Offset 189, 15 lines modifiedOffset 189, 15 lines modified
  
189 o13·:·RingMap·Q·&lt;--·Q</code></pre>189 o13·:·RingMap·Q·&lt;--·Q</code></pre>
190 ············</td>190 ············</td>
191 ··········</tr>191 ··········</tr>
192 ··········<tr>192 ··········<tr>
193 ············<td>193 ············<td>
194 ··············<pre><code·class="language-macaulay2">i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0)194 ··············<pre><code·class="language-macaulay2">i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0)
195 ·--·used·2.53794s·(cpu);·0.559042s·(thread);·0s·(gc)195 ·--·used·2.41164s·(cpu);·0.56543s·(thread);·0s·(gc)
  
196 ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····124196 ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····124
197 o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u}197 o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u}
  
198 o14·:·RationalMapping</code></pre>198 o14·:·RationalMapping</code></pre>
199 ············</td>199 ············</td>
200 ··········</tr>200 ··········</tr>
901 B
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Offset 94, 15 lines modifiedOffset 94, 15 lines modified
94 o11·:·Ideal·of·blowUpSubvar94 o11·:·Ideal·of·blowUpSubvar
95 The·next·example·is·a·birational·map·on·$\mathbb{P}^4$.95 The·next·example·is·a·birational·map·on·$\mathbb{P}^4$.
96 i12·:·Q=QQ[x,y,z,t,u];96 i12·:·Q=QQ[x,y,z,t,u];
97 i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}});97 i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}});
  
98 o13·:·RingMap·Q·<--·Q98 o13·:·RingMap·Q·<--·Q
99 i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0)99 i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0)
100 ·--·used·2.53794s·(cpu);·0.559042s·(thread);·0s·(gc)100 ·--·used·2.41164s·(cpu);·0.56543s·(thread);·0s·(gc)
  
101 ································125···124······120·5····124····100·25·····104101 ································125···124······120·5····124····100·25·····104
102 20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120102 20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120
103 8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6103 8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6
104 28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70104 28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70
105 11···········48·65·12···········52·60·13···········56·55·14···········60·50·15105 11···········48·65·12···········52·60·13···········56·55·14···········60·50·15
106 64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25106 64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25
724 B
./usr/share/doc/Macaulay2/RationalPoints/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=87 #:len=8
8 U29ydEdlbnM=8 U29ydEdlbnM=
9 #:len=2469 #:len=246
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg3LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg3LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJTb3J0R2VucyIsIlNvcnRHZW5zIiwiUmF0aW9uYWxQ11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJTb3J0R2VucyIsIlNvcnRHZW5zIiwiUmF0aW9uYWxQ
743 B
./usr/share/doc/Macaulay2/RationalPoints2/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=207 #:len=20
8 bmV0KFByb2plY3RpdmVQb2ludCk=8 bmV0KFByb2plY3RpdmVQb2ludCk=
9 #:len=2059 #:len=205
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTcsICJ1bmRvY3VtZW50ZWQiID0+IHRy10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTcsICJ1bmRvY3VtZW50ZWQiID0+IHRy
11 dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KG5ldCxQcm9q11 dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KG5ldCxQcm9q
1.26 KB
./usr/share/doc/Macaulay2/RationalPoints2/example-output/_rational__Points.out
    
Offset 48, 15 lines modifiedOffset 48, 15 lines modified
48 ·············0····1····2····3····4····5····6····7····8····9····1048 ·············0····1····2····3····4····5····6····7····8····9····10
  
49 ················ZZ49 ················ZZ
50 o13·:·Ideal·of·---[u·..u··]50 o13·:·Ideal·of·---[u·..u··]
51 ···············101··0···1051 ···············101··0···10
  
52 i14·:·time·rationalPoints(I,·Amount·=>·true)52 i14·:·time·rationalPoints(I,·Amount·=>·true)
53 ·--·used·0.054712s·(cpu);·0.0203051s·(thread);·0s·(gc)53 ·--·used·0.0788427s·(cpu);·0.0193069s·(thread);·0s·(gc)
  
54 o14·=·11046221254112045100154 o14·=·110462212541120451001
  
55 i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z);55 i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z);
  
56 o16·:·Ideal·of·QQ[x..z]56 o16·:·Ideal·of·QQ[x..z]
  
Offset 141, 24 lines modifiedOffset 141, 24 lines modified
141 o30·:·Ideal·of·R141 o30·:·Ideal·of·R
  
142 i31·:·nodes·=·I·+·ideal·jacobian·I;142 i31·:·nodes·=·I·+·ideal·jacobian·I;
  
143 o31·:·Ideal·of·R143 o31·:·Ideal·of·R
  
144 i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true);144 i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true);
145 ·--·used·0.671447s·(cpu);·0.594908s·(thread);·0s·(gc)145 ·--·used·0.872232s·(cpu);·0.745952s·(thread);·0s·(gc)
146 --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)146 --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)
  
147 i33·:·#oo147 i33·:·#oo
  
148 o33·=·31148 o33·=·31
  
149 i34·:·nodes'·=·baseChange_32003·nodes;149 i34·:·nodes'·=·baseChange_32003·nodes;
  
150 o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]150 o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]
  
151 i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true)151 i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true)
152 ·--·used·0.224761s·(cpu);·0.184901s·(thread);·0s·(gc)152 ·--·used·0.254304s·(cpu);·0.208144s·(thread);·0s·(gc)
  
153 o35·=·31153 o35·=·31
  
154 i36·:·154 i36·:·
3.51 KB
./usr/share/doc/Macaulay2/RationalPoints2/html/_rational__Points.html
    
Offset 178, 15 lines modifiedOffset 178, 15 lines modified
178 o13·:·Ideal·of·---[u·..u··]178 o13·:·Ideal·of·---[u·..u··]
179 ···············101··0···10</code></pre>179 ···············101··0···10</code></pre>
180 ············</td>180 ············</td>
181 ··········</tr>181 ··········</tr>
182 ··········<tr>182 ··········<tr>
183 ············<td>183 ············<td>
184 ··············<pre><code·class="language-macaulay2">i14·:·time·rationalPoints(I,·Amount·=>·true)184 ··············<pre><code·class="language-macaulay2">i14·:·time·rationalPoints(I,·Amount·=>·true)
185 ·--·used·0.054712s·(cpu);·0.0203051s·(thread);·0s·(gc)185 ·--·used·0.0788427s·(cpu);·0.0193069s·(thread);·0s·(gc)
  
186 o14·=·110462212541120451001</code></pre>186 o14·=·110462212541120451001</code></pre>
187 ············</td>187 ············</td>
188 ··········</tr>188 ··········</tr>
189 ········</table>189 ········</table>
190 ········<div>190 ········<div>
191 ··········<h4>Over·number·fields</h4>191 ··········<h4>Over·number·fields</h4>
Offset 347, 15 lines modifiedOffset 347, 15 lines modified
  
347 o31·:·Ideal·of·R</code></pre>347 o31·:·Ideal·of·R</code></pre>
348 ············</td>348 ············</td>
349 ··········</tr>349 ··········</tr>
350 ··········<tr>350 ··········<tr>
351 ············<td>351 ············<td>
352 ··············<pre><code·class="language-macaulay2">i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true);352 ··············<pre><code·class="language-macaulay2">i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true);
353 ·--·used·0.671447s·(cpu);·0.594908s·(thread);·0s·(gc)353 ·--·used·0.872232s·(cpu);·0.745952s·(thread);·0s·(gc)
354 --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)</code></pre>354 --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)</code></pre>
355 ············</td>355 ············</td>
356 ··········</tr>356 ··········</tr>
357 ··········<tr>357 ··········<tr>
358 ············<td>358 ············<td>
359 ··············<pre><code·class="language-macaulay2">i33·:·#oo359 ··············<pre><code·class="language-macaulay2">i33·:·#oo
  
Offset 373, 15 lines modifiedOffset 373, 15 lines modified
  
373 o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]</code></pre>373 o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]</code></pre>
374 ············</td>374 ············</td>
375 ··········</tr>375 ··········</tr>
376 ··········<tr>376 ··········<tr>
377 ············<td>377 ············<td>
378 ··············<pre><code·class="language-macaulay2">i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true)378 ··············<pre><code·class="language-macaulay2">i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true)
379 ·--·used·0.224761s·(cpu);·0.184901s·(thread);·0s·(gc)379 ·--·used·0.254304s·(cpu);·0.208144s·(thread);·0s·(gc)
  
380 o35·=·31</code></pre>380 o35·=·31</code></pre>
381 ············</td>381 ············</td>
382 ··········</tr>382 ··········</tr>
383 ········</table>383 ········</table>
384 ······</div>384 ······</div>
385 ······<div>385 ······<div>
1.82 KB
html2text {}
    
Offset 89, 15 lines modifiedOffset 89, 15 lines modified
89 o13·=·ideal(u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··)89 o13·=·ideal(u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··)
90 ·············0····1····2····3····4····5····6····7····8····9····1090 ·············0····1····2····3····4····5····6····7····8····9····10
  
91 ················ZZ91 ················ZZ
92 o13·:·Ideal·of·---[u·..u··]92 o13·:·Ideal·of·---[u·..u··]
93 ···············101··0···1093 ···············101··0···10
94 i14·:·time·rationalPoints(I,·Amount·=>·true)94 i14·:·time·rationalPoints(I,·Amount·=>·true)
95 ·--·used·0.054712s·(cpu);·0.0203051s·(thread);·0s·(gc)95 ·--·used·0.0788427s·(cpu);·0.0193069s·(thread);·0s·(gc)
  
96 o14·=·11046221254112045100196 o14·=·110462212541120451001
97 *\x8**\x8**\x8*·O\x8Ov\x8ve\x8er\x8r·n\x8nu\x8um\x8mb\x8be\x8er\x8r·f\x8fi\x8ie\x8el\x8ld\x8ds\x8s·*\x8**\x8**\x8*97 *\x8**\x8**\x8*·O\x8Ov\x8ve\x8er\x8r·n\x8nu\x8um\x8mb\x8be\x8er\x8r·f\x8fi\x8ie\x8el\x8ld\x8ds\x8s·*\x8**\x8**\x8*
98 Over·a·number·field·one·can·use·the·option·Bound·to·specify·a·maximal98 Over·a·number·field·one·can·use·the·option·Bound·to·specify·a·maximal
99 multiplicative·height·given·by·$(x_0:\dots:x_n)\mapsto·\prod_{v}\max_i|x_i|_v·^99 multiplicative·height·given·by·$(x_0:\dots:x_n)\mapsto·\prod_{v}\max_i|x_i|_v·^
100 {d_v/d}$·(this·is·also·available·as·a·method·_\x8g_\x8l_\x8o_\x8b_\x8a_\x8l_\x8H_\x8e_\x8i_\x8g_\x8h_\x8t).100 {d_v/d}$·(this·is·also·available·as·a·method·_\x8g_\x8l_\x8o_\x8b_\x8a_\x8l_\x8H_\x8e_\x8i_\x8g_\x8h_\x8t).
101 i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z);101 i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z);
Offset 196, 25 lines modifiedOffset 196, 25 lines modified
196 (2z-qw)(4(x2+y2-z2)+(1+3(5-q2))w2)2";196 (2z-qw)(4(x2+y2-z2)+(1+3(5-q2))w2)2";
  
197 o30·:·Ideal·of·R197 o30·:·Ideal·of·R
198 i31·:·nodes·=·I·+·ideal·jacobian·I;198 i31·:·nodes·=·I·+·ideal·jacobian·I;
  
199 o31·:·Ideal·of·R199 o31·:·Ideal·of·R
200 i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true);200 i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true);
201 ·--·used·0.671447s·(cpu);·0.594908s·(thread);·0s·(gc)201 ·--·used·0.872232s·(cpu);·0.745952s·(thread);·0s·(gc)
202 --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)202 --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)
203 i33·:·#oo203 i33·:·#oo
  
204 o33·=·31204 o33·=·31
205 Still·it·runs·a·lot·faster·when·reduced·to·a·positive·characteristic.205 Still·it·runs·a·lot·faster·when·reduced·to·a·positive·characteristic.
206 i34·:·nodes'·=·baseChange_32003·nodes;206 i34·:·nodes'·=·baseChange_32003·nodes;
  
207 o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]207 o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]
208 i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true)208 i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true)
209 ·--·used·0.224761s·(cpu);·0.184901s·(thread);·0s·(gc)209 ·--·used·0.254304s·(cpu);·0.208144s·(thread);·0s·(gc)
  
210 o35·=·31210 o35·=·31
211 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*211 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8*
212 For·a·number·field·other·than·QQ,·the·enumeration·of·elements·with·bounded212 For·a·number·field·other·than·QQ,·the·enumeration·of·elements·with·bounded
213 height·depends·on·an·algorithm·by·Doyle–Krumm,·which·is·currently·only213 height·depends·on·an·algorithm·by·Doyle–Krumm,·which·is·currently·only
214 implemented·in·Sage.214 implemented·in·Sage.
215 *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8*215 *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8*
757 B
./usr/share/doc/Macaulay2/ReactionNetworks/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=307 #:len=30
8 bW9kaWZpY2F0aW9uT2ZUd29TdWJzdHJhdGVzSCgp8 bW9kaWZpY2F0aW9uT2ZUd29TdWJzdHJhdGVzSCgp
9 #:len=3449 #:len=344
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg1LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg1LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20gezE6KG1vZGlmaWNhdGlvbk9mVHdvU3Vic3RyYXRlc0gp11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20gezE6KG1vZGlmaWNhdGlvbk9mVHdvU3Vic3RyYXRlc0gp
727 B
./usr/share/doc/Macaulay2/RealRoots/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=177 #:len=17
8 dHJhY2VDb3VudChJZGVhbCk=8 dHJhY2VDb3VudChJZGVhbCk=
9 #:len=2419 #:len=241
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTAyMSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTAyMSwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodHJhY2VDb3VudCxJZGVhbCksInRyYWNlQ291bnQo11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodHJhY2VDb3VudCxJZGVhbCksInRyYWNlQ291bnQo
735 B
./usr/share/doc/Macaulay2/ReesAlgebra/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=207 #:len=20
8 aXNMaW5lYXJUeXBlKE1vZHVsZSk=8 aXNMaW5lYXJUeXBlKE1vZHVsZSk=
9 #:len=2579 #:len=257
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIwNywgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIwNywgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNMaW5lYXJUeXBlLE1vZHVsZSksImlzTGluZWFy11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNMaW5lYXJUeXBlLE1vZHVsZSksImlzTGluZWFy
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./usr/share/doc/Macaulay2/ReesAlgebra/example-output/___Plane__Curve__Singularities.out
    
Offset 331, 15 lines modifiedOffset 331, 15 lines modified
331 ···············2·2····2···2·············2·2····2331 ···············2·2····2···2·············2·2····2
332 ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·)332 ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·)
333 ·········2·1···0······1···0·0·····1·2···0·0····2333 ·········2·1···0······1···0·0·····1·2···0·0····2
  
334 o47·:·Ideal·of·B2334 o47·:·Ideal·of·B2
  
335 i48·:·time·sing2·=·ideal·singularLocus·strictTransform2;335 i48·:·time·sing2·=·ideal·singularLocus·strictTransform2;
336 ·--·used·0.717999s·(cpu);·0.614511s·(thread);·0s·(gc)336 ·--·used·0.86557s·(cpu);·0.714835s·(thread);·0s·(gc)
  
337 ·················ZZ337 ·················ZZ
338 o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y]338 o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y]
339 ···············32003··0···2···0···1339 ···············32003··0···2···0···1
  
340 i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2))340 i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2))
  
1020 B
./usr/share/doc/Macaulay2/ReesAlgebra/example-output/_expected__Rees__Ideal.out
    
Offset 58, 15 lines modifiedOffset 58, 15 lines modified
58 o5·:·Matrix·S··<--·S58 o5·:·Matrix·S··<--·S
  
59 i6·:·I·=·minors(n-1,·M);59 i6·:·I·=·minors(n-1,·M);
  
60 o6·:·Ideal·of·S60 o6·:·Ideal·of·S
  
61 i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec.61 i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec.
62 ·--·used·1.46694s·(cpu);·0.662343s·(thread);·0s·(gc)62 ·--·used·1.4972s·(cpu);·0.720321s·(thread);·0s·(gc)
  
63 o7·:·Ideal·of·S[w·..w·]63 o7·:·Ideal·of·S[w·..w·]
64 ·················0···464 ·················0···4
  
65 i8·:·kk·=·ZZ/101;65 i8·:·kk·=·ZZ/101;
  
66 i9·:·S·=·kk[x,y,z];66 i9·:·S·=·kk[x,y,z];
Offset 77, 19 lines modifiedOffset 77, 19 lines modified
77 o10·:·Matrix·S··<--·S77 o10·:·Matrix·S··<--·S
  
78 i11·:·I·=·minors(3,m);78 i11·:·I·=·minors(3,m);
  
79 o11·:·Ideal·of·S79 o11·:·Ideal·of·S
  
80 i12·:·time·reesIdeal·(I,·I_0);80 i12·:·time·reesIdeal·(I,·I_0);
81 ·--·used·1.42797s·(cpu);·0.995892s·(thread);·0s·(gc)81 ·--·used·1.49437s·(cpu);·1.07521s·(thread);·0s·(gc)
  
82 o12·:·Ideal·of·S[w·..w·]82 o12·:·Ideal·of·S[w·..w·]
83 ··················0···383 ··················0···3
  
84 i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false);84 i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false);
85 ·--·used·1.20795s·(cpu);·1.01965s·(thread);·0s·(gc)85 ·--·used·1.32802s·(cpu);·1.08332s·(thread);·0s·(gc)
  
86 o13·:·Ideal·of·S[w·..w·]86 o13·:·Ideal·of·S[w·..w·]
87 ··················0···387 ··················0···3
  
88 i14·:·88 i14·:·
1.19 KB
./usr/share/doc/Macaulay2/ReesAlgebra/example-output/_rees__Ideal.out
    
Offset 13, 21 lines modifiedOffset 13, 21 lines modified
13 ················3····213 ················3····2
14 ·····-·x·x·x·,·x··-·x·x·)14 ·····-·x·x·x·,·x··-·x·x·)
15 ········0·2·4···1····0·415 ········0·2·4···1····0·4
  
16 o3·:·Ideal·of·S16 o3·:·Ideal·of·S
  
17 i4·:·time·V1·=·reesIdeal·i;17 i4·:·time·V1·=·reesIdeal·i;
18 ·--·used·1.78159s·(cpu);·0.254832s·(thread);·0s·(gc)18 ·--·used·1.47521s·(cpu);·0.25175s·(thread);·0s·(gc)
  
19 o4·:·Ideal·of·S[w·..w·]19 o4·:·Ideal·of·S[w·..w·]
20 ·················0···620 ·················0···6
  
21 i5·:·time·V2·=·reesIdeal(i,i_0);21 i5·:·time·V2·=·reesIdeal(i,i_0);
22 ·--·used·0.772341s·(cpu);·0.205694s·(thread);·0s·(gc)22 ·--·used·0.634795s·(cpu);·0.187904s·(thread);·0s·(gc)
  
23 o5·:·Ideal·of·S[w·..w·]23 o5·:·Ideal·of·S[w·..w·]
24 ·················0···624 ·················0···6
  
25 i6·:·S=kk[a,b,c]25 i6·:·S=kk[a,b,c]
  
26 o6·=·S26 o6·=·S
Offset 47, 21 lines modifiedOffset 47, 21 lines modified
  
47 ·············2········247 ·············2········2
48 o8·=·ideal·(a·,·a*b,·b·)48 o8·=·ideal·(a·,·a*b,·b·)
  
49 o8·:·Ideal·of·S49 o8·:·Ideal·of·S
  
50 i9·:·time·I1·=·reesIdeal·i;50 i9·:·time·I1·=·reesIdeal·i;
51 ·--·used·0.957794s·(cpu);·0.125874s·(thread);·0s·(gc)51 ·--·used·0.83639s·(cpu);·0.124425s·(thread);·0s·(gc)
  
52 o9·:·Ideal·of·S[w·..w·]52 o9·:·Ideal·of·S[w·..w·]
53 ·················0···253 ·················0···2
  
54 i10·:·time·I2·=·reesIdeal(i,i_0);54 i10·:·time·I2·=·reesIdeal(i,i_0);
55 ·--·used·0.249357s·(cpu);·0.0452563s·(thread);·0s·(gc)55 ·--·used·0.206833s·(cpu);·0.0274763s·(thread);·0s·(gc)
  
56 o10·:·Ideal·of·S[w·..w·]56 o10·:·Ideal·of·S[w·..w·]
57 ··················0···257 ··················0···2
  
58 i11·:·transpose·gens·I158 i11·:·transpose·gens·I1
  
59 o11·=·{-1,·-3}·|·aw_1-bw_2····|59 o11·=·{-1,·-3}·|·aw_1-bw_2····|
1.29 KB
./usr/share/doc/Macaulay2/ReesAlgebra/html/___Plane__Curve__Singularities.html
    
Offset 587, 15 lines modifiedOffset 587, 15 lines modified
587 ········<div>587 ········<div>
588 ··········<p>We·compute·the·singular·locus·once·again:</p>588 ··········<p>We·compute·the·singular·locus·once·again:</p>
589 ········</div>589 ········</div>
590 ········<table·class="examples">590 ········<table·class="examples">
591 ··········<tr>591 ··········<tr>
592 ············<td>592 ············<td>
593 ··············<pre><code·class="language-macaulay2">i48·:·time·sing2·=·ideal·singularLocus·strictTransform2;593 ··············<pre><code·class="language-macaulay2">i48·:·time·sing2·=·ideal·singularLocus·strictTransform2;
594 ·--·used·0.717999s·(cpu);·0.614511s·(thread);·0s·(gc)594 ·--·used·0.86557s·(cpu);·0.714835s·(thread);·0s·(gc)
  
595 ·················ZZ595 ·················ZZ
596 o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y]596 o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y]
597 ···············32003··0···2···0···1</code></pre>597 ···············32003··0···2···0···1</code></pre>
598 ············</td>598 ············</td>
599 ··········</tr>599 ··········</tr>
600 ··········<tr>600 ··········<tr>
599 B
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325 ···············2·2····2···2·············2·2····2325 ···············2·2····2···2·············2·2····2
326 ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·)326 ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·)
327 ·········2·1···0······1···0·0·····1·2···0·0····2327 ·········2·1···0······1···0·0·····1·2···0·0····2
  
328 o47·:·Ideal·of·B2328 o47·:·Ideal·of·B2
329 We·compute·the·singular·locus·once·again:329 We·compute·the·singular·locus·once·again:
330 i48·:·time·sing2·=·ideal·singularLocus·strictTransform2;330 i48·:·time·sing2·=·ideal·singularLocus·strictTransform2;
331 ·--·used·0.717999s·(cpu);·0.614511s·(thread);·0s·(gc)331 ·--·used·0.86557s·(cpu);·0.714835s·(thread);·0s·(gc)
  
332 ·················ZZ332 ·················ZZ
333 o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y]333 o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y]
334 ···············32003··0···2···0···1334 ···············32003··0···2···0···1
335 i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2))335 i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2))
  
336 o49·=·ideal·1336 o49·=·ideal·1
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151 o6·:·Ideal·of·S</code></pre>151 o6·:·Ideal·of·S</code></pre>
152 ············</td>152 ············</td>
153 ··········</tr>153 ··········</tr>
154 ··········<tr>154 ··········<tr>
155 ············<td>155 ············<td>
156 ··············<pre><code·class="language-macaulay2">i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·&lt;·1·sec.156 ··············<pre><code·class="language-macaulay2">i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·&lt;·1·sec.
157 ·--·used·1.46694s·(cpu);·0.662343s·(thread);·0s·(gc)157 ·--·used·1.4972s·(cpu);·0.720321s·(thread);·0s·(gc)
  
158 o7·:·Ideal·of·S[w·..w·]158 o7·:·Ideal·of·S[w·..w·]
159 ·················0···4</code></pre>159 ·················0···4</code></pre>
160 ············</td>160 ············</td>
161 ··········</tr>161 ··········</tr>
162 ··········<tr>162 ··········<tr>
163 ············<td>163 ············<td>
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185 o11·:·Ideal·of·S</code></pre>185 o11·:·Ideal·of·S</code></pre>
186 ············</td>186 ············</td>
187 ··········</tr>187 ··········</tr>
188 ··········<tr>188 ··········<tr>
189 ············<td>189 ············<td>
190 ··············<pre><code·class="language-macaulay2">i12·:·time·reesIdeal·(I,·I_0);190 ··············<pre><code·class="language-macaulay2">i12·:·time·reesIdeal·(I,·I_0);
191 ·--·used·1.42797s·(cpu);·0.995892s·(thread);·0s·(gc)191 ·--·used·1.49437s·(cpu);·1.07521s·(thread);·0s·(gc)
  
192 o12·:·Ideal·of·S[w·..w·]192 o12·:·Ideal·of·S[w·..w·]
193 ··················0···3</code></pre>193 ··················0···3</code></pre>
194 ············</td>194 ············</td>
195 ··········</tr>195 ··········</tr>
196 ··········<tr>196 ··········<tr>
197 ············<td>197 ············<td>
198 ··············<pre><code·class="language-macaulay2">i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false);198 ··············<pre><code·class="language-macaulay2">i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false);
199 ·--·used·1.20795s·(cpu);·1.01965s·(thread);·0s·(gc)199 ·--·used·1.32802s·(cpu);·1.08332s·(thread);·0s·(gc)
  
200 o13·:·Ideal·of·S[w·..w·]200 o13·:·Ideal·of·S[w·..w·]
201 ··················0···3</code></pre>201 ··················0···3</code></pre>
202 ············</td>202 ············</td>
203 ··········</tr>203 ··········</tr>
204 ········</table>204 ········</table>
205 ······</div>205 ······</div>
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Offset 86, 34 lines modifiedOffset 86, 34 lines modified
  
86 ·············5······486 ·············5······4
87 o5·:·Matrix·S··<--·S87 o5·:·Matrix·S··<--·S
88 i6·:·I·=·minors(n-1,·M);88 i6·:·I·=·minors(n-1,·M);
  
89 o6·:·Ideal·of·S89 o6·:·Ideal·of·S
90 i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec.90 i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec.
91 ·--·used·1.46694s·(cpu);·0.662343s·(thread);·0s·(gc)91 ·--·used·1.4972s·(cpu);·0.720321s·(thread);·0s·(gc)
  
92 o7·:·Ideal·of·S[w·..w·]92 o7·:·Ideal·of·S[w·..w·]
93 ·················0···493 ·················0···4
94 i8·:·kk·=·ZZ/101;94 i8·:·kk·=·ZZ/101;
95 i9·:·S·=·kk[x,y,z];95 i9·:·S·=·kk[x,y,z];
96 i10·:·m·=·random(S^3,·S^{4:-2});96 i10·:·m·=·random(S^3,·S^{4:-2});
  
97 ··············3······497 ··············3······4
98 o10·:·Matrix·S··<--·S98 o10·:·Matrix·S··<--·S
99 i11·:·I·=·minors(3,m);99 i11·:·I·=·minors(3,m);
  
100 o11·:·Ideal·of·S100 o11·:·Ideal·of·S
101 i12·:·time·reesIdeal·(I,·I_0);101 i12·:·time·reesIdeal·(I,·I_0);
102 ·--·used·1.42797s·(cpu);·0.995892s·(thread);·0s·(gc)102 ·--·used·1.49437s·(cpu);·1.07521s·(thread);·0s·(gc)
  
103 o12·:·Ideal·of·S[w·..w·]103 o12·:·Ideal·of·S[w·..w·]
104 ··················0···3104 ··················0···3
105 i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false);105 i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false);
106 ·--·used·1.20795s·(cpu);·1.01965s·(thread);·0s·(gc)106 ·--·used·1.32802s·(cpu);·1.08332s·(thread);·0s·(gc)
  
107 o13·:·Ideal·of·S[w·..w·]107 o13·:·Ideal·of·S[w·..w·]
108 ··················0···3108 ··················0···3
109 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*109 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
110 ····*·_\x8s_\x8y_\x8m_\x8m_\x8e_\x8t_\x8r_\x8i_\x8c_\x8A_\x8l_\x8g_\x8e_\x8b_\x8r_\x8a_\x8I_\x8d_\x8e_\x8a_\x8l·--·Ideal·of·the·symmetric·algebra·of·an·ideal·or110 ····*·_\x8s_\x8y_\x8m_\x8m_\x8e_\x8t_\x8r_\x8i_\x8c_\x8A_\x8l_\x8g_\x8e_\x8b_\x8r_\x8a_\x8I_\x8d_\x8e_\x8a_\x8l·--·Ideal·of·the·symmetric·algebra·of·an·ideal·or
111 ······module111 ······module
112 ····*·_\x8j_\x8a_\x8c_\x8o_\x8b_\x8i_\x8a_\x8n_\x8D_\x8u_\x8a_\x8l·--·Computes·the·'jacobian·dual',·part·of·a·method·of·finding112 ····*·_\x8j_\x8a_\x8c_\x8o_\x8b_\x8i_\x8a_\x8n_\x8D_\x8u_\x8a_\x8l·--·Computes·the·'jacobian·dual',·part·of·a·method·of·finding
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110 o3·:·Ideal·of·S</code></pre>110 o3·:·Ideal·of·S</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i4·:·time·V1·=·reesIdeal·i;115 ··············<pre><code·class="language-macaulay2">i4·:·time·V1·=·reesIdeal·i;
116 ·--·used·1.78159s·(cpu);·0.254832s·(thread);·0s·(gc)116 ·--·used·1.47521s·(cpu);·0.25175s·(thread);·0s·(gc)
  
117 o4·:·Ideal·of·S[w·..w·]117 o4·:·Ideal·of·S[w·..w·]
118 ·················0···6</code></pre>118 ·················0···6</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i5·:·time·V2·=·reesIdeal(i,i_0);123 ··············<pre><code·class="language-macaulay2">i5·:·time·V2·=·reesIdeal(i,i_0);
124 ·--·used·0.772341s·(cpu);·0.205694s·(thread);·0s·(gc)124 ·--·used·0.634795s·(cpu);·0.187904s·(thread);·0s·(gc)
  
125 o5·:·Ideal·of·S[w·..w·]125 o5·:·Ideal·of·S[w·..w·]
126 ·················0···6</code></pre>126 ·················0···6</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ········</table>129 ········</table>
130 ········<div>130 ········<div>
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164 o8·:·Ideal·of·S</code></pre>164 o8·:·Ideal·of·S</code></pre>
165 ············</td>165 ············</td>
166 ··········</tr>166 ··········</tr>
167 ··········<tr>167 ··········<tr>
168 ············<td>168 ············<td>
169 ··············<pre><code·class="language-macaulay2">i9·:·time·I1·=·reesIdeal·i;169 ··············<pre><code·class="language-macaulay2">i9·:·time·I1·=·reesIdeal·i;
170 ·--·used·0.957794s·(cpu);·0.125874s·(thread);·0s·(gc)170 ·--·used·0.83639s·(cpu);·0.124425s·(thread);·0s·(gc)
  
171 o9·:·Ideal·of·S[w·..w·]171 o9·:·Ideal·of·S[w·..w·]
172 ·················0···2</code></pre>172 ·················0···2</code></pre>
173 ············</td>173 ············</td>
174 ··········</tr>174 ··········</tr>
175 ··········<tr>175 ··········<tr>
176 ············<td>176 ············<td>
177 ··············<pre><code·class="language-macaulay2">i10·:·time·I2·=·reesIdeal(i,i_0);177 ··············<pre><code·class="language-macaulay2">i10·:·time·I2·=·reesIdeal(i,i_0);
178 ·--·used·0.249357s·(cpu);·0.0452563s·(thread);·0s·(gc)178 ·--·used·0.206833s·(cpu);·0.0274763s·(thread);·0s·(gc)
  
179 o10·:·Ideal·of·S[w·..w·]179 o10·:·Ideal·of·S[w·..w·]
180 ··················0···2</code></pre>180 ··················0···2</code></pre>
181 ············</td>181 ············</td>
182 ··········</tr>182 ··········</tr>
183 ··········<tr>183 ··········<tr>
184 ············<td>184 ············<td>
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51 ·····------------------------------------------------------------------------51 ·····------------------------------------------------------------------------
52 ················3····252 ················3····2
53 ·····-·x·x·x·,·x··-·x·x·)53 ·····-·x·x·x·,·x··-·x·x·)
54 ········0·2·4···1····0·454 ········0·2·4···1····0·4
  
55 o3·:·Ideal·of·S55 o3·:·Ideal·of·S
56 i4·:·time·V1·=·reesIdeal·i;56 i4·:·time·V1·=·reesIdeal·i;
57 ·--·used·1.78159s·(cpu);·0.254832s·(thread);·0s·(gc)57 ·--·used·1.47521s·(cpu);·0.25175s·(thread);·0s·(gc)
  
58 o4·:·Ideal·of·S[w·..w·]58 o4·:·Ideal·of·S[w·..w·]
59 ·················0···659 ·················0···6
60 i5·:·time·V2·=·reesIdeal(i,i_0);60 i5·:·time·V2·=·reesIdeal(i,i_0);
61 ·--·used·0.772341s·(cpu);·0.205694s·(thread);·0s·(gc)61 ·--·used·0.634795s·(cpu);·0.187904s·(thread);·0s·(gc)
  
62 o5·:·Ideal·of·S[w·..w·]62 o5·:·Ideal·of·S[w·..w·]
63 ·················0···663 ·················0···6
64 The·following·example·shows·how·we·handle·degrees64 The·following·example·shows·how·we·handle·degrees
65 i6·:·S=kk[a,b,c]65 i6·:·S=kk[a,b,c]
  
66 o6·=·S66 o6·=·S
Offset 81, 20 lines modifiedOffset 81, 20 lines modified
81 i8·:·i=minors(2,m)81 i8·:·i=minors(2,m)
  
82 ·············2········282 ·············2········2
83 o8·=·ideal·(a·,·a*b,·b·)83 o8·=·ideal·(a·,·a*b,·b·)
  
84 o8·:·Ideal·of·S84 o8·:·Ideal·of·S
85 i9·:·time·I1·=·reesIdeal·i;85 i9·:·time·I1·=·reesIdeal·i;
86 ·--·used·0.957794s·(cpu);·0.125874s·(thread);·0s·(gc)86 ·--·used·0.83639s·(cpu);·0.124425s·(thread);·0s·(gc)
  
87 o9·:·Ideal·of·S[w·..w·]87 o9·:·Ideal·of·S[w·..w·]
88 ·················0···288 ·················0···2
89 i10·:·time·I2·=·reesIdeal(i,i_0);89 i10·:·time·I2·=·reesIdeal(i,i_0);
90 ·--·used·0.249357s·(cpu);·0.0452563s·(thread);·0s·(gc)90 ·--·used·0.206833s·(cpu);·0.0274763s·(thread);·0s·(gc)
  
91 o10·:·Ideal·of·S[w·..w·]91 o10·:·Ideal·of·S[w·..w·]
92 ··················0···292 ··················0···2
93 i11·:·transpose·gens·I193 i11·:·transpose·gens·I1
  
94 o11·=·{-1,·-3}·|·aw_1-bw_2····|94 o11·=·{-1,·-3}·|·aw_1-bw_2····|
95 ······{-1,·-3}·|·aw_0-bw_1····|95 ······{-1,·-3}·|·aw_0-bw_1····|
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=77 #:len=7
8 S1NFbnRyeQ==8 S1NFbnRyeQ==
9 #:len=24389 #:len=2438
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZW50cnkgZnJvbSB0aGUgS3JldXpl10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZW50cnkgZnJvbSB0aGUgS3JldXpl
11 ci1Ta2Fya2UgZGF0YWJhc2Ugb2YgZGltZW5zaW9uIDMgYW5kIDQgcmVmbGV4aXZlIHBvbHl0b3Bl11 ci1Ta2Fya2UgZGF0YWJhc2Ugb2YgZGltZW5zaW9uIDMgYW5kIDQgcmVmbGV4aXZlIHBvbHl0b3Bl
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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6 #·End·of·header6 #·End·of·header
7 #:len=107 #:len=10
8 UmVndWxhcml0eQ==8 UmVndWxhcml0eQ==
9 #:len=7979 #:len=797
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBDYXN0ZWxudW92by1NdW1m10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBDYXN0ZWxudW92by1NdW1m
11 b3JkIHJlZ3VsYXJpdHkgb2YgYSBob21vZ2VuZW91cyBpZGVhbCIsIERlc2NyaXB0aW9uID0+IChQ11 b3JkIHJlZ3VsYXJpdHkgb2YgYSBob21vZ2VuZW91cyBpZGVhbCIsIERlc2NyaXB0aW9uID0+IChQ
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71 ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·)71 ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·)
72 ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·572 ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5
  
73 o7·:·Ideal·of·R73 o7·:·Ideal·of·R
  
74 i8·:·benchmark·"mRegularity·I1"74 i8·:·benchmark·"mRegularity·I1"
  
75 o8·=·.198912684769230775 o8·=·.2231835765
  
76 o8·:·RR·(of·precision·53)76 o8·:·RR·(of·precision·53)
  
77 i9·:·R·=·QQ[x_0..x_5]77 i9·:·R·=·QQ[x_0..x_5]
  
78 o9·=·R78 o9·=·R
  
Offset 87, 17 lines modifiedOffset 87, 17 lines modified
  
87 i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,·x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3);87 i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,·x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3);
  
88 o10·:·Ideal·of·R88 o10·:·Ideal·of·R
  
89 i11·:·benchmark·"·mRegularity·I2"89 i11·:·benchmark·"·mRegularity·I2"
  
90 o11·=·.0599348457142857290 o11·=·.06309084509090908
  
91 o11·:·RR·(of·precision·53)91 o11·:·RR·(of·precision·53)
  
92 i12·:·time·regularity·I2··92 i12·:·time·regularity·I2··
93 ·--·used·0.00367934s·(cpu);·0.00241766s·(thread);·0s·(gc)93 ·--·used·0.0015896s·(cpu);·0.00220362s·(thread);·0s·(gc)
  
94 o12·=·494 o12·=·4
  
95 i13·:·95 i13·:·
2.47 KB
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176 o7·:·Ideal·of·R</code></pre>176 o7·:·Ideal·of·R</code></pre>
177 ············</td>177 ············</td>
178 ··········</tr>178 ··········</tr>
179 ··········<tr>179 ··········<tr>
180 ············<td>180 ············<td>
181 ··············<pre><code·class="language-macaulay2">i8·:·benchmark·&quot;mRegularity·I1&quot;181 ··············<pre><code·class="language-macaulay2">i8·:·benchmark·&quot;mRegularity·I1&quot;
  
182 o8·=·.1989126847692307182 o8·=·.2231835765
  
183 o8·:·RR·(of·precision·53)</code></pre>183 o8·:·RR·(of·precision·53)</code></pre>
184 ············</td>184 ············</td>
185 ··········</tr>185 ··········</tr>
186 ········</table>186 ········</table>
187 ········<p>This·is·an·example·where·regularity·is·faster·than·mRegularity.</p>187 ········<p>This·is·an·example·where·regularity·is·faster·than·mRegularity.</p>
188 ········<table·class="examples">188 ········<table·class="examples">
Offset 204, 23 lines modifiedOffset 204, 23 lines modified
204 o10·:·Ideal·of·R</code></pre>204 o10·:·Ideal·of·R</code></pre>
205 ············</td>205 ············</td>
206 ··········</tr>206 ··········</tr>
207 ··········<tr>207 ··········<tr>
208 ············<td>208 ············<td>
209 ··············<pre><code·class="language-macaulay2">i11·:·benchmark·&quot;·mRegularity·I2&quot;209 ··············<pre><code·class="language-macaulay2">i11·:·benchmark·&quot;·mRegularity·I2&quot;
  
210 o11·=·.05993484571428572210 o11·=·.06309084509090908
  
211 o11·:·RR·(of·precision·53)</code></pre>211 o11·:·RR·(of·precision·53)</code></pre>
212 ············</td>212 ············</td>
213 ··········</tr>213 ··········</tr>
214 ··········<tr>214 ··········<tr>
215 ············<td>215 ············<td>
216 ··············<pre><code·class="language-macaulay2">i12·:·time·regularity·I2··216 ··············<pre><code·class="language-macaulay2">i12·:·time·regularity·I2··
217 ·--·used·0.00367934s·(cpu);·0.00241766s·(thread);·0s·(gc)217 ·--·used·0.0015896s·(cpu);·0.00220362s·(thread);·0s·(gc)
  
218 o12·=·4</code></pre>218 o12·=·4</code></pre>
219 ············</td>219 ············</td>
220 ··········</tr>220 ··········</tr>
221 ········</table>221 ········</table>
222 ········<p>This·symbol·is·provided·by·the·package·Regularity.</p>222 ········<p>This·symbol·is·provided·by·the·package·Regularity.</p>
223 ······</div>223 ······</div>
1.17 KB
html2text {}
    
Offset 94, 34 lines modifiedOffset 94, 34 lines modified
94 ··············3····2········2············3····3······294 ··············3····2········2············3····3······2
95 ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·)95 ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·)
96 ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·596 ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5
  
97 o7·:·Ideal·of·R97 o7·:·Ideal·of·R
98 i8·:·benchmark·"mRegularity·I1"98 i8·:·benchmark·"mRegularity·I1"
  
99 o8·=·.198912684769230799 o8·=·.2231835765
  
100 o8·:·RR·(of·precision·53)100 o8·:·RR·(of·precision·53)
101 This·is·an·example·where·regularity·is·faster·than·mRegularity.101 This·is·an·example·where·regularity·is·faster·than·mRegularity.
102 i9·:·R·=·QQ[x_0..x_5]102 i9·:·R·=·QQ[x_0..x_5]
  
103 o9·=·R103 o9·=·R
  
104 o9·:·PolynomialRing104 o9·:·PolynomialRing
105 i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,105 i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,
106 x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3);106 x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3);
  
107 o10·:·Ideal·of·R107 o10·:·Ideal·of·R
108 i11·:·benchmark·"·mRegularity·I2"108 i11·:·benchmark·"·mRegularity·I2"
  
109 o11·=·.05993484571428572109 o11·=·.06309084509090908
  
110 o11·:·RR·(of·precision·53)110 o11·:·RR·(of·precision·53)
111 i12·:·time·regularity·I2111 i12·:·time·regularity·I2
112 ·--·used·0.00367934s·(cpu);·0.00241766s·(thread);·0s·(gc)112 ·--·used·0.0015896s·(cpu);·0.00220362s·(thread);·0s·(gc)
  
113 o12·=·4113 o12·=·4
114 This·symbol·is·provided·by·the·package·Regularity.114 This·symbol·is·provided·by·the·package·Regularity.
115 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*115 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
116 ····*·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y·--·compute·the·Castelnuovo-Mumford·regularity116 ····*·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y·--·compute·the·Castelnuovo-Mumford·regularity
117 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8ri\x8it\x8ty\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*117 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8ri\x8it\x8ty\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*
118 ····*·mRegularity(Ideal)118 ····*·mRegularity(Ideal)
768 B
./usr/share/doc/Macaulay2/RelativeCanonicalResolution/dump/rawdocumentation.dump
    
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7 #:len=207 #:len=20
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741 B
./usr/share/doc/Macaulay2/ResLengthThree/dump/rawdocumentation.dump
    
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2 #:version=1.12 #:version=1.1
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8 bXVsdFRhYmxlT25lVHdvKFJpbmcp8 bXVsdFRhYmxlT25lVHdvKFJpbmcp
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11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtdWx0VGFibGVPbmVUd28sUmluZyksIm11bHRUYWJs11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtdWx0VGFibGVPbmVUd28sUmluZyksIm11bHRUYWJs
748 B
./usr/share/doc/Macaulay2/ResidualIntersections/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=157 #:len=15
8 Z2VuZXJpY1Jlc2lkdWFs8 Z2VuZXJpY1Jlc2lkdWFs
9 #:len=17399 #:len=1739
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgZ2VuZXJpYyByZXNpZHVh10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgZ2VuZXJpYyByZXNpZHVh
11 bCBpbnRlcnNlY3Rpb25zIG9mIGFuIGlkZWFsIiwgImxpbmVudW0iID0+IDg4NiwgSW5wdXRzID0+11 bCBpbnRlcnNlY3Rpb25zIG9mIGFuIGlkZWFsIiwgImxpbmVudW0iID0+IDg4NiwgSW5wdXRzID0+
805 B
./usr/share/doc/Macaulay2/ResolutionsOfStanleyReisnerRings/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=417 #:len=41
8 YmFyeWNlbnRyaWNTdWJkaXZpc2lvbihTaW1wbGljaWFsQ29tcGxleCk=8 YmFyeWNlbnRyaWNTdWJkaXZpc2lvbihTaW1wbGljaWFsQ29tcGxleCk=
9 #:len=3819 #:len=381
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzI5LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzI5LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhiYXJ5Y2VudHJpY1N1YmRpdmlzaW9uLFNpbXBsaWNp11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhiYXJ5Y2VudHJpY1N1YmRpdmlzaW9uLFNpbXBsaWNp
753 B
./usr/share/doc/Macaulay2/Resultants/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=357 #:len=35
8 aHVyd2l0ekZvcm0oLi4uLFNpbmd1bGFyTG9jdXM9Pi4uLik=8 aHVyd2l0ekZvcm0oLi4uLFNpbmd1bGFyTG9jdXM9Pi4uLik=
9 #:len=2779 #:len=277
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMyOSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMyOSwgc3ltYm9sIERvY3VtZW50VGFn
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1.65 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_cayley__Trick.out
    
Offset 5, 18 lines modifiedOffset 5, 18 lines modified
5 o2·=·ideal(x·x··-·x·x·)5 o2·=·ideal(x·x··-·x·x·)
6 ············0·1····2·36 ············0·1····2·3
  
7 o2·:·Ideal·of·QQ[x·..x·]7 o2·:·Ideal·of·QQ[x·..x·]
8 ··················0···38 ··················0···3
  
9 i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2);9 i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2);
10 ·--·used·0.0391455s·(cpu);·0.0398698s·(thread);·0s·(gc)10 ·--·used·0.0555615s·(cpu);·0.0555018s·(thread);·0s·(gc)
  
11 i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1)11 i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1)
12 ·--·used·0.0953295s·(cpu);·0.0623364s·(thread);·0s·(gc)12 ·--·used·0.116121s·(cpu);·0.0739718s·(thread);·0s·(gc)
  
13 ···········································································13 ···········································································
14 o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,14 o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,
15 ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3·15 ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3·
16 ·····------------------------------------------------------------------------16 ·····------------------------------------------------------------------------
17 ············································································17 ············································································
18 ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x···18 ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x···
Offset 37, 17 lines modifiedOffset 37, 17 lines modified
37 ··············································2···237 ··············································2···2
38 ·····4x···x···x···x····-·2x···x···x···x····+·x···x···))38 ·····4x···x···x···x····-·2x···x···x···x····+·x···x···))
39 ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,339 ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,3
  
40 o4·:·Sequence40 o4·:·Sequence
  
41 i5·:·time·cayleyTrick(P1xP1,1,Duality=>true);41 i5·:·time·cayleyTrick(P1xP1,1,Duality=>true);
42 ·--·used·0.112199s·(cpu);·0.0832487s·(thread);·0s·(gc)42 ·--·used·0.138193s·(cpu);·0.0991304s·(thread);·0s·(gc)
  
43 i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))43 i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))
  
44 i7·:·time·cayleyTrick(P1xP1,2,Duality=>true);44 i7·:·time·cayleyTrick(P1xP1,2,Duality=>true);
45 ·--·used·0.12098s·(cpu);·0.0872498s·(thread);·0s·(gc)45 ·--·used·0.178856s·(cpu);·0.1113s·(thread);·0s·(gc)
  
46 i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))46 i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))
  
47 i9·:·47 i9·:·
2.56 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_chow__Equations.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·)9 o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·)
10 ·············0····1····2····3···0·1····1·2····2·310 ·············0····1····2····3···0·1····1·2····2·3
  
11 o2·:·Ideal·of·P311 o2·:·Ideal·of·P3
  
12 i3·:·--·Chow·equations·of·C12 i3·:·--·Chow·equations·of·C
13 ·····time·eqsC·=·chowEquations·chowForm·C13 ·····time·eqsC·=·chowEquations·chowForm·C
14 ·--·used·0.0369285s·(cpu);·0.037131s·(thread);·0s·(gc)14 ·--·used·0.0399458s·(cpu);·0.0393854s·(thread);·0s·(gc)
  
15 ·············2·2····2·2····2·2····4················2······2·2···2······15 ·············2·2····2·2····2·2····4················2······2·2···2······
16 o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+16 o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+
17 ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3··17 ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3··
18 ·····------------------------------------------------------------------------18 ·····------------------------------------------------------------------------
19 ······2········3···········2·········2······3···3·········2··········2····2·219 ······2········3···········2·········2······3···3·········2··········2····2·2
20 ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x·20 ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x·
Offset 72, 15 lines modifiedOffset 72, 15 lines modified
72 o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·)72 o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·)
73 ·············1····0·2···2····0·1·3···1·2····0·373 ·············1····0·2···2····0·1·3···1·2····0·3
  
74 o5·:·Ideal·of·P374 o5·:·Ideal·of·P3
  
75 i6·:·--·Chow·equations·of·D75 i6·:·--·Chow·equations·of·D
76 ·····time·eqsD·=·chowEquations·chowForm·D76 ·····time·eqsD·=·chowEquations·chowForm·D
77 ·--·used·0.079526s·(cpu);·0.0429132s·(thread);·0s·(gc)77 ·--·used·0.0874898s·(cpu);·0.0525426s·(thread);·0s·(gc)
  
78 ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2·78 ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2·
79 o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,79 o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,
80 ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3·80 ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3·
81 ·····------------------------------------------------------------------------81 ·····------------------------------------------------------------------------
82 ··········2······3·2···3········3·2···4·········2·········2·2·······3····82 ··········2······3·2···3········3·2···4·········2·········2·2·······3····
83 ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··-83 ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··-
Offset 117, 24 lines modifiedOffset 117, 24 lines modified
117 o9·=·ideal(x·x··+·x·x·)117 o9·=·ideal(x·x··+·x·x·)
118 ············0·1····2·3118 ············0·1····2·3
  
119 o9·:·Ideal·of·P3119 o9·:·Ideal·of·P3
  
120 i10·:·--·tangential·Chow·forms·of·Q120 i10·:·--·tangential·Chow·forms·of·Q
121 ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2))121 ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2))
122 ·--·used·0.110669s·(cpu);·0.0758087s·(thread);·0s·(gc)122 ·--·used·0.12062s·(cpu);·0.0986453s·(thread);·0s·(gc)
  
123 ·····················2······························2123 ·····················2······························2
124 o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+124 o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+
125 ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3··125 ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3··
126 ······-----------------------------------------------------------------------126 ······-----------------------------------------------------------------------
127 ······x·····x·····)127 ······x·····x·····)
128 ·······0,2,3·1,2,3128 ·······0,2,3·1,2,3
  
129 o10·:·Sequence129 o10·:·Sequence
  
130 i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2))130 i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2))
131 ·--·used·0.0558416s·(cpu);·0.056609s·(thread);·0s·(gc)131 ·--·used·0.0565585s·(cpu);·0.0569067s·(thread);·0s·(gc)
  
132 o11·=·true132 o11·=·true
  
133 i12·:·133 i12·:·
7.81 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_chow__Form.out
    
Offset 16, 15 lines modifiedOffset 16, 15 lines modified
  
16 ···············ZZ16 ···············ZZ
17 o2·:·Ideal·of·----[x·..x·]17 o2·:·Ideal·of·----[x·..x·]
18 ··············3331··0···518 ··············3331··0···5
  
19 i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian)19 i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian)
20 ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3})20 ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3})
21 ·--·used·4.41024s·(cpu);·4.26416s·(thread);·0s·(gc)21 ·--·used·4.75643s·(cpu);·4.53933s·(thread);·0s·(gc)
  
22 ······4···············2··············2·····2···············2············22 ······4···············2··············2·····2···············2············
23 o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+23 o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+
24 ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5··24 ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5··
25 ·····------------------------------------------------------------------------25 ·····------------------------------------------------------------------------
26 ······2·····2··············2·······································26 ······2·····2··············2·······································
27 ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+27 ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+
Offset 143, 19 lines modifiedOffset 143, 19 lines modified
143 ··········································································································································································································································································································································································································································································································································································································································································································································································3331··0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,4···0,1,5···0,2,5···1,2,5···0,3,5···1,3,5···2,3,5···0,4,5···1,4,5···2,4,5···3,4,5143 ··········································································································································································································································································································································································································································································································································································································································································································································································3331··0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,4···0,1,5···0,2,5···1,2,5···0,3,5···1,3,5···2,3,5···0,4,5···1,4,5···2,4,5···3,4,5
144 o3·:·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------144 o3·:·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
145 ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····)145 ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····)
146 ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4146 ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4
  
147 i4·:·--·equivalently·(but·faster)...147 i4·:·--·equivalently·(but·faster)...
148 ·····time·assert(ChowV·===·chowForm·f)148 ·····time·assert(ChowV·===·chowForm·f)
149 ·--·used·1.0665s·(cpu);·0.994859s·(thread);·0s·(gc)149 ·--·used·1.08211s·(cpu);·0.972457s·(thread);·0s·(gc)
  
150 i5·:·--·X-resultant·of·V150 i5·:·--·X-resultant·of·V
151 ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV;151 ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV;
152 ·--·used·0.166367s·(cpu);·0.135265s·(thread);·0s·(gc)152 ·--·used·0.203276s·(cpu);·0.166603s·(thread);·0s·(gc)
  
153 i6·:·--·three·generic·ternary·quadrics153 i6·:·--·three·generic·ternary·quadrics
154 ·····F·=·genericPolynomials({2,2,2},ZZ/3331)154 ·····F·=·genericPolynomials({2,2,2},ZZ/3331)
  
155 ·········2···············2························2·····2···············2··155 ·········2···············2························2·····2···············2··
156 o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+156 o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+
157 ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1··157 ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1··
Offset 164, 12 lines modifiedOffset 164, 12 lines modified
164 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}164 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}
165 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2165 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2
  
166 o6·:·List166 o6·:·List
  
167 i7·:·--·resultant·of·the·three·forms167 i7·:·--·resultant·of·the·three·forms
168 ·····time·resF·=·resultant·F;168 ·····time·resF·=·resultant·F;
169 ·--·used·0.166113s·(cpu);·0.136166s·(thread);·0s·(gc)169 ·--·used·0.215597s·(cpu);·0.153987s·(thread);·0s·(gc)
  
170 i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres))170 i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres))
  
171 i9·:·171 i9·:·
1.71 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_discriminant_lp__Ring__Element_rp.out
    
Offset 4, 30 lines modifiedOffset 4, 30 lines modified
  
4 ········2··············24 ········2··············2
5 o2·=·a*x··+·b*x*y·+·c*y5 o2·=·a*x··+·b*x*y·+·c*y
  
6 o2·:·ZZ[a..c][x..y]6 o2·:·ZZ[a..c][x..y]
  
7 i3·:·time·discriminant·F7 i3·:·time·discriminant·F
8 ·--·used·0.011002s·(cpu);·0.00712899s·(thread);·0s·(gc)8 ·--·used·0.0120057s·(cpu);·0.0114892s·(thread);·0s·(gc)
  
9 ········29 ········2
10 o3·=·-·b··+·4a*c10 o3·=·-·b··+·4a*c
  
11 o3·:·ZZ[a..c]11 o3·:·ZZ[a..c]
  
12 i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^312 i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^3
  
13 ········3······2·········2······313 ········3······2·········2······3
14 o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y14 o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y
  
15 o5·:·ZZ[a..d][x..y]15 o5·:·ZZ[a..d][x..y]
  
16 i6·:·time·discriminant·F16 i6·:·time·discriminant·F
17 ·--·used·0.00786001s·(cpu);·0.00829917s·(thread);·0s·(gc)17 ·--·used·0.0113987s·(cpu);·0.0114849s·(thread);·0s·(gc)
  
18 ········2·2·······3·····3···················2·218 ········2·2·······3·····3···················2·2
19 o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d19 o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d
  
20 o6·:·ZZ[a..d]20 o6·:·ZZ[a..d]
  
21 i7·:·x=symbol·x;·R=ZZ/331[x_0..x_3]21 i7·:·x=symbol·x;·R=ZZ/331[x_0..x_3]
Offset 59, 15 lines modifiedOffset 59, 15 lines modified
59 ················4········3······4·············4········3······459 ················4········3······4·············4········3······4
60 o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x60 o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x
61 ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·361 ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3
  
62 o12·:·R'62 o12·:·R'
  
63 i13·:·time·D=discriminant·pencil63 i13·:·time·D=discriminant·pencil
64 ·--·used·0.298472s·(cpu);·0.297019s·(thread);·0s·(gc)64 ·--·used·0.458643s·(cpu);·0.454823s·(thread);·0s·(gc)
  
65 ···········108······106·2·······102·6······100·8·······98·10·······96·12··65 ···········108······106·2·······102·6······100·8·······98·10·······96·12··
66 o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+66 o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+
67 ···········0········0···1·······0···1······0···1·······0··1········0··1···67 ···········0········0···1·······0···1······0···1·······0··1········0··1···
68 ······-----------------------------------------------------------------------68 ······-----------------------------------------------------------------------
69 ··········94·14·······92·16······90·18······88·20······86·22·······84·24··69 ··········94·14·······92·16······90·18······88·20······86·22·······84·24··
70 ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+70 ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+
1.57 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_dual__Variety.out
    
Offset 9, 25 lines modifiedOffset 9, 25 lines modified
9 ·····x·x·)9 ·····x·x·)
10 ······0·310 ······0·3
  
11 o1·:·Ideal·of·QQ[x·..x·]11 o1·:·Ideal·of·QQ[x·..x·]
12 ··················0···512 ··················0···5
  
13 i2·:·time·V'·=·dualVariety·V13 i2·:·time·V'·=·dualVariety·V
14 ·--·used·0.0814975s·(cpu);·0.0811424s·(thread);·0s·(gc)14 ·--·used·0.10812s·(cpu);·0.10755s·(thread);·0s·(gc)
  
15 ············2·················2····215 ············2·················2····2
16 o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·)16 o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·)
17 ············2·3····1·2·4····0·4····1·5·····0·3·517 ············2·3····1·2·4····0·4····1·5·····0·3·5
  
18 o2·:·Ideal·of·QQ[x·..x·]18 o2·:·Ideal·of·QQ[x·..x·]
19 ··················0···519 ··················0···5
  
20 i3·:·time·V·==·dualVariety·V'20 i3·:·time·V·==·dualVariety·V'
21 ·--·used·0.15223s·(cpu);·0.122225s·(thread);·0s·(gc)21 ·--·used·0.171863s·(cpu);·0.139171s·(thread);·0s·(gc)
  
22 o3·=·true22 o3·=·true
  
23 i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331)23 i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331)
  
24 ········3······2··········2······3······2···················2··········2··24 ········3······2··········2······3······2···················2··········2··
25 o4·=·a·x··+·a·x·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x·x··+·a·x·x··+·a·x·x··+25 o4·=·a·x··+·a·x·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x·x··+·a·x·x··+·a·x·x··+
Offset 38, 22 lines modifiedOffset 38, 22 lines modified
38 ······8·1·2····9·238 ······8·1·2····9·2
  
39 ······ZZ39 ······ZZ
40 o4·:·----[a·..a·][x·..x·]40 o4·:·----[a·..a·][x·..x·]
41 ·····3331··0···9···0···241 ·····3331··0···9···0···2
  
42 i5·:·time·discF·=·ideal·discriminant·F;42 i5·:·time·discF·=·ideal·discriminant·F;
43 ·--·used·0.0472808s·(cpu);·0.0499993s·(thread);·0s·(gc)43 ·--·used·0.0790692s·(cpu);·0.0784505s·(thread);·0s·(gc)
  
44 ···············ZZ44 ···············ZZ
45 o5·:·Ideal·of·----[a·..a·]45 o5·:·Ideal·of·----[a·..a·]
46 ··············3331··0···946 ··············3331··0···9
  
47 i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true);47 i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true);
48 ·--·used·0.543213s·(cpu);·0.509202s·(thread);·0s·(gc)48 ·--·used·0.745516s·(cpu);·0.680422s·(thread);·0s·(gc)
  
49 ···············ZZ49 ···············ZZ
50 o6·:·Ideal·of·----[x·..x·]50 o6·:·Ideal·of·----[x·..x·]
51 ··············3331··0···951 ··············3331··0···9
  
52 i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z)52 i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z)
  
2.72 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_from__Plucker__To__Stiefel.out
    
Offset 6, 15 lines modifiedOffset 6, 15 lines modified
6 o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·)6 o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·)
7 ·············2····1·3···1·2····0·3···1····0·27 ·············2····1·3···1·2····0·3···1····0·2
  
8 o1·:·Ideal·of·QQ[x·..x·]8 o1·:·Ideal·of·QQ[x·..x·]
9 ··················0···39 ··················0···3
  
10 i2·:·time·fromPluckerToStiefel·dualize·chowForm·C10 i2·:·time·fromPluckerToStiefel·dualize·chowForm·C
11 ·--·used·0.0343204s·(cpu);·0.0352705s·(thread);·0s·(gc)11 ·--·used·0.0384802s·(cpu);·0.0409787s·(thread);·0s·(gc)
  
12 ········3···3··········2···2··············2·······2··········2···3····12 ········3···3··········2···2··············2·······2··········2···3····
13 o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····-13 o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····-
14 ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1··14 ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1··
15 ·····------------------------------------------------------------------------15 ·····------------------------------------------------------------------------
16 ······2·······2···············2···2···································16 ······2·······2···············2···2···································
17 ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····-17 ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····-
Offset 56, 15 lines modifiedOffset 56, 15 lines modified
56 ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x56 ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x
57 ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,357 ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3
  
58 o2·:·QQ[x···..x···]58 o2·:·QQ[x···..x···]
59 ·········0,0···1,359 ·········0,0···1,3
  
60 i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1})60 i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1})
61 ·--·used·0.0837715s·(cpu);·0.0494865s·(thread);·0s·(gc)61 ·--·used·0.0911433s·(cpu);·0.0533314s·(thread);·0s·(gc)
  
62 ············3··········2·························2························62 ············3··········2·························2························
63 o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····-63 o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····-
64 ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3··64 ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3··
65 ·····------------------------------------------------------------------------65 ·····------------------------------------------------------------------------
66 ···········2······3······266 ···········2······3······2
67 ·····2x···x····+·x····+·x67 ·····2x···x····+·x····+·x
Offset 85, 15 lines modifiedOffset 85, 15 lines modified
  
85 o4·:·QQ[a···..a···]85 o4·:·QQ[a···..a···]
86 ·········0,0···1,186 ·········0,0···1,1
  
87 i5·:·w·=·chowForm·C;87 i5·:·w·=·chowForm·C;
  
88 i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s))88 i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s))
89 ·--·used·0.0159991s·(cpu);·0.016392s·(thread);·0s·(gc)89 ·--·used·0.0210956s·(cpu);·0.0202506s·(thread);·0s·(gc)
  
90 ···················3··········2··········3·······················2········90 ···················3··········2··········3·······················2········
91 o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+91 o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+
92 ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3··92 ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3··
93 ·····------------------------------------------------------------------------93 ·····------------------------------------------------------------------------
94 ·························2······2············2···3···············2········94 ·························2······2············2···3···············2········
95 ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+95 ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+
Offset 130, 14 lines modifiedOffset 130, 14 lines modified
130 ···········2······3······2130 ···········2······3······2
131 ·····2x···x····-·x····+·x···)}131 ·····2x···x····-·x····+·x···)}
132 ·······0,0·1,1····1,1····1,0132 ·······0,0·1,1····1,1····1,0
  
133 o6·:·List133 o6·:·List
  
134 i7·:·time·apply(U,u->dim·singularLocus·u)134 i7·:·time·apply(U,u->dim·singularLocus·u)
135 ·--·used·0.0120012s·(cpu);·0.0143212s·(thread);·0s·(gc)135 ·--·used·0.0169758s·(cpu);·0.0181462s·(thread);·0s·(gc)
  
136 o7·=·{2,·2,·2,·2,·2,·2}136 o7·=·{2,·2,·2,·2,·2,·2}
  
137 o7·:·List137 o7·:·List
  
138 i8·:·138 i8·:·
908 B
./usr/share/doc/Macaulay2/Resultants/example-output/_hurwitz__Form.out
    
Offset 10, 15 lines modifiedOffset 10, 15 lines modified
10 ·····+·-p··+·-p·p··+·7p·p··+·6p·p··+·-p·p··+·--p·)10 ·····+·-p··+·-p·p··+·7p·p··+·6p·p··+·-p·p··+·--p·)
11 ·······4·3···9·0·4·····1·4·····2·4···9·3·4···10·411 ·······4·3···9·0·4·····1·4·····2·4···9·3·4···10·4
  
12 o1·:·Ideal·of·QQ[p·..p·]12 o1·:·Ideal·of·QQ[p·..p·]
13 ··················0···413 ··················0···4
  
14 i2·:·time·hurwitzForm·Q14 i2·:·time·hurwitzForm·Q
15 ·--·used·0.031789s·(cpu);·0.0329835s·(thread);·0s·(gc)15 ·--·used·0.0424349s·(cpu);·0.0406452s·(thread);·0s·(gc)
  
16 ··············2·································2······················16 ··············2·································2······················
17 o2·=·11966535p····+·14645610p···p····+·11354175p····+·1666980p···p····+17 o2·=·11966535p····+·14645610p···p····+·11354175p····+·1666980p···p····+
18 ··············0,1············0,1·0,2············0,2···········0,1·1,2··18 ··············0,1············0,1·0,2············0,2···········0,1·1,2··
19 ·····------------------------------------------------------------------------19 ·····------------------------------------------------------------------------
20 ·······························2··········································20 ·······························2··········································
21 ·····4456620p···p····+·1127196p····+·54176850p···p····+·20326950p···p····+21 ·····4456620p···p····+·1127196p····+·54176850p···p····+·20326950p···p····+
1.06 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_is__Coisotropic.out
    
Offset 26, 15 lines modifiedOffset 26, 15 lines modified
26 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]26 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]
27 ·········0,1···0,2···1,2···0,3···1,3···2,327 ·········0,1···0,2···1,2···0,3···1,3···2,3
28 o1·:·--------------------------------------28 o1·:·--------------------------------------
29 ·········p···p····-·p···p····+·p···p29 ·········p···p····-·p···p····+·p···p
30 ··········1,2·0,3····0,2·1,3····0,1·2,330 ··········1,2·0,3····0,2·1,3····0,1·2,3
  
31 i2·:·time·isCoisotropic·w31 i2·:·time·isCoisotropic·w
32 ·--·used·0.00400137s·(cpu);·0.00724592s·(thread);·0s·(gc)32 ·--·used·0.0102693s·(cpu);·0.00979179s·(thread);·0s·(gc)
  
33 o2·=·true33 o2·=·true
  
34 i3·:·--·random·quadric·in·G(1,3)34 i3·:·--·random·quadric·in·G(1,3)
35 ·····w'·=·random(2,Grass(1,3))35 ·····w'·=·random(2,Grass(1,3))
  
36 ·······2·····5···········10·2·····2··························2······3········36 ·······2·····5···········10·2·····2··························2······3········
Offset 56, 12 lines modifiedOffset 56, 12 lines modified
56 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]56 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]
57 ·········0,1···0,2···1,2···0,3···1,3···2,357 ·········0,1···0,2···1,2···0,3···1,3···2,3
58 o3·:·--------------------------------------58 o3·:·--------------------------------------
59 ·········p···p····-·p···p····+·p···p59 ·········p···p····-·p···p····+·p···p
60 ··········1,2·0,3····0,2·1,3····0,1·2,360 ··········1,2·0,3····0,2·1,3····0,1·2,3
  
61 i4·:·time·isCoisotropic·w'61 i4·:·time·isCoisotropic·w'
62 ·--·used·0.00399805s·(cpu);·0.00571698s·(thread);·0s·(gc)62 ·--·used·0.00487026s·(cpu);·0.00814648s·(thread);·0s·(gc)
  
63 o4·=·false63 o4·=·false
  
64 i5·:·64 i5·:·
476 B
./usr/share/doc/Macaulay2/Resultants/example-output/_is__In__Coisotropic.out
    
Offset 31, 12 lines modifiedOffset 31, 12 lines modified
31 ··········4········531 ··········4········5
  
32 ················ZZ32 ················ZZ
33 o3·:·Ideal·of·-----[x·..x·]33 o3·:·Ideal·of·-----[x·..x·]
34 ··············33331··0···534 ··············33331··0···5
  
35 i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I))35 i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I))
36 ·--·used·0.0140353s·(cpu);·0.0174852s·(thread);·0s·(gc)36 ·--·used·0.018228s·(cpu);·0.0186896s·(thread);·0s·(gc)
  
37 o4·=·true37 o4·=·true
  
38 i5·:·38 i5·:·
1.66 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_macaulay__Formula.out
    
Offset 13, 15 lines modifiedOffset 13, 15 lines modified
13 ···················2··········2········2······313 ···················2··········2········2······3
14 ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·}14 ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·}
15 ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·215 ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2
  
16 o1·:·List16 o1·:·List
  
17 i2·:·time·(D,D')·=·macaulayFormula·F17 i2·:·time·(D,D')·=·macaulayFormula·F
18 ·--·used·0.00530655s·(cpu);·0.00297374s·(thread);·0s·(gc)18 ·--·used·0.00400653s·(cpu);·0.00343988s·(thread);·0s·(gc)
  
19 o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0··19 o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0··
20 ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0··20 ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0··
21 ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0··21 ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0··
22 ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0··22 ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0··
23 ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0··23 ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0··
24 ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0··24 ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0··
Offset 78, 15 lines modifiedOffset 78, 15 lines modified
78 ·····10···2···7···2···5·378 ·····10···2···7···2···5·3
79 ·····--p·p··+·-p·p··+·-p·}79 ·····--p·p··+·-p·p··+·-p·}
80 ······9·0·2···8·1·2···6·280 ······9·0·2···8·1·2···6·2
  
81 o3·:·List81 o3·:·List
  
82 i4·:·time·(D,D')·=·macaulayFormula·F82 i4·:·time·(D,D')·=·macaulayFormula·F
83 ·--·used·0.000114933s·(cpu);·0.00199944s·(thread);·0s·(gc)83 ·--·used·0.00275349s·(cpu);·0.0024385s·(thread);·0s·(gc)
  
84 o4·=·(|·9/2·9/4·3/4·7/4··7/9··7/10·0····0····0····0····0···0···0····0····0···84 o4·=·(|·9/2·9/4·3/4·7/4··7/9··7/10·0····0····0····0····0···0···0····0····0···
85 ······|·0···9/2·0···9/4··3/4··0····7/4··7/9··7/10·0····0···0···0····0····0···85 ······|·0···9/2·0···9/4··3/4··0····7/4··7/9··7/10·0····0···0···0····0····0···
86 ······|·0···0···9/2·0····9/4··3/4··0····7/4··7/9··7/10·0···0···0····0····0···86 ······|·0···0···9/2·0····9/4··3/4··0····7/4··7/9··7/10·0···0···0····0····0···
87 ······|·0···0···0···9/2··0····0····9/4··3/4··0····0····7/4·7/9·7/10·0····0···87 ······|·0···0···0···9/2··0····0····9/4··3/4··0····0····7/4·7/9·7/10·0····0···
88 ······|·0···0···0···0····9/2··0····0····9/4··3/4··0····0···7/4·7/9··7/10·0···88 ······|·0···0···0···0····9/2··0····0····9/4··3/4··0····0···7/4·7/9··7/10·0···
89 ······|·0···0···0···0····0····9/2··0····0····9/4··3/4··0···0···7/4··7/9··7/1089 ······|·0···0···0···0····0····9/2··0····0····9/4··3/4··0···0···7/4··7/9··7/10
1.94 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_plucker.out
    
Offset 9, 29 lines modifiedOffset 9, 29 lines modified
9 ·····------------------------------------------------------------------------9 ·····------------------------------------------------------------------------
10 ·····664x·)10 ·····664x·)
11 ·········411 ·········4
  
12 o3·:·Ideal·of·P412 o3·:·Ideal·of·P4
  
13 i4·:·time·p·=·plucker·L13 i4·:·time·p·=·plucker·L
14 ·--·used·0.00417327s·(cpu);·0.00387254s·(thread);·0s·(gc)14 ·--·used·0.00445093s·(cpu);·0.00463992s·(thread);·0s·(gc)
  
15 o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+15 o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+
16 ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3··16 ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3··
17 ·····------------------------------------------------------------------------17 ·····------------------------------------------------------------------------
18 ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+18 ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+
19 ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2··19 ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2··
20 ·····------------------------------------------------------------------------20 ·····------------------------------------------------------------------------
21 ·····11804x···,·x····+·14854x···)21 ·····11804x···,·x····+·14854x···)
22 ···········3,4···0,1·········3,422 ···········3,4···0,1·········3,4
  
23 o4·:·Ideal·of·G'1'423 o4·:·Ideal·of·G'1'4
  
24 i5·:·time·L'·=·plucker·p24 i5·:·time·L'·=·plucker·p
25 ·--·used·0.0249875s·(cpu);·0.0265876s·(thread);·0s·(gc)25 ·--·used·0.0299986s·(cpu);·0.0297164s·(thread);·0s·(gc)
  
26 o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··-26 o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··-
27 ·············2········3·········4···1········3·········4···0·········3··27 ·············2········3·········4···1········3·········4···0·········3··
28 ·····------------------------------------------------------------------------28 ·····------------------------------------------------------------------------
29 ·····664x·)29 ·····664x·)
30 ·········430 ·········4
  
Offset 40, 25 lines modifiedOffset 40, 25 lines modified
40 i6·:·assert(L'·==·L)40 i6·:·assert(L'·==·L)
  
41 i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve41 i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve
  
42 o7·:·Ideal·of·G'1'442 o7·:·Ideal·of·G'1'4
  
43 i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y43 i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y
44 ·--·used·0.0808757s·(cpu);·0.0523908s·(thread);·0s·(gc)44 ·--·used·0.0766138s·(cpu);·0.0422324s·(thread);·0s·(gc)
  
45 o8·:·Ideal·of·P445 o8·:·Ideal·of·P4
  
46 i9·:·(codim·W,degree·W)46 i9·:·(codim·W,degree·W)
  
47 o9·=·(2,·5)47 o9·=·(2,·5)
  
48 o9·:·Sequence48 o9·:·Sequence
  
49 i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W49 i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W
50 ·--·used·0.127366s·(cpu);·0.128568s·(thread);·0s·(gc)50 ·--·used·0.17979s·(cpu);·0.179979s·(thread);·0s·(gc)
  
51 o10·:·Ideal·of·G'1'451 o10·:·Ideal·of·G'1'4
  
52 i11·:·assert(Y'·==·Y)52 i11·:·assert(Y'·==·Y)
  
53 i12·:·53 i12·:·
3.37 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_resultant_lp..._cm__Algorithm_eq_gt..._rp.out
    
Offset 35, 15 lines modifiedOffset 35, 15 lines modified
35 ·····3·····2····9····7·····2····9········3·······1····8····435 ·····3·····2····9····7·····2····9········3·······1····8····4
36 ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w}36 ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w}
37 ·····4··········8····8··········7················4····3····537 ·····4··········8····8··········7················4····3····5
  
38 o2·:·List38 o2·:·List
  
39 i3·:·time·resultant(F,Algorithm=>"Poisson2")39 i3·:·time·resultant(F,Algorithm=>"Poisson2")
40 ·--·used·0.214497s·(cpu);·0.157181s·(thread);·0s·(gc)40 ·--·used·0.267135s·(cpu);·0.181296s·(thread);·0s·(gc)
  
41 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···41 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
42 o3·=·-·-----------------------------a··-·-------------------------------a·b·-42 o3·=·-·-----------------------------a··-·-------------------------------a·b·-
43 ···········2222549728809984000000············12700284164628480000000·········43 ···········2222549728809984000000············12700284164628480000000·········
44 ·····------------------------------------------------------------------------44 ·····------------------------------------------------------------------------
45 ·····348237304382147063838108483692249·3·2··45 ·····348237304382147063838108483692249·3·2··
46 ·····---------------------------------a·b··-46 ·····---------------------------------a·b··-
Offset 56, 15 lines modifiedOffset 56, 15 lines modified
56 ·····1146977327343523453866040839029···4···194441910898734675845094443·556 ·····1146977327343523453866040839029···4···194441910898734675845094443·5
57 ·····-------------------------------a*b··-·---------------------------b57 ·····-------------------------------a*b··-·---------------------------b
58 ··········1119954511872000000000················89596360949760000058 ··········1119954511872000000000················895963609497600000
  
59 o3·:·QQ[a..b]59 o3·:·QQ[a..b]
  
60 i4·:·time·resultant(F,Algorithm=>"Macaulay2")60 i4·:·time·resultant(F,Algorithm=>"Macaulay2")
61 ·--·used·0.0603554s·(cpu);·0.0607234s·(thread);·0s·(gc)61 ·--·used·0.0872349s·(cpu);·0.0893436s·(thread);·0s·(gc)
  
62 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···62 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
63 o4·=·-·-----------------------------a··-·-------------------------------a·b·-63 o4·=·-·-----------------------------a··-·-------------------------------a·b·-
64 ···········2222549728809984000000············12700284164628480000000·········64 ···········2222549728809984000000············12700284164628480000000·········
65 ·····------------------------------------------------------------------------65 ·····------------------------------------------------------------------------
66 ·····348237304382147063838108483692249·3·2··66 ·····348237304382147063838108483692249·3·2··
67 ·····---------------------------------a·b··-67 ·····---------------------------------a·b··-
Offset 77, 15 lines modifiedOffset 77, 15 lines modified
77 ·····1146977327343523453866040839029···4···194441910898734675845094443·577 ·····1146977327343523453866040839029···4···194441910898734675845094443·5
78 ·····-------------------------------a*b··-·---------------------------b78 ·····-------------------------------a*b··-·---------------------------b
79 ··········1119954511872000000000················89596360949760000079 ··········1119954511872000000000················895963609497600000
  
80 o4·:·QQ[a..b]80 o4·:·QQ[a..b]
  
81 i5·:·time·resultant(F,Algorithm=>"Poisson")81 i5·:·time·resultant(F,Algorithm=>"Poisson")
82 ·--·used·0.268621s·(cpu);·0.237589s·(thread);·0s·(gc)82 ·--·used·0.362645s·(cpu);·0.32476s·(thread);·0s·(gc)
  
83 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···83 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
84 o5·=·-·-----------------------------a··-·-------------------------------a·b·-84 o5·=·-·-----------------------------a··-·-------------------------------a·b·-
85 ···········2222549728809984000000············12700284164628480000000·········85 ···········2222549728809984000000············12700284164628480000000·········
86 ·····------------------------------------------------------------------------86 ·····------------------------------------------------------------------------
87 ·····348237304382147063838108483692249·3·2··87 ·····348237304382147063838108483692249·3·2··
88 ·····---------------------------------a·b··-88 ·····---------------------------------a·b··-
Offset 98, 15 lines modifiedOffset 98, 15 lines modified
98 ·····1146977327343523453866040839029···4···194441910898734675845094443·598 ·····1146977327343523453866040839029···4···194441910898734675845094443·5
99 ·····-------------------------------a*b··-·---------------------------b99 ·····-------------------------------a*b··-·---------------------------b
100 ··········1119954511872000000000················895963609497600000100 ··········1119954511872000000000················895963609497600000
  
101 o5·:·QQ[a..b]101 o5·:·QQ[a..b]
  
102 i6·:·time·resultant(F,Algorithm=>"Macaulay")102 i6·:·time·resultant(F,Algorithm=>"Macaulay")
103 ·--·used·0.451197s·(cpu);·0.423115s·(thread);·0s·(gc)103 ·--·used·0.598137s·(cpu);·0.560047s·(thread);·0s·(gc)
  
104 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···104 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
105 o6·=·-·-----------------------------a··-·-------------------------------a·b·-105 o6·=·-·-----------------------------a··-·-------------------------------a·b·-
106 ···········2222549728809984000000············12700284164628480000000·········106 ···········2222549728809984000000············12700284164628480000000·········
107 ·····------------------------------------------------------------------------107 ·····------------------------------------------------------------------------
108 ·····348237304382147063838108483692249·3·2··108 ·····348237304382147063838108483692249·3·2··
109 ·····---------------------------------a·b··-109 ·····---------------------------------a·b··-
1.95 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_resultant_lp__Matrix_rp.out
    
Offset 10, 15 lines modifiedOffset 10, 15 lines modified
  
10 ·······2···············2····························3······2·········410 ·······2···············2····························3······2·········4
11 o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·}11 o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·}
  
12 o2·:·List12 o2·:·List
  
13 i3·:·time·resultant·F13 i3·:·time·resultant·F
14 ·--·used·0.0230989s·(cpu);·0.020533s·(thread);·0s·(gc)14 ·--·used·0.0266299s·(cpu);·0.0260982s·(thread);·0s·(gc)
  
15 ··········12·········11·2·········10·3·········9·4··········8·5··········7·615 ··········12·········11·2·········10·3·········9·4··········8·5··········7·6
16 o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u·16 o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u·
17 ·····------------------------------------------------------------------------17 ·····------------------------------------------------------------------------
18 ··············6·7··········5·8·······11··········10·2·········9·3··18 ··············6·7··········5·8·······11··········10·2·········9·3··
19 ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+19 ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+
20 ·····------------------------------------------------------------------------20 ·····------------------------------------------------------------------------
Offset 64, 15 lines modifiedOffset 64, 15 lines modified
64 ··········364 ··········3
65 ·····+·c·x·}65 ·····+·c·x·}
66 ········9·266 ········9·2
  
67 o4·:·List67 o4·:·List
  
68 i5·:·time·resultant·F68 i5·:·time·resultant·F
69 ·--·used·1.7778s·(cpu);·1.45356s·(thread);·0s·(gc)69 ·--·used·2.04727s·(cpu);·1.59536s·(thread);·0s·(gc)
  
70 ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2··70 ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2··
71 o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··-71 o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··-
72 ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0··72 ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0··
73 ·····------------------------------------------------------------------------73 ·····------------------------------------------------------------------------
74 ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2··74 ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2··
75 ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··-75 ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··-
Offset 1690, 12 lines modifiedOffset 1690, 12 lines modified
1690 ··························2·····2···············2························21690 ··························2·····2···············2························2
1691 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}1691 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}
1692 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·21692 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2
  
1693 o6·:·List1693 o6·:·List
  
1694 i7·:·time·#·terms·resultant·F1694 i7·:·time·#·terms·resultant·F
1695 ·--·used·0.370806s·(cpu);·0.303331s·(thread);·0s·(gc)1695 ·--·used·0.384467s·(cpu);·0.31323s·(thread);·0s·(gc)
  
1696 o7·=·218941696 o7·=·21894
  
1697 i8·:·1697 i8·:·
4.0 KB
./usr/share/doc/Macaulay2/Resultants/example-output/_tangential__Chow__Form.out
    
Offset 8, 15 lines modifiedOffset 8, 15 lines modified
8 ···············1·2····0·3·····1·3····0·4·····3····2·48 ···············1·2····0·3·····1·3····0·4·····3····2·4
  
9 o2·:·Ideal·of·QQ[p·..p·]9 o2·:·Ideal·of·QQ[p·..p·]
10 ··················0···410 ··················0···4
  
11 i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form)11 i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form)
12 ·····time·tangentialChowForm(S,0)12 ·····time·tangentialChowForm(S,0)
13 ·--·used·0.0258548s·(cpu);·0.0256399s·(thread);·0s·(gc)13 ·--·used·0.0311866s·(cpu);·0.0286425s·(thread);·0s·(gc)
  
14 ······2·······················································2········14 ······2·······················································2········
15 o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+15 o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+
16 ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4··16 ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4··
17 ·····------------------------------------------------------------------------17 ·····------------------------------------------------------------------------
18 ······218 ······2
19 ·····p···p····-·2p···p···p····-·p···p···p19 ·····p···p····-·2p···p···p····-·p···p···p
Offset 26, 15 lines modifiedOffset 26, 15 lines modified
26 ··························································0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,426 ··························································0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4
27 o3·:·----------------------------------------------------------------------------------------------------------------------------------------------------------------27 o3·:·----------------------------------------------------------------------------------------------------------------------------------------------------------------
28 ·····(p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···)28 ·····(p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···)
29 ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,329 ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,3
  
30 i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4)30 i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4)
31 ·····time·tangentialChowForm(S,1)31 ·····time·tangentialChowForm(S,1)
32 ·--·used·0.0434599s·(cpu);·0.0461125s·(thread);·0s·(gc)32 ·--·used·0.0571841s·(cpu);·0.0562841s·(thread);·0s·(gc)
  
33 ······2·····2········2·····2···············3········2·····2······33 ······2·····2········2·····2···············3········2·····2······
34 o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······-34 o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······-
35 ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4··35 ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4··
36 ·····------------------------------------------------------------------------36 ·····------------------------------------------------------------------------
37 ·············3·········3···············3············37 ·············3·········3···············3············
38 ·····4p·····p······-·4p·····p······-·2p·····p······+38 ·····4p·····p······-·4p·····p······-·2p·····p······+
Offset 68, 32 lines modifiedOffset 68, 32 lines modified
68 ··············································································0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,468 ··············································································0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,4
69 o4·:·----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------69 o4·:·----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
70 ·····(p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····)70 ·····(p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····)
71 ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,471 ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4
  
72 i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S)72 i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S)
73 ·····time·tangentialChowForm(S,2)73 ·····time·tangentialChowForm(S,2)
74 ·--·used·0.0695898s·(cpu);·0.0424074s·(thread);·0s·(gc)74 ·--·used·0.110597s·(cpu);·0.0519151s·(thread);·0s·(gc)
  
75 ··············2·············································275 ··············2·············································2
76 o5·=·p·······p········-·p·······p·······p········+·p·······p76 o5·=·p·······p········-·p·······p·······p········+·p·······p
77 ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,477 ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4
  
78 o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······]78 o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······]
79 ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,479 ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4
  
80 i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing80 i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing
81 ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2)81 ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2)
82 ·--·used·0.0336126s·(cpu);·0.0346874s·(thread);·0s·(gc)82 ·--·used·0.0411523s·(cpu);·0.0418658s·(thread);·0s·(gc)
  
83 ············2···············283 ············2···············2
84 o6·=·ideal(p·p··-·p·p·p··+·p·p·)84 o6·=·ideal(p·p··-·p·p·p··+·p·p·)
85 ············1·2····0·1·3····0·485 ············1·2····0·1·3····0·4
  
86 o6·:·Ideal·of·QQ[p·..p·]86 o6·:·Ideal·of·QQ[p·..p·]
87 ··················0···487 ··················0···4
  
88 i7·:·--·we·then·can·recover·S88 i7·:·--·we·then·can·recover·S
89 ·····time·assert(dualize·tangentialChowForm(S',3)·==·S)89 ·····time·assert(dualize·tangentialChowForm(S',3)·==·S)
90 ·--·used·0.111376s·(cpu);·0.0867692s·(thread);·0s·(gc)90 ·--·used·0.166675s·(cpu);·0.101515s·(thread);·0s·(gc)
  
91 i8·:·91 i8·:·
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Offset 86, 24 lines modifiedOffset 86, 24 lines modified
86 o2·:·Ideal·of·QQ[x·..x·]86 o2·:·Ideal·of·QQ[x·..x·]
87 ··················0···3</code></pre>87 ··················0···3</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2);92 ··············<pre><code·class="language-macaulay2">i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2);
93 ·--·used·0.0391455s·(cpu);·0.0398698s·(thread);·0s·(gc)</code></pre>93 ·--·used·0.0555615s·(cpu);·0.0555018s·(thread);·0s·(gc)</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ········</table>96 ········</table>
97 ········<p>In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its·dual·variety.</p>97 ········<p>In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its·dual·variety.</p>
98 ········<table·class="examples">98 ········<table·class="examples">
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1)101 ··············<pre><code·class="language-macaulay2">i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1)
102 ·--·used·0.0953295s·(cpu);·0.0623364s·(thread);·0s·(gc)102 ·--·used·0.116121s·(cpu);·0.0739718s·(thread);·0s·(gc)
  
103 ···········································································103 ···········································································
104 o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,104 o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,
105 ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3·105 ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3·
106 ·····------------------------------------------------------------------------106 ·····------------------------------------------------------------------------
107 ············································································107 ············································································
108 ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x···108 ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x···
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130 ··········</tr>130 ··········</tr>
131 ········</table>131 ········</table>
132 ········<p>If·the·option·<span·class="tt">Duality</span>·is·set·to·<span·class="tt">true</span>,·then·the·method·applies·the·so-called·&quot;dual·Cayley·trick&quot;.</p>132 ········<p>If·the·option·<span·class="tt">Duality</span>·is·set·to·<span·class="tt">true</span>,·then·the·method·applies·the·so-called·&quot;dual·Cayley·trick&quot;.</p>
133 ········<table·class="examples">133 ········<table·class="examples">
134 ··········<tr>134 ··········<tr>
135 ············<td>135 ············<td>
136 ··············<pre><code·class="language-macaulay2">i5·:·time·cayleyTrick(P1xP1,1,Duality=>true);136 ··············<pre><code·class="language-macaulay2">i5·:·time·cayleyTrick(P1xP1,1,Duality=>true);
137 ·--·used·0.112199s·(cpu);·0.0832487s·(thread);·0s·(gc)</code></pre>137 ·--·used·0.138193s·(cpu);·0.0991304s·(thread);·0s·(gc)</code></pre>
138 ············</td>138 ············</td>
139 ··········</tr>139 ··········</tr>
140 ··········<tr>140 ··········<tr>
141 ············<td>141 ············<td>
142 ··············<pre><code·class="language-macaulay2">i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))</code></pre>142 ··············<pre><code·class="language-macaulay2">i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))</code></pre>
143 ············</td>143 ············</td>
144 ··········</tr>144 ··········</tr>
145 ··········<tr>145 ··········<tr>
146 ············<td>146 ············<td>
147 ··············<pre><code·class="language-macaulay2">i7·:·time·cayleyTrick(P1xP1,2,Duality=>true);147 ··············<pre><code·class="language-macaulay2">i7·:·time·cayleyTrick(P1xP1,2,Duality=>true);
148 ·--·used·0.12098s·(cpu);·0.0872498s·(thread);·0s·(gc)</code></pre>148 ·--·used·0.178856s·(cpu);·0.1113s·(thread);·0s·(gc)</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
152 ············<td>152 ············<td>
153 ··············<pre><code·class="language-macaulay2">i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))</code></pre>153 ··············<pre><code·class="language-macaulay2">i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))</code></pre>
154 ············</td>154 ············</td>
155 ··········</tr>155 ··········</tr>
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38 o2·=·ideal(x·x··-·x·x·)38 o2·=·ideal(x·x··-·x·x·)
39 ············0·1····2·339 ············0·1····2·3
  
40 o2·:·Ideal·of·QQ[x·..x·]40 o2·:·Ideal·of·QQ[x·..x·]
41 ··················0···341 ··················0···3
42 i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2);42 i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2);
43 ·--·used·0.0391455s·(cpu);·0.0398698s·(thread);·0s·(gc)43 ·--·used·0.0555615s·(cpu);·0.0555018s·(thread);·0s·(gc)
44 In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb44 In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb
45 {P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its45 {P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its
46 dual·variety.46 dual·variety.
47 i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1)47 i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1)
48 ·--·used·0.0953295s·(cpu);·0.0623364s·(thread);·0s·(gc)48 ·--·used·0.116121s·(cpu);·0.0739718s·(thread);·0s·(gc)
  
  
49 o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,49 o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,
50 ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,350 ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3
51 ·····------------------------------------------------------------------------51 ·····------------------------------------------------------------------------
  
52 ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x52 ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x
Offset 73, 18 lines modifiedOffset 73, 18 lines modified
73 ·····4x···x···x···x····-·2x···x···x···x····+·x···x···))73 ·····4x···x···x···x····-·2x···x···x···x····+·x···x···))
74 ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,374 ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,3
  
75 o4·:·Sequence75 o4·:·Sequence
76 If·the·option·Duality·is·set·to·true,·then·the·method·applies·the·so-called76 If·the·option·Duality·is·set·to·true,·then·the·method·applies·the·so-called
77 "dual·Cayley·trick".77 "dual·Cayley·trick".
78 i5·:·time·cayleyTrick(P1xP1,1,Duality=>true);78 i5·:·time·cayleyTrick(P1xP1,1,Duality=>true);
79 ·--·used·0.112199s·(cpu);·0.0832487s·(thread);·0s·(gc)79 ·--·used·0.138193s·(cpu);·0.0991304s·(thread);·0s·(gc)
80 i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))80 i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))
81 i7·:·time·cayleyTrick(P1xP1,2,Duality=>true);81 i7·:·time·cayleyTrick(P1xP1,2,Duality=>true);
82 ·--·used·0.12098s·(cpu);·0.0872498s·(thread);·0s·(gc)82 ·--·used·0.178856s·(cpu);·0.1113s·(thread);·0s·(gc)
83 i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))83 i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))
84 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*84 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
85 ····*·_\x8d_\x8u_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·projective·dual·variety85 ····*·_\x8d_\x8u_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·projective·dual·variety
86 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ca\x8ay\x8yl\x8le\x8ey\x8yT\x8Tr\x8ri\x8ic\x8ck\x8k:\x8:·*\x8**\x8**\x8**\x8**\x8*86 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ca\x8ay\x8yl\x8le\x8ey\x8yT\x8Tr\x8ri\x8ic\x8ck\x8k:\x8:·*\x8**\x8**\x8**\x8**\x8*
87 ····*·cayleyTrick(Ideal,ZZ)87 ····*·cayleyTrick(Ideal,ZZ)
88 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*88 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
89 The·object·_\x8c_\x8a_\x8y_\x8l_\x8e_\x8y_\x8T_\x8r_\x8i_\x8c_\x8k·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.89 The·object·_\x8c_\x8a_\x8y_\x8l_\x8e_\x8y_\x8T_\x8r_\x8i_\x8c_\x8k·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
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90 o2·:·Ideal·of·P3</code></pre>90 o2·:·Ideal·of·P3</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i3·:·--·Chow·equations·of·C95 ··············<pre><code·class="language-macaulay2">i3·:·--·Chow·equations·of·C
96 ·····time·eqsC·=·chowEquations·chowForm·C96 ·····time·eqsC·=·chowEquations·chowForm·C
97 ·--·used·0.0369285s·(cpu);·0.037131s·(thread);·0s·(gc)97 ·--·used·0.0399458s·(cpu);·0.0393854s·(thread);·0s·(gc)
  
98 ·············2·2····2·2····2·2····4················2······2·2···2······98 ·············2·2····2·2····2·2····4················2······2·2···2······
99 o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+99 o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+
100 ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3··100 ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3··
101 ·····------------------------------------------------------------------------101 ·····------------------------------------------------------------------------
102 ······2········3···········2·········2······3···3·········2··········2····2·2102 ······2········3···········2·········2······3···3·········2··········2····2·2
103 ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x·103 ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x·
Offset 162, 15 lines modifiedOffset 162, 15 lines modified
162 o5·:·Ideal·of·P3</code></pre>162 o5·:·Ideal·of·P3</code></pre>
163 ············</td>163 ············</td>
164 ··········</tr>164 ··········</tr>
165 ··········<tr>165 ··········<tr>
166 ············<td>166 ············<td>
167 ··············<pre><code·class="language-macaulay2">i6·:·--·Chow·equations·of·D167 ··············<pre><code·class="language-macaulay2">i6·:·--·Chow·equations·of·D
168 ·····time·eqsD·=·chowEquations·chowForm·D168 ·····time·eqsD·=·chowEquations·chowForm·D
169 ·--·used·0.079526s·(cpu);·0.0429132s·(thread);·0s·(gc)169 ·--·used·0.0874898s·(cpu);·0.0525426s·(thread);·0s·(gc)
  
170 ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2·170 ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2·
171 o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,171 o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,
172 ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3·172 ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3·
173 ·····------------------------------------------------------------------------173 ·····------------------------------------------------------------------------
174 ··········2······3·2···3········3·2···4·········2·········2·2·······3····174 ··········2······3·2···3········3·2···4·········2·········2·2·······3····
175 ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··-175 ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··-
Offset 222, 30 lines modifiedOffset 222, 30 lines modified
222 o9·:·Ideal·of·P3</code></pre>222 o9·:·Ideal·of·P3</code></pre>
223 ············</td>223 ············</td>
224 ··········</tr>224 ··········</tr>
225 ··········<tr>225 ··········<tr>
226 ············<td>226 ············<td>
227 ··············<pre><code·class="language-macaulay2">i10·:·--·tangential·Chow·forms·of·Q227 ··············<pre><code·class="language-macaulay2">i10·:·--·tangential·Chow·forms·of·Q
228 ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2))228 ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2))
229 ·--·used·0.110669s·(cpu);·0.0758087s·(thread);·0s·(gc)229 ·--·used·0.12062s·(cpu);·0.0986453s·(thread);·0s·(gc)
  
230 ·····················2······························2230 ·····················2······························2
231 o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+231 o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+
232 ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3··232 ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3··
233 ······-----------------------------------------------------------------------233 ······-----------------------------------------------------------------------
234 ······x·····x·····)234 ······x·····x·····)
235 ·······0,2,3·1,2,3235 ·······0,2,3·1,2,3
  
236 o10·:·Sequence</code></pre>236 o10·:·Sequence</code></pre>
237 ············</td>237 ············</td>
238 ··········</tr>238 ··········</tr>
239 ··········<tr>239 ··········<tr>
240 ············<td>240 ············<td>
241 ··············<pre><code·class="language-macaulay2">i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2))241 ··············<pre><code·class="language-macaulay2">i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2))
242 ·--·used·0.0558416s·(cpu);·0.056609s·(thread);·0s·(gc)242 ·--·used·0.0565585s·(cpu);·0.0569067s·(thread);·0s·(gc)
  
243 o11·=·true</code></pre>243 o11·=·true</code></pre>
244 ············</td>244 ············</td>
245 ··········</tr>245 ··········</tr>
246 ········</table>246 ········</table>
247 ········<p>Note·that·<span·class="tt">chowEquations(W,0)</span>·is·not·the·same·as·<span·class="tt">chowEquations·W</span>.</p>247 ········<p>Note·that·<span·class="tt">chowEquations(W,0)</span>·is·not·the·same·as·<span·class="tt">chowEquations·W</span>.</p>
248 ······</div>248 ······</div>
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Offset 28, 15 lines modifiedOffset 28, 15 lines modified
28 ·············2····2····2····228 ·············2····2····2····2
29 o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·)29 o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·)
30 ·············0····1····2····3···0·1····1·2····2·330 ·············0····1····2····3···0·1····1·2····2·3
  
31 o2·:·Ideal·of·P331 o2·:·Ideal·of·P3
32 i3·:·--·Chow·equations·of·C32 i3·:·--·Chow·equations·of·C
33 ·····time·eqsC·=·chowEquations·chowForm·C33 ·····time·eqsC·=·chowEquations·chowForm·C
34 ·--·used·0.0369285s·(cpu);·0.037131s·(thread);·0s·(gc)34 ·--·used·0.0399458s·(cpu);·0.0393854s·(thread);·0s·(gc)
  
35 ·············2·2····2·2····2·2····4················2······2·2···235 ·············2·2····2·2····2·2····4················2······2·2···2
36 o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+36 o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+
37 ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·337 ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3
38 ·····------------------------------------------------------------------------38 ·····------------------------------------------------------------------------
39 ······2········3···········2·········2······3···3·········2··········2····2·239 ······2········3···········2·········2······3···3·········2··········2····2·2
40 ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x40 ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x
Offset 88, 15 lines modifiedOffset 88, 15 lines modified
88 ·············2··········3··············2····288 ·············2··········3··············2····2
89 o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·)89 o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·)
90 ·············1····0·2···2····0·1·3···1·2····0·390 ·············1····0·2···2····0·1·3···1·2····0·3
  
91 o5·:·Ideal·of·P391 o5·:·Ideal·of·P3
92 i6·:·--·Chow·equations·of·D92 i6·:·--·Chow·equations·of·D
93 ·····time·eqsD·=·chowEquations·chowForm·D93 ·····time·eqsD·=·chowEquations·chowForm·D
94 ·--·used·0.079526s·(cpu);·0.0429132s·(thread);·0s·(gc)94 ·--·used·0.0874898s·(cpu);·0.0525426s·(thread);·0s·(gc)
  
95 ·············4······3·2·····3········2·2·····3······2···2···2·2······2···295 ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2
96 o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,96 o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,
97 ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·397 ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3
98 ·····------------------------------------------------------------------------98 ·····------------------------------------------------------------------------
99 ··········2······3·2···3········3·2···4·········2·········2·2·······399 ··········2······3·2···3········3·2···4·········2·········2·2·······3
100 ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··-100 ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··-
Offset 135, 27 lines modifiedOffset 135, 27 lines modified
135 o9·=·ideal(x·x··+·x·x·)135 o9·=·ideal(x·x··+·x·x·)
136 ············0·1····2·3136 ············0·1····2·3
  
137 o9·:·Ideal·of·P3137 o9·:·Ideal·of·P3
138 i10·:·--·tangential·Chow·forms·of·Q138 i10·:·--·tangential·Chow·forms·of·Q
139 ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm139 ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm
140 (Q,1),tangentialChowForm(Q,2))140 (Q,1),tangentialChowForm(Q,2))
141 ·--·used·0.110669s·(cpu);·0.0758087s·(thread);·0s·(gc)141 ·--·used·0.12062s·(cpu);·0.0986453s·(thread);·0s·(gc)
  
142 ·····················2······························2142 ·····················2······························2
143 o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+143 o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+
144 ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3144 ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3
145 ······-----------------------------------------------------------------------145 ······-----------------------------------------------------------------------
146 ······x·····x·····)146 ······x·····x·····)
147 ·······0,2,3·1,2,3147 ·······0,2,3·1,2,3
  
148 o10·:·Sequence148 o10·:·Sequence
149 i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations149 i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations
150 (W2,2))150 (W2,2))
151 ·--·used·0.0558416s·(cpu);·0.056609s·(thread);·0s·(gc)151 ·--·used·0.0565585s·(cpu);·0.0569067s·(thread);·0s·(gc)
  
152 o11·=·true152 o11·=·true
153 Note·that·chowEquations(W,0)·is·not·the·same·as·chowEquations·W.153 Note·that·chowEquations(W,0)·is·not·the·same·as·chowEquations·W.
154 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wE\x8Eq\x8qu\x8ua\x8at\x8ti\x8io\x8on\x8ns\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*154 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wE\x8Eq\x8qu\x8ua\x8at\x8ti\x8io\x8on\x8ns\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8*
155 ····*·chowEquations(RingElement)155 ····*·chowEquations(RingElement)
156 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*156 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
157 The·object·_\x8c_\x8h_\x8o_\x8w_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.157 The·object·_\x8c_\x8h_\x8o_\x8w_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
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./usr/share/doc/Macaulay2/Resultants/html/_chow__Form.html
    
Offset 97, 15 lines modifiedOffset 97, 15 lines modified
97 ··············3331··0···5</code></pre>97 ··············3331··0···5</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian)102 ··············<pre><code·class="language-macaulay2">i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian)
103 ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3})103 ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3})
104 ·--·used·4.41024s·(cpu);·4.26416s·(thread);·0s·(gc)104 ·--·used·4.75643s·(cpu);·4.53933s·(thread);·0s·(gc)
  
105 ······4···············2··············2·····2···············2············105 ······4···············2··············2·····2···············2············
106 o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+106 o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+
107 ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5··107 ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5··
108 ·····------------------------------------------------------------------------108 ·····------------------------------------------------------------------------
109 ······2·····2··············2·······································109 ······2·····2··············2·······································
110 ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+110 ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+
Offset 227, 22 lines modifiedOffset 227, 22 lines modified
227 ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre>227 ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre>
228 ············</td>228 ············</td>
229 ··········</tr>229 ··········</tr>
230 ··········<tr>230 ··········<tr>
231 ············<td>231 ············<td>
232 ··············<pre><code·class="language-macaulay2">i4·:·--·equivalently·(but·faster)...232 ··············<pre><code·class="language-macaulay2">i4·:·--·equivalently·(but·faster)...
233 ·····time·assert(ChowV·===·chowForm·f)233 ·····time·assert(ChowV·===·chowForm·f)
234 ·--·used·1.0665s·(cpu);·0.994859s·(thread);·0s·(gc)</code></pre>234 ·--·used·1.08211s·(cpu);·0.972457s·(thread);·0s·(gc)</code></pre>
235 ············</td>235 ············</td>
236 ··········</tr>236 ··········</tr>
237 ··········<tr>237 ··········<tr>
238 ············<td>238 ············<td>
239 ··············<pre><code·class="language-macaulay2">i5·:·--·X-resultant·of·V239 ··············<pre><code·class="language-macaulay2">i5·:·--·X-resultant·of·V
240 ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV;240 ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV;
241 ·--·used·0.166367s·(cpu);·0.135265s·(thread);·0s·(gc)</code></pre>241 ·--·used·0.203276s·(cpu);·0.166603s·(thread);·0s·(gc)</code></pre>
242 ············</td>242 ············</td>
243 ··········</tr>243 ··········</tr>
244 ··········<tr>244 ··········<tr>
245 ············<td>245 ············<td>
246 ··············<pre><code·class="language-macaulay2">i6·:·--·three·generic·ternary·quadrics246 ··············<pre><code·class="language-macaulay2">i6·:·--·three·generic·ternary·quadrics
247 ·····F·=·genericPolynomials({2,2,2},ZZ/3331)247 ·····F·=·genericPolynomials({2,2,2},ZZ/3331)
  
Offset 257, 15 lines modifiedOffset 257, 15 lines modified
257 o6·:·List</code></pre>257 o6·:·List</code></pre>
258 ············</td>258 ············</td>
259 ··········</tr>259 ··········</tr>
260 ··········<tr>260 ··········<tr>
261 ············<td>261 ············<td>
262 ··············<pre><code·class="language-macaulay2">i7·:·--·resultant·of·the·three·forms262 ··············<pre><code·class="language-macaulay2">i7·:·--·resultant·of·the·three·forms
263 ·····time·resF·=·resultant·F;263 ·····time·resF·=·resultant·F;
264 ·--·used·0.166113s·(cpu);·0.136166s·(thread);·0s·(gc)</code></pre>264 ·--·used·0.215597s·(cpu);·0.153987s·(thread);·0s·(gc)</code></pre>
265 ············</td>265 ············</td>
266 ··········</tr>266 ··········</tr>
267 ··········<tr>267 ··········<tr>
268 ············<td>268 ············<td>
269 ··············<pre><code·class="language-macaulay2">i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres))</code></pre>269 ··············<pre><code·class="language-macaulay2">i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres))</code></pre>
270 ············</td>270 ············</td>
271 ··········</tr>271 ··········</tr>
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Offset 41, 15 lines modifiedOffset 41, 15 lines modified
  
41 ···············ZZ41 ···············ZZ
42 o2·:·Ideal·of·----[x·..x·]42 o2·:·Ideal·of·----[x·..x·]
43 ··············3331··0···543 ··············3331··0···5
44 i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an44 i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an
45 affine·chart·of·the·Grassmannian)45 affine·chart·of·the·Grassmannian)
46 ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3})46 ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3})
47 ·--·used·4.41024s·(cpu);·4.26416s·(thread);·0s·(gc)47 ·--·used·4.75643s·(cpu);·4.53933s·(thread);·0s·(gc)
  
48 ······4···············2··············2·····2···············248 ······4···············2··············2·····2···············2
49 o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+49 o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+
50 ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,550 ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5
51 ·····------------------------------------------------------------------------51 ·····------------------------------------------------------------------------
52 ······2·····2··············252 ······2·····2··············2
53 ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+53 ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+
Offset 234, 33 lines modifiedOffset 234, 33 lines modified
234 1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5234 1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5
235 0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4235 0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4
236 1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4236 1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4
237 0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3237 0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3
238 0,1,4····0,1,3·0,2,4····0,1,2·0,3,4238 0,1,4····0,1,3·0,2,4····0,1,2·0,3,4
239 i4·:·--·equivalently·(but·faster)...239 i4·:·--·equivalently·(but·faster)...
240 ·····time·assert(ChowV·===·chowForm·f)240 ·····time·assert(ChowV·===·chowForm·f)
241 ·--·used·1.0665s·(cpu);·0.994859s·(thread);·0s·(gc)241 ·--·used·1.08211s·(cpu);·0.972457s·(thread);·0s·(gc)
242 i5·:·--·X-resultant·of·V242 i5·:·--·X-resultant·of·V
243 ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV;243 ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV;
244 ·--·used·0.166367s·(cpu);·0.135265s·(thread);·0s·(gc)244 ·--·used·0.203276s·(cpu);·0.166603s·(thread);·0s·(gc)
245 i6·:·--·three·generic·ternary·quadrics245 i6·:·--·three·generic·ternary·quadrics
246 ·····F·=·genericPolynomials({2,2,2},ZZ/3331)246 ·····F·=·genericPolynomials({2,2,2},ZZ/3331)
  
247 ·········2···············2························2·····2···············2247 ·········2···············2························2·····2···············2
248 o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+248 o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+
249 ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1249 ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1
250 ·····------------------------------------------------------------------------250 ·····------------------------------------------------------------------------
251 ··························2·····2···············2························2251 ··························2·····2···············2························2
252 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}252 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}
253 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2253 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2
  
254 o6·:·List254 o6·:·List
255 i7·:·--·resultant·of·the·three·forms255 i7·:·--·resultant·of·the·three·forms
256 ·····time·resF·=·resultant·F;256 ·····time·resF·=·resultant·F;
257 ·--·used·0.166113s·(cpu);·0.136166s·(thread);·0s·(gc)257 ·--·used·0.215597s·(cpu);·0.153987s·(thread);·0s·(gc)
258 i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring258 i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring
259 Xres))259 Xres))
260 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*260 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
261 ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety261 ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety
262 ····*·_\x8h_\x8u_\x8r_\x8w_\x8i_\x8t_\x8z_\x8F_\x8o_\x8r_\x8m·--·Hurwitz·form·of·a·projective·variety262 ····*·_\x8h_\x8u_\x8r_\x8w_\x8i_\x8t_\x8z_\x8F_\x8o_\x8r_\x8m·--·Hurwitz·form·of·a·projective·variety
263 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8*263 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8*
264 ····*·chowForm(Ideal)264 ····*·chowForm(Ideal)
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./usr/share/doc/Macaulay2/Resultants/html/_discriminant_lp__Ring__Element_rp.html
    
Offset 83, 15 lines modifiedOffset 83, 15 lines modified
  
83 o2·:·ZZ[a..c][x..y]</code></pre>83 o2·:·ZZ[a..c][x..y]</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·time·discriminant·F88 ··············<pre><code·class="language-macaulay2">i3·:·time·discriminant·F
89 ·--·used·0.011002s·(cpu);·0.00712899s·(thread);·0s·(gc)89 ·--·used·0.0120057s·(cpu);·0.0114892s·(thread);·0s·(gc)
  
90 ········290 ········2
91 o3·=·-·b··+·4a*c91 o3·=·-·b··+·4a*c
  
92 o3·:·ZZ[a..c]</code></pre>92 o3·:·ZZ[a..c]</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
Offset 104, 15 lines modifiedOffset 104, 15 lines modified
  
104 o5·:·ZZ[a..d][x..y]</code></pre>104 o5·:·ZZ[a..d][x..y]</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i6·:·time·discriminant·F109 ··············<pre><code·class="language-macaulay2">i6·:·time·discriminant·F
110 ·--·used·0.00786001s·(cpu);·0.00829917s·(thread);·0s·(gc)110 ·--·used·0.0113987s·(cpu);·0.0114849s·(thread);·0s·(gc)
  
111 ········2·2·······3·····3···················2·2111 ········2·2·······3·····3···················2·2
112 o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d112 o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d
  
113 o6·:·ZZ[a..d]</code></pre>113 o6·:·ZZ[a..d]</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
Offset 165, 15 lines modifiedOffset 165, 15 lines modified
  
165 o12·:·R'</code></pre>165 o12·:·R'</code></pre>
166 ············</td>166 ············</td>
167 ··········</tr>167 ··········</tr>
168 ··········<tr>168 ··········<tr>
169 ············<td>169 ············<td>
170 ··············<pre><code·class="language-macaulay2">i13·:·time·D=discriminant·pencil170 ··············<pre><code·class="language-macaulay2">i13·:·time·D=discriminant·pencil
171 ·--·used·0.298472s·(cpu);·0.297019s·(thread);·0s·(gc)171 ·--·used·0.458643s·(cpu);·0.454823s·(thread);·0s·(gc)
  
172 ···········108······106·2·······102·6······100·8·······98·10·······96·12··172 ···········108······106·2·······102·6······100·8·······98·10·······96·12··
173 o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+173 o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+
174 ···········0········0···1·······0···1······0···1·······0··1········0··1···174 ···········0········0···1·······0···1······0···1·······0··1········0··1···
175 ······-----------------------------------------------------------------------175 ······-----------------------------------------------------------------------
176 ··········94·14·······92·16······90·18······88·20······86·22·······84·24··176 ··········94·14·······92·16······90·18······88·20······86·22·······84·24··
177 ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+177 ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+
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Offset 23, 28 lines modifiedOffset 23, 28 lines modified
23 i1·:·ZZ[a,b,c][x,y];·F·=·a*x^2+b*x*y+c*y^223 i1·:·ZZ[a,b,c][x,y];·F·=·a*x^2+b*x*y+c*y^2
  
24 ········2··············224 ········2··············2
25 o2·=·a*x··+·b*x*y·+·c*y25 o2·=·a*x··+·b*x*y·+·c*y
  
26 o2·:·ZZ[a..c][x..y]26 o2·:·ZZ[a..c][x..y]
27 i3·:·time·discriminant·F27 i3·:·time·discriminant·F
28 ·--·used·0.011002s·(cpu);·0.00712899s·(thread);·0s·(gc)28 ·--·used·0.0120057s·(cpu);·0.0114892s·(thread);·0s·(gc)
  
29 ········229 ········2
30 o3·=·-·b··+·4a*c30 o3·=·-·b··+·4a*c
  
31 o3·:·ZZ[a..c]31 o3·:·ZZ[a..c]
32 i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^332 i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^3
  
33 ········3······2·········2······333 ········3······2·········2······3
34 o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y34 o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y
  
35 o5·:·ZZ[a..d][x..y]35 o5·:·ZZ[a..d][x..y]
36 i6·:·time·discriminant·F36 i6·:·time·discriminant·F
37 ·--·used·0.00786001s·(cpu);·0.00829917s·(thread);·0s·(gc)37 ·--·used·0.0113987s·(cpu);·0.0114849s·(thread);·0s·(gc)
  
38 ········2·2·······3·····3···················2·238 ········2·2·······3·····3···················2·2
39 o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d39 o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d
  
40 o6·:·ZZ[a..d]40 o6·:·ZZ[a..d]
41 The·next·example·illustrates·how·computing·the·intersection·of·a·pencil41 The·next·example·illustrates·how·computing·the·intersection·of·a·pencil
42 generated·by·two·degree·$d$·forms·$F(x_0,\ldots,x_n),·G(x_0,\ldots,x_n)$·with42 generated·by·two·degree·$d$·forms·$F(x_0,\ldots,x_n),·G(x_0,\ldots,x_n)$·with
Offset 74, 15 lines modifiedOffset 74, 15 lines modified
  
74 ················4········3······4·············4········3······474 ················4········3······4·············4········3······4
75 o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x75 o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x
76 ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·376 ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3
  
77 o12·:·R'77 o12·:·R'
78 i13·:·time·D=discriminant·pencil78 i13·:·time·D=discriminant·pencil
79 ·--·used·0.298472s·(cpu);·0.297019s·(thread);·0s·(gc)79 ·--·used·0.458643s·(cpu);·0.454823s·(thread);·0s·(gc)
  
80 ···········108······106·2·······102·6······100·8·······98·10·······96·1280 ···········108······106·2·······102·6······100·8·······98·10·······96·12
81 o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+81 o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+
82 ···········0········0···1·······0···1······0···1·······0··1········0··182 ···········0········0···1·······0···1······0···1·······0··1········0··1
83 ······-----------------------------------------------------------------------83 ······-----------------------------------------------------------------------
84 ··········94·14·······92·16······90·18······88·20······86·22·······84·2484 ··········94·14·······92·16······90·18······88·20······86·22·······84·24
85 ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+85 ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+
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Offset 90, 28 lines modifiedOffset 90, 28 lines modified
90 o1·:·Ideal·of·QQ[x·..x·]90 o1·:·Ideal·of·QQ[x·..x·]
91 ··················0···5</code></pre>91 ··················0···5</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i2·:·time·V'·=·dualVariety·V96 ··············<pre><code·class="language-macaulay2">i2·:·time·V'·=·dualVariety·V
97 ·--·used·0.0814975s·(cpu);·0.0811424s·(thread);·0s·(gc)97 ·--·used·0.10812s·(cpu);·0.10755s·(thread);·0s·(gc)
  
98 ············2·················2····298 ············2·················2····2
99 o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·)99 o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·)
100 ············2·3····1·2·4····0·4····1·5·····0·3·5100 ············2·3····1·2·4····0·4····1·5·····0·3·5
  
101 o2·:·Ideal·of·QQ[x·..x·]101 o2·:·Ideal·of·QQ[x·..x·]
102 ··················0···5</code></pre>102 ··················0···5</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i3·:·time·V·==·dualVariety·V'107 ··············<pre><code·class="language-macaulay2">i3·:·time·V·==·dualVariety·V'
108 ·--·used·0.15223s·(cpu);·0.122225s·(thread);·0s·(gc)108 ·--·used·0.171863s·(cpu);·0.139171s·(thread);·0s·(gc)
  
109 o3·=·true</code></pre>109 o3·=·true</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ········</table>112 ········</table>
113 ········<p>In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic·form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the·plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$</p>113 ········<p>In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic·form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the·plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$</p>
114 ········<table·class="examples">114 ········<table·class="examples">
Offset 131, 25 lines modifiedOffset 131, 25 lines modified
131 o4·:·----[a·..a·][x·..x·]131 o4·:·----[a·..a·][x·..x·]
132 ·····3331··0···9···0···2</code></pre>132 ·····3331··0···9···0···2</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i5·:·time·discF·=·ideal·discriminant·F;137 ··············<pre><code·class="language-macaulay2">i5·:·time·discF·=·ideal·discriminant·F;
138 ·--·used·0.0472808s·(cpu);·0.0499993s·(thread);·0s·(gc)138 ·--·used·0.0790692s·(cpu);·0.0784505s·(thread);·0s·(gc)
  
139 ···············ZZ139 ···············ZZ
140 o5·:·Ideal·of·----[a·..a·]140 o5·:·Ideal·of·----[a·..a·]
141 ··············3331··0···9</code></pre>141 ··············3331··0···9</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ··········<tr>144 ··········<tr>
145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true);146 ··············<pre><code·class="language-macaulay2">i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true);
147 ·--·used·0.543213s·(cpu);·0.509202s·(thread);·0s·(gc)147 ·--·used·0.745516s·(cpu);·0.680422s·(thread);·0s·(gc)
  
148 ···············ZZ148 ···············ZZ
149 o6·:·Ideal·of·----[x·..x·]149 o6·:·Ideal·of·----[x·..x·]
150 ··············3331··0···9</code></pre>150 ··············3331··0···9</code></pre>
151 ············</td>151 ············</td>
152 ··········</tr>152 ··········</tr>
153 ··········<tr>153 ··········<tr>
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Offset 31, 24 lines modifiedOffset 31, 24 lines modified
31 ·····------------------------------------------------------------------------31 ·····------------------------------------------------------------------------
32 ·····x·x·)32 ·····x·x·)
33 ······0·333 ······0·3
  
34 o1·:·Ideal·of·QQ[x·..x·]34 o1·:·Ideal·of·QQ[x·..x·]
35 ··················0···535 ··················0···5
36 i2·:·time·V'·=·dualVariety·V36 i2·:·time·V'·=·dualVariety·V
37 ·--·used·0.0814975s·(cpu);·0.0811424s·(thread);·0s·(gc)37 ·--·used·0.10812s·(cpu);·0.10755s·(thread);·0s·(gc)
  
38 ············2·················2····238 ············2·················2····2
39 o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·)39 o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·)
40 ············2·3····1·2·4····0·4····1·5·····0·3·540 ············2·3····1·2·4····0·4····1·5·····0·3·5
  
41 o2·:·Ideal·of·QQ[x·..x·]41 o2·:·Ideal·of·QQ[x·..x·]
42 ··················0···542 ··················0···5
43 i3·:·time·V·==·dualVariety·V'43 i3·:·time·V·==·dualVariety·V'
44 ·--·used·0.15223s·(cpu);·0.122225s·(thread);·0s·(gc)44 ·--·used·0.171863s·(cpu);·0.139171s·(thread);·0s·(gc)
  
45 o3·=·true45 o3·=·true
46 In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic46 In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic
47 form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the47 form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the
48 plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$48 plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$
49 i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331)49 i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331)
  
Offset 60, 21 lines modifiedOffset 60, 21 lines modified
60 ·····a·x·x··+·a·x60 ·····a·x·x··+·a·x
61 ······8·1·2····9·261 ······8·1·2····9·2
  
62 ······ZZ62 ······ZZ
63 o4·:·----[a·..a·][x·..x·]63 o4·:·----[a·..a·][x·..x·]
64 ·····3331··0···9···0···264 ·····3331··0···9···0···2
65 i5·:·time·discF·=·ideal·discriminant·F;65 i5·:·time·discF·=·ideal·discriminant·F;
66 ·--·used·0.0472808s·(cpu);·0.0499993s·(thread);·0s·(gc)66 ·--·used·0.0790692s·(cpu);·0.0784505s·(thread);·0s·(gc)
  
67 ···············ZZ67 ···············ZZ
68 o5·:·Ideal·of·----[a·..a·]68 o5·:·Ideal·of·----[a·..a·]
69 ··············3331··0···969 ··············3331··0···9
70 i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true);70 i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true);
71 ·--·used·0.543213s·(cpu);·0.509202s·(thread);·0s·(gc)71 ·--·used·0.745516s·(cpu);·0.680422s·(thread);·0s·(gc)
  
72 ···············ZZ72 ···············ZZ
73 o6·:·Ideal·of·----[x·..x·]73 o6·:·Ideal·of·----[x·..x·]
74 ··············3331··0···974 ··············3331··0···9
75 i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z)75 i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z)
  
76 o7·=·true76 o7·=·true
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85 o1·:·Ideal·of·QQ[x·..x·]85 o1·:·Ideal·of·QQ[x·..x·]
86 ··················0···3</code></pre>86 ··················0···3</code></pre>
87 ············</td>87 ············</td>
88 ··········</tr>88 ··········</tr>
89 ··········<tr>89 ··········<tr>
90 ············<td>90 ············<td>
91 ··············<pre><code·class="language-macaulay2">i2·:·time·fromPluckerToStiefel·dualize·chowForm·C91 ··············<pre><code·class="language-macaulay2">i2·:·time·fromPluckerToStiefel·dualize·chowForm·C
92 ·--·used·0.0343204s·(cpu);·0.0352705s·(thread);·0s·(gc)92 ·--·used·0.0384802s·(cpu);·0.0409787s·(thread);·0s·(gc)
  
93 ········3···3··········2···2··············2·······2··········2···3····93 ········3···3··········2···2··············2·······2··········2···3····
94 o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····-94 o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····-
95 ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1··95 ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1··
96 ·····------------------------------------------------------------------------96 ·····------------------------------------------------------------------------
97 ······2·······2···············2···2···································97 ······2·······2···············2···2···································
98 ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····-98 ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····-
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138 o2·:·QQ[x···..x···]138 o2·:·QQ[x···..x···]
139 ·········0,0···1,3</code></pre>139 ·········0,0···1,3</code></pre>
140 ············</td>140 ············</td>
141 ··········</tr>141 ··········</tr>
142 ··········<tr>142 ··········<tr>
143 ············<td>143 ············<td>
144 ··············<pre><code·class="language-macaulay2">i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1})144 ··············<pre><code·class="language-macaulay2">i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1})
145 ·--·used·0.0837715s·(cpu);·0.0494865s·(thread);·0s·(gc)145 ·--·used·0.0911433s·(cpu);·0.0533314s·(thread);·0s·(gc)
  
146 ············3··········2·························2························146 ············3··········2·························2························
147 o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····-147 o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····-
148 ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3··148 ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3··
149 ·····------------------------------------------------------------------------149 ·····------------------------------------------------------------------------
150 ···········2······3······2150 ···········2······3······2
151 ·····2x···x····+·x····+·x151 ·····2x···x····+·x····+·x
Offset 179, 15 lines modifiedOffset 179, 15 lines modified
179 ············<td>179 ············<td>
180 ··············<pre><code·class="language-macaulay2">i5·:·w·=·chowForm·C;</code></pre>180 ··············<pre><code·class="language-macaulay2">i5·:·w·=·chowForm·C;</code></pre>
181 ············</td>181 ············</td>
182 ··········</tr>182 ··········</tr>
183 ··········<tr>183 ··········<tr>
184 ············<td>184 ············<td>
185 ··············<pre><code·class="language-macaulay2">i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s))185 ··············<pre><code·class="language-macaulay2">i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s))
186 ·--·used·0.0159991s·(cpu);·0.016392s·(thread);·0s·(gc)186 ·--·used·0.0210956s·(cpu);·0.0202506s·(thread);·0s·(gc)
  
187 ···················3··········2··········3·······················2········187 ···················3··········2··········3·······················2········
188 o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+188 o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+
189 ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3··189 ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3··
190 ·····------------------------------------------------------------------------190 ·····------------------------------------------------------------------------
191 ·························2······2············2···3···············2········191 ·························2······2············2···3···············2········
192 ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+192 ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+
Offset 227, 15 lines modifiedOffset 227, 15 lines modified
  
227 o6·:·List</code></pre>227 o6·:·List</code></pre>
228 ············</td>228 ············</td>
229 ··········</tr>229 ··········</tr>
230 ··········<tr>230 ··········<tr>
231 ············<td>231 ············<td>
232 ··············<pre><code·class="language-macaulay2">i7·:·time·apply(U,u->dim·singularLocus·u)232 ··············<pre><code·class="language-macaulay2">i7·:·time·apply(U,u->dim·singularLocus·u)
233 ·--·used·0.0120012s·(cpu);·0.0143212s·(thread);·0s·(gc)233 ·--·used·0.0169758s·(cpu);·0.0181462s·(thread);·0s·(gc)
  
234 o7·=·{2,·2,·2,·2,·2,·2}234 o7·=·{2,·2,·2,·2,·2,·2}
  
235 o7·:·List</code></pre>235 o7·:·List</code></pre>
236 ············</td>236 ············</td>
237 ··········</tr>237 ··········</tr>
238 ········</table>238 ········</table>
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26 ·············2·······················226 ·············2·······················2
27 o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·)27 o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·)
28 ·············2····1·3···1·2····0·3···1····0·228 ·············2····1·3···1·2····0·3···1····0·2
  
29 o1·:·Ideal·of·QQ[x·..x·]29 o1·:·Ideal·of·QQ[x·..x·]
30 ··················0···330 ··················0···3
31 i2·:·time·fromPluckerToStiefel·dualize·chowForm·C31 i2·:·time·fromPluckerToStiefel·dualize·chowForm·C
32 ·--·used·0.0343204s·(cpu);·0.0352705s·(thread);·0s·(gc)32 ·--·used·0.0384802s·(cpu);·0.0409787s·(thread);·0s·(gc)
  
33 ········3···3··········2···2··············2·······2··········2···333 ········3···3··········2···2··············2·······2··········2···3
34 o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····-34 o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····-
35 ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,135 ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1
36 ·····------------------------------------------------------------------------36 ·····------------------------------------------------------------------------
37 ······2·······2···············2···237 ······2·······2···············2···2
38 ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····-38 ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····-
Offset 75, 15 lines modifiedOffset 75, 15 lines modified
75 ··········2·······2·······2···········2······2···········2······3···375 ··········2·······2·······2···········2······2···········2······3···3
76 ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x76 ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x
77 ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,377 ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3
  
78 o2·:·QQ[x···..x···]78 o2·:·QQ[x···..x···]
79 ·········0,0···1,379 ·········0,0···1,3
80 i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1})80 i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1})
81 ·--·used·0.0837715s·(cpu);·0.0494865s·(thread);·0s·(gc)81 ·--·used·0.0911433s·(cpu);·0.0533314s·(thread);·0s·(gc)
  
82 ············3··········2·························282 ············3··········2·························2
83 o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····-83 o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····-
84 ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,384 ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3
85 ·····------------------------------------------------------------------------85 ·····------------------------------------------------------------------------
86 ···········2······3······286 ···········2······3······2
87 ·····2x···x····+·x····+·x87 ·····2x···x····+·x····+·x
Offset 105, 15 lines modifiedOffset 105, 15 lines modified
105 o4·:·QQ[a···..a···]105 o4·:·QQ[a···..a···]
106 ·········0,0···1,1106 ·········0,0···1,1
107 As·another·application,·we·check·that·the·singular·locus·of·the·Chow·form·of107 As·another·application,·we·check·that·the·singular·locus·of·the·Chow·form·of
108 the·twisted·cubic·has·dimension·2·(on·each·standard·chart).108 the·twisted·cubic·has·dimension·2·(on·each·standard·chart).
109 i5·:·w·=·chowForm·C;109 i5·:·w·=·chowForm·C;
110 i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel110 i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel
111 (w,AffineChartGrass=>s))111 (w,AffineChartGrass=>s))
112 ·--·used·0.0159991s·(cpu);·0.016392s·(thread);·0s·(gc)112 ·--·used·0.0210956s·(cpu);·0.0202506s·(thread);·0s·(gc)
  
113 ···················3··········2··········3·······················2113 ···················3··········2··········3·······················2
114 o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+114 o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+
115 ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3115 ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3
116 ·····------------------------------------------------------------------------116 ·····------------------------------------------------------------------------
117 ·························2······2············2···3···············2117 ·························2······2············2···3···············2
118 ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+118 ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+
Offset 149, 15 lines modifiedOffset 149, 15 lines modified
149 ·····------------------------------------------------------------------------149 ·····------------------------------------------------------------------------
150 ···········2······3······2150 ···········2······3······2
151 ·····2x···x····-·x····+·x···)}151 ·····2x···x····-·x····+·x···)}
152 ·······0,0·1,1····1,1····1,0152 ·······0,0·1,1····1,1····1,0
  
153 o6·:·List153 o6·:·List
154 i7·:·time·apply(U,u->dim·singularLocus·u)154 i7·:·time·apply(U,u->dim·singularLocus·u)
155 ·--·used·0.0120012s·(cpu);·0.0143212s·(thread);·0s·(gc)155 ·--·used·0.0169758s·(cpu);·0.0181462s·(thread);·0s·(gc)
  
156 o7·=·{2,·2,·2,·2,·2,·2}156 o7·=·{2,·2,·2,·2,·2,·2}
  
157 o7·:·List157 o7·:·List
158 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fr\x8ro\x8om\x8mP\x8Pl\x8lu\x8uc\x8ck\x8ke\x8er\x8rT\x8To\x8oS\x8St\x8ti\x8ie\x8ef\x8fe\x8el\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*158 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fr\x8ro\x8om\x8mP\x8Pl\x8lu\x8uc\x8ck\x8ke\x8er\x8rT\x8To\x8oS\x8St\x8ti\x8ie\x8ef\x8fe\x8el\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8*
159 ····*·fromPluckerToStiefel(Ideal)159 ····*·fromPluckerToStiefel(Ideal)
160 ····*·fromPluckerToStiefel(Matrix)160 ····*·fromPluckerToStiefel(Matrix)
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Offset 92, 15 lines modifiedOffset 92, 15 lines modified
92 o1·:·Ideal·of·QQ[p·..p·]92 o1·:·Ideal·of·QQ[p·..p·]
93 ··················0···4</code></pre>93 ··················0···4</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i2·:·time·hurwitzForm·Q98 ··············<pre><code·class="language-macaulay2">i2·:·time·hurwitzForm·Q
99 ·--·used·0.031789s·(cpu);·0.0329835s·(thread);·0s·(gc)99 ·--·used·0.0424349s·(cpu);·0.0406452s·(thread);·0s·(gc)
  
100 ··············2·································2······················100 ··············2·································2······················
101 o2·=·11966535p····+·14645610p···p····+·11354175p····+·1666980p···p····+101 o2·=·11966535p····+·14645610p···p····+·11354175p····+·1666980p···p····+
102 ··············0,1············0,1·0,2············0,2···········0,1·1,2··102 ··············0,1············0,1·0,2············0,2···········0,1·1,2··
103 ·····------------------------------------------------------------------------103 ·····------------------------------------------------------------------------
104 ·······························2··········································104 ·······························2··········································
105 ·····4456620p···p····+·1127196p····+·54176850p···p····+·20326950p···p····+105 ·····4456620p···p····+·1127196p····+·54176850p···p····+·20326950p···p····+
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34 ·······5·2···7·······················2········3·234 ·······5·2···7·······················2········3·2
35 ·····+·-p··+·-p·p··+·7p·p··+·6p·p··+·-p·p··+·--p·)35 ·····+·-p··+·-p·p··+·7p·p··+·6p·p··+·-p·p··+·--p·)
36 ·······4·3···9·0·4·····1·4·····2·4···9·3·4···10·436 ·······4·3···9·0·4·····1·4·····2·4···9·3·4···10·4
  
37 o1·:·Ideal·of·QQ[p·..p·]37 o1·:·Ideal·of·QQ[p·..p·]
38 ··················0···438 ··················0···4
39 i2·:·time·hurwitzForm·Q39 i2·:·time·hurwitzForm·Q
40 ·--·used·0.031789s·(cpu);·0.0329835s·(thread);·0s·(gc)40 ·--·used·0.0424349s·(cpu);·0.0406452s·(thread);·0s·(gc)
  
41 ··············2·································241 ··············2·································2
42 o2·=·11966535p····+·14645610p···p····+·11354175p····+·1666980p···p····+42 o2·=·11966535p····+·14645610p···p····+·11354175p····+·1666980p···p····+
43 ··············0,1············0,1·0,2············0,2···········0,1·1,243 ··············0,1············0,1·0,2············0,2···········0,1·1,2
44 ·····------------------------------------------------------------------------44 ·····------------------------------------------------------------------------
45 ·······························245 ·······························2
46 ·····4456620p···p····+·1127196p····+·54176850p···p····+·20326950p···p····+46 ·····4456620p···p····+·1127196p····+·54176850p···p····+·20326950p···p····+
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104 ·········p···p····-·p···p····+·p···p104 ·········p···p····-·p···p····+·p···p
105 ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre>105 ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ··········<tr>108 ··········<tr>
109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i2·:·time·isCoisotropic·w110 ··············<pre><code·class="language-macaulay2">i2·:·time·isCoisotropic·w
111 ·--·used·0.00400137s·(cpu);·0.00724592s·(thread);·0s·(gc)111 ·--·used·0.0102693s·(cpu);·0.00979179s·(thread);·0s·(gc)
  
112 o2·=·true</code></pre>112 o2·=·true</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i3·:·--·random·quadric·in·G(1,3)117 ··············<pre><code·class="language-macaulay2">i3·:·--·random·quadric·in·G(1,3)
Offset 140, 15 lines modifiedOffset 140, 15 lines modified
140 ·········p···p····-·p···p····+·p···p140 ·········p···p····-·p···p····+·p···p
141 ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre>141 ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ··········<tr>144 ··········<tr>
145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i4·:·time·isCoisotropic·w'146 ··············<pre><code·class="language-macaulay2">i4·:·time·isCoisotropic·w'
147 ·--·used·0.00399805s·(cpu);·0.00571698s·(thread);·0s·(gc)147 ·--·used·0.00487026s·(cpu);·0.00814648s·(thread);·0s·(gc)
  
148 o4·=·false</code></pre>148 o4·=·false</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ········</table>151 ········</table>
152 ······</div>152 ······</div>
153 ······<div>153 ······<div>
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44 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]44 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]
45 ·········0,1···0,2···1,2···0,3···1,3···2,345 ·········0,1···0,2···1,2···0,3···1,3···2,3
46 o1·:·--------------------------------------46 o1·:·--------------------------------------
47 ·········p···p····-·p···p····+·p···p47 ·········p···p····-·p···p····+·p···p
48 ··········1,2·0,3····0,2·1,3····0,1·2,348 ··········1,2·0,3····0,2·1,3····0,1·2,3
49 i2·:·time·isCoisotropic·w49 i2·:·time·isCoisotropic·w
50 ·--·used·0.00400137s·(cpu);·0.00724592s·(thread);·0s·(gc)50 ·--·used·0.0102693s·(cpu);·0.00979179s·(thread);·0s·(gc)
  
51 o2·=·true51 o2·=·true
52 i3·:·--·random·quadric·in·G(1,3)52 i3·:·--·random·quadric·in·G(1,3)
53 ·····w'·=·random(2,Grass(1,3))53 ·····w'·=·random(2,Grass(1,3))
  
54 ·······2·····5···········10·2·····2··························2······354 ·······2·····5···········10·2·····2··························2······3
55 o3·=·6p····+·-p···p····+·--p····+·-p···p····+·10p···p····+·5p····+·--p···p55 o3·=·6p····+·-p···p····+·--p····+·-p···p····+·10p···p····+·5p····+·--p···p
Offset 72, 15 lines modifiedOffset 72, 15 lines modified
  
72 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]72 ·····QQ[p···..p···,·p···,·p···,·p···,·p···]
73 ·········0,1···0,2···1,2···0,3···1,3···2,373 ·········0,1···0,2···1,2···0,3···1,3···2,3
74 o3·:·--------------------------------------74 o3·:·--------------------------------------
75 ·········p···p····-·p···p····+·p···p75 ·········p···p····-·p···p····+·p···p
76 ··········1,2·0,3····0,2·1,3····0,1·2,376 ··········1,2·0,3····0,2·1,3····0,1·2,3
77 i4·:·time·isCoisotropic·w'77 i4·:·time·isCoisotropic·w'
78 ·--·used·0.00399805s·(cpu);·0.00571698s·(thread);·0s·(gc)78 ·--·used·0.00487026s·(cpu);·0.00814648s·(thread);·0s·(gc)
  
79 o4·=·false79 o4·=·false
80 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8*80 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8*
81 ····*·isCoisotropic(RingElement)81 ····*·isCoisotropic(RingElement)
82 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*82 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
83 The·object·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.83 The·object·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
84 ===============================================================================84 ===============================================================================
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117 o3·:·Ideal·of·-----[x·..x·]117 o3·:·Ideal·of·-----[x·..x·]
118 ··············33331··0···5</code></pre>118 ··············33331··0···5</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I))123 ··············<pre><code·class="language-macaulay2">i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I))
124 ·--·used·0.0140353s·(cpu);·0.0174852s·(thread);·0s·(gc)124 ·--·used·0.018228s·(cpu);·0.0186896s·(thread);·0s·(gc)
  
125 o4·=·true</code></pre>125 o4·=·true</code></pre>
126 ············</td>126 ············</td>
127 ··········</tr>127 ··········</tr>
128 ········</table>128 ········</table>
129 ······</div>129 ······</div>
130 ······<div>130 ······<div>
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54 ·····2380x··+·9482x·)54 ·····2380x··+·9482x·)
55 ··········4········555 ··········4········5
  
56 ················ZZ56 ················ZZ
57 o3·:·Ideal·of·-----[x·..x·]57 o3·:·Ideal·of·-----[x·..x·]
58 ··············33331··0···558 ··············33331··0···5
59 i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I))59 i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I))
60 ·--·used·0.0140353s·(cpu);·0.0174852s·(thread);·0s·(gc)60 ·--·used·0.018228s·(cpu);·0.0186896s·(thread);·0s·(gc)
  
61 o4·=·true61 o4·=·true
62 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*62 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
63 ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety63 ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety
64 ····*·_\x8p_\x8l_\x8u_\x8c_\x8k_\x8e_\x8r·--·get·the·Plücker·coordinates·of·a·linear·subspace64 ····*·_\x8p_\x8l_\x8u_\x8c_\x8k_\x8e_\x8r·--·get·the·Plücker·coordinates·of·a·linear·subspace
65 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sI\x8In\x8nC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8*65 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sI\x8In\x8nC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8*
66 ····*·isInCoisotropic(Ideal,Ideal)66 ····*·isInCoisotropic(Ideal,Ideal)
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87 o1·:·List</code></pre>87 o1·:·List</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i2·:·time·(D,D')·=·macaulayFormula·F92 ··············<pre><code·class="language-macaulay2">i2·:·time·(D,D')·=·macaulayFormula·F
93 ·--·used·0.00530655s·(cpu);·0.00297374s·(thread);·0s·(gc)93 ·--·used·0.00400653s·(cpu);·0.00343988s·(thread);·0s·(gc)
  
94 o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0··94 o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0··
95 ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0··95 ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0··
96 ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0··96 ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0··
97 ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0··97 ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0··
98 ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0··98 ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0··
99 ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0··99 ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0··
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158 o3·:·List</code></pre>158 o3·:·List</code></pre>
159 ············</td>159 ············</td>
160 ··········</tr>160 ··········</tr>
161 ··········<tr>161 ··········<tr>
162 ············<td>162 ············<td>
163 ··············<pre><code·class="language-macaulay2">i4·:·time·(D,D')·=·macaulayFormula·F163 ··············<pre><code·class="language-macaulay2">i4·:·time·(D,D')·=·macaulayFormula·F
164 ·--·used·0.000114933s·(cpu);·0.00199944s·(thread);·0s·(gc)164 ·--·used·0.00275349s·(cpu);·0.0024385s·(thread);·0s·(gc)
  
165 o4·=·(|·9/2·9/4·3/4·7/4··7/9··7/10·0····0····0····0····0···0···0····0····0···165 o4·=·(|·9/2·9/4·3/4·7/4··7/9··7/10·0····0····0····0····0···0···0····0····0···
166 ······|·0···9/2·0···9/4··3/4··0····7/4··7/9··7/10·0····0···0···0····0····0···166 ······|·0···9/2·0···9/4··3/4··0····7/4··7/9··7/10·0····0···0···0····0····0···
167 ······|·0···0···9/2·0····9/4··3/4··0····7/4··7/9··7/10·0···0···0····0····0···167 ······|·0···0···9/2·0····9/4··3/4··0····7/4··7/9··7/10·0···0···0····0····0···
168 ······|·0···0···0···9/2··0····0····9/4··3/4··0····0····7/4·7/9·7/10·0····0···168 ······|·0···0···0···9/2··0····0····9/4··3/4··0····0····7/4·7/9·7/10·0····0···
169 ······|·0···0···0···0····9/2··0····0····9/4··3/4··0····0···7/4·7/9··7/10·0···169 ······|·0···0···0···0····9/2··0····0····9/4··3/4··0····0···7/4·7/9··7/10·0···
170 ······|·0···0···0···0····0····9/2··0····0····9/4··3/4··0···0···7/4··7/9··7/10170 ······|·0···0···0···0····0····9/2··0····0····9/4··3/4··0···0···7/4··7/9··7/10
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28 ·····------------------------------------------------------------------------28 ·····------------------------------------------------------------------------
29 ···················2··········2········2······329 ···················2··········2········2······3
30 ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·}30 ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·}
31 ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·231 ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2
  
32 o1·:·List32 o1·:·List
33 i2·:·time·(D,D')·=·macaulayFormula·F33 i2·:·time·(D,D')·=·macaulayFormula·F
34 ·--·used·0.00530655s·(cpu);·0.00297374s·(thread);·0s·(gc)34 ·--·used·0.00400653s·(cpu);·0.00343988s·(thread);·0s·(gc)
  
35 o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···035 o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0
36 ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···036 ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0
37 ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···037 ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0
38 ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···038 ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0
39 ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···039 ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0
40 ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···040 ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0
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91 ·····------------------------------------------------------------------------91 ·····------------------------------------------------------------------------
92 ·····10···2···7···2···5·392 ·····10···2···7···2···5·3
93 ·····--p·p··+·-p·p··+·-p·}93 ·····--p·p··+·-p·p··+·-p·}
94 ······9·0·2···8·1·2···6·294 ······9·0·2···8·1·2···6·2
  
95 o3·:·List95 o3·:·List
96 i4·:·time·(D,D')·=·macaulayFormula·F96 i4·:·time·(D,D')·=·macaulayFormula·F
97 ·--·used·0.000114933s·(cpu);·0.00199944s·(thread);·0s·(gc)97 ·--·used·0.00275349s·(cpu);·0.0024385s·(thread);·0s·(gc)
  
98 o4·=·(|·9/2·9/4·3/4·7/4··7/9··7/10·0····0····0····0····0···0···0····0····098 o4·=·(|·9/2·9/4·3/4·7/4··7/9··7/10·0····0····0····0····0···0···0····0····0
99 ······|·0···9/2·0···9/4··3/4··0····7/4··7/9··7/10·0····0···0···0····0····099 ······|·0···9/2·0···9/4··3/4··0····7/4··7/9··7/10·0····0···0···0····0····0
100 ······|·0···0···9/2·0····9/4··3/4··0····7/4··7/9··7/10·0···0···0····0····0100 ······|·0···0···9/2·0····9/4··3/4··0····7/4··7/9··7/10·0···0···0····0····0
101 ······|·0···0···0···9/2··0····0····9/4··3/4··0····0····7/4·7/9·7/10·0····0101 ······|·0···0···0···9/2··0····0····9/4··3/4··0····0····7/4·7/9·7/10·0····0
102 ······|·0···0···0···0····9/2··0····0····9/4··3/4··0····0···7/4·7/9··7/10·0102 ······|·0···0···0···0····9/2··0····0····9/4··3/4··0····0···7/4·7/9··7/10·0
103 ······|·0···0···0···0····0····9/2··0····0····9/4··3/4··0···0···7/4··7/9··7/10103 ······|·0···0···0···0····0····9/2··0····0····9/4··3/4··0···0···7/4··7/9··7/10
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92 o3·:·Ideal·of·P4</code></pre>92 o3·:·Ideal·of·P4</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i4·:·time·p·=·plucker·L97 ··············<pre><code·class="language-macaulay2">i4·:·time·p·=·plucker·L
98 ·--·used·0.00417327s·(cpu);·0.00387254s·(thread);·0s·(gc)98 ·--·used·0.00445093s·(cpu);·0.00463992s·(thread);·0s·(gc)
  
99 o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+99 o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+
100 ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3··100 ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3··
101 ·····------------------------------------------------------------------------101 ·····------------------------------------------------------------------------
102 ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+102 ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+
103 ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2··103 ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2··
104 ·····------------------------------------------------------------------------104 ·····------------------------------------------------------------------------
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109 o4·:·Ideal·of·G'1'4</code></pre>109 o4·:·Ideal·of·G'1'4</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i5·:·time·L'·=·plucker·p114 ··············<pre><code·class="language-macaulay2">i5·:·time·L'·=·plucker·p
115 ·--·used·0.0249875s·(cpu);·0.0265876s·(thread);·0s·(gc)115 ·--·used·0.0299986s·(cpu);·0.0297164s·(thread);·0s·(gc)
  
116 o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··-116 o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··-
117 ·············2········3·········4···1········3·········4···0·········3··117 ·············2········3·········4···1········3·········4···0·········3··
118 ·····------------------------------------------------------------------------118 ·····------------------------------------------------------------------------
119 ·····664x·)119 ·····664x·)
120 ·········4120 ·········4
  
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138 o7·:·Ideal·of·G'1'4</code></pre>138 o7·:·Ideal·of·G'1'4</code></pre>
139 ············</td>139 ············</td>
140 ··········</tr>140 ··········</tr>
141 ··········<tr>141 ··········<tr>
142 ············<td>142 ············<td>
143 ··············<pre><code·class="language-macaulay2">i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y143 ··············<pre><code·class="language-macaulay2">i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y
144 ·--·used·0.0808757s·(cpu);·0.0523908s·(thread);·0s·(gc)144 ·--·used·0.0766138s·(cpu);·0.0422324s·(thread);·0s·(gc)
  
145 o8·:·Ideal·of·P4</code></pre>145 o8·:·Ideal·of·P4</code></pre>
146 ············</td>146 ············</td>
147 ··········</tr>147 ··········</tr>
148 ··········<tr>148 ··········<tr>
149 ············<td>149 ············<td>
150 ··············<pre><code·class="language-macaulay2">i9·:·(codim·W,degree·W)150 ··············<pre><code·class="language-macaulay2">i9·:·(codim·W,degree·W)
Offset 158, 15 lines modifiedOffset 158, 15 lines modified
158 ··········</tr>158 ··········</tr>
159 ········</table>159 ········</table>
160 ········<p>In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb{P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$.</p>160 ········<p>In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb{P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$.</p>
161 ········<table·class="examples">161 ········<table·class="examples">
162 ··········<tr>162 ··········<tr>
163 ············<td>163 ············<td>
164 ··············<pre><code·class="language-macaulay2">i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W164 ··············<pre><code·class="language-macaulay2">i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W
165 ·--·used·0.127366s·(cpu);·0.128568s·(thread);·0s·(gc)165 ·--·used·0.17979s·(cpu);·0.179979s·(thread);·0s·(gc)
  
166 o10·:·Ideal·of·G'1'4</code></pre>166 o10·:·Ideal·of·G'1'4</code></pre>
167 ············</td>167 ············</td>
168 ··········</tr>168 ··········</tr>
169 ··········<tr>169 ··········<tr>
170 ············<td>170 ············<td>
171 ··············<pre><code·class="language-macaulay2">i11·:·assert(Y'·==·Y)</code></pre>171 ··············<pre><code·class="language-macaulay2">i11·:·assert(Y'·==·Y)</code></pre>
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28 ·············2········3·········4···1········3·········4···0·········328 ·············2········3·········4···1········3·········4···0·········3
29 ·····------------------------------------------------------------------------29 ·····------------------------------------------------------------------------
30 ·····664x·)30 ·····664x·)
31 ·········431 ·········4
  
32 o3·:·Ideal·of·P432 o3·:·Ideal·of·P4
33 i4·:·time·p·=·plucker·L33 i4·:·time·p·=·plucker·L
34 ·--·used·0.00417327s·(cpu);·0.00387254s·(thread);·0s·(gc)34 ·--·used·0.00445093s·(cpu);·0.00463992s·(thread);·0s·(gc)
  
35 o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+35 o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+
36 ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,336 ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3
37 ·····------------------------------------------------------------------------37 ·····------------------------------------------------------------------------
38 ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+38 ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+
39 ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,239 ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2
40 ·····------------------------------------------------------------------------40 ·····------------------------------------------------------------------------
41 ·····11804x···,·x····+·14854x···)41 ·····11804x···,·x····+·14854x···)
42 ···········3,4···0,1·········3,442 ···········3,4···0,1·········3,4
  
43 o4·:·Ideal·of·G'1'443 o4·:·Ideal·of·G'1'4
44 i5·:·time·L'·=·plucker·p44 i5·:·time·L'·=·plucker·p
45 ·--·used·0.0249875s·(cpu);·0.0265876s·(thread);·0s·(gc)45 ·--·used·0.0299986s·(cpu);·0.0297164s·(thread);·0s·(gc)
  
46 o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··-46 o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··-
47 ·············2········3·········4···1········3·········4···0·········347 ·············2········3·········4···1········3·········4···0·········3
48 ·····------------------------------------------------------------------------48 ·····------------------------------------------------------------------------
49 ·····664x·)49 ·····664x·)
50 ·········450 ·········4
  
Offset 60, 26 lines modifiedOffset 60, 26 lines modified
60 $W\subset\mathbb{P}^n$·swept·out·by·the·linear·spaces·corresponding·to·points60 $W\subset\mathbb{P}^n$·swept·out·by·the·linear·spaces·corresponding·to·points
61 of·$Y$.·As·an·example,·we·now·compute·a·surface·scroll·$W\subset\mathbb{P}^4$61 of·$Y$.·As·an·example,·we·now·compute·a·surface·scroll·$W\subset\mathbb{P}^4$
62 over·an·elliptic·curve·$Y\subset\mathbb{G}(1,\mathbb{P}^4)$.62 over·an·elliptic·curve·$Y\subset\mathbb{G}(1,\mathbb{P}^4)$.
63 i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve63 i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve
  
64 o7·:·Ideal·of·G'1'464 o7·:·Ideal·of·G'1'4
65 i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y65 i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y
66 ·--·used·0.0808757s·(cpu);·0.0523908s·(thread);·0s·(gc)66 ·--·used·0.0766138s·(cpu);·0.0422324s·(thread);·0s·(gc)
  
67 o8·:·Ideal·of·P467 o8·:·Ideal·of·P4
68 i9·:·(codim·W,degree·W)68 i9·:·(codim·W,degree·W)
  
69 o9·=·(2,·5)69 o9·=·(2,·5)
  
70 o9·:·Sequence70 o9·:·Sequence
71 In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb71 In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb
72 {P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$.72 {P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$.
73 i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W73 i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W
74 ·--·used·0.127366s·(cpu);·0.128568s·(thread);·0s·(gc)74 ·--·used·0.17979s·(cpu);·0.179979s·(thread);·0s·(gc)
  
75 o10·:·Ideal·of·G'1'475 o10·:·Ideal·of·G'1'4
76 i11·:·assert(Y'·==·Y)76 i11·:·assert(Y'·==·Y)
77 W\x8Wa\x8ar\x8rn\x8ni\x8in\x8ng\x8g:·Notice·that,·by·default,·the·computation·is·done·on·a·randomly·chosen77 W\x8Wa\x8ar\x8rn\x8ni\x8in\x8ng\x8g:·Notice·that,·by·default,·the·computation·is·done·on·a·randomly·chosen
78 affine·chart·on·the·Grassmannian.·To·change·this·behavior,·you·can·use·the78 affine·chart·on·the·Grassmannian.·To·change·this·behavior,·you·can·use·the
79 _\x8A_\x8f_\x8f_\x8i_\x8n_\x8e_\x8C_\x8h_\x8a_\x8r_\x8t_\x8G_\x8r_\x8a_\x8s_\x8s·option.79 _\x8A_\x8f_\x8f_\x8i_\x8n_\x8e_\x8C_\x8h_\x8a_\x8r_\x8t_\x8G_\x8r_\x8a_\x8s_\x8s·option.
80 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pl\x8lu\x8uc\x8ck\x8ke\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*80 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pl\x8lu\x8uc\x8ck\x8ke\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
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108 o2·:·List</code></pre>108 o2·:·List</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i3·:·time·resultant(F,Algorithm=>&quot;Poisson2&quot;)113 ··············<pre><code·class="language-macaulay2">i3·:·time·resultant(F,Algorithm=>&quot;Poisson2&quot;)
114 ·--·used·0.214497s·(cpu);·0.157181s·(thread);·0s·(gc)114 ·--·used·0.267135s·(cpu);·0.181296s·(thread);·0s·(gc)
  
115 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···115 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
116 o3·=·-·-----------------------------a··-·-------------------------------a·b·-116 o3·=·-·-----------------------------a··-·-------------------------------a·b·-
117 ···········2222549728809984000000············12700284164628480000000·········117 ···········2222549728809984000000············12700284164628480000000·········
118 ·····------------------------------------------------------------------------118 ·····------------------------------------------------------------------------
119 ·····348237304382147063838108483692249·3·2··119 ·····348237304382147063838108483692249·3·2··
120 ·····---------------------------------a·b··-120 ·····---------------------------------a·b··-
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132 o3·:·QQ[a..b]</code></pre>132 o3·:·QQ[a..b]</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ··········<tr>135 ··········<tr>
136 ············<td>136 ············<td>
137 ··············<pre><code·class="language-macaulay2">i4·:·time·resultant(F,Algorithm=>&quot;Macaulay2&quot;)137 ··············<pre><code·class="language-macaulay2">i4·:·time·resultant(F,Algorithm=>&quot;Macaulay2&quot;)
138 ·--·used·0.0603554s·(cpu);·0.0607234s·(thread);·0s·(gc)138 ·--·used·0.0872349s·(cpu);·0.0893436s·(thread);·0s·(gc)
  
139 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···139 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
140 o4·=·-·-----------------------------a··-·-------------------------------a·b·-140 o4·=·-·-----------------------------a··-·-------------------------------a·b·-
141 ···········2222549728809984000000············12700284164628480000000·········141 ···········2222549728809984000000············12700284164628480000000·········
142 ·····------------------------------------------------------------------------142 ·····------------------------------------------------------------------------
143 ·····348237304382147063838108483692249·3·2··143 ·····348237304382147063838108483692249·3·2··
144 ·····---------------------------------a·b··-144 ·····---------------------------------a·b··-
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156 o4·:·QQ[a..b]</code></pre>156 o4·:·QQ[a..b]</code></pre>
157 ············</td>157 ············</td>
158 ··········</tr>158 ··········</tr>
159 ··········<tr>159 ··········<tr>
160 ············<td>160 ············<td>
161 ··············<pre><code·class="language-macaulay2">i5·:·time·resultant(F,Algorithm=>&quot;Poisson&quot;)161 ··············<pre><code·class="language-macaulay2">i5·:·time·resultant(F,Algorithm=>&quot;Poisson&quot;)
162 ·--·used·0.268621s·(cpu);·0.237589s·(thread);·0s·(gc)162 ·--·used·0.362645s·(cpu);·0.32476s·(thread);·0s·(gc)
  
163 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···163 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
164 o5·=·-·-----------------------------a··-·-------------------------------a·b·-164 o5·=·-·-----------------------------a··-·-------------------------------a·b·-
165 ···········2222549728809984000000············12700284164628480000000·········165 ···········2222549728809984000000············12700284164628480000000·········
166 ·····------------------------------------------------------------------------166 ·····------------------------------------------------------------------------
167 ·····348237304382147063838108483692249·3·2··167 ·····348237304382147063838108483692249·3·2··
168 ·····---------------------------------a·b··-168 ·····---------------------------------a·b··-
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180 o5·:·QQ[a..b]</code></pre>180 o5·:·QQ[a..b]</code></pre>
181 ············</td>181 ············</td>
182 ··········</tr>182 ··········</tr>
183 ··········<tr>183 ··········<tr>
184 ············<td>184 ············<td>
185 ··············<pre><code·class="language-macaulay2">i6·:·time·resultant(F,Algorithm=>&quot;Macaulay&quot;)185 ··············<pre><code·class="language-macaulay2">i6·:·time·resultant(F,Algorithm=>&quot;Macaulay&quot;)
186 ·--·used·0.451197s·(cpu);·0.423115s·(thread);·0s·(gc)186 ·--·used·0.598137s·(cpu);·0.560047s·(thread);·0s·(gc)
  
187 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···187 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4···
188 o6·=·-·-----------------------------a··-·-------------------------------a·b·-188 o6·=·-·-----------------------------a··-·-------------------------------a·b·-
189 ···········2222549728809984000000············12700284164628480000000·········189 ···········2222549728809984000000············12700284164628480000000·········
190 ·····------------------------------------------------------------------------190 ·····------------------------------------------------------------------------
191 ·····348237304382147063838108483692249·3·2··191 ·····348237304382147063838108483692249·3·2··
192 ·····---------------------------------a·b··-192 ·····---------------------------------a·b··-
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58 ·····------------------------------------------------------------------------58 ·····------------------------------------------------------------------------
59 ·····3·····2····9····7·····2····9········3·······1····8····459 ·····3·····2····9····7·····2····9········3·······1····8····4
60 ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w}60 ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w}
61 ·····4··········8····8··········7················4····3····561 ·····4··········8····8··········7················4····3····5
  
62 o2·:·List62 o2·:·List
63 i3·:·time·resultant(F,Algorithm=>"Poisson2")63 i3·:·time·resultant(F,Algorithm=>"Poisson2")
64 ·--·used·0.214497s·(cpu);·0.157181s·(thread);·0s·(gc)64 ·--·used·0.267135s·(cpu);·0.181296s·(thread);·0s·(gc)
  
65 ·······21002161660529014459938925799·5···2085933800619238998825958079203·465 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4
66 o3·=·-·-----------------------------a··-·-------------------------------a·b·-66 o3·=·-·-----------------------------a··-·-------------------------------a·b·-
67 ···········2222549728809984000000············1270028416462848000000067 ···········2222549728809984000000············12700284164628480000000
68 ·····------------------------------------------------------------------------68 ·····------------------------------------------------------------------------
69 ·····348237304382147063838108483692249·3·269 ·····348237304382147063838108483692249·3·2
70 ·····---------------------------------a·b··-70 ·····---------------------------------a·b··-
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78 ·····------------------------------------------------------------------------78 ·····------------------------------------------------------------------------
79 ·····1146977327343523453866040839029···4···194441910898734675845094443·579 ·····1146977327343523453866040839029···4···194441910898734675845094443·5
80 ·····-------------------------------a*b··-·---------------------------b80 ·····-------------------------------a*b··-·---------------------------b
81 ··········1119954511872000000000················89596360949760000081 ··········1119954511872000000000················895963609497600000
  
82 o3·:·QQ[a..b]82 o3·:·QQ[a..b]
83 i4·:·time·resultant(F,Algorithm=>"Macaulay2")83 i4·:·time·resultant(F,Algorithm=>"Macaulay2")
84 ·--·used·0.0603554s·(cpu);·0.0607234s·(thread);·0s·(gc)84 ·--·used·0.0872349s·(cpu);·0.0893436s·(thread);·0s·(gc)
  
85 ·······21002161660529014459938925799·5···2085933800619238998825958079203·485 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4
86 o4·=·-·-----------------------------a··-·-------------------------------a·b·-86 o4·=·-·-----------------------------a··-·-------------------------------a·b·-
87 ···········2222549728809984000000············1270028416462848000000087 ···········2222549728809984000000············12700284164628480000000
88 ·····------------------------------------------------------------------------88 ·····------------------------------------------------------------------------
89 ·····348237304382147063838108483692249·3·289 ·····348237304382147063838108483692249·3·2
90 ·····---------------------------------a·b··-90 ·····---------------------------------a·b··-
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98 ·····------------------------------------------------------------------------98 ·····------------------------------------------------------------------------
99 ·····1146977327343523453866040839029···4···194441910898734675845094443·599 ·····1146977327343523453866040839029···4···194441910898734675845094443·5
100 ·····-------------------------------a*b··-·---------------------------b100 ·····-------------------------------a*b··-·---------------------------b
101 ··········1119954511872000000000················895963609497600000101 ··········1119954511872000000000················895963609497600000
  
102 o4·:·QQ[a..b]102 o4·:·QQ[a..b]
103 i5·:·time·resultant(F,Algorithm=>"Poisson")103 i5·:·time·resultant(F,Algorithm=>"Poisson")
104 ·--·used·0.268621s·(cpu);·0.237589s·(thread);·0s·(gc)104 ·--·used·0.362645s·(cpu);·0.32476s·(thread);·0s·(gc)
  
105 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4105 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4
106 o5·=·-·-----------------------------a··-·-------------------------------a·b·-106 o5·=·-·-----------------------------a··-·-------------------------------a·b·-
107 ···········2222549728809984000000············12700284164628480000000107 ···········2222549728809984000000············12700284164628480000000
108 ·····------------------------------------------------------------------------108 ·····------------------------------------------------------------------------
109 ·····348237304382147063838108483692249·3·2109 ·····348237304382147063838108483692249·3·2
110 ·····---------------------------------a·b··-110 ·····---------------------------------a·b··-
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118 ·····------------------------------------------------------------------------118 ·····------------------------------------------------------------------------
119 ·····1146977327343523453866040839029···4···194441910898734675845094443·5119 ·····1146977327343523453866040839029···4···194441910898734675845094443·5
120 ·····-------------------------------a*b··-·---------------------------b120 ·····-------------------------------a*b··-·---------------------------b
121 ··········1119954511872000000000················895963609497600000121 ··········1119954511872000000000················895963609497600000
  
122 o5·:·QQ[a..b]122 o5·:·QQ[a..b]
123 i6·:·time·resultant(F,Algorithm=>"Macaulay")123 i6·:·time·resultant(F,Algorithm=>"Macaulay")
124 ·--·used·0.451197s·(cpu);·0.423115s·(thread);·0s·(gc)124 ·--·used·0.598137s·(cpu);·0.560047s·(thread);·0s·(gc)
  
125 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4125 ·······21002161660529014459938925799·5···2085933800619238998825958079203·4
126 o6·=·-·-----------------------------a··-·-------------------------------a·b·-126 o6·=·-·-----------------------------a··-·-------------------------------a·b·-
127 ···········2222549728809984000000············12700284164628480000000127 ···········2222549728809984000000············12700284164628480000000
128 ·····------------------------------------------------------------------------128 ·····------------------------------------------------------------------------
129 ·····348237304382147063838108483692249·3·2129 ·····348237304382147063838108483692249·3·2
130 ·····---------------------------------a·b··-130 ·····---------------------------------a·b··-
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Offset 92, 15 lines modifiedOffset 92, 15 lines modified
  
92 o2·:·List</code></pre>92 o2·:·List</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i3·:·time·resultant·F97 ··············<pre><code·class="language-macaulay2">i3·:·time·resultant·F
98 ·--·used·0.0230989s·(cpu);·0.020533s·(thread);·0s·(gc)98 ·--·used·0.0266299s·(cpu);·0.0260982s·(thread);·0s·(gc)
  
99 ··········12·········11·2·········10·3·········9·4··········8·5··········7·699 ··········12·········11·2·········10·3·········9·4··········8·5··········7·6
100 o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u·100 o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u·
101 ·····------------------------------------------------------------------------101 ·····------------------------------------------------------------------------
102 ··············6·7··········5·8·······11··········10·2·········9·3··102 ··············6·7··········5·8·······11··········10·2·········9·3··
103 ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+103 ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+
104 ·····------------------------------------------------------------------------104 ·····------------------------------------------------------------------------
Offset 155, 15 lines modifiedOffset 155, 15 lines modified
  
155 o4·:·List</code></pre>155 o4·:·List</code></pre>
156 ············</td>156 ············</td>
157 ··········</tr>157 ··········</tr>
158 ··········<tr>158 ··········<tr>
159 ············<td>159 ············<td>
160 ··············<pre><code·class="language-macaulay2">i5·:·time·resultant·F160 ··············<pre><code·class="language-macaulay2">i5·:·time·resultant·F
161 ·--·used·1.7778s·(cpu);·1.45356s·(thread);·0s·(gc)161 ·--·used·2.04727s·(cpu);·1.59536s·(thread);·0s·(gc)
  
162 ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2··162 ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2··
163 o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··-163 o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··-
164 ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0··164 ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0··
165 ·····------------------------------------------------------------------------165 ·····------------------------------------------------------------------------
166 ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2··166 ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2··
167 ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··-167 ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··-
Offset 1790, 15 lines modifiedOffset 1790, 15 lines modified
  
1790 o6·:·List</code></pre>1790 o6·:·List</code></pre>
1791 ············</td>1791 ············</td>
1792 ··········</tr>1792 ··········</tr>
1793 ··········<tr>1793 ··········<tr>
1794 ············<td>1794 ············<td>
1795 ··············<pre><code·class="language-macaulay2">i7·:·time·#·terms·resultant·F1795 ··············<pre><code·class="language-macaulay2">i7·:·time·#·terms·resultant·F
1796 ·--·used·0.370806s·(cpu);·0.303331s·(thread);·0s·(gc)1796 ·--·used·0.384467s·(cpu);·0.31323s·(thread);·0s·(gc)
  
1797 o7·=·21894</code></pre>1797 o7·=·21894</code></pre>
1798 ············</td>1798 ············</td>
1799 ··········</tr>1799 ··········</tr>
1800 ········</table>1800 ········</table>
1801 ······</div>1801 ······</div>
1802 ······<div>1802 ······<div>
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Offset 32, 15 lines modifiedOffset 32, 15 lines modified
32 i2·:·F·=·{x^2+3*t*y*z-u*z^2,(t+3*u-1)*x-y,-t*x*y^3+t*x^2*y*z+u*z^4}32 i2·:·F·=·{x^2+3*t*y*z-u*z^2,(t+3*u-1)*x-y,-t*x*y^3+t*x^2*y*z+u*z^4}
  
33 ·······2···············2····························3······2·········433 ·······2···············2····························3······2·········4
34 o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·}34 o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·}
  
35 o2·:·List35 o2·:·List
36 i3·:·time·resultant·F36 i3·:·time·resultant·F
37 ·--·used·0.0230989s·(cpu);·0.020533s·(thread);·0s·(gc)37 ·--·used·0.0266299s·(cpu);·0.0260982s·(thread);·0s·(gc)
  
38 ··········12·········11·2·········10·3·········9·4··········8·5··········7·638 ··········12·········11·2·········10·3·········9·4··········8·5··········7·6
39 o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u39 o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u
40 ·····------------------------------------------------------------------------40 ·····------------------------------------------------------------------------
41 ··············6·7··········5·8·······11··········10·2·········9·341 ··············6·7··········5·8·······11··········10·2·········9·3
42 ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+42 ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+
43 ·····------------------------------------------------------------------------43 ·····------------------------------------------------------------------------
Offset 86, 15 lines modifiedOffset 86, 15 lines modified
86 ·····------------------------------------------------------------------------86 ·····------------------------------------------------------------------------
87 ··········387 ··········3
88 ·····+·c·x·}88 ·····+·c·x·}
89 ········9·289 ········9·2
  
90 o4·:·List90 o4·:·List
91 i5·:·time·resultant·F91 i5·:·time·resultant·F
92 ·--·used·1.7778s·(cpu);·1.45356s·(thread);·0s·(gc)92 ·--·used·2.04727s·(cpu);·1.59536s·(thread);·0s·(gc)
  
93 ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···293 ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2
94 o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··-94 o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··-
95 ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·095 ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0
96 ·····------------------------------------------------------------------------96 ·····------------------------------------------------------------------------
97 ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·297 ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2
98 ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··-98 ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··-
Offset 1712, 15 lines modifiedOffset 1712, 15 lines modified
1712 ·····------------------------------------------------------------------------1712 ·····------------------------------------------------------------------------
1713 ··························2·····2···············2························21713 ··························2·····2···············2························2
1714 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}1714 ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·}
1715 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·21715 ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2
  
1716 o6·:·List1716 o6·:·List
1717 i7·:·time·#·terms·resultant·F1717 i7·:·time·#·terms·resultant·F
1718 ·--·used·0.370806s·(cpu);·0.303331s·(thread);·0s·(gc)1718 ·--·used·0.384467s·(cpu);·0.31323s·(thread);·0s·(gc)
  
1719 o7·=·218941719 o7·=·21894
1720 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*1720 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
1721 ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety1721 ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety
1722 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8R_\x8i_\x8n_\x8g_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8)1722 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8R_\x8i_\x8n_\x8g_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8)
1723 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*1723 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
1724 ····*·resultant(List)1724 ····*·resultant(List)
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Offset 97, 15 lines modifiedOffset 97, 15 lines modified
97 ··················0···4</code></pre>97 ··················0···4</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form)102 ··············<pre><code·class="language-macaulay2">i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form)
103 ·····time·tangentialChowForm(S,0)103 ·····time·tangentialChowForm(S,0)
104 ·--·used·0.0258548s·(cpu);·0.0256399s·(thread);·0s·(gc)104 ·--·used·0.0311866s·(cpu);·0.0286425s·(thread);·0s·(gc)
  
105 ······2·······················································2········105 ······2·······················································2········
106 o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+106 o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+
107 ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4··107 ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4··
108 ·····------------------------------------------------------------------------108 ·····------------------------------------------------------------------------
109 ······2109 ······2
110 ·····p···p····-·2p···p···p····-·p···p···p110 ·····p···p····-·2p···p···p····-·p···p···p
Offset 118, 15 lines modifiedOffset 118, 15 lines modified
118 ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,3</code></pre>118 ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,3</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4)123 ··············<pre><code·class="language-macaulay2">i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4)
124 ·····time·tangentialChowForm(S,1)124 ·····time·tangentialChowForm(S,1)
125 ·--·used·0.0434599s·(cpu);·0.0461125s·(thread);·0s·(gc)125 ·--·used·0.0571841s·(cpu);·0.0562841s·(thread);·0s·(gc)
  
126 ······2·····2········2·····2···············3········2·····2······126 ······2·····2········2·····2···············3········2·····2······
127 o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······-127 o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······-
128 ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4··128 ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4··
129 ·····------------------------------------------------------------------------129 ·····------------------------------------------------------------------------
130 ·············3·········3···············3············130 ·············3·········3···············3············
131 ·····4p·····p······-·4p·····p······-·2p·····p······+131 ·····4p·····p······-·4p·····p······-·2p·····p······+
Offset 163, 43 lines modifiedOffset 163, 43 lines modified
163 ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre>163 ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre>
164 ············</td>164 ············</td>
165 ··········</tr>165 ··········</tr>
166 ··········<tr>166 ··········<tr>
167 ············<td>167 ············<td>
168 ··············<pre><code·class="language-macaulay2">i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S)168 ··············<pre><code·class="language-macaulay2">i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S)
169 ·····time·tangentialChowForm(S,2)169 ·····time·tangentialChowForm(S,2)
170 ·--·used·0.0695898s·(cpu);·0.0424074s·(thread);·0s·(gc)170 ·--·used·0.110597s·(cpu);·0.0519151s·(thread);·0s·(gc)
  
171 ··············2·············································2171 ··············2·············································2
172 o5·=·p·······p········-·p·······p·······p········+·p·······p172 o5·=·p·······p········-·p·······p·······p········+·p·······p
173 ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4173 ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4
  
174 o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······]174 o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······]
175 ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4</code></pre>175 ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4</code></pre>
176 ············</td>176 ············</td>
177 ··········</tr>177 ··········</tr>
178 ··········<tr>178 ··········<tr>
179 ············<td>179 ············<td>
180 ··············<pre><code·class="language-macaulay2">i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing180 ··············<pre><code·class="language-macaulay2">i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing
181 ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2)181 ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2)
182 ·--·used·0.0336126s·(cpu);·0.0346874s·(thread);·0s·(gc)182 ·--·used·0.0411523s·(cpu);·0.0418658s·(thread);·0s·(gc)
  
183 ············2···············2183 ············2···············2
184 o6·=·ideal(p·p··-·p·p·p··+·p·p·)184 o6·=·ideal(p·p··-·p·p·p··+·p·p·)
185 ············1·2····0·1·3····0·4185 ············1·2····0·1·3····0·4
  
186 o6·:·Ideal·of·QQ[p·..p·]186 o6·:·Ideal·of·QQ[p·..p·]
187 ··················0···4</code></pre>187 ··················0···4</code></pre>
188 ············</td>188 ············</td>
189 ··········</tr>189 ··········</tr>
190 ··········<tr>190 ··········<tr>
191 ············<td>191 ············<td>
192 ··············<pre><code·class="language-macaulay2">i7·:·--·we·then·can·recover·S192 ··············<pre><code·class="language-macaulay2">i7·:·--·we·then·can·recover·S
193 ·····time·assert(dualize·tangentialChowForm(S',3)·==·S)193 ·····time·assert(dualize·tangentialChowForm(S',3)·==·S)
194 ·--·used·0.111376s·(cpu);·0.0867692s·(thread);·0s·(gc)</code></pre>194 ·--·used·0.166675s·(cpu);·0.101515s·(thread);·0s·(gc)</code></pre>
195 ············</td>195 ············</td>
196 ··········</tr>196 ··········</tr>
197 ········</table>197 ········</table>
198 ······</div>198 ······</div>
199 ······<div>199 ······<div>
200 ········<h2>See·also</h2>200 ········<h2>See·also</h2>
201 ········<ul>201 ········<ul>
3.47 KB
html2text {}
    
Offset 63, 15 lines modifiedOffset 63, 15 lines modified
63 o2·=·ideal·(-·p·p··+·p·p·,·-·p·p··+·p·p·,·-·p··+·p·p·)63 o2·=·ideal·(-·p·p··+·p·p·,·-·p·p··+·p·p·,·-·p··+·p·p·)
64 ···············1·2····0·3·····1·3····0·4·····3····2·464 ···············1·2····0·3·····1·3····0·4·····3····2·4
  
65 o2·:·Ideal·of·QQ[p·..p·]65 o2·:·Ideal·of·QQ[p·..p·]
66 ··················0···466 ··················0···4
67 i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form)67 i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form)
68 ·····time·tangentialChowForm(S,0)68 ·····time·tangentialChowForm(S,0)
69 ·--·used·0.0258548s·(cpu);·0.0256399s·(thread);·0s·(gc)69 ·--·used·0.0311866s·(cpu);·0.0286425s·(thread);·0s·(gc)
  
70 ······2·······················································270 ······2·······················································2
71 o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+71 o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+
72 ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,472 ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4
73 ·····------------------------------------------------------------------------73 ·····------------------------------------------------------------------------
74 ······274 ······2
75 ·····p···p····-·2p···p···p····-·p···p···p75 ·····p···p····-·2p···p···p····-·p···p···p
Offset 88, 15 lines modifiedOffset 88, 15 lines modified
88 -·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p88 -·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p
89 p···)89 p···)
90 ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,490 ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4
91 0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,191 0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1
92 2,392 2,3
93 i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4)93 i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4)
94 ·····time·tangentialChowForm(S,1)94 ·····time·tangentialChowForm(S,1)
95 ·--·used·0.0434599s·(cpu);·0.0461125s·(thread);·0s·(gc)95 ·--·used·0.0571841s·(cpu);·0.0562841s·(thread);·0s·(gc)
  
96 ······2·····2········2·····2···············3········2·····296 ······2·····2········2·····2···············3········2·····2
97 o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······-97 o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······-
98 ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,498 ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4
99 ·····------------------------------------------------------------------------99 ·····------------------------------------------------------------------------
100 ·············3·········3···············3100 ·············3·········3···············3
101 ·····4p·····p······-·4p·····p······-·2p·····p······+101 ·····4p·····p······-·4p·····p······-·2p·····p······+
Offset 138, 35 lines modifiedOffset 138, 35 lines modified
138 p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····)138 p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····)
139 ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4139 ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4
140 0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3140 0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3
141 1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4141 1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4
142 i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent142 i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent
143 hyperplanes·to·S)143 hyperplanes·to·S)
144 ·····time·tangentialChowForm(S,2)144 ·····time·tangentialChowForm(S,2)
145 ·--·used·0.0695898s·(cpu);·0.0424074s·(thread);·0s·(gc)145 ·--·used·0.110597s·(cpu);·0.0519151s·(thread);·0s·(gc)
  
146 ··············2·············································2146 ··············2·············································2
147 o5·=·p·······p········-·p·······p·······p········+·p·······p147 o5·=·p·······p········-·p·······p·······p········+·p·······p
148 ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4148 ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4
  
149 o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······]149 o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······]
150 ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4150 ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4
151 i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing151 i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing
152 ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2)152 ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2)
153 ·--·used·0.0336126s·(cpu);·0.0346874s·(thread);·0s·(gc)153 ·--·used·0.0411523s·(cpu);·0.0418658s·(thread);·0s·(gc)
  
154 ············2···············2154 ············2···············2
155 o6·=·ideal(p·p··-·p·p·p··+·p·p·)155 o6·=·ideal(p·p··-·p·p·p··+·p·p·)
156 ············1·2····0·1·3····0·4156 ············1·2····0·1·3····0·4
  
157 o6·:·Ideal·of·QQ[p·..p·]157 o6·:·Ideal·of·QQ[p·..p·]
158 ··················0···4158 ··················0···4
159 i7·:·--·we·then·can·recover·S159 i7·:·--·we·then·can·recover·S
160 ·····time·assert(dualize·tangentialChowForm(S',3)·==·S)160 ·····time·assert(dualize·tangentialChowForm(S',3)·==·S)
161 ·--·used·0.111376s·(cpu);·0.0867692s·(thread);·0s·(gc)161 ·--·used·0.166675s·(cpu);·0.101515s·(thread);·0s·(gc)
162 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*162 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
163 ····*·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·--·whether·a·hypersurface·of·a·Grassmannian·is·a·tangential163 ····*·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·--·whether·a·hypersurface·of·a·Grassmannian·is·a·tangential
164 ······Chow·form164 ······Chow·form
165 ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety165 ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety
166 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8ta\x8an\x8ng\x8ge\x8en\x8nt\x8ti\x8ia\x8al\x8lC\x8Ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8*166 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8ta\x8an\x8ng\x8ge\x8en\x8nt\x8ti\x8ia\x8al\x8lC\x8Ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8*
167 ····*·tangentialChowForm(Ideal,ZZ)167 ····*·tangentialChowForm(Ideal,ZZ)
168 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*168 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
736 B
./usr/share/doc/Macaulay2/RunExternalM2/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=187 #:len=18
8 aXNFeHRlcm5hbE0yUGFyZW508 aXNFeHRlcm5hbE0yUGFyZW50
9 #:len=10439 #:len=1043
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiaW5kaWNhdGUgaWYgdGhpcyBwcm9jZXNz10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiaW5kaWNhdGUgaWYgdGhpcyBwcm9jZXNz
11 IGlzIGEgcGFyZW50IHByb2Nlc3Mgb3Igbm90IiwgImxpbmVudW0iID0+IDg5NCwgImZpbGVuYW1l11 IGlzIGEgcGFyZW50IHByb2Nlc3Mgb3Igbm90IiwgImxpbmVudW0iID0+IDg5NCwgImZpbGVuYW1l
1.39 KB
./usr/share/doc/Macaulay2/RunExternalM2/example-output/_resource_splimits.out
    
Offset 1, 19 lines modifiedOffset 1, 24 lines modified
1 --·-*-·M2-comint·-*-·hash:·13323964676561 --·-*-·M2-comint·-*-·hash:·1332396467656
  
2 i1·:·run("ulimit·-a")2 i1·:·run("ulimit·-a")
3 time(seconds)········700 
4 file(blocks)·········unlimited 
5 data(kbytes)·········unlimited 
6 stack(kbytes)········8192 
7 coredump(blocks)·····0 
8 memory(kbytes)·······850000 
9 locked·memory(kbytes)·3077552 
10 process··············96079 
11 nofiles··············512 
12 vmemory(kbytes)······unlimited3 real-time·non-blocking·time··(microseconds,·-R)·unlimited
 4 core·file·size··············(blocks,·-c)·0
 5 data·seg·size···············(kbytes,·-d)·unlimited
 6 scheduling·priority·················(-e)·0
 7 file·size···················(blocks,·-f)·unlimited
 8 pending·signals·····················(-i)·95981
 9 max·locked·memory···········(kbytes,·-l)·3076784
 10 max·memory·size·············(kbytes,·-m)·850000
 11 open·files··························(-n)·512
 12 pipe·size················(512·bytes,·-p)·8
 13 POSIX·message·queues·········(bytes,·-q)·819200
 14 real-time·priority··················(-r)·0
 15 stack·size··················(kbytes,·-s)·8192
 16 cpu·time···················(seconds,·-t)·700
 17 max·user·processes··················(-u)·95981
 18 virtual·memory··············(kbytes,·-v)·unlimited
13 locks················unlimited19 file·locks··························(-x)·unlimited
14 rtprio···············0 
  
15 o1·=·020 o1·=·0
  
16 i2·:·21 i2·:·
9.18 KB
./usr/share/doc/Macaulay2/RunExternalM2/example-output/_run__External__M2.out
    
Offset 1, 137 lines modifiedOffset 1, 136 lines modified
1 --·-*-·M2-comint·-*-·hash:·29279780664557873951 --·-*-·M2-comint·-*-·hash:·2927978066455787395
  
2 i1·:·fn=temporaryFileName()|".m2"2 i1·:·fn=temporaryFileName()|".m2"
  
3 o1·=·/tmp/M2-1221558-0/0.m23 o1·=·/tmp/M2-1244714-0/0.m2
  
4 i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl;4 i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl;
  
5 i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;5 i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;
  
6 i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime();·while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl;6 i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime();·while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl;
  
7 i5·:·fn<<flush;7 i5·:·fn<<flush;
  
8 i6·:·h=runExternalM2(fn,"square",(4));8 i6·:·h=runExternalM2(fn,"square",(4));
9 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1221558-0/1.m2"·>"/tmp/M2-1221558-0/1.out"·2>&1·))9 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1244714-0/1.m2"·>"/tmp/M2-1244714-0/1.out"·2>&1·))
10 Finished·running.10 Finished·running.
  
11 i7·:·h11 i7·:·h
  
12 o7·=·HashTable{"answer·file"·=>·null}12 o7·=·HashTable{"answer·file"·=>·null}
13 ···············"exit·code"·=>·013 ···············"exit·code"·=>·0
14 ···············"output·file"·=>·null14 ···············"output·file"·=>·null
15 ···············"return·code"·=>·015 ···············"return·code"·=>·0
16 ···············"statistics"·=>·null16 ···············"statistics"·=>·null
17 ···············"time·used"·=>·217 ···············"time·used"·=>·4
18 ···············value·=>·1618 ···············value·=>·16
  
19 o7·:·HashTable19 o7·:·HashTable
  
20 i8·:·h#value===4^220 i8·:·h#value===4^2
  
21 o8·=·true21 o8·=·true
  
22 i9·:·h#"exit·code"===022 i9·:·h#"exit·code"===0
  
23 o9·=·true23 o9·=·true
  
24 i10·:·h=runExternalM2(fn,"justexit",());24 i10·:·h=runExternalM2(fn,"justexit",());
25 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1221558-0/2.m2"·>"/tmp/M2-1221558-0/2.out"·2>&1·))25 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1244714-0/2.m2"·>"/tmp/M2-1244714-0/2.out"·2>&1·))
26 Finished·running.26 Finished·running.
27 RunExternalM2:·expected·answer·file·does·not·exist27 RunExternalM2:·expected·answer·file·does·not·exist
  
28 i11·:·h28 i11·:·h
  
29 o11·=·HashTable{"answer·file"·=>·/tmp/M2-1221558-0/2.ans}29 o11·=·HashTable{"answer·file"·=>·/tmp/M2-1244714-0/2.ans}
30 ················"exit·code"·=>·2730 ················"exit·code"·=>·27
31 ················"output·file"·=>·/tmp/M2-1221558-0/2.out31 ················"output·file"·=>·/tmp/M2-1244714-0/2.out
32 ················"return·code"·=>·691232 ················"return·code"·=>·6912
33 ················"statistics"·=>·null33 ················"statistics"·=>·null
34 ················"time·used"·=>·234 ················"time·used"·=>·3
35 ················value·=>·null35 ················value·=>·null
  
36 o11·:·HashTable36 o11·:·HashTable
  
37 i12·:·fileExists(h#"output·file")37 i12·:·fileExists(h#"output·file")
  
38 o12·=·true38 o12·=·true
  
39 i13·:·fileExists(h#"answer·file")39 i13·:·fileExists(h#"answer·file")
  
40 o13·=·false40 o13·=·false
  
41 i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2");41 i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2");
42 Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1221558-0/3.m2"·>"/tmp/M2-1221558-0/3.out"·2>&1·))42 Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1244714-0/3.m2"·>"/tmp/M2-1244714-0/3.out"·2>&1·))
43 Killed 
44 Finished·running.43 Finished·running.
45 RunExternalM2:·expected·answer·file·does·not·exist44 RunExternalM2:·expected·answer·file·does·not·exist
  
46 i15·:·h45 i15·:·h
  
47 o15·=·HashTable{"answer·file"·=>·/tmp/M2-1221558-0/3.ans}46 o15·=·HashTable{"answer·file"·=>·/tmp/M2-1244714-0/3.ans}
48 ················"exit·code"·=>·047 ················"exit·code"·=>·0
49 ················"output·file"·=>·/tmp/M2-1221558-0/3.out48 ················"output·file"·=>·/tmp/M2-1244714-0/3.out
50 ················"return·code"·=>·949 ················"return·code"·=>·9
51 ················"statistics"·=>·null50 ················"statistics"·=>·null
52 ················"time·used"·=>·451 ················"time·used"·=>·5
53 ················value·=>·null52 ················value·=>·null
  
54 o15·:·HashTable53 o15·:·HashTable
  
55 i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file")54 i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file")
  
56 o16·=·55 o16·=·
57 ······i1·:·--·Script·/tmp/M2-1221558-0/3.m2·automatically·generated·by·RunExternalM256 ······i1·:·--·Script·/tmp/M2-1244714-0/3.m2·automatically·generated·by·RunExternalM2
58 ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true});57 ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true});
  
59 ······i2·:·load·"/tmp/M2-1221558-0/0.m2";58 ······i2·:·load·"/tmp/M2-1244714-0/0.m2";
  
60 ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-1221558-0/3.ans",spin·(10));59 ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-1244714-0/3.ans",spin·(10));
61 ······Spinning!!60 ······Spinning!!
  
  
62 i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file")61 i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file")
  
63 i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true);62 i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true);
64 Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1221558-0/4.m2"·>"/tmp/M2-1221558-0/4.out"·2>&1')·>"/tmp/M2-1221558-0/4.stat"·2>&1·))63 Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1244714-0/4.m2"·>"/tmp/M2-1244714-0/4.out"·2>&1')·>"/tmp/M2-1244714-0/4.stat"·2>&1·))
65 Finished·running.64 Finished·running.
  
66 i19·:·h#"statistics"65 i19·:·h#"statistics"
  
67 o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1221558-0/4.m2"·>"/tmp/M2-1221558-0/4.out"·2>&1"66 o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-1244714-0/4.m2"·>"/tmp/M2-1244714-0/4.out"·2>&1"
68 ··············User·time·(seconds):·4.8167 ··············User·time·(seconds):·5.01
69 ··············System·time·(seconds):·0.1068 ··············System·time·(seconds):·0.25
70 ··············Percent·of·CPU·this·job·got:·79%69 ··············Percent·of·CPU·this·job·got:·36%
71 ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:06.1870 ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:14.32
72 ··············Average·shared·text·size·(kbytes):·071 ··············Average·shared·text·size·(kbytes):·0
73 ··············Average·unshared·data·size·(kbytes):·072 ··············Average·unshared·data·size·(kbytes):·0
74 ··············Average·stack·size·(kbytes):·073 ··············Average·stack·size·(kbytes):·0
75 ··············Average·total·size·(kbytes):·074 ··············Average·total·size·(kbytes):·0
76 ··············Maximum·resident·set·size·(kbytes):·30383275 ··············Maximum·resident·set·size·(kbytes):·300816
77 ··············Average·resident·set·size·(kbytes):·076 ··············Average·resident·set·size·(kbytes):·0
78 ··············Major·(requiring·I/O)·page·faults:·077 ··············Major·(requiring·I/O)·page·faults:·0
79 ··············Minor·(reclaiming·a·frame)·page·faults:·1059678 ··············Minor·(reclaiming·a·frame)·page·faults:·70623
80 ··············Voluntary·context·switches:·280079 ··············Voluntary·context·switches:·5325
81 ··············Involuntary·context·switches:·65980 ··············Involuntary·context·switches:·2894
82 ··············Swaps:·081 ··············Swaps:·0
83 ··············File·system·inputs:·082 ··············File·system·inputs:·0
84 ··············File·system·outputs:·2483 ··············File·system·outputs:·24
85 ··············Socket·messages·sent:·084 ··············Socket·messages·sent:·0
86 ··············Socket·messages·received:·085 ··············Socket·messages·received:·0
87 ··············Signals·delivered:·086 ··············Signals·delivered:·0
88 ··············Page·size·(bytes):·409687 ··············Page·size·(bytes):·4096
89 ··············Exit·status:·088 ··············Exit·status:·0
  
  
90 i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///;89 i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///;
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68 ··········<p>which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits·unchanged.</p>68 ··········<p>which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits·unchanged.</p>
69 ··········<p><b>From·within·Macaulay2</b>,·you·can·<b>view</b>·the·ulimits·currently·available·to·the·Macaulay2·process·by·using·the·<a·title="run·an·external·command"·href="../../Macaulay2Doc/html/_run.html">run</a>·command:</p>69 ··········<p><b>From·within·Macaulay2</b>,·you·can·<b>view</b>·the·ulimits·currently·available·to·the·Macaulay2·process·by·using·the·<a·title="run·an·external·command"·href="../../Macaulay2Doc/html/_run.html">run</a>·command:</p>
70 ········</div>70 ········</div>
71 ········<table·class="examples">71 ········<table·class="examples">
72 ··········<tr>72 ··········<tr>
73 ············<td>73 ············<td>
74 ··············<pre><code·class="language-macaulay2">i1·:·run(&quot;ulimit·-a&quot;)74 ··············<pre><code·class="language-macaulay2">i1·:·run(&quot;ulimit·-a&quot;)
75 time(seconds)········700 
76 file(blocks)·········unlimited 
77 data(kbytes)·········unlimited 
78 stack(kbytes)········8192 
79 coredump(blocks)·····0 
80 memory(kbytes)·······850000 
81 locked·memory(kbytes)·3077552 
82 process··············96079 
83 nofiles··············512 
84 vmemory(kbytes)······unlimited75 real-time·non-blocking·time··(microseconds,·-R)·unlimited
 76 core·file·size··············(blocks,·-c)·0
 77 data·seg·size···············(kbytes,·-d)·unlimited
 78 scheduling·priority·················(-e)·0
 79 file·size···················(blocks,·-f)·unlimited
 80 pending·signals·····················(-i)·95981
 81 max·locked·memory···········(kbytes,·-l)·3076784
 82 max·memory·size·············(kbytes,·-m)·850000
 83 open·files··························(-n)·512
 84 pipe·size················(512·bytes,·-p)·8
 85 POSIX·message·queues·········(bytes,·-q)·819200
 86 real-time·priority··················(-r)·0
 87 stack·size··················(kbytes,·-s)·8192
 88 cpu·time···················(seconds,·-t)·700
 89 max·user·processes··················(-u)·95981
 90 virtual·memory··············(kbytes,·-v)·unlimited
85 locks················unlimited91 file·locks··························(-x)·unlimited
86 rtprio···············0 
  
87 o1·=·0</code></pre>92 o1·=·0</code></pre>
88 ············</td>93 ············</td>
89 ··········</tr>94 ··········</tr>
90 ········</table>95 ········</table>
91 ········<div>96 ········<div>
92 ··········<p>This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case·provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this·should·be·the·same·as·the·ulimits·of·Macaulay2·itself.</p>97 ··········<p>This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case·provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this·should·be·the·same·as·the·ulimits·of·Macaulay2·itself.</p>
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28 b\x8be\x8es\x8st\x8t·w\x8wa\x8ay\x8y·t\x8to\x8o·s\x8se\x8et\x8t·the·limits·on·a·specific·process·is·to·run·something·like28 b\x8be\x8es\x8st\x8t·w\x8wa\x8ay\x8y·t\x8to\x8o·s\x8se\x8et\x8t·the·limits·on·a·specific·process·is·to·run·something·like
29 (ulimit·-S·-m·123456·-S·-t·5;·M2)29 (ulimit·-S·-m·123456·-S·-t·5;·M2)
30 which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits30 which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits
31 unchanged.31 unchanged.
32 F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·you·can·v\x8vi\x8ie\x8ew\x8w·the·ulimits·currently·available·to·the32 F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·you·can·v\x8vi\x8ie\x8ew\x8w·the·ulimits·currently·available·to·the
33 Macaulay2·process·by·using·the·_\x8r_\x8u_\x8n·command:33 Macaulay2·process·by·using·the·_\x8r_\x8u_\x8n·command:
34 i1·:·run("ulimit·-a")34 i1·:·run("ulimit·-a")
35 time(seconds)········700 
36 file(blocks)·········unlimited 
37 data(kbytes)·········unlimited 
38 stack(kbytes)········8192 
39 coredump(blocks)·····0 
40 memory(kbytes)·······850000 
41 locked·memory(kbytes)·3077552 
42 process··············96079 
43 nofiles··············512 
44 vmemory(kbytes)······unlimited35 real-time·non-blocking·time··(microseconds,·-R)·unlimited
 36 core·file·size··············(blocks,·-c)·0
 37 data·seg·size···············(kbytes,·-d)·unlimited
 38 scheduling·priority·················(-e)·0
 39 file·size···················(blocks,·-f)·unlimited
 40 pending·signals·····················(-i)·95981
 41 max·locked·memory···········(kbytes,·-l)·3076784
 42 max·memory·size·············(kbytes,·-m)·850000
 43 open·files··························(-n)·512
 44 pipe·size················(512·bytes,·-p)·8
 45 POSIX·message·queues·········(bytes,·-q)·819200
 46 real-time·priority··················(-r)·0
 47 stack·size··················(kbytes,·-s)·8192
 48 cpu·time···················(seconds,·-t)·700
 49 max·user·processes··················(-u)·95981
 50 virtual·memory··············(kbytes,·-v)·unlimited
45 locks················unlimited51 file·locks··························(-x)·unlimited
46 rtprio···············0 
  
47 o1·=·052 o1·=·0
48 This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case53 This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case
49 provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this54 provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this
50 should·be·the·same·as·the·ulimits·of·Macaulay2·itself.55 should·be·the·same·as·the·ulimits·of·Macaulay2·itself.
51 F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·it·is·not·possible·to·set·ulimits·on·the·current56 F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·it·is·not·possible·to·set·ulimits·on·the·current
52 Macaulay2·process·because·Macaulay2·does·not·provide·access·to·the·setrlimit57 Macaulay2·process·because·Macaulay2·does·not·provide·access·to·the·setrlimit
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./usr/share/doc/Macaulay2/RunExternalM2/html/_run__External__M2.html
    
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84 ··········<p>For·example,·we·can·write·a·few·functions·to·a·temporary·file:</p>84 ··········<p>For·example,·we·can·write·a·few·functions·to·a·temporary·file:</p>
85 ········</div>85 ········</div>
86 ········<table·class="examples">86 ········<table·class="examples">
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i1·:·fn=temporaryFileName()|&quot;.m2&quot;89 ··············<pre><code·class="language-macaulay2">i1·:·fn=temporaryFileName()|&quot;.m2&quot;
  
90 o1·=·/tmp/M2-1221558-0/0.m2</code></pre>90 o1·=·/tmp/M2-1244714-0/0.m2</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i2·:·fn&lt;&lt;///·square·=·(x)·->·(stderr&lt;&lt;&quot;Running&quot;&lt;&lt;endl;·sleep(1);·x^2);·///&lt;&lt;endl;</code></pre>95 ··············<pre><code·class="language-macaulay2">i2·:·fn&lt;&lt;///·square·=·(x)·->·(stderr&lt;&lt;&quot;Running&quot;&lt;&lt;endl;·sleep(1);·x^2);·///&lt;&lt;endl;</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
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115 ········<div>115 ········<div>
116 ··········<p>and·then·call·them:</p>116 ··········<p>and·then·call·them:</p>
117 ········</div>117 ········</div>
118 ········<table·class="examples">118 ········<table·class="examples">
119 ··········<tr>119 ··········<tr>
120 ············<td>120 ············<td>
121 ··············<pre><code·class="language-macaulay2">i6·:·h=runExternalM2(fn,&quot;square&quot;,(4));121 ··············<pre><code·class="language-macaulay2">i6·:·h=runExternalM2(fn,&quot;square&quot;,(4));
122 Running·(true·&amp;&amp;·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··&lt;&quot;/tmp/M2-1221558-0/1.m2&quot;·>&quot;/tmp/M2-1221558-0/1.out&quot;·2>&amp;1·))122 Running·(true·&amp;&amp;·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··&lt;&quot;/tmp/M2-1244714-0/1.m2&quot;·>&quot;/tmp/M2-1244714-0/1.out&quot;·2>&amp;1·))
123 Finished·running.</code></pre>123 Finished·running.</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i7·:·h128 ··············<pre><code·class="language-macaulay2">i7·:·h
  
129 o7·=·HashTable{&quot;answer·file&quot;·=>·null}129 o7·=·HashTable{&quot;answer·file&quot;·=>·null}
130 ···············&quot;exit·code&quot;·=>·0130 ···············&quot;exit·code&quot;·=>·0
131 ···············&quot;output·file&quot;·=>·null131 ···············&quot;output·file&quot;·=>·null
132 ···············&quot;return·code&quot;·=>·0132 ···············&quot;return·code&quot;·=>·0
133 ···············&quot;statistics&quot;·=>·null133 ···············&quot;statistics&quot;·=>·null
134 ···············&quot;time·used&quot;·=>·2134 ···············&quot;time·used&quot;·=>·4
135 ···············value·=>·16135 ···············value·=>·16
  
136 o7·:·HashTable</code></pre>136 o7·:·HashTable</code></pre>
137 ············</td>137 ············</td>
138 ··········</tr>138 ··········</tr>
139 ··········<tr>139 ··········<tr>
140 ············<td>140 ············<td>
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157 ··········<p></p>157 ··········<p></p>
158 ··········<p>An·abnormal·program·exit·will·have·a·nonzero·<span·class="tt">exit·code</span>;·also,·the·<span·class="tt">value</span>·will·be·null,·the·<span·class="tt">output·file</span>·should·exist,·but·the·<span·class="tt">answer·file</span>·may·not·exist·unless·the·routine·finished·successfully.</p>158 ··········<p>An·abnormal·program·exit·will·have·a·nonzero·<span·class="tt">exit·code</span>;·also,·the·<span·class="tt">value</span>·will·be·null,·the·<span·class="tt">output·file</span>·should·exist,·but·the·<span·class="tt">answer·file</span>·may·not·exist·unless·the·routine·finished·successfully.</p>
159 ········</div>159 ········</div>
160 ········<table·class="examples">160 ········<table·class="examples">
161 ··········<tr>161 ··········<tr>
162 ············<td>162 ············<td>
163 ··············<pre><code·class="language-macaulay2">i10·:·h=runExternalM2(fn,&quot;justexit&quot;,());163 ··············<pre><code·class="language-macaulay2">i10·:·h=runExternalM2(fn,&quot;justexit&quot;,());
164 Running·(true·&amp;&amp;·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··&lt;&quot;/tmp/M2-1221558-0/2.m2&quot;·>&quot;/tmp/M2-1221558-0/2.out&quot;·2>&amp;1·))164 Running·(true·&amp;&amp;·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··&lt;&quot;/tmp/M2-1244714-0/2.m2&quot;·>&quot;/tmp/M2-1244714-0/2.out&quot;·2>&amp;1·))
165 Finished·running.165 Finished·running.
166 RunExternalM2:·expected·answer·file·does·not·exist</code></pre>166 RunExternalM2:·expected·answer·file·does·not·exist</code></pre>
167 ············</td>167 ············</td>
168 ··········</tr>168 ··········</tr>
169 ··········<tr>169 ··········<tr>
170 ············<td>170 ············<td>
171 ··············<pre><code·class="language-macaulay2">i11·:·h171 ··············<pre><code·class="language-macaulay2">i11·:·h
  
172 o11·=·HashTable{&quot;answer·file&quot;·=>·/tmp/M2-1221558-0/2.ans}172 o11·=·HashTable{&quot;answer·file&quot;·=>·/tmp/M2-1244714-0/2.ans}
173 ················&quot;exit·code&quot;·=>·27173 ················&quot;exit·code&quot;·=>·27
174 ················&quot;output·file&quot;·=>·/tmp/M2-1221558-0/2.out174 ················&quot;output·file&quot;·=>·/tmp/M2-1244714-0/2.out
175 ················&quot;return·code&quot;·=>·6912175 ················&quot;return·code&quot;·=>·6912
176 ················&quot;statistics&quot;·=>·null176 ················&quot;statistics&quot;·=>·null
177 ················&quot;time·used&quot;·=>·2177 ················&quot;time·used&quot;·=>·3
178 ················value·=>·null178 ················value·=>·null
  
179 o11·:·HashTable</code></pre>179 o11·:·HashTable</code></pre>
180 ············</td>180 ············</td>
181 ··········</tr>181 ··········</tr>
182 ··········<tr>182 ··········<tr>
183 ············<td>183 ············<td>
Offset 199, 46 lines modifiedOffset 199, 45 lines modified
199 ········<div>199 ········<div>
200 ··········<p>Here,·we·use·<a·title="how·to·use·resource·limits·with·Macaulay2"·href="_resource_splimits.html">resource·limits</a>·to·limit·the·routine·to·2·seconds·of·computational·time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time:</p>200 ··········<p>Here,·we·use·<a·title="how·to·use·resource·limits·with·Macaulay2"·href="_resource_splimits.html">resource·limits</a>·to·limit·the·routine·to·2·seconds·of·computational·time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time:</p>
201 ········</div>201 ········</div>
202 ········<table·class="examples">202 ········<table·class="examples">
203 ··········<tr>203 ··········<tr>
204 ············<td>204 ············<td>
205 ··············<pre><code·class="language-macaulay2">i14·:·h=runExternalM2(fn,&quot;spin&quot;,10,PreRunScript=>&quot;ulimit·-t·2&quot;);205 ··············<pre><code·class="language-macaulay2">i14·:·h=runExternalM2(fn,&quot;spin&quot;,10,PreRunScript=>&quot;ulimit·-t·2&quot;);
206 Running·(ulimit·-t·2·&amp;&amp;·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··&lt;&quot;/tmp/M2-1221558-0/3.m2&quot;·>&quot;/tmp/M2-1221558-0/3.out&quot;·2>&amp;1·))206 Running·(ulimit·-t·2·&amp;&amp;·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··&lt;&quot;/tmp/M2-1244714-0/3.m2&quot;·>&quot;/tmp/M2-1244714-0/3.out&quot;·2>&amp;1·))
207 Killed 
208 Finished·running.207 Finished·running.
209 RunExternalM2:·expected·answer·file·does·not·exist</code></pre>208 RunExternalM2:·expected·answer·file·does·not·exist</code></pre>
210 ············</td>209 ············</td>
211 ··········</tr>210 ··········</tr>
212 ··········<tr>211 ··········<tr>
213 ············<td>212 ············<td>
214 ··············<pre><code·class="language-macaulay2">i15·:·h213 ··············<pre><code·class="language-macaulay2">i15·:·h
  
215 o15·=·HashTable{&quot;answer·file&quot;·=>·/tmp/M2-1221558-0/3.ans}214 o15·=·HashTable{&quot;answer·file&quot;·=>·/tmp/M2-1244714-0/3.ans}
216 ················&quot;exit·code&quot;·=>·0215 ················&quot;exit·code&quot;·=>·0
217 ················&quot;output·file&quot;·=>·/tmp/M2-1221558-0/3.out216 ················&quot;output·file&quot;·=>·/tmp/M2-1244714-0/3.out
218 ················&quot;return·code&quot;·=>·9217 ················&quot;return·code&quot;·=>·9
219 ················&quot;statistics&quot;·=>·null218 ················&quot;statistics&quot;·=>·null
220 ················&quot;time·used&quot;·=>·4219 ················&quot;time·used&quot;·=>·5
221 ················value·=>·null220 ················value·=>·null
  
222 o15·:·HashTable</code></pre>221 o15·:·HashTable</code></pre>
223 ············</td>222 ············</td>
224 ··········</tr>223 ··········</tr>
225 ··········<tr>224 ··········<tr>
226 ············<td>225 ············<td>
227 ··············<pre><code·class="language-macaulay2">i16·:·if·h#&quot;output·file&quot;·=!=·null·and·fileExists(h#&quot;output·file&quot;)·then·get(h#&quot;output·file&quot;)226 ··············<pre><code·class="language-macaulay2">i16·:·if·h#&quot;output·file&quot;·=!=·null·and·fileExists(h#&quot;output·file&quot;)·then·get(h#&quot;output·file&quot;)
  
228 o16·=·227 o16·=·
229 ······i1·:·--·Script·/tmp/M2-1221558-0/3.m2·automatically·generated·by·RunExternalM2228 ······i1·:·--·Script·/tmp/M2-1244714-0/3.m2·automatically·generated·by·RunExternalM2
230 ···········needsPackage(&quot;RunExternalM2&quot;,Configuration=>{&quot;isChild&quot;=>true});229 ···········needsPackage(&quot;RunExternalM2&quot;,Configuration=>{&quot;isChild&quot;=>true});
  
231 ······i2·:·load·&quot;/tmp/M2-1221558-0/0.m2&quot;;230 ······i2·:·load·&quot;/tmp/M2-1244714-0/0.m2&quot;;
  
232 ······i3·:·runExternalM2ReturnAnswer(&quot;/tmp/M2-1221558-0/3.ans&quot;,spin·(10));231 ······i3·:·runExternalM2ReturnAnswer(&quot;/tmp/M2-1244714-0/3.ans&quot;,spin·(10));
233 ······Spinning!!</code></pre>232 ······Spinning!!</code></pre>
234 ············</td>233 ············</td>
235 ··········</tr>234 ··········</tr>
236 ··········<tr>235 ··········<tr>
237 ············<td>236 ············<td>
238 ··············<pre><code·class="language-macaulay2">i17·:·if·h#&quot;answer·file&quot;·=!=·null·and·fileExists(h#&quot;answer·file&quot;)·then·get(h#&quot;answer·file&quot;)</code></pre>237 ··············<pre><code·class="language-macaulay2">i17·:·if·h#&quot;answer·file&quot;·=!=·null·and·fileExists(h#&quot;answer·file&quot;)·then·get(h#&quot;answer·file&quot;)</code></pre>
239 ············</td>238 ············</td>
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248 ··········<p></p>247 ··········<p></p>
249 ··········<p>We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">KeepStatistics</a>·command:</p>248 ··········<p>We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">KeepStatistics</a>·command:</p>
250 ········</div>249 ········</div>
251 ········<table·class="examples">250 ········<table·class="examples">
252 ··········<tr>251 ··········<tr>
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45 the·output·file·(unless·it·was·deleted),·the·name·of·the·answer·file·(unless·it45 the·output·file·(unless·it·was·deleted),·the·name·of·the·answer·file·(unless·it
46 was·deleted),·any·statistics·recorded·about·the·resource·usage,·and·the·value46 was·deleted),·any·statistics·recorded·about·the·resource·usage,·and·the·value
47 returned·by·the·function·func.·If·the·child·process·terminates·abnormally,·then47 returned·by·the·function·func.·If·the·child·process·terminates·abnormally,·then
48 usually·the·exit·code·is·nonzero·and·the·value·returned·is·_\x8n_\x8u_\x8l_\x8l.48 usually·the·exit·code·is·nonzero·and·the·value·returned·is·_\x8n_\x8u_\x8l_\x8l.
49 For·example,·we·can·write·a·few·functions·to·a·temporary·file:49 For·example,·we·can·write·a·few·functions·to·a·temporary·file:
50 i1·:·fn=temporaryFileName()|".m2"50 i1·:·fn=temporaryFileName()|".m2"
  
51 o1·=·/tmp/M2-1221558-0/0.m251 o1·=·/tmp/M2-1244714-0/0.m2
52 i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///52 i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///
53 <<endl;53 <<endl;
54 i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;54 i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;
55 i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime();55 i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime();
56 while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl;56 while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl;
57 i5·:·fn<<flush;57 i5·:·fn<<flush;
58 and·then·call·them:58 and·then·call·them:
59 i6·:·h=runExternalM2(fn,"square",(4));59 i6·:·h=runExternalM2(fn,"square",(4));
60 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/60 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/
61 M2-1221558-0/1.m2"·>"/tmp/M2-1221558-0/1.out"·2>&1·))61 M2-1244714-0/1.m2"·>"/tmp/M2-1244714-0/1.out"·2>&1·))
62 Finished·running.62 Finished·running.
63 i7·:·h63 i7·:·h
  
64 o7·=·HashTable{"answer·file"·=>·null}64 o7·=·HashTable{"answer·file"·=>·null}
65 ···············"exit·code"·=>·065 ···············"exit·code"·=>·0
66 ···············"output·file"·=>·null66 ···············"output·file"·=>·null
67 ···············"return·code"·=>·067 ···············"return·code"·=>·0
68 ···············"statistics"·=>·null68 ···············"statistics"·=>·null
69 ···············"time·used"·=>·269 ···············"time·used"·=>·4
70 ···············value·=>·1670 ···············value·=>·16
  
71 o7·:·HashTable71 o7·:·HashTable
72 i8·:·h#value===4^272 i8·:·h#value===4^2
  
73 o8·=·true73 o8·=·true
74 i9·:·h#"exit·code"===074 i9·:·h#"exit·code"===0
  
75 o9·=·true75 o9·=·true
76 An·abnormal·program·exit·will·have·a·nonzero·exit·code;·also,·the·value·will·be76 An·abnormal·program·exit·will·have·a·nonzero·exit·code;·also,·the·value·will·be
77 null,·the·output·file·should·exist,·but·the·answer·file·may·not·exist·unless77 null,·the·output·file·should·exist,·but·the·answer·file·may·not·exist·unless
78 the·routine·finished·successfully.78 the·routine·finished·successfully.
79 i10·:·h=runExternalM2(fn,"justexit",());79 i10·:·h=runExternalM2(fn,"justexit",());
80 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/80 Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/
81 M2-1221558-0/2.m2"·>"/tmp/M2-1221558-0/2.out"·2>&1·))81 M2-1244714-0/2.m2"·>"/tmp/M2-1244714-0/2.out"·2>&1·))
82 Finished·running.82 Finished·running.
83 RunExternalM2:·expected·answer·file·does·not·exist83 RunExternalM2:·expected·answer·file·does·not·exist
84 i11·:·h84 i11·:·h
  
85 o11·=·HashTable{"answer·file"·=>·/tmp/M2-1221558-0/2.ans}85 o11·=·HashTable{"answer·file"·=>·/tmp/M2-1244714-0/2.ans}
86 ················"exit·code"·=>·2786 ················"exit·code"·=>·27
87 ················"output·file"·=>·/tmp/M2-1221558-0/2.out87 ················"output·file"·=>·/tmp/M2-1244714-0/2.out
88 ················"return·code"·=>·691288 ················"return·code"·=>·6912
89 ················"statistics"·=>·null89 ················"statistics"·=>·null
90 ················"time·used"·=>·290 ················"time·used"·=>·3
91 ················value·=>·null91 ················value·=>·null
  
92 o11·:·HashTable92 o11·:·HashTable
93 i12·:·fileExists(h#"output·file")93 i12·:·fileExists(h#"output·file")
  
94 o12·=·true94 o12·=·true
95 i13·:·fileExists(h#"answer·file")95 i13·:·fileExists(h#"answer·file")
  
96 o13·=·false96 o13·=·false
97 Here,·we·use·_\x8r_\x8e_\x8s_\x8o_\x8u_\x8r_\x8c_\x8e_\x8·_\x8l_\x8i_\x8m_\x8i_\x8t_\x8s·to·limit·the·routine·to·2·seconds·of·computational97 Here,·we·use·_\x8r_\x8e_\x8s_\x8o_\x8u_\x8r_\x8c_\x8e_\x8·_\x8l_\x8i_\x8m_\x8i_\x8t_\x8s·to·limit·the·routine·to·2·seconds·of·computational
98 time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time:98 time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time:
99 i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2");99 i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2");
100 Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-100 Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-
101 q··<"/tmp/M2-1221558-0/3.m2"·>"/tmp/M2-1221558-0/3.out"·2>&1·))101 q··<"/tmp/M2-1244714-0/3.m2"·>"/tmp/M2-1244714-0/3.out"·2>&1·))
102 Killed 
103 Finished·running.102 Finished·running.
104 RunExternalM2:·expected·answer·file·does·not·exist103 RunExternalM2:·expected·answer·file·does·not·exist
105 i15·:·h104 i15·:·h
  
106 o15·=·HashTable{"answer·file"·=>·/tmp/M2-1221558-0/3.ans}105 o15·=·HashTable{"answer·file"·=>·/tmp/M2-1244714-0/3.ans}
107 ················"exit·code"·=>·0106 ················"exit·code"·=>·0
108 ················"output·file"·=>·/tmp/M2-1221558-0/3.out107 ················"output·file"·=>·/tmp/M2-1244714-0/3.out
109 ················"return·code"·=>·9108 ················"return·code"·=>·9
110 ················"statistics"·=>·null109 ················"statistics"·=>·null
111 ················"time·used"·=>·4110 ················"time·used"·=>·5
112 ················value·=>·null111 ················value·=>·null
  
113 o15·:·HashTable112 o15·:·HashTable
114 i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get113 i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get
115 (h#"output·file")114 (h#"output·file")
  
116 o16·=115 o16·=
117 ······i1·:·--·Script·/tmp/M2-1221558-0/3.m2·automatically·generated·by116 ······i1·:·--·Script·/tmp/M2-1244714-0/3.m2·automatically·generated·by
118 RunExternalM2117 RunExternalM2
119 ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true});118 ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true});
  
120 ······i2·:·load·"/tmp/M2-1221558-0/0.m2";119 ······i2·:·load·"/tmp/M2-1244714-0/0.m2";
  
121 ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-1221558-0/3.ans",spin·(10));120 ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-1244714-0/3.ans",spin·(10));
122 ······Spinning!!121 ······Spinning!!
123 i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get122 i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get
124 (h#"answer·file")123 (h#"answer·file")
125 We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·_\x8K_\x8e_\x8e_\x8p_\x8S_\x8t_\x8a_\x8t_\x8i_\x8s_\x8t_\x8i_\x8c_\x8s124 We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·_\x8K_\x8e_\x8e_\x8p_\x8S_\x8t_\x8a_\x8t_\x8i_\x8s_\x8t_\x8i_\x8c_\x8s
126 command:125 command:
127 i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true);126 i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true);
128 Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·-127 Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·-
129 -no-debug·--silent··-q··<"/tmp/M2-1221558-0/4.m2"·>"/tmp/M2-1221558-0/4.out"128 -no-debug·--silent··-q··<"/tmp/M2-1244714-0/4.m2"·>"/tmp/M2-1244714-0/4.out"
130 2>&1')·>"/tmp/M2-1221558-0/4.stat"·2>&1·))129 2>&1')·>"/tmp/M2-1244714-0/4.stat"·2>&1·))
131 Finished·running.130 Finished·running.
132 i19·:·h#"statistics"131 i19·:·h#"statistics"
  
133 o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug132 o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug
134 --silent··-q··<"/tmp/M2-1221558-0/4.m2"·>"/tmp/M2-1221558-0/4.out"·2>&1"133 --silent··-q··<"/tmp/M2-1244714-0/4.m2"·>"/tmp/M2-1244714-0/4.out"·2>&1"
135 ··············User·time·(seconds):·4.81134 ··············User·time·(seconds):·5.01
136 ··············System·time·(seconds):·0.10135 ··············System·time·(seconds):·0.25
137 ··············Percent·of·CPU·this·job·got:·79%136 ··············Percent·of·CPU·this·job·got:·36%
138 ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:06.18137 ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:14.32
139 ··············Average·shared·text·size·(kbytes):·0138 ··············Average·shared·text·size·(kbytes):·0
140 ··············Average·unshared·data·size·(kbytes):·0139 ··············Average·unshared·data·size·(kbytes):·0
141 ··············Average·stack·size·(kbytes):·0140 ··············Average·stack·size·(kbytes):·0
142 ··············Average·total·size·(kbytes):·0141 ··············Average·total·size·(kbytes):·0
143 ··············Maximum·resident·set·size·(kbytes):·303832142 ··············Maximum·resident·set·size·(kbytes):·300816
144 ··············Average·resident·set·size·(kbytes):·0143 ··············Average·resident·set·size·(kbytes):·0
145 ··············Major·(requiring·I/O)·page·faults:·0144 ··············Major·(requiring·I/O)·page·faults:·0
146 ··············Minor·(reclaiming·a·frame)·page·faults:·10596145 ··············Minor·(reclaiming·a·frame)·page·faults:·70623
147 ··············Voluntary·context·switches:·2800146 ··············Voluntary·context·switches:·5325
148 ··············Involuntary·context·switches:·659147 ··············Involuntary·context·switches:·2894
149 ··············Swaps:·0148 ··············Swaps:·0
150 ··············File·system·inputs:·0149 ··············File·system·inputs:·0
151 ··············File·system·outputs:·24150 ··············File·system·outputs:·24
152 ··············Socket·messages·sent:·0151 ··············Socket·messages·sent:·0
153 ··············Socket·messages·received:·0152 ··············Socket·messages·received:·0
154 ··············Signals·delivered:·0153 ··············Signals·delivered:·0
155 ··············Page·size·(bytes):·4096154 ··············Page·size·(bytes):·4096
156 ··············Exit·status:·0155 ··············Exit·status:·0
Max diff block lines reached; 3300/9830 bytes (33.57%) of diff not shown.
739 B
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735 B
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741 B
./usr/share/doc/Macaulay2/SLPexpressions/dump/rawdocumentation.dump
    
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1.14 KB
./usr/share/doc/Macaulay2/SLPexpressions/example-output/___S__L__Pexpressions.out
    
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30 ············································)30 ············································)
  
31 ··························"variable·positions"·=>·{-1}31 ··························"variable·positions"·=>·{-1}
  
32 o5·:·InterpretedSLProgram32 o5·:·InterpretedSLProgram
  
33 i6·:·time·A·=·evaluate(slp,matrix{{1}});33 i6·:·time·A·=·evaluate(slp,matrix{{1}});
34 ·--·used·0.0015623s·(cpu);·0.000170276s·(thread);·0s·(gc)34 ·--·used·1.7714e-05s·(cpu);·0.000249598s·(thread);·0s·(gc)
  
35 ··············1·······135 ··············1·······1
36 o6·:·Matrix·ZZ··<--·ZZ36 o6·:·Matrix·ZZ··<--·ZZ
  
37 i7·:·ZZ[y];37 i7·:·ZZ[y];
  
38 i8·:·time·B·=·sub((y+1)^(2^n),{y=>1})38 i8·:·time·B·=·sub((y+1)^(2^n),{y=>1})
39 ·--·used·3.20377s·(cpu);·2.53982s·(thread);·0s·(gc)39 ·--·used·3.52825s·(cpu);·2.62728s·(thread);·0s·(gc)
  
40 o8·=·10443888814131525066917527107166243825799642490473837803842334832839539040 o8·=·104438888141315250669175271071662438257996424904738378038423348328395390
41 ·····79715574568488268119349975583408901067144392628379875734381857936072632341 ·····797155745684882681193499755834089010671443926283798757343818579360726323
42 ·····60878513652779459569765437099983403615901343837183144280700118559462263742 ·····608785136527794595697654370999834036159013438371831442807001185594622637
43 ·····63188393977127456723346843445866174968079087058037040712840487401186091143 ·····631883939771274567233468434458661749680790870580370407128404874011860911
44 ·····44679777835980290066869389768817877859469056301902609405995794534328234644 ·····446797778359802900668693897688178778594690563019026094059957945343282346
45 ·····93030266964430590250159723998677142155416938355598852914863182379144344945 ·····930302669644305902501597239986771421554169383555988529148631823791443449
2.44 KB
./usr/share/doc/Macaulay2/SLPexpressions/html/index.html
    
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104 o5·:·InterpretedSLProgram</code></pre>104 o5·:·InterpretedSLProgram</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i6·:·time·A·=·evaluate(slp,matrix{{1}});109 ··············<pre><code·class="language-macaulay2">i6·:·time·A·=·evaluate(slp,matrix{{1}});
110 ·--·used·0.0015623s·(cpu);·0.000170276s·(thread);·0s·(gc)110 ·--·used·1.7714e-05s·(cpu);·0.000249598s·(thread);·0s·(gc)
  
111 ··············1·······1111 ··············1·······1
112 o6·:·Matrix·ZZ··&lt;--·ZZ</code></pre>112 o6·:·Matrix·ZZ··&lt;--·ZZ</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i7·:·ZZ[y];</code></pre>117 ··············<pre><code·class="language-macaulay2">i7·:·ZZ[y];</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i8·:·time·B·=·sub((y+1)^(2^n),{y=>1})122 ··············<pre><code·class="language-macaulay2">i8·:·time·B·=·sub((y+1)^(2^n),{y=>1})
123 ·--·used·3.20377s·(cpu);·2.53982s·(thread);·0s·(gc)123 ·--·used·3.52825s·(cpu);·2.62728s·(thread);·0s·(gc)
  
124 o8·=·104438888141315250669175271071662438257996424904738378038423348328395390124 o8·=·104438888141315250669175271071662438257996424904738378038423348328395390
125 ·····797155745684882681193499755834089010671443926283798757343818579360726323125 ·····797155745684882681193499755834089010671443926283798757343818579360726323
126 ·····608785136527794595697654370999834036159013438371831442807001185594622637126 ·····608785136527794595697654370999834036159013438371831442807001185594622637
127 ·····631883939771274567233468434458661749680790870580370407128404874011860911127 ·····631883939771274567233468434458661749680790870580370407128404874011860911
128 ·····446797778359802900668693897688178778594690563019026094059957945343282346128 ·····446797778359802900668693897688178778594690563019026094059957945343282346
129 ·····930302669644305902501597239986771421554169383555988529148631823791443449129 ·····930302669644305902501597239986771421554169383555988529148631823791443449
1.06 KB
html2text {}
    
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38 ············································output·nodes:·138 ············································output·nodes:·1
39 ············································)39 ············································)
  
40 ··························"variable·positions"·=>·{-1}40 ··························"variable·positions"·=>·{-1}
  
41 o5·:·InterpretedSLProgram41 o5·:·InterpretedSLProgram
42 i6·:·time·A·=·evaluate(slp,matrix{{1}});42 i6·:·time·A·=·evaluate(slp,matrix{{1}});
43 ·--·used·0.0015623s·(cpu);·0.000170276s·(thread);·0s·(gc)43 ·--·used·1.7714e-05s·(cpu);·0.000249598s·(thread);·0s·(gc)
  
44 ··············1·······144 ··············1·······1
45 o6·:·Matrix·ZZ··<--·ZZ45 o6·:·Matrix·ZZ··<--·ZZ
46 i7·:·ZZ[y];46 i7·:·ZZ[y];
47 i8·:·time·B·=·sub((y+1)^(2^n),{y=>1})47 i8·:·time·B·=·sub((y+1)^(2^n),{y=>1})
48 ·--·used·3.20377s·(cpu);·2.53982s·(thread);·0s·(gc)48 ·--·used·3.52825s·(cpu);·2.62728s·(thread);·0s·(gc)
  
49 o8·=·10443888814131525066917527107166243825799642490473837803842334832839539049 o8·=·104438888141315250669175271071662438257996424904738378038423348328395390
50 ·····79715574568488268119349975583408901067144392628379875734381857936072632350 ·····797155745684882681193499755834089010671443926283798757343818579360726323
51 ·····60878513652779459569765437099983403615901343837183144280700118559462263751 ·····608785136527794595697654370999834036159013438371831442807001185594622637
52 ·····63188393977127456723346843445866174968079087058037040712840487401186091152 ·····631883939771274567233468434458661749680790870580370407128404874011860911
53 ·····44679777835980290066869389768817877859469056301902609405995794534328234653 ·····446797778359802900668693897688178778594690563019026094059957945343282346
54 ·····93030266964430590250159723998677142155416938355598852914863182379144344954 ·····930302669644305902501597239986771421554169383555988529148631823791443449
766 B
./usr/share/doc/Macaulay2/SLnEquivariantMatrices/dump/rawdocumentation.dump
    
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758 B
./usr/share/doc/Macaulay2/SRdeformations/dump/rawdocumentation.dump
    
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2 #:version=1.12 #:version=1.1
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696 B
./usr/share/doc/Macaulay2/SRdeformations/example-output/___Complex.out
    
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56 o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)56 o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)
57 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·157 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1
  
58 i8·:·complement·C58 i8·:·complement·C
  
59 o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··59 o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··
60 ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·260 ·········3·4·5··1·4·5··2·1·5··2·3·4··3·0·4··1·0·4··2·3·1··2·1·0
  
61 o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)61 o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)
62 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·162 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1
  
63 i9·:·R=QQ[x_0..x_5]63 i9·:·R=QQ[x_0..x_5]
  
64 o9·=·R64 o9·=·R
1.32 KB
./usr/share/doc/Macaulay2/SRdeformations/html/___Complex.html
    
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168 ············</td>168 ············</td>
169 ··········</tr>169 ··········</tr>
170 ··········<tr>170 ··········<tr>
171 ············<td>171 ············<td>
172 ··············<pre><code·class="language-macaulay2">i8·:·complement·C172 ··············<pre><code·class="language-macaulay2">i8·:·complement·C
  
173 o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··173 o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··
174 ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·2174 ·········3·4·5··1·4·5··2·1·5··2·3·4··3·0·4··1·0·4··2·3·1··2·1·0
  
175 o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)175 o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)
176 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre>176 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre>
177 ············</td>177 ············</td>
178 ··········</tr>178 ··········</tr>
179 ········</table>179 ········</table>
180 ········<div>180 ········<div>
641 B
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95 ·········0·1·2··0·1·4··0·3·4··1·2·3··1·2·5··1·4·5··2·3·4··3·4·595 ·········0·1·2··0·1·4··0·3·4··1·2·3··1·2·5··1·4·5··2·3·4··3·4·5
  
96 o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)96 o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)
97 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·197 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1
98 i8·:·complement·C98 i8·:·complement·C
  
99 o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x99 o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x
100 ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·2100 ·········3·4·5··1·4·5··2·1·5··2·3·4··3·0·4··1·0·4··2·3·1··2·1·0
  
101 o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)101 o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets)
102 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1102 ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1
103 i9·:·R=QQ[x_0..x_5]103 i9·:·R=QQ[x_0..x_5]
  
104 o9·=·R104 o9·=·R
  
726 B
./usr/share/doc/Macaulay2/SVDComplexes/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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6 #·End·of·header6 #·End·of·header
7 #:len=107 #:len=10
8 U1ZEQ29tcGxleA==8 U1ZEQ29tcGxleA==
9 #:len=31509 #:len=3150
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZSB0aGUgU1ZEIGRlY29tcG9z10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZSB0aGUgU1ZEIGRlY29tcG9z
11 aXRpb24gb2YgYSBjaGFpbkNvbXBsZXggb3ZlciBSUiIsICJsaW5lbnVtIiA9PiAxMTAyLCBJbnB111 aXRpb24gb2YgYSBjaGFpbkNvbXBsZXggb3ZlciBSUiIsICJsaW5lbnVtIiA9PiAxMTAyLCBJbnB1
1.19 KB
./usr/share/doc/Macaulay2/SVDComplexes/example-output/___S__V__D__Complex.out
    
Offset 15, 15 lines modifiedOffset 15, 15 lines modified
15 i3·:·r={5,11,3,2}15 i3·:·r={5,11,3,2}
  
16 o3·=·{5,·11,·3,·2}16 o3·=·{5,·11,·3,·2}
  
17 o3·:·List17 o3·:·List
  
18 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4)18 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4)
19 ·--·.00566794s·elapsed19 ·--·.0289456s·elapsed
  
20 ·······6·······19·······19·······7·······320 ·······6·······19·······19·······7·······3
21 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ21 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ
22 ········································22 ········································
23 ·····0·······1········2········3·······423 ·····0·······1········2········3·······4
  
24 o4·:·ChainComplex24 o4·:·ChainComplex
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51 ·······53········53·········53·········53········5351 ·······53········53·········53·········53········53
52 ················································52 ················································
53 ·····-1········0··········1··········2·········353 ·····-1········0··········1··········2·········3
  
54 o6·:·ChainComplex54 o6·:·ChainComplex
  
55 i7·:·elapsedTime·(h,U)=SVDComplex·CR;55 i7·:·elapsedTime·(h,U)=SVDComplex·CR;
56 ·--·.00203268s·elapsed56 ·--·.00234315s·elapsed
  
57 i8·:·h57 i8·:·h
  
58 o8·=·HashTable{-1·=>·1}58 o8·=·HashTable{-1·=>·1}
59 ···············0·=>·359 ···············0·=>·3
60 ···············1·=>·560 ···············1·=>·5
61 ···············2·=>·261 ···············2·=>·2
Offset 95, 15 lines modifiedOffset 95, 15 lines modified
95 i12·:·maximalEntry·chainComplex·errors95 i12·:·maximalEntry·chainComplex·errors
  
96 o12·=·{8.43769e-15,·6.39488e-14,·1.06581e-13,·9.76996e-15}96 o12·=·{8.43769e-15,·6.39488e-14,·1.06581e-13,·9.76996e-15}
  
97 o12·:·List97 o12·:·List
  
98 i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian);98 i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian);
99 ·--·.00434274s·elapsed99 ·--·.0331287s·elapsed
  
100 i14·:·hL·===·h100 i14·:·hL·===·h
  
101 o14·=·true101 o14·=·true
  
102 i15·:·SigmaL·=source·U;102 i15·:·SigmaL·=source·U;
  
1.41 KB
./usr/share/doc/Macaulay2/SVDComplexes/example-output/___S__V__D__Homology.out
    
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15 i3·:·r={4,3,3}15 i3·:·r={4,3,3}
  
16 o3·=·{4,·3,·3}16 o3·=·{4,·3,·3}
  
17 o3·:·List17 o3·:·List
  
18 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)18 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
19 ·--·.00256367s·elapsed19 ·--·.00658502s·elapsed
  
20 ·······5·······10·······11·······520 ·······5·······10·······11·······5
21 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ21 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
22 ································22 ································
23 ·····0·······1········2········323 ·····0·······1········2········3
  
24 o4·:·ChainComplex24 o4·:·ChainComplex
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47 ·······53········53·········53·········5347 ·······53········53·········53·········53
48 ······································48 ······································
49 ·····0·········1··········2··········349 ·····0·········1··········2··········3
  
50 o6·:·ChainComplex50 o6·:·ChainComplex
  
51 i7·:·elapsedTime·(h,h1)=SVDHomology·CR51 i7·:·elapsedTime·(h,h1)=SVDHomology·CR
52 ·--·.000693606s·elapsed52 ·--·.000598192s·elapsed
  
53 o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········})53 o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········})
54 ················1·=>·3·············2·=>·(37.9214,·30.3707,·1.61954e-14)54 ················1·=>·3·············2·=>·(37.9214,·30.3707,·1.61954e-14)
55 ················2·=>·5·············3·=>·(14.972,·8.57847,·3.90646e-15)55 ················2·=>·5·············3·=>·(14.972,·8.57847,·3.90646e-15)
56 ················3·=>·256 ················3·=>·2
  
57 o7·:·Sequence57 o7·:·Sequence
  
58 i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian)58 i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian)
59 ·--·.00126526s·elapsed59 ·--·.00117002s·elapsed
  
60 o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······})60 o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······})
61 ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13)61 ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13)
62 ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13)62 ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13)
63 ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13)63 ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13)
  
64 o8·:·Sequence64 o8·:·Sequence
498 B
./usr/share/doc/Macaulay2/SVDComplexes/example-output/_common__Entries.out
    
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18 i4·:·r={4,3,5}18 i4·:·r={4,3,5}
  
19 o4·=·{4,·3,·5}19 o4·=·{4,·3,·5}
  
20 o4·:·List20 o4·:·List
  
21 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true)21 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true)
22 ·--·.00323436s·elapsed22 ·--·.00760726s·elapsed
  
23 ·······6·······10·······13·······823 ·······6·······10·······13·······8
24 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ24 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
25 ································25 ································
26 ·····0·······1········2········326 ·····0·······1········2········3
  
27 o5·:·ChainComplex27 o5·:·ChainComplex
502 B
./usr/share/doc/Macaulay2/SVDComplexes/example-output/_euclidean__Distance.out
    
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18 i4·:·r={4,3,3}18 i4·:·r={4,3,3}
  
19 o4·=·{4,·3,·3}19 o4·=·{4,·3,·3}
  
20 o4·:·List20 o4·:·List
  
21 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)21 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
22 ·--·.00249562s·elapsed22 ·--·.002672s·elapsed
  
23 ·······6·······10·······11·······523 ·······6·······10·······11·······5
24 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ24 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
25 ································25 ································
26 ·····0·······1········2········326 ·····0·······1········2········3
  
27 o5·:·ChainComplex27 o5·:·ChainComplex
506 B
./usr/share/doc/Macaulay2/SVDComplexes/example-output/_project__To__Complex.out
    
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18 i4·:·r={4,3,3}18 i4·:·r={4,3,3}
  
19 o4·=·{4,·3,·3}19 o4·=·{4,·3,·3}
  
20 o4·:·List20 o4·:·List
  
21 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)21 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
22 ·--·.00257691s·elapsed22 ·--·.00244388s·elapsed
  
23 ·······6·······10·······11·······523 ·······6·······10·······11·······5
24 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ24 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
25 ································25 ································
26 ·····0·······1········2········326 ·····0·······1········2········3
  
27 o5·:·ChainComplex27 o5·:·ChainComplex
2.73 KB
./usr/share/doc/Macaulay2/SVDComplexes/html/___S__V__D__Complex.html
    
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105 o3·:·List</code></pre>105 o3·:·List</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ··········<tr>108 ··········<tr>
109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4)110 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4)
111 ·--·.00566794s·elapsed111 ·--·.0289456s·elapsed
  
112 ·······6·······19·······19·······7·······3112 ·······6·······19·······19·······7·······3
113 o4·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ··&lt;--·ZZ113 o4·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ··&lt;--·ZZ
114 ········································114 ········································
115 ·····0·······1········2········3·······4115 ·····0·······1········2········3·······4
  
116 o4·:·ChainComplex</code></pre>116 o4·:·ChainComplex</code></pre>
Offset 150, 15 lines modifiedOffset 150, 15 lines modified
  
150 o6·:·ChainComplex</code></pre>150 o6·:·ChainComplex</code></pre>
151 ············</td>151 ············</td>
152 ··········</tr>152 ··········</tr>
153 ··········<tr>153 ··········<tr>
154 ············<td>154 ············<td>
155 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,U)=SVDComplex·CR;155 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,U)=SVDComplex·CR;
156 ·--·.00203268s·elapsed</code></pre>156 ·--·.00234315s·elapsed</code></pre>
157 ············</td>157 ············</td>
158 ··········</tr>158 ··········</tr>
159 ··········<tr>159 ··········<tr>
160 ············<td>160 ············<td>
161 ··············<pre><code·class="language-macaulay2">i8·:·h161 ··············<pre><code·class="language-macaulay2">i8·:·h
  
162 o8·=·HashTable{-1·=>·1}162 o8·=·HashTable{-1·=>·1}
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212 o12·:·List</code></pre>212 o12·:·List</code></pre>
213 ············</td>213 ············</td>
214 ··········</tr>214 ··········</tr>
215 ··········<tr>215 ··········<tr>
216 ············<td>216 ············<td>
217 ··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian);217 ··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian);
218 ·--·.00434274s·elapsed</code></pre>218 ·--·.0331287s·elapsed</code></pre>
219 ············</td>219 ············</td>
220 ··········</tr>220 ··········</tr>
221 ··········<tr>221 ··········<tr>
222 ············<td>222 ············<td>
223 ··············<pre><code·class="language-macaulay2">i14·:·hL·===·h223 ··············<pre><code·class="language-macaulay2">i14·:·hL·===·h
  
224 o14·=·true</code></pre>224 o14·=·true</code></pre>
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37 o2·:·List37 o2·:·List
38 i3·:·r={5,11,3,2}38 i3·:·r={5,11,3,2}
  
39 o3·=·{5,·11,·3,·2}39 o3·=·{5,·11,·3,·2}
  
40 o3·:·List40 o3·:·List
41 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4)41 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4)
42 ·--·.00566794s·elapsed42 ·--·.0289456s·elapsed
  
43 ·······6·······19·······19·······7·······343 ·······6·······19·······19·······7·······3
44 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ44 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ
  
45 ·····0·······1········2········3·······445 ·····0·······1········2········3·······4
  
46 o4·:·ChainComplex46 o4·:·ChainComplex
Offset 70, 15 lines modifiedOffset 70, 15 lines modified
70 o6·=·RR····<--·RR·····<--·RR·····<--·RR····<--·RR70 o6·=·RR····<--·RR·····<--·RR·····<--·RR····<--·RR
71 ·······53········53·········53·········53········5371 ·······53········53·········53·········53········53
  
72 ·····-1········0··········1··········2·········372 ·····-1········0··········1··········2·········3
  
73 o6·:·ChainComplex73 o6·:·ChainComplex
74 i7·:·elapsedTime·(h,U)=SVDComplex·CR;74 i7·:·elapsedTime·(h,U)=SVDComplex·CR;
75 ·--·.00203268s·elapsed75 ·--·.00234315s·elapsed
76 i8·:·h76 i8·:·h
  
77 o8·=·HashTable{-1·=>·1}77 o8·=·HashTable{-1·=>·1}
78 ···············0·=>·378 ···············0·=>·3
79 ···············1·=>·579 ···············1·=>·5
80 ···············2·=>·280 ···············2·=>·2
81 ···············3·=>·181 ···············3·=>·1
Offset 109, 15 lines modifiedOffset 109, 15 lines modified
109 1)*Sigma.dd_ell*transpose·U_ell);109 1)*Sigma.dd_ell*transpose·U_ell);
110 i12·:·maximalEntry·chainComplex·errors110 i12·:·maximalEntry·chainComplex·errors
  
111 o12·=·{8.43769e-15,·6.39488e-14,·1.06581e-13,·9.76996e-15}111 o12·=·{8.43769e-15,·6.39488e-14,·1.06581e-13,·9.76996e-15}
  
112 o12·:·List112 o12·:·List
113 i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian);113 i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian);
114 ·--·.00434274s·elapsed114 ·--·.0331287s·elapsed
115 i14·:·hL·===·h115 i14·:·hL·===·h
  
116 o14·=·true116 o14·=·true
117 i15·:·SigmaL·=source·U;117 i15·:·SigmaL·=source·U;
118 i16·:·for·i·from·min·CR+1·to·max·CR·list·maximalEntry(SigmaL.dd_i·-Sigma.dd_i)118 i16·:·for·i·from·min·CR+1·to·max·CR·list·maximalEntry(SigmaL.dd_i·-Sigma.dd_i)
  
119 o16·=·{1.77636e-14,·6.39488e-14,·8.52651e-14,·3.55271e-15}119 o16·=·{1.77636e-14,·6.39488e-14,·8.52651e-14,·3.55271e-15}
2.92 KB
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107 o3·:·List</code></pre>107 o3·:·List</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)112 ··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
113 ·--·.00256367s·elapsed113 ·--·.00658502s·elapsed
  
114 ·······5·······10·······11·······5114 ·······5·······10·······11·······5
115 o4·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ115 o4·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ
116 ································116 ································
117 ·····0·······1········2········3117 ·····0·······1········2········3
  
118 o4·:·ChainComplex</code></pre>118 o4·:·ChainComplex</code></pre>
Offset 148, 28 lines modifiedOffset 148, 28 lines modified
  
148 o6·:·ChainComplex</code></pre>148 o6·:·ChainComplex</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
152 ············<td>152 ············<td>
153 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,h1)=SVDHomology·CR153 ··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,h1)=SVDHomology·CR
154 ·--·.000693606s·elapsed154 ·--·.000598192s·elapsed
  
155 o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········})155 o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········})
156 ················1·=>·3·············2·=>·(37.9214,·30.3707,·1.61954e-14)156 ················1·=>·3·············2·=>·(37.9214,·30.3707,·1.61954e-14)
157 ················2·=>·5·············3·=>·(14.972,·8.57847,·3.90646e-15)157 ················2·=>·5·············3·=>·(14.972,·8.57847,·3.90646e-15)
158 ················3·=>·2158 ················3·=>·2
  
159 o7·:·Sequence</code></pre>159 o7·:·Sequence</code></pre>
160 ············</td>160 ············</td>
161 ··········</tr>161 ··········</tr>
162 ··········<tr>162 ··········<tr>
163 ············<td>163 ············<td>
164 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian)164 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian)
165 ·--·.00126526s·elapsed165 ·--·.00117002s·elapsed
  
166 o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······})166 o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······})
167 ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13)167 ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13)
168 ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13)168 ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13)
169 ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13)169 ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13)
  
170 o8·:·Sequence</code></pre>170 o8·:·Sequence</code></pre>
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Offset 40, 15 lines modifiedOffset 40, 15 lines modified
40 o2·:·List40 o2·:·List
41 i3·:·r={4,3,3}41 i3·:·r={4,3,3}
  
42 o3·=·{4,·3,·3}42 o3·=·{4,·3,·3}
  
43 o3·:·List43 o3·:·List
44 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)44 i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
45 ·--·.00256367s·elapsed45 ·--·.00658502s·elapsed
  
46 ·······5·······10·······11·······546 ·······5·······10·······11·······5
47 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ47 o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
  
48 ·····0·······1········2········348 ·····0·······1········2········3
  
49 o4·:·ChainComplex49 o4·:·ChainComplex
Offset 69, 24 lines modifiedOffset 69, 24 lines modified
69 o6·=·RR····<--·RR·····<--·RR·····<--·RR69 o6·=·RR····<--·RR·····<--·RR·····<--·RR
70 ·······53········53·········53·········5370 ·······53········53·········53·········53
  
71 ·····0·········1··········2··········371 ·····0·········1··········2··········3
  
72 o6·:·ChainComplex72 o6·:·ChainComplex
73 i7·:·elapsedTime·(h,h1)=SVDHomology·CR73 i7·:·elapsedTime·(h,h1)=SVDHomology·CR
74 ·--·.000693606s·elapsed74 ·--·.000598192s·elapsed
  
75 o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········})75 o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········})
76 ················1·=>·3·············2·=>·(37.9214,·30.3707,·1.61954e-14)76 ················1·=>·3·············2·=>·(37.9214,·30.3707,·1.61954e-14)
77 ················2·=>·5·············3·=>·(14.972,·8.57847,·3.90646e-15)77 ················2·=>·5·············3·=>·(14.972,·8.57847,·3.90646e-15)
78 ················3·=>·278 ················3·=>·2
  
79 o7·:·Sequence79 o7·:·Sequence
80 i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian)80 i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian)
81 ·--·.00126526s·elapsed81 ·--·.00117002s·elapsed
  
82 o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······})82 o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······})
83 ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13)83 ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13)
84 ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13)84 ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13)
85 ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13)85 ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13)
  
86 o8·:·Sequence86 o8·:·Sequence
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110 o4·:·List</code></pre>110 o4·:·List</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true)115 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true)
116 ·--·.00323436s·elapsed116 ·--·.00760726s·elapsed
  
117 ·······6·······10·······13·······8117 ·······6·······10·······13·······8
118 o5·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ118 o5·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ
119 ································119 ································
120 ·····0·······1········2········3120 ·····0·······1········2········3
  
121 o5·:·ChainComplex</code></pre>121 o5·:·ChainComplex</code></pre>
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34 o3·:·List34 o3·:·List
35 i4·:·r={4,3,5}35 i4·:·r={4,3,5}
  
36 o4·=·{4,·3,·5}36 o4·=·{4,·3,·5}
  
37 o4·:·List37 o4·:·List
38 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true)38 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true)
39 ·--·.00323436s·elapsed39 ·--·.00760726s·elapsed
  
40 ·······6·······10·······13·······840 ·······6·······10·······13·······8
41 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ41 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
  
42 ·····0·······1········2········342 ·····0·······1········2········3
  
43 o5·:·ChainComplex43 o5·:·ChainComplex
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Offset 104, 15 lines modifiedOffset 104, 15 lines modified
  
104 o4·:·List</code></pre>104 o4·:·List</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)109 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
110 ·--·.00249562s·elapsed110 ·--·.002672s·elapsed
  
111 ·······6·······10·······11·······5111 ·······6·······10·······11·······5
112 o5·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ112 o5·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ
113 ································113 ································
114 ·····0·······1········2········3114 ·····0·······1········2········3
  
115 o5·:·ChainComplex</code></pre>115 o5·:·ChainComplex</code></pre>
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29 o3·:·List29 o3·:·List
30 i4·:·r={4,3,3}30 i4·:·r={4,3,3}
  
31 o4·=·{4,·3,·3}31 o4·=·{4,·3,·3}
  
32 o4·:·List32 o4·:·List
33 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)33 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
34 ·--·.00249562s·elapsed34 ·--·.002672s·elapsed
  
35 ·······6·······10·······11·······535 ·······6·······10·······11·······5
36 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ36 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
  
37 ·····0·······1········2········337 ·····0·······1········2········3
  
38 o5·:·ChainComplex38 o5·:·ChainComplex
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Offset 104, 15 lines modifiedOffset 104, 15 lines modified
  
104 o4·:·List</code></pre>104 o4·:·List</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)109 ··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
110 ·--·.00257691s·elapsed110 ·--·.00244388s·elapsed
  
111 ·······6·······10·······11·······5111 ·······6·······10·······11·······5
112 o5·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ112 o5·=·ZZ··&lt;--·ZZ···&lt;--·ZZ···&lt;--·ZZ
113 ································113 ································
114 ·····0·······1········2········3114 ·····0·······1········2········3
  
115 o5·:·ChainComplex</code></pre>115 o5·:·ChainComplex</code></pre>
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29 o3·:·List29 o3·:·List
30 i4·:·r={4,3,3}30 i4·:·r={4,3,3}
  
31 o4·=·{4,·3,·3}31 o4·=·{4,·3,·3}
  
32 o4·:·List32 o4·:·List
33 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)33 i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true)
34 ·--·.00257691s·elapsed34 ·--·.00244388s·elapsed
  
35 ·······6·······10·······11·······535 ·······6·······10·······11·······5
36 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ36 o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ
  
37 ·····0·······1········2········337 ·····0·······1········2········3
  
38 o5·:·ChainComplex38 o5·:·ChainComplex
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8 d2VpZ2h0VmVjdG9yc1JlYWxpemluZ1NBR0JJ8 d2VpZ2h0VmVjdG9yc1JlYWxpemluZ1NBR0JJ
9 #:len=18199 #:len=1819
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVGhlIG1haW4gZnVuY3Rpb24gZm9yIGRl10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVGhlIG1haW4gZnVuY3Rpb24gZm9yIGRl
11 dGVjdGluZyBTQUdCSSBiYXNlcyIsICJsaW5lbnVtIiA9PiAyMTUsIElucHV0cyA9PiB7U1BBTntU11 dGVjdGluZyBTQUdCSSBiYXNlcyIsICJsaW5lbnVtIiA9PiAyMTUsIElucHV0cyA9PiB7U1BBTntU
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOSwgInVuZG9jdW1lbnRlZCIgPT4gdHJ110 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOSwgInVuZG9jdW1lbnRlZCIgPT4gdHJ1
11 ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2F0dXJhdGUs11 ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2F0dXJhdGUs
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38 o5·:·Ideal·of·S38 o5·:·Ideal·of·S
  
39 i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5));39 i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5));
  
40 o6·:·Ideal·of·S40 o6·:·Ideal·of·S
  
41 i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate);41 i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate);
42 ·--·used·0.310093s·(cpu);·0.26042s·(thread);·0s·(gc)42 ·--·used·0.383689s·(cpu);·0.341937s·(thread);·0s·(gc)
  
43 o7·:·Ideal·of·S43 o7·:·Ideal·of·S
  
44 i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient);44 i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient);
45 ·--·used·0.47579s·(cpu);·0.427822s·(thread);·0s·(gc)45 ·--·used·0.549887s·(cpu);·0.48454s·(thread);·0s·(gc)
  
46 o8·:·Ideal·of·S46 o8·:·Ideal·of·S
  
47 i9·:·S·=·ZZ/101[vars(0..4)];47 i9·:·S·=·ZZ/101[vars(0..4)];
  
48 i10·:·I·=·ideal·vars·S;48 i10·:·I·=·ideal·vars·S;
  
49 o10·:·Ideal·of·S49 o10·:·Ideal·of·S
  
50 i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate);50 i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate);
51 ·--·used·0.0199995s·(cpu);·0.0191814s·(thread);·0s·(gc)51 ·--·used·0.021851s·(cpu);·0.0232311s·(thread);·0s·(gc)
  
52 o11·:·Ideal·of·S52 o11·:·Ideal·of·S
  
53 i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient);53 i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient);
54 ·--·used·0.00376564s·(cpu);·0.00639922s·(thread);·0s·(gc)54 ·--·used·0.00415118s·(cpu);·0.00724792s·(thread);·0s·(gc)
  
55 o12·:·Ideal·of·S55 o12·:·Ideal·of·S
  
56 i13·:·56 i13·:·
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126 o6·:·Ideal·of·S</code></pre>126 o6·:·Ideal·of·S</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate);131 ··············<pre><code·class="language-macaulay2">i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate);
132 ·--·used·0.310093s·(cpu);·0.26042s·(thread);·0s·(gc)132 ·--·used·0.383689s·(cpu);·0.341937s·(thread);·0s·(gc)
  
133 o7·:·Ideal·of·S</code></pre>133 o7·:·Ideal·of·S</code></pre>
134 ············</td>134 ············</td>
135 ··········</tr>135 ··········</tr>
136 ··········<tr>136 ··········<tr>
137 ············<td>137 ············<td>
138 ··············<pre><code·class="language-macaulay2">i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient);138 ··············<pre><code·class="language-macaulay2">i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient);
139 ·--·used·0.47579s·(cpu);·0.427822s·(thread);·0s·(gc)139 ·--·used·0.549887s·(cpu);·0.48454s·(thread);·0s·(gc)
  
140 o8·:·Ideal·of·S</code></pre>140 o8·:·Ideal·of·S</code></pre>
141 ············</td>141 ············</td>
142 ··········</tr>142 ··········</tr>
143 ········</table>143 ········</table>
144 ········<div>144 ········<div>
145 ··········<p><span·class="tt">Strategy·=>·Quotient</span>·is·faster·in·other·cases:</p>145 ··········<p><span·class="tt">Strategy·=>·Quotient</span>·is·faster·in·other·cases:</p>
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159 o10·:·Ideal·of·S</code></pre>159 o10·:·Ideal·of·S</code></pre>
160 ············</td>160 ············</td>
161 ··········</tr>161 ··········</tr>
162 ··········<tr>162 ··········<tr>
163 ············<td>163 ············<td>
164 ··············<pre><code·class="language-macaulay2">i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate);164 ··············<pre><code·class="language-macaulay2">i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate);
165 ·--·used·0.0199995s·(cpu);·0.0191814s·(thread);·0s·(gc)165 ·--·used·0.021851s·(cpu);·0.0232311s·(thread);·0s·(gc)
  
166 o11·:·Ideal·of·S</code></pre>166 o11·:·Ideal·of·S</code></pre>
167 ············</td>167 ············</td>
168 ··········</tr>168 ··········</tr>
169 ··········<tr>169 ··········<tr>
170 ············<td>170 ············<td>
171 ··············<pre><code·class="language-macaulay2">i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient);171 ··············<pre><code·class="language-macaulay2">i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient);
172 ·--·used·0.00376564s·(cpu);·0.00639922s·(thread);·0s·(gc)172 ·--·used·0.00415118s·(cpu);·0.00724792s·(thread);·0s·(gc)
  
173 o12·:·Ideal·of·S</code></pre>173 o12·:·Ideal·of·S</code></pre>
174 ············</td>174 ············</td>
175 ··········</tr>175 ··········</tr>
176 ········</table>176 ········</table>
177 ······</div>177 ······</div>
178 ······<div>178 ······<div>
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57 i5·:·I·=·monomialCurveIdeal(S,·1..n-1);57 i5·:·I·=·monomialCurveIdeal(S,·1..n-1);
  
58 o5·:·Ideal·of·S58 o5·:·Ideal·of·S
59 i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5));59 i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5));
  
60 o6·:·Ideal·of·S60 o6·:·Ideal·of·S
61 i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate);61 i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate);
62 ·--·used·0.310093s·(cpu);·0.26042s·(thread);·0s·(gc)62 ·--·used·0.383689s·(cpu);·0.341937s·(thread);·0s·(gc)
  
63 o7·:·Ideal·of·S63 o7·:·Ideal·of·S
64 i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient);64 i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient);
65 ·--·used·0.47579s·(cpu);·0.427822s·(thread);·0s·(gc)65 ·--·used·0.549887s·(cpu);·0.48454s·(thread);·0s·(gc)
  
66 o8·:·Ideal·of·S66 o8·:·Ideal·of·S
67 Strategy·=>·Quotient·is·faster·in·other·cases:67 Strategy·=>·Quotient·is·faster·in·other·cases:
68 i9·:·S·=·ZZ/101[vars(0..4)];68 i9·:·S·=·ZZ/101[vars(0..4)];
69 i10·:·I·=·ideal·vars·S;69 i10·:·I·=·ideal·vars·S;
  
70 o10·:·Ideal·of·S70 o10·:·Ideal·of·S
71 i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate);71 i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate);
72 ·--·used·0.0199995s·(cpu);·0.0191814s·(thread);·0s·(gc)72 ·--·used·0.021851s·(cpu);·0.0232311s·(thread);·0s·(gc)
  
73 o11·:·Ideal·of·S73 o11·:·Ideal·of·S
74 i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient);74 i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient);
75 ·--·used·0.00376564s·(cpu);·0.00639922s·(thread);·0s·(gc)75 ·--·used·0.00415118s·(cpu);·0.00724792s·(thread);·0s·(gc)
  
76 o12·:·Ideal·of·S76 o12·:·Ideal·of·S
77 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*77 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8*
78 For·further·information·see·for·example·Exercise·15.41·in·Eisenbud's78 For·further·information·see·for·example·Exercise·15.41·in·Eisenbud's
79 Commutative·Algebra·with·a·View·Towards·Algebraic·Geometry.79 Commutative·Algebra·with·a·View·Towards·Algebraic·Geometry.
80 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·S\x8St\x8tr\x8ra\x8at\x8te\x8eg\x8gy\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*80 *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·S\x8St\x8tr\x8ra\x8at\x8te\x8eg\x8gy\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8*
81 ····*·addHook(...,Strategy=>...)·--·see·_\x8a_\x8d_\x8d_\x8H_\x8o_\x8o_\x8k·--·add·a·hook·function·to·an81 ····*·addHook(...,Strategy=>...)·--·see·_\x8a_\x8d_\x8d_\x8H_\x8o_\x8o_\x8k·--·add·a·hook·function·to·an
747 B
./usr/share/doc/Macaulay2/Schubert2/dump/rawdocumentation.dump
    
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1.48 KB
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40 ··········)40 ··········)
  
41 o6·=·f41 o6·=·f
  
42 o6·:·FunctionClosure42 o6·:·FunctionClosure
  
43 i7·:·for·n·from·2·to·10·list·time·f·n43 i7·:·for·n·from·2·to·10·list·time·f·n
44 ·--·used·0.00400187s·(cpu);·0.00384489s·(thread);·0s·(gc)44 ·--·used·0.00400354s·(cpu);·0.00616803s·(thread);·0s·(gc)
45 ·--·used·0.0611215s·(cpu);·0.0228292s·(thread);·0s·(gc) 
46 ·--·used·0.00582947s·(cpu);·0.00883061s·(thread);·0s·(gc) 
47 ·--·used·0.0145851s·(cpu);·0.0151256s·(thread);·0s·(gc)45 ·--·used·0.0714089s·(cpu);·0.0245727s·(thread);·0s·(gc)
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50 ·--·used·0.0750207s·(cpu);·0.0760107s·(thread);·0s·(gc)46 ·--·used·0.00830745s·(cpu);·0.0102879s·(thread);·0s·(gc)
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52 ·--·used·0.255708s·(cpu);·0.214829s·(thread);·0s·(gc)52 ·--·used·0.321979s·(cpu);·0.25137s·(thread);·0s·(gc)
  
53 o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,53 o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,
54 ·····------------------------------------------------------------------------54 ·····------------------------------------------------------------------------
55 ·····289139638632755625,·520764738758073845321}55 ·····289139638632755625,·520764738758073845321}
  
56 o7·:·List56 o7·:·List
  
3.07 KB
./usr/share/doc/Macaulay2/Schubert2/html/___Lines_spon_sphypersurfaces.html
    
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126 o6·:·FunctionClosure</code></pre>126 o6·:·FunctionClosure</code></pre>
127 ············</td>127 ············</td>
128 ··········</tr>128 ··········</tr>
129 ··········<tr>129 ··········<tr>
130 ············<td>130 ············<td>
131 ··············<pre><code·class="language-macaulay2">i7·:·for·n·from·2·to·10·list·time·f·n131 ··············<pre><code·class="language-macaulay2">i7·:·for·n·from·2·to·10·list·time·f·n
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134 ·--·used·0.00582947s·(cpu);·0.00883061s·(thread);·0s·(gc) 
135 ·--·used·0.0145851s·(cpu);·0.0151256s·(thread);·0s·(gc)133 ·--·used·0.0714089s·(cpu);·0.0245727s·(thread);·0s·(gc)
136 ·--·used·0.0255103s·(cpu);·0.0268049s·(thread);·0s·(gc) 
137 ·--·used·0.0447676s·(cpu);·0.0450233s·(thread);·0s·(gc) 
138 ·--·used·0.0750207s·(cpu);·0.0760107s·(thread);·0s·(gc)134 ·--·used·0.00830745s·(cpu);·0.0102879s·(thread);·0s·(gc)
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141 o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,141 o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,
142 ·····------------------------------------------------------------------------142 ·····------------------------------------------------------------------------
143 ·····289139638632755625,·520764738758073845321}143 ·····289139638632755625,·520764738758073845321}
  
144 o7·:·List</code></pre>144 o7·:·List</code></pre>
145 ············</td>145 ············</td>
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56 ··········integral·chern·symmetricPower_(2*n-3)·last·bundles·G56 ··········integral·chern·symmetricPower_(2*n-3)·last·bundles·G
57 ··········)57 ··········)
  
58 o6·=·f58 o6·=·f
  
59 o6·:·FunctionClosure59 o6·:·FunctionClosure
60 i7·:·for·n·from·2·to·10·list·time·f·n60 i7·:·for·n·from·2·to·10·list·time·f·n
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63 ·--·used·0.00582947s·(cpu);·0.00883061s·(thread);·0s·(gc) 
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66 ·--·used·0.0447676s·(cpu);·0.0450233s·(thread);·0s·(gc) 
67 ·--·used·0.0750207s·(cpu);·0.0760107s·(thread);·0s·(gc)63 ·--·used·0.00830745s·(cpu);·0.0102879s·(thread);·0s·(gc)
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70 o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,70 o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775,
71 ·····------------------------------------------------------------------------71 ·····------------------------------------------------------------------------
72 ·····289139638632755625,·520764738758073845321}72 ·····289139638632755625,·520764738758073845321}
  
73 o7·:·List73 o7·:·List
74 Note:·in·characteristic·zero,·using·Bertini's·theorem,·the·numbers·computed·can74 Note:·in·characteristic·zero,·using·Bertini's·theorem,·the·numbers·computed·can
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjQ0OSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjQ0OSwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2NodXJSZXNvbHV0aW9uLFJpbmdFbGVtZW50LExp11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2NodXJSZXNvbHV0aW9uLFJpbmdFbGVtZW50LExp
732 B
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./usr/share/doc/Macaulay2/SectionRing/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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6 #·End·of·header6 #·End·of·header
7 #:len=87 #:len=8
8 bVJlZ3VsYXI=8 bVJlZ3VsYXI=
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibVJlZ3VsYXIoRixHKSBjb21wdXRlcyB010 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibVJlZ3VsYXIoRixHKSBjb21wdXRlcyB0
11 aGUgcmVndWxhcml0eSBvZiBGIHdpdGggcmVzcGVjdCB0byBHIChnbG9iYWxseSBnZW5lcmF0ZWQp11 aGUgcmVndWxhcml0eSBvZiBGIHdpdGggcmVzcGVjdCB0byBHIChnbG9iYWxseSBnZW5lcmF0ZWQp
745 B
./usr/share/doc/Macaulay2/SegreClasses/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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7 #:len=267 #:len=26
8 bWFrZVByb2R1Y3RSaW5nKFJpbmcsTGlzdCk=8 bWFrZVByb2R1Y3RSaW5nKFJpbmcsTGlzdCk=
9 #:len=2779 #:len=277
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTQxLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTQxLCBzeW1ib2wgRG9jdW1lbnRUYWcg
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1000 B
./usr/share/doc/Macaulay2/SegreClasses/example-output/_is__Component__Contained.out
    
Offset 53, 15 lines modifiedOffset 53, 15 lines modified
53 o9·:·Ideal·of·R53 o9·:·Ideal·of·R
  
54 i10·:·X=((W)*ideal(y)+ideal(f));54 i10·:·X=((W)*ideal(y)+ideal(f));
  
55 o10·:·Ideal·of·R55 o10·:·Ideal·of·R
  
56 i11·:·time·isComponentContained(X,Y)56 i11·:·time·isComponentContained(X,Y)
57 ·--·used·36.7812s·(cpu);·6.77737s·(thread);·0s·(gc)57 ·--·used·35.0879s·(cpu);·6.65436s·(thread);·0s·(gc)
  
58 o11·=·true58 o11·=·true
  
59 i12·:·print·"we·could·confirm·this·with·the·computation:"59 i12·:·print·"we·could·confirm·this·with·the·computation:"
60 we·could·confirm·this·with·the·computation:60 we·could·confirm·this·with·the·computation:
  
61 i13·:·B=ideal(x)*ideal(y)*ideal(z)61 i13·:·B=ideal(x)*ideal(y)*ideal(z)
Offset 71, 12 lines modifiedOffset 71, 12 lines modified
71 ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g,71 ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g,
72 ······-----------------------------------------------------------------------72 ······-----------------------------------------------------------------------
73 ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i)73 ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i)
  
74 o13·:·Ideal·of·R74 o13·:·Ideal·of·R
  
75 i14·:·time·isSubset(saturate(Y,B),saturate(X,B))75 i14·:·time·isSubset(saturate(Y,B),saturate(X,B))
76 ·--·used·82.4154s·(cpu);·51.1568s·(thread);·0s·(gc)76 ·--·used·85.7408s·(cpu);·56.797s·(thread);·0s·(gc)
  
77 o14·=·true77 o14·=·true
  
78 i15·:·78 i15·:·
743 B
./usr/share/doc/Macaulay2/SegreClasses/example-output/_segre__Dim__X.out
    
Offset 23, 24 lines modifiedOffset 23, 24 lines modified
23 i5·:·A·=·makeChowRing(R)23 i5·:·A·=·makeChowRing(R)
  
24 o5·=·A24 o5·=·A
  
25 o5·:·QuotientRing25 o5·:·QuotientRing
  
26 i6·:·time·s·=·segreDimX(X,Y,A)26 i6·:·time·s·=·segreDimX(X,Y,A)
27 ·--·used·5.21891s·(cpu);·0.676154s·(thread);·0s·(gc)27 ·--·used·5.53241s·(cpu);·0.704565s·(thread);·0s·(gc)
  
28 ·······2·············228 ·······2·············2
29 o6·=·2H··+·4H·H··+·2H29 o6·=·2H··+·4H·H··+·2H
30 ·······1·····1·2·····230 ·······1·····1·2·····2
  
31 o6·:·A31 o6·:·A
  
32 i7·:·time·segre(X,Y,A)32 i7·:·time·segre(X,Y,A)
33 ·--·used·0.116048s·(cpu);·0.0917042s·(thread);·0s·(gc)33 ·--·used·0.457363s·(cpu);·0.117294s·(thread);·0s·(gc)
  
34 ········2·2·····2·········2·····2·············234 ········2·2·····2·········2·····2·············2
35 o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H35 o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H
36 ········1·2·····1·2·····1·2·····1·····1·2·····236 ········1·2·····1·2·····1·2·····1·····1·2·····2
  
37 o7·:·A37 o7·:·A
  
2.58 KB
./usr/share/doc/Macaulay2/SegreClasses/html/_is__Component__Contained.html
    
Offset 162, 15 lines modifiedOffset 162, 15 lines modified
  
162 o10·:·Ideal·of·R</code></pre>162 o10·:·Ideal·of·R</code></pre>
163 ············</td>163 ············</td>
164 ··········</tr>164 ··········</tr>
165 ··········<tr>165 ··········<tr>
166 ············<td>166 ············<td>
167 ··············<pre><code·class="language-macaulay2">i11·:·time·isComponentContained(X,Y)167 ··············<pre><code·class="language-macaulay2">i11·:·time·isComponentContained(X,Y)
168 ·--·used·36.7812s·(cpu);·6.77737s·(thread);·0s·(gc)168 ·--·used·35.0879s·(cpu);·6.65436s·(thread);·0s·(gc)
  
169 o11·=·true</code></pre>169 o11·=·true</code></pre>
170 ············</td>170 ············</td>
171 ··········</tr>171 ··········</tr>
172 ··········<tr>172 ··········<tr>
173 ············<td>173 ············<td>
174 ··············<pre><code·class="language-macaulay2">i12·:·print·&quot;we·could·confirm·this·with·the·computation:&quot;174 ··············<pre><code·class="language-macaulay2">i12·:·print·&quot;we·could·confirm·this·with·the·computation:&quot;
Offset 189, 15 lines modifiedOffset 189, 15 lines modified
  
189 o13·:·Ideal·of·R</code></pre>189 o13·:·Ideal·of·R</code></pre>
190 ············</td>190 ············</td>
191 ··········</tr>191 ··········</tr>
192 ··········<tr>192 ··········<tr>
193 ············<td>193 ············<td>
194 ··············<pre><code·class="language-macaulay2">i14·:·time·isSubset(saturate(Y,B),saturate(X,B))194 ··············<pre><code·class="language-macaulay2">i14·:·time·isSubset(saturate(Y,B),saturate(X,B))
195 ·--·used·82.4154s·(cpu);·51.1568s·(thread);·0s·(gc)195 ·--·used·85.7408s·(cpu);·56.797s·(thread);·0s·(gc)
  
196 o14·=·true</code></pre>196 o14·=·true</code></pre>
197 ············</td>197 ············</td>
198 ··········</tr>198 ··········</tr>
199 ········</table>199 ········</table>
200 ······</div>200 ······</div>
201 ······<div>201 ······<div>
1.48 KB
html2text {}
    
Offset 68, 30 lines modifiedOffset 68, 30 lines modified
68 i9·:·Y=ideal·(z_0*W_0-z_1*W_1)+ideal(f);68 i9·:·Y=ideal·(z_0*W_0-z_1*W_1)+ideal(f);
  
69 o9·:·Ideal·of·R69 o9·:·Ideal·of·R
70 i10·:·X=((W)*ideal(y)+ideal(f));70 i10·:·X=((W)*ideal(y)+ideal(f));
  
71 o10·:·Ideal·of·R71 o10·:·Ideal·of·R
72 i11·:·time·isComponentContained(X,Y)72 i11·:·time·isComponentContained(X,Y)
73 ·--·used·36.7812s·(cpu);·6.77737s·(thread);·0s·(gc)73 ·--·used·35.0879s·(cpu);·6.65436s·(thread);·0s·(gc)
  
74 o11·=·true74 o11·=·true
75 i12·:·print·"we·could·confirm·this·with·the·computation:"75 i12·:·print·"we·could·confirm·this·with·the·computation:"
76 we·could·confirm·this·with·the·computation:76 we·could·confirm·this·with·the·computation:
77 i13·:·B=ideal(x)*ideal(y)*ideal(z)77 i13·:·B=ideal(x)*ideal(y)*ideal(z)
  
78 o13·=·ideal·(a*d*g,·a*d*h,·a*d*i,·a*e*g,·a*e*h,·a*e*i,·a*f*g,·a*f*h,·a*f*i,78 o13·=·ideal·(a*d*g,·a*d*h,·a*d*i,·a*e*g,·a*e*h,·a*e*i,·a*f*g,·a*f*h,·a*f*i,
79 ······-----------------------------------------------------------------------79 ······-----------------------------------------------------------------------
80 ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g,80 ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g,
81 ······-----------------------------------------------------------------------81 ······-----------------------------------------------------------------------
82 ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i)82 ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i)
  
83 o13·:·Ideal·of·R83 o13·:·Ideal·of·R
84 i14·:·time·isSubset(saturate(Y,B),saturate(X,B))84 i14·:·time·isSubset(saturate(Y,B),saturate(X,B))
85 ·--·used·82.4154s·(cpu);·51.1568s·(thread);·0s·(gc)85 ·--·used·85.7408s·(cpu);·56.797s·(thread);·0s·(gc)
  
86 o14·=·true86 o14·=·true
87 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8tC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8ne\x8ed\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*87 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8tC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8ne\x8ed\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
88 ····*·isComponentContained(Ideal,Ideal)88 ····*·isComponentContained(Ideal,Ideal)
89 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*89 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
90 The·object·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8C_\x8o_\x8n_\x8t_\x8a_\x8i_\x8n_\x8e_\x8d·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.90 The·object·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8C_\x8o_\x8n_\x8t_\x8a_\x8i_\x8n_\x8e_\x8d·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s.
91 ===============================================================================91 ===============================================================================
1.67 KB
./usr/share/doc/Macaulay2/SegreClasses/html/_segre__Dim__X.html
    
Offset 118, 27 lines modifiedOffset 118, 27 lines modified
  
118 o5·:·QuotientRing</code></pre>118 o5·:·QuotientRing</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i6·:·time·s·=·segreDimX(X,Y,A)123 ··············<pre><code·class="language-macaulay2">i6·:·time·s·=·segreDimX(X,Y,A)
124 ·--·used·5.21891s·(cpu);·0.676154s·(thread);·0s·(gc)124 ·--·used·5.53241s·(cpu);·0.704565s·(thread);·0s·(gc)
  
125 ·······2·············2125 ·······2·············2
126 o6·=·2H··+·4H·H··+·2H126 o6·=·2H··+·4H·H··+·2H
127 ·······1·····1·2·····2127 ·······1·····1·2·····2
  
128 o6·:·A</code></pre>128 o6·:·A</code></pre>
129 ············</td>129 ············</td>
130 ··········</tr>130 ··········</tr>
131 ··········<tr>131 ··········<tr>
132 ············<td>132 ············<td>
133 ··············<pre><code·class="language-macaulay2">i7·:·time·segre(X,Y,A)133 ··············<pre><code·class="language-macaulay2">i7·:·time·segre(X,Y,A)
134 ·--·used·0.116048s·(cpu);·0.0917042s·(thread);·0s·(gc)134 ·--·used·0.457363s·(cpu);·0.117294s·(thread);·0s·(gc)
  
135 ········2·2·····2·········2·····2·············2135 ········2·2·····2·········2·····2·············2
136 o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H136 o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H
137 ········1·2·····1·2·····1·2·····1·····1·2·····2137 ········1·2·····1·2·····1·2·····1·····1·2·····2
  
138 o7·:·A</code></pre>138 o7·:·A</code></pre>
139 ············</td>139 ············</td>
728 B
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48 o4·:·Ideal·of·R48 o4·:·Ideal·of·R
49 i5·:·A·=·makeChowRing(R)49 i5·:·A·=·makeChowRing(R)
  
50 o5·=·A50 o5·=·A
  
51 o5·:·QuotientRing51 o5·:·QuotientRing
52 i6·:·time·s·=·segreDimX(X,Y,A)52 i6·:·time·s·=·segreDimX(X,Y,A)
53 ·--·used·5.21891s·(cpu);·0.676154s·(thread);·0s·(gc)53 ·--·used·5.53241s·(cpu);·0.704565s·(thread);·0s·(gc)
  
54 ·······2·············254 ·······2·············2
55 o6·=·2H··+·4H·H··+·2H55 o6·=·2H··+·4H·H··+·2H
56 ·······1·····1·2·····256 ·······1·····1·2·····2
  
57 o6·:·A57 o6·:·A
58 i7·:·time·segre(X,Y,A)58 i7·:·time·segre(X,Y,A)
59 ·--·used·0.116048s·(cpu);·0.0917042s·(thread);·0s·(gc)59 ·--·used·0.457363s·(cpu);·0.117294s·(thread);·0s·(gc)
  
60 ········2·2·····2·········2·····2·············260 ········2·2·····2·········2·····2·············2
61 o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H61 o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H
62 ········1·2·····1·2·····1·2·····1·····1·2·····262 ········1·2·····1·2·····1·2·····1·····1·2·····2
  
63 o7·:·A63 o7·:·A
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11 bmFsIG1hdHJpY2VzIiwgImxpbmVudW0iID0+IDE0MjUsIElucHV0cyA9PiB7U1BBTntUVHsiTSJ911 bmFsIG1hdHJpY2VzIiwgImxpbmVudW0iID0+IDE0MjUsIElucHV0cyA9PiB7U1BBTntUVHsiTSJ9
757 B
./usr/share/doc/Macaulay2/SparseResultants/example-output/_degree__Determinant.out
    
Offset 3, 24 lines modifiedOffset 3, 24 lines modified
3 i1·:·n·=·{2,3,2}3 i1·:·n·=·{2,3,2}
  
4 o1·=·{2,·3,·2}4 o1·=·{2,·3,·2}
  
5 o1·:·List5 o1·:·List
  
6 i2·:·time·degreeDeterminant·n6 i2·:·time·degreeDeterminant·n
7 ·--·used·0.000157777s·(cpu);·5.4993e-05s·(thread);·0s·(gc)7 ·--·used·0.00117805s·(cpu);·6.4911e-05s·(thread);·0s·(gc)
  
8 o2·=·68 o2·=·6
  
9 i3·:·M·=·genericMultidimensionalMatrix·n;9 i3·:·M·=·genericMultidimensionalMatrix·n;
  
10 o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····]10 o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····]
11 ······················································0,0,0···1,2,111 ······················································0,0,0···1,2,1
  
12 i4·:·time·degree·determinant·M12 i4·:·time·degree·determinant·M
13 ·--·used·0.568494s·(cpu);·0.133408s·(thread);·0s·(gc)13 ·--·used·0.614752s·(cpu);·0.139934s·(thread);·0s·(gc)
  
14 o4·=·{6}14 o4·=·{6}
  
15 o4·:·List15 o4·:·List
  
16 i5·:·16 i5·:·
678 B
./usr/share/doc/Macaulay2/SparseResultants/example-output/_dense__Discriminant.out
    
Offset 1, 13 lines modifiedOffset 1, 13 lines modified
1 --·-*-·M2-comint·-*-·hash:·171303219021082231781 --·-*-·M2-comint·-*-·hash:·17130321902108223178
  
2 i1·:·(d,n)·:=·(2,3);2 i1·:·(d,n)·:=·(2,3);
  
3 i2·:·time·Disc·=·denseDiscriminant(d,n)3 i2·:·time·Disc·=·denseDiscriminant(d,n)
4 ·--·used·0.224465s·(cpu);·0.169441s·(thread);·0s·(gc)4 ·--·used·0.260339s·(cpu);·0.180462s·(thread);·0s·(gc)
  
5 o2·=·Disc5 o2·=·Disc
  
6 o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|)6 o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|)
7 ···························································|·0·0·0·1·1·2·0·0·1·0·|7 ···························································|·0·0·0·1·1·2·0·0·1·0·|
8 ···························································|·0·1·2·0·1·0·0·1·0·0·|8 ···························································|·0·1·2·0·1·0·0·1·0·0·|
  
897 B
./usr/share/doc/Macaulay2/SparseResultants/example-output/_dense__Resultant.out
    
Offset 9, 18 lines modifiedOffset 9, 18 lines modified
9 ·················29 ·················2
10 ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·)10 ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·)
11 ······4·1·2····2·2····3·1····1·2····011 ······4·1·2····2·2····3·1····1·2····0
  
12 o1·:·Sequence12 o1·:·Sequence
  
13 i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula13 i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula
14 ·--·used·0.0672386s·(cpu);·0.0675537s·(thread);·0s·(gc)14 ·--·used·0.0799461s·(cpu);·0.0800767s·(thread);·0s·(gc)
  
15 i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula15 i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula
16 ·--·used·0.205879s·(cpu);·0.178439s·(thread);·0s·(gc)16 ·--·used·0.307027s·(cpu);·0.267114s·(thread);·0s·(gc)
  
17 i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant17 i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant
18 ·--·used·0.522551s·(cpu);·0.252911s·(thread);·0s·(gc)18 ·--·used·0.49804s·(cpu);·0.273683s·(thread);·0s·(gc)
  
19 i5·:·assert(o2·==·o3·and·o3·==·o4)19 i5·:·assert(o2·==·o3·and·o3·==·o4)
  
20 i6·:·20 i6·:·
1.31 KB
./usr/share/doc/Macaulay2/SparseResultants/example-output/_determinant_lp__Multidimensional__Matrix_rp.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2,5 o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2,
6 ·····------------------------------------------------------------------------6 ·····------------------------------------------------------------------------
7 ·····3}}}}7 ·····3}}}}
  
8 o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ8 o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ
  
9 i2·:·time·det·M9 i2·:·time·det·M
10 ·--·used·1.07874s·(cpu);·0.19457s·(thread);·0s·(gc)10 ·--·used·1.0645s·(cpu);·0.211556s·(thread);·0s·(gc)
  
11 o2·=·969833799042151219211 o2·=·9698337990421512192
  
12 i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5)12 i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5)
  
13 o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5,13 o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5,
14 ·····------------------------------------------------------------------------14 ·····------------------------------------------------------------------------
Offset 24, 13 lines modifiedOffset 24, 13 lines modified
24 ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6,24 ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6,
25 ·····------------------------------------------------------------------------25 ·····------------------------------------------------------------------------
26 ·····4,·8,·4,·2}}}}}26 ·····4,·8,·4,·2}}}}}
  
27 o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ27 o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ
  
28 i4·:·time·det·M28 i4·:·time·det·M
29 ·--·used·0.380118s·(cpu);·0.323273s·(thread);·0s·(gc)29 ·--·used·0.474565s·(cpu);·0.395518s·(thread);·0s·(gc)
  
30 o4·=·91298449999693898047944772788564453075318452578698694073740730127880628730 o4·=·912984499996938980479447727885644530753184525786986940737407301278806287
31 ·····925713949392658640018792781388831 ·····9257139493926586400187927813888
  
32 i5·:·32 i5·:·
2.98 KB
./usr/share/doc/Macaulay2/SparseResultants/example-output/_generic__Skew__Multidimensional__Matrix.out
Ordering differences only
    
Offset 16, 41 lines modifiedOffset 16, 41 lines modified
  
16 o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·]16 o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·]
17 ······················································0···317 ······················································0···3
  
18 i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101)18 i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101)
  
19 o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0,19 o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0,
20 ······························3····2········3·······0········2···0···········20 ······························1····0········1·······2········0···2···········
21 ·····------------------------------------------------------------------------21 ·····------------------------------------------------------------------------
22 ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·,22 ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·,
23 ·········3···2····················3··········1······2······1··············3·23 ·········1···0····················1··········3······0······3··············1·
24 ·····------------------------------------------------------------------------24 ·····------------------------------------------------------------------------
25 ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·,25 ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·,
26 ·········0·····3·········1····················0····1·················2····0·26 ·········2·····1·········3····················2····3·················0····2·
27 ·····------------------------------------------------------------------------27 ·····------------------------------------------------------------------------
28 ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}}28 ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}}
29 ···········2·······1········0···129 ···········0·······3········2···3
  
30 ···················································ZZ30 ···················································ZZ
31 o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·]31 o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·]
32 ··················································101··0···332 ··················································101··0···3
  
33 i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b")33 i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b")
  
34 o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0,34 o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0,
35 ······························1····0········1·······2········0···2···········35 ······························3····2········3·······0········2···0···········
36 ·····------------------------------------------------------------------------36 ·····------------------------------------------------------------------------
37 ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·,37 ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·,
38 ·········1···0····················1··········3······0······3··············1·38 ·········3···2····················3··········1······2······1··············3·
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
40 ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·,40 ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·,
41 ·········2·····1·········3····················2····3·················0····2·41 ·········0·····3·········1····················0····1·················2····0·
42 ·····------------------------------------------------------------------------42 ·····------------------------------------------------------------------------
43 ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}}43 ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}}
44 ···········0·······3········2···344 ···········2·······1········0···1
  
45 ···················································ZZ45 ···················································ZZ
46 o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·]46 o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·]
47 ··················································101··0···347 ··················································101··0···3
  
48 i4·:·48 i4·:·
967 B
./usr/share/doc/Macaulay2/SparseResultants/example-output/_sparse__Discriminant.out
    
Offset 11, 15 lines modifiedOffset 11, 15 lines modified
11 ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z11 ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z
12 ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·112 ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1
  
13 o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·]13 o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·]
14 ·········0,0,0···1,2,1···0···1···0···2···0···114 ·········0,0,0···1,2,1···0···1···0···2···0···1
  
15 i2·:·time·sparseDiscriminant·f15 i2·:·time·sparseDiscriminant·f
16 ·--·used·2.02758s·(cpu);·1.90203s·(thread);·0s·(gc)16 ·--·used·2.41807s·(cpu);·2.203s·(thread);·0s·(gc)
  
17 ···················································2························17 ···················································2························
18 o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······-18 o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······-
19 ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0··19 ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0··
20 ·····------------------------------------------------------------------------20 ·····------------------------------------------------------------------------
21 ············2·····2································2············21 ············2·····2································2············
22 ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······-22 ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······-
3.39 KB
./usr/share/doc/Macaulay2/SparseResultants/example-output/_sparse__Resultant.out
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 --·-*-·M2-comint·-*-·hash:·162283638219457300641 --·-*-·M2-comint·-*-·hash:·16228363821945730064
  
2 i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}})2 i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}})
3 ·--·used·0.71034s·(cpu);·0.428105s·(thread);·0s·(gc)3 ·--·used·0.741612s·(cpu);·0.491724s·(thread);·0s·(gc)
  
4 o1·=·Res4 o1·=·Res
  
5 o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|})5 o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|})
6 ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|6 ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|
  
7 i2·:·QQ[c_(1,1)..c_(3,4)][x,y];7 i2·:·QQ[c_(1,1)..c_(3,4)][x,y];
Offset 18, 15 lines modifiedOffset 18, 15 lines modified
18 ·····------------------------------------------------------------------------18 ·····------------------------------------------------------------------------
19 ·····c···x*y·+·c···x·+·c···y·+·c···)19 ·····c···x*y·+·c···x·+·c···y·+·c···)
20 ······3,3·······3,4·····3,2·····3,120 ······3,3·······3,4·····3,2·····3,1
  
21 o3·:·Sequence21 o3·:·Sequence
  
22 i4·:·time·Res(f,g,h)22 i4·:·time·Res(f,g,h)
23 ·--·used·0.00923988s·(cpu);·0.00780478s·(thread);·0s·(gc)23 ·--·used·0.0120956s·(cpu);·0.0109334s·(thread);·0s·(gc)
  
24 ········2·······················4······2···2···············4····24 ········2·······················4······2···2···············4····
25 o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+25 o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+
26 ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1··26 ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1··
27 ·····------------------------------------------------------------------------27 ·····------------------------------------------------------------------------
28 ······3·······2·······3···············2···················3········28 ······3·······2·······3···············2···················3········
29 ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+29 ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+
Offset 730, 30 lines modifiedOffset 730, 30 lines modified
  
730 o4·:·QQ[c···..c···]730 o4·:·QQ[c···..c···]
731 ·········1,1···3,4731 ·········1,1···3,4
  
732 i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h))732 i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h))
  
733 i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331);733 i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331);
734 ·--·used·0.615419s·(cpu);·0.104985s·(thread);·0s·(gc)734 ·--·used·0.700064s·(cpu);·0.0987878s·(thread);·0s·(gc)
  
735 o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331)735 o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331)
736 ·····························································|·0·1·0·1·|736 ·····························································|·0·1·0·1·|
  
737 i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y];737 i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y];
  
738 i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y,·c_0·+·c_1*x·+·c_2*y·+·c_3*x*y)738 i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y,·c_0·+·c_1*x·+·c_2*y·+·c_3*x*y)
  
739 o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·)739 o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·)
740 ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0740 ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0
  
741 o8·:·Sequence741 o8·:·Sequence
  
742 i9·:·time·Res(f,g,h)742 i9·:·time·Res(f,g,h)
743 ·--·used·0.00380737s·(cpu);·0.00298827s·(thread);·0s·(gc)743 ·--·used·0.000357881s·(cpu);·0.0033719s·(thread);·0s·(gc)
  
744 ······2·····2············2············2········2·2····2··········744 ······2·····2············2············2········2·2····2··········
745 o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··-745 o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··-
746 ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1··746 ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1··
747 ·····------------------------------------------------------------------------747 ·····------------------------------------------------------------------------
748 ·························2·······················2·························748 ·························2·······················2·························
749 ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+749 ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+
Offset 822, 15 lines modifiedOffset 822, 15 lines modified
822 ··················2822 ··················2
823 ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·)823 ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·)
824 ·······4·1·2····2·2····3·1····1·2····0824 ·······4·1·2····2·2····3·1····1·2····0
  
825 o11·:·Sequence825 o11·:·Sequence
  
826 i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true));826 i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true));
827 ·--·used·1.41139s·(cpu);·0.463307s·(thread);·0s·(gc)827 ·--·used·1.34126s·(cpu);·0.564581s·(thread);·0s·(gc)
  
828 i13·:·quotientRemainder(UnmixedRes,MixedRes)828 i13·:·quotientRemainder(UnmixedRes,MixedRes)
  
829 ········2·2···················2····2·······························2·2829 ········2·2···················2····2·······························2·2
830 o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0)830 o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0)
831 ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5831 ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5
  
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Offset 76, 15 lines modifiedOffset 76, 15 lines modified
  
76 o1·:·List</code></pre>76 o1·:·List</code></pre>
77 ············</td>77 ············</td>
78 ··········</tr>78 ··········</tr>
79 ··········<tr>79 ··········<tr>
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i2·:·time·degreeDeterminant·n81 ··············<pre><code·class="language-macaulay2">i2·:·time·degreeDeterminant·n
82 ·--·used·0.000157777s·(cpu);·5.4993e-05s·(thread);·0s·(gc)82 ·--·used·0.00117805s·(cpu);·6.4911e-05s·(thread);·0s·(gc)
  
83 o2·=·6</code></pre>83 o2·=·6</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
86 ··········<tr>86 ··········<tr>
87 ············<td>87 ············<td>
88 ··············<pre><code·class="language-macaulay2">i3·:·M·=·genericMultidimensionalMatrix·n;88 ··············<pre><code·class="language-macaulay2">i3·:·M·=·genericMultidimensionalMatrix·n;
Offset 92, 15 lines modifiedOffset 92, 15 lines modified
92 o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····]92 o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····]
93 ······················································0,0,0···1,2,1</code></pre>93 ······················································0,0,0···1,2,1</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i4·:·time·degree·determinant·M98 ··············<pre><code·class="language-macaulay2">i4·:·time·degree·determinant·M
99 ·--·used·0.568494s·(cpu);·0.133408s·(thread);·0s·(gc)99 ·--·used·0.614752s·(cpu);·0.139934s·(thread);·0s·(gc)
  
100 o4·=·{6}100 o4·=·{6}
  
101 o4·:·List</code></pre>101 o4·:·List</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ········</table>104 ········</table>
896 B
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15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
16 i1·:·n·=·{2,3,2}16 i1·:·n·=·{2,3,2}
  
17 o1·=·{2,·3,·2}17 o1·=·{2,·3,·2}
  
18 o1·:·List18 o1·:·List
19 i2·:·time·degreeDeterminant·n19 i2·:·time·degreeDeterminant·n
20 ·--·used·0.000157777s·(cpu);·5.4993e-05s·(thread);·0s·(gc)20 ·--·used·0.00117805s·(cpu);·6.4911e-05s·(thread);·0s·(gc)
  
21 o2·=·621 o2·=·6
22 i3·:·M·=·genericMultidimensionalMatrix·n;22 i3·:·M·=·genericMultidimensionalMatrix·n;
  
23 o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····]23 o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····]
24 ······················································0,0,0···1,2,124 ······················································0,0,0···1,2,1
25 i4·:·time·degree·determinant·M25 i4·:·time·degree·determinant·M
26 ·--·used·0.568494s·(cpu);·0.133408s·(thread);·0s·(gc)26 ·--·used·0.614752s·(cpu);·0.139934s·(thread);·0s·(gc)
  
27 o4·=·{6}27 o4·=·{6}
  
28 o4·:·List28 o4·:·List
29 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
30 ····*·_\x8d_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·hyperdeterminant·of·a30 ····*·_\x8d_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·hyperdeterminant·of·a
31 ······multidimensional·matrix31 ······multidimensional·matrix
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./usr/share/doc/Macaulay2/SparseResultants/html/_dense__Discriminant.html
    
Offset 80, 15 lines modifiedOffset 80, 15 lines modified
80 ············<td>80 ············<td>
81 ··············<pre><code·class="language-macaulay2">i1·:·(d,n)·:=·(2,3);</code></pre>81 ··············<pre><code·class="language-macaulay2">i1·:·(d,n)·:=·(2,3);</code></pre>
82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i2·:·time·Disc·=·denseDiscriminant(d,n)86 ··············<pre><code·class="language-macaulay2">i2·:·time·Disc·=·denseDiscriminant(d,n)
87 ·--·used·0.224465s·(cpu);·0.169441s·(thread);·0s·(gc)87 ·--·used·0.260339s·(cpu);·0.180462s·(thread);·0s·(gc)
  
88 o2·=·Disc88 o2·=·Disc
  
89 o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|)89 o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|)
90 ···························································|·0·0·0·1·1·2·0·0·1·0·|90 ···························································|·0·0·0·1·1·2·0·0·1·0·|
91 ···························································|·0·1·2·0·1·0·0·1·0·0·|</code></pre>91 ···························································|·0·1·2·0·1·0·0·1·0·0·|</code></pre>
92 ············</td>92 ············</td>
874 B
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Offset 18, 15 lines modifiedOffset 18, 15 lines modified
18 ····*·Outputs:18 ····*·Outputs:
19 ··········o·for·(d,n),·this·is·the·same·as·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x19 ··········o·for·(d,n),·this·is·the·same·as·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x
20 ············"\x8"g\x8ge\x8en\x8ne\x8er\x8ri\x8ic\x8c·p\x8po\x8ol\x8ly\x8yn\x8no\x8om\x8mi\x8ia\x8al\x8l·o\x8of\x8f·d\x8de\x8eg\x8gr\x8re\x8ee\x8e·d\x8d·i\x8in\x8n·n\x8n·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s"\x8";\x8;20 ············"\x8"g\x8ge\x8en\x8ne\x8er\x8ri\x8ic\x8c·p\x8po\x8ol\x8ly\x8yn\x8no\x8om\x8mi\x8ia\x8al\x8l·o\x8of\x8f·d\x8de\x8eg\x8gr\x8re\x8ee\x8e·d\x8d·i\x8in\x8n·n\x8n·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s"\x8";\x8;
21 ··········o·for·f,·this·is·the·same·as·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t(f).21 ··········o·for·f,·this·is·the·same·as·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t(f).
22 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*22 *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8*
23 i1·:·(d,n)·:=·(2,3);23 i1·:·(d,n)·:=·(2,3);
24 i2·:·time·Disc·=·denseDiscriminant(d,n)24 i2·:·time·Disc·=·denseDiscriminant(d,n)
25 ·--·used·0.224465s·(cpu);·0.169441s·(thread);·0s·(gc)25 ·--·used·0.260339s·(cpu);·0.180462s·(thread);·0s·(gc)
  
26 o2·=·Disc26 o2·=·Disc
  
27 o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·127 o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1
28 2·|)28 2·|)
29 ···························································|·0·0·0·1·1·2·0·0·129 ···························································|·0·0·0·1·1·2·0·0·1
30 0·|30 0·|
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./usr/share/doc/Macaulay2/SparseResultants/html/_dense__Resultant.html
    
Offset 90, 27 lines modifiedOffset 90, 27 lines modified
  
90 o1·:·Sequence</code></pre>90 o1·:·Sequence</code></pre>
91 ············</td>91 ············</td>
92 ··········</tr>92 ··········</tr>
93 ··········<tr>93 ··········<tr>
94 ············<td>94 ············<td>
95 ··············<pre><code·class="language-macaulay2">i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula95 ··············<pre><code·class="language-macaulay2">i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula
96 ·--·used·0.0672386s·(cpu);·0.0675537s·(thread);·0s·(gc)</code></pre>96 ·--·used·0.0799461s·(cpu);·0.0800767s·(thread);·0s·(gc)</code></pre>
97 ············</td>97 ············</td>
98 ··········</tr>98 ··········</tr>
99 ··········<tr>99 ··········<tr>
100 ············<td>100 ············<td>
101 ··············<pre><code·class="language-macaulay2">i3·:·time·denseResultant(f0,f1,f2,Algorithm=>&quot;Macaulay&quot;);·--·using·Macaulay·formula101 ··············<pre><code·class="language-macaulay2">i3·:·time·denseResultant(f0,f1,f2,Algorithm=>&quot;Macaulay&quot;);·--·using·Macaulay·formula
102 ·--·used·0.205879s·(cpu);·0.178439s·(thread);·0s·(gc)</code></pre>102 ·--·used·0.307027s·(cpu);·0.267114s·(thread);·0s·(gc)</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant107 ··············<pre><code·class="language-macaulay2">i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant
108 ·--·used·0.522551s·(cpu);·0.252911s·(thread);·0s·(gc)</code></pre>108 ·--·used·0.49804s·(cpu);·0.273683s·(thread);·0s·(gc)</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i5·:·assert(o2·==·o3·and·o3·==·o4)</code></pre>113 ··············<pre><code·class="language-macaulay2">i5·:·assert(o2·==·o3·and·o3·==·o4)</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
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28 ·····------------------------------------------------------------------------28 ·····------------------------------------------------------------------------
29 ·················229 ·················2
30 ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·)30 ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·)
31 ······4·1·2····2·2····3·1····1·2····031 ······4·1·2····2·2····3·1····1·2····0
  
32 o1·:·Sequence32 o1·:·Sequence
33 i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula33 i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula
34 ·--·used·0.0672386s·(cpu);·0.0675537s·(thread);·0s·(gc)34 ·--·used·0.0799461s·(cpu);·0.0800767s·(thread);·0s·(gc)
35 i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay35 i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay
36 formula36 formula
37 ·--·used·0.205879s·(cpu);·0.178439s·(thread);·0s·(gc)37 ·--·used·0.307027s·(cpu);·0.267114s·(thread);·0s·(gc)
38 i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant38 i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant
39 ·--·used·0.522551s·(cpu);·0.252911s·(thread);·0s·(gc)39 ·--·used·0.49804s·(cpu);·0.273683s·(thread);·0s·(gc)
40 i5·:·assert(o2·==·o3·and·o3·==·o4)40 i5·:·assert(o2·==·o3·and·o3·==·o4)
41 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*41 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
42 ····*·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·sparse·resultant·(A-resultant)42 ····*·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·sparse·resultant·(A-resultant)
43 ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·affine·resultant43 ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·affine·resultant
44 ····*·_\x8d_\x8e_\x8n_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·dense·discriminant·(classical·discriminant)44 ····*·_\x8d_\x8e_\x8n_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·dense·discriminant·(classical·discriminant)
45 ····*·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·exponents·in·one·or·more·polynomials45 ····*·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·exponents·in·one·or·more·polynomials
46 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8L_\x8a_\x8u_\x8r_\x8e_\x8n_\x8t_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·generic·(Laurent)·polynomials46 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8L_\x8a_\x8u_\x8r_\x8e_\x8n_\x8t_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·generic·(Laurent)·polynomials
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Offset 84, 15 lines modifiedOffset 84, 15 lines modified
  
84 o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ</code></pre>84 o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i2·:·time·det·M89 ··············<pre><code·class="language-macaulay2">i2·:·time·det·M
90 ·--·used·1.07874s·(cpu);·0.19457s·(thread);·0s·(gc)90 ·--·used·1.0645s·(cpu);·0.211556s·(thread);·0s·(gc)
  
91 o2·=·9698337990421512192</code></pre>91 o2·=·9698337990421512192</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5)96 ··············<pre><code·class="language-macaulay2">i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5)
Offset 109, 15 lines modifiedOffset 109, 15 lines modified
  
109 o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ</code></pre>109 o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i4·:·time·det·M114 ··············<pre><code·class="language-macaulay2">i4·:·time·det·M
115 ·--·used·0.380118s·(cpu);·0.323273s·(thread);·0s·(gc)115 ·--·used·0.474565s·(cpu);·0.395518s·(thread);·0s·(gc)
  
116 o4·=·912984499996938980479447727885644530753184525786986940737407301278806287116 o4·=·912984499996938980479447727885644530753184525786986940737407301278806287
117 ·····9257139493926586400187927813888</code></pre>117 ·····9257139493926586400187927813888</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ········</table>120 ········</table>
121 ······</div>121 ······</div>
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Offset 25, 15 lines modifiedOffset 25, 15 lines modified
  
25 o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2,25 o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2,
26 ·····------------------------------------------------------------------------26 ·····------------------------------------------------------------------------
27 ·····3}}}}27 ·····3}}}}
  
28 o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ28 o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ
29 i2·:·time·det·M29 i2·:·time·det·M
30 ·--·used·1.07874s·(cpu);·0.19457s·(thread);·0s·(gc)30 ·--·used·1.0645s·(cpu);·0.211556s·(thread);·0s·(gc)
  
31 o2·=·969833799042151219231 o2·=·9698337990421512192
32 i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5)32 i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5)
  
33 o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5,33 o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5,
34 ·····------------------------------------------------------------------------34 ·····------------------------------------------------------------------------
35 ·····6}}},·{{{3,·5,·7,·7,·9},·{4,·5,·0,·4,·3}},·{{1,·8,·9,·1,·2},·{9,·6,·6,35 ·····6}}},·{{{3,·5,·7,·7,·9},·{4,·5,·0,·4,·3}},·{{1,·8,·9,·1,·2},·{9,·6,·6,
Offset 42, 15 lines modifiedOffset 42, 15 lines modified
42 ·····------------------------------------------------------------------------42 ·····------------------------------------------------------------------------
43 ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6,43 ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6,
44 ·····------------------------------------------------------------------------44 ·····------------------------------------------------------------------------
45 ·····4,·8,·4,·2}}}}}45 ·····4,·8,·4,·2}}}}}
  
46 o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ46 o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ
47 i4·:·time·det·M47 i4·:·time·det·M
48 ·--·used·0.380118s·(cpu);·0.323273s·(thread);·0s·(gc)48 ·--·used·0.474565s·(cpu);·0.395518s·(thread);·0s·(gc)
  
49 o4·=·91298449999693898047944772788564453075318452578698694073740730127880628749 o4·=·912984499996938980479447727885644530753184525786986940737407301278806287
50 ·····925713949392658640018792781388850 ·····9257139493926586400187927813888
51 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*51 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
52 ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·the·class·of·all·multidimensional·matrices52 ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·the·class·of·all·multidimensional·matrices
53 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8D_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·degree·of·the·hyperdeterminant·of·a·generic53 ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8D_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·degree·of·the·hyperdeterminant·of·a·generic
54 ······multidimensional·matrix54 ······multidimensional·matrix
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./usr/share/doc/Macaulay2/SparseResultants/html/_generic__Skew__Multidimensional__Matrix.html
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Offset 95, 45 lines modifiedOffset 95, 45 lines modified
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101)99 ··············<pre><code·class="language-macaulay2">i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101)
  
100 o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0,100 o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0,
101 ······························3····2········3·······0········2···0···········101 ······························1····0········1·······2········0···2···········
102 ·····------------------------------------------------------------------------102 ·····------------------------------------------------------------------------
103 ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·,103 ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·,
104 ·········3···2····················3··········1······2······1··············3·104 ·········1···0····················1··········3······0······3··············1·
105 ·····------------------------------------------------------------------------105 ·····------------------------------------------------------------------------
106 ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·,106 ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·,
107 ·········0·····3·········1····················0····1·················2····0·107 ·········2·····1·········3····················2····3·················0····2·
108 ·····------------------------------------------------------------------------108 ·····------------------------------------------------------------------------
109 ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}}109 ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}}
110 ···········2·······1········0···1110 ···········0·······3········2···3
  
111 ···················································ZZ111 ···················································ZZ
112 o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·]112 o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·]
113 ··················································101··0···3</code></pre>113 ··················································101··0···3</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ··········<tr>116 ··········<tr>
117 ············<td>117 ············<td>
118 ··············<pre><code·class="language-macaulay2">i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>&quot;b&quot;)118 ··············<pre><code·class="language-macaulay2">i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>&quot;b&quot;)
  
119 o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0,119 o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0,
120 ······························1····0········1·······2········0···2···········120 ······························3····2········3·······0········2···0···········
121 ·····------------------------------------------------------------------------121 ·····------------------------------------------------------------------------
122 ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·,122 ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·,
123 ·········1···0····················1··········3······0······3··············1·123 ·········3···2····················3··········1······2······1··············3·
124 ·····------------------------------------------------------------------------124 ·····------------------------------------------------------------------------
125 ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·,125 ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·,
126 ·········2·····1·········3····················2····3·················0····2·126 ·········0·····3·········1····················0····1·················2····0·
127 ·····------------------------------------------------------------------------127 ·····------------------------------------------------------------------------
128 ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}}128 ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}}
129 ···········0·······3········2···3129 ···········2·······1········0···1
  
130 ···················································ZZ130 ···················································ZZ
131 o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·]131 o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·]
132 ··················································101··0···3</code></pre>132 ··················································101··0···3</code></pre>
133 ············</td>133 ············</td>
134 ··········</tr>134 ··········</tr>
135 ········</table>135 ········</table>
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Offset 33, 42 lines modifiedOffset 33, 42 lines modified
33 ···········0·······3········2···333 ···········0·······3········2···3
  
34 o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·]34 o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·]
35 ······················································0···335 ······················································0···3
36 i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101)36 i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101)
  
37 o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0,37 o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0,
38 ······························3····2········3·······0········2···038 ······························1····0········1·······2········0···2
39 ·····------------------------------------------------------------------------39 ·····------------------------------------------------------------------------
40 ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·,40 ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·,
41 ·········3···2····················3··········1······2······1··············341 ·········1···0····················1··········3······0······3··············1
42 ·····------------------------------------------------------------------------42 ·····------------------------------------------------------------------------
43 ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·,43 ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·,
44 ·········0·····3·········1····················0····1·················2····044 ·········2·····1·········3····················2····3·················0····2
45 ·····------------------------------------------------------------------------45 ·····------------------------------------------------------------------------
46 ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}}46 ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}}
47 ···········2·······1········0···147 ···········0·······3········2···3
  
48 ···················································ZZ48 ···················································ZZ
49 o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·]49 o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·]
50 ··················································101··0···350 ··················································101··0···3
51 i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/51 i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/
52 101,Variable=>"b")52 101,Variable=>"b")
  
53 o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0,53 o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0,
54 ······························1····0········1·······2········0···254 ······························3····2········3·······0········2···0
55 ·····------------------------------------------------------------------------55 ·····------------------------------------------------------------------------
56 ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·,56 ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·,
57 ·········1···0····················1··········3······0······3··············157 ·········3···2····················3··········1······2······1··············3
58 ·····------------------------------------------------------------------------58 ·····------------------------------------------------------------------------
59 ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·,59 ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·,
60 ·········2·····1·········3····················2····3·················0····260 ·········0·····3·········1····················0····1·················2····0
61 ·····------------------------------------------------------------------------61 ·····------------------------------------------------------------------------
62 ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}}62 ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}}
63 ···········0·······3········2···363 ···········2·······1········0···1
  
64 ···················································ZZ64 ···················································ZZ
65 o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·]65 o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·]
66 ··················································101··0···366 ··················································101··0···3
67 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*67 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
68 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·make·a·generic·multidimensional·matrix68 ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·make·a·generic·multidimensional·matrix
69 ······of·variables69 ······of·variables
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Offset 90, 15 lines modifiedOffset 90, 15 lines modified
90 o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·]90 o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·]
91 ·········0,0,0···1,2,1···0···1···0···2···0···1</code></pre>91 ·········0,0,0···1,2,1···0···1···0···2···0···1</code></pre>
92 ············</td>92 ············</td>
93 ··········</tr>93 ··········</tr>
94 ··········<tr>94 ··········<tr>
95 ············<td>95 ············<td>
96 ··············<pre><code·class="language-macaulay2">i2·:·time·sparseDiscriminant·f96 ··············<pre><code·class="language-macaulay2">i2·:·time·sparseDiscriminant·f
97 ·--·used·2.02758s·(cpu);·1.90203s·(thread);·0s·(gc)97 ·--·used·2.41807s·(cpu);·2.203s·(thread);·0s·(gc)
  
98 ···················································2························98 ···················································2························
99 o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······-99 o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······-
100 ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0··100 ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0··
101 ·····------------------------------------------------------------------------101 ·····------------------------------------------------------------------------
102 ············2·····2································2············102 ············2·····2································2············
103 ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······-103 ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······-
864 B
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Offset 37, 15 lines modifiedOffset 37, 15 lines modified
37 ·····------------------------------------------------------------------------37 ·····------------------------------------------------------------------------
38 ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z38 ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z
39 ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·139 ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1
  
40 o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·]40 o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·]
41 ·········0,0,0···1,2,1···0···1···0···2···0···141 ·········0,0,0···1,2,1···0···1···0···2···0···1
42 i2·:·time·sparseDiscriminant·f42 i2·:·time·sparseDiscriminant·f
43 ·--·used·2.02758s·(cpu);·1.90203s·(thread);·0s·(gc)43 ·--·used·2.41807s·(cpu);·2.203s·(thread);·0s·(gc)
  
44 ···················································244 ···················································2
45 o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······-45 o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······-
46 ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,046 ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0
47 ·····------------------------------------------------------------------------47 ·····------------------------------------------------------------------------
48 ············2·····2································248 ············2·····2································2
49 ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······-49 ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······-
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Offset 74, 15 lines modifiedOffset 74, 15 lines modified
74 ········<h2>Description</h2>74 ········<h2>Description</h2>
75 ········<p>Alternatively,·one·can·apply·the·method·directly·to·the·list·of·Laurent·polynomials·$f_0,\ldots,f_n$.·In·this·case,·the·matrices·$A_0,\ldots,A_n$·are·automatically·determined·by·<a·title="exponents·in·one·or·more·polynomials"·href="_exponents__Matrix.html">exponentsMatrix</a>.·If·you·want·require·that·$A_0=\cdots=A_n$,·then·use·the·option·<span·class="tt">Unmixed=>true</span>·(this·could·be·faster).·Below·we·consider·some·examples.</p>75 ········<p>Alternatively,·one·can·apply·the·method·directly·to·the·list·of·Laurent·polynomials·$f_0,\ldots,f_n$.·In·this·case,·the·matrices·$A_0,\ldots,A_n$·are·automatically·determined·by·<a·title="exponents·in·one·or·more·polynomials"·href="_exponents__Matrix.html">exponentsMatrix</a>.·If·you·want·require·that·$A_0=\cdots=A_n$,·then·use·the·option·<span·class="tt">Unmixed=>true</span>·(this·could·be·faster).·Below·we·consider·some·examples.</p>
76 ········<p>In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to·the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{(1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{(2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$.</p>76 ········<p>In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to·the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{(1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{(2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$.</p>
77 ········<table·class="examples">77 ········<table·class="examples">
78 ··········<tr>78 ··········<tr>
79 ············<td>79 ············<td>
80 ··············<pre><code·class="language-macaulay2">i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}})80 ··············<pre><code·class="language-macaulay2">i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}})
81 ·--·used·0.71034s·(cpu);·0.428105s·(thread);·0s·(gc)81 ·--·used·0.741612s·(cpu);·0.491724s·(thread);·0s·(gc)
  
82 o1·=·Res82 o1·=·Res
  
83 o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|})83 o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|})
84 ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|</code></pre>84 ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|</code></pre>
85 ············</td>85 ············</td>
86 ··········</tr>86 ··········</tr>
Offset 104, 15 lines modifiedOffset 104, 15 lines modified
  
104 o3·:·Sequence</code></pre>104 o3·:·Sequence</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i4·:·time·Res(f,g,h)109 ··············<pre><code·class="language-macaulay2">i4·:·time·Res(f,g,h)
110 ·--·used·0.00923988s·(cpu);·0.00780478s·(thread);·0s·(gc)110 ·--·used·0.0120956s·(cpu);·0.0109334s·(thread);·0s·(gc)
  
111 ········2·······················4······2···2···············4····111 ········2·······················4······2···2···············4····
112 o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+112 o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+
113 ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1··113 ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1··
114 ·····------------------------------------------------------------------------114 ·····------------------------------------------------------------------------
115 ······3·······2·······3···············2···················3········115 ······3·······2·······3···············2···················3········
116 ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+116 ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+
Offset 825, 15 lines modifiedOffset 825, 15 lines modified
825 ··········</tr>825 ··········</tr>
826 ········</table>826 ········</table>
827 ········<p>In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to·the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0·+·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over·$\mathbb{Z}/3331$.</p>827 ········<p>In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to·the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0·+·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over·$\mathbb{Z}/3331$.</p>
828 ········<table·class="examples">828 ········<table·class="examples">
829 ··········<tr>829 ··········<tr>
830 ············<td>830 ············<td>
831 ··············<pre><code·class="language-macaulay2">i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331);831 ··············<pre><code·class="language-macaulay2">i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331);
832 ·--·used·0.615419s·(cpu);·0.104985s·(thread);·0s·(gc)832 ·--·used·0.700064s·(cpu);·0.0987878s·(thread);·0s·(gc)
  
833 o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331)833 o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331)
834 ·····························································|·0·1·0·1·|</code></pre>834 ·····························································|·0·1·0·1·|</code></pre>
835 ············</td>835 ············</td>
836 ··········</tr>836 ··········</tr>
837 ··········<tr>837 ··········<tr>
838 ············<td>838 ············<td>
Offset 849, 15 lines modifiedOffset 849, 15 lines modified
  
849 o8·:·Sequence</code></pre>849 o8·:·Sequence</code></pre>
850 ············</td>850 ············</td>
851 ··········</tr>851 ··········</tr>
852 ··········<tr>852 ··········<tr>
853 ············<td>853 ············<td>
854 ··············<pre><code·class="language-macaulay2">i9·:·time·Res(f,g,h)854 ··············<pre><code·class="language-macaulay2">i9·:·time·Res(f,g,h)
855 ·--·used·0.00380737s·(cpu);·0.00298827s·(thread);·0s·(gc)855 ·--·used·0.000357881s·(cpu);·0.0033719s·(thread);·0s·(gc)
  
856 ······2·····2············2············2········2·2····2··········856 ······2·····2············2············2········2·2····2··········
857 o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··-857 o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··-
858 ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1··858 ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1··
859 ·····------------------------------------------------------------------------859 ·····------------------------------------------------------------------------
860 ·························2·······················2·························860 ·························2·······················2·························
861 ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+861 ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+
Offset 938, 15 lines modifiedOffset 938, 15 lines modified
  
938 o11·:·Sequence</code></pre>938 o11·:·Sequence</code></pre>
939 ············</td>939 ············</td>
940 ··········</tr>940 ··········</tr>
941 ··········<tr>941 ··········<tr>
942 ············<td>942 ············<td>
943 ··············<pre><code·class="language-macaulay2">i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true));943 ··············<pre><code·class="language-macaulay2">i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true));
944 ·--·used·1.41139s·(cpu);·0.463307s·(thread);·0s·(gc)</code></pre>944 ·--·used·1.34126s·(cpu);·0.564581s·(thread);·0s·(gc)</code></pre>
945 ············</td>945 ············</td>
946 ··········</tr>946 ··········</tr>
947 ··········<tr>947 ··········<tr>
948 ············<td>948 ············<td>
949 ··············<pre><code·class="language-macaulay2">i13·:·quotientRemainder(UnmixedRes,MixedRes)949 ··············<pre><code·class="language-macaulay2">i13·:·quotientRemainder(UnmixedRes,MixedRes)
  
950 ········2·2···················2····2·······························2·2950 ········2·2···················2····2·······························2·2
3.82 KB
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Offset 34, 15 lines modifiedOffset 34, 15 lines modified
34 In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to34 In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to
35 the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$.35 the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$.
36 Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{36 Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{
37 (1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{37 (1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{
38 (2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$.38 (2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$.
39 i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},39 i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},
40 {1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}})40 {1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}})
41 ·--·used·0.71034s·(cpu);·0.428105s·(thread);·0s·(gc)41 ·--·used·0.741612s·(cpu);·0.491724s·(thread);·0s·(gc)
  
42 o1·=·Res42 o1·=·Res
  
43 o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·143 o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1
44 2·2·|,·|·0·0·1·1·|})44 2·2·|,·|·0·0·1·1·|})
45 ····························································|·0·0·1·1·|··|·1·045 ····························································|·0·0·1·1·|··|·1·0
46 1·2·|··|·0·1·0·1·|46 1·2·|··|·0·1·0·1·|
Offset 55, 15 lines modifiedOffset 55, 15 lines modified
55 ·······1,3·······1,2·······1,4·····1,1···2,2········2,3·······2,4·····2,155 ·······1,3·······1,2·······1,4·····1,1···2,2········2,3·······2,4·····2,1
56 ·····------------------------------------------------------------------------56 ·····------------------------------------------------------------------------
57 ·····c···x*y·+·c···x·+·c···y·+·c···)57 ·····c···x*y·+·c···x·+·c···y·+·c···)
58 ······3,3·······3,4·····3,2·····3,158 ······3,3·······3,4·····3,2·····3,1
  
59 o3·:·Sequence59 o3·:·Sequence
60 i4·:·time·Res(f,g,h)60 i4·:·time·Res(f,g,h)
61 ·--·used·0.00923988s·(cpu);·0.00780478s·(thread);·0s·(gc)61 ·--·used·0.0120956s·(cpu);·0.0109334s·(thread);·0s·(gc)
  
62 ········2·······················4······2···2···············462 ········2·······················4······2···2···············4
63 o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+63 o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+
64 ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,164 ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1
65 ·····------------------------------------------------------------------------65 ·····------------------------------------------------------------------------
66 ······3·······2·······3···············2···················366 ······3·······2·······3···············2···················3
67 ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+67 ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+
Offset 771, 29 lines modifiedOffset 771, 29 lines modified
771 In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to771 In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to
772 the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials772 the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials
773 $f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0773 $f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0
774 +·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over774 +·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over
775 $\mathbb{Z}/3331$.775 $\mathbb{Z}/3331$.
776 i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},776 i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},
777 {0,1,0,1}},CoefficientRing=>ZZ/3331);777 {0,1,0,1}},CoefficientRing=>ZZ/3331);
778 ·--·used·0.615419s·(cpu);·0.104985s·(thread);·0s·(gc)778 ·--·used·0.700064s·(cpu);·0.0987878s·(thread);·0s·(gc)
  
779 o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over779 o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over
780 ZZ/3331)780 ZZ/3331)
781 ·····························································|·0·1·0·1·|781 ·····························································|·0·1·0·1·|
782 i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y];782 i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y];
783 i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y,783 i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y,
784 c_0·+·c_1*x·+·c_2*y·+·c_3*x*y)784 c_0·+·c_1*x·+·c_2*y·+·c_3*x*y)
  
785 o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·)785 o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·)
786 ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0786 ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0
  
787 o8·:·Sequence787 o8·:·Sequence
788 i9·:·time·Res(f,g,h)788 i9·:·time·Res(f,g,h)
789 ·--·used·0.00380737s·(cpu);·0.00298827s·(thread);·0s·(gc)789 ·--·used·0.000357881s·(cpu);·0.0033719s·(thread);·0s·(gc)
  
790 ······2·····2············2············2········2·2····2790 ······2·····2············2············2········2·2····2
791 o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··-791 o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··-
792 ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1792 ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1
793 ·····------------------------------------------------------------------------793 ·····------------------------------------------------------------------------
794 ·························2·······················2794 ·························2·······················2
795 ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+795 ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+
Offset 863, 15 lines modifiedOffset 863, 15 lines modified
863 ··················2863 ··················2
864 ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·)864 ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·)
865 ·······4·1·2····2·2····3·1····1·2····0865 ·······4·1·2····2·2····3·1····1·2····0
  
866 o11·:·Sequence866 o11·:·Sequence
867 i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant867 i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant
868 (f,g,h,Unmixed=>true));868 (f,g,h,Unmixed=>true));
869 ·--·used·1.41139s·(cpu);·0.463307s·(thread);·0s·(gc)869 ·--·used·1.34126s·(cpu);·0.564581s·(thread);·0s·(gc)
870 i13·:·quotientRemainder(UnmixedRes,MixedRes)870 i13·:·quotientRemainder(UnmixedRes,MixedRes)
  
871 ········2·2···················2····2·······························2·2871 ········2·2···················2····2·······························2·2
872 o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0)872 o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0)
873 ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5873 ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5
  
874 o13·:·Sequence874 o13·:·Sequence
761 B
./usr/share/doc/Macaulay2/SpechtModule/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=387 #:len=38
8 c2NodXJQb2x5bm9taWFsKC4uLixBc0V4cHJlc3Npb249Pi4uLik=8 c2NodXJQb2x5bm9taWFsKC4uLixBc0V4cHJlc3Npb249Pi4uLik=
9 #:len=2879 #:len=287
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzMwNSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzMwNSwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc2NodXJQb2x5bm9taWFsLEFzRXhwcmVzc2lvbl0s11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc2NodXJQb2x5bm9taWFsLEFzRXhwcmVzc2lvbl0s
2.44 KB
./usr/share/doc/Macaulay2/SpechtModule/example-output/_higher__Specht__Polynomial_lp__Young__Tableau_cm__Young__Tableau_cm__Polynomial__Ring_rp.out
    
Offset 25, 15 lines modifiedOffset 25, 15 lines modified
25 o4·=·|·0·1·|25 o4·=·|·0·1·|
26 ·····|·2·3·|26 ·····|·2·3·|
27 ·····|·4·|27 ·····|·4·|
  
28 o4·:·YoungTableau28 o4·:·YoungTableau
  
29 i5·:·time·higherSpechtPolynomial(S,T,R)29 i5·:·time·higherSpechtPolynomial(S,T,R)
30 ·--·used·0.000657459s·(cpu);·0.00123139s·(thread);·0s·(gc)30 ·--·used·0.000978515s·(cpu);·0.00141033s·(thread);·0s·(gc)
  
31 ······3·2··········2·3······3·····2········3·2····3···2······2···3····31 ······3·2··········2·3······3·····2········3·2····3···2······2···3····
32 o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-32 o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
33 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··33 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··
34 ·····------------------------------------------------------------------------34 ·····------------------------------------------------------------------------
35 ······3·2········3·2········2·3········2·3········3···2········3·2····35 ······3·2········3·2········2·3········2·3········3···2········3·2····
36 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-36 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
Offset 46, 15 lines modifiedOffset 46, 15 lines modified
46 ········2···3····2·····3····2·····3······2···3········2·3········2·346 ········2···3····2·····3····2·····3······2···3········2·3········2·3
47 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x47 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x
48 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·448 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4
  
49 o5·:·R49 o5·:·R
  
50 i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false)50 i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false)
51 ·--·used·0.00107092s·(cpu);·0.0009569s·(thread);·0s·(gc)51 ·--·used·0.00115348s·(cpu);·0.00141848s·(thread);·0s·(gc)
  
52 ······3·2··········2·3······3·····2········3·2····3···2······2···3····52 ······3·2··········2·3······3·····2········3·2····3···2······2···3····
53 o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-53 o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
54 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··54 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··
55 ·····------------------------------------------------------------------------55 ·····------------------------------------------------------------------------
56 ······3·2········3·2········2·3········2·3········3···2········3·2····56 ······3·2········3·2········2·3········2·3········3···2········3·2····
57 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-57 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
Offset 67, 15 lines modifiedOffset 67, 15 lines modified
67 ········2···3····2·····3····2·····3······2···3········2·3········2·367 ········2···3····2·····3····2·····3······2···3········2·3········2·3
68 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x68 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x
69 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·469 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4
  
70 o6·:·R70 o6·:·R
  
71 i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true)71 i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true)
72 ·--·used·0.000821016s·(cpu);·0.00164152s·(thread);·0s·(gc)72 ·--·used·0.00176784s·(cpu);·0.00208782s·(thread);·0s·(gc)
  
73 o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·))73 o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·))
74 ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···074 ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0
  
75 o7·:·Expression·of·class·Product75 o7·:·Expression·of·class·Product
  
76 i8·:·76 i8·:·
751 B
./usr/share/doc/Macaulay2/SpechtModule/example-output/_representation__Multiplicity.out
    
Offset 25, 15 lines modifiedOffset 25, 15 lines modified
25 o2·:·List25 o2·:·List
  
26 i3·:·tal·:=·tally·apply·(H,h->conjugacyClass·h);26 i3·:·tal·:=·tally·apply·(H,h->conjugacyClass·h);
  
27 i4·:·partis·=·partitions·6;27 i4·:·partis·=·partitions·6;
  
28 i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p))28 i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p))
29 ·--·used·0.220418s·(cpu);·0.194382s·(thread);·0s·(gc)29 ·--·used·0.248535s·(cpu);·0.211121s·(thread);·0s·(gc)
  
30 o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1}30 o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1}
31 ···············Partition{2,·1,·1,·1,·1}·=>·031 ···············Partition{2,·1,·1,·1,·1}·=>·0
32 ···············Partition{2,·2,·1,·1}·=>·132 ···············Partition{2,·2,·1,·1}·=>·1
33 ···············Partition{2,·2,·2}·=>·133 ···············Partition{2,·2,·2}·=>·1
34 ···············Partition{3,·1,·1,·1}·=>·034 ···············Partition{3,·1,·1,·1}·=>·0
35 ···············Partition{3,·2,·1}·=>·035 ···············Partition{3,·2,·1}·=>·0
876 B
./usr/share/doc/Macaulay2/SpechtModule/example-output/_secondary__Invariants_lp__List_cm__Polynomial__Ring_rp.out
    
Offset 9, 15 lines modifiedOffset 9, 15 lines modified
9 i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}}9 i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}}
  
10 o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}}10 o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}}
  
11 o2·:·List11 o2·:·List
  
12 i3·:·time·seco·=·secondaryInvariants(genList,R);12 i3·:·time·seco·=·secondaryInvariants(genList,R);
13 ·--·used·0.446214s·(cpu);·0.376237s·(thread);·0s·(gc)13 ·--·used·0.512363s·(cpu);·0.395961s·(thread);·0s·(gc)
14 (Partition{6},·Ambient_Dimension,·1,·Rank,·1)14 (Partition{6},·Ambient_Dimension,·1,·Rank,·1)
15 (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0)15 (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0)
16 (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1)16 (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1)
17 (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0)17 (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0)
18 (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1)18 (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1)
19 (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0)19 (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0)
20 (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0)20 (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0)
4.72 KB
./usr/share/doc/Macaulay2/SpechtModule/html/_higher__Specht__Polynomial_lp__Young__Tableau_cm__Young__Tableau_cm__Polynomial__Ring_rp.html
    
Offset 125, 15 lines modifiedOffset 125, 15 lines modified
  
125 o4·:·YoungTableau</code></pre>125 o4·:·YoungTableau</code></pre>
126 ············</td>126 ············</td>
127 ··········</tr>127 ··········</tr>
128 ··········<tr>128 ··········<tr>
129 ············<td>129 ············<td>
130 ··············<pre><code·class="language-macaulay2">i5·:·time·higherSpechtPolynomial(S,T,R)130 ··············<pre><code·class="language-macaulay2">i5·:·time·higherSpechtPolynomial(S,T,R)
131 ·--·used·0.000657459s·(cpu);·0.00123139s·(thread);·0s·(gc)131 ·--·used·0.000978515s·(cpu);·0.00141033s·(thread);·0s·(gc)
  
132 ······3·2··········2·3······3·····2········3·2····3···2······2···3····132 ······3·2··········2·3······3·····2········3·2····3···2······2···3····
133 o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-133 o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
134 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··134 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··
135 ·····------------------------------------------------------------------------135 ·····------------------------------------------------------------------------
136 ······3·2········3·2········2·3········2·3········3···2········3·2····136 ······3·2········3·2········2·3········2·3········3···2········3·2····
137 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-137 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
Offset 149, 15 lines modifiedOffset 149, 15 lines modified
  
149 o5·:·R</code></pre>149 o5·:·R</code></pre>
150 ············</td>150 ············</td>
151 ··········</tr>151 ··········</tr>
152 ··········<tr>152 ··········<tr>
153 ············<td>153 ············<td>
154 ··············<pre><code·class="language-macaulay2">i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false)154 ··············<pre><code·class="language-macaulay2">i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false)
155 ·--·used·0.00107092s·(cpu);·0.0009569s·(thread);·0s·(gc)155 ·--·used·0.00115348s·(cpu);·0.00141848s·(thread);·0s·(gc)
  
156 ······3·2··········2·3······3·····2········3·2····3···2······2···3····156 ······3·2··········2·3······3·····2········3·2····3···2······2···3····
157 o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-157 o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
158 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··158 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4··
159 ·····------------------------------------------------------------------------159 ·····------------------------------------------------------------------------
160 ······3·2········3·2········2·3········2·3········3···2········3·2····160 ······3·2········3·2········2·3········2·3········3···2········3·2····
161 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-161 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
Offset 173, 15 lines modifiedOffset 173, 15 lines modified
  
173 o6·:·R</code></pre>173 o6·:·R</code></pre>
174 ············</td>174 ············</td>
175 ··········</tr>175 ··········</tr>
176 ··········<tr>176 ··········<tr>
177 ············<td>177 ············<td>
178 ··············<pre><code·class="language-macaulay2">i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true)178 ··············<pre><code·class="language-macaulay2">i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true)
179 ·--·used·0.000821016s·(cpu);·0.00164152s·(thread);·0s·(gc)179 ·--·used·0.00176784s·(cpu);·0.00208782s·(thread);·0s·(gc)
  
180 o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·))180 o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·))
181 ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0181 ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0
  
182 o7·:·Expression·of·class·Product</code></pre>182 o7·:·Expression·of·class·Product</code></pre>
183 ············</td>183 ············</td>
184 ··········</tr>184 ··········</tr>
2.3 KB
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Offset 68, 15 lines modifiedOffset 68, 15 lines modified
  
68 o4·=·|·0·1·|68 o4·=·|·0·1·|
69 ·····|·2·3·|69 ·····|·2·3·|
70 ·····|·4·|70 ·····|·4·|
  
71 o4·:·YoungTableau71 o4·:·YoungTableau
72 i5·:·time·higherSpechtPolynomial(S,T,R)72 i5·:·time·higherSpechtPolynomial(S,T,R)
73 ·--·used·0.000657459s·(cpu);·0.00123139s·(thread);·0s·(gc)73 ·--·used·0.000978515s·(cpu);·0.00141033s·(thread);·0s·(gc)
  
74 ······3·2··········2·3······3·····2········3·2····3···2······2···374 ······3·2··········2·3······3·····2········3·2····3···2······2···3
75 o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-75 o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
76 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·476 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4
77 ·····------------------------------------------------------------------------77 ·····------------------------------------------------------------------------
78 ······3·2········3·2········2·3········2·3········3···2········3·278 ······3·2········3·2········2·3········2·3········3···2········3·2
79 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-79 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
Offset 88, 15 lines modifiedOffset 88, 15 lines modified
88 ·····------------------------------------------------------------------------88 ·····------------------------------------------------------------------------
89 ········2···3····2·····3····2·····3······2···3········2·3········2·389 ········2···3····2·····3····2·····3······2···3········2·3········2·3
90 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x90 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x
91 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·491 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4
  
92 o5·:·R92 o5·:·R
93 i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false)93 i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false)
94 ·--·used·0.00107092s·(cpu);·0.0009569s·(thread);·0s·(gc)94 ·--·used·0.00115348s·(cpu);·0.00141848s·(thread);·0s·(gc)
  
95 ······3·2··········2·3······3·····2········3·2····3···2······2···395 ······3·2··········2·3······3·····2········3·2····3···2······2···3
96 o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-96 o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
97 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·497 ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4
98 ·····------------------------------------------------------------------------98 ·····------------------------------------------------------------------------
99 ······3·2········3·2········2·3········2·3········3···2········3·299 ······3·2········3·2········2·3········2·3········3···2········3·2
100 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-100 ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··-
Offset 108, 15 lines modifiedOffset 108, 15 lines modified
108 ·····------------------------------------------------------------------------108 ·····------------------------------------------------------------------------
109 ········2···3····2·····3····2·····3······2···3········2·3········2·3109 ········2···3····2·····3····2·····3······2···3········2·3········2·3
110 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x110 ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x
111 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4111 ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4
  
112 o6·:·R112 o6·:·R
113 i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true)113 i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true)
114 ·--·used·0.000821016s·(cpu);·0.00164152s·(thread);·0s·(gc)114 ·--·used·0.00176784s·(cpu);·0.00208782s·(thread);·0s·(gc)
  
115 o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)115 o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)
116 (x·)(x·))116 (x·)(x·))
117 ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4117 ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4
118 2···0118 2···0
  
119 o7·:·Expression·of·class·Product119 o7·:·Expression·of·class·Product
1.61 KB
./usr/share/doc/Macaulay2/SpechtModule/html/_representation__Multiplicity.html
    
Offset 126, 15 lines modifiedOffset 126, 15 lines modified
126 ············<td>126 ············<td>
127 ··············<pre><code·class="language-macaulay2">i4·:·partis·=·partitions·6;</code></pre>127 ··············<pre><code·class="language-macaulay2">i4·:·partis·=·partitions·6;</code></pre>
128 ············</td>128 ············</td>
129 ··········</tr>129 ··········</tr>
130 ··········<tr>130 ··········<tr>
131 ············<td>131 ············<td>
132 ··············<pre><code·class="language-macaulay2">i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p))132 ··············<pre><code·class="language-macaulay2">i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p))
133 ·--·used·0.220418s·(cpu);·0.194382s·(thread);·0s·(gc)133 ·--·used·0.248535s·(cpu);·0.211121s·(thread);·0s·(gc)
  
134 o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1}134 o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1}
135 ···············Partition{2,·1,·1,·1,·1}·=>·0135 ···············Partition{2,·1,·1,·1,·1}·=>·0
136 ···············Partition{2,·2,·1,·1}·=>·1136 ···············Partition{2,·2,·1,·1}·=>·1
137 ···············Partition{2,·2,·2}·=>·1137 ···············Partition{2,·2,·2}·=>·1
138 ···············Partition{3,·1,·1,·1}·=>·0138 ···············Partition{3,·1,·1,·1}·=>·0
139 ···············Partition{3,·2,·1}·=>·0139 ···············Partition{3,·2,·1}·=>·0
776 B
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Offset 63, 15 lines modifiedOffset 63, 15 lines modified
63 representations·of·$H$·in·each·irreducible·representation·of·$S_6$.·We·take63 representations·of·$H$·in·each·irreducible·representation·of·$S_6$.·We·take
64 into·account·that·there·are·multiple·copies·of·each·representation·by64 into·account·that·there·are·multiple·copies·of·each·representation·by
65 multiplying·the·values·with·the·number·of·copies·which·is·given·by·the65 multiplying·the·values·with·the·number·of·copies·which·is·given·by·the
66 hookLengthFormula.66 hookLengthFormula.
67 i4·:·partis·=·partitions·6;67 i4·:·partis·=·partitions·6;
68 i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity68 i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity
69 (tal,p))69 (tal,p))
70 ·--·used·0.220418s·(cpu);·0.194382s·(thread);·0s·(gc)70 ·--·used·0.248535s·(cpu);·0.211121s·(thread);·0s·(gc)
  
71 o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1}71 o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1}
72 ···············Partition{2,·1,·1,·1,·1}·=>·072 ···············Partition{2,·1,·1,·1,·1}·=>·0
73 ···············Partition{2,·2,·1,·1}·=>·173 ···············Partition{2,·2,·1,·1}·=>·1
74 ···············Partition{2,·2,·2}·=>·174 ···············Partition{2,·2,·2}·=>·1
75 ···············Partition{3,·1,·1,·1}·=>·075 ···············Partition{3,·1,·1,·1}·=>·0
76 ···············Partition{3,·2,·1}·=>·076 ···············Partition{3,·2,·1}·=>·0
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Offset 98, 15 lines modifiedOffset 98, 15 lines modified
  
98 o2·:·List</code></pre>98 o2·:·List</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i3·:·time·seco·=·secondaryInvariants(genList,R);103 ··············<pre><code·class="language-macaulay2">i3·:·time·seco·=·secondaryInvariants(genList,R);
104 ·--·used·0.446214s·(cpu);·0.376237s·(thread);·0s·(gc)104 ·--·used·0.512363s·(cpu);·0.395961s·(thread);·0s·(gc)
105 (Partition{6},·Ambient_Dimension,·1,·Rank,·1)105 (Partition{6},·Ambient_Dimension,·1,·Rank,·1)
106 (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0)106 (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0)
107 (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1)107 (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1)
108 (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0)108 (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0)
109 (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1)109 (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1)
110 (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0)110 (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0)
111 (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0)111 (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0)
695 B
html2text {}
    
Offset 45, 15 lines modifiedOffset 45, 15 lines modified
45 o1·:·PolynomialRing45 o1·:·PolynomialRing
46 i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}}46 i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}}
  
47 o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}}47 o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}}
  
48 o2·:·List48 o2·:·List
49 i3·:·time·seco·=·secondaryInvariants(genList,R);49 i3·:·time·seco·=·secondaryInvariants(genList,R);
50 ·--·used·0.446214s·(cpu);·0.376237s·(thread);·0s·(gc)50 ·--·used·0.512363s·(cpu);·0.395961s·(thread);·0s·(gc)
51 (Partition{6},·Ambient_Dimension,·1,·Rank,·1)51 (Partition{6},·Ambient_Dimension,·1,·Rank,·1)
52 (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0)52 (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0)
53 (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1)53 (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1)
54 (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0)54 (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0)
55 (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1)55 (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1)
56 (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0)56 (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0)
57 (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0)57 (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0)
769 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/dump/rawdocumentation.dump
    
Offset 1, 11 lines modifiedOffset 1, 11 lines modified
1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=317 #:len=31
8 SW50ZXJzZWN0aW9uT2ZUaHJlZVF1YWRyaWNzSW5QNw==8 SW50ZXJzZWN0aW9uT2ZUaHJlZVF1YWRyaWNzSW5QNw==
9 #:len=6259 #:len=625
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGNsYXNzIG9mIGFsbCBzcGVjaWFs10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGNsYXNzIG9mIGFsbCBzcGVjaWFs
11 IGludGVyc2VjdGlvbiBvZiB0aHJlZSBxdWFkcmljcyBpbiBQXjciLCAibGluZW51bSIgPT4gMzY111 IGludGVyc2VjdGlvbiBvZiB0aHJlZSBxdWFkcmljcyBpbiBQXjciLCAibGluZW51bSIgPT4gMzY1
725 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_associated__Castelnuovo__Surface.out
    
Offset 10, 15 lines modifiedOffset 10, 15 lines modified
10 ·····of·discriminant·31·=·det|·8·1·|10 ·····of·discriminant·31·=·det|·8·1·|
11 ·····························|·1·4·|11 ·····························|·1·4·|
12 ·····containing·a·surface·of·degree·1·and·sectional·genus·012 ·····containing·a·surface·of·degree·1·and·sectional·genus·0
13 ·····cut·out·by·5·hypersurfaces·of·degree·113 ·····cut·out·by·5·hypersurfaces·of·degree·1
14 ·····(This·is·a·classical·example·of·rational·fourfold)14 ·····(This·is·a·classical·example·of·rational·fourfold)
  
15 i3·:·time·U'·=·associatedCastelnuovoSurface·X;15 i3·:·time·U'·=·associatedCastelnuovoSurface·X;
16 ·--·used·3.66555s·(cpu);·1.02964s·(thread);·0s·(gc)16 ·--·used·4.92611s·(cpu);·1.26083s·(thread);·0s·(gc)
  
17 o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X17 o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X
  
18 i4·:·(mu,U,C,f)·=·building·U';18 i4·:·(mu,U,C,f)·=·building·U';
  
19 i5·:·?·mu19 i5·:·?·mu
  
688 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_associated__K3surface_lp__Special__Cubic__Fourfold_rp.out
    
Offset 7, 15 lines modifiedOffset 7, 15 lines modified
7 i2·:·describe·X7 i2·:·describe·X
  
8 o2·=·Special·cubic·fourfold·of·discriminant·148 o2·=·Special·cubic·fourfold·of·discriminant·14
9 ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·09 ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0
10 ·····cut·out·by·6·hypersurfaces·of·degree·210 ·····cut·out·by·6·hypersurfaces·of·degree·2
  
11 i3·:·time·U'·=·associatedK3surface·X;11 i3·:·time·U'·=·associatedK3surface·X;
12 ·--·used·3.52274s·(cpu);·1.05706s·(thread);·0s·(gc)12 ·--·used·3.6542s·(cpu);·1.0586s·(thread);·0s·(gc)
  
13 o3·:·ProjectiveVariety,·K3·surface·associated·to·X13 o3·:·ProjectiveVariety,·K3·surface·associated·to·X
  
14 i4·:·(mu,U,C,f)·=·building·U';14 i4·:·(mu,U,C,f)·=·building·U';
  
15 i5·:·?·mu15 i5·:·?·mu
  
776 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_associated__K3surface_lp__Special__Gushel__Mukai__Fourfold_rp.out
    
Offset 10, 15 lines modifiedOffset 10, 15 lines modified
10 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·010 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0
11 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)11 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)
12 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)12 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)
13 ·····Type:·ordinary13 ·····Type:·ordinary
14 ·····(case·1·of·Table·1·in·arXiv:2002.07026)14 ·····(case·1·of·Table·1·in·arXiv:2002.07026)
  
15 i3·:·time·U'·=·associatedK3surface·X;15 i3·:·time·U'·=·associatedK3surface·X;
16 ·--·used·7.44895s·(cpu);·3.54361s·(thread);·0s·(gc)16 ·--·used·9.16154s·(cpu);·3.84085s·(thread);·0s·(gc)
  
17 o3·:·ProjectiveVariety,·K3·surface·associated·to·X17 o3·:·ProjectiveVariety,·K3·surface·associated·to·X
  
18 i4·:·(mu,U,C,f)·=·building·U';18 i4·:·(mu,U,C,f)·=·building·U';
  
19 i5·:·?·mu19 i5·:·?·mu
  
1.28 KB
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_detect__Congruence_lp__Special__Cubic__Fourfold_cm__Z__Z_rp.out
    
Offset 8, 28 lines modifiedOffset 8, 28 lines modified
8 i2·:·describe·X8 i2·:·describe·X
  
9 o2·=·Special·cubic·fourfold·of·discriminant·269 o2·=·Special·cubic·fourfold·of·discriminant·26
10 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·010 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0
11 ·····cut·out·by·13·hypersurfaces·of·degree·311 ·····cut·out·by·13·hypersurfaces·of·degree·3
  
12 i3·:·time·f·=·detectCongruence(X,Verbose=>true);12 i3·:·time·f·=·detectCongruence(X,Verbose=>true);
13 ·--·used·2.46194s·(cpu);·1.43868s·(thread);·0s·(gc)13 ·--·used·3.17798s·(cpu);·1.57316s·(thread);·0s·(gc)
14 number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·814 number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8
15 number·2-secant·lines·=·715 number·2-secant·lines·=·7
16 number·5-secant·conics·=·116 number·5-secant·conics·=·1
  
17 o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^517 o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5
  
18 i4·:·p·:=·point·ambient·X·--·random·point·on·P^518 i4·:·p·:=·point·ambient·X·--·random·point·on·P^5
  
19 o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1]19 o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1]
  
20 o4·:·ProjectiveVariety,·a·point·in·PP^520 o4·:·ProjectiveVariety,·a·point·in·PP^5
  
21 i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface21 i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface
22 ·--·used·0.20401s·(cpu);·0.19161s·(thread);·0s·(gc)22 ·--·used·0.344729s·(cpu);·0.226081s·(thread);·0s·(gc)
  
23 o5·:·ProjectiveVariety,·curve·in·PP^523 o5·:·ProjectiveVariety,·curve·in·PP^5
  
24 i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C))24 i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C))
  
25 i7·:·25 i7·:·
1.48 KB
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_detect__Congruence_lp__Special__Gushel__Mukai__Fourfold_cm__Z__Z_rp.out
    
Offset 11, 15 lines modifiedOffset 11, 15 lines modified
11 ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·211 ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·2
12 ·····cut·out·by·19·hypersurfaces·of·degree·212 ·····cut·out·by·19·hypersurfaces·of·degree·2
13 ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2)13 ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2)
14 ·····Type:·ordinary14 ·····Type:·ordinary
15 ·····(case·17·of·Table·1·in·arXiv:2002.07026)15 ·····(case·17·of·Table·1·in·arXiv:2002.07026)
  
16 i3·:·time·f·=·detectCongruence(X,Verbose=>true);16 i3·:·time·f·=·detectCongruence(X,Verbose=>true);
17 ·--·used·9.99197s·(cpu);·5.20211s·(thread);·0s·(gc)17 ·--·used·11.8404s·(cpu);·5.51154s·(thread);·0s·(gc)
18 number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·718 number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7
19 number·1-secant·lines·=·619 number·1-secant·lines·=·6
20 number·3-secant·conics·=·120 number·3-secant·conics·=·1
  
21 o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^821 o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8
  
22 i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X22 i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X
Offset 29, 15 lines modifiedOffset 29, 15 lines modified
29 i5·:·p·:=·point·Y·--·random·point·on·Y29 i5·:·p·:=·point·Y·--·random·point·on·Y
  
30 o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1]30 o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1]
  
31 o5·:·ProjectiveVariety,·a·point·in·PP^831 o5·:·ProjectiveVariety,·a·point·in·PP^8
  
32 i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface32 i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface
33 ·--·used·0.360134s·(cpu);·0.218719s·(thread);·0s·(gc)33 ·--·used·0.377225s·(cpu);·0.210632s·(thread);·0s·(gc)
  
34 o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)34 o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)
  
35 i7·:·S·=·surface·X;35 i7·:·S·=·surface·X;
  
36 o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y)36 o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y)
  
606 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_discriminant_lp__Special__Cubic__Fourfold_rp.out
    
Offset 1, 12 lines modifiedOffset 1, 12 lines modified
1 --·-*-·M2-comint·-*-·hash:·17298908135795611111 --·-*-·M2-comint·-*-·hash:·1729890813579561111
  
2 i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface";2 i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface";
  
3 o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·13 o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1
  
4 i2·:·time·discriminant·X4 i2·:·time·discriminant·X
5 ·--·used·0.198024s·(cpu);·0.0840817s·(thread);·0s·(gc)5 ·--·used·0.255308s·(cpu);·0.101065s·(thread);·0s·(gc)
  
6 o2·=·146 o2·=·14
  
7 i3·:·7 i3·:·
607 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_discriminant_lp__Special__Gushel__Mukai__Fourfold_rp.out
    
Offset 1, 12 lines modifiedOffset 1, 12 lines modified
1 --·-*-·M2-comint·-*-·hash:·17302209324187387131 --·-*-·M2-comint·-*-·hash:·1730220932418738713
  
2 i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric";2 i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric";
  
3 o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·03 o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0
  
4 i2·:·time·discriminant·X4 i2·:·time·discriminant·X
5 ·--·used·1.05068s·(cpu);·0.417605s·(thread);·0s·(gc)5 ·--·used·1.10361s·(cpu);·0.36425s·(thread);·0s·(gc)
  
6 o2·=·106 o2·=·10
  
7 i3·:·7 i3·:·
803 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_parameter__Count.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 o2·:·ProjectiveVariety,·curve·in·PP^55 o2·:·ProjectiveVariety,·curve·in·PP^5
  
6 i3·:·X·=·random({{2},{2},{2}},S);6 i3·:·X·=·random({{2},{2},{2}},S);
  
7 o3·:·ProjectiveVariety,·surface·in·PP^57 o3·:·ProjectiveVariety,·surface·in·PP^5
  
8 i4·:·time·parameterCount(S,X,Verbose=>true)8 i4·:·time·parameterCount(S,X,Verbose=>true)
9 ·--·used·0.228008s·(cpu);·0.169064s·(thread);·0s·(gc)9 ·--·used·0.254576s·(cpu);·0.189213s·(thread);·0s·(gc)
10 S:·rational·normal·curve·of·degree·5·in·PP^510 S:·rational·normal·curve·of·degree·5·in·PP^5
11 X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·211 X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2
12 (assumption:·h^1(N_{S,P^5})·=·0)12 (assumption:·h^1(N_{S,P^5})·=·0)
13 h^0(N_{S,P^5})·=·3213 h^0(N_{S,P^5})·=·32
14 h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2));14 h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2));
15 in·particular,·h^0(I_{S,P^5}(2))·is·minimal15 in·particular,·h^0(I_{S,P^5}(2))·is·minimal
16 dim·GG(2,9)·=·2116 dim·GG(2,9)·=·21
848 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_parameter__Count_lp__Special__Cubic__Fourfold_rp.out
    
Offset 5, 15 lines modifiedOffset 5, 15 lines modified
5 o2·:·ProjectiveVariety,·surface·in·PP^55 o2·:·ProjectiveVariety,·surface·in·PP^5
  
6 i3·:·X·=·specialCubicFourfold·V;6 i3·:·X·=·specialCubicFourfold·V;
  
7 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·07 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0
  
8 i4·:·time·parameterCount(X,Verbose=>true)8 i4·:·time·parameterCount(X,Verbose=>true)
9 ·--·used·0.461283s·(cpu);·0.303868s·(thread);·0s·(gc)9 ·--·used·0.510861s·(cpu);·0.33023s·(thread);·0s·(gc)
10 S:·Veronese·surface·in·PP^510 S:·Veronese·surface·in·PP^5
11 X:·smooth·cubic·hypersurface·in·PP^511 X:·smooth·cubic·hypersurface·in·PP^5
12 (assumption:·h^1(N_{S,P^5})·=·0)12 (assumption:·h^1(N_{S,P^5})·=·0)
13 h^0(N_{S,P^5})·=·2713 h^0(N_{S,P^5})·=·27
14 h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3));14 h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3));
15 in·particular,·h^0(I_{S,P^5}(3))·is·minimal15 in·particular,·h^0(I_{S,P^5}(3))·is·minimal
16 h^0(N_{S,P^5})·+·27·=·5416 h^0(N_{S,P^5})·+·27·=·54
927 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_parameter__Count_lp__Special__Gushel__Mukai__Fourfold_rp.out
    
Offset 11, 15 lines modifiedOffset 11, 15 lines modified
11 o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G)11 o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G)
  
12 i3·:·X·=·specialGushelMukaiFourfold·S;12 i3·:·X·=·specialGushelMukaiFourfold·S;
  
13 o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·013 o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0
  
14 i4·:·time·parameterCount(X,Verbose=>true)14 i4·:·time·parameterCount(X,Verbose=>true)
15 ·--·used·3.00398s·(cpu);·2.23979s·(thread);·0s·(gc)15 ·--·used·2.99482s·(cpu);·2.13094s·(thread);·0s·(gc)
16 S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2)16 S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2)
17 X:·GM·fourfold·containing·S17 X:·GM·fourfold·containing·S
18 Y:·del·Pezzo·fivefold·containing·X18 Y:·del·Pezzo·fivefold·containing·X
19 h^1(N_{S,Y})·=·019 h^1(N_{S,Y})·=·0
20 h^0(N_{S,Y})·=·1120 h^0(N_{S,Y})·=·11
21 h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2));21 h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2));
22 in·particular,·h^0(I_{S,Y}(2))·is·minimal22 in·particular,·h^0(I_{S,Y}(2))·is·minimal
692 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_parametrize__Fano__Fourfold.out
    
Offset 6, 15 lines modifiedOffset 6, 15 lines modified
  
6 i3·:·?·X6 i3·:·?·X
  
7 o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees7 o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees
8 ·····1^2·2^58 ·····1^2·2^5
  
9 i4·:·time·parametrizeFanoFourfold·X9 i4·:·time·parametrizeFanoFourfold·X
10 ·--·used·2.03176s·(cpu);·0.758056s·(thread);·0s·(gc)10 ·--·used·2.07715s·(cpu);·0.692117s·(thread);·0s·(gc)
  
11 o4·=·multi-rational·map·consisting·of·one·single·rational·map11 o4·=·multi-rational·map·consisting·of·one·single·rational·map
12 ·····source·variety:·PP^412 ·····source·variety:·PP^4
13 ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5·13 ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5·
14 ·····dominance:·true14 ·····dominance:·true
15 ·····degree:·115 ·····degree:·1
  
1.45 KB
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_special__Cubic__Fourfold.out
    
Offset 7, 22 lines modifiedOffset 7, 22 lines modified
7 o3·:·ProjectiveVariety,·surface·in·PP^57 o3·:·ProjectiveVariety,·surface·in·PP^5
  
8 i4·:·X·=·projectiveVariety·ideal(x_1^2*x_3+x_0*x_2*x_3-6*x_1*x_2*x_3-x_0*x_3^2-4*x_1*x_3^2-3*x_2*x_3^2+2*x_0^2*x_4-10*x_0*x_1*x_4+13*x_1^2*x_4-x_0*x_2*x_4-3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2);8 i4·:·X·=·projectiveVariety·ideal(x_1^2*x_3+x_0*x_2*x_3-6*x_1*x_2*x_3-x_0*x_3^2-4*x_1*x_3^2-3*x_2*x_3^2+2*x_0^2*x_4-10*x_0*x_1*x_4+13*x_1^2*x_4-x_0*x_2*x_4-3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2);
  
9 o4·:·ProjectiveVariety,·hypersurface·in·PP^59 o4·:·ProjectiveVariety,·hypersurface·in·PP^5
  
10 i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3);10 i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3);
11 ·--·used·0.00800442s·(cpu);·0.00762065s·(thread);·0s·(gc)11 ·--·used·0.00799622s·(cpu);·0.00968169s·(thread);·0s·(gc)
  
12 o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·012 o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0
  
13 i6·:·time·describe·F13 i6·:·time·describe·F
14 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it14 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
15 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·986815 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
16 ·--·used·0.308696s·(cpu);·0.16513s·(thread);·0s·(gc)16 ·--·used·0.802024s·(cpu);·0.204896s·(thread);·0s·(gc)
  
17 o6·=·Special·cubic·fourfold·of·discriminant·2617 o6·=·Special·cubic·fourfold·of·discriminant·26
18 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·018 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0
19 ·····cut·out·by·13·hypersurfaces·of·degree·319 ·····cut·out·by·13·hypersurfaces·of·degree·3
  
20 i7·:·assert(F·==·X)20 i7·:·assert(F·==·X)
  
1.62 KB
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_special__Gushel__Mukai__Fourfold.out
    
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7 o3·:·ProjectiveVariety,·surface·in·PP^87 o3·:·ProjectiveVariety,·surface·in·PP^8
  
8 i4·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8);8 i4·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8);
  
9 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^89 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8
  
10 i5·:·time·F·=·specialGushelMukaiFourfold(S,X);10 i5·:·time·F·=·specialGushelMukaiFourfold(S,X);
11 ·--·used·1.46847s·(cpu);·1.18763s·(thread);·0s·(gc)11 ·--·used·1.58162s·(cpu);·1.26197s·(thread);·0s·(gc)
  
12 o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·012 o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0
  
13 i6·:·time·describe·F13 i6·:·time·describe·F
14 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it14 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
15 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·986815 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
16 ·--·used·7.18628s·(cpu);·2.85211s·(thread);·0s·(gc)16 ·--·used·8.24383s·(cpu);·2.90951s·(thread);·0s·(gc)
  
17 o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')17 o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')
18 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·018 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0
19 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)19 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)
20 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)20 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)
21 ·····Type:·ordinary21 ·····Type:·ordinary
22 ·····(case·1·of·Table·1·in·arXiv:2002.07026)22 ·····(case·1·of·Table·1·in·arXiv:2002.07026)
1.34 KB
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_to__Grass.out
    
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5 i2·:·X·=·specialGushelMukaiFourfold(ideal(x_6-x_7,·x_5,·x_3-x_4,·x_1,·x_0-x_4,·x_2*x_7-x_4*x_8),·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8));5 i2·:·X·=·specialGushelMukaiFourfold(ideal(x_6-x_7,·x_5,·x_3-x_4,·x_1,·x_0-x_4,·x_2*x_7-x_4*x_8),·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8));
  
6 o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·06 o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0
  
7 i3·:·time·toGrass·X7 i3·:·time·toGrass·X
8 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it8 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
9 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·98689 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
10 ·--·used·6.30822s·(cpu);·2.55839s·(thread);·0s·(gc)10 ·--·used·7.15313s·(cpu);·2.75512s·(thread);·0s·(gc)
  
11 o3·=·multi-rational·map·consisting·of·one·single·rational·map11 o3·=·multi-rational·map·consisting·of·one·single·rational·map
12 ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·212 ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2
13 ·····target·variety:·GG(1,4)··PP^913 ·····target·variety:·GG(1,4)··PP^9
  
14 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))14 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))
  
1.06 KB
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_to__Grass_lp__Embedded__Projective__Variety_rp.out
    
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5 i2·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8);5 i2·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8);
  
6 o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^86 o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8
  
7 i3·:·time·toGrass·X7 i3·:·time·toGrass·X
8 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it8 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
9 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·98689 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
10 ·--·used·6.17467s·(cpu);·2.42428s·(thread);·0s·(gc)10 ·--·used·6.8357s·(cpu);·2.73868s·(thread);·0s·(gc)
  
11 o3·=·multi-rational·map·consisting·of·one·single·rational·map11 o3·=·multi-rational·map·consisting·of·one·single·rational·map
12 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·212 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2
13 ·····target·variety:·GG(1,4)··PP^913 ·····target·variety:·GG(1,4)··PP^9
  
14 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))14 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))
  
633 B
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/example-output/_unirational__Parametrization.out
    
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5 o2·:·ProjectiveVariety,·surface·in·PP^55 o2·:·ProjectiveVariety,·surface·in·PP^5
  
6 i3·:·X·=·specialCubicFourfold·S;6 i3·:·X·=·specialCubicFourfold·S;
  
7 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·07 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0
  
8 i4·:·time·f·=·unirationalParametrization·X;8 i4·:·time·f·=·unirationalParametrization·X;
9 ·--·used·1.04818s·(cpu);·0.428468s·(thread);·0s·(gc)9 ·--·used·1.15578s·(cpu);·0.43858s·(thread);·0s·(gc)
  
10 o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)10 o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)
  
11 i5·:·degreeSequence·f11 i5·:·degreeSequence·f
  
12 o5·=·{[10]}12 o5·=·{[10]}
  
1.53 KB
./usr/share/doc/Macaulay2/SpecialFanoFourfolds/html/_associated__Castelnuovo__Surface.html
    
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106 ·····cut·out·by·5·hypersurfaces·of·degree·1106 ·····cut·out·by·5·hypersurfaces·of·degree·1
107 ·····(This·is·a·classical·example·of·rational·fourfold)</code></pre>107 ·····(This·is·a·classical·example·of·rational·fourfold)</code></pre>
108 ············</td>108 ············</td>
109 ··········</tr>109 ··········</tr>
110 ··········<tr>110 ··········<tr>
111 ············<td>111 ············<td>
112 ··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedCastelnuovoSurface·X;112 ··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedCastelnuovoSurface·X;
113 ·--·used·3.66555s·(cpu);·1.02964s·(thread);·0s·(gc)113 ·--·used·4.92611s·(cpu);·1.26083s·(thread);·0s·(gc)
  
114 o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X</code></pre>114 o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X</code></pre>
115 ············</td>115 ············</td>
116 ··········</tr>116 ··········</tr>
117 ··········<tr>117 ··········<tr>
118 ············<td>118 ············<td>
119 ··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre>119 ··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre>
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41 o2·=·Complete·intersection·of·3·quadrics·in·PP^741 o2·=·Complete·intersection·of·3·quadrics·in·PP^7
42 ·····of·discriminant·31·=·det|·8·1·|42 ·····of·discriminant·31·=·det|·8·1·|
43 ·····························|·1·4·|43 ·····························|·1·4·|
44 ·····containing·a·surface·of·degree·1·and·sectional·genus·044 ·····containing·a·surface·of·degree·1·and·sectional·genus·0
45 ·····cut·out·by·5·hypersurfaces·of·degree·145 ·····cut·out·by·5·hypersurfaces·of·degree·1
46 ·····(This·is·a·classical·example·of·rational·fourfold)46 ·····(This·is·a·classical·example·of·rational·fourfold)
47 i3·:·time·U'·=·associatedCastelnuovoSurface·X;47 i3·:·time·U'·=·associatedCastelnuovoSurface·X;
48 ·--·used·3.66555s·(cpu);·1.02964s·(thread);·0s·(gc)48 ·--·used·4.92611s·(cpu);·1.26083s·(thread);·0s·(gc)
  
49 o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X49 o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X
50 i4·:·(mu,U,C,f)·=·building·U';50 i4·:·(mu,U,C,f)·=·building·U';
51 i5·:·?·mu51 i5·:·?·mu
  
52 o5·=·multi-rational·map·consisting·of·one·single·rational·map52 o5·=·multi-rational·map·consisting·of·one·single·rational·map
53 ·····source·variety:·5-dimensional·subvariety·of·PP^7·cut·out·by·253 ·····source·variety:·5-dimensional·subvariety·of·PP^7·cut·out·by·2
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104 ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0104 ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0
105 ·····cut·out·by·6·hypersurfaces·of·degree·2</code></pre>105 ·····cut·out·by·6·hypersurfaces·of·degree·2</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ··········<tr>108 ··········<tr>
109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X;110 ··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X;
111 ·--·used·3.52274s·(cpu);·1.05706s·(thread);·0s·(gc)111 ·--·used·3.6542s·(cpu);·1.0586s·(thread);·0s·(gc)
  
112 o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre>112 o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre>
113 ············</td>113 ············</td>
114 ··········</tr>114 ··········</tr>
115 ··········<tr>115 ··········<tr>
116 ············<td>116 ············<td>
117 ··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre>117 ··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre>
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41 sectional·genus·041 sectional·genus·0
42 i2·:·describe·X42 i2·:·describe·X
  
43 o2·=·Special·cubic·fourfold·of·discriminant·1443 o2·=·Special·cubic·fourfold·of·discriminant·14
44 ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·044 ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0
45 ·····cut·out·by·6·hypersurfaces·of·degree·245 ·····cut·out·by·6·hypersurfaces·of·degree·2
46 i3·:·time·U'·=·associatedK3surface·X;46 i3·:·time·U'·=·associatedK3surface·X;
47 ·--·used·3.52274s·(cpu);·1.05706s·(thread);·0s·(gc)47 ·--·used·3.6542s·(cpu);·1.0586s·(thread);·0s·(gc)
  
48 o3·:·ProjectiveVariety,·K3·surface·associated·to·X48 o3·:·ProjectiveVariety,·K3·surface·associated·to·X
49 i4·:·(mu,U,C,f)·=·building·U';49 i4·:·(mu,U,C,f)·=·building·U';
50 i5·:·?·mu50 i5·:·?·mu
  
51 o5·=·multi-rational·map·consisting·of·one·single·rational·map51 o5·=·multi-rational·map·consisting·of·one·single·rational·map
52 ·····source·variety:·PP^552 ·····source·variety:·PP^5
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107 ·····Type:·ordinary107 ·····Type:·ordinary
108 ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre>108 ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre>
109 ············</td>109 ············</td>
110 ··········</tr>110 ··········</tr>
111 ··········<tr>111 ··········<tr>
112 ············<td>112 ············<td>
113 ··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X;113 ··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X;
114 ·--·used·7.44895s·(cpu);·3.54361s·(thread);·0s·(gc)114 ·--·used·9.16154s·(cpu);·3.84085s·(thread);·0s·(gc)
  
115 o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre>115 o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre>
116 ············</td>116 ············</td>
117 ··········</tr>117 ··········</tr>
118 ··········<tr>118 ··········<tr>
119 ············<td>119 ············<td>
120 ··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre>120 ··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre>
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43 o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')43 o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')
44 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·044 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0
45 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)45 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)
46 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)46 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)
47 ·····Type:·ordinary47 ·····Type:·ordinary
48 ·····(case·1·of·Table·1·in·arXiv:2002.07026)48 ·····(case·1·of·Table·1·in·arXiv:2002.07026)
49 i3·:·time·U'·=·associatedK3surface·X;49 i3·:·time·U'·=·associatedK3surface·X;
50 ·--·used·7.44895s·(cpu);·3.54361s·(thread);·0s·(gc)50 ·--·used·9.16154s·(cpu);·3.84085s·(thread);·0s·(gc)
  
51 o3·:·ProjectiveVariety,·K3·surface·associated·to·X51 o3·:·ProjectiveVariety,·K3·surface·associated·to·X
52 i4·:·(mu,U,C,f)·=·building·U';52 i4·:·(mu,U,C,f)·=·building·U';
53 i5·:·?·mu53 i5·:·?·mu
  
54 o5·=·multi-rational·map·consisting·of·one·single·rational·map54 o5·=·multi-rational·map·consisting·of·one·single·rational·map
55 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·555 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5
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91 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·091 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0
92 ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre>92 ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true);97 ··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true);
98 ·--·used·2.46194s·(cpu);·1.43868s·(thread);·0s·(gc)98 ·--·used·3.17798s·(cpu);·1.57316s·(thread);·0s·(gc)
99 number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·899 number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8
100 number·2-secant·lines·=·7100 number·2-secant·lines·=·7
101 number·5-secant·conics·=·1101 number·5-secant·conics·=·1
  
102 o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5</code></pre>102 o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
Offset 111, 15 lines modifiedOffset 111, 15 lines modified
  
111 o4·:·ProjectiveVariety,·a·point·in·PP^5</code></pre>111 o4·:·ProjectiveVariety,·a·point·in·PP^5</code></pre>
112 ············</td>112 ············</td>
113 ··········</tr>113 ··········</tr>
114 ··········<tr>114 ··········<tr>
115 ············<td>115 ············<td>
116 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface116 ··············<pre><code·class="language-macaulay2">i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface
117 ·--·used·0.20401s·(cpu);·0.19161s·(thread);·0s·(gc)117 ·--·used·0.344729s·(cpu);·0.226081s·(thread);·0s·(gc)
  
118 o5·:·ProjectiveVariety,·curve·in·PP^5</code></pre>118 o5·:·ProjectiveVariety,·curve·in·PP^5</code></pre>
119 ············</td>119 ············</td>
120 ··········</tr>120 ··········</tr>
121 ··········<tr>121 ··········<tr>
122 ············<td>122 ············<td>
123 ··············<pre><code·class="language-macaulay2">i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C))</code></pre>123 ··············<pre><code·class="language-macaulay2">i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C))</code></pre>
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30 sectional·genus·030 sectional·genus·0
31 i2·:·describe·X31 i2·:·describe·X
  
32 o2·=·Special·cubic·fourfold·of·discriminant·2632 o2·=·Special·cubic·fourfold·of·discriminant·26
33 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·033 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0
34 ·····cut·out·by·13·hypersurfaces·of·degree·334 ·····cut·out·by·13·hypersurfaces·of·degree·3
35 i3·:·time·f·=·detectCongruence(X,Verbose=>true);35 i3·:·time·f·=·detectCongruence(X,Verbose=>true);
36 ·--·used·2.46194s·(cpu);·1.43868s·(thread);·0s·(gc)36 ·--·used·3.17798s·(cpu);·1.57316s·(thread);·0s·(gc)
37 number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a37 number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a
38 general·point:·838 general·point:·8
39 number·2-secant·lines·=·739 number·2-secant·lines·=·7
40 number·5-secant·conics·=·140 number·5-secant·conics·=·1
  
41 o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^541 o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5
42 i4·:·p·:=·point·ambient·X·--·random·point·on·P^542 i4·:·p·:=·point·ambient·X·--·random·point·on·P^5
  
43 o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1]43 o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1]
  
44 o4·:·ProjectiveVariety,·a·point·in·PP^544 o4·:·ProjectiveVariety,·a·point·in·PP^5
45 i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface45 i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface
46 ·--·used·0.20401s·(cpu);·0.19161s·(thread);·0s·(gc)46 ·--·used·0.344729s·(cpu);·0.226081s·(thread);·0s·(gc)
  
47 o5·:·ProjectiveVariety,·curve·in·PP^547 o5·:·ProjectiveVariety,·curve·in·PP^5
48 i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree48 i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree
49 (C·*·surface·X)·==·5·and·isSubset(p,·C))49 (C·*·surface·X)·==·5·and·isSubset(p,·C))
50 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*50 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
51 ····*·_\x8d_\x8e_\x8t_\x8e_\x8c_\x8t_\x8C_\x8o_\x8n_\x8g_\x8r_\x8u_\x8e_\x8n_\x8c_\x8e_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8,_\x8Z_\x8Z_\x8)·--·detect·and·return·a51 ····*·_\x8d_\x8e_\x8t_\x8e_\x8c_\x8t_\x8C_\x8o_\x8n_\x8g_\x8r_\x8u_\x8e_\x8n_\x8c_\x8e_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8,_\x8Z_\x8Z_\x8)·--·detect·and·return·a
52 ······congruence·of·(2e-1)-secant·curves·of·degree·e·inside·a·del·Pezzo52 ······congruence·of·(2e-1)-secant·curves·of·degree·e·inside·a·del·Pezzo
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94 ·····Type:·ordinary94 ·····Type:·ordinary
95 ·····(case·17·of·Table·1·in·arXiv:2002.07026)</code></pre>95 ·····(case·17·of·Table·1·in·arXiv:2002.07026)</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true);100 ··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true);
101 ·--·used·9.99197s·(cpu);·5.20211s·(thread);·0s·(gc)101 ·--·used·11.8404s·(cpu);·5.51154s·(thread);·0s·(gc)
102 number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7102 number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7
103 number·1-secant·lines·=·6103 number·1-secant·lines·=·6
104 number·3-secant·conics·=·1104 number·3-secant·conics·=·1
  
105 o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8</code></pre>105 o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
Offset 121, 15 lines modifiedOffset 121, 15 lines modified
  
121 o5·:·ProjectiveVariety,·a·point·in·PP^8</code></pre>121 o5·:·ProjectiveVariety,·a·point·in·PP^8</code></pre>
122 ············</td>122 ············</td>
123 ··········</tr>123 ··········</tr>
124 ··········<tr>124 ··········<tr>
125 ············<td>125 ············<td>
126 ··············<pre><code·class="language-macaulay2">i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface126 ··············<pre><code·class="language-macaulay2">i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface
127 ·--·used·0.360134s·(cpu);·0.218719s·(thread);·0s·(gc)127 ·--·used·0.377225s·(cpu);·0.210632s·(thread);·0s·(gc)
  
128 o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)</code></pre>128 o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)</code></pre>
129 ············</td>129 ············</td>
130 ··········</tr>130 ··········</tr>
131 ··········<tr>131 ··········<tr>
132 ············<td>132 ············<td>
133 ··············<pre><code·class="language-macaulay2">i7·:·S·=·surface·X;133 ··············<pre><code·class="language-macaulay2">i7·:·S·=·surface·X;
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36 o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·2036 o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·20
37 ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·237 ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·2
38 ·····cut·out·by·19·hypersurfaces·of·degree·238 ·····cut·out·by·19·hypersurfaces·of·degree·2
39 ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2)39 ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2)
40 ·····Type:·ordinary40 ·····Type:·ordinary
41 ·····(case·17·of·Table·1·in·arXiv:2002.07026)41 ·····(case·17·of·Table·1·in·arXiv:2002.07026)
42 i3·:·time·f·=·detectCongruence(X,Verbose=>true);42 i3·:·time·f·=·detectCongruence(X,Verbose=>true);
43 ·--·used·9.99197s·(cpu);·5.20211s·(thread);·0s·(gc)43 ·--·used·11.8404s·(cpu);·5.51154s·(thread);·0s·(gc)
44 number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a44 number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a
45 general·point:·745 general·point:·7
46 number·1-secant·lines·=·646 number·1-secant·lines·=·6
47 number·3-secant·conics·=·147 number·3-secant·conics·=·1
  
48 o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^848 o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8
49 i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X49 i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X
Offset 53, 15 lines modifiedOffset 53, 15 lines modified
53 i5·:·p·:=·point·Y·--·random·point·on·Y53 i5·:·p·:=·point·Y·--·random·point·on·Y
  
54 o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,54 o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,
55 13402,·1]55 13402,·1]
  
56 o5·:·ProjectiveVariety,·a·point·in·PP^856 o5·:·ProjectiveVariety,·a·point·in·PP^8
57 i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface57 i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface
58 ·--·used·0.360134s·(cpu);·0.218719s·(thread);·0s·(gc)58 ·--·used·0.377225s·(cpu);·0.210632s·(thread);·0s·(gc)
  
59 o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)59 o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)
60 i7·:·S·=·surface·X;60 i7·:·S·=·surface·X;
  
61 o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y)61 o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y)
62 i8·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C*S)·==·0·and·degree(C*S)·==·362 i8·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C*S)·==·0·and·degree(C*S)·==·3
63 and·isSubset(p,C)·and·isSubset(C,Y))63 and·isSubset(p,C)·and·isSubset(C,Y))
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80 o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1</code></pre>80 o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X85 ··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X
86 ·--·used·0.198024s·(cpu);·0.0840817s·(thread);·0s·(gc)86 ·--·used·0.255308s·(cpu);·0.101065s·(thread);·0s·(gc)
  
87 o2·=·14</code></pre>87 o2·=·14</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ········</table>90 ········</table>
91 ······</div>91 ······</div>
92 ······<div>92 ······<div>
892 B
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20 thanks·to·the·functions·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm20 thanks·to·the·functions·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm
21 allows·you·to·select·the·method).21 allows·you·to·select·the·method).
22 i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface";22 i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface";
  
23 o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and23 o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and
24 sectional·genus·124 sectional·genus·1
25 i2·:·time·discriminant·X25 i2·:·time·discriminant·X
26 ·--·used·0.198024s·(cpu);·0.0840817s·(thread);·0s·(gc)26 ·--·used·0.255308s·(cpu);·0.101065s·(thread);·0s·(gc)
  
27 o2·=·1427 o2·=·14
28 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
29 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special29 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special
30 ······Gushel-Mukai·fourfold30 ······Gushel-Mukai·fourfold
31 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*31 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
32 ····*·discriminant(HodgeSpecialFourfold)32 ····*·discriminant(HodgeSpecialFourfold)
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80 o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre>80 o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X85 ··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X
86 ·--·used·1.05068s·(cpu);·0.417605s·(thread);·0s·(gc)86 ·--·used·1.10361s·(cpu);·0.36425s·(thread);·0s·(gc)
  
87 o2·=·10</code></pre>87 o2·=·10</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ········</table>90 ········</table>
91 ······</div>91 ······</div>
92 ······<div>92 ······<div>
989 B
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20 the·functions·_\x8c_\x8y_\x8c_\x8l_\x8e_\x8C_\x8l_\x8a_\x8s_\x8s,·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm20 the·functions·_\x8c_\x8y_\x8c_\x8l_\x8e_\x8C_\x8l_\x8a_\x8s_\x8s,·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm
21 allows·you·to·select·the·method).21 allows·you·to·select·the·method).
22 i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric";22 i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric";
  
23 o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and23 o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and
24 sectional·genus·024 sectional·genus·0
25 i2·:·time·discriminant·X25 i2·:·time·discriminant·X
26 ·--·used·1.05068s·(cpu);·0.417605s·(thread);·0s·(gc)26 ·--·used·1.10361s·(cpu);·0.36425s·(thread);·0s·(gc)
  
27 o2·=·1027 o2·=·10
28 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*28 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
29 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special·cubic29 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special·cubic
30 ······fourfold30 ······fourfold
31 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*31 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
32 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special32 ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special
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88 o3·:·ProjectiveVariety,·surface·in·PP^5</code></pre>88 o3·:·ProjectiveVariety,·surface·in·PP^5</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(S,X,Verbose=>true)93 ··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(S,X,Verbose=>true)
94 ·--·used·0.228008s·(cpu);·0.169064s·(thread);·0s·(gc)94 ·--·used·0.254576s·(cpu);·0.189213s·(thread);·0s·(gc)
95 S:·rational·normal·curve·of·degree·5·in·PP^595 S:·rational·normal·curve·of·degree·5·in·PP^5
96 X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·296 X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2
97 (assumption:·h^1(N_{S,P^5})·=·0)97 (assumption:·h^1(N_{S,P^5})·=·0)
98 h^0(N_{S,P^5})·=·3298 h^0(N_{S,P^5})·=·32
99 h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2));99 h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2));
100 in·particular,·h^0(I_{S,P^5}(2))·is·minimal100 in·particular,·h^0(I_{S,P^5}(2))·is·minimal
101 dim·GG(2,9)·=·21101 dim·GG(2,9)·=·21
680 B
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23 i1·:·K·=·ZZ/33331;·S·=·PP_K^(1,5);23 i1·:·K·=·ZZ/33331;·S·=·PP_K^(1,5);
  
24 o2·:·ProjectiveVariety,·curve·in·PP^524 o2·:·ProjectiveVariety,·curve·in·PP^5
25 i3·:·X·=·random({{2},{2},{2}},S);25 i3·:·X·=·random({{2},{2},{2}},S);
  
26 o3·:·ProjectiveVariety,·surface·in·PP^526 o3·:·ProjectiveVariety,·surface·in·PP^5
27 i4·:·time·parameterCount(S,X,Verbose=>true)27 i4·:·time·parameterCount(S,X,Verbose=>true)
28 ·--·used·0.228008s·(cpu);·0.169064s·(thread);·0s·(gc)28 ·--·used·0.254576s·(cpu);·0.189213s·(thread);·0s·(gc)
29 S:·rational·normal·curve·of·degree·5·in·PP^529 S:·rational·normal·curve·of·degree·5·in·PP^5
30 X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·330 X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3
31 hypersurfaces·of·degree·231 hypersurfaces·of·degree·2
32 (assumption:·h^1(N_{S,P^5})·=·0)32 (assumption:·h^1(N_{S,P^5})·=·0)
33 h^0(N_{S,P^5})·=·3233 h^0(N_{S,P^5})·=·32
34 h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2));34 h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2));
35 in·particular,·h^0(I_{S,P^5}(2))·is·minimal35 in·particular,·h^0(I_{S,P^5}(2))·is·minimal
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89 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre>89 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true)94 ··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true)
95 ·--·used·0.461283s·(cpu);·0.303868s·(thread);·0s·(gc)95 ·--·used·0.510861s·(cpu);·0.33023s·(thread);·0s·(gc)
96 S:·Veronese·surface·in·PP^596 S:·Veronese·surface·in·PP^5
97 X:·smooth·cubic·hypersurface·in·PP^597 X:·smooth·cubic·hypersurface·in·PP^5
98 (assumption:·h^1(N_{S,P^5})·=·0)98 (assumption:·h^1(N_{S,P^5})·=·0)
99 h^0(N_{S,P^5})·=·2799 h^0(N_{S,P^5})·=·27
100 h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3));100 h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3));
101 in·particular,·h^0(I_{S,P^5}(3))·is·minimal101 in·particular,·h^0(I_{S,P^5}(3))·is·minimal
102 h^0(N_{S,P^5})·+·27·=·54102 h^0(N_{S,P^5})·+·27·=·54
643 B
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33 o2·:·ProjectiveVariety,·surface·in·PP^533 o2·:·ProjectiveVariety,·surface·in·PP^5
34 i3·:·X·=·specialCubicFourfold·V;34 i3·:·X·=·specialCubicFourfold·V;
  
35 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and35 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and
36 sectional·genus·036 sectional·genus·0
37 i4·:·time·parameterCount(X,Verbose=>true)37 i4·:·time·parameterCount(X,Verbose=>true)
38 ·--·used·0.461283s·(cpu);·0.303868s·(thread);·0s·(gc)38 ·--·used·0.510861s·(cpu);·0.33023s·(thread);·0s·(gc)
39 S:·Veronese·surface·in·PP^539 S:·Veronese·surface·in·PP^5
40 X:·smooth·cubic·hypersurface·in·PP^540 X:·smooth·cubic·hypersurface·in·PP^5
41 (assumption:·h^1(N_{S,P^5})·=·0)41 (assumption:·h^1(N_{S,P^5})·=·0)
42 h^0(N_{S,P^5})·=·2742 h^0(N_{S,P^5})·=·27
43 h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3));43 h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3));
44 in·particular,·h^0(I_{S,P^5}(3))·is·minimal44 in·particular,·h^0(I_{S,P^5}(3))·is·minimal
45 h^0(N_{S,P^5})·+·27·=·5445 h^0(N_{S,P^5})·+·27·=·54
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98 o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0</code></pre>98 o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true)103 ··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true)
104 ·--·used·3.00398s·(cpu);·2.23979s·(thread);·0s·(gc)104 ·--·used·2.99482s·(cpu);·2.13094s·(thread);·0s·(gc)
105 S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2)105 S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2)
106 X:·GM·fourfold·containing·S106 X:·GM·fourfold·containing·S
107 Y:·del·Pezzo·fivefold·containing·X107 Y:·del·Pezzo·fivefold·containing·X
108 h^1(N_{S,Y})·=·0108 h^1(N_{S,Y})·=·0
109 h^0(N_{S,Y})·=·11109 h^0(N_{S,Y})·=·11
110 h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2));110 h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2));
111 in·particular,·h^0(I_{S,Y}(2))·is·minimal111 in·particular,·h^0(I_{S,Y}(2))·is·minimal
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35 o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G)35 o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G)
36 i3·:·X·=·specialGushelMukaiFourfold·S;36 i3·:·X·=·specialGushelMukaiFourfold·S;
  
37 o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and37 o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and
38 sectional·genus·038 sectional·genus·0
39 i4·:·time·parameterCount(X,Verbose=>true)39 i4·:·time·parameterCount(X,Verbose=>true)
40 ·--·used·3.00398s·(cpu);·2.23979s·(thread);·0s·(gc)40 ·--·used·2.99482s·(cpu);·2.13094s·(thread);·0s·(gc)
41 S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2)41 S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2)
42 X:·GM·fourfold·containing·S42 X:·GM·fourfold·containing·S
43 Y:·del·Pezzo·fivefold·containing·X43 Y:·del·Pezzo·fivefold·containing·X
44 h^1(N_{S,Y})·=·044 h^1(N_{S,Y})·=·0
45 h^0(N_{S,Y})·=·1145 h^0(N_{S,Y})·=·11
46 h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2));46 h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2));
47 in·particular,·h^0(I_{S,Y}(2))·is·minimal47 in·particular,·h^0(I_{S,Y}(2))·is·minimal
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88 o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees88 o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees
89 ·····1^2·2^5</code></pre>89 ·····1^2·2^5</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i4·:·time·parametrizeFanoFourfold·X94 ··············<pre><code·class="language-macaulay2">i4·:·time·parametrizeFanoFourfold·X
95 ·--·used·2.03176s·(cpu);·0.758056s·(thread);·0s·(gc)95 ·--·used·2.07715s·(cpu);·0.692117s·(thread);·0s·(gc)
  
96 o4·=·multi-rational·map·consisting·of·one·single·rational·map96 o4·=·multi-rational·map·consisting·of·one·single·rational·map
97 ·····source·variety:·PP^497 ·····source·variety:·PP^4
98 ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5·98 ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5·
99 ·····dominance:·true99 ·····dominance:·true
100 ·····degree:·1100 ·····degree:·1
  
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29 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^929 o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^9
30 i3·:·?·X30 i3·:·?·X
  
31 o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees31 o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees
32 ·····1^2·2^532 ·····1^2·2^5
33 i4·:·time·parametrizeFanoFourfold·X33 i4·:·time·parametrizeFanoFourfold·X
34 ·--·used·2.03176s·(cpu);·0.758056s·(thread);·0s·(gc)34 ·--·used·2.07715s·(cpu);·0.692117s·(thread);·0s·(gc)
  
35 o4·=·multi-rational·map·consisting·of·one·single·rational·map35 o4·=·multi-rational·map·consisting·of·one·single·rational·map
36 ·····source·variety:·PP^436 ·····source·variety:·PP^4
37 ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·737 ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7
38 hypersurfaces·of·degrees·1^2·2^538 hypersurfaces·of·degrees·1^2·2^5
39 ·····dominance:·true39 ·····dominance:·true
40 ·····degree:·140 ·····degree:·1
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95 o4·:·ProjectiveVariety,·hypersurface·in·PP^5</code></pre>95 o4·:·ProjectiveVariety,·hypersurface·in·PP^5</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3);100 ··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3);
101 ·--·used·0.00800442s·(cpu);·0.00762065s·(thread);·0s·(gc)101 ·--·used·0.00799622s·(cpu);·0.00968169s·(thread);·0s·(gc)
  
102 o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0</code></pre>102 o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0</code></pre>
103 ············</td>103 ············</td>
104 ··········</tr>104 ··········</tr>
105 ··········<tr>105 ··········<tr>
106 ············<td>106 ············<td>
107 ··············<pre><code·class="language-macaulay2">i6·:·time·describe·F107 ··············<pre><code·class="language-macaulay2">i6·:·time·describe·F
108 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it108 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
109 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868109 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
110 ·--·used·0.308696s·(cpu);·0.16513s·(thread);·0s·(gc)110 ·--·used·0.802024s·(cpu);·0.204896s·(thread);·0s·(gc)
  
111 o6·=·Special·cubic·fourfold·of·discriminant·26111 o6·=·Special·cubic·fourfold·of·discriminant·26
112 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0112 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0
113 ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre>113 ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre>
114 ············</td>114 ············</td>
115 ··········</tr>115 ··········</tr>
116 ··········<tr>116 ··········<tr>
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115 3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-115 3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-
116 7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-116 7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-
117 x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-117 x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-
118 x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2);118 x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2);
  
119 o4·:·ProjectiveVariety,·hypersurface·in·PP^5119 o4·:·ProjectiveVariety,·hypersurface·in·PP^5
120 i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3);120 i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3);
121 ·--·used·0.00800442s·(cpu);·0.00762065s·(thread);·0s·(gc)121 ·--·used·0.00799622s·(cpu);·0.00968169s·(thread);·0s·(gc)
  
122 o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and122 o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and
123 sectional·genus·0123 sectional·genus·0
124 i6·:·time·describe·F124 i6·:·time·describe·F
125 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables125 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables
126 based·on·it126 based·on·it
127 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--127 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--
128 debug·9868128 debug·9868
129 ·--·used·0.308696s·(cpu);·0.16513s·(thread);·0s·(gc)129 ·--·used·0.802024s·(cpu);·0.204896s·(thread);·0s·(gc)
  
130 o6·=·Special·cubic·fourfold·of·discriminant·26130 o6·=·Special·cubic·fourfold·of·discriminant·26
131 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0131 ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0
132 ·····cut·out·by·13·hypersurfaces·of·degree·3132 ·····cut·out·by·13·hypersurfaces·of·degree·3
133 i7·:·assert(F·==·X)133 i7·:·assert(F·==·X)
134 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*134 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
135 ····*·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8(_\x8E_\x8m_\x8b_\x8e_\x8d_\x8d_\x8e_\x8d_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·random·special·cubic135 ····*·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8(_\x8E_\x8m_\x8b_\x8e_\x8d_\x8d_\x8e_\x8d_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·random·special·cubic
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93 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8</code></pre>93 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8</code></pre>
94 ············</td>94 ············</td>
95 ··········</tr>95 ··········</tr>
96 ··········<tr>96 ··········<tr>
97 ············<td>97 ············<td>
98 ··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialGushelMukaiFourfold(S,X);98 ··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialGushelMukaiFourfold(S,X);
99 ·--·used·1.46847s·(cpu);·1.18763s·(thread);·0s·(gc)99 ·--·used·1.58162s·(cpu);·1.26197s·(thread);·0s·(gc)
  
100 o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre>100 o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre>
101 ············</td>101 ············</td>
102 ··········</tr>102 ··········</tr>
103 ··········<tr>103 ··········<tr>
104 ············<td>104 ············<td>
105 ··············<pre><code·class="language-macaulay2">i6·:·time·describe·F105 ··············<pre><code·class="language-macaulay2">i6·:·time·describe·F
106 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it106 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
107 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868107 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
108 ·--·used·7.18628s·(cpu);·2.85211s·(thread);·0s·(gc)108 ·--·used·8.24383s·(cpu);·2.90951s·(thread);·0s·(gc)
  
109 o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')109 o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')
110 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0110 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0
111 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)111 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)
112 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)112 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)
113 ·····Type:·ordinary113 ·····Type:·ordinary
114 ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre>114 ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre>
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33 x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-33 x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-
34 x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-34 x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-
35 2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-35 2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-
36 3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8);36 3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8);
  
37 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^837 o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8
38 i5·:·time·F·=·specialGushelMukaiFourfold(S,X);38 i5·:·time·F·=·specialGushelMukaiFourfold(S,X);
39 ·--·used·1.46847s·(cpu);·1.18763s·(thread);·0s·(gc)39 ·--·used·1.58162s·(cpu);·1.26197s·(thread);·0s·(gc)
  
40 o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and40 o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and
41 sectional·genus·041 sectional·genus·0
42 i6·:·time·describe·F42 i6·:·time·describe·F
43 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables43 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables
44 based·on·it44 based·on·it
45 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--45 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--
46 debug·986846 debug·9868
47 ·--·used·7.18628s·(cpu);·2.85211s·(thread);·0s·(gc)47 ·--·used·8.24383s·(cpu);·2.90951s·(thread);·0s·(gc)
  
48 o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')48 o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(')
49 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·049 ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0
50 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)50 ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2)
51 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)51 ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2)
52 ·····Type:·ordinary52 ·····Type:·ordinary
53 ·····(case·1·of·Table·1·in·arXiv:2002.07026)53 ·····(case·1·of·Table·1·in·arXiv:2002.07026)
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81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X85 ··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X
86 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it86 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
87 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·986887 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
88 ·--·used·6.30822s·(cpu);·2.55839s·(thread);·0s·(gc)88 ·--·used·7.15313s·(cpu);·2.75512s·(thread);·0s·(gc)
  
89 o3·=·multi-rational·map·consisting·of·one·single·rational·map89 o3·=·multi-rational·map·consisting·of·one·single·rational·map
90 ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·290 ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2
91 ·····target·variety:·GG(1,4)··PP^991 ·····target·variety:·GG(1,4)··PP^9
  
92 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre>92 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre>
93 ············</td>93 ············</td>
704 B
html2text {}
    
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26 o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and26 o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and
27 sectional·genus·027 sectional·genus·0
28 i3·:·time·toGrass·X28 i3·:·time·toGrass·X
29 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables29 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables
30 based·on·it30 based·on·it
31 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--31 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--
32 debug·986832 debug·9868
33 ·--·used·6.30822s·(cpu);·2.55839s·(thread);·0s·(gc)33 ·--·used·7.15313s·(cpu);·2.75512s·(thread);·0s·(gc)
  
34 o3·=·multi-rational·map·consisting·of·one·single·rational·map34 o3·=·multi-rational·map·consisting·of·one·single·rational·map
35 ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces35 ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces
36 of·degree·236 of·degree·2
37 ·····target·variety:·GG(1,4)·âŠ‚·PP^937 ·····target·variety:·GG(1,4)·âŠ‚·PP^9
  
38 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))38 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))
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./usr/share/doc/Macaulay2/SpecialFanoFourfolds/html/_to__Grass_lp__Embedded__Projective__Variety_rp.html
    
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82 ············</td>82 ············</td>
83 ··········</tr>83 ··········</tr>
84 ··········<tr>84 ··········<tr>
85 ············<td>85 ············<td>
86 ··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X86 ··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X
87 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it87 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it
88 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·986888 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868
89 ·--·used·6.17467s·(cpu);·2.42428s·(thread);·0s·(gc)89 ·--·used·6.8357s·(cpu);·2.73868s·(thread);·0s·(gc)
  
90 o3·=·multi-rational·map·consisting·of·one·single·rational·map90 o3·=·multi-rational·map·consisting·of·one·single·rational·map
91 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·291 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2
92 ·····target·variety:·GG(1,4)··PP^992 ·····target·variety:·GG(1,4)··PP^9
  
93 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre>93 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre>
94 ············</td>94 ············</td>
670 B
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25 o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^825 o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8
26 i3·:·time·toGrass·X26 i3·:·time·toGrass·X
27 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables27 warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables
28 based·on·it28 based·on·it
29 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--29 ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--
30 debug·986830 debug·9868
31 ·--·used·6.17467s·(cpu);·2.42428s·(thread);·0s·(gc)31 ·--·used·6.8357s·(cpu);·2.73868s·(thread);·0s·(gc)
  
32 o3·=·multi-rational·map·consisting·of·one·single·rational·map32 o3·=·multi-rational·map·consisting·of·one·single·rational·map
33 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·533 ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5
34 hypersurfaces·of·degree·234 hypersurfaces·of·degree·2
35 ·····target·variety:·GG(1,4)·âŠ‚·PP^935 ·····target·variety:·GG(1,4)·âŠ‚·PP^9
  
36 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))36 o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))
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./usr/share/doc/Macaulay2/SpecialFanoFourfolds/html/_unirational__Parametrization.html
    
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82 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre>82 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i4·:·time·f·=·unirationalParametrization·X;87 ··············<pre><code·class="language-macaulay2">i4·:·time·f·=·unirationalParametrization·X;
88 ·--·used·1.04818s·(cpu);·0.428468s·(thread);·0s·(gc)88 ·--·used·1.15578s·(cpu);·0.43858s·(thread);·0s·(gc)
  
89 o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)</code></pre>89 o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)</code></pre>
90 ············</td>90 ············</td>
91 ··········</tr>91 ··········</tr>
92 ··········<tr>92 ··········<tr>
93 ············<td>93 ············<td>
94 ··············<pre><code·class="language-macaulay2">i5·:·degreeSequence·f94 ··············<pre><code·class="language-macaulay2">i5·:·degreeSequence·f
477 B
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18 o2·:·ProjectiveVariety,·surface·in·PP^518 o2·:·ProjectiveVariety,·surface·in·PP^5
19 i3·:·X·=·specialCubicFourfold·S;19 i3·:·X·=·specialCubicFourfold·S;
  
20 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and20 o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and
21 sectional·genus·021 sectional·genus·0
22 i4·:·time·f·=·unirationalParametrization·X;22 i4·:·time·f·=·unirationalParametrization·X;
23 ·--·used·1.04818s·(cpu);·0.428468s·(thread);·0s·(gc)23 ·--·used·1.15578s·(cpu);·0.43858s·(thread);·0s·(gc)
  
24 o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)24 o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)
25 i5·:·degreeSequence·f25 i5·:·degreeSequence·f
  
26 o5·=·{[10]}26 o5·=·{[10]}
  
27 o5·:·List27 o5·:·List
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./usr/share/doc/Macaulay2/SpectralSequences/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/StatGraphs/dump/rawdocumentation.dump
    
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731 B
./usr/share/doc/Macaulay2/StatePolytope/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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773 B
./usr/share/doc/Macaulay2/StronglyStableIdeals/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzkyLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzkyLCBzeW1ib2wgRG9jdW1lbnRUYWcg
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./usr/share/doc/Macaulay2/Style/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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./usr/share/doc/Macaulay2/Style/example-output/_generate__Grammar.out
    
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1 --·-*-·M2-comint·-*-·hash:·34557011436665345881 --·-*-·M2-comint·-*-·hash:·3455701143666534588
  
2 i1·:·outfile·=·temporaryFileName()2 i1·:·outfile·=·temporaryFileName()
  
3 o1·=·/tmp/M2-1074308-0/03 o1·=·/tmp/M2-976726-0/0
  
4 i2·:·template·=·outfile·|·".in"4 i2·:·template·=·outfile·|·".in"
  
5 o2·=·/tmp/M2-1074308-0/0.in5 o2·=·/tmp/M2-976726-0/0.in
  
6 i3·:·template·<<·"@M2BANNER@"·<<·endl·<<·endl;6 i3·:·template·<<·"@M2BANNER@"·<<·endl·<<·endl;
  
7 i4·:·template·<<·"This·is·an·example·file·for·the·generateGrammar·method!";7 i4·:·template·<<·"This·is·an·example·file·for·the·generateGrammar·method!";
  
8 i5·:·template·<<·endl;8 i5·:·template·<<·endl;
  
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30 ······String·regex:·@M2STRINGS@30 ······String·regex:·@M2STRINGS@
31 ······List·of·keywords:·{31 ······List·of·keywords:·{
32 ··········@M2KEYWORDS@32 ··········@M2KEYWORDS@
33 ······}33 ······}
  
  
34 i11·:·generateGrammar(template,·outfile,·x·->·demark(",\n····",·x))34 i11·:·generateGrammar(template,·outfile,·x·->·demark(",\n····",·x))
35 ·--·generating·/tmp/M2-1074308-0/035 ·--·generating·/tmp/M2-976726-0/0
  
36 i12·:·get·outfile36 i12·:·get·outfile
  
37 o12·=·Auto-generated·for·Macaulay2-1.25.06.·Do·not·modify·this·file·manually.37 o12·=·Auto-generated·for·Macaulay2-1.25.06.·Do·not·modify·this·file·manually.
  
38 ······This·is·an·example·file·for·the·generateGrammar·method!38 ······This·is·an·example·file·for·the·generateGrammar·method!
39 ······String·regex:·"///\\(/?/?[^/]\\|\\(//\\)*////[^/]\\)*\\(//\\)*///"39 ······String·regex:·"///\\(/?/?[^/]\\|\\(//\\)*////[^/]\\)*\\(//\\)*///"
3.15 KB
./usr/share/doc/Macaulay2/Style/html/_generate__Grammar.html
    
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82 ··········<p>The·function·<samp>demarkf</samp>·indicates·how·the·elements·of·each·of·the·lists·will·be·demarked·in·the·resulting·file.···The·file·<samp>outfile</samp>·will·then·be·generated,·replacing·each·of·these·strings·as·indicated·above.</p>82 ··········<p>The·function·<samp>demarkf</samp>·indicates·how·the·elements·of·each·of·the·lists·will·be·demarked·in·the·resulting·file.···The·file·<samp>outfile</samp>·will·then·be·generated,·replacing·each·of·these·strings·as·indicated·above.</p>
83 ········</div>83 ········</div>
84 ········<table·class="examples">84 ········<table·class="examples">
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i1·:·outfile·=·temporaryFileName()87 ··············<pre><code·class="language-macaulay2">i1·:·outfile·=·temporaryFileName()
  
88 o1·=·/tmp/M2-1074308-0/0</code></pre>88 o1·=·/tmp/M2-976726-0/0</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i2·:·template·=·outfile·|·&quot;.in&quot;93 ··············<pre><code·class="language-macaulay2">i2·:·template·=·outfile·|·&quot;.in&quot;
  
94 o2·=·/tmp/M2-1074308-0/0.in</code></pre>94 o2·=·/tmp/M2-976726-0/0.in</code></pre>
95 ············</td>95 ············</td>
96 ··········</tr>96 ··········</tr>
97 ··········<tr>97 ··········<tr>
98 ············<td>98 ············<td>
99 ··············<pre><code·class="language-macaulay2">i3·:·template·&lt;&lt;·&quot;@M2BANNER@&quot;·&lt;&lt;·endl·&lt;&lt;·endl;</code></pre>99 ··············<pre><code·class="language-macaulay2">i3·:·template·&lt;&lt;·&quot;@M2BANNER@&quot;·&lt;&lt;·endl·&lt;&lt;·endl;</code></pre>
100 ············</td>100 ············</td>
101 ··········</tr>101 ··········</tr>
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143 ··········@M2KEYWORDS@143 ··········@M2KEYWORDS@
144 ······}</code></pre>144 ······}</code></pre>
145 ············</td>145 ············</td>
146 ··········</tr>146 ··········</tr>
147 ··········<tr>147 ··········<tr>
148 ············<td>148 ············<td>
149 ··············<pre><code·class="language-macaulay2">i11·:·generateGrammar(template,·outfile,·x·->·demark(&quot;,\n····&quot;,·x))149 ··············<pre><code·class="language-macaulay2">i11·:·generateGrammar(template,·outfile,·x·->·demark(&quot;,\n····&quot;,·x))
150 ·--·generating·/tmp/M2-1074308-0/0</code></pre>150 ·--·generating·/tmp/M2-976726-0/0</code></pre>
151 ············</td>151 ············</td>
152 ··········</tr>152 ··········</tr>
153 ··········<tr>153 ··········<tr>
154 ············<td>154 ············<td>
155 ··············<pre><code·class="language-macaulay2">i12·:·get·outfile155 ··············<pre><code·class="language-macaulay2">i12·:·get·outfile
  
156 o12·=·Auto-generated·for·Macaulay2-1.25.06.·Do·not·modify·this·file·manually.156 o12·=·Auto-generated·for·Macaulay2-1.25.06.·Do·not·modify·this·file·manually.
1.46 KB
html2text {}
    
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26 ····*·@M2CONSTANTS@,·for·a·list·of·Macaulay2·symbols·and·packages.26 ····*·@M2CONSTANTS@,·for·a·list·of·Macaulay2·symbols·and·packages.
27 ····*·@M2STRINGS@,·for·a·regular·expression·that·matches·Macaulay2·strings.27 ····*·@M2STRINGS@,·for·a·regular·expression·that·matches·Macaulay2·strings.
28 The·function·demarkf·indicates·how·the·elements·of·each·of·the·lists·will·be28 The·function·demarkf·indicates·how·the·elements·of·each·of·the·lists·will·be
29 demarked·in·the·resulting·file.·The·file·outfile·will·then·be·generated,29 demarked·in·the·resulting·file.·The·file·outfile·will·then·be·generated,
30 replacing·each·of·these·strings·as·indicated·above.30 replacing·each·of·these·strings·as·indicated·above.
31 i1·:·outfile·=·temporaryFileName()31 i1·:·outfile·=·temporaryFileName()
  
32 o1·=·/tmp/M2-1074308-0/032 o1·=·/tmp/M2-976726-0/0
33 i2·:·template·=·outfile·|·".in"33 i2·:·template·=·outfile·|·".in"
  
34 o2·=·/tmp/M2-1074308-0/0.in34 o2·=·/tmp/M2-976726-0/0.in
35 i3·:·template·<<·"@M2BANNER@"·<<·endl·<<·endl;35 i3·:·template·<<·"@M2BANNER@"·<<·endl·<<·endl;
36 i4·:·template·<<·"This·is·an·example·file·for·the·generateGrammar·method!";36 i4·:·template·<<·"This·is·an·example·file·for·the·generateGrammar·method!";
37 i5·:·template·<<·endl;37 i5·:·template·<<·endl;
38 i6·:·template·<<·"String·regex:·@M2STRINGS@"·<<·endl;38 i6·:·template·<<·"String·regex:·@M2STRINGS@"·<<·endl;
39 i7·:·template·<<·"List·of·keywords:·{"·<<·endl;39 i7·:·template·<<·"List·of·keywords:·{"·<<·endl;
40 i8·:·template·<<·"····@M2KEYWORDS@"·<<·endl;40 i8·:·template·<<·"····@M2KEYWORDS@"·<<·endl;
41 i9·:·template·<<·"}"·<<·endl·<<·close;41 i9·:·template·<<·"}"·<<·endl·<<·close;
Offset 47, 15 lines modifiedOffset 47, 15 lines modified
  
47 ······This·is·an·example·file·for·the·generateGrammar·method!47 ······This·is·an·example·file·for·the·generateGrammar·method!
48 ······String·regex:·@M2STRINGS@48 ······String·regex:·@M2STRINGS@
49 ······List·of·keywords:·{49 ······List·of·keywords:·{
50 ··········@M2KEYWORDS@50 ··········@M2KEYWORDS@
51 ······}51 ······}
52 i11·:·generateGrammar(template,·outfile,·x·->·demark(",\n····",·x))52 i11·:·generateGrammar(template,·outfile,·x·->·demark(",\n····",·x))
53 ·--·generating·/tmp/M2-1074308-0/053 ·--·generating·/tmp/M2-976726-0/0
54 i12·:·get·outfile54 i12·:·get·outfile
  
55 o12·=·Auto-generated·for·Macaulay2-1.25.06.·Do·not·modify·this·file·manually.55 o12·=·Auto-generated·for·Macaulay2-1.25.06.·Do·not·modify·this·file·manually.
  
56 ······This·is·an·example·file·for·the·generateGrammar·method!56 ······This·is·an·example·file·for·the·generateGrammar·method!
57 ······String·regex:·"///\\(/?/?[^/]\\|\\(//\\)*////[^/]\\)*\\(//\\)*///"57 ······String·regex:·"///\\(/?/?[^/]\\|\\(//\\)*////[^/]\\)*\\(//\\)*///"
58 ······List·of·keywords:·{58 ······List·of·keywords:·{
747 B
./usr/share/doc/Macaulay2/SubalgebraBases/dump/rawdocumentation.dump
    
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9 #:len=3009 #:len=300
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU3OSwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU3OSwgc3ltYm9sIERvY3VtZW50VGFn
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751 B
./usr/share/doc/Macaulay2/SumsOfSquares/dump/rawdocumentation.dump
    
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9 #:len=3029 #:len=302
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODg4LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODg4LCBzeW1ib2wgRG9jdW1lbnRUYWcg
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729 B
./usr/share/doc/Macaulay2/SuperLinearAlgebra/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
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6 #·End·of·header6 #·End·of·header
7 #:len=67 #:len=6
8 cGFyaXR58 cGFyaXR5
9 #:len=17099 #:len=1709
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11 YSBzdXBlciByaW5nLiIsICJsaW5lbnVtIiA9PiA2MTIsIElucHV0cyA9PiB7U1BBTntUVHsiZiJ911 YSBzdXBlciByaW5nLiIsICJsaW5lbnVtIiA9PiA2MTIsIElucHV0cyA9PiB7U1BBTntUVHsiZiJ9
759 B
./usr/share/doc/Macaulay2/SwitchingFields/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=337 #:len=33
8 ZmllbGRCYXNlQ2hhbmdlKFJpbmcsR2Fsb2lzRmllbGQp8 ZmllbGRCYXNlQ2hhbmdlKFJpbmcsR2Fsb2lzRmllbGQp
9 #:len=3009 #:len=300
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk4LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk4LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmaWVsZEJhc2VDaGFuZ2UsUmluZyxHYWxvaXNGaWVs11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmaWVsZEJhc2VDaGFuZ2UsUmluZyxHYWxvaXNGaWVs
734 B
./usr/share/doc/Macaulay2/SymbolicPowers/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=157 #:len=15
8 bm9QYWNrZWRBbGxTdWJz8 bm9QYWNrZWRBbGxTdWJz
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11 b2YgdmFyaWFibGVzIGJ5IDEgYW5kL29yIDAgZm9yIHdoaWNoIGlkZWFsIGlzIG5vdCBLb25pZy4i11 b2YgdmFyaWFibGVzIGJ5IDEgYW5kL29yIDAgZm9yIHdoaWNoIGlkZWFsIGlzIG5vdCBLb25pZy4i
827 B
./usr/share/doc/Macaulay2/SymbolicPowers/example-output/_symbolic__Power.out
    
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31 o5·:·Ideal·of·QQ[x..z]31 o5·:·Ideal·of·QQ[x..z]
  
32 i6·:·isHomogeneous·P32 i6·:·isHomogeneous·P
  
33 o6·=·false33 o6·=·false
  
34 i7·:·time·symbolicPower(P,4);34 i7·:·time·symbolicPower(P,4);
35 ·--·used·0.194239s·(cpu);·0.136886s·(thread);·0s·(gc)35 ·--·used·0.264276s·(cpu);·0.164577s·(thread);·0s·(gc)
  
36 o7·:·Ideal·of·QQ[x..z]36 o7·:·Ideal·of·QQ[x..z]
  
37 i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5})37 i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5})
  
38 ·············2·········3·········2·····238 ·············2·········3·········2·····2
39 o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·)39 o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·)
Offset 47, 12 lines modifiedOffset 47, 12 lines modified
47 o8·:·Ideal·of·QQ[x..z]47 o8·:·Ideal·of·QQ[x..z]
  
48 i9·:·isHomogeneous·Q48 i9·:·isHomogeneous·Q
  
49 o9·=·true49 o9·=·true
  
50 i10·:·time·symbolicPower(Q,4);50 i10·:·time·symbolicPower(Q,4);
51 ·--·used·0.0289823s·(cpu);·0.0285412s·(thread);·0s·(gc)51 ·--·used·0.0373099s·(cpu);·0.0349777s·(thread);·0s·(gc)
  
52 o10·:·Ideal·of·QQ[x..z]52 o10·:·Ideal·of·QQ[x..z]
  
53 i11·:·53 i11·:·
2.12 KB
./usr/share/doc/Macaulay2/SymbolicPowers/html/_symbolic__Power.html
    
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141 o6·=·false</code></pre>141 o6·=·false</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ··········<tr>144 ··········<tr>
145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i7·:·time·symbolicPower(P,4);146 ··············<pre><code·class="language-macaulay2">i7·:·time·symbolicPower(P,4);
147 ·--·used·0.194239s·(cpu);·0.136886s·(thread);·0s·(gc)147 ·--·used·0.264276s·(cpu);·0.164577s·(thread);·0s·(gc)
  
148 o7·:·Ideal·of·QQ[x..z]</code></pre>148 o7·:·Ideal·of·QQ[x..z]</code></pre>
149 ············</td>149 ············</td>
150 ··········</tr>150 ··········</tr>
151 ··········<tr>151 ··········<tr>
152 ············<td>152 ············<td>
153 ··············<pre><code·class="language-macaulay2">i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5})153 ··············<pre><code·class="language-macaulay2">i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5})
Offset 166, 15 lines modifiedOffset 166, 15 lines modified
  
166 o9·=·true</code></pre>166 o9·=·true</code></pre>
167 ············</td>167 ············</td>
168 ··········</tr>168 ··········</tr>
169 ··········<tr>169 ··········<tr>
170 ············<td>170 ············<td>
171 ··············<pre><code·class="language-macaulay2">i10·:·time·symbolicPower(Q,4);171 ··············<pre><code·class="language-macaulay2">i10·:·time·symbolicPower(Q,4);
172 ·--·used·0.0289823s·(cpu);·0.0285412s·(thread);·0s·(gc)172 ·--·used·0.0373099s·(cpu);·0.0349777s·(thread);·0s·(gc)
  
173 o10·:·Ideal·of·QQ[x..z]</code></pre>173 o10·:·Ideal·of·QQ[x..z]</code></pre>
174 ············</td>174 ············</td>
175 ··········</tr>175 ··········</tr>
176 ········</table>176 ········</table>
177 ······</div>177 ······</div>
178 ······<div>178 ······<div>
1.03 KB
html2text {}
    
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59 o5·=·ideal·(y··-·x*z,·x·y·-·z·,·x··-·y*z)59 o5·=·ideal·(y··-·x*z,·x·y·-·z·,·x··-·y*z)
  
60 o5·:·Ideal·of·QQ[x..z]60 o5·:·Ideal·of·QQ[x..z]
61 i6·:·isHomogeneous·P61 i6·:·isHomogeneous·P
  
62 o6·=·false62 o6·=·false
63 i7·:·time·symbolicPower(P,4);63 i7·:·time·symbolicPower(P,4);
64 ·--·used·0.194239s·(cpu);·0.136886s·(thread);·0s·(gc)64 ·--·used·0.264276s·(cpu);·0.164577s·(thread);·0s·(gc)
  
65 o7·:·Ideal·of·QQ[x..z]65 o7·:·Ideal·of·QQ[x..z]
66 i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5})66 i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5})
  
67 ·············2·········3·········2·····267 ·············2·········3·········2·····2
68 o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·)68 o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·)
  
69 o8·:·Ideal·of·QQ[x..z]69 o8·:·Ideal·of·QQ[x..z]
70 i9·:·isHomogeneous·Q70 i9·:·isHomogeneous·Q
  
71 o9·=·true71 o9·=·true
72 i10·:·time·symbolicPower(Q,4);72 i10·:·time·symbolicPower(Q,4);
73 ·--·used·0.0289823s·(cpu);·0.0285412s·(thread);·0s·(gc)73 ·--·used·0.0373099s·(cpu);·0.0349777s·(thread);·0s·(gc)
  
74 o10·:·Ideal·of·QQ[x..z]74 o10·:·Ideal·of·QQ[x..z]
75 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*75 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
76 ····*·_\x8s_\x8y_\x8m_\x8b_\x8P_\x8o_\x8w_\x8e_\x8r_\x8P_\x8r_\x8i_\x8m_\x8e_\x8P_\x8o_\x8s_\x8C_\x8h_\x8a_\x8r76 ····*·_\x8s_\x8y_\x8m_\x8b_\x8P_\x8o_\x8w_\x8e_\x8r_\x8P_\x8r_\x8i_\x8m_\x8e_\x8P_\x8o_\x8s_\x8C_\x8h_\x8a_\x8r
77 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8ym\x8mb\x8bo\x8ol\x8li\x8ic\x8cP\x8Po\x8ow\x8we\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*77 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8ym\x8mb\x8bo\x8ol\x8li\x8ic\x8cP\x8Po\x8ow\x8we\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
78 ····*·symbolicPower(Ideal,ZZ)78 ····*·symbolicPower(Ideal,ZZ)
79 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*79 *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8*
770 B
./usr/share/doc/Macaulay2/SymmetricPolynomials/dump/rawdocumentation.dump
    
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755 B
./usr/share/doc/Macaulay2/TSpreadIdeals/dump/rawdocumentation.dump
    
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2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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7 #:len=317 #:len=31
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723 B
./usr/share/doc/Macaulay2/TangentCone/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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7 #:len=117 #:len=11
8 VGFuZ2VudENvbmU=8 VGFuZ2VudENvbmU=
9 #:len=3129 #:len=312
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11 aW9uID0+IDE6KCJUaGlzIHBhY2thZ2UgcHJvdmlkZXMgYSBzaW5nbGUgZnVuY3Rpb24gdGhhdCBj11 aW9uID0+IDE6KCJUaGlzIHBhY2thZ2UgcHJvdmlkZXMgYSBzaW5nbGUgZnVuY3Rpb24gdGhhdCBj
765 B
./usr/share/doc/Macaulay2/TateOnProducts/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=397 #:len=39
8 YWN0aW9uT25EaXJlY3RJbWFnZShJZGVhbCxDaGFpbkNvbXBsZXgp8 YWN0aW9uT25EaXJlY3RJbWFnZShJZGVhbCxDaGFpbkNvbXBsZXgp
9 #:len=3189 #:len=318
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjA3Miwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjA3Miwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYWN0aW9uT25EaXJlY3RJbWFnZSxJZGVhbCxDaGFp11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYWN0aW9uT25EaXJlY3RJbWFnZSxJZGVhbCxDaGFp
575 B
./usr/share/doc/Macaulay2/TateOnProducts/example-output/_beilinson__Window.out
    
Offset 10, 15 lines modifiedOffset 10, 15 lines modified
10 o3·=·0··<--·E··<--·010 o3·=·0··<--·E··<--·0
11 ····················11 ····················
12 ·····-1·····0······112 ·····-1·····0······1
  
13 o3·:·ChainComplex13 o3·:·ChainComplex
  
14 i4·:·time·T=tateExtension·W;14 i4·:·time·T=tateExtension·W;
15 ·--·used·0.278772s·(cpu);·0.143799s·(thread);·0s·(gc)15 ·--·used·0.25317s·(cpu);·0.134522s·(thread);·0s·(gc)
  
16 i5·:·cohomologyMatrix(T,-{3,3},{3,3})16 i5·:·cohomologyMatrix(T,-{3,3},{3,3})
  
17 o5·=·|·8h··4h··0·4··8··12·16·|17 o5·=·|·8h··4h··0·4··8··12·16·|
18 ·····|·6h··3h··0·3··6··9··12·|18 ·····|·6h··3h··0·3··6··9··12·|
19 ·····|·4h··2h··0·2··4··6··8··|19 ·····|·4h··2h··0·2··4··6··8··|
20 ·····|·2h··h···0·1··2··3··4··|20 ·····|·2h··h···0·1··2··3··4··|
1.11 KB
./usr/share/doc/Macaulay2/TateOnProducts/html/_beilinson__Window.html
    
Offset 92, 15 lines modifiedOffset 92, 15 lines modified
  
92 o3·:·ChainComplex</code></pre>92 o3·:·ChainComplex</code></pre>
93 ············</td>93 ············</td>
94 ··········</tr>94 ··········</tr>
95 ··········<tr>95 ··········<tr>
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i4·:·time·T=tateExtension·W;97 ··············<pre><code·class="language-macaulay2">i4·:·time·T=tateExtension·W;
98 ·--·used·0.278772s·(cpu);·0.143799s·(thread);·0s·(gc)</code></pre>98 ·--·used·0.25317s·(cpu);·0.134522s·(thread);·0s·(gc)</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ··········<tr>101 ··········<tr>
102 ············<td>102 ············<td>
103 ··············<pre><code·class="language-macaulay2">i5·:·cohomologyMatrix(T,-{3,3},{3,3})103 ··············<pre><code·class="language-macaulay2">i5·:·cohomologyMatrix(T,-{3,3},{3,3})
  
104 o5·=·|·8h··4h··0·4··8··12·16·|104 o5·=·|·8h··4h··0·4··8··12·16·|
467 B
html2text {}
    
Offset 23, 15 lines modifiedOffset 23, 15 lines modified
23 ·············123 ·············1
24 o3·=·0··<--·E··<--·024 o3·=·0··<--·E··<--·0
  
25 ·····-1·····0······125 ·····-1·····0······1
  
26 o3·:·ChainComplex26 o3·:·ChainComplex
27 i4·:·time·T=tateExtension·W;27 i4·:·time·T=tateExtension·W;
28 ·--·used·0.278772s·(cpu);·0.143799s·(thread);·0s·(gc)28 ·--·used·0.25317s·(cpu);·0.134522s·(thread);·0s·(gc)
29 i5·:·cohomologyMatrix(T,-{3,3},{3,3})29 i5·:·cohomologyMatrix(T,-{3,3},{3,3})
  
30 o5·=·|·8h··4h··0·4··8··12·16·|30 o5·=·|·8h··4h··0·4··8··12·16·|
31 ·····|·6h··3h··0·3··6··9··12·|31 ·····|·6h··3h··0·3··6··9··12·|
32 ·····|·4h··2h··0·2··4··6··8··|32 ·····|·4h··2h··0·2··4··6··8··|
33 ·····|·2h··h···0·1··2··3··4··|33 ·····|·2h··h···0·1··2··3··4··|
34 ·····|·0···0···0·0··0··0··0··|34 ·····|·0···0···0·0··0··0··0··|
759 B
./usr/share/doc/Macaulay2/TensorComplexes/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=317 #:len=31
8 bWlub3JzTWFwKE1hdHJpeCxMYWJlbGVkTW9kdWxlKQ==8 bWlub3JzTWFwKE1hdHJpeCxMYWJlbGVkTW9kdWxlKQ==
9 #:len=2859 #:len=285
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTkzOCwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTkzOCwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobWlub3JzTWFwLE1hdHJpeCxMYWJlbGVkTW9kdWxl11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobWlub3JzTWFwLE1hdHJpeCxMYWJlbGVkTW9kdWxl
747 B
./usr/share/doc/Macaulay2/TerraciniLoci/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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8 dGVycmFjaW5pTG9jdXMoWlosUmluZ01hcCk=8 dGVycmFjaW5pTG9jdXMoWlosUmluZ01hcCk=
9 #:len=2789 #:len=278
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjA5LCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjA5LCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0ZXJyYWNpbmlMb2N1cyxaWixSaW5nTWFwKSwidGVy11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0ZXJyYWNpbmlMb2N1cyxaWixSaW5nTWFwKSwidGVy
729 B
./usr/share/doc/Macaulay2/TestIdeals/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
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7 #:len=177 #:len=17
8 ZnJvYmVuaXVzUHJlaW1hZ2U=8 ZnJvYmVuaXVzUHJlaW1hZ2U=
9 #:len=9349 #:len=934
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZHMgdGhlIGlkZWFsIG9mIGVsZW1l10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZHMgdGhlIGlkZWFsIG9mIGVsZW1l
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647 B
./usr/share/doc/Macaulay2/TestIdeals/example-output/_frobenius__Root.out
    
Offset 63, 20 lines modifiedOffset 63, 20 lines modified
63 o15·:·Ideal·of·R63 o15·:·Ideal·of·R
  
64 i16·:·I3·=·ideal(x^50*y^50*z^50);64 i16·:·I3·=·ideal(x^50*y^50*z^50);
  
65 o16·:·Ideal·of·R65 o16·:·Ideal·of·R
  
66 i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3});66 i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3});
67 ·--·used·0.666902s·(cpu);·0.568268s·(thread);·0s·(gc)67 ·--·used·0.754648s·(cpu);·0.609659s·(thread);·0s·(gc)
  
68 o17·:·Ideal·of·R68 o17·:·Ideal·of·R
  
69 i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12);69 i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12);
70 ·--·used·1.99062s·(cpu);·1.73087s·(thread);·0s·(gc)70 ·--·used·2.2344s·(cpu);·1.90963s·(thread);·0s·(gc)
  
71 o18·:·Ideal·of·R71 o18·:·Ideal·of·R
  
72 i19·:·J1·==·J272 i19·:·J1·==·J2
  
73 o19·=·true73 o19·=·true
  
683 B
./usr/share/doc/Macaulay2/TestIdeals/example-output/_is__Cohen__Macaulay.out
    
Offset 7, 20 lines modifiedOffset 7, 20 lines modified
7 i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3});7 i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3});
  
8 o3·:·RingMap·T·<--·S8 o3·:·RingMap·T·<--·S
  
9 i4·:·R·=·S/(ker·g);9 i4·:·R·=·S/(ker·g);
  
10 i5·:·time·isCohenMacaulay(R)10 i5·:·time·isCohenMacaulay(R)
11 ·--·used·0.00399811s·(cpu);·0.00158985s·(thread);·0s·(gc)11 ·--·used·0.00409022s·(cpu);·0.00284656s·(thread);·0s·(gc)
  
12 o5·=·true12 o5·=·true
  
13 i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true)13 i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true)
14 ·--·used·0.00348912s·(cpu);·0.00407512s·(thread);·0s·(gc)14 ·--·used·0.00585679s·(cpu);·0.00666526s·(thread);·0s·(gc)
  
15 o6·=·true15 o6·=·true
  
16 i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v);16 i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v);
  
17 i8·:·isCohenMacaulay(R)17 i8·:·isCohenMacaulay(R)
  
1.47 KB
./usr/share/doc/Macaulay2/TestIdeals/example-output/_is__F__Injective.out
    
Offset 60, 49 lines modifiedOffset 60, 49 lines modified
60 i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3)60 i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3)
  
61 o19·=·R61 o19·=·R
  
62 o19·:·QuotientRing62 o19·:·QuotientRing
  
63 i20·:·time·isFInjective(R)63 i20·:·time·isFInjective(R)
64 ·--·used·0.0879219s·(cpu);·0.0531274s·(thread);·0s·(gc)64 ·--·used·0.119233s·(cpu);·0.0579528s·(thread);·0s·(gc)
  
65 o20·=·true65 o20·=·true
  
66 i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null)66 i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null)
67 ·--·used·1.60108s·(cpu);·1.0786s·(thread);·0s·(gc)67 ·--·used·1.9148s·(cpu);·1.16956s·(thread);·0s·(gc)
  
68 o21·=·true68 o21·=·true
  
69 i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);69 i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);
  
70 i23·:·time·isFInjective(R)70 i23·:·time·isFInjective(R)
71 ·--·used·0.0597832s·(cpu);·0.0591517s·(thread);·0s·(gc)71 ·--·used·0.0623056s·(cpu);·0.0629939s·(thread);·0s·(gc)
  
72 o23·=·false72 o23·=·false
  
73 i24·:·time·isFInjective(R,·AtOrigin·=>·true)73 i24·:·time·isFInjective(R,·AtOrigin·=>·true)
74 ·--·used·0.108705s·(cpu);·0.0798244s·(thread);·0s·(gc)74 ·--·used·0.123574s·(cpu);·0.0831399s·(thread);·0s·(gc)
  
75 o24·=·true75 o24·=·true
  
76 i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt];76 i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt];
  
77 i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2);77 i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2);
  
78 i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t});78 i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t});
  
79 o27·:·RingMap·EP1·<--·S79 o27·:·RingMap·EP1·<--·S
  
80 i28·:·R·=·S/(ker·f);80 i28·:·R·=·S/(ker·f);
  
81 i29·:·time·isFInjective(R)81 i29·:·time·isFInjective(R)
82 ·--·used·0.774547s·(cpu);·0.66491s·(thread);·0s·(gc)82 ·--·used·0.821239s·(cpu);·0.690338s·(thread);·0s·(gc)
  
83 o29·=·false83 o29·=·false
  
84 i30·:·time·isFInjective(R,·AssumeCM·=>·true)84 i30·:·time·isFInjective(R,·AssumeCM·=>·true)
85 ·--·used·0.276848s·(cpu);·0.215365s·(thread);·0s·(gc)85 ·--·used·0.273594s·(cpu);·0.192815s·(thread);·0s·(gc)
  
86 o30·=·true86 o30·=·true
  
87 i31·:·87 i31·:·
831 B
./usr/share/doc/Macaulay2/TestIdeals/example-output/_is__F__Regular.out
    
Offset 79, 20 lines modifiedOffset 79, 20 lines modified
79 i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}});79 i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}});
  
80 o25·:·Ideal·of·S80 o25·:·Ideal·of·S
  
81 i26·:·debugLevel·=·1;81 i26·:·debugLevel·=·1;
  
82 i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1)82 i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1)
83 ·--·used·0.0885545s·(cpu);·0.0549313s·(thread);·0s·(gc)83 ·--·used·0.0916261s·(cpu);·0.057646s·(thread);·0s·(gc)
84 isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply.84 isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply.
  
85 o27·=·false85 o27·=·false
  
86 i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2)86 i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2)
87 ·--·used·0.169821s·(cpu);·0.137219s·(thread);·0s·(gc)87 ·--·used·0.207883s·(cpu);·0.152003s·(thread);·0s·(gc)
  
88 o28·=·true88 o28·=·true
  
89 i29·:·debugLevel·=·0;89 i29·:·debugLevel·=·0;
  
90 i30·:·90 i30·:·
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./usr/share/doc/Macaulay2/TestIdeals/example-output/_test__Ideal.out
    
Offset 81, 21 lines modifiedOffset 81, 21 lines modified
81 i22·:·testIdeal({3/4,·2/3,·3/5},·L)81 i22·:·testIdeal({3/4,·2/3,·3/5},·L)
  
82 o22·=·ideal·(y,·x)82 o22·=·ideal·(y,·x)
  
83 o22·:·Ideal·of·R83 o22·:·Ideal·of·R
  
84 i23·:·time·testIdeal({3/4,·2/3,·3/5},·L)84 i23·:·time·testIdeal({3/4,·2/3,·3/5},·L)
85 ·--·used·0.215431s·(cpu);·0.15513s·(thread);·0s·(gc)85 ·--·used·0.24757s·(cpu);·0.162185s·(thread);·0s·(gc)
  
86 o23·=·ideal·(y,·x)86 o23·=·ideal·(y,·x)
  
87 o23·:·Ideal·of·R87 o23·:·Ideal·of·R
  
88 i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36)88 i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36)
89 ·--·used·0.320428s·(cpu);·0.229082s·(thread);·0s·(gc)89 ·--·used·0.371769s·(cpu);·0.246982s·(thread);·0s·(gc)
  
90 o24·=·ideal·(y,·x)90 o24·=·ideal·(y,·x)
  
91 o24·:·Ideal·of·R91 o24·:·Ideal·of·R
  
92 i25·:·92 i25·:·
1.64 KB
./usr/share/doc/Macaulay2/TestIdeals/html/_frobenius__Root.html
    
Offset 226, 23 lines modifiedOffset 226, 23 lines modified
  
226 o16·:·Ideal·of·R</code></pre>226 o16·:·Ideal·of·R</code></pre>
227 ············</td>227 ············</td>
228 ··········</tr>228 ··········</tr>
229 ··········<tr>229 ··········<tr>
230 ············<td>230 ············<td>
231 ··············<pre><code·class="language-macaulay2">i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3});231 ··············<pre><code·class="language-macaulay2">i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3});
232 ·--·used·0.666902s·(cpu);·0.568268s·(thread);·0s·(gc)232 ·--·used·0.754648s·(cpu);·0.609659s·(thread);·0s·(gc)
  
233 o17·:·Ideal·of·R</code></pre>233 o17·:·Ideal·of·R</code></pre>
234 ············</td>234 ············</td>
235 ··········</tr>235 ··········</tr>
236 ··········<tr>236 ··········<tr>
237 ············<td>237 ············<td>
238 ··············<pre><code·class="language-macaulay2">i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12);238 ··············<pre><code·class="language-macaulay2">i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12);
239 ·--·used·1.99062s·(cpu);·1.73087s·(thread);·0s·(gc)239 ·--·used·2.2344s·(cpu);·1.90963s·(thread);·0s·(gc)
  
240 o18·:·Ideal·of·R</code></pre>240 o18·:·Ideal·of·R</code></pre>
241 ············</td>241 ············</td>
242 ··········</tr>242 ··········</tr>
243 ··········<tr>243 ··········<tr>
244 ············<td>244 ············<td>
245 ··············<pre><code·class="language-macaulay2">i19·:·J1·==·J2245 ··············<pre><code·class="language-macaulay2">i19·:·J1·==·J2
717 B
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Offset 106, 19 lines modifiedOffset 106, 19 lines modified
106 i15·:·I2·=·ideal(x^20*y^100,·x·+·z^100);106 i15·:·I2·=·ideal(x^20*y^100,·x·+·z^100);
  
107 o15·:·Ideal·of·R107 o15·:·Ideal·of·R
108 i16·:·I3·=·ideal(x^50*y^50*z^50);108 i16·:·I3·=·ideal(x^50*y^50*z^50);
  
109 o16·:·Ideal·of·R109 o16·:·Ideal·of·R
110 i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3});110 i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3});
111 ·--·used·0.666902s·(cpu);·0.568268s·(thread);·0s·(gc)111 ·--·used·0.754648s·(cpu);·0.609659s·(thread);·0s·(gc)
  
112 o17·:·Ideal·of·R112 o17·:·Ideal·of·R
113 i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12);113 i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12);
114 ·--·used·1.99062s·(cpu);·1.73087s·(thread);·0s·(gc)114 ·--·used·2.2344s·(cpu);·1.90963s·(thread);·0s·(gc)
  
115 o18·:·Ideal·of·R115 o18·:·Ideal·of·R
116 i19·:·J1·==·J2116 i19·:·J1·==·J2
  
117 o19·=·true117 o19·=·true
118 For·legacy·reasons,·the·last·ideal·in·the·list·can·be·specified·separately,118 For·legacy·reasons,·the·last·ideal·in·the·list·can·be·specified·separately,
119 using·frobeniusRoot(e,·\{a_1,\ldots,a_n\},·\{I_1,\ldots,I_n\},·I).·The·last119 using·frobeniusRoot(e,·\{a_1,\ldots,a_n\},·\{I_1,\ldots,I_n\},·I).·The·last
1.62 KB
./usr/share/doc/Macaulay2/TestIdeals/html/_is__Cohen__Macaulay.html
    
Offset 96, 23 lines modifiedOffset 96, 23 lines modified
96 ············<td>96 ············<td>
97 ··············<pre><code·class="language-macaulay2">i4·:·R·=·S/(ker·g);</code></pre>97 ··············<pre><code·class="language-macaulay2">i4·:·R·=·S/(ker·g);</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i5·:·time·isCohenMacaulay(R)102 ··············<pre><code·class="language-macaulay2">i5·:·time·isCohenMacaulay(R)
103 ·--·used·0.00399811s·(cpu);·0.00158985s·(thread);·0s·(gc)103 ·--·used·0.00409022s·(cpu);·0.00284656s·(thread);·0s·(gc)
  
104 o5·=·true</code></pre>104 o5·=·true</code></pre>
105 ············</td>105 ············</td>
106 ··········</tr>106 ··········</tr>
107 ··········<tr>107 ··········<tr>
108 ············<td>108 ············<td>
109 ··············<pre><code·class="language-macaulay2">i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true)109 ··············<pre><code·class="language-macaulay2">i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true)
110 ·--·used·0.00348912s·(cpu);·0.00407512s·(thread);·0s·(gc)110 ·--·used·0.00585679s·(cpu);·0.00666526s·(thread);·0s·(gc)
  
111 o6·=·true</code></pre>111 o6·=·true</code></pre>
112 ············</td>112 ············</td>
113 ··········</tr>113 ··········</tr>
114 ········</table>114 ········</table>
115 ········<table·class="examples">115 ········<table·class="examples">
116 ··········<tr>116 ··········<tr>
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Offset 23, 19 lines modifiedOffset 23, 19 lines modified
23 i1·:·T·=·ZZ/5[x,y];23 i1·:·T·=·ZZ/5[x,y];
24 i2·:·S·=·ZZ/5[a,b,c,d];24 i2·:·S·=·ZZ/5[a,b,c,d];
25 i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3});25 i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3});
  
26 o3·:·RingMap·T·<--·S26 o3·:·RingMap·T·<--·S
27 i4·:·R·=·S/(ker·g);27 i4·:·R·=·S/(ker·g);
28 i5·:·time·isCohenMacaulay(R)28 i5·:·time·isCohenMacaulay(R)
29 ·--·used·0.00399811s·(cpu);·0.00158985s·(thread);·0s·(gc)29 ·--·used·0.00409022s·(cpu);·0.00284656s·(thread);·0s·(gc)
  
30 o5·=·true30 o5·=·true
31 i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true)31 i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true)
32 ·--·used·0.00348912s·(cpu);·0.00407512s·(thread);·0s·(gc)32 ·--·used·0.00585679s·(cpu);·0.00666526s·(thread);·0s·(gc)
  
33 o6·=·true33 o6·=·true
34 i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v);34 i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v);
35 i8·:·isCohenMacaulay(R)35 i8·:·isCohenMacaulay(R)
  
36 o8·=·false36 o8·=·false
37 The·function·isCohenMacaulay·considers·$R$·as·a·quotient·of·a·polynomial·ring,37 The·function·isCohenMacaulay·considers·$R$·as·a·quotient·of·a·polynomial·ring,
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./usr/share/doc/Macaulay2/TestIdeals/html/_is__F__Injective.html
    
Offset 214, 23 lines modifiedOffset 214, 23 lines modified
  
214 o19·:·QuotientRing</code></pre>214 o19·:·QuotientRing</code></pre>
215 ············</td>215 ············</td>
216 ··········</tr>216 ··········</tr>
217 ··········<tr>217 ··········<tr>
218 ············<td>218 ············<td>
219 ··············<pre><code·class="language-macaulay2">i20·:·time·isFInjective(R)219 ··············<pre><code·class="language-macaulay2">i20·:·time·isFInjective(R)
220 ·--·used·0.0879219s·(cpu);·0.0531274s·(thread);·0s·(gc)220 ·--·used·0.119233s·(cpu);·0.0579528s·(thread);·0s·(gc)
  
221 o20·=·true</code></pre>221 o20·=·true</code></pre>
222 ············</td>222 ············</td>
223 ··········</tr>223 ··········</tr>
224 ··········<tr>224 ··········<tr>
225 ············<td>225 ············<td>
226 ··············<pre><code·class="language-macaulay2">i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null)226 ··············<pre><code·class="language-macaulay2">i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null)
227 ·--·used·1.60108s·(cpu);·1.0786s·(thread);·0s·(gc)227 ·--·used·1.9148s·(cpu);·1.16956s·(thread);·0s·(gc)
  
228 o21·=·true</code></pre>228 o21·=·true</code></pre>
229 ············</td>229 ············</td>
230 ··········</tr>230 ··········</tr>
231 ········</table>231 ········</table>
232 ········<div>232 ········<div>
233 ··········<p>If·the·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·<span·class="tt">isFInjective</span>·will·only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$-injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be·slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$-injective·ring.</p>233 ··········<p>If·the·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·<span·class="tt">isFInjective</span>·will·only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$-injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be·slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$-injective·ring.</p>
Offset 240, 23 lines modifiedOffset 240, 23 lines modified
240 ············<td>240 ············<td>
241 ··············<pre><code·class="language-macaulay2">i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);</code></pre>241 ··············<pre><code·class="language-macaulay2">i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);</code></pre>
242 ············</td>242 ············</td>
243 ··········</tr>243 ··········</tr>
244 ··········<tr>244 ··········<tr>
245 ············<td>245 ············<td>
246 ··············<pre><code·class="language-macaulay2">i23·:·time·isFInjective(R)246 ··············<pre><code·class="language-macaulay2">i23·:·time·isFInjective(R)
247 ·--·used·0.0597832s·(cpu);·0.0591517s·(thread);·0s·(gc)247 ·--·used·0.0623056s·(cpu);·0.0629939s·(thread);·0s·(gc)
  
248 o23·=·false</code></pre>248 o23·=·false</code></pre>
249 ············</td>249 ············</td>
250 ··········</tr>250 ··········</tr>
251 ··········<tr>251 ··········<tr>
252 ············<td>252 ············<td>
253 ··············<pre><code·class="language-macaulay2">i24·:·time·isFInjective(R,·AtOrigin·=>·true)253 ··············<pre><code·class="language-macaulay2">i24·:·time·isFInjective(R,·AtOrigin·=>·true)
254 ·--·used·0.108705s·(cpu);·0.0798244s·(thread);·0s·(gc)254 ·--·used·0.123574s·(cpu);·0.0831399s·(thread);·0s·(gc)
  
255 o24·=·true</code></pre>255 o24·=·true</code></pre>
256 ············</td>256 ············</td>
257 ··········</tr>257 ··········</tr>
258 ········</table>258 ········</table>
259 ········<div>259 ········<div>
260 ··········<p>If·the·option·<span·class="tt">AssumeCM</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·then·<span·class="tt">isFInjective</span>·only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much·faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective·Frobenius·occurs·in·a·lower·degree.··Consider·the·example·of·the·cone·over·a·supersingular·elliptic·curve·times·$\mathbb{P}^1$.</p>260 ··········<p>If·the·option·<span·class="tt">AssumeCM</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·then·<span·class="tt">isFInjective</span>·only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much·faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective·Frobenius·occurs·in·a·lower·degree.··Consider·the·example·of·the·cone·over·a·supersingular·elliptic·curve·times·$\mathbb{P}^1$.</p>
Offset 283, 23 lines modifiedOffset 283, 23 lines modified
283 ············<td>283 ············<td>
284 ··············<pre><code·class="language-macaulay2">i28·:·R·=·S/(ker·f);</code></pre>284 ··············<pre><code·class="language-macaulay2">i28·:·R·=·S/(ker·f);</code></pre>
285 ············</td>285 ············</td>
286 ··········</tr>286 ··········</tr>
287 ··········<tr>287 ··········<tr>
288 ············<td>288 ············<td>
289 ··············<pre><code·class="language-macaulay2">i29·:·time·isFInjective(R)289 ··············<pre><code·class="language-macaulay2">i29·:·time·isFInjective(R)
290 ·--·used·0.774547s·(cpu);·0.66491s·(thread);·0s·(gc)290 ·--·used·0.821239s·(cpu);·0.690338s·(thread);·0s·(gc)
  
291 o29·=·false</code></pre>291 o29·=·false</code></pre>
292 ············</td>292 ············</td>
293 ··········</tr>293 ··········</tr>
294 ··········<tr>294 ··········<tr>
295 ············<td>295 ············<td>
296 ··············<pre><code·class="language-macaulay2">i30·:·time·isFInjective(R,·AssumeCM·=>·true)296 ··············<pre><code·class="language-macaulay2">i30·:·time·isFInjective(R,·AssumeCM·=>·true)
297 ·--·used·0.276848s·(cpu);·0.215365s·(thread);·0s·(gc)297 ·--·used·0.273594s·(cpu);·0.192815s·(thread);·0s·(gc)
  
298 o30·=·true</code></pre>298 o30·=·true</code></pre>
299 ············</td>299 ············</td>
300 ··········</tr>300 ··········</tr>
301 ········</table>301 ········</table>
302 ········<div>302 ········<div>
303 ··········<p>If·the·option·<span·class="tt">AssumedReduced</span>·is·set·to·<span·class="tt">true</span>·(its·default·behavior),·then·the·bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top·potentially·nonzero·Ext·is·not·computed).</p>303 ··········<p>If·the·option·<span·class="tt">AssumedReduced</span>·is·set·to·<span·class="tt">true</span>·(its·default·behavior),·then·the·bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top·potentially·nonzero·Ext·is·not·computed).</p>
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Offset 81, 52 lines modifiedOffset 81, 52 lines modified
81 much·faster.81 much·faster.
82 i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3)82 i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3)
  
83 o19·=·R83 o19·=·R
  
84 o19·:·QuotientRing84 o19·:·QuotientRing
85 i20·:·time·isFInjective(R)85 i20·:·time·isFInjective(R)
86 ·--·used·0.0879219s·(cpu);·0.0531274s·(thread);·0s·(gc)86 ·--·used·0.119233s·(cpu);·0.0579528s·(thread);·0s·(gc)
  
87 o20·=·true87 o20·=·true
88 i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null)88 i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null)
89 ·--·used·1.60108s·(cpu);·1.0786s·(thread);·0s·(gc)89 ·--·used·1.9148s·(cpu);·1.16956s·(thread);·0s·(gc)
  
90 o21·=·true90 o21·=·true
91 If·the·option·AtOrigin·(default·value·false)·is·set·to·true,·isFInjective·will91 If·the·option·AtOrigin·(default·value·false)·is·set·to·true,·isFInjective·will
92 only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$-92 only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$-
93 injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be93 injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be
94 slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$-94 slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$-
95 injective·ring.95 injective·ring.
96 i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);96 i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);
97 i23·:·time·isFInjective(R)97 i23·:·time·isFInjective(R)
98 ·--·used·0.0597832s·(cpu);·0.0591517s·(thread);·0s·(gc)98 ·--·used·0.0623056s·(cpu);·0.0629939s·(thread);·0s·(gc)
  
99 o23·=·false99 o23·=·false
100 i24·:·time·isFInjective(R,·AtOrigin·=>·true)100 i24·:·time·isFInjective(R,·AtOrigin·=>·true)
101 ·--·used·0.108705s·(cpu);·0.0798244s·(thread);·0s·(gc)101 ·--·used·0.123574s·(cpu);·0.0831399s·(thread);·0s·(gc)
  
102 o24·=·true102 o24·=·true
103 If·the·option·AssumeCM·(default·value·false)·is·set·to·true,·then·isFInjective103 If·the·option·AssumeCM·(default·value·false)·is·set·to·true,·then·isFInjective
104 only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much104 only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much
105 faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective105 faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective
106 Frobenius·occurs·in·a·lower·degree.·Consider·the·example·of·the·cone·over·a106 Frobenius·occurs·in·a·lower·degree.·Consider·the·example·of·the·cone·over·a
107 supersingular·elliptic·curve·times·$\mathbb{P}^1$.107 supersingular·elliptic·curve·times·$\mathbb{P}^1$.
108 i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt];108 i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt];
109 i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2);109 i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2);
110 i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t});110 i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t});
  
111 o27·:·RingMap·EP1·<--·S111 o27·:·RingMap·EP1·<--·S
112 i28·:·R·=·S/(ker·f);112 i28·:·R·=·S/(ker·f);
113 i29·:·time·isFInjective(R)113 i29·:·time·isFInjective(R)
114 ·--·used·0.774547s·(cpu);·0.66491s·(thread);·0s·(gc)114 ·--·used·0.821239s·(cpu);·0.690338s·(thread);·0s·(gc)
  
115 o29·=·false115 o29·=·false
116 i30·:·time·isFInjective(R,·AssumeCM·=>·true)116 i30·:·time·isFInjective(R,·AssumeCM·=>·true)
117 ·--·used·0.276848s·(cpu);·0.215365s·(thread);·0s·(gc)117 ·--·used·0.273594s·(cpu);·0.192815s·(thread);·0s·(gc)
  
118 o30·=·true118 o30·=·true
119 If·the·option·AssumedReduced·is·set·to·true·(its·default·behavior),·then·the119 If·the·option·AssumedReduced·is·set·to·true·(its·default·behavior),·then·the
120 bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top120 bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top
121 potentially·nonzero·Ext·is·not·computed).121 potentially·nonzero·Ext·is·not·computed).
122 If·the·option·AssumeNormal·(default·value·false)·is·set·to·true,·then·the122 If·the·option·AssumeNormal·(default·value·false)·is·set·to·true,·then·the
123 bottom·two·local·cohomology·modules·(or,·rather,·their·duals)·need·not·be123 bottom·two·local·cohomology·modules·(or,·rather,·their·duals)·need·not·be
2.26 KB
./usr/share/doc/Macaulay2/TestIdeals/html/_is__F__Regular.html
    
Offset 272, 24 lines modifiedOffset 272, 24 lines modified
272 ············<td>272 ············<td>
273 ··············<pre><code·class="language-macaulay2">i26·:·debugLevel·=·1;</code></pre>273 ··············<pre><code·class="language-macaulay2">i26·:·debugLevel·=·1;</code></pre>
274 ············</td>274 ············</td>
275 ··········</tr>275 ··········</tr>
276 ··········<tr>276 ··········<tr>
277 ············<td>277 ············<td>
278 ··············<pre><code·class="language-macaulay2">i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1)278 ··············<pre><code·class="language-macaulay2">i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1)
279 ·--·used·0.0885545s·(cpu);·0.0549313s·(thread);·0s·(gc)279 ·--·used·0.0916261s·(cpu);·0.057646s·(thread);·0s·(gc)
280 isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply.280 isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply.
  
281 o27·=·false</code></pre>281 o27·=·false</code></pre>
282 ············</td>282 ············</td>
283 ··········</tr>283 ··········</tr>
284 ··········<tr>284 ··········<tr>
285 ············<td>285 ············<td>
286 ··············<pre><code·class="language-macaulay2">i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2)286 ··············<pre><code·class="language-macaulay2">i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2)
287 ·--·used·0.169821s·(cpu);·0.137219s·(thread);·0s·(gc)287 ·--·used·0.207883s·(cpu);·0.152003s·(thread);·0s·(gc)
  
288 o28·=·true</code></pre>288 o28·=·true</code></pre>
289 ············</td>289 ············</td>
290 ··········</tr>290 ··········</tr>
291 ··········<tr>291 ··········<tr>
292 ············<td>292 ············<td>
293 ··············<pre><code·class="language-macaulay2">i29·:·debugLevel·=·0;</code></pre>293 ··············<pre><code·class="language-macaulay2">i29·:·debugLevel·=·0;</code></pre>
1.08 KB
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Offset 112, 21 lines modifiedOffset 112, 21 lines modified
112 also·use·the·option·DepthOfSearch·to·increase·the·depth·of·search.112 also·use·the·option·DepthOfSearch·to·increase·the·depth·of·search.
113 i24·:·S·=·ZZ/7[x,y,z,u,v,w];113 i24·:·S·=·ZZ/7[x,y,z,u,v,w];
114 i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}});114 i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}});
  
115 o25·:·Ideal·of·S115 o25·:·Ideal·of·S
116 i26·:·debugLevel·=·1;116 i26·:·debugLevel·=·1;
117 i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1)117 i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1)
118 ·--·used·0.0885545s·(cpu);·0.0549313s·(thread);·0s·(gc)118 ·--·used·0.0916261s·(cpu);·0.057646s·(thread);·0s·(gc)
119 isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing119 isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing
120 DepthOfSearch·will·let·the·function·search·more·deeply.120 DepthOfSearch·will·let·the·function·search·more·deeply.
  
121 o27·=·false121 o27·=·false
122 i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2)122 i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2)
123 ·--·used·0.169821s·(cpu);·0.137219s·(thread);·0s·(gc)123 ·--·used·0.207883s·(cpu);·0.152003s·(thread);·0s·(gc)
  
124 o28·=·true124 o28·=·true
125 i29·:·debugLevel·=·0;125 i29·:·debugLevel·=·0;
126 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*126 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
127 ····*·_\x8t_\x8e_\x8s_\x8t_\x8I_\x8d_\x8e_\x8a_\x8l·--·compute·a·test·ideal·in·a·Q-Gorenstein·ring127 ····*·_\x8t_\x8e_\x8s_\x8t_\x8I_\x8d_\x8e_\x8a_\x8l·--·compute·a·test·ideal·in·a·Q-Gorenstein·ring
128 ····*·_\x8i_\x8s_\x8F_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·ring·is·F-rational128 ····*·_\x8i_\x8s_\x8F_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·ring·is·F-rational
129 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sF\x8FR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*129 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sF\x8FR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8*
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./usr/share/doc/Macaulay2/TestIdeals/html/_test__Ideal.html
    
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255 ········<div>255 ········<div>
256 ··········<p>It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common·denominator·and·passing·a·single·element,·since·<span·class="tt">testIdeal</span>·can·do·things·in·a·more·intelligent·way·for·such·a·list.</p>256 ··········<p>It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common·denominator·and·passing·a·single·element,·since·<span·class="tt">testIdeal</span>·can·do·things·in·a·more·intelligent·way·for·such·a·list.</p>
257 ········</div>257 ········</div>
258 ········<table·class="examples">258 ········<table·class="examples">
259 ··········<tr>259 ··········<tr>
260 ············<td>260 ············<td>
261 ··············<pre><code·class="language-macaulay2">i23·:·time·testIdeal({3/4,·2/3,·3/5},·L)261 ··············<pre><code·class="language-macaulay2">i23·:·time·testIdeal({3/4,·2/3,·3/5},·L)
262 ·--·used·0.215431s·(cpu);·0.15513s·(thread);·0s·(gc)262 ·--·used·0.24757s·(cpu);·0.162185s·(thread);·0s·(gc)
  
263 o23·=·ideal·(y,·x)263 o23·=·ideal·(y,·x)
  
264 o23·:·Ideal·of·R</code></pre>264 o23·:·Ideal·of·R</code></pre>
265 ············</td>265 ············</td>
266 ··········</tr>266 ··········</tr>
267 ··········<tr>267 ··········<tr>
268 ············<td>268 ············<td>
269 ··············<pre><code·class="language-macaulay2">i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36)269 ··············<pre><code·class="language-macaulay2">i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36)
270 ·--·used·0.320428s·(cpu);·0.229082s·(thread);·0s·(gc)270 ·--·used·0.371769s·(cpu);·0.246982s·(thread);·0s·(gc)
  
271 o24·=·ideal·(y,·x)271 o24·=·ideal·(y,·x)
  
272 o24·:·Ideal·of·R</code></pre>272 o24·:·Ideal·of·R</code></pre>
273 ············</td>273 ············</td>
274 ··········</tr>274 ··········</tr>
275 ········</table>275 ········</table>
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100 o22·=·ideal·(y,·x)100 o22·=·ideal·(y,·x)
  
101 o22·:·Ideal·of·R101 o22·:·Ideal·of·R
102 It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common102 It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common
103 denominator·and·passing·a·single·element,·since·testIdeal·can·do·things·in·a103 denominator·and·passing·a·single·element,·since·testIdeal·can·do·things·in·a
104 more·intelligent·way·for·such·a·list.104 more·intelligent·way·for·such·a·list.
105 i23·:·time·testIdeal({3/4,·2/3,·3/5},·L)105 i23·:·time·testIdeal({3/4,·2/3,·3/5},·L)
106 ·--·used·0.215431s·(cpu);·0.15513s·(thread);·0s·(gc)106 ·--·used·0.24757s·(cpu);·0.162185s·(thread);·0s·(gc)
  
107 o23·=·ideal·(y,·x)107 o23·=·ideal·(y,·x)
  
108 o23·:·Ideal·of·R108 o23·:·Ideal·of·R
109 i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36)109 i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36)
110 ·--·used·0.320428s·(cpu);·0.229082s·(thread);·0s·(gc)110 ·--·used·0.371769s·(cpu);·0.246982s·(thread);·0s·(gc)
  
111 o24·=·ideal·(y,·x)111 o24·=·ideal·(y,·x)
  
112 o24·:·Ideal·of·R112 o24·:·Ideal·of·R
113 The·option·AssumeDomain·(default·value·false)·is·used·when·finding·a·test113 The·option·AssumeDomain·(default·value·false)·is·used·when·finding·a·test
114 element.·The·option·FrobeniusRootStrategy·(default·value·Substitution)·is114 element.·The·option·FrobeniusRootStrategy·(default·value·Substitution)·is
115 passed·to·internal·_\x8f_\x8r_\x8o_\x8b_\x8e_\x8n_\x8i_\x8u_\x8s_\x8R_\x8o_\x8o_\x8t·calls.115 passed·to·internal·_\x8f_\x8r_\x8o_\x8b_\x8e_\x8n_\x8i_\x8u_\x8s_\x8R_\x8o_\x8o_\x8t·calls.
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./usr/share/doc/Macaulay2/Text/dump/rawdocumentation.dump
    
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./usr/share/doc/Macaulay2/ThreadedGB/example-output/___Minimal.out
    
Offset 2, 31 lines modifiedOffset 2, 34 lines modified
  
2 i1·:·S·=·ZZ/101[a,b,c];2 i1·:·S·=·ZZ/101[a,b,c];
  
3 i2·:·allowableThreads=·2;3 i2·:·allowableThreads=·2;
  
4 i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true)4 i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true)
  
5 o3·=·LineageTable{((0,·2),·0)·=>·null}5 o3·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 6 ··················((0,·1),·0)·=>·null
6 ··································27 ··································2
7 ··················((1,·2),·0)·=>·c8 ··················((1,·2),·0)·=>·c
8 ··················(0,·1)·=>·null9 ··················(0,·1)·=>·null
9 ··················(0,·2)·=>·null10 ··················(0,·2)·=>·null
10 ··················(1,·2)·=>·a*c11 ··················(1,·2)·=>·a*c
11 ··················0·=>·null12 ··················0·=>·null
12 ··················1·=>·null13 ··················1·=>·null
13 ························214 ························2
14 ··················2·=>·b15 ··················2·=>·b
  
15 o3·:·LineageTable16 o3·:·LineageTable
  
16 i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2")17 i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2")
  
 18 ········································3
 19 o4·=·LineageTable{(((0,·1),·0),·0)·=>·-c·}
17 ···································320 ·····································2
18 o4·=·LineageTable{((0,·2),·0)·=>·-c······}21 ··················((0,·1),·0)·=>·-a*c
19 ···································222 ···································2
20 ··················((1,·2),·0)·=>·-c23 ··················((1,·2),·0)·=>·-c
21 ·····························224 ·····························2
22 ··················(0,·1)·=>·a·c25 ··················(0,·1)·=>·a·c
23 ·······························226 ·······························2
24 ··················(0,·2)·=>·b*c27 ··················(0,·2)·=>·b*c
25 ··················(1,·2)·=>·-a*c28 ··················(1,·2)·=>·-a*c
Offset 37, 15 lines modifiedOffset 40, 16 lines modified
37 ························240 ························2
38 ··················2·=>·b41 ··················2·=>·b
  
39 o4·:·LineageTable42 o4·:·LineageTable
  
40 i5·:·minimize·T43 i5·:·minimize·T
  
41 o5·=·LineageTable{((0,·2),·0)·=>·null}44 o5·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 45 ··················((0,·1),·0)·=>·null
42 ··································246 ··································2
43 ··················((1,·2),·0)·=>·c47 ··················((1,·2),·0)·=>·c
44 ··················(0,·1)·=>·null48 ··················(0,·1)·=>·null
45 ··················(0,·2)·=>·null49 ··················(0,·2)·=>·null
46 ··················(1,·2)·=>·a*c50 ··················(1,·2)·=>·a*c
47 ··················0·=>·null51 ··················0·=>·null
48 ··················1·=>·null52 ··················1·=>·null
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./usr/share/doc/Macaulay2/ThreadedGB/example-output/_reduce.out
    
Offset 2, 16 lines modifiedOffset 2, 18 lines modified
  
2 i1·:·R·=·ZZ/101[a,b,c];2 i1·:·R·=·ZZ/101[a,b,c];
  
3 i2·:·allowableThreads=·2;3 i2·:·allowableThreads=·2;
  
4 i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2"4 i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2"
  
 5 ········································3
 6 o3·=·LineageTable{(((0,·1),·0),·0)·=>·-c·}
5 ···································37 ·····································2
6 o3·=·LineageTable{((0,·2),·0)·=>·-c······}8 ··················((0,·1),·0)·=>·-a*c
7 ···································29 ···································2
8 ··················((1,·2),·0)·=>·-c10 ··················((1,·2),·0)·=>·-c
9 ·····························211 ·····························2
10 ··················(0,·1)·=>·a·c12 ··················(0,·1)·=>·a·c
11 ·······························213 ·······························2
12 ··················(0,·2)·=>·b*c14 ··················(0,·2)·=>·b*c
13 ··················(1,·2)·=>·-a*c15 ··················(1,·2)·=>·-a*c
Offset 22, 15 lines modifiedOffset 24, 16 lines modified
22 ························224 ························2
23 ··················2·=>·b25 ··················2·=>·b
  
24 o3·:·LineageTable26 o3·:·LineageTable
  
25 i4·:·reduce·T27 i4·:·reduce·T
  
26 o4·=·LineageTable{((0,·2),·0)·=>·null}28 o4·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 29 ··················((0,·1),·0)·=>·null
27 ··································230 ··································2
28 ··················((1,·2),·0)·=>·c31 ··················((1,·2),·0)·=>·c
29 ··················(0,·1)·=>·null32 ··················(0,·1)·=>·null
30 ··················(0,·2)·=>·null33 ··················(0,·2)·=>·null
31 ··················(1,·2)·=>·a*c34 ··················(1,·2)·=>·a*c
32 ··················0·=>·null35 ··················0·=>·null
33 ··················1·=>·null36 ··················1·=>·null
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./usr/share/doc/Macaulay2/ThreadedGB/example-output/_tgb.out
    
Offset 6, 32 lines modifiedOffset 6, 40 lines modified
  
6 o2·:·Ideal·of·R6 o2·:·Ideal·of·R
  
7 i3·:·allowableThreads··=·4;7 i3·:·allowableThreads··=·4;
  
8 i4·:·H·=·tgb·I8 i4·:·H·=·tgb·I
  
 9 ·············································2·8
 10 o4·=·LineageTable{(((1,·3),·(0,·1)),·2)·=>·9y·z········}
 11 ···············································2·6
 12 ··················(((1,·3),·(0,·1)),·3)·=>·-25y·z
 13 ···································4·4······3·6
 14 ··················((0,·1),·2)·=>·9y·z··-·27y·z
 15 ··············································2·4
 16 ··················((0,·2),·((0,·1),·2))·=>·41y·z
 17 ····················································2·5
 18 ··················((0,·2),·((1,·3),·(0,·1)))·=>·-13y·z
9 ······································2·5······2·419 ···········································3·4······2·4
10 o4·=·LineageTable{((0,·1),·2)·=>·-·48y·z··+·19y·z·}20 ··················((0,·3),·(0,·1))·=>·-·25y·z··-·40y·z
 21 ··········································3·6
 22 ··················((1,·3),·(0,·1))·=>·-46y·z
11 ·····································2·423 ····································3·6
12 ··················((0,·1),·3)·=>·-19y·z24 ··················((1,·3),·1)·=>·41y·z
13 ····································2·425 ···································2·9
14 ··················((0,·2),·1)·=>·25y·z26 ··················((1,·3),·2)·=>·9y·z
15 ·································5·2······3·427 ·································5·2······3·4
16 ··················(0,·1)·=>·-·25y·z··-·19y·z28 ··················(0,·1)·=>·-·25y·z··-·19y·z
17 ·································3·5·····2·429 ·································3·5·····2·4
18 ··················(0,·2)·=>·-·24y·z··+·9y·z30 ··················(0,·2)·=>·-·24y·z··+·9y·z
19 ·······························5·······3·431 ·······························5·······3·4
20 ··················(0,·3)·=>·28y·z·-·24y·z32 ··················(0,·3)·=>·28y·z·-·24y·z
21 ·······························3·4······2·733 ·······························3·7······3·6
22 ··················(1,·2)·=>·21y·z··-·14y·z 
23 ·································2·6······2·5 
24 ··················(1,·3)·=>·-·14y·z··-·38y·z34 ··················(1,·3)·=>·30y·z··-·34y·z
25 ······························3·4·····2·4 
26 ··················(2,·3)·=>·7y·z··-·9y·z 
27 ·······························235 ·······························2
28 ··················0·=>·2x·+·10y·z36 ··················0·=>·2x·+·10y·z
29 ·························2···········337 ·························2···········3
30 ··················1·=>·8x·y·+·10x*y*z38 ··················1·=>·8x·y·+·10x*y*z
31 ···························3·2·······339 ···························3·2·······3
32 ··················2·=>·5x*y·z··+·9x*z40 ··················2·=>·5x*y·z··+·9x*z
33 ···························3·········341 ···························3·········3
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./usr/share/doc/Macaulay2/ThreadedGB/html/___Minimal.html
    
Offset 73, 15 lines modifiedOffset 73, 16 lines modified
73 ··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre>73 ··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre>
74 ············</td>74 ············</td>
75 ··········</tr>75 ··········</tr>
76 ··········<tr>76 ··········<tr>
77 ············<td>77 ············<td>
78 ··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb(·ideal·&quot;abc+c2,ab2-b3c+ac,b2&quot;,·Minimal=>true)78 ··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb(·ideal·&quot;abc+c2,ab2-b3c+ac,b2&quot;,·Minimal=>true)
  
79 o3·=·LineageTable{((0,·2),·0)·=>·null}79 o3·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 80 ··················((0,·1),·0)·=>·null
80 ··································281 ··································2
81 ··················((1,·2),·0)·=>·c82 ··················((1,·2),·0)·=>·c
82 ··················(0,·1)·=>·null83 ··················(0,·1)·=>·null
83 ··················(0,·2)·=>·null84 ··················(0,·2)·=>·null
84 ··················(1,·2)·=>·a*c85 ··················(1,·2)·=>·a*c
85 ··················0·=>·null86 ··················0·=>·null
86 ··················1·=>·null87 ··················1·=>·null
Offset 96, 16 lines modifiedOffset 97, 18 lines modified
96 ··········<p>By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the·distributed·computation·is·finished:</p>97 ··········<p>By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the·distributed·computation·is·finished:</p>
97 ········</div>98 ········</div>
98 ········<table·class="examples">99 ········<table·class="examples">
99 ··········<tr>100 ··········<tr>
100 ············<td>101 ············<td>
101 ··············<pre><code·class="language-macaulay2">i4·:·T·=·tgb(·ideal·&quot;abc+c2,ab2-b3c+ac,b2&quot;)102 ··············<pre><code·class="language-macaulay2">i4·:·T·=·tgb(·ideal·&quot;abc+c2,ab2-b3c+ac,b2&quot;)
  
 103 ········································3
 104 o4·=·LineageTable{(((0,·1),·0),·0)·=>·-c·}
102 ···································3105 ·····································2
103 o4·=·LineageTable{((0,·2),·0)·=>·-c······}106 ··················((0,·1),·0)·=>·-a*c
104 ···································2107 ···································2
105 ··················((1,·2),·0)·=>·-c108 ··················((1,·2),·0)·=>·-c
106 ·····························2109 ·····························2
107 ··················(0,·1)·=>·a·c110 ··················(0,·1)·=>·a·c
108 ·······························2111 ·······························2
109 ··················(0,·2)·=>·b*c112 ··················(0,·2)·=>·b*c
110 ··················(1,·2)·=>·-a*c113 ··················(1,·2)·=>·-a*c
Offset 119, 15 lines modifiedOffset 122, 16 lines modified
119 o4·:·LineageTable</code></pre>122 o4·:·LineageTable</code></pre>
120 ············</td>123 ············</td>
121 ··········</tr>124 ··········</tr>
122 ··········<tr>125 ··········<tr>
123 ············<td>126 ············<td>
124 ··············<pre><code·class="language-macaulay2">i5·:·minimize·T127 ··············<pre><code·class="language-macaulay2">i5·:·minimize·T
  
125 o5·=·LineageTable{((0,·2),·0)·=>·null}128 o5·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 129 ··················((0,·1),·0)·=>·null
126 ··································2130 ··································2
127 ··················((1,·2),·0)·=>·c131 ··················((1,·2),·0)·=>·c
128 ··················(0,·1)·=>·null132 ··················(0,·1)·=>·null
129 ··················(0,·2)·=>·null133 ··················(0,·2)·=>·null
130 ··················(1,·2)·=>·a*c134 ··················(1,·2)·=>·a*c
131 ··················0·=>·null135 ··················0·=>·null
132 ··················1·=>·null136 ··················1·=>·null
1.91 KB
html2text {}
    
Offset 12, 15 lines modifiedOffset 12, 16 lines modified
12 Gr\"obner·basis·is·minimized.·Lineages·of·non-minimal·Gr\"obner·basis·elements12 Gr\"obner·basis·is·minimized.·Lineages·of·non-minimal·Gr\"obner·basis·elements
13 that·were·added·to·the·basis·during·the·distributed·computation·are·saved,·with13 that·were·added·to·the·basis·during·the·distributed·computation·are·saved,·with
14 the·corresponding·entry·in·the·table·being·null.14 the·corresponding·entry·in·the·table·being·null.
15 i1·:·S·=·ZZ/101[a,b,c];15 i1·:·S·=·ZZ/101[a,b,c];
16 i2·:·allowableThreads=·2;16 i2·:·allowableThreads=·2;
17 i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true)17 i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true)
  
18 o3·=·LineageTable{((0,·2),·0)·=>·null}18 o3·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 19 ··················((0,·1),·0)·=>·null
19 ··································220 ··································2
20 ··················((1,·2),·0)·=>·c21 ··················((1,·2),·0)·=>·c
21 ··················(0,·1)·=>·null22 ··················(0,·1)·=>·null
22 ··················(0,·2)·=>·null23 ··················(0,·2)·=>·null
23 ··················(1,·2)·=>·a*c24 ··················(1,·2)·=>·a*c
24 ··················0·=>·null25 ··················0·=>·null
25 ··················1·=>·null26 ··················1·=>·null
Offset 28, 16 lines modifiedOffset 29, 18 lines modified
28 ··················2·=>·b29 ··················2·=>·b
  
29 o3·:·LineageTable30 o3·:·LineageTable
30 By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the31 By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the
31 distributed·computation·is·finished:32 distributed·computation·is·finished:
32 i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2")33 i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2")
  
 34 ········································3
 35 o4·=·LineageTable{(((0,·1),·0),·0)·=>·-c·}
33 ···································336 ·····································2
34 o4·=·LineageTable{((0,·2),·0)·=>·-c······}37 ··················((0,·1),·0)·=>·-a*c
35 ···································238 ···································2
36 ··················((1,·2),·0)·=>·-c39 ··················((1,·2),·0)·=>·-c
37 ·····························240 ·····························2
38 ··················(0,·1)·=>·a·c41 ··················(0,·1)·=>·a·c
39 ·······························242 ·······························2
40 ··················(0,·2)·=>·b*c43 ··················(0,·2)·=>·b*c
41 ··················(1,·2)·=>·-a*c44 ··················(1,·2)·=>·-a*c
Offset 47, 15 lines modifiedOffset 50, 16 lines modified
47 ··················1·=>·-·b·c·+·a*b··+·a*c50 ··················1·=>·-·b·c·+·a*b··+·a*c
48 ························251 ························2
49 ··················2·=>·b52 ··················2·=>·b
  
50 o4·:·LineageTable53 o4·:·LineageTable
51 i5·:·minimize·T54 i5·:·minimize·T
  
52 o5·=·LineageTable{((0,·2),·0)·=>·null}55 o5·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 56 ··················((0,·1),·0)·=>·null
53 ··································257 ··································2
54 ··················((1,·2),·0)·=>·c58 ··················((1,·2),·0)·=>·c
55 ··················(0,·1)·=>·null59 ··················(0,·1)·=>·null
56 ··················(0,·2)·=>·null60 ··················(0,·2)·=>·null
57 ··················(1,·2)·=>·a*c61 ··················(1,·2)·=>·a*c
58 ··················0·=>·null62 ··················0·=>·null
59 ··················1·=>·null63 ··················1·=>·null
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./usr/share/doc/Macaulay2/ThreadedGB/html/_reduce.html
    
Offset 82, 16 lines modifiedOffset 82, 18 lines modified
82 ··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre>82 ··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre>
83 ············</td>83 ············</td>
84 ··········</tr>84 ··········</tr>
85 ··········<tr>85 ··········<tr>
86 ············<td>86 ············<td>
87 ··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb·ideal·&quot;abc+c2,ab2-b3c+ac,b2&quot;87 ··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb·ideal·&quot;abc+c2,ab2-b3c+ac,b2&quot;
  
 88 ········································3
 89 o3·=·LineageTable{(((0,·1),·0),·0)·=>·-c·}
88 ···································390 ·····································2
89 o3·=·LineageTable{((0,·2),·0)·=>·-c······}91 ··················((0,·1),·0)·=>·-a*c
90 ···································292 ···································2
91 ··················((1,·2),·0)·=>·-c93 ··················((1,·2),·0)·=>·-c
92 ·····························294 ·····························2
93 ··················(0,·1)·=>·a·c95 ··················(0,·1)·=>·a·c
94 ·······························296 ·······························2
95 ··················(0,·2)·=>·b*c97 ··················(0,·2)·=>·b*c
96 ··················(1,·2)·=>·-a*c98 ··················(1,·2)·=>·-a*c
Offset 105, 15 lines modifiedOffset 107, 16 lines modified
105 o3·:·LineageTable</code></pre>107 o3·:·LineageTable</code></pre>
106 ············</td>108 ············</td>
107 ··········</tr>109 ··········</tr>
108 ··········<tr>110 ··········<tr>
109 ············<td>111 ············<td>
110 ··············<pre><code·class="language-macaulay2">i4·:·reduce·T112 ··············<pre><code·class="language-macaulay2">i4·:·reduce·T
  
111 o4·=·LineageTable{((0,·2),·0)·=>·null}113 o4·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 114 ··················((0,·1),·0)·=>·null
112 ··································2115 ··································2
113 ··················((1,·2),·0)·=>·c116 ··················((1,·2),·0)·=>·c
114 ··················(0,·1)·=>·null117 ··················(0,·1)·=>·null
115 ··················(0,·2)·=>·null118 ··················(0,·2)·=>·null
116 ··················(1,·2)·=>·a*c119 ··················(1,·2)·=>·a*c
117 ··················0·=>·null120 ··················0·=>·null
118 ··················1·=>·null121 ··················1·=>·null
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20 remainder·on·the·division·by·the·remaining·values·H.20 remainder·on·the·division·by·the·remaining·values·H.
21 If·values·H·constitute·a·Gr\"obner·basis·of·the·ideal·they·generate,·this21 If·values·H·constitute·a·Gr\"obner·basis·of·the·ideal·they·generate,·this
22 method·returns·a·reduced·Gr\"obner·basis.22 method·returns·a·reduced·Gr\"obner·basis.
23 i1·:·R·=·ZZ/101[a,b,c];23 i1·:·R·=·ZZ/101[a,b,c];
24 i2·:·allowableThreads=·2;24 i2·:·allowableThreads=·2;
25 i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2"25 i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2"
  
 26 ········································3
 27 o3·=·LineageTable{(((0,·1),·0),·0)·=>·-c·}
26 ···································328 ·····································2
27 o3·=·LineageTable{((0,·2),·0)·=>·-c······}29 ··················((0,·1),·0)·=>·-a*c
28 ···································230 ···································2
29 ··················((1,·2),·0)·=>·-c31 ··················((1,·2),·0)·=>·-c
30 ·····························232 ·····························2
31 ··················(0,·1)·=>·a·c33 ··················(0,·1)·=>·a·c
32 ·······························234 ·······························2
33 ··················(0,·2)·=>·b*c35 ··················(0,·2)·=>·b*c
34 ··················(1,·2)·=>·-a*c36 ··················(1,·2)·=>·-a*c
Offset 39, 15 lines modifiedOffset 41, 16 lines modified
39 ··················1·=>·-·b·c·+·a*b··+·a*c41 ··················1·=>·-·b·c·+·a*b··+·a*c
40 ························242 ························2
41 ··················2·=>·b43 ··················2·=>·b
  
42 o3·:·LineageTable44 o3·:·LineageTable
43 i4·:·reduce·T45 i4·:·reduce·T
  
44 o4·=·LineageTable{((0,·2),·0)·=>·null}46 o4·=·LineageTable{(((0,·1),·0),·0)·=>·null}
 47 ··················((0,·1),·0)·=>·null
45 ··································248 ··································2
46 ··················((1,·2),·0)·=>·c49 ··················((1,·2),·0)·=>·c
47 ··················(0,·1)·=>·null50 ··················(0,·1)·=>·null
48 ··················(0,·2)·=>·null51 ··················(0,·2)·=>·null
49 ··················(1,·2)·=>·a*c52 ··················(1,·2)·=>·a*c
50 ··················0·=>·null53 ··················0·=>·null
51 ··················1·=>·null54 ··················1·=>·null
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./usr/share/doc/Macaulay2/ThreadedGB/html/_tgb.html
    
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95 ··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=·4;</code></pre>95 ··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=·4;</code></pre>
96 ············</td>96 ············</td>
97 ··········</tr>97 ··········</tr>
98 ··········<tr>98 ··········<tr>
99 ············<td>99 ············<td>
100 ··············<pre><code·class="language-macaulay2">i4·:·H·=·tgb·I100 ··············<pre><code·class="language-macaulay2">i4·:·H·=·tgb·I
  
 101 ·············································2·8
 102 o4·=·LineageTable{(((1,·3),·(0,·1)),·2)·=>·9y·z········}
 103 ···············································2·6
 104 ··················(((1,·3),·(0,·1)),·3)·=>·-25y·z
 105 ···································4·4······3·6
 106 ··················((0,·1),·2)·=>·9y·z··-·27y·z
 107 ··············································2·4
 108 ··················((0,·2),·((0,·1),·2))·=>·41y·z
 109 ····················································2·5
 110 ··················((0,·2),·((1,·3),·(0,·1)))·=>·-13y·z
101 ······································2·5······2·4111 ···········································3·4······2·4
102 o4·=·LineageTable{((0,·1),·2)·=>·-·48y·z··+·19y·z·}112 ··················((0,·3),·(0,·1))·=>·-·25y·z··-·40y·z
 113 ··········································3·6
 114 ··················((1,·3),·(0,·1))·=>·-46y·z
103 ·····································2·4115 ····································3·6
104 ··················((0,·1),·3)·=>·-19y·z116 ··················((1,·3),·1)·=>·41y·z
105 ····································2·4117 ···································2·9
106 ··················((0,·2),·1)·=>·25y·z118 ··················((1,·3),·2)·=>·9y·z
107 ·································5·2······3·4119 ·································5·2······3·4
108 ··················(0,·1)·=>·-·25y·z··-·19y·z120 ··················(0,·1)·=>·-·25y·z··-·19y·z
109 ·································3·5·····2·4121 ·································3·5·····2·4
110 ··················(0,·2)·=>·-·24y·z··+·9y·z122 ··················(0,·2)·=>·-·24y·z··+·9y·z
111 ·······························5·······3·4123 ·······························5·······3·4
112 ··················(0,·3)·=>·28y·z·-·24y·z124 ··················(0,·3)·=>·28y·z·-·24y·z
113 ·······························3·4······2·7125 ·······························3·7······3·6
114 ··················(1,·2)·=>·21y·z··-·14y·z 
115 ·································2·6······2·5 
116 ··················(1,·3)·=>·-·14y·z··-·38y·z126 ··················(1,·3)·=>·30y·z··-·34y·z
117 ······························3·4·····2·4 
118 ··················(2,·3)·=>·7y·z··-·9y·z 
119 ·······························2127 ·······························2
120 ··················0·=>·2x·+·10y·z128 ··················0·=>·2x·+·10y·z
121 ·························2···········3129 ·························2···········3
122 ··················1·=>·8x·y·+·10x*y*z130 ··················1·=>·8x·y·+·10x*y*z
123 ···························3·2·······3131 ···························3·2·······3
124 ··················2·=>·5x*y·z··+·9x*z132 ··················2·=>·5x*y·z··+·9x*z
125 ···························3·········3133 ···························3·········3
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26 i2·:·I·=·ideal·{2*x·+·10*y^2*z,·8*x^2*y·+·10*x*y*z^3,·5*x*y^3*z^2·+·9*x*z^3,26 i2·:·I·=·ideal·{2*x·+·10*y^2*z,·8*x^2*y·+·10*x*y*z^3,·5*x*y^3*z^2·+·9*x*z^3,
27 9*x*y^3*z·+·10*x*y^3};27 9*x*y^3*z·+·10*x*y^3};
  
28 o2·:·Ideal·of·R28 o2·:·Ideal·of·R
29 i3·:·allowableThreads··=·4;29 i3·:·allowableThreads··=·4;
30 i4·:·H·=·tgb·I30 i4·:·H·=·tgb·I
  
 31 ·············································2·8
 32 o4·=·LineageTable{(((1,·3),·(0,·1)),·2)·=>·9y·z········}
 33 ···············································2·6
 34 ··················(((1,·3),·(0,·1)),·3)·=>·-25y·z
 35 ···································4·4······3·6
 36 ··················((0,·1),·2)·=>·9y·z··-·27y·z
 37 ··············································2·4
 38 ··················((0,·2),·((0,·1),·2))·=>·41y·z
 39 ····················································2·5
 40 ··················((0,·2),·((1,·3),·(0,·1)))·=>·-13y·z
31 ······································2·5······2·441 ···········································3·4······2·4
32 o4·=·LineageTable{((0,·1),·2)·=>·-·48y·z··+·19y·z·}42 ··················((0,·3),·(0,·1))·=>·-·25y·z··-·40y·z
 43 ··········································3·6
 44 ··················((1,·3),·(0,·1))·=>·-46y·z
33 ·····································2·445 ····································3·6
34 ··················((0,·1),·3)·=>·-19y·z46 ··················((1,·3),·1)·=>·41y·z
35 ····································2·447 ···································2·9
36 ··················((0,·2),·1)·=>·25y·z48 ··················((1,·3),·2)·=>·9y·z
37 ·································5·2······3·449 ·································5·2······3·4
38 ··················(0,·1)·=>·-·25y·z··-·19y·z50 ··················(0,·1)·=>·-·25y·z··-·19y·z
39 ·································3·5·····2·451 ·································3·5·····2·4
40 ··················(0,·2)·=>·-·24y·z··+·9y·z52 ··················(0,·2)·=>·-·24y·z··+·9y·z
41 ·······························5·······3·453 ·······························5·······3·4
42 ··················(0,·3)·=>·28y·z·-·24y·z54 ··················(0,·3)·=>·28y·z·-·24y·z
43 ·······························3·4······2·755 ·······························3·7······3·6
44 ··················(1,·2)·=>·21y·z··-·14y·z 
45 ·································2·6······2·5 
46 ··················(1,·3)·=>·-·14y·z··-·38y·z56 ··················(1,·3)·=>·30y·z··-·34y·z
47 ······························3·4·····2·4 
48 ··················(2,·3)·=>·7y·z··-·9y·z 
49 ·······························257 ·······························2
50 ··················0·=>·2x·+·10y·z58 ··················0·=>·2x·+·10y·z
51 ·························2···········359 ·························2···········3
52 ··················1·=>·8x·y·+·10x*y*z60 ··················1·=>·8x·y·+·10x*y*z
53 ···························3·2·······361 ···························3·2·······3
54 ··················2·=>·5x*y·z··+·9x*z62 ··················2·=>·5x*y·z··+·9x*z
55 ···························3·········363 ···························3·········3
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6 #·End·of·header6 #·End·of·header
7 #:len=57 #:len=5
8 ZWREZWc=8 ZWREZWc=
9 #:len=25019 #:len=2501
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIChnZW5lcmljKSBF10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIChnZW5lcmljKSBF
11 dWNsaWRlYW4gZGlzdGFuY2UgZGVncmVlIG9mIGEgcHJvamVjdGl2ZSB0b3JpYyB2YXJpZXR5Iiwg11 dWNsaWRlYW4gZGlzdGFuY2UgZGVncmVlIG9mIGEgcHJvamVjdGl2ZSB0b3JpYyB2YXJpZXR5Iiwg
1020 B
./usr/share/doc/Macaulay2/ToricInvariants/example-output/_ed__Deg.out
    
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31 ·····|·0·1·2·0·2·0·|31 ·····|·0·1·2·0·2·0·|
32 ·····|·1·1·1·1·1·1·|32 ·····|·1·1·1·1·1·1·|
  
33 ··············4·······633 ··············4·······6
34 o3·:·Matrix·ZZ··<--·ZZ34 o3·:·Matrix·ZZ··<--·ZZ
  
35 i4·:·time·edDeg(A)35 i4·:·time·edDeg(A)
36 ·--·used·0.881105s·(cpu);·0.674434s·(thread);·0s·(gc)36 ·--·used·1.08584s·(cpu);·0.798102s·(thread);·0s·(gc)
  
37 The·toric·variety·has·degree·=·2837 The·toric·variety·has·degree·=·28
38 The·dual·variety·has·degree·=·45,·and·codimension·=·138 The·dual·variety·has·degree·=·45,·and·codimension·=·1
39 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}39 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}
40 Polar·Degrees:·{45,·98,·81,·28}40 Polar·Degrees:·{45,·98,·81,·28}
41 ED·Degree·=·25241 ED·Degree·=·252
  
Offset 47, 15 lines modifiedOffset 47, 15 lines modified
47 Chern-Mather·Class:·20h··+·23h··+·31h··+·28h47 Chern-Mather·Class:·20h··+·23h··+·31h··+·28h
  
48 o4·=·25248 o4·=·252
  
49 o4·:·QQ49 o4·:·QQ
  
50 i5·:·time·edDeg(A,ForceAmat=>true)50 i5·:·time·edDeg(A,ForceAmat=>true)
51 ·--·used·3.40686s·(cpu);·2.54453s·(thread);·0s·(gc)51 ·--·used·4.20645s·(cpu);·2.8807s·(thread);·0s·(gc)
  
52 The·toric·variety·has·degree·=·2852 The·toric·variety·has·degree·=·28
53 The·dual·variety·has·degree·=·45,·and·codimension·=·153 The·dual·variety·has·degree·=·45,·and·codimension·=·1
54 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}54 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}
55 Polar·Degrees:·{45,·98,·81,·28}55 Polar·Degrees:·{45,·98,·81,·28}
56 ED·Degree·=·25256 ED·Degree·=·252
  
2.08 KB
./usr/share/doc/Macaulay2/ToricInvariants/html/_ed__Deg.html
    
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122 ··············4·······6122 ··············4·······6
123 o3·:·Matrix·ZZ··&lt;--·ZZ</code></pre>123 o3·:·Matrix·ZZ··&lt;--·ZZ</code></pre>
124 ············</td>124 ············</td>
125 ··········</tr>125 ··········</tr>
126 ··········<tr>126 ··········<tr>
127 ············<td>127 ············<td>
128 ··············<pre><code·class="language-macaulay2">i4·:·time·edDeg(A)128 ··············<pre><code·class="language-macaulay2">i4·:·time·edDeg(A)
129 ·--·used·0.881105s·(cpu);·0.674434s·(thread);·0s·(gc)129 ·--·used·1.08584s·(cpu);·0.798102s·(thread);·0s·(gc)
  
130 The·toric·variety·has·degree·=·28130 The·toric·variety·has·degree·=·28
131 The·dual·variety·has·degree·=·45,·and·codimension·=·1131 The·dual·variety·has·degree·=·45,·and·codimension·=·1
132 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}132 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}
133 Polar·Degrees:·{45,·98,·81,·28}133 Polar·Degrees:·{45,·98,·81,·28}
134 ED·Degree·=·252134 ED·Degree·=·252
  
Offset 141, 15 lines modifiedOffset 141, 15 lines modified
  
141 o4·:·QQ</code></pre>141 o4·:·QQ</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ··········<tr>144 ··········<tr>
145 ············<td>145 ············<td>
146 ··············<pre><code·class="language-macaulay2">i5·:·time·edDeg(A,ForceAmat=>true)146 ··············<pre><code·class="language-macaulay2">i5·:·time·edDeg(A,ForceAmat=>true)
147 ·--·used·3.40686s·(cpu);·2.54453s·(thread);·0s·(gc)147 ·--·used·4.20645s·(cpu);·2.8807s·(thread);·0s·(gc)
  
148 The·toric·variety·has·degree·=·28148 The·toric·variety·has·degree·=·28
149 The·dual·variety·has·degree·=·45,·and·codimension·=·1149 The·dual·variety·has·degree·=·45,·and·codimension·=·1
150 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}150 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}
151 Polar·Degrees:·{45,·98,·81,·28}151 Polar·Degrees:·{45,·98,·81,·28}
152 ED·Degree·=·252152 ED·Degree·=·252
  
953 B
html2text {}
    
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57 ·····|·3·5·0·2·1·3·|57 ·····|·3·5·0·2·1·3·|
58 ·····|·0·1·2·0·2·0·|58 ·····|·0·1·2·0·2·0·|
59 ·····|·1·1·1·1·1·1·|59 ·····|·1·1·1·1·1·1·|
  
60 ··············4·······660 ··············4·······6
61 o3·:·Matrix·ZZ··<--·ZZ61 o3·:·Matrix·ZZ··<--·ZZ
62 i4·:·time·edDeg(A)62 i4·:·time·edDeg(A)
63 ·--·used·0.881105s·(cpu);·0.674434s·(thread);·0s·(gc)63 ·--·used·1.08584s·(cpu);·0.798102s·(thread);·0s·(gc)
  
64 The·toric·variety·has·degree·=·2864 The·toric·variety·has·degree·=·28
65 The·dual·variety·has·degree·=·45,·and·codimension·=·165 The·dual·variety·has·degree·=·45,·and·codimension·=·1
66 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}66 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}
67 Polar·Degrees:·{45,·98,·81,·28}67 Polar·Degrees:·{45,·98,·81,·28}
68 ED·Degree·=·25268 ED·Degree·=·252
  
69 ·······················5······4······3······269 ·······················5······4······3······2
70 Chern-Mather·Class:·20h··+·23h··+·31h··+·28h70 Chern-Mather·Class:·20h··+·23h··+·31h··+·28h
  
71 o4·=·25271 o4·=·252
  
72 o4·:·QQ72 o4·:·QQ
73 i5·:·time·edDeg(A,ForceAmat=>true)73 i5·:·time·edDeg(A,ForceAmat=>true)
74 ·--·used·3.40686s·(cpu);·2.54453s·(thread);·0s·(gc)74 ·--·used·4.20645s·(cpu);·2.8807s·(thread);·0s·(gc)
  
75 The·toric·variety·has·degree·=·2875 The·toric·variety·has·degree·=·28
76 The·dual·variety·has·degree·=·45,·and·codimension·=·176 The·dual·variety·has·degree·=·45,·and·codimension·=·1
77 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}77 Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28}
78 Polar·Degrees:·{45,·98,·81,·28}78 Polar·Degrees:·{45,·98,·81,·28}
79 ED·Degree·=·25279 ED·Degree·=·252
  
735 B
./usr/share/doc/Macaulay2/ToricTopology/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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8 aGVzc2VuYmVyZ1ZhcmlldHk=8 aGVzc2VuYmVyZ1ZhcmlldHk=
9 #:len=7369 #:len=736
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiSGVzc2VuYmVyZyB2YXJpZXR5IGFzc2Nv10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiSGVzc2VuYmVyZyB2YXJpZXR5IGFzc2Nv
11 aWF0ZWQgdG8gdGhlIG4tcGVybXV0YWhlZHJvbiIsICJsaW5lbnVtIiA9PiA2MzksIElucHV0cyA911 aWF0ZWQgdG8gdGhlIG4tcGVybXV0YWhlZHJvbiIsICJsaW5lbnVtIiA9PiA2MzksIElucHV0cyA9
754 B
./usr/share/doc/Macaulay2/ToricVectorBundles/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
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6 #·End·of·header6 #·End·of·header
7 #:len=237 #:len=23
8 ZHVhbChUb3JpY1ZlY3RvckJ1bmRsZSk=8 ZHVhbChUb3JpY1ZlY3RvckJ1bmRsZSk=
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiIHRoZSBkdWFsIGJ1bmRsZSBvZiBhIHRv10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiIHRoZSBkdWFsIGJ1bmRsZSBvZiBhIHRv
11 cmljIHZlY3RvciBidW5kbGUiLCAibGluZW51bSIgPT4gMjgwOCwgSW5wdXRzID0+IHtTUEFOe1RU11 cmljIHZlY3RvciBidW5kbGUiLCAibGluZW51bSIgPT4gMjgwOCwgSW5wdXRzID0+IHtTUEFOe1RU
733 B
./usr/share/doc/Macaulay2/TriangularSets/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=147 #:len=14
8 Y2hlY2tJbnRlcmZhY2U=8 Y2hlY2tJbnRlcmZhY2U=
9 #:len=7929 #:len=792
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAid2hldGhlciB0aGUgTWFwbGUgaW50ZXJm10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAid2hldGhlciB0aGUgTWFwbGUgaW50ZXJm
11 YWNlIGlzIHdvcmtpbmcgKGZvciBkZXZlbG9wZXJzKSIsICJsaW5lbnVtIiA9PiAzMzUsIElucHV011 YWNlIGlzIHdvcmtpbmcgKGZvciBkZXZlbG9wZXJzKSIsICJsaW5lbnVtIiA9PiAzMzUsIElucHV0
737 B
./usr/share/doc/Macaulay2/Triangulations/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
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6 #·End·of·header6 #·End·of·header
7 #:len=177 #:len=17
8 YWxsVHJpYW5ndWxhdGlvbnM=8 YWxsVHJpYW5ndWxhdGlvbnM=
9 #:len=2859 #:len=285
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzcyLCBzeW1ib2wgRG9jdW1lbnRUYWcg10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzcyLCBzeW1ib2wgRG9jdW1lbnRUYWcg
11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJhbGxUcmlhbmd1bGF0aW9ucyIsImFsbFRyaWFuZ3Vs11 PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJhbGxUcmlhbmd1bGF0aW9ucyIsImFsbFRyaWFuZ3Vs
1.32 KB
./usr/share/doc/Macaulay2/Triangulations/example-output/___Triangulations.out
    
Offset 17, 15 lines modifiedOffset 17, 15 lines modified
17 ·····|·-1·1··2··-1·-1·1·-1·1·0·0·|17 ·····|·-1·1··2··-1·-1·1·-1·1·0·0·|
18 ·····|·1··0··-1·0··0··0·0··0·0·0·|18 ·····|·1··0··-1·0··0··0·0··0·0·0·|
  
19 ··············4·······1019 ··············4·······10
20 o2·:·Matrix·ZZ··<--·ZZ20 o2·:·Matrix·ZZ··<--·ZZ
  
21 i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true);21 i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true);
22 ·--·.126564s·elapsed22 ·--·.147652s·elapsed
  
23 i4·:·select(Ts,·T·->·isStar·T)23 i4·:·select(Ts,·T·->·isStar·T)
  
24 o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,24 o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,
25 ·····------------------------------------------------------------------------25 ·····------------------------------------------------------------------------
26 ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3,26 ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3,
27 ·····------------------------------------------------------------------------27 ·····------------------------------------------------------------------------
Offset 50, 14 lines modifiedOffset 50, 14 lines modified
50 i7·:·T·=·regularFineTriangulation·A50 i7·:·T·=·regularFineTriangulation·A
  
51 o7·=·triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,·1,·6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},·{0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,·7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,·3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}}51 o7·=·triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,·1,·6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},·{0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,·7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,·3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}}
  
52 o7·:·Triangulation52 o7·:·Triangulation
  
53 i8·:·elapsedTime·Ts2·=·generateTriangulations·T;53 i8·:·elapsedTime·Ts2·=·generateTriangulations·T;
54 ·--·1.11952s·elapsed54 ·--·2.65224s·elapsed
  
55 i9·:·#Ts2·==·#Ts55 i9·:·#Ts2·==·#Ts
  
56 o9·=·true56 o9·=·true
  
57 i10·:·57 i10·:·
49.4 KB
./usr/share/doc/Macaulay2/Triangulations/example-output/_generate__Triangulations.out
    
Offset 21, 57 lines modifiedOffset 21, 15 lines modified
  
21 o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6},·{3,·5,·6,·7}}21 o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6},·{3,·5,·6,·7}}
  
22 o3·:·Triangulation22 o3·:·Triangulation
  
23 i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's.23 i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's.
  
24 o4·=·{triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, 
25 ·····------------------------------------------------------------------------ 
26 ·····{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, 
27 ·····------------------------------------------------------------------------ 
28 ·····{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},·triangulation 
29 ·····------------------------------------------------------------------------ 
30 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·6}, 
31 ·····------------------------------------------------------------------------ 
32 ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·6}, 
33 ·····------------------------------------------------------------------------ 
34 ·····{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation·{{0,·1,·3,·5}, 
35 ·····------------------------------------------------------------------------ 
36 ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}}, 
37 ·····------------------------------------------------------------------------ 
38 ·····triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, 
39 ·····------------------------------------------------------------------------ 
40 ·····{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4}, 
41 ·····------------------------------------------------------------------------ 
42 ·····{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},·triangulation 
43 ·····------------------------------------------------------------------------ 
44 ·····{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7}, 
45 ·····------------------------------------------------------------------------ 
46 ·····{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},·{0,·3,·4,·6}, 
47 ·····------------------------------------------------------------------------ 
48 ·····{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, 
49 ·····------------------------------------------------------------------------ 
50 ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}}, 
51 ·····------------------------------------------------------------------------ 
52 ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7}, 
53 ·····------------------------------------------------------------------------ 
54 ·····{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},·{0,·1,·4,·6}, 
55 ·····------------------------------------------------------------------------ 
56 ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation 
57 ·····------------------------------------------------------------------------ 
58 ·····{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·7}, 
59 ·····------------------------------------------------------------------------ 
60 ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},·{0,·2,·3,·6}, 
61 ·····------------------------------------------------------------------------ 
62 ·····{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, 
63 ·····------------------------------------------------------------------------ 
64 ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}}, 
65 ·····------------------------------------------------------------------------ 
66 ·····triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},24 o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},
67 ·····------------------------------------------------------------------------25 ·····------------------------------------------------------------------------
68 ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},26 ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},
69 ·····------------------------------------------------------------------------27 ·····------------------------------------------------------------------------
70 ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation28 ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation
71 ·····------------------------------------------------------------------------29 ·····------------------------------------------------------------------------
72 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7},30 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7},
73 ·····------------------------------------------------------------------------31 ·····------------------------------------------------------------------------
Offset 227, 57 lines modifiedOffset 185, 63 lines modified
227 ·····------------------------------------------------------------------------185 ·····------------------------------------------------------------------------
228 ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},186 ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},
229 ·····------------------------------------------------------------------------187 ·····------------------------------------------------------------------------
230 ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation188 ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation
231 ·····------------------------------------------------------------------------189 ·····------------------------------------------------------------------------
232 ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7},190 ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7},
233 ·····------------------------------------------------------------------------191 ·····------------------------------------------------------------------------
 192 ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},
234 ·····{1,·4,·6,·7}}} 
  
235 o4·:·List 
  
236 i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets 
  
237 o5·=·{{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, 
238 ·····------------------------------------------------------------------------193 ·····------------------------------------------------------------------------
239 ·····{0,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},194 ·····{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},
240 ·····------------------------------------------------------------------------195 ·····------------------------------------------------------------------------
241 ·····{0,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},196 ·····{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},
242 ·····------------------------------------------------------------------------197 ·····------------------------------------------------------------------------
243 ·····{0,·3,·5,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},198 ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},
244 ·····------------------------------------------------------------------------199 ·····------------------------------------------------------------------------
245 ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},200 ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},
246 ·····------------------------------------------------------------------------201 ·····------------------------------------------------------------------------
247 ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},202 ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation
248 ·····------------------------------------------------------------------------203 ·····------------------------------------------------------------------------
249 ·····{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5},·{2,·3,·5,·6},204 ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},
250 ·····------------------------------------------------------------------------205 ·····------------------------------------------------------------------------
251 ·····{3,·5,·6,·7}},·{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},206 ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},
252 ·····------------------------------------------------------------------------207 ·····------------------------------------------------------------------------
253 ·····{2,·4,·6,·7},·{3,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},208 ·····{1,·2,·3,·5},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},
254 ·····------------------------------------------------------------------------209 ·····------------------------------------------------------------------------
255 ·····{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}},·{{0,·1,·3,·4},·{0,·2,·3,·6},210 ·····{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},
256 ·····------------------------------------------------------------------------211 ·····------------------------------------------------------------------------
257 ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·{{0,·1,·2,·5},212 ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},
258 ·····------------------------------------------------------------------------213 ·····------------------------------------------------------------------------
259 ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}},214 ·····{3,·4,·5,·7},·{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},
260 ·····------------------------------------------------------------------------215 ·····------------------------------------------------------------------------
261 ·····{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},216 ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation
262 ·····------------------------------------------------------------------------217 ·····------------------------------------------------------------------------
263 ·····{2,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},218 ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},
264 ·····------------------------------------------------------------------------219 ·····------------------------------------------------------------------------
265 ·····{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},220 ·····{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},
266 ·····------------------------------------------------------------------------221 ·····------------------------------------------------------------------------
267 ·····{1,·4,·5,·7},·{2,·3,·4,·7},·{2,·4,·6,·7}},·{{0,·1,·3,·6},·{0,·1,·4,·6},222 ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},
268 ·····------------------------------------------------------------------------223 ·····------------------------------------------------------------------------
269 ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·5},224 ·····{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},
270 ·····------------------------------------------------------------------------225 ·····------------------------------------------------------------------------
271 ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},226 ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},
272 ·····------------------------------------------------------------------------227 ·····------------------------------------------------------------------------
 228 ·····{2,·3,·4,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},
 229 ·····------------------------------------------------------------------------
 230 ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation
 231 ·····------------------------------------------------------------------------
 232 ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},
 233 ·····------------------------------------------------------------------------
 234 ·····{2,·5,·6,·7}}}
  
 235 o4·:·List
  
 236 i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets
  
273 ·····{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7},237 o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7},
274 ·····------------------------------------------------------------------------238 ·····------------------------------------------------------------------------
275 ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},239 ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},
276 ·····------------------------------------------------------------------------240 ·····------------------------------------------------------------------------
277 ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},241 ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},
278 ·····------------------------------------------------------------------------242 ·····------------------------------------------------------------------------
279 ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},243 ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},
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./usr/share/doc/Macaulay2/Triangulations/html/_generate__Triangulations.html
    
Offset 117, 57 lines modifiedOffset 117, 15 lines modified
117 o3·:·Triangulation</code></pre>117 o3·:·Triangulation</code></pre>
118 ············</td>118 ············</td>
119 ··········</tr>119 ··········</tr>
120 ··········<tr>120 ··········<tr>
121 ············<td>121 ············<td>
122 ··············<pre><code·class="language-macaulay2">i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's.122 ··············<pre><code·class="language-macaulay2">i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's.
  
123 o4·=·{triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, 
124 ·····------------------------------------------------------------------------ 
125 ·····{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, 
126 ·····------------------------------------------------------------------------ 
127 ·····{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},·triangulation 
128 ·····------------------------------------------------------------------------ 
129 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·6}, 
130 ·····------------------------------------------------------------------------ 
131 ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·6}, 
132 ·····------------------------------------------------------------------------ 
133 ·····{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation·{{0,·1,·3,·5}, 
134 ·····------------------------------------------------------------------------ 
135 ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}}, 
136 ·····------------------------------------------------------------------------ 
137 ·····triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, 
138 ·····------------------------------------------------------------------------ 
139 ·····{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4}, 
140 ·····------------------------------------------------------------------------ 
141 ·····{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},·triangulation 
142 ·····------------------------------------------------------------------------ 
143 ·····{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7}, 
144 ·····------------------------------------------------------------------------ 
145 ·····{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},·{0,·3,·4,·6}, 
146 ·····------------------------------------------------------------------------ 
147 ·····{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, 
148 ·····------------------------------------------------------------------------ 
149 ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}}, 
150 ·····------------------------------------------------------------------------ 
151 ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7}, 
152 ·····------------------------------------------------------------------------ 
153 ·····{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},·{0,·1,·4,·6}, 
154 ·····------------------------------------------------------------------------ 
155 ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation 
156 ·····------------------------------------------------------------------------ 
157 ·····{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·7}, 
158 ·····------------------------------------------------------------------------ 
159 ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},·{0,·2,·3,·6}, 
160 ·····------------------------------------------------------------------------ 
161 ·····{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, 
162 ·····------------------------------------------------------------------------ 
163 ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}}, 
164 ·····------------------------------------------------------------------------ 
165 ·····triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},123 o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},
166 ·····------------------------------------------------------------------------124 ·····------------------------------------------------------------------------
167 ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},125 ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},
168 ·····------------------------------------------------------------------------126 ·····------------------------------------------------------------------------
169 ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation127 ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation
170 ·····------------------------------------------------------------------------128 ·····------------------------------------------------------------------------
171 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7},129 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7},
172 ·····------------------------------------------------------------------------130 ·····------------------------------------------------------------------------
Offset 323, 60 lines modifiedOffset 281, 66 lines modified
323 ·····------------------------------------------------------------------------281 ·····------------------------------------------------------------------------
324 ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},282 ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},
325 ·····------------------------------------------------------------------------283 ·····------------------------------------------------------------------------
326 ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation284 ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation
327 ·····------------------------------------------------------------------------285 ·····------------------------------------------------------------------------
328 ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7},286 ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7},
329 ·····------------------------------------------------------------------------287 ·····------------------------------------------------------------------------
 288 ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},
330 ·····{1,·4,·6,·7}}} 
  
331 o4·:·List</code></pre> 
332 ············</td> 
333 ··········</tr> 
334 ··········<tr> 
335 ············<td> 
336 ··············<pre><code·class="language-macaulay2">i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets 
  
337 o5·=·{{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, 
338 ·····------------------------------------------------------------------------289 ·····------------------------------------------------------------------------
339 ·····{0,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},290 ·····{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},
340 ·····------------------------------------------------------------------------291 ·····------------------------------------------------------------------------
341 ·····{0,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},292 ·····{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},
342 ·····------------------------------------------------------------------------293 ·····------------------------------------------------------------------------
343 ·····{0,·3,·5,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},294 ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},
344 ·····------------------------------------------------------------------------295 ·····------------------------------------------------------------------------
345 ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},296 ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},
346 ·····------------------------------------------------------------------------297 ·····------------------------------------------------------------------------
347 ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},298 ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation
348 ·····------------------------------------------------------------------------299 ·····------------------------------------------------------------------------
349 ·····{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5},·{2,·3,·5,·6},300 ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},
350 ·····------------------------------------------------------------------------301 ·····------------------------------------------------------------------------
351 ·····{3,·5,·6,·7}},·{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},302 ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},
352 ·····------------------------------------------------------------------------303 ·····------------------------------------------------------------------------
353 ·····{2,·4,·6,·7},·{3,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},304 ·····{1,·2,·3,·5},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},
354 ·····------------------------------------------------------------------------305 ·····------------------------------------------------------------------------
355 ·····{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}},·{{0,·1,·3,·4},·{0,·2,·3,·6},306 ·····{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},
356 ·····------------------------------------------------------------------------307 ·····------------------------------------------------------------------------
357 ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·{{0,·1,·2,·5},308 ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},
358 ·····------------------------------------------------------------------------309 ·····------------------------------------------------------------------------
359 ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}},310 ·····{3,·4,·5,·7},·{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},
360 ·····------------------------------------------------------------------------311 ·····------------------------------------------------------------------------
 312 ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation
 313 ·····------------------------------------------------------------------------
361 ·····{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},314 ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},
 315 ·····------------------------------------------------------------------------
 316 ·····{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},
362 ·····------------------------------------------------------------------------317 ·····------------------------------------------------------------------------
363 ·····{2,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},318 ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},
364 ·····------------------------------------------------------------------------319 ·····------------------------------------------------------------------------
365 ·····{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},320 ·····{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},
366 ·····------------------------------------------------------------------------321 ·····------------------------------------------------------------------------
367 ·····{1,·4,·5,·7},·{2,·3,·4,·7},·{2,·4,·6,·7}},·{{0,·1,·3,·6},·{0,·1,·4,·6},322 ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},
368 ·····------------------------------------------------------------------------323 ·····------------------------------------------------------------------------
369 ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·5},324 ·····{2,·3,·4,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},
370 ·····------------------------------------------------------------------------325 ·····------------------------------------------------------------------------
371 ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},326 ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation
372 ·····------------------------------------------------------------------------327 ·····------------------------------------------------------------------------
 328 ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},
 329 ·····------------------------------------------------------------------------
 330 ·····{2,·5,·6,·7}}}
  
 331 o4·:·List</code></pre>
 332 ············</td>
 333 ··········</tr>
 334 ··········<tr>
 335 ············<td>
 336 ··············<pre><code·class="language-macaulay2">i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets
  
373 ·····{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7},337 o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7},
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Offset 57, 57 lines modifiedOffset 57, 15 lines modified
  
57 o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,57 o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,
58 4,·5,·6},·{3,·5,·6,·7}}58 4,·5,·6},·{3,·5,·6,·7}}
  
59 o3·:·Triangulation59 o3·:·Triangulation
60 i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's.60 i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's.
  
61 o4·=·{triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, 
62 ·····------------------------------------------------------------------------ 
63 ·····{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, 
64 ·····------------------------------------------------------------------------ 
65 ·····{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},·triangulation 
66 ·····------------------------------------------------------------------------ 
67 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·6}, 
68 ·····------------------------------------------------------------------------ 
69 ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·6}, 
70 ·····------------------------------------------------------------------------ 
71 ·····{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation·{{0,·1,·3,·5}, 
72 ·····------------------------------------------------------------------------ 
73 ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}}, 
74 ·····------------------------------------------------------------------------ 
75 ·····triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, 
76 ·····------------------------------------------------------------------------ 
77 ·····{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4}, 
78 ·····------------------------------------------------------------------------ 
79 ·····{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},·triangulation 
80 ·····------------------------------------------------------------------------ 
81 ·····{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7}, 
82 ·····------------------------------------------------------------------------ 
83 ·····{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},·{0,·3,·4,·6}, 
84 ·····------------------------------------------------------------------------ 
85 ·····{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, 
86 ·····------------------------------------------------------------------------ 
87 ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}}, 
88 ·····------------------------------------------------------------------------ 
89 ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7}, 
90 ·····------------------------------------------------------------------------ 
91 ·····{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},·{0,·1,·4,·6}, 
92 ·····------------------------------------------------------------------------ 
93 ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation 
94 ·····------------------------------------------------------------------------ 
95 ·····{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·7}, 
96 ·····------------------------------------------------------------------------ 
97 ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},·{0,·2,·3,·6}, 
98 ·····------------------------------------------------------------------------ 
99 ·····{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, 
100 ·····------------------------------------------------------------------------ 
101 ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}}, 
102 ·····------------------------------------------------------------------------ 
103 ·····triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},61 o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},
104 ·····------------------------------------------------------------------------62 ·····------------------------------------------------------------------------
105 ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},63 ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},
106 ·····------------------------------------------------------------------------64 ·····------------------------------------------------------------------------
107 ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation65 ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation
108 ·····------------------------------------------------------------------------66 ·····------------------------------------------------------------------------
109 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7},67 ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7},
110 ·····------------------------------------------------------------------------68 ·····------------------------------------------------------------------------
Offset 263, 56 lines modifiedOffset 221, 62 lines modified
263 ·····------------------------------------------------------------------------221 ·····------------------------------------------------------------------------
264 ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},222 ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},
265 ·····------------------------------------------------------------------------223 ·····------------------------------------------------------------------------
266 ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation224 ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation
267 ·····------------------------------------------------------------------------225 ·····------------------------------------------------------------------------
268 ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7},226 ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7},
269 ·····------------------------------------------------------------------------227 ·····------------------------------------------------------------------------
 228 ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},
270 ·····{1,·4,·6,·7}}} 
  
271 o4·:·List 
272 i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets 
  
273 o5·=·{{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, 
274 ·····------------------------------------------------------------------------229 ·····------------------------------------------------------------------------
275 ·····{0,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},230 ·····{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},
276 ·····------------------------------------------------------------------------231 ·····------------------------------------------------------------------------
277 ·····{0,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},232 ·····{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},
278 ·····------------------------------------------------------------------------233 ·····------------------------------------------------------------------------
279 ·····{0,·3,·5,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},234 ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},
280 ·····------------------------------------------------------------------------235 ·····------------------------------------------------------------------------
281 ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},236 ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},
282 ·····------------------------------------------------------------------------237 ·····------------------------------------------------------------------------
283 ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},238 ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation
284 ·····------------------------------------------------------------------------239 ·····------------------------------------------------------------------------
285 ·····{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5},·{2,·3,·5,·6},240 ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},
286 ·····------------------------------------------------------------------------241 ·····------------------------------------------------------------------------
287 ·····{3,·5,·6,·7}},·{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},242 ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},
288 ·····------------------------------------------------------------------------243 ·····------------------------------------------------------------------------
289 ·····{2,·4,·6,·7},·{3,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},244 ·····{1,·2,·3,·5},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},
290 ·····------------------------------------------------------------------------245 ·····------------------------------------------------------------------------
291 ·····{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}},·{{0,·1,·3,·4},·{0,·2,·3,·6},246 ·····{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},
292 ·····------------------------------------------------------------------------247 ·····------------------------------------------------------------------------
 248 ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},
 249 ·····------------------------------------------------------------------------
 250 ·····{3,·4,·5,·7},·{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},
 251 ·····------------------------------------------------------------------------
293 ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·{{0,·1,·2,·5},252 ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation
294 ·····------------------------------------------------------------------------253 ·····------------------------------------------------------------------------
295 ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}},254 ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},
 255 ·····------------------------------------------------------------------------
 256 ·····{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},
296 ·····------------------------------------------------------------------------257 ·····------------------------------------------------------------------------
297 ·····{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},258 ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},
298 ·····------------------------------------------------------------------------259 ·····------------------------------------------------------------------------
299 ·····{2,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},260 ·····{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},
300 ·····------------------------------------------------------------------------261 ·····------------------------------------------------------------------------
301 ·····{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},262 ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},
302 ·····------------------------------------------------------------------------263 ·····------------------------------------------------------------------------
303 ·····{1,·4,·5,·7},·{2,·3,·4,·7},·{2,·4,·6,·7}},·{{0,·1,·3,·6},·{0,·1,·4,·6},264 ·····{2,·3,·4,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},
304 ·····------------------------------------------------------------------------265 ·····------------------------------------------------------------------------
305 ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·5},266 ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation
306 ·····------------------------------------------------------------------------267 ·····------------------------------------------------------------------------
307 ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},268 ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},
308 ·····------------------------------------------------------------------------269 ·····------------------------------------------------------------------------
 270 ·····{2,·5,·6,·7}}}
  
 271 o4·:·List
 272 i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets
  
309 ·····{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7},273 o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7},
310 ·····------------------------------------------------------------------------274 ·····------------------------------------------------------------------------
311 ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},275 ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},
312 ·····------------------------------------------------------------------------276 ·····------------------------------------------------------------------------
313 ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},277 ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},
314 ·····------------------------------------------------------------------------278 ·····------------------------------------------------------------------------
315 ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},279 ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},
316 ·····------------------------------------------------------------------------280 ·····------------------------------------------------------------------------
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./usr/share/doc/Macaulay2/Triangulations/html/index.html
    
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150 ··············4·······10150 ··············4·······10
151 o2·:·Matrix·ZZ··&lt;--·ZZ</code></pre>151 o2·:·Matrix·ZZ··&lt;--·ZZ</code></pre>
152 ············</td>152 ············</td>
153 ··········</tr>153 ··········</tr>
154 ··········<tr>154 ··········<tr>
155 ············<td>155 ············<td>
156 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true);156 ··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true);
157 ·--·.126564s·elapsed</code></pre>157 ·--·.147652s·elapsed</code></pre>
158 ············</td>158 ············</td>
159 ··········</tr>159 ··········</tr>
160 ··········<tr>160 ··········<tr>
161 ············<td>161 ············<td>
162 ··············<pre><code·class="language-macaulay2">i4·:·select(Ts,·T·->·isStar·T)162 ··············<pre><code·class="language-macaulay2">i4·:·select(Ts,·T·->·isStar·T)
  
163 o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,163 o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,
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198 o7·:·Triangulation</code></pre>198 o7·:·Triangulation</code></pre>
199 ············</td>199 ············</td>
200 ··········</tr>200 ··········</tr>
201 ··········<tr>201 ··········<tr>
202 ············<td>202 ············<td>
203 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·Ts2·=·generateTriangulations·T;203 ··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·Ts2·=·generateTriangulations·T;
204 ·--·1.11952s·elapsed</code></pre>204 ·--·2.65224s·elapsed</code></pre>
205 ············</td>205 ············</td>
206 ··········</tr>206 ··········</tr>
207 ··········<tr>207 ··········<tr>
208 ············<td>208 ············<td>
209 ··············<pre><code·class="language-macaulay2">i9·:·#Ts2·==·#Ts209 ··············<pre><code·class="language-macaulay2">i9·:·#Ts2·==·#Ts
  
210 o9·=·true</code></pre>210 o9·=·true</code></pre>
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54 ·····|·0··0··0··1··0··0·-1·0·0·0·|54 ·····|·0··0··0··1··0··0·-1·0·0·0·|
55 ·····|·-1·1··2··-1·-1·1·-1·1·0·0·|55 ·····|·-1·1··2··-1·-1·1·-1·1·0·0·|
56 ·····|·1··0··-1·0··0··0·0··0·0·0·|56 ·····|·1··0··-1·0··0··0·0··0·0·0·|
  
57 ··············4·······1057 ··············4·······10
58 o2·:·Matrix·ZZ··<--·ZZ58 o2·:·Matrix·ZZ··<--·ZZ
59 i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true);59 i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true);
60 ·--·.126564s·elapsed60 ·--·.147652s·elapsed
61 i4·:·select(Ts,·T·->·isStar·T)61 i4·:·select(Ts,·T·->·isStar·T)
  
62 o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,62 o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,
63 ·····------------------------------------------------------------------------63 ·····------------------------------------------------------------------------
64 ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3,64 ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3,
65 ·····------------------------------------------------------------------------65 ·····------------------------------------------------------------------------
66 ·····5,·7,·9},·{0,·3,·5,·8,·9},·{0,·4,·6,·8,·9},·{0,·5,·6,·7,·9},·{0,·5,·6,66 ·····5,·7,·9},·{0,·3,·5,·8,·9},·{0,·4,·6,·8,·9},·{0,·5,·6,·7,·9},·{0,·5,·6,
Offset 86, 15 lines modifiedOffset 86, 15 lines modified
86 6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},86 6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},
87 {0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,87 {0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,
88 7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,88 7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,
89 3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}}89 3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}}
  
90 o7·:·Triangulation90 o7·:·Triangulation
91 i8·:·elapsedTime·Ts2·=·generateTriangulations·T;91 i8·:·elapsedTime·Ts2·=·generateTriangulations·T;
92 ·--·1.11952s·elapsed92 ·--·2.65224s·elapsed
93 i9·:·#Ts2·==·#Ts93 i9·:·#Ts2·==·#Ts
  
94 o9·=·true94 o9·=·true
95 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*95 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8*
96 ····*·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·--·for·computations·with·convex·polyhedra,·cones,·and·fans96 ····*·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·--·for·computations·with·convex·polyhedra,·cones,·and·fans
97 ····*·_\x8T_\x8o_\x8p_\x8c_\x8o_\x8m·--·interface·to·selected·functions·from·topcom·package97 ····*·_\x8T_\x8o_\x8p_\x8c_\x8o_\x8m·--·interface·to·selected·functions·from·topcom·package
98 ····*·_\x8R_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8v_\x8e_\x8P_\x8o_\x8l_\x8y_\x8t_\x8o_\x8p_\x8e_\x8s_\x8D_\x8B·--·simple·access·to·Kreuzer-Skarke·database·of98 ····*·_\x8R_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8v_\x8e_\x8P_\x8o_\x8l_\x8y_\x8t_\x8o_\x8p_\x8e_\x8s_\x8D_\x8B·--·simple·access·to·Kreuzer-Skarke·database·of
712 B
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./usr/share/doc/Macaulay2/VersalDeformations/example-output/___Smart__Lift.out
    
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6 o2·=·|·xz·yz·z2·x3·|6 o2·=·|·xz·yz·z2·x3·|
  
7 ·············1······47 ·············1······4
8 o2·:·Matrix·S··<--·S8 o2·:·Matrix·S··<--·S
  
9 i3·:·time·(F,R,G,C)=localHilbertScheme(F0);9 i3·:·time·(F,R,G,C)=localHilbertScheme(F0);
10 ·--·used·0.886432s·(cpu);·0.631977s·(thread);·0s·(gc)10 ·--·used·1.08916s·(cpu);·0.671759s·(thread);·0s·(gc)
  
11 i4·:·T=ring·first·G;11 i4·:·T=ring·first·G;
  
12 i5·:·sum·G12 i5·:·sum·G
  
13 o5·=·|·t_1t_16·············|13 o5·=·|·t_1t_16·············|
14 ·····|·t_9t_16·············|14 ·····|·t_9t_16·············|
15 ·····|·-t_4t_16············|15 ·····|·-t_4t_16············|
16 ·····|·-2t_14t_16+t_15t_16·|16 ·····|·-2t_14t_16+t_15t_16·|
  
17 ·············4······117 ·············4······1
18 o5·:·Matrix·T··<--·T18 o5·:·Matrix·T··<--·T
  
19 i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false);19 i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false);
20 ·--·used·0.619195s·(cpu);·0.418919s·(thread);·0s·(gc)20 ·--·used·0.676812s·(cpu);·0.437382s·(thread);·0s·(gc)
  
21 i7·:·sum·G21 i7·:·sum·G
  
22 o7·=·|·t_1t_16·····························································22 o7·=·|·t_1t_16·····························································
23 ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+23 ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+
24 ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t24 ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t
25 ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2-25 ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2-
2.66 KB
./usr/share/doc/Macaulay2/VersalDeformations/html/___Smart__Lift.html
    
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71 ··········</tr>71 ··········</tr>
72 ········</table>72 ········</table>
73 ········<p>With·the·default·setting·<span·class="tt">SmartLift=>true</span>·we·get·very·nice·equations·for·the·base·space:</p>73 ········<p>With·the·default·setting·<span·class="tt">SmartLift=>true</span>·we·get·very·nice·equations·for·the·base·space:</p>
74 ········<table·class="examples">74 ········<table·class="examples">
75 ··········<tr>75 ··········<tr>
76 ············<td>76 ············<td>
77 ··············<pre><code·class="language-macaulay2">i3·:·time·(F,R,G,C)=localHilbertScheme(F0);77 ··············<pre><code·class="language-macaulay2">i3·:·time·(F,R,G,C)=localHilbertScheme(F0);
78 ·--·used·0.886432s·(cpu);·0.631977s·(thread);·0s·(gc)</code></pre>78 ·--·used·1.08916s·(cpu);·0.671759s·(thread);·0s·(gc)</code></pre>
79 ············</td>79 ············</td>
80 ··········</tr>80 ··········</tr>
81 ··········<tr>81 ··········<tr>
82 ············<td>82 ············<td>
83 ··············<pre><code·class="language-macaulay2">i4·:·T=ring·first·G;</code></pre>83 ··············<pre><code·class="language-macaulay2">i4·:·T=ring·first·G;</code></pre>
84 ············</td>84 ············</td>
85 ··········</tr>85 ··········</tr>
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98 ··········</tr>98 ··········</tr>
99 ········</table>99 ········</table>
100 ········<p>With·the·setting·<span·class="tt">SmartLift=>false</span>·the·calculation·is·faster,·but·the·equations·are·no·longer·homogeneous:</p>100 ········<p>With·the·setting·<span·class="tt">SmartLift=>false</span>·the·calculation·is·faster,·but·the·equations·are·no·longer·homogeneous:</p>
101 ········<table·class="examples">101 ········<table·class="examples">
102 ··········<tr>102 ··········<tr>
103 ············<td>103 ············<td>
104 ··············<pre><code·class="language-macaulay2">i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false);104 ··············<pre><code·class="language-macaulay2">i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false);
105 ·--·used·0.619195s·(cpu);·0.418919s·(thread);·0s·(gc)</code></pre>105 ·--·used·0.676812s·(cpu);·0.437382s·(thread);·0s·(gc)</code></pre>
106 ············</td>106 ············</td>
107 ··········</tr>107 ··········</tr>
108 ··········<tr>108 ··········<tr>
109 ············<td>109 ············<td>
110 ··············<pre><code·class="language-macaulay2">i7·:·sum·G110 ··············<pre><code·class="language-macaulay2">i7·:·sum·G
  
111 o7·=·|·t_1t_16·····························································111 o7·=·|·t_1t_16·····························································
1.15 KB
html2text {}
    
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18 o2·=·|·xz·yz·z2·x3·|18 o2·=·|·xz·yz·z2·x3·|
  
19 ·············1······419 ·············1······4
20 o2·:·Matrix·S··<--·S20 o2·:·Matrix·S··<--·S
21 With·the·default·setting·SmartLift=>true·we·get·very·nice·equations·for·the21 With·the·default·setting·SmartLift=>true·we·get·very·nice·equations·for·the
22 base·space:22 base·space:
23 i3·:·time·(F,R,G,C)=localHilbertScheme(F0);23 i3·:·time·(F,R,G,C)=localHilbertScheme(F0);
24 ·--·used·0.886432s·(cpu);·0.631977s·(thread);·0s·(gc)24 ·--·used·1.08916s·(cpu);·0.671759s·(thread);·0s·(gc)
25 i4·:·T=ring·first·G;25 i4·:·T=ring·first·G;
26 i5·:·sum·G26 i5·:·sum·G
  
27 o5·=·|·t_1t_16·············|27 o5·=·|·t_1t_16·············|
28 ·····|·t_9t_16·············|28 ·····|·t_9t_16·············|
29 ·····|·-t_4t_16············|29 ·····|·-t_4t_16············|
30 ·····|·-2t_14t_16+t_15t_16·|30 ·····|·-2t_14t_16+t_15t_16·|
  
31 ·············4······131 ·············4······1
32 o5·:·Matrix·T··<--·T32 o5·:·Matrix·T··<--·T
33 With·the·setting·SmartLift=>false·the·calculation·is·faster,·but·the·equations33 With·the·setting·SmartLift=>false·the·calculation·is·faster,·but·the·equations
34 are·no·longer·homogeneous:34 are·no·longer·homogeneous:
35 i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false);35 i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false);
36 ·--·used·0.619195s·(cpu);·0.418919s·(thread);·0s·(gc)36 ·--·used·0.676812s·(cpu);·0.437382s·(thread);·0s·(gc)
37 i7·:·sum·G37 i7·:·sum·G
  
38 o7·=·|·t_1t_1638 o7·=·|·t_1t_16
39 ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+39 ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+
40 ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t40 ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t
41 ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2-41 ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2-
42 ·····------------------------------------------------------------------------42 ·····------------------------------------------------------------------------
777 B
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./usr/share/doc/Macaulay2/WeylAlgebras/example-output/_factor__Weyl__Algebra.out
    
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7 o1·:·PolynomialRing,·1·differential·variable(s)7 o1·:·PolynomialRing,·1·differential·variable(s)
  
8 i2·:·factorWA(x^5*dx^2+7*x^4*dx+8*x^3-x*dx^2+dx)8 i2·:·factorWA(x^5*dx^2+7*x^4*dx+8*x^3-x*dx^2+dx)
  
9 ····································2·········3·······2··················2··9 ····································2·········3·······2··················2··
10 o2·=·{(x*dx·-·1)(dx)(x·-·1)(x·+·1)(x··+·1),·(x·dx·+·3x··-·x*dx·+·1)(dx)(x··+10 o2·=·{(x*dx·-·1)(dx)(x·-·1)(x·+·1)(x··+·1),·(x·dx·+·3x··-·x*dx·+·1)(dx)(x··+
11 ·····------------------------------------------------------------------------11 ·····------------------------------------------------------------------------
12 ···············3················2·········3·······2························· 
13 ·····1),·(dx)(x·dx·-·x*dx·+·2)(x··+·1),·(x·dx·+·3x··+·x*dx·-·1)(dx)(x·-·1)(x12 ···········3·······2······································3··················
 13 ·····1),·(x·dx·+·3x··+·x*dx·-·1)(dx)(x·-·1)(x·+·1),·(dx)(x·dx·+·x*dx·-·2)(x·-
14 ·····------------------------------------------------------------------------14 ·····------------------------------------------------------------------------
15 ·················315 ······················3················2
16 ·····+·1),·(dx)(x·dx·+·x*dx·-·2)(x·-·1)(x·+·1)}16 ·····1)(x·+·1),·(dx)(x·dx·-·x*dx·+·2)(x··+·1)}
  
17 o2·:·List17 o2·:·List
  
18 i3·:·18 i3·:·
2.68 KB
./usr/share/doc/Macaulay2/WeylAlgebras/html/_factor__Weyl__Algebra.html
    
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87 ··········<tr>87 ··········<tr>
88 ············<td>88 ············<td>
89 ··············<pre><code·class="language-macaulay2">i2·:·factorWA(x^5*dx^2+7*x^4*dx+8*x^3-x*dx^2+dx)89 ··············<pre><code·class="language-macaulay2">i2·:·factorWA(x^5*dx^2+7*x^4*dx+8*x^3-x*dx^2+dx)
  
90 ····································2·········3·······2··················2··90 ····································2·········3·······2··················2··
91 o2·=·{(x*dx·-·1)(dx)(x·-·1)(x·+·1)(x··+·1),·(x·dx·+·3x··-·x*dx·+·1)(dx)(x··+91 o2·=·{(x*dx·-·1)(dx)(x·-·1)(x·+·1)(x··+·1),·(x·dx·+·3x··-·x*dx·+·1)(dx)(x··+
92 ·····------------------------------------------------------------------------92 ·····------------------------------------------------------------------------
93 ···············3················2·········3·······2························· 
94 ·····1),·(dx)(x·dx·-·x*dx·+·2)(x··+·1),·(x·dx·+·3x··+·x*dx·-·1)(dx)(x·-·1)(x93 ···········3·······2······································3··················
 94 ·····1),·(x·dx·+·3x··+·x*dx·-·1)(dx)(x·-·1)(x·+·1),·(dx)(x·dx·+·x*dx·-·2)(x·-
95 ·····------------------------------------------------------------------------95 ·····------------------------------------------------------------------------
96 ·················396 ······················3················2
97 ·····+·1),·(dx)(x·dx·+·x*dx·-·2)(x·-·1)(x·+·1)}97 ·····1)(x·+·1),·(dx)(x·dx·-·x*dx·+·2)(x··+·1)}
  
98 o2·:·List</code></pre>98 o2·:·List</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ········</table>101 ········</table>
102 ········<div>102 ········<div>
103 ··········<p>To·reduce·their·number,·two·factorisations·are·considered·equivalent·if·they·can·be·related·by·(1)» switching·commuting·irreducible·factors·or·(2)·switching·monomials·and·degree·0·factors;·a·normal·order·is·chosen·where·commuting·factors·are·sorted,·and·monomials·are·pushed·to·the·right/left·if·they're·differential/not.</p>103 ··········<p>To·reduce·their·number,·two·factorisations·are·considered·equivalent·if·they·can·be·related·by·(1)» switching·commuting·irreducible·factors·or·(2)·switching·monomials·and·degree·0·factors;·a·normal·order·is·chosen·where·commuting·factors·are·sorted,·and·monomials·are·pushed·to·the·right/left·if·they're·differential/not.</p>
1.2 KB
html2text {}
    
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23 o1·:·PolynomialRing,·1·differential·variable(s)23 o1·:·PolynomialRing,·1·differential·variable(s)
24 i2·:·factorWA(x^5*dx^2+7*x^4*dx+8*x^3-x*dx^2+dx)24 i2·:·factorWA(x^5*dx^2+7*x^4*dx+8*x^3-x*dx^2+dx)
  
25 ····································2·········3·······2··················225 ····································2·········3·······2··················2
26 o2·=·{(x*dx·-·1)(dx)(x·-·1)(x·+·1)(x··+·1),·(x·dx·+·3x··-·x*dx·+·1)(dx)(x··+26 o2·=·{(x*dx·-·1)(dx)(x·-·1)(x·+·1)(x··+·1),·(x·dx·+·3x··-·x*dx·+·1)(dx)(x··+
27 ·····------------------------------------------------------------------------27 ·····------------------------------------------------------------------------
28 ···············3················2·········3·······2 
29 ·····1),·(dx)(x·dx·-·x*dx·+·2)(x··+·1),·(x·dx·+·3x··+·x*dx·-·1)(dx)(x·-·1)(x28 ···········3·······2······································3
 29 ·····1),·(x·dx·+·3x··+·x*dx·-·1)(dx)(x·-·1)(x·+·1),·(dx)(x·dx·+·x*dx·-·2)(x·-
30 ·····------------------------------------------------------------------------30 ·····------------------------------------------------------------------------
31 ·················331 ······················3················2
32 ·····+·1),·(dx)(x·dx·+·x*dx·-·2)(x·-·1)(x·+·1)}32 ·····1)(x·+·1),·(dx)(x·dx·-·x*dx·+·2)(x··+·1)}
  
33 o2·:·List33 o2·:·List
34 To·reduce·their·number,·two·factorisations·are·considered·equivalent·if·they34 To·reduce·their·number,·two·factorisations·are·considered·equivalent·if·they
35 can·be·related·by·(1)·switching·commuting·irreducible·factors·or·(2)·switching35 can·be·related·by·(1)·switching·commuting·irreducible·factors·or·(2)·switching
36 monomials·and·degree·0·factors;·a·normal·order·is·chosen·where·commuting36 monomials·and·degree·0·factors;·a·normal·order·is·chosen·where·commuting
37 factors·are·sorted,·and·monomials·are·pushed·to·the·right/left·if·they're37 factors·are·sorted,·and·monomials·are·pushed·to·the·right/left·if·they're
38 differential/not.38 differential/not.
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./usr/share/doc/Macaulay2/WeylGroups/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
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552 B
./usr/share/doc/Macaulay2/WeylGroups/example-output/_eval_lp__Root__System_cm__Z__Z_cm__Root_rp.out
    
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4 o1·=·RootSystem{...8...}4 o1·=·RootSystem{...8...}
  
5 o1·:·RootSystem5 o1·:·RootSystem
  
6 i2·:·L=toList(positiveRoots(R))6 i2·:·L=toList(positiveRoots(R))
  
7 o2·=·{|··2·|,·|·-1·|,·|·1·|}7 o2·=·{|·1·|,·|··2·|,·|·-1·|}
8 ······|·-1·|··|··2·|··|·1·|8 ······|·1·|··|·-1·|··|··2·|
  
9 o2·:·List9 o2·:·List
  
10 i3·:·eval(R,1,L#0)10 i3·:·eval(R,1,L#0)
  
11 o3·=·111 o3·=·1
  
12 i4·:·eval(R,1,L#1)12 i4·:·eval(R,1,L#1)
  
13 o4·=·013 o4·=·1
  
14 i5·:·eval(R,1,L#2)14 i5·:·eval(R,1,L#2)
  
15 o5·=·115 o5·=·0
  
16 i6·:·16 i6·:·
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./usr/share/doc/Macaulay2/WeylGroups/example-output/_interval__Bruhat_lp__Weyl__Group__Element_cm__Weyl__Group__Element_rp.out
    
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20 ···········································|·-2·|20 ···········································|·-2·|
21 ···········································|··1·|21 ···········································|··1·|
  
22 o3·:·WeylGroupElement22 o3·:·WeylGroupElement
  
23 i4·:·myInterval=intervalBruhat(w1,w2)23 i4·:·myInterval=intervalBruhat(w1,w2)
  
24 o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}} 
25 ··························································|·-2·|········|·-1·|·······|··2·|··············································|·-3·|········|··1·|············································|·-1·|········|·-1·|··············································|·-1·| 
26 ··························································|··1·|········|··2·|·······|·-1·|··············································|··1·|········|··1·|············································|··2·|········|··2·|···································[·...·truncated·by·diffoscope;·len:·17,·SHA:·5ebd410378763a0377949c88c0bf38c02207bbfbe2135b8d5c0d6fe2c1deafe7·...·]24 o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}},·{{WeylGroupElement{RootSystem[·...·truncated·by·diffoscope;·len:·25,·SHA:·681e071fee4a8cf2af531899a8824f2395fb7ebd9aba6210a84a4873acf6536f·...·]
 25 ··························································|·-2·|········|··2·|·······|·-1·|··············································|·-1·|········|·-1·|············································|·-3·|········|··1·|··············································|·-1·|
 26 ··························································|··1·|········|·-1·|·······|··2·|··············································|··2·|········|··2·|············································|··1·|········|··1·|··············································|··3·|
  
27 o4·:·HasseDiagram27 o4·:·HasseDiagram
  
28 i5·:·myInterval#128 i5·:·myInterval#1
  
29 o5·=·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}},29 o5·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}},
30 ·············································|·-3·|········|··1·|····30 ·············································|·-1·|········|·-1·|····
31 ·············································|··1·|········|··1·|····31 ·············································|··2·|········|··2·|····
32 ·····------------------------------------------------------------------------32 ·····------------------------------------------------------------------------
33 ·····{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}}33 ·····{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}}
34 ············································|·-1·|········|·-1·|34 ············································|·-3·|········|··1·|
35 ············································|··2·|········|··2·|35 ············································|··1·|········|··1·|
  
36 o5·:·List36 o5·:·List
  
37 i6·:·37 i6·:·
6.08 KB
./usr/share/doc/Macaulay2/WeylGroups/example-output/_interval__Bruhat_lp__Weyl__Group__Right__Coset_cm__Weyl__Group__Right__Coset_rp.out
    
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26 ···········································|·-2·|26 ···········································|·-2·|
27 ···········································|··1·|27 ···········································|··1·|
  
28 o4·:·WeylGroupElement28 o4·:·WeylGroupElement
  
29 i5·:·myInterval=intervalBruhat(P·%·w1,P·%·w2)29 i5·:·myInterval=intervalBruhat(P·%·w1,P·%·w2)
  
30 o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|},·{1,·|··2·|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|··2·|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-3·|},·{{0,·|·1·|},·{1,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{1,·|··2·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··3·|},·{{0,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}} 
31 ··························································|·-2·|········|··2·|·······|·-1·|··············································|·-1·|········|··1·|·······|·-1·|·······|·-1·|············································|·-3·|········|··2·|·······|··1·|··············································|·-3·|········|·-1·|·······|·-1·|············································|··1·|········|·0·|·······|·-1·|············································|·-1·|········|·-1·|·······|··2·|··············································|·-2·|········|·-1·|············································|··1·|········|··1·|············································|·-2·|········|·-1·|··············································|·-1·| 
32 ··························································|··1·|········|·-1·|·······|··2·|··············································|··2·|········|··1·|·······|··0·|·······|··2·|············································|··1·|········|·-1·|·······|·[·...·truncated·by·diffoscope;·len:·482,·SHA:·3d37a635eac46574ead4f6ab979f45eea997f34a0dec26b384e44f809d027eab·...·]30 o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{1,·|·-1·|},·{2,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··2·|},·{1,·|··0·|},·{2,·|·[·...·truncated·by·diffoscope;·len:·490,·SHA:·5add286ab891da2b36c359dc10bc0aec42152dfb4751f9a705ef84bd0f592a93·...·]
 31 ··························································|·-2·|········|·-1·|·······|··2·|··············································|·-3·|········|··1·|·······|··2·|············································|·-1·|········|·-1·|·······|·-1·|·······|··1·|··············································|··1·|········|·-1·|·······|·0·|············································|·-1·|········|·-1·|·······|··2·|············································|·-3·|········|·-1·|·······|·-1·|··············································|··1·|········|··1·|············································|·-2·|········|·-1·|············································|·-2·|········|·-1·|··············································|·-1·|
 32 ··························································|··1·|········|··2·|·······|·-1·|··············································|··1·|········|··1·|·······|·-1·|············································|··2·|········|··0·|·······|··2·|·······|··1·|··············································|··1·|········|··2·|·······|·1·|············································|··3·|········|··0·|·······|·-1·|············································|··2·|········|··2·|·······|··0·|··············································|··2·|········|·-1·|············································|··3·|········|··0·|············································|··1·|········|··2·|··············································|··2·|
  
33 o5·:·HasseDiagram33 o5·:·HasseDiagram
  
34 i6·:·myInterval#134 i6·:·myInterval#1
  
35 o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|},·{1,·|··235 o6·=·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{1,·|·-1·|},·{2,·|·-1
 36 ·············································|·-3·|········|··1·|·······|··2
36 ·············································|·-1·|········|··1·|·······|·-137 ·············································|··1·|········|··1·|·······|·-1
37 ·············································|··2·|········|··1·|·······|··0 
38 ·····------------------------------------------------------------------------38 ·····------------------------------------------------------------------------
39 ·····|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,39 ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··2·|},·{1,
40 ·····|·······|·-1·|············································|·-3·|·······40 ·····|············································|·-1·|········|·-1·|······
41 ·····|·······|··2·|············································|··1·|·······41 ·····|············································|··2·|········|··0·|······
42 ·····------------------------------------------------------------------------42 ·····------------------------------------------------------------------------
43 ·····|·-1·|},·{2,·|·-1·|}}}}43 ·····|··0·|},·{2,·|·-1·|}}}}
44 ·····|··2·|·······|··1·| 
45 ·····|·-1·|·······|··1·|44 ·····|·-1·|·······|··1·|
 45 ·····|··2·|·······|··1·|
  
46 o6·:·List46 o6·:·List
  
47 i7·:·47 i7·:·
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4 o1·=·RootSystem{...8...}4 o1·=·RootSystem{...8...}
  
5 o1·:·RootSystem5 o1·:·RootSystem
  
6 i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R)6 i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R)
  
7 o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|},·{1,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|},·{1,·|·1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}} 
8 ··························································|·-1·|········|··2·|·······|·-1·|··············································|·-2·|········|·1·|·······|·-1·|············································|··1·|········|··2·|·······|·1·|···········[·...·truncated·by·diffoscope;·len:·170,·SHA:·95df35d1d4a3ca898ce21b80d759a79b585804cf64fe489cd194787f997357ab·...·]7 o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|},·{1,·|·1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{Wey[·...·truncated·by·diffoscope;·len:·178,·SHA:·1e6c76800ad074b8a47615e8559b42657496871815f336a1db2487088304032d·...·]
 8 ··························································|·-1·|········|··2·|·······|·-1·|··············································|·-2·|········|·-1·|·······|·1·|············································|··1·|········|·1·|·······|··2·|··············································|·-1·|········|··2·|············································|··2·|········|·-1·|··············································|·1·|
  
9 o2·:·HasseDiagram9 o2·:·HasseDiagram
  
10 i3·:·ZZ[x]10 i3·:·ZZ[x]
  
11 o3·=·ZZ[x]11 o3·=·ZZ[x]
  
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10 o2·=·set·{1,·2}10 o2·=·set·{1,·2}
  
11 o2·:·Parabolic11 o2·:·Parabolic
  
12 i3·:·positiveRoots(R,P)12 i3·:·positiveRoots(R,P)
  
13 o3·=·set·{|··1·|,·|··2·|,·|·-1·|}13 o3·=·set·{|·-1·|,·|··1·|,·|··2·|}
 14 ··········|··2·|··|··1·|··|·-1·|
14 ··········|··1·|··|·-1·|··|··2·|15 ··········|·-1·|··|·-1·|··|··0·|
15 ··········|·-1·|··|··0·|··|·-1·| 
16 ··········|··0·|··|··0·|··|··0·|16 ··········|··0·|··|··0·|··|··0·|
  
17 o3·:·Set17 o3·:·Set
  
18 i4·:·18 i4·:·
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80 o1·:·RootSystem</code></pre>80 o1·:·RootSystem</code></pre>
81 ············</td>81 ············</td>
82 ··········</tr>82 ··········</tr>
83 ··········<tr>83 ··········<tr>
84 ············<td>84 ············<td>
85 ··············<pre><code·class="language-macaulay2">i2·:·L=toList(positiveRoots(R))85 ··············<pre><code·class="language-macaulay2">i2·:·L=toList(positiveRoots(R))
  
86 o2·=·{|··2·|,·|·-1·|,·|·1·|}86 o2·=·{|·1·|,·|··2·|,·|·-1·|}
87 ······|·-1·|··|··2·|··|·1·|87 ······|·1·|··|·-1·|··|··2·|
  
88 o2·:·List</code></pre>88 o2·:·List</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i3·:·eval(R,1,L#0)93 ··············<pre><code·class="language-macaulay2">i3·:·eval(R,1,L#0)
Offset 97, 22 lines modifiedOffset 97, 22 lines modified
97 o3·=·1</code></pre>97 o3·=·1</code></pre>
98 ············</td>98 ············</td>
99 ··········</tr>99 ··········</tr>
100 ··········<tr>100 ··········<tr>
101 ············<td>101 ············<td>
102 ··············<pre><code·class="language-macaulay2">i4·:·eval(R,1,L#1)102 ··············<pre><code·class="language-macaulay2">i4·:·eval(R,1,L#1)
  
103 o4·=·0</code></pre>103 o4·=·1</code></pre>
104 ············</td>104 ············</td>
105 ··········</tr>105 ··········</tr>
106 ··········<tr>106 ··········<tr>
107 ············<td>107 ············<td>
108 ··············<pre><code·class="language-macaulay2">i5·:·eval(R,1,L#2)108 ··············<pre><code·class="language-macaulay2">i5·:·eval(R,1,L#2)
  
109 o5·=·1</code></pre>109 o5·=·0</code></pre>
110 ············</td>110 ············</td>
111 ··········</tr>111 ··········</tr>
112 ········</table>112 ········</table>
113 ······</div>113 ······</div>
114 ······<div>114 ······<div>
115 ········<div·class="waystouse">115 ········<div·class="waystouse">
116 ··········<h2>Ways·to·use·this·method:</h2>116 ··········<h2>Ways·to·use·this·method:</h2>
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19 i1·:·R=rootSystemA(2)19 i1·:·R=rootSystemA(2)
  
20 o1·=·RootSystem{...8...}20 o1·=·RootSystem{...8...}
  
21 o1·:·RootSystem21 o1·:·RootSystem
22 i2·:·L=toList(positiveRoots(R))22 i2·:·L=toList(positiveRoots(R))
  
23 o2·=·{|··2·|,·|·-1·|,·|·1·|}23 o2·=·{|·1·|,·|··2·|,·|·-1·|}
24 ······|·-1·|··|··2·|··|·1·|24 ······|·1·|··|·-1·|··|··2·|
  
25 o2·:·List25 o2·:·List
26 i3·:·eval(R,1,L#0)26 i3·:·eval(R,1,L#0)
  
27 o3·=·127 o3·=·1
28 i4·:·eval(R,1,L#1)28 i4·:·eval(R,1,L#1)
  
29 o4·=·029 o4·=·1
30 i5·:·eval(R,1,L#2)30 i5·:·eval(R,1,L#2)
  
31 o5·=·131 o5·=·0
32 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*32 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
33 ····*·_\x8e_\x8v_\x8a_\x8l_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8Z_\x8Z_\x8,_\x8R_\x8o_\x8o_\x8t_\x8)·--·evaluate·the·dual·of·a·root·at·a·fundamental33 ····*·_\x8e_\x8v_\x8a_\x8l_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8Z_\x8Z_\x8,_\x8R_\x8o_\x8o_\x8t_\x8)·--·evaluate·the·dual·of·a·root·at·a·fundamental
34 ······weight34 ······weight
35 ===============================================================================35 ===============================================================================
36 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-36 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
37 1.25.06+ds/M2/Macaulay2/packages/WeylGroups.m2:2512:0.37 1.25.06+ds/M2/Macaulay2/packages/WeylGroups.m2:2512:0.
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101 o3·:·WeylGroupElement</code></pre>101 o3·:·WeylGroupElement</code></pre>
102 ············</td>102 ············</td>
103 ··········</tr>103 ··········</tr>
104 ··········<tr>104 ··········<tr>
105 ············<td>105 ············<td>
106 ··············<pre><code·class="language-macaulay2">i4·:·myInterval=intervalBruhat(w1,w2)106 ··············<pre><code·class="language-macaulay2">i4·:·myInterval=intervalBruhat(w1,w2)
  
107 o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}} 
108 ··························································|·-2·|········|·-1·|·······|··2·|··············································|·-3·|········|··1·|············································|·-1·|········|·-1·|··············································|·-1·| 
109 ··························································|··1·|········|··2·|·······|·-1·|··············································|··1·|········|··1·|············································|··2·|········|··2·|···································[·...·truncated·by·diffoscope;·len:·17,·SHA:·5ebd410378763a0377949c88c0bf38c02207bbfbe2135b8d5c0d6fe2c1deafe7·...·]107 o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}},·{{WeylGroupElement{RootSystem[·...·truncated·by·diffoscope;·len:·25,·SHA:·681e071fee4a8cf2af531899a8824f2395fb7ebd9aba6210a84a4873acf6536f·...·]
 108 ··························································|·-2·|········|··2·|·······|·-1·|··············································|·-1·|········|·-1·|············································|·-3·|········|··1·|··············································|·-1·|
 109 ··························································|··1·|········|·-1·|·······|··2·|··············································|··2·|········|··2·|············································|··1·|········|··1·|··············································|··3·|
  
110 o4·:·HasseDiagram</code></pre>110 o4·:·HasseDiagram</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ········</table>113 ········</table>
114 ········<div>114 ········<div>
115 ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p>115 ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p>
116 ········</div>116 ········</div>
117 ········<table·class="examples">117 ········<table·class="examples">
118 ··········<tr>118 ··········<tr>
119 ············<td>119 ············<td>
120 ··············<pre><code·class="language-macaulay2">i5·:·myInterval#1120 ··············<pre><code·class="language-macaulay2">i5·:·myInterval#1
  
121 o5·=·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}},121 o5·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}},
122 ·············································|·-3·|········|··1·|····122 ·············································|·-1·|········|·-1·|····
123 ·············································|··1·|········|··1·|····123 ·············································|··2·|········|··2·|····
124 ·····------------------------------------------------------------------------124 ·····------------------------------------------------------------------------
125 ·····{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}}125 ·····{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}}
126 ············································|·-1·|········|·-1·|126 ············································|·-3·|········|··1·|
127 ············································|··2·|········|··2·|127 ············································|··1·|········|··1·|
  
128 o5·:·List</code></pre>128 o5·:·List</code></pre>
129 ············</td>129 ············</td>
130 ··········</tr>130 ··········</tr>
131 ········</table>131 ········</table>
132 ······</div>132 ······</div>
133 ······<div>133 ······<div>
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36 o3·=·WeylGroupElement{RootSystem{...8...},·|·-1·|}36 o3·=·WeylGroupElement{RootSystem{...8...},·|·-1·|}
37 ···········································|·-2·|37 ···········································|·-2·|
38 ···········································|··1·|38 ···········································|··1·|
  
39 o3·:·WeylGroupElement39 o3·:·WeylGroupElement
40 i4·:·myInterval=intervalBruhat(w1,w2)40 i4·:·myInterval=intervalBruhat(w1,w2)
  
41 o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··041 o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-
42 |},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-42 1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|
43 1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}},·{43 0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}},·{
44 {WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}}44 {WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}}
45 ··························································|·-2·|········|·-1·|45 ··························································|·-2·|········|··2·|
46 |··2·|··············································|·-3·|········|··1·|46 |·-1·|··············································|·-1·|········|·-1·|
47 |·-1·|········|·-1·|··············································|·-1·|47 |·-3·|········|··1·|··············································|·-1·|
48 ··························································|··1·|········|··2·|48 ··························································|··1·|········|·-1·|
49 |·-1·|··············································|··1·|········|··1·|49 |··2·|··············································|··2·|········|··2·|
50 |··2·|········|··2·|··············································|··3·|50 |··1·|········|··1·|··············································|··3·|
  
51 o4·:·HasseDiagram51 o4·:·HasseDiagram
52 Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length52 Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length
53 together·with·their·links·to·the·next·row.53 together·with·their·links·to·the·next·row.
54 i5·:·myInterval#154 i5·:·myInterval#1
  
55 o5·=·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}},55 o5·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}},
56 ·············································|·-3·|········|··1·|56 ·············································|·-1·|········|·-1·|
57 ·············································|··1·|········|··1·|57 ·············································|··2·|········|··2·|
58 ·····------------------------------------------------------------------------58 ·····------------------------------------------------------------------------
59 ·····{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}}59 ·····{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}}
60 ············································|·-1·|········|·-1·|60 ············································|·-3·|········|··1·|
61 ············································|··2·|········|··2·|61 ············································|··1·|········|··1·|
  
62 o5·:·List62 o5·:·List
63 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*63 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
64 ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8)·--·elements·between·two64 ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8)·--·elements·between·two
65 ······given·ones·for·the·Bruhat·order·on·a·Weyl·group65 ······given·ones·for·the·Bruhat·order·on·a·Weyl·group
66 ===============================================================================66 ===============================================================================
67 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-67 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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./usr/share/doc/Macaulay2/WeylGroups/html/_interval__Bruhat_lp__Weyl__Group__Right__Coset_cm__Weyl__Group__Right__Coset_rp.html
    
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110 o4·:·WeylGroupElement</code></pre>110 o4·:·WeylGroupElement</code></pre>
111 ············</td>111 ············</td>
112 ··········</tr>112 ··········</tr>
113 ··········<tr>113 ··········<tr>
114 ············<td>114 ············<td>
115 ··············<pre><code·class="language-macaulay2">i5·:·myInterval=intervalBruhat(P·%·w1,P·%·w2)115 ··············<pre><code·class="language-macaulay2">i5·:·myInterval=intervalBruhat(P·%·w1,P·%·w2)
  
116 o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|},·{1,·|··2·|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|··2·|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-3·|},·{{0,·|·1·|},·{1,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{1,·|··2·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··3·|},·{{0,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}} 
117 ··························································|·-2·|········|··2·|·······|·-1·|··············································|·-1·|········|··1·|·······|·-1·|·······|·-1·|············································|·-3·|········|··2·|·······|··1·|··············································|·-3·|········|·-1·|·······|·-1·|············································|··1·|········|·0·|·······|·-1·|············································|·-1·|········|·-1·|·······|··2·|··············································|·-2·|········|·-1·|············································|··1·|········|··1·|············································|·-2·|········|·-1·|··············································|·-1·| 
118 ··························································|··1·|········|·-1·|·······|··2·|··············································|··2·|········|··1·|·······|··0·|·······|··2·|············································|··1·|········|·-1·|·······|·[·...·truncated·by·diffoscope;·len:·482,·SHA:·3d37a635eac46574ead4f6ab979f45eea997f34a0dec26b384e44f809d027eab·...·]116 o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{1,·|·-1·|},·{2,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··2·|},·{1,·|··0·|},·{2,·|·[·...·truncated·by·diffoscope;·len:·490,·SHA:·5add286ab891da2b36c359dc10bc0aec42152dfb4751f9a705ef84bd0f592a93·...·]
 117 ··························································|·-2·|········|·-1·|·······|··2·|··············································|·-3·|········|··1·|·······|··2·|············································|·-1·|········|·-1·|·······|·-1·|·······|··1·|··············································|··1·|········|·-1·|·······|·0·|············································|·-1·|········|·-1·|·······|··2·|············································|·-3·|········|·-1·|·······|·-1·|··············································|··1·|········|··1·|············································|·-2·|········|·-1·|············································|·-2·|········|·-1·|··············································|·-1·|
 118 ··························································|··1·|········|··2·|·······|·-1·|··············································|··1·|········|··1·|·······|·-1·|············································|··2·|········|··0·|·······|··2·|·······|··1·|··············································|··1·|········|··2·|·······|·1·|············································|··3·|········|··0·|·······|·-1·|············································|··2·|········|··2·|·······|··0·|··············································|··2·|········|·-1·|············································|··3·|········|··0·|············································|··1·|········|··2·|··············································|··2·|
  
119 o5·:·HasseDiagram</code></pre>119 o5·:·HasseDiagram</code></pre>
120 ············</td>120 ············</td>
121 ··········</tr>121 ··········</tr>
122 ········</table>122 ········</table>
123 ········<div>123 ········<div>
124 ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p>124 ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p>
125 ········</div>125 ········</div>
126 ········<table·class="examples">126 ········<table·class="examples">
127 ··········<tr>127 ··········<tr>
128 ············<td>128 ············<td>
129 ··············<pre><code·class="language-macaulay2">i6·:·myInterval#1129 ··············<pre><code·class="language-macaulay2">i6·:·myInterval#1
  
130 o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|},·{1,·|··2130 o6·=·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{1,·|·-1·|},·{2,·|·-1
 131 ·············································|·-3·|········|··1·|·······|··2
131 ·············································|·-1·|········|··1·|·······|·-1132 ·············································|··1·|········|··1·|·······|·-1
132 ·············································|··2·|········|··1·|·······|··0 
133 ·····------------------------------------------------------------------------133 ·····------------------------------------------------------------------------
134 ·····|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,134 ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··2·|},·{1,
135 ·····|·······|·-1·|············································|·-3·|·······135 ·····|············································|·-1·|········|·-1·|······
136 ·····|·······|··2·|············································|··1·|·······136 ·····|············································|··2·|········|··0·|······
137 ·····------------------------------------------------------------------------137 ·····------------------------------------------------------------------------
138 ·····|·-1·|},·{2,·|·-1·|}}}}138 ·····|··0·|},·{2,·|·-1·|}}}}
139 ·····|··2·|·······|··1·| 
140 ·····|·-1·|·······|··1·|139 ·····|·-1·|·······|··1·|
 140 ·····|··2·|·······|··1·|
  
141 o6·:·List</code></pre>141 o6·:·List</code></pre>
142 ············</td>142 ············</td>
143 ··········</tr>143 ··········</tr>
144 ········</table>144 ········</table>
145 ······</div>145 ······</div>
146 ······<div>146 ······<div>
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41 o4·=·WeylGroupElement{RootSystem{...8...},·|·-1·|}41 o4·=·WeylGroupElement{RootSystem{...8...},·|·-1·|}
42 ···········································|·-2·|42 ···········································|·-2·|
43 ···········································|··1·|43 ···········································|··1·|
  
44 o4·:·WeylGroupElement44 o4·:·WeylGroupElement
45 i5·:·myInterval=intervalBruhat(P·%·w1,P·%·w2)45 i5·:·myInterval=intervalBruhat(P·%·w1,P·%·w2)
  
46 o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-46 o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0
 47 |},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{1,·|·-
47 1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-48 1·|},·{2,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··2
48 1·|},·{1,·|··2·|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1 
49 |},·{{0,·|·-1·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2 
50 |},·{{0,·|··2·|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·- 
51 3·|},·{{0,·|·1·|},·{1,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·- 
52 1·|},·{{1,·|··2·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|49 |},·{1,·|··0·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-
 50 3·|},·{{0,·|··0·|},·{2,·|·1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-
 51 1·|},·{{0,·|··2·|},·{1,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··2
 52 |},·{{1,·|··0·|},·{2,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-
53 3·|},·{{0,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··153 2·|},·{{0,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2
54 |}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|}}}},·{54 |}}},·{WeylGroupElement{RootSystem{...8...},·|··3·|},·{{0,·|··0·|}}}},·{
55 {WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}}55 {WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}}
56 ··························································|·-2·|········|··2·|56 ··························································|·-2·|········|·-1·|
57 |·-1·|··············································|·-1·|········|··1·|57 |··2·|··············································|·-3·|········|··1·|
58 |·-1·|·······|·-1·|············································|·-3·|········| 
59 2·|·······|··1·|··············································|·-3·|········|·- 
60 1·|·······|·-1·|············································|··1·|········|·0·| 
61 |·-1·|············································|·-1·|········|·-1·|·······|58 |··2·|············································|·-1·|········|·-1·|·······|
62 2·|··············································|·-2·|········|·-1·| 
63 |··1·|········|··1·|············································|·-2·|········| 
64 -1·|··············································|·-1·| 
65 ··························································|··1·|········|·-1·| 
66 |··2·|··············································|··2·|········|··1·| 
67 |··0·|·······|··2·|············································|··1·|········| 
68 -1·|·······|··1·|··············································|··2·|········|59 -1·|·······|··1·|··············································|··1·|········|
 60 -1·|·······|·0·|············································|·-1·|········|·-
69 0·|·······|··2·|············································|··1·|········|·1·|61 1·|·······|··2·|············································|·-3·|········|·-
 62 1·|·······|·-1·|··············································|··1·|········|
70 |··2·|············································|··3·|········|··0·|·······|63 1·|············································|·-2·|········|·-1·|
 64 |·-2·|········|·-1·|··············································|·-1·|
 65 ··························································|··1·|········|··2·|
71 -1·|··············································|··1·|········|··2·|66 |·-1·|··············································|··1·|········|··1·|
 67 |·-1·|············································|··2·|········|··0·|·······|
 68 2·|·······|··1·|··············································|··1·|········|
 69 2·|·······|·1·|············································|··3·|········|··0·|
 70 |·-1·|············································|··2·|········|··2·|·······|
 71 0·|··············································|··2·|········|·-1·|
72 |··2·|········|·-1·|············································|··3·|········|72 |··3·|········|··0·|············································|··1·|········|
73 0·|··············································|··2·|73 2·|··············································|··2·|
  
74 o5·:·HasseDiagram74 o5·:·HasseDiagram
75 Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length75 Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length
76 together·with·their·links·to·the·next·row.76 together·with·their·links·to·the·next·row.
77 i6·:·myInterval#177 i6·:·myInterval#1
  
78 o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|},·{1,·|··278 o6·=·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{1,·|·-1·|},·{2,·|·-1
 79 ·············································|·-3·|········|··1·|·······|··2
79 ·············································|·-1·|········|··1·|·······|·-180 ·············································|··1·|········|··1·|·······|·-1
80 ·············································|··2·|········|··1·|·······|··0 
81 ·····------------------------------------------------------------------------81 ·····------------------------------------------------------------------------
82 ·····|},·{2,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,82 ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··2·|},·{1,
83 ·····|·······|·-1·|············································|·-3·|83 ·····|············································|·-1·|········|·-1·|
84 ·····|·······|··2·|············································|··1·|84 ·····|············································|··2·|········|··0·|
85 ·····------------------------------------------------------------------------85 ·····------------------------------------------------------------------------
86 ·····|·-1·|},·{2,·|·-1·|}}}}86 ·····|··0·|},·{2,·|·-1·|}}}}
87 ·····|··2·|·······|··1·| 
88 ·····|·-1·|·······|··1·|87 ·····|·-1·|·······|··1·|
 88 ·····|··2·|·······|··1·|
  
89 o6·:·List89 o6·:·List
90 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*90 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
91 ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8R_\x8i_\x8g_\x8h_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8R_\x8i_\x8g_\x8h_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8)·--·elements91 ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8R_\x8i_\x8g_\x8h_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8R_\x8i_\x8g_\x8h_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8)·--·elements
92 ······between·two·given·ones·for·the·Bruhat·order·on·a·quotient·of·a·Weyl·group92 ······between·two·given·ones·for·the·Bruhat·order·on·a·quotient·of·a·Weyl·group
93 ===============================================================================93 ===============================================================================
94 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-94 The·source·of·this·document·is·in·/build/reproducible-path/macaulay2-
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79 o1·:·RootSystem</code></pre>79 o1·:·RootSystem</code></pre>
80 ············</td>80 ············</td>
81 ··········</tr>81 ··········</tr>
82 ··········<tr>82 ··········<tr>
83 ············<td>83 ············<td>
84 ··············<pre><code·class="language-macaulay2">i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R)84 ··············<pre><code·class="language-macaulay2">i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R)
  
85 o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|},·{1,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|},·{1,·|·1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}} 
86 ··························································|·-1·|········|··2·|·······|·-1·|··············································|·-2·|········|·1·|·······|·-1·|············································|··1·|········|··2·|·······|·1·|···········[·...·truncated·by·diffoscope;·len:·170,·SHA:·95df35d1d4a3ca898ce21b80d759a79b585804cf64fe489cd194787f997357ab·...·]85 o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|},·{1,·|·1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{Wey[·...·truncated·by·diffoscope;·len:·178,·SHA:·1e6c76800ad074b8a47615e8559b42657496871815f336a1db2487088304032d·...·]
 86 ··························································|·-1·|········|··2·|·······|·-1·|··············································|·-2·|········|·-1·|·······|·1·|············································|··1·|········|·1·|·······|··2·|··············································|·-1·|········|··2·|············································|··2·|········|·-1·|··············································|·1·|
  
87 o2·:·HasseDiagram</code></pre>87 o2·:·HasseDiagram</code></pre>
88 ············</td>88 ············</td>
89 ··········</tr>89 ··········</tr>
90 ··········<tr>90 ··········<tr>
91 ············<td>91 ············<td>
92 ··············<pre><code·class="language-macaulay2">i3·:·ZZ[x]92 ··············<pre><code·class="language-macaulay2">i3·:·ZZ[x]
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20 o1·=·RootSystem{...8...}20 o1·=·RootSystem{...8...}
  
21 o1·:·RootSystem21 o1·:·RootSystem
22 i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R)22 i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R)
  
23 o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-23 o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-
24 1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·124 1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|
25 |},·{1,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-25 2·|},·{1,·|·1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1
26 1·|},·{1,·|·1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··226 |},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-
27 |}}},·{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}}},·{27 1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|}}}},·{
28 {WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}}28 {WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}}
29 ··························································|·-1·|········|··2·|29 ··························································|·-1·|········|··2·|
30 |·-1·|··············································|·-2·|········|·1·|·······| 
31 -1·|············································|··1·|········|··2·|·······|·1 
32 |··············································|··2·|········|·-1·|30 |·-1·|··············································|·-2·|········|·-1·|
 31 |·1·|············································|··1·|········|·1·|·······|··2
 32 |··············································|·-1·|········|··2·|
33 |·-1·|········|··2·|··············································|·1·|33 |··2·|········|·-1·|··············································|·1·|
  
34 o2·:·HasseDiagram34 o2·:·HasseDiagram
35 i3·:·ZZ[x]35 i3·:·ZZ[x]
  
36 o3·=·ZZ[x]36 o3·=·ZZ[x]
  
37 o3·:·PolynomialRing37 o3·:·PolynomialRing
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88 o2·:·Parabolic</code></pre>88 o2·:·Parabolic</code></pre>
89 ············</td>89 ············</td>
90 ··········</tr>90 ··········</tr>
91 ··········<tr>91 ··········<tr>
92 ············<td>92 ············<td>
93 ··············<pre><code·class="language-macaulay2">i3·:·positiveRoots(R,P)93 ··············<pre><code·class="language-macaulay2">i3·:·positiveRoots(R,P)
  
94 o3·=·set·{|··1·|,·|··2·|,·|·-1·|}94 o3·=·set·{|·-1·|,·|··1·|,·|··2·|}
 95 ··········|··2·|··|··1·|··|·-1·|
95 ··········|··1·|··|·-1·|··|··2·|96 ··········|·-1·|··|·-1·|··|··0·|
96 ··········|·-1·|··|··0·|··|·-1·| 
97 ··········|··0·|··|··0·|··|··0·|97 ··········|··0·|··|··0·|··|··0·|
  
98 o3·:·Set</code></pre>98 o3·:·Set</code></pre>
99 ············</td>99 ············</td>
100 ··········</tr>100 ··········</tr>
101 ········</table>101 ········</table>
102 ······</div>102 ······</div>
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23 i2·:·P=parabolic(R,set{1,2})23 i2·:·P=parabolic(R,set{1,2})
  
24 o2·=·set·{1,·2}24 o2·=·set·{1,·2}
  
25 o2·:·Parabolic25 o2·:·Parabolic
26 i3·:·positiveRoots(R,P)26 i3·:·positiveRoots(R,P)
  
27 o3·=·set·{|··1·|,·|··2·|,·|·-1·|}27 o3·=·set·{|·-1·|,·|··1·|,·|··2·|}
 28 ··········|··2·|··|··1·|··|·-1·|
28 ··········|··1·|··|·-1·|··|··2·|29 ··········|·-1·|··|·-1·|··|··0·|
29 ··········|·-1·|··|··0·|··|·-1·| 
30 ··········|··0·|··|··0·|··|··0·|30 ··········|··0·|··|··0·|··|··0·|
  
31 o3·:·Set31 o3·:·Set
32 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*32 *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8*
33 ····*·_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8v_\x8e_\x8R_\x8o_\x8o_\x8t_\x8s_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8P_\x8a_\x8r_\x8a_\x8b_\x8o_\x8l_\x8i_\x8c_\x8)·--·the·set·of·all·positive·roots·in·a33 ····*·_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8v_\x8e_\x8R_\x8o_\x8o_\x8t_\x8s_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8P_\x8a_\x8r_\x8a_\x8b_\x8o_\x8l_\x8i_\x8c_\x8)·--·the·set·of·all·positive·roots·in·a
34 ······parabolic·sugroups34 ······parabolic·sugroups
35 ===============================================================================35 ===============================================================================
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8 Y29ub3JtYWw=8 Y29ub3JtYWw=
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10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIGNvbm9ybWFsIHZh10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIGNvbm9ybWFsIHZh
11 cmlldHkiLCAibGluZW51bSIgPT4gNjc2LCBJbnB1dHMgPT4ge1NQQU57VFR7IkkifSwiLCAiLFNQ11 cmlldHkiLCAibGluZW51bSIgPT4gNjc2LCBJbnB1dHMgPT4ge1NQQU57VFR7IkkifSwiLCAiLFNQ
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./usr/share/doc/Macaulay2/WhitneyStratifications/example-output/_map__Stratify.out
    
Offset 90, 41 lines modifiedOffset 90, 41 lines modified
90 i22·:·peek·last·ms90 i22·:·peek·last·ms
  
91 o22·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}91 o22·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}
92 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}92 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}
93 ·······················2·=>·{ideal·0}93 ·······················2·=>·{ideal·0}
  
94 i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly")94 i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly")
95 ·--·used·1.72659s·(cpu);·0.987247s·(thread);·0s·(gc)95 ·--·used·2.10327s·(cpu);·1.12693s·(thread);·0s·(gc)
  
96 o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}96 o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
97 o23·:·List97 o23·:·List
  
98 i24·:·peek·last·ms98 i24·:·peek·last·ms
  
99 o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}99 o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}
100 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}100 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}
101 ·······················2·=>·{ideal·0}101 ·······················2·=>·{ideal·0}
  
102 i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most")102 i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most")
103 ·--·used·18.0959s·(cpu);·4.28365s·(thread);·0s·(gc)103 ·--·used·17.9527s·(cpu);·4.09298s·(thread);·0s·(gc)
  
104 o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}104 o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
105 o25·:·List105 o25·:·List
  
106 i26·:·peek·last·ms106 i26·:·peek·last·ms
  
107 o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}107 o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}
108 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}108 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}
109 ·······················2·=>·{ideal·0}109 ·······················2·=>·{ideal·0}
  
110 i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all")110 i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all")
111 ·--·used·19.5625s·(cpu);·4.46595s·(thread);·0s·(gc)111 ·--·used·20.2467s·(cpu);·4.75098s·(thread);·0s·(gc)
  
112 o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}112 o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
113 o27·:·List113 o27·:·List
  
114 i28·:·peek·last·ms114 i28·:·peek·last·ms
  
4.55 KB
./usr/share/doc/Macaulay2/WhitneyStratifications/html/_map__Stratify.html
    
Offset 260, 15 lines modifiedOffset 260, 15 lines modified
260 ········<div>260 ········<div>
261 ··········<p>Finally·we·remark·that·the·option:·StratsToFind,·may·be·used·with·this·function,·but·should·only·be·used·with·care.·The·default·setting·is·StratsToFind=>&quot;all&quot;,·and·this·is·the·only·value·of·the·option·which·is·guaranteed·to·compute·the·complete·stratification,·the·other·options·may·fail·to·find·all·strata·but·are·provided·to·allow·the·user·to·obtain·partial·information·on·larger·examples·which·may·take·too·long·to·run·on·the·default·&quot;all&quot;·setting.·The·other·possible·values·are·StratsToFind=>&quot;singularOnly&quot;,·and·StratsToFind=>&quot;most&quot;.·The·option··StratsToFind=>&quot;singularOnly&quot;·is·the·fastest,·but·also·the·most·likely·to·return·incomplete·answers,·and·hence·the·output·of·this·command·should·be·treated·as·a·partial·answer·only.·The·option·StratsToFind=>&quot;most&quot;·will·most·often·get·the·full·answer,·but·can·miss·strata,·so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below·all·options·return·the·complete·answer,·but·only·the·output·with·StratsToFind=>&quot;all&quot;·should·be·considered·complete;·StratsToFind=>&quot;all&quot;·is·run·when·no·option·is·given.</p>261 ··········<p>Finally·we·remark·that·the·option:·StratsToFind,·may·be·used·with·this·function,·but·should·only·be·used·with·care.·The·default·setting·is·StratsToFind=>&quot;all&quot;,·and·this·is·the·only·value·of·the·option·which·is·guaranteed·to·compute·the·complete·stratification,·the·other·options·may·fail·to·find·all·strata·but·are·provided·to·allow·the·user·to·obtain·partial·information·on·larger·examples·which·may·take·too·long·to·run·on·the·default·&quot;all&quot;·setting.·The·other·possible·values·are·StratsToFind=>&quot;singularOnly&quot;,·and·StratsToFind=>&quot;most&quot;.·The·option··StratsToFind=>&quot;singularOnly&quot;·is·the·fastest,·but·also·the·most·likely·to·return·incomplete·answers,·and·hence·the·output·of·this·command·should·be·treated·as·a·partial·answer·only.·The·option·StratsToFind=>&quot;most&quot;·will·most·often·get·the·full·answer,·but·can·miss·strata,·so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below·all·options·return·the·complete·answer,·but·only·the·output·with·StratsToFind=>&quot;all&quot;·should·be·considered·complete;·StratsToFind=>&quot;all&quot;·is·run·when·no·option·is·given.</p>
262 ········</div>262 ········</div>
263 ········<table·class="examples">263 ········<table·class="examples">
264 ··········<tr>264 ··········<tr>
265 ············<td>265 ············<td>
266 ··············<pre><code·class="language-macaulay2">i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>&quot;singularOnly&quot;)266 ··············<pre><code·class="language-macaulay2">i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>&quot;singularOnly&quot;)
267 ·--·used·1.72659s·(cpu);·0.987247s·(thread);·0s·(gc)267 ·--·used·2.10327s·(cpu);·1.12693s·(thread);·0s·(gc)
  
268 o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}268 o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
269 o23·:·List</code></pre>269 o23·:·List</code></pre>
270 ············</td>270 ············</td>
271 ··········</tr>271 ··········</tr>
272 ··········<tr>272 ··········<tr>
Offset 279, 15 lines modifiedOffset 279, 15 lines modified
279 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}279 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}
280 ·······················2·=>·{ideal·0}</code></pre>280 ·······················2·=>·{ideal·0}</code></pre>
281 ············</td>281 ············</td>
282 ··········</tr>282 ··········</tr>
283 ··········<tr>283 ··········<tr>
284 ············<td>284 ············<td>
285 ··············<pre><code·class="language-macaulay2">i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>&quot;most&quot;)285 ··············<pre><code·class="language-macaulay2">i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>&quot;most&quot;)
286 ·--·used·18.0959s·(cpu);·4.28365s·(thread);·0s·(gc)286 ·--·used·17.9527s·(cpu);·4.09298s·(thread);·0s·(gc)
  
287 o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}287 o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
288 o25·:·List</code></pre>288 o25·:·List</code></pre>
289 ············</td>289 ············</td>
290 ··········</tr>290 ··········</tr>
291 ··········<tr>291 ··········<tr>
Offset 298, 15 lines modifiedOffset 298, 15 lines modified
298 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}298 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}
299 ·······················2·=>·{ideal·0}</code></pre>299 ·······················2·=>·{ideal·0}</code></pre>
300 ············</td>300 ············</td>
301 ··········</tr>301 ··········</tr>
302 ··········<tr>302 ··········<tr>
303 ············<td>303 ············<td>
304 ··············<pre><code·class="language-macaulay2">i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>&quot;all&quot;)304 ··············<pre><code·class="language-macaulay2">i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>&quot;all&quot;)
305 ·--·used·19.5625s·(cpu);·4.46595s·(thread);·0s·(gc)305 ·--·used·20.2467s·(cpu);·4.75098s·(thread);·0s·(gc)
  
306 o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}306 o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
307 o27·:·List</code></pre>307 o27·:·List</code></pre>
308 ············</td>308 ············</td>
309 ··········</tr>309 ··········</tr>
310 ··········<tr>310 ··········<tr>
1.63 KB
html2text {}
    
Offset 148, 37 lines modifiedOffset 148, 37 lines modified
148 this·command·should·be·treated·as·a·partial·answer·only.·The·option148 this·command·should·be·treated·as·a·partial·answer·only.·The·option
149 StratsToFind=>"most"·will·most·often·get·the·full·answer,·but·can·miss·strata,149 StratsToFind=>"most"·will·most·often·get·the·full·answer,·but·can·miss·strata,
150 so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below150 so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below
151 all·options·return·the·complete·answer,·but·only·the·output·with151 all·options·return·the·complete·answer,·but·only·the·output·with
152 StratsToFind=>"all"·should·be·considered·complete;·StratsToFind=>"all"·is·run152 StratsToFind=>"all"·should·be·considered·complete;·StratsToFind=>"all"·is·run
153 when·no·option·is·given.153 when·no·option·is·given.
154 i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly")154 i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly")
155 ·--·used·1.72659s·(cpu);·0.987247s·(thread);·0s·(gc)155 ·--·used·2.10327s·(cpu);·1.12693s·(thread);·0s·(gc)
  
156 o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}156 o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
157 o23·:·List157 o23·:·List
158 i24·:·peek·last·ms158 i24·:·peek·last·ms
  
159 o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}159 o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}
160 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}160 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}
161 ·······················2·=>·{ideal·0}161 ·······················2·=>·{ideal·0}
162 i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most")162 i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most")
163 ·--·used·18.0959s·(cpu);·4.28365s·(thread);·0s·(gc)163 ·--·used·17.9527s·(cpu);·4.09298s·(thread);·0s·(gc)
  
164 o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}164 o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
165 o25·:·List165 o25·:·List
166 i26·:·peek·last·ms166 i26·:·peek·last·ms
  
167 o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}167 o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}
168 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}168 ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)}
169 ·······················2·=>·{ideal·0}169 ·······················2·=>·{ideal·0}
170 i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all")170 i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all")
171 ·--·used·19.5625s·(cpu);·4.46595s·(thread);·0s·(gc)171 ·--·used·20.2467s·(cpu);·4.75098s·(thread);·0s·(gc)
  
172 o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}172 o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}}
  
173 o27·:·List173 o27·:·List
174 i28·:·peek·last·ms174 i28·:·peek·last·ms
  
175 o28·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}175 o28·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················}
727 B
./usr/share/doc/Macaulay2/XML/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=257 #:len=25
8 Z2V0QXR0cmlidXRlcyhMaWJ4bWxOb2RlKQ==8 Z2V0QXR0cmlidXRlcyhMaWJ4bWxOb2RlKQ==
9 #:len=4659 #:len=465
10 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZ2V0IHRoZSBsaXN0IG9mIGF0dHJpYnV010 bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZ2V0IHRoZSBsaXN0IG9mIGF0dHJpYnV0
11 ZXMgb2YgYW4gWE1MIG5vZGUiLCBEZXNjcmlwdGlvbiA9PiAxOihUQUJMRXsiY2xhc3MiID0+ICJl11 ZXMgb2YgYW4gWE1MIG5vZGUiLCBEZXNjcmlwdGlvbiA9PiAxOihUQUJMRXsiY2xhc3MiID0+ICJl
755 B
./usr/share/doc/Macaulay2/gfanInterface/dump/rawdocumentation.dump
    
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1 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Jun··2·04:39:21·20251 #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Tue·Jun··3·06:39:21·2025
2 #:version=1.12 #:version=1.1
3 #:file=rawdocumentation-dcba-8.db3 #:file=rawdocumentation-dcba-8.db
4 #:uid=1111,user=pbuilder1,gid=1111,group=pbuilder1,mode=6444 #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644
5 #:format=standard5 #:format=standard
6 #·End·of·header6 #·End·of·header
7 #:len=337 #:len=33
8 Z2ZhblBvbHlub21pYWxTZXRVbmlvbihMaXN0LExpc3Qp8 Z2ZhblBvbHlub21pYWxTZXRVbmlvbihMaXN0LExpc3Qp
9 #:len=3099 #:len=309
10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzY0Miwgc3ltYm9sIERvY3VtZW50VGFn10 bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzY0Miwgc3ltYm9sIERvY3VtZW50VGFn
11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2ZhblBvbHlub21pYWxTZXRVbmlvbixMaXN0LExp11 ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2ZhblBvbHlub21pYWxTZXRVbmlvbixMaXN0LExp
38.8 KB
./usr/share/doc/Macaulay2/gfanInterface/example-output/___Installation_spand_sp__Configuration_spof_spgfan__Interface.out
    
Offset 19, 15 lines modifiedOffset 19, 15 lines modified
19 i4·:·prefixDirectory·|·currentLayout#"programs"19 i4·:·prefixDirectory·|·currentLayout#"programs"
  
20 o4·=·/usr/x86_64-Linux-20 o4·=·/usr/x86_64-Linux-
21 ·····Debian-13/libexec/Macaulay2/bin/21 ·····Debian-13/libexec/Macaulay2/bin/
  
22 i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true);22 i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true);
23 ·--·warning:·reloading·gfanInterface;·recreate·instances·of·types·from·this·package23 ·--·warning:·reloading·gfanInterface;·recreate·instances·of·types·from·this·package
24 ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-1150570-0/17224 ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-1142962-0/172
25 This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm.25 This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm.
26 Options:26 Options:
27 -g:27 -g:
28 ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis.28 ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis.
  
29 --symmetry:29 --symmetry:
30 ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup.30 ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup.
Offset 38, 16 lines modifiedOffset 38, 16 lines modified
38 --disableSymmetryTest:38 --disableSymmetryTest:
39 ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal.39 ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal.
  
40 --parameters·value:40 --parameters·value:
41 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.41 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.
42 --interrupt·value:42 --interrupt·value:
43 ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans).43 ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans).
44 using·temporary·file·/tmp/M2-1150570-0/17244 using·temporary·file·/tmp/M2-1142962-0/172
45 ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-1150570-0/17445 ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-1142962-0/174
46 This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]).46 This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]).
47 Options:47 Options:
48 -w:48 -w:
49 ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read.49 ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read.
  
50 -r:50 -r:
51 ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used.51 ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used.
Offset 56, 69 lines modifiedOffset 56, 69 lines modified
56 ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored.56 ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored.
  
57 -g:57 -g:
58 ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used.58 ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used.
  
59 --parameters·value:59 --parameters·value:
60 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.60 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.
61 using·temporary·file·/tmp/M2-1150570-0/17461 using·temporary·file·/tmp/M2-1142962-0/174
62 ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-1150570-0/17662 ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-1142962-0/176
63 This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false.63 This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false.
64 Options:64 Options:
65 --remainder:65 --remainder:
66 ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1.66 ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1.
67 --multiplier:67 --multiplier:
68 ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division.68 ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division.
69 using·temporary·file·/tmp/M2-1150570-0/17669 using·temporary·file·/tmp/M2-1142962-0/176
70 ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-1150570-0/17870 ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-1142962-0/178
71 This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement.71 This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement.
72 Options:72 Options:
73 -i1·value:73 -i1·value:
74 ·Specify·the·name·of·the·first·input·file.74 ·Specify·the·name·of·the·first·input·file.
75 -i2·value:75 -i2·value:
76 ·Specify·the·name·of·the·second·input·file.76 ·Specify·the·name·of·the·second·input·file.
77 --stable:77 --stable:
78 ·Compute·the·stable·intersection.78 ·Compute·the·stable·intersection.
79 using·temporary·file·/tmp/M2-1150570-0/17879 using·temporary·file·/tmp/M2-1142962-0/178
80 ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-1150570-0/18080 ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-1142962-0/180
81 This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector.81 This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector.
82 Options:82 Options:
83 -i·value:83 -i·value:
84 ·Specify·the·name·of·the·input·file.84 ·Specify·the·name·of·the·input·file.
85 --symmetry:85 --symmetry:
86 ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input.86 ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input.
  
87 --star:87 --star:
88 ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector.88 ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector.
89 using·temporary·file·/tmp/M2-1150570-0/18089 using·temporary·file·/tmp/M2-1142962-0/180
90 ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-1150570-0/18290 ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-1142962-0/182
91 This·program·takes·two·polyhedral·fans·and·computes·their·product.91 This·program·takes·two·polyhedral·fans·and·computes·their·product.
92 Options:92 Options:
93 -i1·value:93 -i1·value:
94 ·Specify·the·name·of·the·first·input·file.94 ·Specify·the·name·of·the·first·input·file.
95 -i2·value:95 -i2·value:
96 ·Specify·the·name·of·the·second·input·file.96 ·Specify·the·name·of·the·second·input·file.
97 using·temporary·file·/tmp/M2-1150570-0/18297 using·temporary·file·/tmp/M2-1142962-0/182
98 ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-1150570-0/18498 ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-1142962-0/184
99 This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS.99 This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS.
100 Options:100 Options:
101 --restrict:101 --restrict:
102 ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant.102 ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant.
103 --pair:103 --pair:
104 ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual.104 ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual.
105 --asfan:105 --asfan:
106 ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed.106 ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed.
107 --vectorinput:107 --vectorinput:
108 ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations.108 ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations.
109 using·temporary·file·/tmp/M2-1150570-0/184109 using·temporary·file·/tmp/M2-1142962-0/184
110 ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-1150570-0/186110 ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-1142962-0/186
111 This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose.111 This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose.
112 Options:112 Options:
113 using·temporary·file·/tmp/M2-1150570-0/186113 using·temporary·file·/tmp/M2-1142962-0/186
114 ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-1150570-0/188114 ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-1142962-0/188
115 This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree.115 This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree.
116 Example:116 Example:
117 Input:117 Input:
118 Q[x,y]{y-1}118 Q[x,y]{y-1}
119 z119 z
120 Output:120 Output:
121 Q[x,y,z]{y-z}121 Q[x,y,z]{y-z}
Offset 126, 30 lines modifiedOffset 126, 30 lines modified
126 -i:126 -i:
127 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it.127 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it.
128 -w:128 -w:
129 ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials.129 ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials.
  
130 -H:130 -H:
131 ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input.131 ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input.
132 using·temporary·file·/tmp/M2-1150570-0/188132 using·temporary·file·/tmp/M2-1142962-0/188
133 ·--·running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2-1150570-0/190133 ·--·running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2-1142962-0/190
134 This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list.134 This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list.
135 Options:135 Options:
136 --ideal:136 --ideal:
137 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program.137 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program.
  
138 --pair:138 --pair:
139 ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal.139 ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal.
  
140 --mark:140 --mark:
141 ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector.141 ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector.
142 --list:142 --list:
143 ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output.143 ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output.
144 using·temporary·file·/tmp/M2-1150570-0/190144 using·temporary·file·/tmp/M2-1142962-0/190
145 ·--·running:·/usr/bin/gfan·_interactive·--help·<·/tmp/M2-1150570-0/192145 ·--·running:·/usr/bin/gfan·_interactive·--help·<·/tmp/M2-1142962-0/192
146 This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program.146 This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program.
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./usr/share/doc/Macaulay2/gfanInterface/html/___Installation_spand_sp__Configuration_spof_spgfan__Interface.html
    
Offset 109, 15 lines modifiedOffset 109, 15 lines modified
109 ··········<p></p>109 ··········<p></p>
110 ········</div>110 ········</div>
111 ········<table·class="examples">111 ········<table·class="examples">
112 ··········<tr>112 ··········<tr>
113 ············<td>113 ············<td>
114 ··············<pre><code·class="language-macaulay2">i5·:·loadPackage(&quot;gfanInterface&quot;,·Configuration·=>·{·&quot;keepfiles&quot;·=>·true,·&quot;verbose&quot;·=>·true},·Reload·=>·true);114 ··············<pre><code·class="language-macaulay2">i5·:·loadPackage(&quot;gfanInterface&quot;,·Configuration·=>·{·&quot;keepfiles&quot;·=>·true,·&quot;verbose&quot;·=>·true},·Reload·=>·true);
115 ·--·warning:·reloading·gfanInterface;·recreate·instances·of·types·from·this·package115 ·--·warning:·reloading·gfanInterface;·recreate·instances·of·types·from·this·package
116 ·--·running:·/usr/bin/gfan·gfan·--help·&lt;·/tmp/M2-1150570-0/172116 ·--·running:·/usr/bin/gfan·gfan·--help·&lt;·/tmp/M2-1142962-0/172
117 This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm.117 This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm.
118 Options:118 Options:
119 -g:119 -g:
120 ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis.120 ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis.
  
121 --symmetry:121 --symmetry:
122 ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup.122 ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup.
Offset 128, 16 lines modifiedOffset 128, 16 lines modified
128 --disableSymmetryTest:128 --disableSymmetryTest:
129 ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal.129 ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal.
  
130 --parameters·value:130 --parameters·value:
131 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.131 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.
132 --interrupt·value:132 --interrupt·value:
133 ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans).133 ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans).
134 using·temporary·file·/tmp/M2-1150570-0/172134 using·temporary·file·/tmp/M2-1142962-0/172
135 ·--·running:·/usr/bin/gfan·_buchberger·--help·&lt;·/tmp/M2-1150570-0/174135 ·--·running:·/usr/bin/gfan·_buchberger·--help·&lt;·/tmp/M2-1142962-0/174
136 This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]).136 This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]).
137 Options:137 Options:
138 -w:138 -w:
139 ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read.139 ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read.
  
140 -r:140 -r:
141 ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used.141 ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used.
Offset 146, 69 lines modifiedOffset 146, 69 lines modified
146 ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored.146 ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored.
  
147 -g:147 -g:
148 ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used.148 ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used.
  
149 --parameters·value:149 --parameters·value:
150 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.150 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters.
151 using·temporary·file·/tmp/M2-1150570-0/174151 using·temporary·file·/tmp/M2-1142962-0/174
152 ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·&lt;·/tmp/M2-1150570-0/176152 ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·&lt;·/tmp/M2-1142962-0/176
153 This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false.153 This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false.
154 Options:154 Options:
155 --remainder:155 --remainder:
156 ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1.156 ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1.
157 --multiplier:157 --multiplier:
158 ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division.158 ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division.
159 using·temporary·file·/tmp/M2-1150570-0/176159 using·temporary·file·/tmp/M2-1142962-0/176
160 ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·&lt;·/tmp/M2-1150570-0/178160 ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·&lt;·/tmp/M2-1142962-0/178
161 This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement.161 This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement.
162 Options:162 Options:
163 -i1·value:163 -i1·value:
164 ·Specify·the·name·of·the·first·input·file.164 ·Specify·the·name·of·the·first·input·file.
165 -i2·value:165 -i2·value:
166 ·Specify·the·name·of·the·second·input·file.166 ·Specify·the·name·of·the·second·input·file.
167 --stable:167 --stable:
168 ·Compute·the·stable·intersection.168 ·Compute·the·stable·intersection.
169 using·temporary·file·/tmp/M2-1150570-0/178169 using·temporary·file·/tmp/M2-1142962-0/178
170 ·--·running:·/usr/bin/gfan·_fanlink·--help·&lt;·/tmp/M2-1150570-0/180170 ·--·running:·/usr/bin/gfan·_fanlink·--help·&lt;·/tmp/M2-1142962-0/180
171 This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector.171 This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector.
172 Options:172 Options:
173 -i·value:173 -i·value:
174 ·Specify·the·name·of·the·input·file.174 ·Specify·the·name·of·the·input·file.
175 --symmetry:175 --symmetry:
176 ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input.176 ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input.
  
177 --star:177 --star:
178 ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector.178 ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector.
179 using·temporary·file·/tmp/M2-1150570-0/180179 using·temporary·file·/tmp/M2-1142962-0/180
180 ·--·running:·/usr/bin/gfan·_fanproduct·--help·&lt;·/tmp/M2-1150570-0/182180 ·--·running:·/usr/bin/gfan·_fanproduct·--help·&lt;·/tmp/M2-1142962-0/182
181 This·program·takes·two·polyhedral·fans·and·computes·their·product.181 This·program·takes·two·polyhedral·fans·and·computes·their·product.
182 Options:182 Options:
183 -i1·value:183 -i1·value:
184 ·Specify·the·name·of·the·first·input·file.184 ·Specify·the·name·of·the·first·input·file.
185 -i2·value:185 -i2·value:
186 ·Specify·the·name·of·the·second·input·file.186 ·Specify·the·name·of·the·second·input·file.
187 using·temporary·file·/tmp/M2-1150570-0/182187 using·temporary·file·/tmp/M2-1142962-0/182
188 ·--·running:·/usr/bin/gfan·_groebnercone·--help·&lt;·/tmp/M2-1150570-0/184188 ·--·running:·/usr/bin/gfan·_groebnercone·--help·&lt;·/tmp/M2-1142962-0/184
189 This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS.189 This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS.
190 Options:190 Options:
191 --restrict:191 --restrict:
192 ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant.192 ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant.
193 --pair:193 --pair:
194 ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual.194 ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual.
195 --asfan:195 --asfan:
196 ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed.196 ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed.
197 --vectorinput:197 --vectorinput:
198 ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations.198 ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations.
199 using·temporary·file·/tmp/M2-1150570-0/184199 using·temporary·file·/tmp/M2-1142962-0/184
200 ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·&lt;·/tmp/M2-1150570-0/186200 ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·&lt;·/tmp/M2-1142962-0/186
201 This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose.201 This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose.
202 Options:202 Options:
203 using·temporary·file·/tmp/M2-1150570-0/186203 using·temporary·file·/tmp/M2-1142962-0/186
204 ·--·running:·/usr/bin/gfan·_homogenize·--help·&lt;·/tmp/M2-1150570-0/188204 ·--·running:·/usr/bin/gfan·_homogenize·--help·&lt;·/tmp/M2-1142962-0/188
205 This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree.205 This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree.
206 Example:206 Example:
207 Input:207 Input:
208 Q[x,y]{y-1}208 Q[x,y]{y-1}
209 z209 z
210 Output:210 Output:
211 Q[x,y,z]{y-z}211 Q[x,y,z]{y-z}
Offset 216, 30 lines modifiedOffset 216, 30 lines modified
216 -i:216 -i:
217 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it.217 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it.
218 -w:218 -w:
219 ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials.219 ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials.
  
220 -H:220 -H:
221 ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input.221 ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input.
222 using·temporary·file·/tmp/M2-1150570-0/188222 using·temporary·file·/tmp/M2-1142962-0/188
223 ·--·running:·/usr/bin/gfan·_initialforms·--help·&lt;·/tmp/M2-1150570-0/190223 ·--·running:·/usr/bin/gfan·_initialforms·--help·&lt;·/tmp/M2-1142962-0/190
224 This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list.224 This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list.
225 Options:225 Options:
226 --ideal:226 --ideal:
227 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program.227 ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program.
  
228 --pair:228 --pair:
229 ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal.229 ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal.
  
230 --mark:230 --mark:
231 ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector.231 ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector.
232 --list:232 --list:
233 ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output.233 ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output.
234 using·temporary·file·/tmp/M2-1150570-0/190234 using·temporary·file·/tmp/M2-1142962-0/190
235 ·--·running:·/usr/bin/gfan·_interactive·--help·&lt;·/tmp/M2-1150570-0/192235 ·--·running:·/usr/bin/gfan·_interactive·--help·&lt;·/tmp/M2-1142962-0/192
236 This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program.236 This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program.
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43 If·you·would·like·to·see·the·input·and·output·files·used·to·communicate·with43 If·you·would·like·to·see·the·input·and·output·files·used·to·communicate·with
44 gfan·you·can·set·the·"keepfiles"·configuration·option·to·true.·If·"verbose"·is44 gfan·you·can·set·the·"keepfiles"·configuration·option·to·true.·If·"verbose"·is
45 set·to·true,·gfanInterface·will·output·the·names·of·the·temporary·files·used.45 set·to·true,·gfanInterface·will·output·the·names·of·the·temporary·files·used.
46 i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,46 i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,
47 "verbose"·=>·true},·Reload·=>·true);47 "verbose"·=>·true},·Reload·=>·true);
48 ·--·warning:·reloading·gfanInterface;·recreate·instances·of·types·from·this48 ·--·warning:·reloading·gfanInterface;·recreate·instances·of·types·from·this
49 package49 package
50 ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-1150570-0/17250 ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-1142962-0/172
51 This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial51 This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial
52 ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By52 ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By
53 default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the53 default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the
54 ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done54 ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done
55 up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting55 up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting
56 Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it56 Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it
57 will·compute·one·using·Buchberger's·algorithm.57 will·compute·one·using·Buchberger's·algorithm.
Offset 81, 16 lines modifiedOffset 81, 16 lines modified
81 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters81 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters
82 instead·of·variables.·This·makes·it·possible·to·do·computations·where·the82 instead·of·variables.·This·makes·it·possible·to·do·computations·where·the
83 coefficient·field·is·the·field·of·rational·functions·in·the·parameters.83 coefficient·field·is·the·field·of·rational·functions·in·the·parameters.
84 --interrupt·value:84 --interrupt·value:
85 ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been85 ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been
86 computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for86 computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for
87 non-symmetric·traversals·or·for·traversals·restricted·to·fans).87 non-symmetric·traversals·or·for·traversals·restricted·to·fans).
88 using·temporary·file·/tmp/M2-1150570-0/17288 using·temporary·file·/tmp/M2-1142962-0/172
89 ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-1150570-0/17489 ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-1142962-0/174
90 This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial90 This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial
91 ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.91 ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.
92 The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q92 The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q
93 [a,b,c,...]).93 [a,b,c,...]).
94 Options:94 Options:
95 -w:95 -w:
96 ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with96 ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with
Offset 111, 63 lines modifiedOffset 111, 63 lines modified
111 minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.111 minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.
112 The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used.112 The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used.
  
113 --parameters·value:113 --parameters·value:
114 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters114 ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters
115 instead·of·variables.·This·makes·it·possible·to·do·computations·where·the115 instead·of·variables.·This·makes·it·possible·to·do·computations·where·the
116 coefficient·field·is·the·field·of·rational·functions·in·the·parameters.116 coefficient·field·is·the·field·of·rational·functions·in·the·parameters.
117 using·temporary·file·/tmp/M2-1150570-0/174117 using·temporary·file·/tmp/M2-1142962-0/174
118 ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-1150570-0/176118 ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-1142962-0/176
119 This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of119 This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of
120 polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by120 polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by
121 applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and121 applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and
122 0·for·false.122 0·for·false.
123 Options:123 Options:
124 --remainder:124 --remainder:
125 ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than125 ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than
126 outputting·0·or·1.126 outputting·0·or·1.
127 --multiplier:127 --multiplier:
128 ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided128 ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided
129 before·doing·the·division.129 before·doing·the·division.
130 using·temporary·file·/tmp/M2-1150570-0/176130 using·temporary·file·/tmp/M2-1142962-0/176
131 ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-1150570-0/178131 ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-1142962-0/178
132 This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement.132 This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement.
133 Options:133 Options:
134 -i1·value:134 -i1·value:
135 ·Specify·the·name·of·the·first·input·file.135 ·Specify·the·name·of·the·first·input·file.
136 -i2·value:136 -i2·value:
137 ·Specify·the·name·of·the·second·input·file.137 ·Specify·the·name·of·the·second·input·file.
138 --stable:138 --stable:
139 ·Compute·the·stable·intersection.139 ·Compute·the·stable·intersection.
140 using·temporary·file·/tmp/M2-1150570-0/178140 using·temporary·file·/tmp/M2-1142962-0/178
141 ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-1150570-0/180141 ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-1142962-0/180
142 This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the142 This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the
143 polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension143 polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension
144 equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan144 equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan
145 containing·the·vector.145 containing·the·vector.
146 Options:146 Options:
147 -i·value:147 -i·value:
148 ·Specify·the·name·of·the·input·file.148 ·Specify·the·name·of·the·input·file.
149 --symmetry:149 --symmetry:
150 ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must150 ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must
151 be·given·on·the·standard·input.151 be·given·on·the·standard·input.
  
152 --star:152 --star:
153 ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan153 ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan
154 containing·all·cones·of·the·original·fan·containing·the·vector.154 containing·all·cones·of·the·original·fan·containing·the·vector.
155 using·temporary·file·/tmp/M2-1150570-0/180155 using·temporary·file·/tmp/M2-1142962-0/180
156 ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-1150570-0/182156 ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-1142962-0/182
157 This·program·takes·two·polyhedral·fans·and·computes·their·product.157 This·program·takes·two·polyhedral·fans·and·computes·their·product.
158 Options:158 Options:
159 -i1·value:159 -i1·value:
160 ·Specify·the·name·of·the·first·input·file.160 ·Specify·the·name·of·the·first·input·file.
161 -i2·value:161 -i2·value:
162 ·Specify·the·name·of·the·second·input·file.162 ·Specify·the·name·of·the·second·input·file.
163 using·temporary·file·/tmp/M2-1150570-0/182163 using·temporary·file·/tmp/M2-1142962-0/182
164 ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-1150570-0/184164 ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-1142962-0/184
165 This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The165 This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The
166 input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is166 input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is
167 computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone167 computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone
168 computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones168 computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones
169 are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case169 are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case
170 is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of170 is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of
171 Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.171 Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.
Offset 184, 24 lines modifiedOffset 184, 24 lines modified
184 --asfan:184 --asfan:
185 ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way185 ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way
186 the·extreme·rays·of·the·cone·are·also·computed.186 the·extreme·rays·of·the·cone·are·also·computed.
187 --vectorinput:187 --vectorinput:
188 ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The188 ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The
189 input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list189 input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list
190 of·inequalities·given·as·vectors·and·a·list·of·equations.190 of·inequalities·given·as·vectors·and·a·list·of·equations.
191 using·temporary·file·/tmp/M2-1150570-0/184191 using·temporary·file·/tmp/M2-1142962-0/184
192 ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-1150570-0/186192 ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-1142962-0/186
193 This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a193 This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a
194 cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section194 cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section
195 LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first195 LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first
196 compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A196 compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A
197 reduced·Groebner·basis·will·always·suffice·for·this·purpose.197 reduced·Groebner·basis·will·always·suffice·for·this·purpose.
198 Options:198 Options:
199 using·temporary·file·/tmp/M2-1150570-0/186199 using·temporary·file·/tmp/M2-1142962-0/186
200 ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-1150570-0/188200 ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-1142962-0/188
201 This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra201 This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra
202 variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input202 variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input
203 after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done203 after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done
204 with·respect·to·total·degree.204 with·respect·to·total·degree.
205 Example:205 Example:
206 Input:206 Input:
207 Q[x,y]{y-1}207 Q[x,y]{y-1}
Offset 217, 16 lines modifiedOffset 217, 16 lines modified
217 ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as217 ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as
218 the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after218 the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after
219 the·list·of·polynomials.219 the·list·of·polynomials.
  
220 -H:220 -H:
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00017f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00017f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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00017fd0:·2020·2020·2020·2020·2020·2020·2020·2020··················00017fd0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00017fe0:·2020·2020·2020·2020·2020·2020·2020·2020··················00017fe0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00017ff0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|·····00017ff0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|·····
00018000:·2020·2020·2020·2020·2020·2020·2020·2020··················00018000:·2020·2020·2020·2020·2020·2020·2020·2020··················
00018010:·2020·2020·2020·2020·2020·2020·2020·2020··················00018010:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00018030:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|·00018030:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|·
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000181f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000181f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00018200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00018200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00018210:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:·00018210:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:·
00018220:·656c·6170·7365·6454·696d·6520·6275·726b··elapsedTime·burk00018220:·656c·6170·7365·6454·696d·6520·6275·726b··elapsedTime·burk
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Benchmark.info
    
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 00000ec0:·2832·3032·352d·3034·2d32·3529·2078·3836··(2025-04-25)·x86
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Bertini.info
    
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000136e0:·3a20·546f·7044·6972·6563·746f·7279·2c20··:·TopDirectory,·000136e0:·3a20·546f·7044·6972·6563·746f·7279·2c20··:·TopDirectory,·
000136f0:·3d3e·202e·2e2e·2c20·6465·6661·756c·7420··=>·...,·default·000136f0:·3d3e·202e·2e2e·2c20·6465·6661·756c·7420··=>·...,·default·
00013700:·7661·6c75·650a·2020·2020·2020·2020·222f··value.········"/00013700:·7661·6c75·650a·2020·2020·2020·2020·222f··value.········"/
00013710:·746d·702f·4d32·2d31·3230·3939·3336·2d30··tmp/M2-1209936-000013710:·746d·702f·4d32·2d31·3232·3737·3133·2d30··tmp/M2-1227713-0
00013720:·2f30·222c·204f·7074·696f·6e20·746f·2063··/0",·Option·to·c00013720:·2f30·222c·204f·7074·696f·6e20·746f·2063··/0",·Option·to·c
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00013770:·5472·6163·6b48·6f6d·6f74·6f70·795f·6c70··TrackHomotopy_lp00013770:·5472·6163·6b48·6f6d·6f74·6f70·795f·6c70··TrackHomotopy_lp
00013780:·5f70·645f·7064·5f70·645f·636d·5665·7262··_pd_pd_pd_cmVerb00013780:·5f70·645f·7064·5f70·645f·636d·5665·7262··_pd_pd_pd_cmVerb
Offset 5473, 15 lines modifiedOffset 5473, 15 lines modified
00015600:·2020·2020·2020·206f·7220·7261·6e64·6f6d·········or·random00015600:·2020·2020·2020·206f·7220·7261·6e64·6f6d·········or·random
00015610:·2063·6f6d·706c·6578·206e·756d·6265·720a···complex·number.00015610:·2063·6f6d·706c·6578·206e·756d·6265·720a···complex·number.
00015620:·2020·2020·2020·2a20·2a6e·6f74·6520·546f········*·*note·To00015620:·2020·2020·2020·2a20·2a6e·6f74·6520·546f········*·*note·To
00015630:·7044·6972·6563·746f·7279·3a20·546f·7044··pDirectory:·TopD00015630:·7044·6972·6563·746f·7279·3a20·546f·7044··pDirectory:·TopD
00015640:·6972·6563·746f·7279·2c20·3d3e·202e·2e2e··irectory,·=>·...00015640:·6972·6563·746f·7279·2c20·3d3e·202e·2e2e··irectory,·=>·...
00015650:·2c20·6465·6661·756c·7420·7661·6c75·650a··,·default·value.00015650:·2c20·6465·6661·756c·7420·7661·6c75·650a··,·default·value.
00015660:·2020·2020·2020·2020·222f·746d·702f·4d32··········"/tmp/M200015660:·2020·2020·2020·2020·222f·746d·702f·4d32··········"/tmp/M2
00015670:·2d31·3230·3939·3336·2d30·2f30·222c·204f··-1209936-0/0",·O00015670:·2d31·3232·3737·3133·2d30·2f30·222c·204f··-1227713-0/0",·O
00015680:·7074·696f·6e20·746f·2063·6861·6e67·6520··ption·to·change·00015680:·7074·696f·6e20·746f·2063·6861·6e67·6520··ption·to·change·
00015690:·6469·7265·6374·6f72·7920·666f·7220·6669··directory·for·fi00015690:·6469·7265·6374·6f72·7920·666f·7220·6669··directory·for·fi
000156a0:·6c65·2073·746f·7261·6765·2e0a·2020·2020··le·storage..····000156a0:·6c65·2073·746f·7261·6765·2e0a·2020·2020··le·storage..····
000156b0:·2020·2a20·5573·6552·6567·656e·6572·6174····*·UseRegenerat000156b0:·2020·2a20·5573·6552·6567·656e·6572·6174····*·UseRegenerat
000156c0:·696f·6e20·286d·6973·7369·6e67·2064·6f63··ion·(missing·doc000156c0:·696f·6e20·286d·6973·7369·6e67·2064·6f63··ion·(missing·doc
000156d0:·756d·656e·7461·7469·6f6e·2920·3d3e·202e··umentation)·=>·.000156d0:·756d·656e·7461·7469·6f6e·2920·3d3e·202e··umentation)·=>·.
000156e0:·2e2e·2c20·6465·6661·756c·7420·7661·6c75··..,·default·valu000156e0:·2e2e·2c20·6465·6661·756c·7420·7661·6c75··..,·default·valu
5.63 KB
./usr/share/info/BettiCharacters.info.gz
5.56 KB
BettiCharacters.info
    
Offset 12973, 15 lines modifiedOffset 12973, 15 lines modified
00032ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00032ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00032ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00032ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00032ae0:·2d2b·0a7c·6939·203a·2065·6c61·7073·6564··-+.|i9·:·elapsed00032ae0:·2d2b·0a7c·6939·203a·2065·6c61·7073·6564··-+.|i9·:·elapsed
00032af0:·5469·6d65·2063·203d·2063·6861·7261·6374··Time·c·=·charact00032af0:·5469·6d65·2063·203d·2063·6861·7261·6374··Time·c·=·charact
00032b00:·6572·2041·2020·2020·2020·2020·2020·2020··er·A············00032b00:·6572·2041·2020·2020·2020·2020·2020·2020··er·A············
00032b10:·2020·2020·2020·2020·2020·2020·2020·2020··················00032b10:·2020·2020·2020·2020·2020·2020·2020·2020··················
00032b20:·2020·2020·2020·2020·2020·2020·2020·2020··················00032b20:·2020·2020·2020·2020·2020·2020·2020·2020··················
00032b30:·207c·0a7c·202d·2d20·2e34·3633·3036·3273···|.|·--·.463062s00032b30:·207c·0a7c·202d·2d20·312e·3433·3538·3873···|.|·--·1.43588s
00032b40:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········00032b40:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········
00032b50:·2020·2020·2020·2020·2020·2020·2020·2020··················00032b50:·2020·2020·2020·2020·2020·2020·2020·2020··················
00032b60:·2020·2020·2020·2020·2020·2020·2020·2020··················00032b60:·2020·2020·2020·2020·2020·2020·2020·2020··················
00032b70:·2020·2020·2020·2020·2020·2020·2020·2020··················00032b70:·2020·2020·2020·2020·2020·2020·2020·2020··················
00032b80:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············00032b80:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············
00032b90:·2020·2020·2020·2020·2020·2020·2020·2020··················00032b90:·2020·2020·2020·2020·2020·2020·2020·2020··················
00032ba0:·2020·2020·2020·2020·2020·2020·2020·2020··················00032ba0:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 14183, 15 lines modifiedOffset 14183, 15 lines modified
00037660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00037660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00037670:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937·203a··---------+.|i7·:00037670:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937·203a··---------+.|i7·:
00037680:·2065·6c61·7073·6564·5469·6d65·2063·3d63···elapsedTime·c=c00037680:·2065·6c61·7073·6564·5469·6d65·2063·3d63···elapsedTime·c=c
00037690:·6861·7261·6374·6572·2041·2020·2020·2020··haracter·A······00037690:·6861·7261·6374·6572·2041·2020·2020·2020··haracter·A······
000376a0:·2020·2020·2020·2020·2020·2020·2020·2020··················000376a0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000376b0:·2020·2020·2020·2020·2020·2020·2020·2020··················000376b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000376c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--·000376c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--·
000376d0:·2e33·3136·3334·3373·2065·6c61·7073·6564··.316343s·elapsed000376d0:·312e·3331·3833·3473·2065·6c61·7073·6564··1.31834s·elapsed
000376e0:·2020·2020·2020·2020·2020·2020·2020·2020··················000376e0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000376f0:·2020·2020·2020·2020·2020·2020·2020·2020··················000376f0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00037700:·2020·2020·2020·2020·2020·2020·2020·2020··················00037700:·2020·2020·2020·2020·2020·2020·2020·2020··················
00037710:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|····00037710:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|····
00037720:·2020·2020·2020·2020·2020·2020·2020·2020··················00037720:·2020·2020·2020·2020·2020·2020·2020·2020··················
00037730:·2020·2020·2020·2020·2020·2020·2020·2020··················00037730:·2020·2020·2020·2020·2020·2020·2020·2020··················
00037740:·2020·2020·2020·2020·2020·2020·2020·2020··················00037740:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 15614, 15 lines modifiedOffset 15614, 15 lines modified
0003cfd0:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+--------0003cfd0:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+--------
0003cfe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0003cfe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0003cff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0003cff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0003d000:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3230··----------+.|i200003d000:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3230··----------+.|i20
0003d010:·203a·2065·6c61·7073·6564·5469·6d65·2061···:·elapsedTime·a0003d010:·203a·2065·6c61·7073·6564·5469·6d65·2061···:·elapsedTime·a
0003d020:·3120·3d20·6368·6172·6163·7465·7220·4131··1·=·character·A10003d020:·3120·3d20·6368·6172·6163·7465·7220·4131··1·=·character·A1
0003d030:·2020·2020·2020·2020·2020·2020·2020·207c·················|0003d030:·2020·2020·2020·2020·2020·2020·2020·207c·················|
0003d040:·0a7c·202d·2d20·2e36·3430·3430·3573·2065··.|·--·.640405s·e0003d040:·0a7c·202d·2d20·322e·3133·3638·3373·2065··.|·--·2.13683s·e
0003d050:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········0003d050:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········
0003d060:·2020·2020·2020·2020·2020·2020·2020·2020··················0003d060:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003d070:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|·········0003d070:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|·········
0003d080:·2020·2020·2020·2020·2020·2020·2020·2020··················0003d080:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003d090:·2020·2020·2020·2020·2020·2020·2020·2020··················0003d090:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003d0a0:·2020·2020·2020·2020·207c·0a7c·6f32·3020···········|.|o20·0003d0a0:·2020·2020·2020·2020·207c·0a7c·6f32·3020···········|.|o20·
0003d0b0:·3d20·4368·6172·6163·7465·7220·6f76·6572··=·Character·over0003d0b0:·3d20·4368·6172·6163·7465·7220·6f76·6572··=·Character·over
Offset 15654, 15 lines modifiedOffset 15654, 15 lines modified
0003d250:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------0003d250:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------
0003d260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0003d260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0003d270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0003d270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0003d280:·2d2d·2d2d·2d2d·2b0a·7c69·3231·203a·2065··------+.|i21·:·e0003d280:·2d2d·2d2d·2d2d·2b0a·7c69·3231·203a·2065··------+.|i21·:·e
0003d290:·6c61·7073·6564·5469·6d65·2061·3220·3d20··lapsedTime·a2·=·0003d290:·6c61·7073·6564·5469·6d65·2061·3220·3d20··lapsedTime·a2·=·
0003d2a0:·6368·6172·6163·7465·7220·4132·2020·2020··character·A2····0003d2a0:·6368·6172·6163·7465·7220·4132·2020·2020··character·A2····
0003d2b0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·-0003d2b0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·-
0003d2c0:·2d20·3333·2e33·3233·3873·2065·6c61·7073··-·33.3238s·elaps0003d2c0:·2d20·3634·2e37·3234·3573·2065·6c61·7073··-·64.7245s·elaps
0003d2d0:·6564·2020·2020·2020·2020·2020·2020·2020··ed··············0003d2d0:·6564·2020·2020·2020·2020·2020·2020·2020··ed··············
0003d2e0:·2020·2020·2020·2020·2020·2020·2020·2020··················0003d2e0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003d2f0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|·············0003d2f0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|·············
0003d300:·2020·2020·2020·2020·2020·2020·2020·2020··················0003d300:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003d310:·2020·2020·2020·2020·2020·2020·2020·2020··················0003d310:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003d320:·2020·2020·207c·0a7c·6f32·3120·3d20·4368·······|.|o21·=·Ch0003d320:·2020·2020·207c·0a7c·6f32·3120·3d20·4368·······|.|o21·=·Ch
0003d330:·6172·6163·7465·7220·6f76·6572·2052·2020··aracter·over·R··0003d330:·6172·6163·7465·7220·6f76·6572·2052·2020··aracter·over·R··
Offset 16112, 15 lines modifiedOffset 16112, 15 lines modified
0003eef0:·6374·696f·6e4f·6e47·7261·6465·644d·6f64··ctionOnGradedMod0003eef0:·6374·696f·6e4f·6e47·7261·6465·644d·6f64··ctionOnGradedMod
0003ef00:·756c·6520·2020·2020·2020·2020·2020·7c0a··ule···········|.0003ef00:·756c·6520·2020·2020·2020·2020·2020·7c0a··ule···········|.
0003ef10:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+---------------0003ef10:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+---------------
0003ef20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0003ef20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0003ef30:·2d2d·2d2d·2d2d·2b0a·7c69·3332·203a·2065··------+.|i32·:·e0003ef30:·2d2d·2d2d·2d2d·2b0a·7c69·3332·203a·2065··------+.|i32·:·e
0003ef40:·6c61·7073·6564·5469·6d65·2062·203d·2063··lapsedTime·b·=·c0003ef40:·6c61·7073·6564·5469·6d65·2062·203d·2063··lapsedTime·b·=·c
0003ef50:·6861·7261·6374·6572·2842·2c32·3129·7c0a··haracter(B,21)|.0003ef50:·6861·7261·6374·6572·2842·2c32·3129·7c0a··haracter(B,21)|.
0003ef60:·7c20·2d2d·2031·392e·3233·3932·7320·656c··|·--·19.2392s·el0003ef60:·7c20·2d2d·2032·392e·3139·3931·7320·656c··|·--·29.1991s·el
0003ef70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed···········0003ef70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed···········
0003ef80:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|·······0003ef80:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|·······
0003ef90:·2020·2020·2020·2020·2020·2020·2020·2020··················0003ef90:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003efa0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.0003efa0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
0003efb0:·7c6f·3332·203d·2043·6861·7261·6374·6572··|o32·=·Character0003efb0:·7c6f·3332·203d·2043·6861·7261·6374·6572··|o32·=·Character
0003efc0:·206f·7665·7220·5220·2020·2020·2020·2020···over·R·········0003efc0:·206f·7665·7220·5220·2020·2020·2020·2020···over·R·········
0003efd0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|·······0003efd0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|·······
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./usr/share/info/Bruns.info.gz
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Bruns.info
    
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00010c80:·6c20·7a2c·2043·656c·6c20·6f66·2064·696d··l·z,·Cell·of·dim00010c80:·6c20·782c·2043·656c·6c20·6f66·2064·696d··l·x,·Cell·of·dim
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00009700:·7c69·3920·3a20·656c·6170·7365·6454·696d··|i9·:·elapsedTim00009700:·7c69·3920·3a20·656c·6170·7365·6454·696d··|i9·:·elapsedTim
00009710:·6520·4120·3d20·636f·6e6e·6563·7469·6f6e··e·A·=·connection00009710:·6520·4120·3d20·636f·6e6e·6563·7469·6f6e··e·A·=·connection
00009720:·4d61·7472·6963·6573·2049·3b20·2020·2020··Matrices·I;·····00009720:·4d61·7472·6963·6573·2049·3b20·2020·2020··Matrices·I;·····
00009730:·2020·2020·2020·2020·2020·2020·2020·2020··················00009730:·2020·2020·2020·2020·2020·2020·2020·2020··················
00009740:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.00009740:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
00009750:·7c20·2d2d·2032·2e30·3739·3835·7320·656c··|·--·2.07985s·el00009750:·7c20·2d2d·2034·2e37·3838·3631·7320·656c··|·--·4.78861s·el
00009760:·6170·7365·6420·2020·2020·2020·2020·2020··apsed···········00009760:·6170·7365·6420·2020·2020·2020·2020·2020··apsed···········
00009770:·2020·2020·2020·2020·2020·2020·2020·2020··················00009770:·2020·2020·2020·2020·2020·2020·2020·2020··················
00009780:·2020·2020·2020·2020·2020·2020·2020·2020··················00009780:·2020·2020·2020·2020·2020·2020·2020·2020··················
00009790:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.00009790:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
000097a0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+---------------000097a0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+---------------
000097b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000097b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000097c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000097c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000097d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000097d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000097e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+.000097e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+.
000097f0:·7c69·3130·203a·2065·6c61·7073·6564·5469··|i10·:·elapsedTi000097f0:·7c69·3130·203a·2065·6c61·7073·6564·5469··|i10·:·elapsedTi
00009800:·6d65·2061·7373·6572·7420·6973·496e·7465··me·assert·isInte00009800:·6d65·2061·7373·6572·7420·6973·496e·7465··me·assert·isInte
00009810:·6772·6162·6c65·2041·2020·2020·2020·2020··grable·A········00009810:·6772·6162·6c65·2041·2020·2020·2020·2020··grable·A········
00009820:·2020·2020·2020·2020·2020·2020·2020·2020··················00009820:·2020·2020·2020·2020·2020·2020·2020·2020··················
00009830:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.00009830:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
00009840:·7c20·2d2d·2033·2e37·3635·3873·2065·6c61··|·--·3.7658s·ela00009840:·7c20·2d2d·2038·2e38·3135·3735·7320·656c··|·--·8.81575s·el
00009850:·7073·6564·2020·2020·2020·2020·2020·2020··psed············00009850:·6170·7365·6420·2020·2020·2020·2020·2020··apsed···········
00009860:·2020·2020·2020·2020·2020·2020·2020·2020··················00009860:·2020·2020·2020·2020·2020·2020·2020·2020··················
00009870:·2020·2020·2020·2020·2020·2020·2020·2020··················00009870:·2020·2020·2020·2020·2020·2020·2020·2020··················
00009880:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.00009880:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
00009890:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+---------------00009890:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+---------------
000098a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000098a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000098b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000098b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000098c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000098c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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00011ce0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011ce0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011d00:·2b0a·7c69·3134·203a·2065·6c61·7073·6564··+.|i14·:·elapsed00011d00:·2b0a·7c69·3134·203a·2065·6c61·7073·6564··+.|i14·:·elapsed
00011d10:·5469·6d65·2067·203d·2067·6175·6765·4d61··Time·g·=·gaugeMa00011d10:·5469·6d65·2067·203d·2067·6175·6765·4d61··Time·g·=·gaugeMa
00011d20:·7472·6978·2849·2c20·4229·3b20·2020·2020··trix(I,·B);·····00011d20:·7472·6978·2849·2c20·4229·3b20·2020·2020··trix(I,·B);·····
00011d30:·2020·2020·2020·2020·2020·2020·2020·2020··················00011d30:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011d40:·2020·2020·2020·2020·2020·2020·2020·2020··················00011d40:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011d50:·7c0a·7c20·2d2d·202e·3431·3638·3138·7320··|.|·--·.416818s·00011d50:·7c0a·7c20·2d2d·2031·2e34·3033·3437·7320··|.|·--·1.40347s·
00011d60:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed·········00011d60:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed·········
00011d70:·2020·2020·2020·2020·2020·2020·2020·2020··················00011d70:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011d80:·2020·2020·2020·2020·2020·2020·2020·2020··················00011d80:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011d90:·2020·2020·2020·2020·2020·2020·2020·2020··················00011d90:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011da0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|·············00011da0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|·············
00011db0:·2020·2020·2020·2020·2020·2020·2020·2020··················00011db0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011dc0:·2020·2020·2020·2020·2020·2020·2020·2020··················00011dc0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00011ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011ee0:·2b0a·7c69·3135·203a·2065·6c61·7073·6564··+.|i15·:·elapsed00011ee0:·2b0a·7c69·3135·203a·2065·6c61·7073·6564··+.|i15·:·elapsed
00011ef0:·5469·6d65·2041·3120·3d20·6761·7567·6554··Time·A1·=·gaugeT00011ef0:·5469·6d65·2041·3120·3d20·6761·7567·6554··Time·A1·=·gaugeT
00011f00:·7261·6e73·666f·726d·2867·2c20·4129·3b20··ransform(g,·A);·00011f00:·7261·6e73·666f·726d·2867·2c20·4129·3b20··ransform(g,·A);·
00011f10:·2020·2020·2020·2020·2020·2020·2020·2020··················00011f10:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011f20:·2020·2020·2020·2020·2020·2020·2020·2020··················00011f20:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011f30:·7c0a·7c20·2d2d·2031·2e30·3532·3131·7320··|.|·--·1.05211s·00011f30:·7c0a·7c20·2d2d·2032·2e34·3137·3835·7320··|.|·--·2.41785s·
00011f40:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed·········00011f40:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed·········
00011f50:·2020·2020·2020·2020·2020·2020·2020·2020··················00011f50:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011f60:·2020·2020·2020·2020·2020·2020·2020·2020··················00011f60:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011f70:·2020·2020·2020·2020·2020·2020·2020·2020··················00011f70:·2020·2020·2020·2020·2020·2020·2020·2020··················
00011f80:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+-------------00011f80:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+-------------
00011f90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011f90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011fa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011fa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00011fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00011fd0:·2b0a·7c69·3136·203a·2065·6c61·7073·6564··+.|i16·:·elapsed00011fd0:·2b0a·7c69·3136·203a·2065·6c61·7073·6564··+.|i16·:·elapsed
00011fe0:·5469·6d65·2061·7373·6572·7420·6973·496e··Time·assert·isIn00011fe0:·5469·6d65·2061·7373·6572·7420·6973·496e··Time·assert·isIn
00011ff0:·7465·6772·6162·6c65·2041·3120·2020·2020··tegrable·A1·····00011ff0:·7465·6772·6162·6c65·2041·3120·2020·2020··tegrable·A1·····
00012000:·2020·2020·2020·2020·2020·2020·2020·2020··················00012000:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012010:·2020·2020·2020·2020·2020·2020·2020·2020··················00012010:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012020:·7c0a·7c20·2d2d·202e·3738·3432·3738·7320··|.|·--·.784278s·00012020:·7c0a·7c20·2d2d·2031·2e39·3431·3539·7320··|.|·--·1.94159s·
00012030:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed·········00012030:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed·········
00012040:·2020·2020·2020·2020·2020·2020·2020·2020··················00012040:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012050:·2020·2020·2020·2020·2020·2020·2020·2020··················00012050:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012060:·2020·2020·2020·2020·2020·2020·2020·2020··················00012060:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012070:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+-------------00012070:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+-------------
00012080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00012080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00012090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00012090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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00013a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00013a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00013a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00013a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00013a70:·2d2d·2d2d·2d2b·0a7c·6931·3920·3a20·656c··-----+.|i19·:·el00013a70:·2d2d·2d2d·2d2b·0a7c·6931·3920·3a20·656c··-----+.|i19·:·el
00013a80:·6170·7365·6454·696d·6520·4132·203d·2067··apsedTime·A2·=·g00013a80:·6170·7365·6454·696d·6520·4132·203d·2067··apsedTime·A2·=·g
00013a90:·6175·6765·5472·616e·7366·6f72·6d28·6368··augeTransform(ch00013a90:·6175·6765·5472·616e·7366·6f72·6d28·6368··augeTransform(ch
00013aa0:·616e·6765·4570·732c·2041·3129·3b20·2020··angeEps,·A1);···00013aa0:·616e·6765·4570·732c·2041·3129·3b20·2020··angeEps,·A1);···
00013ab0:·2020·2020·2020·2020·2020·2020·2020·2020··················00013ab0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013ac0:·2020·2020·207c·0a7c·202d·2d20·2e32·3831·······|.|·--·.28100013ac0:·2020·2020·207c·0a7c·202d·2d20·2e36·3135·······|.|·--·.615
00013ad0:·3137·3273·2065·6c61·7073·6564·2020·2020··172s·elapsed····00013ad0:·3935·3973·2065·6c61·7073·6564·2020·2020··959s·elapsed····
00013ae0:·2020·2020·2020·2020·2020·2020·2020·2020··················00013ae0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013af0:·2020·2020·2020·2020·2020·2020·2020·2020··················00013af0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013b00:·2020·2020·2020·2020·2020·2020·2020·2020··················00013b00:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013b10:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+--------00013b10:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+--------
00013b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00013b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00013b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00013b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00013b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00013b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00013b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00013b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00013b60:·2d2d·2d2d·2d2b·0a7c·6932·3020·3a20·656c··-----+.|i20·:·el00013b60:·2d2d·2d2d·2d2b·0a7c·6932·3020·3a20·656c··-----+.|i20·:·el
00013b70:·6170·7365·6454·696d·6520·6173·7365·7274··apsedTime·assert00013b70:·6170·7365·6454·696d·6520·6173·7365·7274··apsedTime·assert
00013b80:·2069·7349·6e74·6567·7261·626c·6520·4132···isIntegrable·A200013b80:·2069·7349·6e74·6567·7261·626c·6520·4132···isIntegrable·A2
00013b90:·2020·2020·2020·2020·2020·2020·2020·2020··················00013b90:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013ba0:·2020·2020·2020·2020·2020·2020·2020·2020··················00013ba0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013bb0:·2020·2020·207c·0a7c·202d·2d20·2e35·3730·······|.|·--·.57000013bb0:·2020·2020·207c·0a7c·202d·2d20·312e·3430·······|.|·--·1.40
00013bc0:·3031·3973·2065·6c61·7073·6564·2020·2020··019s·elapsed····00013bc0:·3736·3173·2065·6c61·7073·6564·2020·2020··761s·elapsed····
00013bd0:·2020·2020·2020·2020·2020·2020·2020·2020··················00013bd0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00013bf0:·2020·2020·2020·2020·2020·2020·2020·2020··················00013bf0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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0002c290:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c6f·3133··----------|.|o130002c290:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c6f·3133··----------|.|o13
0002c2a0:·203d·207c·7c20·2d31·3520·3920·2d34·2039···=·||·-15·9·-4·90002c2a0:·203d·207c·7c20·3133·2031·3520·3320·3336···=·||·13·15·3·36
0002c2b0:·202d·3437·202d·3720·3139·2033·3120·2d32···-47·-7·19·31·-2 
0002c2c0:·3220·2d31·3320·2d32·3320·2d33·3020·2d33··2·-13·-23·-30·-3 
0002c2d0:·3820·2d31·3620·2d31·3920·3339·202d·3138··8·-16·-19·39·-18 
0002c2e0:·2031·3620·3231·2033·3420·7c0a·7c20·2020···16·21·34·|.|···0002c2b0:·2032·2034·3820·3434·202d·3335·202d·3334···2·48·44·-35·-34
 0002c2c0:·2033·3920·3520·2d33·3220·3334·2031·3920···39·5·-32·34·19·
 0002c2d0:·2d34·3220·2d34·3720·2d31·3620·2d33·3420··-42·-47·-16·-34·
 0002c2e0:·2d33·3920·2d31·3320·2d31·7c0a·7c20·2020··-39·-13·-1|.|···
0002c2f0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c2f0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c330:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c330:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c340:·2020·207c·7c20·3437·2032·202d·3338·202d·····||·47·2·-38·- 
0002c350:·3335·202d·3439·202d·3335·202d·3230·2034··35·-49·-35·-20·4 
0002c360:·3820·2d34·3220·2d34·3820·2d32·3820·3231··8·-42·-48·-28·21 
0002c370:·202d·3135·202d·3238·202d·3130·202d·3437···-15·-28·-10·-47 
0002c380:·202d·3334·2034·3920·3338·7c0a·7c20·2020···-34·49·38|.|···0002c340:·2020·207c·7c20·2d34·3320·3438·2031·3420·····||·-43·48·14·
 0002c350:·3239·202d·3437·202d·3130·2034·3720·3232··29·-47·-10·47·22
 0002c360:·2038·202d·3437·2031·3520·2d32·3620·3220···8·-47·15·-26·2·
 0002c370:·3136·202d·3439·2032·3220·2d32·3820·2d31··16·-49·22·-28·-1
 0002c380:·3820·3435·202d·3438·202d·7c0a·7c20·2020··8·45·-48·-|.|···
0002c390:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c390:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c3e0:·2020·207c·7c20·3135·202d·3430·202d·3133·····||·15·-40·-130002c3e0:·2020·207c·7c20·2d33·2034·3520·3432·2034·····||·-3·45·42·4
0002c3f0:·202d·3435·202d·3332·2039·2033·3420·3130···-45·-32·9·34·10 
0002c400:·202d·3220·2d31·3120·3330·2031·3820·3437···-2·-11·30·18·47 
0002c410:·2031·3920·3330·202d·3136·202d·3137·2031···19·30·-16·-17·1 
0002c420:·3220·3720·3135·2033·3920·7c0a·7c20·2020··2·7·15·39·|.|···0002c3f0:·3720·2d35·3020·3136·202d·3330·2032·3820··7·-50·16·-30·28·
 0002c400:·3433·202d·3136·2032·3420·3139·2031·3520··43·-16·24·19·15·
 0002c410:·2d32·3320·3337·2033·3920·3139·202d·3820··-23·37·39·19·-8·
 0002c420:·3433·202d·3131·202d·3137·7c0a·7c20·2020··43·-11·-17|.|···
0002c430:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c430:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c440:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c440:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c470:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c470:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c480:·2020·207c·7c20·2d32·3220·2d33·3520·3134·····||·-22·-35·14 
0002c490:·202d·3239·202d·3336·202d·3134·202d·3138···-29·-36·-14·-18 
0002c4a0:·202d·3434·202d·3530·2031·2031·3420·3136···-44·-50·1·14·16 
0002c4b0:·2033·3620·3335·2035·2031·3120·2d32·3820···36·35·5·11·-28·0002c480:·2020·207c·7c20·2d34·3920·3720·3332·202d·····||·-49·7·32·-
 0002c490:·3620·2d33·3020·2d34·3120·2d31·3020·3220··6·-30·-41·-10·2·
 0002c4a0:·3434·2031·3120·2d32·3520·3420·3333·2034··44·11·-25·4·33·4
 0002c4b0:·3020·2d31·3920·3131·2033·3520·2d31·3720··0·-19·11·35·-17·
0002c4c0:·3336·202d·3338·2033·3320·7c0a·7c20·2020··36·-38·33·|.|···0002c4c0:·3436·2031·202d·3238·202d·7c0a·7c20·2020··46·1·-28·-|.|···
0002c4d0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c4d0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c4e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c4e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c4f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c4f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c510:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c510:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c520:·2020·207c·7c20·3133·202d·3335·202d·3339·····||·13·-35·-39 
0002c530:·2033·3520·3136·202d·3138·2034·3120·3335···35·16·-18·41·35 
0002c540:·202d·3135·202d·3133·202d·3236·202d·3436···-15·-13·-26·-46 
0002c550:·2032·3220·2d34·3720·2d32·202d·3233·202d···22·-47·-2·-23·- 
0002c560:·3337·202d·3530·202d·3720·7c0a·7c20·2020··37·-50·-7·|.|···0002c520:·2020·207c·7c20·3335·202d·3438·202d·3220·····||·35·-48·-2·
 0002c530:·3435·202d·3335·2032·3920·3334·2031·3220··45·-35·29·34·12·
 0002c540:·2d33·3220·2d32·3320·3530·2032·2032·2032··-32·-23·50·2·2·2
 0002c550:·3920·2d33·202d·3437·202d·3437·202d·3334··9·-3·-47·-47·-34
 0002c560:·2031·3520·2d31·3320·2d33·7c0a·7c20·2020···15·-13·-3|.|···
0002c570:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c570:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c5a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c5a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c5c0:·2020·207c·7c20·3139·202d·3131·202d·3233·····||·19·-11·-230002c5c0:·2020·207c·7c20·3437·2038·202d·3134·2036·····||·47·8·-14·6
0002c5d0:·202d·3331·202d·3335·202d·3336·2032·3820···-31·-35·-36·28· 
0002c5e0:·3430·2033·3820·3234·2034·3120·2d34·3720··40·38·24·41·-47· 
0002c5f0:·3330·202d·3138·2031·3320·3339·202d·3230··30·-18·13·39·-20 
0002c600:·2031·3520·3237·202d·3232·7c0a·7c20·2020···15·27·-22|.|···0002c5d0:·202d·3120·2d31·3320·2d37·2031·3620·2d32···-1·-13·-7·16·-2
 0002c5e0:·3020·3339·202d·3334·202d·3232·202d·3232··0·39·-34·-22·-22
 0002c5f0:·2033·3220·3137·202d·3920·2d31·3820·2d36···32·17·-9·-18·-6
 0002c600:·202d·3332·2032·3420·2d32·7c0a·7c20·2020···-32·24·-2|.|···
0002c610:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c610:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c650:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c650:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c660:·2020·207c·7c20·3431·2032·3920·3439·2031·····||·41·29·49·1 
0002c670:·3420·2d31·3120·3230·2031·3620·3238·202d··4·-11·20·16·28·- 
0002c680:·3438·202d·3230·2030·202d·3520·2d34·3820··48·-20·0·-5·-48· 
0002c690:·2d31·3520·2d34·3620·3339·2031·3720·3120··-15·-46·39·17·1· 
0002c6a0:·3020·3333·202d·3333·202d·7c0a·7c20·2020··0·33·-33·-|.|···0002c660:·2020·207c·7c20·2d32·202d·3336·202d·3339·····||·-2·-36·-39
 0002c670:·2034·3120·2d36·2033·3420·2d31·3020·3432···41·-6·34·-10·42
 0002c680:·2035·2033·3920·3230·2033·3320·3333·202d···5·39·20·33·33·-
 0002c690:·3439·202d·3135·202d·3333·202d·3135·2034··49·-15·-33·-15·4
 0002c6a0:·3120·2d31·3920·2d32·3020·7c0a·7c20·2020··1·-19·-20·|.|···
0002c6b0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c6b0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c6c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c6c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c6d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c6d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c6e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c6e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c6f0:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c6f0:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c700:·2020·207c·7c20·3339·202d·3335·2034·3920·····||·39·-35·49· 
0002c710:·3230·202d·3820·3431·202d·3320·3139·2032··20·-8·41·-3·19·2 
0002c720:·3320·2d31·3120·2d34·202d·3132·202d·3339··3·-11·-4·-12·-39 
0002c730:·2033·3620·3436·2039·202d·3439·202d·3335···36·46·9·-49·-35 
0002c740:·202d·3339·2034·202d·3236·7c0a·7c20·2020···-39·4·-26|.|···0002c700:·2020·207c·7c20·2d33·3020·3337·202d·3920·····||·-30·37·-9·
 0002c710:·3136·202d·3336·2031·3920·2d31·3320·2d31··16·-36·19·-13·-1
 0002c720:·3420·2d31·3920·3920·2d33·3320·3520·3420··4·-19·9·-33·5·4·
 0002c730:·3133·2034·3420·2d32·3620·3336·202d·3132··13·44·-26·36·-12
 0002c740:·2032·3220·2d31·3120·2d34·7c0a·7c20·2020···22·-11·-4|.|···
0002c750:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c750:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c760:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c760:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c790:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···0002c790:·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020··----------|.|···
0002c7a0:·2020·207c·7c20·3237·202d·3720·2d32·3820·····||·27·-7·-28·0002c7a0:·2020·207c·7c20·3237·2034·3120·3332·202d·····||·27·41·32·-
0002c7b0:·3331·2033·3020·3431·202d·3237·2034·3120··31·30·41·-27·41· 
0002c7c0:·3236·202d·3620·3232·202d·3520·3433·202d··26·-6·22·-5·43·- 
0002c7d0:·3820·2d34·3920·3336·202d·3238·202d·3138··8·-49·36·-28·-18 
0002c7e0:·202d·3320·2d32·3220·3431·7c0a·7c20·2020···-3·-22·41|.|···0002c7b0:·3434·2034·3020·2d32·3020·3431·2033·3320··44·40·-20·41·33·
 0002c7c0:·3238·2033·3620·3434·2033·3120·2d32·3220··28·36·44·31·-22·
 0002c7d0:·2d33·3020·3920·3431·202d·3820·3330·2031··-30·9·41·-8·30·1
 0002c7e0:·3620·2d36·202d·3238·2033·7c0a·7c20·2020··6·-6·-28·3|.|···
0002c7f0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------0002c7f0:·2020·202b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····+------------
0002c800:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c800:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c810:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c810:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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000085c0:·2c20·5420·7d2c·202d·2054·2054·2020·2d20··,·T·},·-·T·T··-·000085c0:·2c20·5420·7d2c·202d·2054·2054·2020·2d20··,·T·},·-·T·T··-·
000085d0:·5420·5420·202d·2054·2054·2020·2b20·7a2a··T·T··-·T·T··+·z*000085d0:·5420·5420·202b·2079·2a54·2020·202b·207a··T·T··+·y*T···+·z
000085e0:·5420·2020·2b20·782a·5420·2029·2c20·287b··T···+·x*T··),·({ 
000085f0:·5420·2c20·5420·7d2c·2054·2054·2020·2d20··T·,·T·},·T·T··-·000085e0:·2a54·2020·292c·2028·7b54·202c·2054·207d··*T··),·({T·,·T·}
 000085f0:·2c20·5420·5420·202d·207a·2a54·2020·202b··,·T·T··-·z*T···+
00008600:·2020·7c0a·7c20·2020·2020·2020·2020·2031····|.|··········100008600:·2020·7c0a·7c20·2020·2020·2020·2020·2034····|.|··········4
00008610:·2020·2038·2020·2020·2020·3320·3620·2020·····8······3·6···00008610:·2020·2038·2020·2020·2020·3220·3720·2020·····8······2·7···
00008620:·2035·2037·2020·2020·3120·3820·2020·2020···5·7····1·8····· 
00008630:·2031·3220·2020·2020·2031·3420·2020·2020···12······14·····00008620:·2034·2038·2020·2020·2020·3132·2020·2020···4·8······12····
 00008630:·2020·3134·2020·2020·2020·3320·2020·3920····14······3···9·
00008640:·2034·2020·2039·2020·2020·3420·3920·2020···4···9····4·9···00008640:·2020·2033·2039·2020·2020·2020·3135·2020·····3·9······15··
00008650:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----00008650:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----
00008660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008670:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008670:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008680:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008680:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008690:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008690:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000086a0:·2d2d·7c0a·7c20·2020·2020·2054·2054·2020··--|.|······T·T··000086a0:·2d2d·7c0a·7c20·2020·2020·2079·2a54·2020··--|.|······y*T··
000086b0:·202d·207a·2a54·2020·202b·207a·2a54·2020···-·z*T···+·z*T·· 
000086c0:·292c·2028·7b54·202c·2054·207d·2c20·2d20··),·({T·,·T·},·-·000086b0:·292c·2028·7b54·202c·2054·207d·2c20·2d20··),·({T·,·T·},·-·
000086d0:·5420·5420·202d·2054·2054·2020·2b20·792a··T·T··-·T·T··+·y*000086c0:·5420·5420·202d·2054·2054·2020·2d20·5420··T·T··-·T·T··-·T·
000086e0:·5420·2029·2c20·287b·5420·2c20·5420·7d2c··T··),·({T·,·T·},000086d0:·5420·202b·207a·2a54·2020·202b·2078·2a54··T··+·z*T···+·x*T
 000086e0:·2020·292c·2028·7b54·202c·2054·207d·2c20····),·({T·,·T·},·
000086f0:·202d·7c0a·7c20·2020·2020·2020·3520·3130···-|.|·······5·10000086f0:·2d20·7c0a·7c20·2020·2020·2020·2020·3137··-·|.|·········17
00008700:·2020·2020·2020·3137·2020·2020·2020·3139········17······19 
00008710:·2020·2020·2020·3220·2020·3820·2020·2020········2···8·····00008700:·2020·2020·2020·3320·2020·3620·2020·2020········3···6·····
00008720:·2032·2038·2020·2020·3520·3920·2020·2020···2·8····5·9·····00008710:·2033·2036·2020·2020·3520·3720·2020·2031···3·6····5·7····1
 00008720:·2038·2020·2020·2020·3132·2020·2020·2020···8······12······
00008730:·2031·3520·2020·2020·2035·2020·2037·2020···15······5···7··00008730:·3134·2020·2020·2020·3120·2020·3720·2020··14······1···7···
00008740:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----00008740:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----
00008750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008760:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008760:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008790:·2d2d·7c0a·7c20·2020·2020·2054·2054·2020··--|.|······T·T··00008790:·2d2d·7c0a·7c20·2020·2020·2054·2054·2020··--|.|······T·T··
 000087a0:·2b20·782a·5420·2029·2c20·287b·5420·2c20··+·x*T··),·({T·,·
000087a0:·2d20·5420·5420·202d·2054·2054·2020·2b20··-·T·T··-·T·T··+·000087b0:·5420·7d2c·202d·2054·2054·2020·2d20·5420··T·},·-·T·T··-·T·
000087b0:·7a2a·5420·2020·2b20·782a·5420·2029·2c20··z*T···+·x*T··),·000087c0:·5420·202b·2079·2a54·2020·292c·2028·7b54··T··+·y*T··),·({T
000087c0:·287b·5420·2c20·5420·7d2c·2054·2054·2020··({T·,·T·},·T·T··000087d0:·202c·2054·2020·7d2c·202d·2054·2054·2020···,·T··},·-·T·T··
000087d0:·2b20·5420·5420·202b·2054·2054·2020·2b20··+·T·T··+·T·T··+· 
000087e0:·2020·7c0a·7c20·2020·2020·2020·3320·3620····|.|·······3·6·000087e0:·2b20·7c0a·7c20·2020·2020·2020·3120·3720··+·|.|·······1·7·
000087f0:·2020·2035·2037·2020·2020·3120·3820·2020·····5·7····1·8···000087f0:·2020·2020·2031·3320·2020·2020·2035·2020·······13······5··
00008800:·2020·2031·3220·2020·2020·2031·3420·2020·····12······14···00008800:·2039·2020·2020·2020·3220·3820·2020·2035···9······2·8····5
00008810:·2020·2034·2020·2039·2020·2020·3220·3620·····4···9····2·6· 
00008820:·2020·2033·2038·2020·2020·3420·3920·2020·····3·8····4·9···00008810:·2039·2020·2020·2020·3135·2020·2020·2020···9······15······
 00008820:·3320·2020·3130·2020·2020·2020·3420·3820··3···10······4·8·
00008830:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----00008830:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----
00008840:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008840:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008860:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008860:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008870:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008870:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008880:·2d2d·7c0a·7c20·2020·2020·2079·2a54·2020··--|.|······y*T··00008880:·2d2d·7c0a·7c20·2020·2020·2054·2054·2020··--|.|······T·T··
00008890:·202d·207a·2a54·2020·292c·2028·7b54·202c···-·z*T··),·({T·,00008890:·202d·207a·2a54·2020·202b·2078·2a54·2020···-·z*T···+·x*T··
000088a0:·2054·2020·7d2c·2054·2054·2020·2b20·5420···T··},·T·T··+·T·000088a0:·292c·2028·7b54·202c·2054·207d·2c20·2d20··),·({T·,·T·},·-·
000088b0:·5420·2020·2d20·7a2a·5420·2020·2b20·792a··T···-·z*T···+·y*000088b0:·5420·5420·202d·2054·2054·2020·2b20·792a··T·T··-·T·T··+·y*
000088c0:·5420·2029·2c20·287b·5420·2c20·5420·7d2c··T··),·({T·,·T·},000088c0:·5420·2020·2b20·7a2a·5420·2029·2c20·2020··T···+·z*T··),···
000088d0:·2020·7c0a·7c20·2020·2020·2020·2020·3134····|.|·········14000088d0:·2020·7c0a·7c20·2020·2020·2020·3320·3130····|.|·······3·10
000088e0:·2020·2020·2020·3137·2020·2020·2020·3320········17······3·000088e0:·2020·2020·2020·3138·2020·2020·2020·3139········18······19
000088f0:·2020·3130·2020·2020·3520·3620·2020·2033····10····5·6····3000088f0:·2020·2020·2020·3220·2020·3720·2020·2020········2···7·····
 00008900:·2032·2037·2020·2020·3420·3820·2020·2020···2·7····4·8·····
00008900:·2031·3020·2020·2020·2031·3820·2020·2020···10······18·····00008910:·2031·3220·2020·2020·2031·3420·2020·2020···12······14·····
00008910:·2032·3020·2020·2020·2035·2020·2036·2020···20······5···6·· 
00008920:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----00008920:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----
00008930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008960:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008960:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008970:·2d2d·7c0a·7c20·2020·2020·2054·2054·2020··--|.|······T·T··00008970:·2d2d·7c0a·7c20·2020·2020·2028·7b54·202c··--|.|······({T·,
00008980:·2b20·5420·5420·2020·2d20·7a2a·5420·2020··+·T·T···-·z*T··· 
00008990:·2b20·792a·5420·2029·2c20·287b·5420·2c20··+·y*T··),·({T·,· 
000089a0:·5420·207d·2c20·2d20·5420·5420·202d·2054··T··},·-·T·T··-·T00008980:·2054·207d·2c20·2d20·5420·5420·202b·2054···T·},·-·T·T··+·T
000089b0:·2054·2020·202b·207a·2a54·2020·202b·2020···T···+·z*T···+··00008990:·2054·2020·202d·207a·2a54·2020·202b·2078···T···-·z*T···+·x
 000089a0:·2a54·2020·292c·2028·7b54·202c·2054·2020··*T··),·({T·,·T··
 000089b0:·7d2c·202d·2054·2054·2020·2d20·5420·5420··},·-·T·T··-·T·T·
000089c0:·2020·7c0a·7c20·2020·2020·2020·3520·3620····|.|·······5·6·000089c0:·2020·7c0a·7c20·2020·2020·2020·2020·3420····|.|·········4·
000089d0:·2020·2033·2031·3020·2020·2020·2031·3820·····3·10······18· 
000089e0:·2020·2020·2032·3020·2020·2020·2034·2020·······20······4·· 
000089f0:·2031·3020·2020·2020·2035·2037·2020·2020···10······5·7····000089d0:·2020·3820·2020·2020·2034·2038·2020·2020····8······4·8····
00008a00:·3420·3130·2020·2020·2020·3132·2020·2020··4·10······12····000089e0:·3320·3130·2020·2020·2020·3138·2020·2020··3·10······18····
 000089f0:·2020·3139·2020·2020·2020·3220·2020·3130····19······2···10
 00008a00:·2020·2020·2020·3520·3820·2020·2032·2031········5·8····2·1
00008a10:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----00008a10:·3020·7c0a·7c20·2020·2020·202d·2d2d·2d2d··0·|.|······-----
00008a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008a30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008a30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008a60:·2d2d·7c0a·7c20·2020·2020·207a·2a54·2020··--|.|······z*T··00008a60:·2d2d·7c0a·7c20·2020·2020·202b·2079·2a54··--|.|······+·y*T
 00008a70:·2020·292c·2028·7b54·202c·2054·2020·7d2c····),·({T·,·T··},
 00008a80:·202d·2054·2054·2020·202b·2078·2a54·2020···-·T·T···+·x*T··
00008a70:·292c·2028·7b54·202c·2054·207d·2c20·2d20··),·({T·,·T·},·-·00008a90:·292c·2028·7b54·202c·2054·207d·2c20·2d20··),·({T·,·T·},·-·
00008a80:·5420·5420·202d·2054·2054·2020·2b20·782a··T·T··-·T·T··+·x*00008aa0:·5420·5420·202d·2054·2054·2020·202b·2020··T·T··-·T·T···+··
00008a90:·5420·2029·2c20·287b·5420·2c20·5420·7d2c··T··),·({T·,·T·}, 
00008aa0:·2054·2054·2020·2b20·5420·5420·202d·2020···T·T··+·T·T··-·· 
00008ab0:·2020·7c0a·7c20·2020·2020·2020·2020·3230····|.|·········2000008ab0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|···········
 00008ac0:·3139·2020·2020·2020·3420·2020·3130·2020··19······4···10··
 00008ad0:·2020·2020·3420·3130·2020·2020·2020·3138······4·10······18
00008ac0:·2020·2020·2020·3120·2020·3620·2020·2020········1···6·····00008ae0:·2020·2020·2020·3520·2020·3820·2020·2020········5···8·····
00008ad0:·2031·2036·2020·2020·3420·3720·2020·2020···1·6····4·7·····00008af0:·2035·2038·2020·2020·3220·3130·2020·2020···5·8····2·10····
00008ae0:·2031·3120·2020·2020·2033·2020·2039·2020···11······3···9·· 
00008af0:·2020·3520·3820·2020·2033·2039·2020·2020····5·8····3·9···· 
00008b00:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----00008b00:·2020·7c0a·7c20·2020·2020·202d·2d2d·2d2d····|.|······-----
00008b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00008b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00008b50:·2d2d·7c0a·7c20·2020·2020·207a·2a54·2020··--|.|······z*T··00008b50:·2d2d·7c0a·7c20·2020·2020·2079·2a54·2020··--|.|······y*T··
 00008b60:·292c·2028·7b54·202c·2054·207d·2c20·5420··),·({T·,·T·},·T·
 00008b70:·5420·202b·2078·2a54·2020·202d·207a·2a54··T··+·x*T···-·z*T
00008b60:·202b·2078·2a54·2020·292c·2028·7b54·202c···+·x*T··),·({T·, 
00008b70:·2054·207d·2c20·5420·5420·202b·2054·2054···T·},·T·T··+·T·T 
00008b80:·2020·2d20·7a2a·5420·2020·2b20·792a·5420····-·z*T···+·y*T· 
00008b90:·2029·2c20·287b·5420·2c20·5420·207d·2c20···),·({T·,·T··},·00008b80:·2020·292c·2028·7b54·202c·2054·207d·2c20····),·({T·,·T·},·
 00008b90:·2d20·5420·5420·202d·2054·2054·2020·2d20··-·T·T··-·T·T··-·
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Offset 1860, 15 lines modifiedOffset 1860, 15 lines modified
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00007440:·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a·204c··-------+.|i4·:·L00007440:·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a·204c··-------+.|i4·:·L
00007450:·203d·2061·6e61·6c79·7a65·5374·7261·6e64···=·analyzeStrand00007450:·203d·2061·6e61·6c79·7a65·5374·7261·6e64···=·analyzeStrand
00007460:·2846·2c61·293b·2023·4c20·2020·2020·2020··(F,a);·#L·······00007460:·2846·2c61·293b·2023·4c20·2020·2020·2020··(F,a);·#L·······
00007470:·2020·2020·2020·2020·2020·2020·2020·2020··················00007470:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007480:·2020·2020·2020·2020·2020·2020·2020·2020··················00007480:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007490:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.000007490:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.0
000074a0:·3233·3138·3535·7320·656c·6170·7365·6420··231855s·elapsed·000074a0:·3233·3539·3231·7320·656c·6170·7365·6420··235921s·elapsed·
000074b0:·2020·2020·2020·2020·2020·2020·2020·2020··················000074b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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000074f0:·2020·2020·2020·2020·2020·2020·2020·2020··················000074f0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007500:·2020·2020·2020·2020·2020·2020·2020·2020··················00007500:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007510:·2020·2020·2020·2020·2020·2020·2020·2020··················00007510:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 1995, 35 lines modifiedOffset 1995, 35 lines modified
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00007cb0:·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20··-------+.|i10·:·00007cb0:·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20··-------+.|i10·:·
00007cc0:·6361·7270·6574·4265·7474·6954·6162·6c65··carpetBettiTable00007cc0:·6361·7270·6574·4265·7474·6954·6162·6c65··carpetBettiTable
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00007d00:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.000007d00:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.0
00007d10:·3032·3239·3032·3973·2065·6c61·7073·6564··0229029s·elapsed00007d10:·3032·3235·3930·3973·2065·6c61·7073·6564··0225909s·elapsed
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00007d30:·2020·2020·2020·2020·2020·2020·2020·2020··················00007d30:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007d40:·2020·2020·2020·2020·2020·2020·2020·2020··················00007d40:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007d50:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.000007d50:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.0
00007d60:·3036·3230·3933·3173·2065·6c61·7073·6564··0620931s·elapsed00007d60:·3332·3530·3031·7320·656c·6170·7365·6420··325001s·elapsed·
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00007d90:·2020·2020·2020·2020·2020·2020·2020·2020··················00007d90:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007da0:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.000007da0:·2020·2020·2020·207c·0a7c·202d·2d20·2e31·········|.|·--·.1
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00007df0:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.000007df0:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.0
00007e00:·3039·3031·3730·3573·2065·6c61·7073·6564··0901705s·elapsed00007e00:·3333·3036·3573·2065·6c61·7073·6564·2020··33065s·elapsed··
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00007e30:·2020·2020·2020·2020·2020·2020·2020·2020··················00007e30:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007e40:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.000007e40:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.0
00007e50:·3033·3332·3030·3873·2065·6c61·7073·6564··0332008s·elapsed00007e50:·3038·3737·3632·3673·2065·6c61·7073·6564··0877626s·elapsed
00007e60:·2020·2020·2020·2020·2020·2020·2020·2020··················00007e60:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007e70:·2020·2020·2020·2020·2020·2020·2020·2020··················00007e70:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007e80:·2020·2020·2020·2020·2020·2020·2020·2020··················00007e80:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007e90:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······00007e90:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······
00007ea0:·2020·2020·2020·2020·2020·2020·2020·2020··················00007ea0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007eb0:·2020·2020·2020·2020·2020·2020·2020·2020··················00007eb0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007ec0:·2020·2020·2020·2020·2020·2020·2020·2020··················00007ec0:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 3677, 34 lines modifiedOffset 3677, 34 lines modified
0000e5c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000e5c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000e5d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000e5d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000e5e0:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a·2065··-------+.|i2·:·e0000e5e0:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a·2065··-------+.|i2·:·e
0000e5f0:·6c61·7073·6564·5469·6d65·2054·3d63·6172··lapsedTime·T=car0000e5f0:·6c61·7073·6564·5469·6d65·2054·3d63·6172··lapsedTime·T=car
0000e600:·7065·7442·6574·7469·5461·626c·6528·612c··petBettiTable(a,0000e600:·7065·7442·6574·7469·5461·626c·6528·612c··petBettiTable(a,
0000e610:·622c·3329·2020·2020·2020·2020·2020·2020··b,3)············0000e610:·622c·3329·2020·2020·2020·2020·2020·2020··b,3)············
0000e620:·2020·2020·7c0a·7c20·2d2d·202e·3030·3232······|.|·--·.00220000e620:·2020·2020·7c0a·7c20·2d2d·202e·3030·3232······|.|·--·.0022
0000e630:·3930·3232·7320·656c·6170·7365·6420·2020··9022s·elapsed···0000e630:·3332·3773·2065·6c61·7073·6564·2020·2020··327s·elapsed····
0000e640:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e640:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e650:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e650:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e660:·207c·0a7c·202d·2d20·2e30·3035·3839·3338···|.|·--·.00589380000e660:·207c·0a7c·202d·2d20·2e30·3036·3337·3433···|.|·--·.0063743
0000e670:·3973·2065·6c61·7073·6564·2020·2020·2020··9s·elapsed······0000e670:·3773·2065·6c61·7073·6564·2020·2020·2020··7s·elapsed······
0000e680:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e680:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e690:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.0000e690:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
0000e6a0:·7c20·2d2d·202e·3032·3030·3432·3673·2065··|·--·.0200426s·e0000e6a0:·7c20·2d2d·202e·3032·3432·3535·3173·2065··|·--·.0242551s·e
0000e6b0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········0000e6b0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········
0000e6c0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e6c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e6d0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·-0000e6d0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·-
0000e6e0:·2d20·2e30·3130·3830·3433·7320·656c·6170··-·.0108043s·elap0000e6e0:·2d20·2e30·3233·3938·3434·7320·656c·6170··-·.0239844s·elap
0000e6f0:·7365·6420·2020·2020·2020·2020·2020·2020··sed·············0000e6f0:·7365·6420·2020·2020·2020·2020·2020·2020··sed·············
0000e700:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e700:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e710:·2020·2020·2020·2020·7c0a·7c20·2d2d·202e··········|.|·--·.0000e710:·2020·2020·2020·2020·7c0a·7c20·2d2d·202e··········|.|·--·.
0000e720:·3030·3431·3730·3738·7320·656c·6170·7365··00417078s·elapse0000e720:·3030·3334·3032·3332·7320·656c·6170·7365··00340232s·elapse
0000e730:·6420·2020·2020·2020·2020·2020·2020·2020··d···············0000e730:·6420·2020·2020·2020·2020·2020·2020·2020··d···············
0000e740:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e740:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e750:·2020·2020·207c·0a7c·202d·2d20·2e33·3739·······|.|·--·.3790000e750:·2020·2020·207c·0a7c·202d·2d20·2e35·3839·······|.|·--·.589
0000e760:·3731·3373·2065·6c61·7073·6564·2020·2020··713s·elapsed····0000e760:·3739·3973·2065·6c61·7073·6564·2020·2020··799s·elapsed····
0000e770:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e770:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e780:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e780:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e790:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|···········0000e790:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|···········
0000e7a0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e7a0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e7b0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000e7b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000e7c0:·2020·2020·2020·2020·2020·2020·2020·207c·················|0000e7c0:·2020·2020·2020·2020·2020·2020·2020·207c·················|
0000e7d0:·0a7c·2020·2020·2020·2020·2020·2020·3020··.|············0·0000e7d0:·0a7c·2020·2020·2020·2020·2020·2020·3020··.|············0·
Offset 3764, 15 lines modifiedOffset 3764, 15 lines modified
0000eb30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000eb30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000eb40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000eb40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000eb50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000eb50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000eb60:·2d2d·2b0a·7c69·3420·3a20·656c·6170·7365··--+.|i4·:·elapse0000eb60:·2d2d·2b0a·7c69·3420·3a20·656c·6170·7365··--+.|i4·:·elapse
0000eb70:·6454·696d·6520·5427·3d6d·696e·696d·616c··dTime·T'=minimal0000eb70:·6454·696d·6520·5427·3d6d·696e·696d·616c··dTime·T'=minimal
0000eb80:·4265·7474·6920·4a20·2020·2020·2020·2020··Betti·J·········0000eb80:·4265·7474·6920·4a20·2020·2020·2020·2020··Betti·J·········
0000eb90:·2020·2020·2020·2020·2020·2020·2020·207c·················|0000eb90:·2020·2020·2020·2020·2020·2020·2020·207c·················|
0000eba0:·0a7c·202d·2d20·2e31·3533·3638·3873·2065··.|·--·.153688s·e0000eba0:·0a7c·202d·2d20·2e33·3931·3738·3873·2065··.|·--·.391788s·e
0000ebb0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········0000ebb0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········
0000ebc0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000ebc0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000ebd0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|·0000ebd0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|·
0000ebe0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000ebe0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000ebf0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000ebf0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000ec00:·2020·2020·2020·2020·2020·2020·2020·2020··················0000ec00:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000ec10:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|····0000ec10:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|····
Offset 3848, 42 lines modifiedOffset 3848, 42 lines modified
0000f070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000f070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000f080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000f080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000f090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000f090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000f0a0:·2b0a·7c69·3620·3a20·656c·6170·7365·6454··+.|i6·:·elapsedT0000f0a0:·2b0a·7c69·3620·3a20·656c·6170·7365·6454··+.|i6·:·elapsedT
0000f0b0:·696d·6520·683d·6361·7270·6574·4265·7474··ime·h=carpetBett0000f0b0:·696d·6520·683d·6361·7270·6574·4265·7474··ime·h=carpetBett
0000f0c0:·6954·6162·6c65·7328·362c·3629·3b20·2020··iTables(6,6);···0000f0c0:·6954·6162·6c65·7328·362c·3629·3b20·2020··iTables(6,6);···
0000f0d0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.|0000f0d0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.|
0000f0e0:·202d·2d20·2e30·3034·3137·3831·3373·2065···--·.00417813s·e0000f0e0:·202d·2d20·2e30·3034·3631·3835·3873·2065···--·.00461858s·e
0000f0f0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········0000f0f0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed··········
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0000a5e0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000a5e0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000a5f0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+----0000a5f0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+----
0000a600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000a600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000a610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000a610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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0000a630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.|0000a630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.|
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00026e40:·2020·2020·2020·2020·2020·2020·2020·2020··················00026e40:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00026e90:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+--------------00026e90:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+--------------
00026ea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00026ea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00026eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00026eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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00026ed0:·2023·6175·7446·3720·2020·2020·2020·2020···#autF7·········00026ed0:·2023·6175·7446·3720·2020·2020·2020·2020···#autF7·········
00026ee0:·2020·2020·2020·2020·2020·2020·2020·2020··················00026ee0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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0002c360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0002c360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0002c370:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·:0002c370:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·:
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0002c390:·362c·204d·3529·2020·2020·2020·2020·2020··6,·M5)··········0002c390:·362c·204d·3529·2020·2020·2020·2020·2020··6,·M5)··········
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0002c3c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--·0002c3c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--·
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0002c3e0:·7075·293b·2030·2e39·3734·3733·3673·2028··pu);·0.974736s·( 
0002c3f0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc)0002c3e0:·7075·293b·2031·2e30·3834·3137·7320·2874··pu);·1.08417s·(t
 0002c3f0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)·
0002c400:·2020·2020·2020·2020·2020·2020·2020·2020··················0002c400:·2020·2020·2020·2020·2020·2020·2020·2020··················
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0003a600:·2d2b·0a7c·6935·203a·2074·696d·6520·6973··-+.|i5·:·time·is0003a600:·2d2b·0a7c·6935·203a·2074·696d·6520·6973··-+.|i5·:·time·is
0003a610:·6f6d·6f72·7068·6973·6d28·4d35·2c20·6d69··omorphism(M5,·mi0003a610:·6f6d·6f72·7068·6973·6d28·4d35·2c20·6d69··omorphism(M5,·mi
0003a620:·6e6f·724d·3629·2020·2020·2020·2020·2020··norM6)··········0003a620:·6e6f·724d·3629·2020·2020·2020·2020·2020··norM6)··········
0003a630:·2020·2020·2020·2020·2020·2020·2020·2020··················0003a630:·2020·2020·2020·2020·2020·2020·2020·2020··················
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0003a670:·2e30·3131·3733·3933·7320·2874·6872·6561··.0117393s·(threa0003a670:·2e30·3131·3936·3639·7320·2874·6872·6561··.0119669s·(threa
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0003a690:·2020·2020·2020·2020·2020·2020·2020·2020··················0003a690:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003a6a0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············0003a6a0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············
0003a6b0:·2020·2020·2020·2020·2020·2020·2020·2020··················0003a6b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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0003b170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0003b170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0003b180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0003b180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0003b190:·2d2b·0a7c·6938·203a·2074·696d·6520·7068··-+.|i8·:·time·ph0003b190:·2d2b·0a7c·6938·203a·2074·696d·6520·7068··-+.|i8·:·time·ph
0003b1a0:·6920·3d20·6973·6f6d·6f72·7068·6973·6d28··i·=·isomorphism(0003b1a0:·6920·3d20·6973·6f6d·6f72·7068·6973·6d28··i·=·isomorphism(
0003b1b0:·4e2c·4d36·2920·2020·2020·2020·2020·2020··N,M6)···········0003b1b0:·4e2c·4d36·2920·2020·2020·2020·2020·2020··N,M6)···········
0003b1c0:·2020·2020·2020·2020·2020·2020·2020·2020··················0003b1c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003b1d0:·2020·2020·2020·2020·2020·2020·2020·2020··················0003b1d0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003b1e0:·207c·0a7c·202d·2d20·7573·6564·2033·2e37···|.|·--·used·3.70003b1e0:·207c·0a7c·202d·2d20·7573·6564·2034·2e32···|.|·--·used·4.2
0003b1f0:·3138·3433·7320·2863·7075·293b·2032·2e34··1843s·(cpu);·2.40003b1f0:·3133·3133·7320·2863·7075·293b·2032·2e35··1313s·(cpu);·2.5
0003b200:·3631·3236·7320·2874·6872·6561·6429·3b20··6126s·(thread);·0003b200:·3236·3136·7320·2874·6872·6561·6429·3b20··2616s·(thread);·
0003b210:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)·········0003b210:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)·········
0003b220:·2020·2020·2020·2020·2020·2020·2020·2020··················0003b220:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003b230:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············0003b230:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············
0003b240:·2020·2020·2020·2020·2020·2020·2020·2020··················0003b240:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003b250:·2020·2020·2020·2020·2020·2020·2020·2020··················0003b250:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003b260:·2020·2020·2020·2020·2020·2020·2020·2020··················0003b260:·2020·2020·2020·2020·2020·2020·2020·2020··················
0003b270:·2020·2020·2020·2020·2020·2020·2020·2020··················0003b270:·2020·2020·2020·2020·2020·2020·2020·2020··················
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000477a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000477a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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000477d0:·2052·3130·2020·2020·2020·2020·2020·2020···R10············000477d0:·2052·3130·2020·2020·2020·2020·2020·2020···R10············
000477e0:·2020·2020·2020·2020·2020·2020·2020·2020··················000477e0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00047800:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used00047800:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used
00047810:·2030·2e30·3437·3435·3538·7320·2863·7075···0.0474558s·(cpu00047810:·2030·2e30·3438·3033·7320·2863·7075·293b···0.04803s·(cpu);
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000478a0:·2020·2020·207c·0a7c·6f31·3020·3d20·7472·······|.|o10·=·tr000478a0:·2020·2020·207c·0a7c·6f31·3020·3d20·7472·······|.|o10·=·tr
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Offset 9899, 16 lines modifiedOffset 9899, 16 lines modified
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0000c0b0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c0b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c0c0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c0c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c0d0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.0000c0d0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
0000c0e0:·7c6f·3920·3d20·2836·392c·2038·312c·2039··|o9·=·(69,·81,·90000c0e0:·7c6f·3920·3d20·2837·332c·2038·312c·2038··|o9·=·(73,·81,·8
0000c0f0:·302c·2039·362c·2038·382c·2039·342c·2039··0,·96,·88,·94,·90000c0f0:·372c·2039·352c·2039·342c·2039·372c·2039··7,·95,·94,·97,·9
0000c100:·382c·2039·372c·2039·372c·2039·342c·2039··8,·97,·97,·94,·90000c100:·382c·2039·362c·2039·362c·2039·352c·2039··8,·96,·96,·95,·9
0000c110:·332c·2039·372c·2039·372c·2039·382c·2031··3,·97,·97,·98,·1 
0000c120:·3030·2c20·3936·2c20·3938·2c20·2020·7c0a··00,·96,·98,···|.0000c110:·322c·2039·392c·2039·392c·2039·372c·2039··2,·99,·99,·97,·9
 0000c120:·372c·2039·362c·2039·382c·2039·392c·7c0a··7,·96,·98,·99,|.
0000c130:·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d·2d2d··|·····----------0000c130:·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d·2d2d··|·····----------
0000c140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000c140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000c150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000c150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000c160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000c160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000c170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|.0000c170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|.
0000c180:·7c20·2020·2020·3939·2c20·3938·2c20·3937··|·····99,·98,·970000c180:·7c20·2020·2020·3936·2c20·3938·2c20·3936··|·····96,·98,·96
0000c190:·2c20·3939·2c20·3938·2c20·3937·2c20·3939··,·99,·98,·97,·990000c190:·2c20·3935·2c20·3938·2c20·3938·2c20·3938··,·95,·98,·98,·98
0000c1a0:·2c20·3937·2c20·3939·2c20·3938·2c20·3936··,·97,·99,·98,·960000c1a0:·2c20·3937·2c20·3935·2c20·3938·2c20·3130··,·97,·95,·98,·10
0000c1b0:·2c20·3937·2920·2020·2020·2020·2020·2020··,·97)···········0000c1b0:·3029·2020·2020·2020·2020·2020·2020·2020··0)··············
0000c1c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.0000c1c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
0000c1d0:·7c20·2020·2020·2020·2020·2020·2020·2020··|···············0000c1d0:·7c20·2020·2020·2020·2020·2020·2020·2020··|···············
0000c1e0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c1e0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c1f0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c1f0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c200:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c200:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c210:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.0000c210:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
0000c220:·7c6f·3920·3a20·5365·7175·656e·6365·2020··|o9·:·Sequence··0000c220:·7c6f·3920·3a20·5365·7175·656e·6365·2020··|o9·:·Sequence··
Offset 3130, 26 lines modifiedOffset 3130, 26 lines modified
0000c390:·616e·646f·6d47·7261·7068·7328·6e2c·2031··andomGraphs(n,·10000c390:·616e·646f·6d47·7261·7068·7328·6e2c·2031··andomGraphs(n,·1
0000c3a0:·3030·2c20·2870·726f·6220·6e29·2f32·7c0a··00,·(prob·n)/2|.0000c3a0:·3030·2c20·2870·726f·6220·6e29·2f32·7c0a··00,·(prob·n)/2|.
0000c3b0:·7c20·2020·2020·2020·2020·2020·2020·2020··|···············0000c3b0:·7c20·2020·2020·2020·2020·2020·2020·2020··|···············
0000c3c0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c3c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c3d0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c3d0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c3e0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c3e0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c3f0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.0000c3f0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
0000c400:·7c6f·3130·203d·2028·3136·2c20·392c·2033··|o10·=·(16,·9,·30000c400:·7c6f·3130·203d·2028·3139·2c20·382c·2036··|o10·=·(19,·8,·6
0000c410:·2c20·352c·2032·2c20·342c·2031·2c20·322c··,·5,·2,·4,·1,·2,0000c410:·2c20·352c·2032·2c20·352c·2031·2c20·312c··,·5,·2,·5,·1,·1,
0000c420:·2032·2c20·312c·2032·2c20·322c·2032·2c20···2,·1,·2,·2,·2,·0000c420:·2030·2c20·312c·2032·2c20·312c·2031·2c20···0,·1,·2,·1,·1,·
0000c430:·322c·2031·2c20·302c·2032·2c20·322c·2032··2,·1,·0,·2,·2,·20000c430:·302c·2031·2c20·302c·2030·2c20·302c·2031··0,·1,·0,·0,·0,·1
0000c440:·2c20·302c·2030·2c20·302c·2030·2c20·7c0a··,·0,·0,·0,·0,·|.0000c440:·2c20·312c·2030·2c20·322c·2030·2c20·7c0a··,·1,·0,·2,·0,·|.
0000c450:·7c20·2020·2020·202d·2d2d·2d2d·2d2d·2d2d··|······---------0000c450:·7c20·2020·2020·202d·2d2d·2d2d·2d2d·2d2d··|······---------
0000c460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000c460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000c470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000c470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000c480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0000c480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0000c490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|.0000c490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|.
0000c4a0:·7c20·2020·2020·2032·2c20·312c·2030·2c20··|······2,·1,·0,·0000c4a0:·7c20·2020·2020·2031·2c20·302c·2030·2c20··|······1,·0,·0,·
0000c4b0:·312c·2031·2c20·3029·2020·2020·2020·2020··1,·1,·0)········0000c4b0:·302c·2030·2c20·3129·2020·2020·2020·2020··0,·0,·1)········
0000c4c0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c4c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c4d0:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c4d0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c4e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.0000c4e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
0000c4f0:·7c20·2020·2020·2020·2020·2020·2020·2020··|···············0000c4f0:·7c20·2020·2020·2020·2020·2020·2020·2020··|···············
0000c500:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c500:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c510:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c510:·2020·2020·2020·2020·2020·2020·2020·2020··················
0000c520:·2020·2020·2020·2020·2020·2020·2020·2020··················0000c520:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 4611, 16 lines modifiedOffset 4611, 16 lines modified
00012020:·2b0a·7c69·3220·3a20·6765·6e65·7261·7465··+.|i2·:·generate00012020:·2b0a·7c69·3220·3a20·6765·6e65·7261·7465··+.|i2·:·generate
00012030:·5261·6e64·6f6d·4772·6170·6873·2835·2c20··RandomGraphs(5,·00012030:·5261·6e64·6f6d·4772·6170·6873·2835·2c20··RandomGraphs(5,·
00012040:·3529·2020·2020·2020·2020·2020·2020·2020··5)··············00012040:·3529·2020·2020·2020·2020·2020·2020·2020··5)··············
00012050:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|·····00012050:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|·····
00012060:·2020·2020·2020·2020·2020·2020·2020·2020··················00012060:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012070:·2020·2020·2020·2020·2020·2020·2020·2020··················00012070:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012080:·2020·2020·2020·2020·2020·2020·2020·2020··················00012080:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012090:·7c0a·7c6f·3220·3d20·7b44·5263·2c20·4472··|.|o2·=·{DRc,·Dr00012090:·7c0a·7c6f·3220·3d20·7b44·5d4b·2c20·447b··|.|o2·=·{D]K,·D{
000120a0:·7b2c·2044·6a67·2c20·4478·772c·2044·577b··{,·Djg,·Dxw,·DW{000120a0:·432c·2044·556b·2c20·4443·6f2c·2044·6a73··C,·DUk,·DCo,·Djs
000120b0:·7d20·2020·2020·2020·2020·2020·2020·2020··}···············000120b0:·7d20·2020·2020·2020·2020·2020·2020·2020··}···············
000120c0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|·····000120c0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|·····
000120d0:·2020·2020·2020·2020·2020·2020·2020·2020··················000120d0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000120e0:·2020·2020·2020·2020·2020·2020·2020·2020··················000120e0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000120f0:·2020·2020·2020·2020·2020·2020·2020·2020··················000120f0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012100:·7c0a·7c6f·3220·3a20·4c69·7374·2020·2020··|.|o2·:·List····00012100:·7c0a·7c6f·3220·3a20·4c69·7374·2020·2020··|.|o2·:·List····
00012110:·2020·2020·2020·2020·2020·2020·2020·2020··················00012110:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 4855, 16 lines modifiedOffset 4855, 16 lines modified
00012f60:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|·············00012f60:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|·············
00012f70:·2020·2020·2020·2020·2020·2020·2020·2020··················00012f70:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012f80:·2020·2020·2020·2020·2020·2020·2020·2020··················00012f80:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012f90:·2020·2020·2020·2020·2020·2020·2020·2020··················00012f90:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012fa0:·2020·2020·2020·2020·2020·2020·2020·2020··················00012fa0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00012fb0:·7c0a·7c6f·3220·3d20·7b47·7261·7068·7b22··|.|o2·=·{Graph{"00012fb0:·7c0a·7c6f·3220·3d20·7b47·7261·7068·7b22··|.|o2·=·{Graph{"
00012fc0:·6564·6765·7322·203d·3e20·7b7b·612c·2062··edges"·=>·{{a,·b00012fc0:·6564·6765·7322·203d·3e20·7b7b·612c·2062··edges"·=>·{{a,·b
00012fd0:·7d2c·207b·622c·2063·7d2c·207b·632c·2064··},·{b,·c},·{c,·d00012fd0:·7d2c·207b·622c·2063·7d2c·207b·612c·2064··},·{b,·c},·{a,·d
00012fe0:·7d2c·207b·612c·2065·7d2c·207b·642c·2065··},·{a,·e},·{d,·e00012fe0:·7d2c·207b·632c·2065·7d2c·207b·642c·2065··},·{c,·e},·{d,·e
00012ff0:·7d7d·7d2c·2020·2020·2020·2020·2020·2020··}}},············00012ff0:·7d7d·7d2c·2020·2020·2020·2020·2020·2020··}}},············
00013000:·7c0a·7c20·2020·2020·2020·2020·2020·2022··|.|············"00013000:·7c0a·7c20·2020·2020·2020·2020·2020·2022··|.|············"
00013010:·7269·6e67·2220·3d3e·2052·2020·2020·2020··ring"·=>·R······00013010:·7269·6e67·2220·3d3e·2052·2020·2020·2020··ring"·=>·R······
00013020:·2020·2020·2020·2020·2020·2020·2020·2020··················00013020:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013030:·2020·2020·2020·2020·2020·2020·2020·2020··················00013030:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013040:·2020·2020·2020·2020·2020·2020·2020·2020··················00013040:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013050:·7c0a·7c20·2020·2020·2020·2020·2020·2022··|.|············"00013050:·7c0a·7c20·2020·2020·2020·2020·2020·2022··|.|············"
Offset 4874, 16 lines modifiedOffset 4874, 16 lines modified
00013090:·2020·2020·2020·2020·2020·2020·2020·2020··················00013090:·2020·2020·2020·2020·2020·2020·2020·2020··················
000130a0:·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d··|.|·····--------000130a0:·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d··|.|·····--------
000130b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000130b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000130c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000130c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000130d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000130d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000130e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000130e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000130f0:·7c0a·7c20·2020·2020·4772·6170·687b·2265··|.|·····Graph{"e000130f0:·7c0a·7c20·2020·2020·4772·6170·687b·2265··|.|·····Graph{"e
00013100:·6467·6573·2220·3d3e·207b·7b61·2c20·637d··dges"·=>·{{a,·c}00013100:·6467·6573·2220·3d3e·207b·7b62·2c20·637d··dges"·=>·{{b,·c}
00013110:·2c20·7b62·2c20·647d·2c20·7b63·2c20·647d··,·{b,·d},·{c,·d}00013110:·2c20·7b61·2c20·647d·2c20·7b63·2c20·647d··,·{a,·d},·{c,·d}
00013120:·2c20·7b61·2c20·657d·2c20·7b62·2c20·657d··,·{a,·e},·{b,·e}00013120:·2c20·7b61·2c20·657d·2c20·7b62·2c20·657d··,·{a,·e},·{b,·e}
00013130:·7d7d·2c20·2020·2020·2020·2020·2020·2020··}},·············00013130:·7d7d·2c20·2020·2020·2020·2020·2020·2020··}},·············
00013140:·7c0a·7c20·2020·2020·2020·2020·2020·2272··|.|···········"r00013140:·7c0a·7c20·2020·2020·2020·2020·2020·2272··|.|···········"r
00013150:·696e·6722·203d·3e20·5220·2020·2020·2020··ing"·=>·R·······00013150:·696e·6722·203d·3e20·5220·2020·2020·2020··ing"·=>·R·······
00013160:·2020·2020·2020·2020·2020·2020·2020·2020··················00013160:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013170:·2020·2020·2020·2020·2020·2020·2020·2020··················00013170:·2020·2020·2020·2020·2020·2020·2020·2020··················
00013180:·2020·2020·2020·2020·2020·2020·2020·2020··················00013180:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 4894, 17 lines modifiedOffset 4894, 17 lines modified
000131d0:·2020·2020·2020·2020·2020·2020·2020·2020··················000131d0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000131e0:·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d··|.|·····--------000131e0:·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d··|.|·····--------
000131f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000131f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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Offset 5302, 28 lines modifiedOffset 5302, 28 lines modified
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Offset 3776, 16 lines modifiedOffset 3776, 16 lines modified
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Offset 3962, 16 lines modifiedOffset 3962, 16 lines modified
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00010ec0:·2030·2e30·3030·3539·3834·3231·7320·2874···0.000598421s·(t00010ec0:·2030·2e30·3030·3735·3231·3131·7320·2874···0.000752111s·(t
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Offset 8411, 43 lines modifiedOffset 8411, 43 lines modified
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00005cb0:·2020·7c0a·7c20·2020·2020·2d2d·2075·7365····|.|·····--·use00005cb0:·2020·7c0a·7c20·2020·2020·2d2d·2075·7365····|.|·····--·use
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00005d20:·2e2e·2e20·2020·2020·2020·2020·2020·2020··...·············00005d20:·2e2e·2e20·2020·2020·2020·2020·2020·2020··...·············
00005d30:·2020·2020·2020·2020·2020·2020·2020·2020··················00005d30:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 1795, 41 lines modifiedOffset 1795, 41 lines modified
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00007030:·522c·2032·2c20·4174·7465·6d70·745a·5a20··R,·2,·AttemptZZ·00007030:·522c·2032·2c20·4174·7465·6d70·745a·5a20··R,·2,·AttemptZZ·
00007040:·3d3e·2074·7275·6529·2020·7c0a·7c53·616d··=>·true)··|.|Sam00007040:·3d3e·2074·7275·6529·2020·7c0a·7c53·616d··=>·true)··|.|Sam
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00007060:·7473·202e·2e2e·2020·2020·2020·2020·2020··ts·...··········00007060:·7473·202e·2e2e·2020·2020·2020·2020·2020··ts·...··········
00007070:·2020·2020·2020·2020·2020·2020·2020·2020··················00007070:·2020·2020·2020·2020·2020·2020·2020·2020··················
00007080:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.|00007080:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.|
00007090:·2020·2020·202d·2d20·7573·6564·2030·2073·······--·used·0·s00007090:·2020·2020·202d·2d20·7573·6564·202e·3030·······--·used·.00
000070a0:·6563·6f6e·6473·2020·2020·2020·2020·2020··econds··········000070a0:·3333·3534·3820·7365·636f·6e64·7320·2020··33548·seconds···
000070b0:·2020·2020·2020·2020·2020·2020·2020·2020··················000070b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000070c0:·2020·2020·2020·2020·2020·2020·2020·2020··················000070c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000070d0:·7c0a·7c43·7265·6174·696e·6720·696e·7465··|.|Creating·inte000070d0:·7c0a·7c43·7265·6174·696e·6720·696e·7465··|.|Creating·inte
000070e0:·7270·6f6c·6174·696f·6e20·6d61·7472·6978··rpolation·matrix000070e0:·7270·6f6c·6174·696f·6e20·6d61·7472·6978··rpolation·matrix
000070f0:·202e·2e2e·2020·2020·2020·2020·2020·2020···...············000070f0:·202e·2e2e·2020·2020·2020·2020·2020·2020···...············
00007100:·2020·2020·2020·2020·2020·2020·2020·2020··················00007100:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00007150:·2020·2020·2020·7c0a·7c50·6572·666f·726d········|.|Perform00007150:·2020·2020·2020·7c0a·7c50·6572·666f·726d········|.|Perform
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000071a0:·202d·2d20·7573·6564·2030·2073·6563·6f6e···--·used·0·secon000071a0:·202d·2d20·7573·6564·2030·2073·6563·6f6e···--·used·0·secon
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000071d0:·2020·2020·2020·2020·2020·2020·7c0a·7c43··············|.|C000071d0:·2020·2020·2020·2020·2020·2020·7c0a·7c43··············|.|C
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000072a0:·2020·2020·207c·0a7c·6f33·203d·207c·2079·······|.|o3·=·|·y000072a0:·2020·2020·207c·0a7c·6f33·203d·207c·2079·······|.|o3·=·|·y
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0000aeb0:·2020·2020·2020·207c·0a7c·5361·6d70·6c69·········|.|Sampli0000aeb0:·2020·2020·2020·207c·0a7c·5361·6d70·6c69·········|.|Sampli
0000aec0:·6e67·2069·6d61·6765·2070·6f69·6e74·7320··ng·image·points·0000aec0:·6e67·2069·6d61·6765·2070·6f69·6e74·7320··ng·image·points·
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0000af10:·7573·6564·202e·3030·3934·3933·3137·2073··used·.00949317·s0000af10:·7573·6564·202e·3031·3333·3639·3920·7365··used·.0133699·se
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0000af30:·2020·2020·2020·2020·2020·2020·2020·2020··················0000af30:·2020·2020·2020·2020·2020·2020·2020·2020··················
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0000af50:·2020·207c·0a7c·4372·6561·7469·6e67·2069·····|.|Creating·i0000af50:·2020·207c·0a7c·4372·6561·7469·6e67·2069·····|.|Creating·i
0000af60:·6e74·6572·706f·6c61·7469·6f6e·206d·6174··nterpolation·mat0000af60:·6e74·6572·706f·6c61·7469·6f6e·206d·6174··nterpolation·mat
0000af70:·7269·7820·2e2e·2e20·2020·2020·2020·2020··rix·...·········0000af70:·7269·7820·2e2e·2e20·2020·2020·2020·2020··rix·...·········
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0000afb0:·202e·3030·3833·3533·3732·2073·6563·6f6e···.00835372·secon0000afb0:·202e·3031·3037·3936·3720·7365·636f·6e64···.0107967·second
0000afc0:·6473·2020·2020·2020·2020·2020·2020·2020··ds··············0000afc0:·7320·2020·2020·2020·2020·2020·2020·2020··s···············
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0000afe0:·2020·2020·2020·2020·2020·2020·2020·207c·················|0000afe0:·2020·2020·2020·2020·2020·2020·2020·207c·················|
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0000b000:·6d61·6c69·7a61·7469·6f6e·2070·7265·636f··malization·preco0000b000:·6d61·6c69·7a61·7469·6f6e·2070·7265·636f··malization·preco
0000b010:·6e64·6974·696f·6e69·6e67·202e·2e2e·2020··nditioning·...··0000b010:·6e64·6974·696f·6e69·6e67·202e·2e2e·2020··nditioning·...··
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0000b050:·3333·3830·3835·2073·6563·6f6e·6473·2020··338085·seconds··0000b050:·3737·3430·3636·2073·6563·6f6e·6473·2020··774066·seconds··
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0000b090:·6d70·7574·696e·6720·6e75·6d65·7269·6361··mputing·numerica0000b090:·6d70·7574·696e·6720·6e75·6d65·7269·6361··mputing·numerica
0000b0a0:·6c20·6b65·726e·656c·202e·2e2e·2020·2020··l·kernel·...····0000b0a0:·6c20·6b65·726e·656c·202e·2e2e·2020·2020··l·kernel·...····
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0000b0e0:·202d·2d20·7573·6564·202e·3030·3339·3637···--·used·.0039670000b0e0:·202d·2d20·7573·6564·2030·2073·6563·6f6e···--·used·0·secon
0000b0f0:·3138·2073·6563·6f6e·6473·2020·2020·2020··18·seconds······0000b0f0:·6473·2020·2020·2020·2020·2020·2020·2020··ds··············
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0000b160:·2020·2020·2020·2020·2020·2020·2020·2020··················0000b160:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 2913, 35 lines modifiedOffset 2913, 35 lines modified
0000b600:·4c50·203d·3e20·7472·7565·2920·2020·2020··LP·=>·true)·····0000b600:·4c50·203d·3e20·7472·7565·2920·2020·2020··LP·=>·true)·····
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0000b620:·696e·7465·7270·6f6c·6174·696f·6e20·6d61··interpolation·ma0000b620:·696e·7465·7270·6f6c·6174·696f·6e20·6d61··interpolation·ma
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NumericalSemigroups.info
    
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0001bc90:·7269·7374·6963·536d·6f6f·7468·6e65·7373··risticSmoothness0001bc90:·7269·7374·6963·536d·6f6f·7468·6e65·7373··risticSmoothness
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0001bce0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············0001bce0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············
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00033af0:·6828·4d2c·532c·3329·3b20·2020·2020·2020··h(M,S,3);·······00033af0:·6828·4d2c·532c·3329·3b20·2020·2020·2020··h(M,S,3);·······
00033b00:·2020·2020·2020·2020·2020·2020·2020·2020··················00033b00:·2020·2020·2020·2020·2020·2020·2020·2020··················
00033b10:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--·00033b10:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--·
00033b20:·322e·3337·3339·3873·2065·6c61·7073·6564··2.37398s·elapsed00033b20:·332e·3231·3638·3873·2065·6c61·7073·6564··3.21688s·elapsed
00033b30:·2020·2020·2020·2020·2020·2020·2020·2020··················00033b30:·2020·2020·2020·2020·2020·2020·2020·2020··················
00033b40:·2020·2020·2020·2020·2020·2020·2020·2020··················00033b40:·2020·2020·2020·2020·2020·2020·2020·2020··················
00033b50:·2020·2020·2020·2020·2020·2020·2020·2020··················00033b50:·2020·2020·2020·2020·2020·2020·2020·2020··················
00033b60:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+----00033b60:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+----
00033b70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00033b70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00033b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00033b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00033b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00033b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
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./usr/share/info/Points.info.gz
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Points.info
    
Offset 914, 31 lines modifiedOffset 914, 31 lines modified
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00003920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00003920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00003930:·2d2d·2d2d·2b0a·7c69·3130·203a·2065·6c61··----+.|i10·:·ela00003930:·2d2d·2d2d·2b0a·7c69·3130·203a·2065·6c61··----+.|i10·:·ela
00003940:·7073·6564·5469·6d65·2028·512c·696e·472c··psedTime·(Q,inG,00003940:·7073·6564·5469·6d65·2028·512c·696e·472c··psedTime·(Q,inG,
00003950:·4729·203d·2061·6666·696e·6546·6174·506f··G)·=·affineFatPo00003950:·4729·203d·2061·6666·696e·6546·6174·506f··G)·=·affineFatPo
00003960:·696e·7473·284d·2c6d·756c·7473·2c52·293b··ints(M,mults,R);00003960:·696e·7473·284d·2c6d·756c·7473·2c52·293b··ints(M,mults,R);
00003970:·2020·2020·2020·2020·2020·2020·2020·2020··················00003970:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00003990:·3835·7320·656c·6170·7365·6420·2020·2020··85s·elapsed·····00003990:·3236·7320·656c·6170·7365·6420·2020·2020··26s·elapsed·····
000039a0:·2020·2020·2020·2020·2020·2020·2020·2020··················000039a0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000039b0:·2020·2020·2020·2020·2020·2020·2020·2020··················000039b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000039c0:·2020·2020·2020·2020·2020·2020·2020·2020··················000039c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
000039d0:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+---------000039d0:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+---------
000039e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000039e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000039f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------000039f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00003a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00003a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00003a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00003a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00003a20:·2d2d·2d2d·2b0a·7c69·3131·203a·2065·6c61··----+.|i11·:·ela00003a20:·2d2d·2d2d·2b0a·7c69·3131·203a·2065·6c61··----+.|i11·:·ela
00003a30:·7073·6564·5469·6d65·2048·203d·2061·6666··psedTime·H·=·aff00003a30:·7073·6564·5469·6d65·2048·203d·2061·6666··psedTime·H·=·aff
00003a40:·696e·6546·6174·506f·696e·7473·4279·496e··ineFatPointsByIn00003a40:·696e·6546·6174·506f·696e·7473·4279·496e··ineFatPointsByIn
00003a50:·7465·7273·6563·7469·6f6e·284d·2c6d·756c··tersection(M,mul00003a50:·7465·7273·6563·7469·6f6e·284d·2c6d·756c··tersection(M,mul
00003a60:·7473·2c52·293b·2020·2020·2020·2020·2020··ts,R);··········00003a60:·7473·2c52·293b·2020·2020·2020·2020·2020··ts,R);··········
00003a70:·2020·2020·7c0a·7c20·2d2d·2033·2e37·3737······|.|·--·3.77700003a70:·2020·2020·7c0a·7c20·2d2d·2037·2e32·3037······|.|·--·7.207
00003a80:·3833·7320·656c·6170·7365·6420·2020·2020··83s·elapsed·····00003a80:·3573·2065·6c61·7073·6564·2020·2020·2020··5s·elapsed······
00003a90:·2020·2020·2020·2020·2020·2020·2020·2020··················00003a90:·2020·2020·2020·2020·2020·2020·2020·2020··················
00003aa0:·2020·2020·2020·2020·2020·2020·2020·2020··················00003aa0:·2020·2020·2020·2020·2020·2020·2020·2020··················
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00003ac0:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+---------00003ac0:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+---------
00003ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00003ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00003ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00003ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00003af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00003af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
7.21 KB
./usr/share/info/Posets.info.gz
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Posets.info
    
Offset 9353, 17 lines modifiedOffset 9353, 17 lines modified
00024880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00024880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00024890:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00024890:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
000248a0:·2d2d·2d2d·2b0a·7c69·3420·3a20·7469·6d65··----+.|i4·:·time000248a0:·2d2d·2d2d·2b0a·7c69·3420·3a20·7469·6d65··----+.|i4·:·time
000248b0:·2067·7265·656e·654b·6c65·6974·6d61·6e50···greeneKleitmanP000248b0:·2067·7265·656e·654b·6c65·6974·6d61·6e50···greeneKleitmanP
000248c0:·6172·7469·7469·6f6e·2844·2c20·5374·7261··artition(D,·Stra000248c0:·6172·7469·7469·6f6e·2844·2c20·5374·7261··artition(D,·Stra
000248d0:·7465·6779·203d·3e20·2261·6e74·6963·6861··tegy·=>·"anticha000248d0:·7465·6779·203d·3e20·2261·6e74·6963·6861··tegy·=>·"anticha
000248e0:·696e·7322·297c·0a7c·202d·2d20·7573·6564··ins")|.|·--·used000248e0:·696e·7322·297c·0a7c·202d·2d20·7573·6564··ins")|.|·--·used
000248f0:·2030·2e32·3934·3633·3373·2028·6370·7529···0.294633s·(cpu) 
00024900:·3b20·302e·3139·3732·3531·7320·2874·6872··;·0.197251s·(thr 
00024910:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)···000248f0:·2030·2e33·3932·3238·7320·2863·7075·293b···0.39228s·(cpu);
 00024900:·2030·2e32·3637·3337·3173·2028·7468·7265···0.267371s·(thre
 00024910:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)····
00024920:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|·······00024920:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|·······
00024930:·2020·2020·2020·2020·2020·2020·2020·2020··················00024930:·2020·2020·2020·2020·2020·2020·2020·2020··················
00024940:·2020·2020·2020·2020·2020·2020·2020·2020··················00024940:·2020·2020·2020·2020·2020·2020·2020·2020··················
00024950:·2020·2020·2020·2020·2020·2020·2020·2020··················00024950:·2020·2020·2020·2020·2020·2020·2020·2020··················
00024960:·2020·2020·2020·207c·0a7c·6f34·203d·2050·········|.|o4·=·P00024960:·2020·2020·2020·207c·0a7c·6f34·203d·2050·········|.|o4·=·P
00024970:·6172·7469·7469·6f6e·7b39·2c20·327d·2020··artition{9,·2}··00024970:·6172·7469·7469·6f6e·7b39·2c20·327d·2020··artition{9,·2}··
00024980:·2020·2020·2020·2020·2020·2020·2020·2020··················00024980:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 9381, 18 lines modifiedOffset 9381, 18 lines modified
00024a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00024a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00024a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------00024a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
00024a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935··-----------+.|i500024a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935··-----------+.|i5
00024a70:·203a·2074·696d·6520·6772·6565·6e65·4b6c···:·time·greeneKl00024a70:·203a·2074·696d·6520·6772·6565·6e65·4b6c···:·time·greeneKl
00024a80:·6569·746d·616e·5061·7274·6974·696f·6e28··eitmanPartition(00024a80:·6569·746d·616e·5061·7274·6974·696f·6e28··eitmanPartition(
00024a90:·442c·2053·7472·6174·6567·7920·3d3e·2022··D,·Strategy·=>·"00024a90:·442c·2053·7472·6174·6567·7920·3d3e·2022··D,·Strategy·=>·"
00024aa0:·6368·6169·6e73·2229·2020·2020·7c0a·7c20··chains")····|.|·00024aa0:·6368·6169·6e73·2229·2020·2020·7c0a·7c20··chains")····|.|·
00024ab0:·2d2d·2075·7365·6420·302e·3030·3031·3232··--·used·0.00012200024ab0:·2d2d·2075·7365·6420·302e·3030·3032·3030··--·used·0.000200
00024ac0:·3939·3573·2028·6370·7529·3b20·372e·3236··995s·(cpu);·7.2600024ac0:·3136·3673·2028·6370·7529·3b20·322e·3137··166s·(cpu);·2.17
00024ad0:·3165·2d30·3673·2028·7468·7265·6164·293b··1e-06s·(thread);00024ad0:·652d·3035·7320·2874·6872·6561·6429·3b20··e-05s·(thread);·
00024ae0:·2030·7320·2867·6329·2020·2020·207c·0a7c···0s·(gc)·····|.|00024ae0:·3073·2028·6763·2920·2020·2020·207c·0a7c··0s·(gc)······|.|
00024af0:·2020·2020·2020·2020·2020·2020·2020·2020··················00024af0:·2020·2020·2020·2020·2020·2020·2020·2020··················
00024b00:·2020·2020·2020·2020·2020·2020·2020·2020··················00024b00:·2020·2020·2020·2020·2020·2020·2020·2020··················
00024b10:·2020·2020·2020·2020·2020·2020·2020·2020··················00024b10:·2020·2020·2020·2020·2020·2020·2020·2020··················
00024b20:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.00024b20:·2020·2020·2020·2020·2020·2020·2020·7c0a················|.
00024b30:·7c6f·3520·3d20·5061·7274·6974·696f·6e7b··|o5·=·Partition{00024b30:·7c6f·3520·3d20·5061·7274·6974·696f·6e7b··|o5·=·Partition{
00024b40:·392c·2032·7d20·2020·2020·2020·2020·2020··9,·2}···········00024b40:·392c·2032·7d20·2020·2020·2020·2020·2020··9,·2}···········
00024b50:·2020·2020·2020·2020·2020·2020·2020·2020··················00024b50:·2020·2020·2020·2020·2020·2020·2020·2020··················
Offset 19807, 17 lines modifiedOffset 19807, 17 lines modified
0004d5e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------0004d5e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··----------------
0004d5f0:·2d2b·0a7c·6937·203a·2074·696d·6520·6973··-+.|i7·:·time·is0004d5f0:·2d2b·0a7c·6937·203a·2074·696d·6520·6973··-+.|i7·:·time·is
0004d600:·4469·7374·7269·6275·7469·7665·2043·2020··Distributive·C··0004d600:·4469·7374·7269·6275·7469·7665·2043·2020··Distributive·C··
0004d610:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d610:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d620:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d620:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d630:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d630:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d640:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.00004d640:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0
0004d650:·3031·3332·3837·3573·2028·6370·7529·3b20··0132875s·(cpu);·0004d650:·3031·3839·3337·3373·2028·6370·7529·3b20··0189373s·(cpu);·
0004d660:·352e·3037·3765·2d30·3673·2028·7468·7265··5.077e-06s·(thre 
0004d670:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)····0004d660:·352e·3334·652d·3036·7320·2874·6872·6561··5.34e-06s·(threa
 0004d670:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)·····
0004d680:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d680:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d690:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············0004d690:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············
0004d6a0:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d6a0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d6b0:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d6b0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d6c0:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d6c0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d6d0:·2020·2020·2020·2020·2020·2020·2020·2020··················0004d6d0:·2020·2020·2020·2020·2020·2020·2020·2020··················
0004d6e0:·207c·0a7c·6f37·203d·2074·7275·6520·2020···|.|o7·=·true···0004d6e0:·207c·0a7c·6f37·203d·2074·7275·6520·2020···|.|o7·=·true···
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0001a890:·3e74·7275·6529·2020·2020·2020·2020·2020··>true)··········0001a890:·3e74·7275·6529·2020·2020·2020·2020·2020··>true)··········
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data.tar.xz
289 KB
data.tar
288 KB
./usr/bin/M2-binary
File has been modified after NT_GNU_BUILD_ID has been applied.
16.2 KB
readelf --wide --relocs {}
    
Offset 3528, 42 lines modifiedOffset 3528, 42 lines modified
3528 00000000008744d8··0000000000000008·R_X86_64_RELATIVE·························8821503528 00000000008744d8··0000000000000008·R_X86_64_RELATIVE·························882150
3529 00000000008744e0··0000000000000008·R_X86_64_RELATIVE·························8822403529 00000000008744e0··0000000000000008·R_X86_64_RELATIVE·························882240
3530 00000000008744e8··0000000000000008·R_X86_64_RELATIVE·························8820d83530 00000000008744e8··0000000000000008·R_X86_64_RELATIVE·························8820d8
3531 00000000008744f0··0000000000000008·R_X86_64_RELATIVE·························7243803531 00000000008744f0··0000000000000008·R_X86_64_RELATIVE·························724380
3532 00000000008744f8··0000000000000008·R_X86_64_RELATIVE·························57ee303532 00000000008744f8··0000000000000008·R_X86_64_RELATIVE·························57ee30
3533 0000000000874500··0000000000000008·R_X86_64_RELATIVE·························57ee503533 0000000000874500··0000000000000008·R_X86_64_RELATIVE·························57ee50
3534 0000000000874508··0000000000000008·R_X86_64_RELATIVE·························581b103534 0000000000874508··0000000000000008·R_X86_64_RELATIVE·························581b10
3535 0000000000874520··0000000000000008·R_X86_64_RELATIVE·························6fd1c83535 0000000000874520··0000000000000008·R_X86_64_RELATIVE·························6fd1c5
3536 0000000000874528··0000000000000008·R_X86_64_RELATIVE·························6fd1c83536 0000000000874528··0000000000000008·R_X86_64_RELATIVE·························6fd1c5
3537 0000000000874530··0000000000000008·R_X86_64_RELATIVE·························6fd1f23537 0000000000874530··0000000000000008·R_X86_64_RELATIVE·························6fd1ef
3538 0000000000874538··0000000000000008·R_X86_64_RELATIVE·························6fd1473538 0000000000874538··0000000000000008·R_X86_64_RELATIVE·························6fd147
3539 0000000000874540··0000000000000008·R_X86_64_RELATIVE·························6fd43a3539 0000000000874540··0000000000000008·R_X86_64_RELATIVE·························6fd437
3540 0000000000874548··0000000000000008·R_X86_64_RELATIVE·························6fd43d3540 0000000000874548··0000000000000008·R_X86_64_RELATIVE·························6fd43a
3541 0000000000874550··0000000000000008·R_X86_64_RELATIVE·························6fd4413541 0000000000874550··0000000000000008·R_X86_64_RELATIVE·························6fd43e
3542 0000000000874558··0000000000000008·R_X86_64_RELATIVE·························6fd4453542 0000000000874558··0000000000000008·R_X86_64_RELATIVE·························6fd442
3543 0000000000874560··0000000000000008·R_X86_64_RELATIVE·························6fd44a3543 0000000000874560··0000000000000008·R_X86_64_RELATIVE·························6fd447
3544 0000000000874568··0000000000000008·R_X86_64_RELATIVE·························6fd4503544 0000000000874568··0000000000000008·R_X86_64_RELATIVE·························6fd44d
3545 0000000000874570··0000000000000008·R_X86_64_RELATIVE·························6fd4573545 0000000000874570··0000000000000008·R_X86_64_RELATIVE·························6fd454
3546 0000000000874578··0000000000000008·R_X86_64_RELATIVE·························6fd45f3546 0000000000874578··0000000000000008·R_X86_64_RELATIVE·························6fd45c
3547 0000000000874580··0000000000000008·R_X86_64_RELATIVE·························6fd4683547 0000000000874580··0000000000000008·R_X86_64_RELATIVE·························6fd465
3548 0000000000874588··0000000000000008·R_X86_64_RELATIVE·························6fd4723548 0000000000874588··0000000000000008·R_X86_64_RELATIVE·························6fd46f
3549 0000000000874590··0000000000000008·R_X86_64_RELATIVE·························6fd47d3549 0000000000874590··0000000000000008·R_X86_64_RELATIVE·························6fd47a
3550 0000000000874598··0000000000000008·R_X86_64_RELATIVE·························6fd4893550 0000000000874598··0000000000000008·R_X86_64_RELATIVE·························6fd486
3551 00000000008745a0··0000000000000008·R_X86_64_RELATIVE·························6fd4973551 00000000008745a0··0000000000000008·R_X86_64_RELATIVE·························6fd494
3552 00000000008745a8··0000000000000008·R_X86_64_RELATIVE·························6fd4a63552 00000000008745a8··0000000000000008·R_X86_64_RELATIVE·························6fd4a3
3553 00000000008745b0··0000000000000008·R_X86_64_RELATIVE·························6fd4b63553 00000000008745b0··0000000000000008·R_X86_64_RELATIVE·························6fd4b3
3554 00000000008745b8··0000000000000008·R_X86_64_RELATIVE·························6fd4c73554 00000000008745b8··0000000000000008·R_X86_64_RELATIVE·························6fd4c4
3555 00000000008745c0··0000000000000008·R_X86_64_RELATIVE·························6fd4da3555 00000000008745c0··0000000000000008·R_X86_64_RELATIVE·························6fd4d7
3556 00000000008745c8··0000000000000008·R_X86_64_RELATIVE·························6fd4ee3556 00000000008745c8··0000000000000008·R_X86_64_RELATIVE·························6fd4eb
3557 00000000008745d0··0000000000000008·R_X86_64_RELATIVE·························6fd5033557 00000000008745d0··0000000000000008·R_X86_64_RELATIVE·························6fd500
3558 00000000008745d8··0000000000000008·R_X86_64_RELATIVE·························6fd51a3558 00000000008745d8··0000000000000008·R_X86_64_RELATIVE·························6fd517
3559 00000000008745e0··0000000000000008·R_X86_64_RELATIVE·························6fd5323559 00000000008745e0··0000000000000008·R_X86_64_RELATIVE·························6fd52f
3560 00000000008745e8··0000000000000008·R_X86_64_RELATIVE·························6fd54b3560 00000000008745e8··0000000000000008·R_X86_64_RELATIVE·························6fd548
3561 00000000008745f0··0000000000000008·R_X86_64_RELATIVE·························6fd5663561 00000000008745f0··0000000000000008·R_X86_64_RELATIVE·························6fd563
3562 00000000008745f8··0000000000000008·R_X86_64_RELATIVE·························6fd5823562 00000000008745f8··0000000000000008·R_X86_64_RELATIVE·························6fd57f
3563 0000000000874600··0000000000000008·R_X86_64_RELATIVE·························71aba03563 0000000000874600··0000000000000008·R_X86_64_RELATIVE·························71aba0
3564 0000000000874608··0000000000000008·R_X86_64_RELATIVE·························71abc03564 0000000000874608··0000000000000008·R_X86_64_RELATIVE·························71abc0
3565 0000000000874610··0000000000000008·R_X86_64_RELATIVE·························71abe03565 0000000000874610··0000000000000008·R_X86_64_RELATIVE·························71abe0
3566 0000000000874618··0000000000000008·R_X86_64_RELATIVE·························71ac083566 0000000000874618··0000000000000008·R_X86_64_RELATIVE·························71ac08
3567 0000000000874620··0000000000000008·R_X86_64_RELATIVE·························71ac303567 0000000000874620··0000000000000008·R_X86_64_RELATIVE·························71ac30
3568 0000000000874628··0000000000000008·R_X86_64_RELATIVE·························71ac583568 0000000000874628··0000000000000008·R_X86_64_RELATIVE·························71ac58
3569 0000000000874630··0000000000000008·R_X86_64_RELATIVE·························71ac803569 0000000000874630··0000000000000008·R_X86_64_RELATIVE·························71ac80
Offset 9821, 28 lines modifiedOffset 9821, 28 lines modified
9821 0000000000885290··0000000000000008·R_X86_64_RELATIVE·························6fae329821 0000000000885290··0000000000000008·R_X86_64_RELATIVE·························6fae32
9822 0000000000885298··0000000000000008·R_X86_64_RELATIVE·························6fa27d9822 0000000000885298··0000000000000008·R_X86_64_RELATIVE·························6fa27d
9823 00000000008852a0··0000000000000008·R_X86_64_RELATIVE·························6fc6999823 00000000008852a0··0000000000000008·R_X86_64_RELATIVE·························6fc699
9824 00000000008852a8··0000000000000008·R_X86_64_RELATIVE·························6fcaa09824 00000000008852a8··0000000000000008·R_X86_64_RELATIVE·························6fcaa0
9825 00000000008852b0··0000000000000008·R_X86_64_RELATIVE·························6fcb539825 00000000008852b0··0000000000000008·R_X86_64_RELATIVE·························6fcb53
9826 00000000008852b8··0000000000000008·R_X86_64_RELATIVE·························6fb6159826 00000000008852b8··0000000000000008·R_X86_64_RELATIVE·························6fb615
9827 00000000008852c0··0000000000000008·R_X86_64_RELATIVE·························6fb55f9827 00000000008852c0··0000000000000008·R_X86_64_RELATIVE·························6fb55f
9828 00000000008852c8··0000000000000008·R_X86_64_RELATIVE·························6fd2cc9828 00000000008852c8··0000000000000008·R_X86_64_RELATIVE·························6fd2c9
9829 00000000008852d0··0000000000000008·R_X86_64_RELATIVE·························6fad609829 00000000008852d0··0000000000000008·R_X86_64_RELATIVE·························6fad60
9830 00000000008852d8··0000000000000008·R_X86_64_RELATIVE·························6fad609830 00000000008852d8··0000000000000008·R_X86_64_RELATIVE·························6fad60
9831 00000000008852e0··0000000000000008·R_X86_64_RELATIVE·························6fcaab9831 00000000008852e0··0000000000000008·R_X86_64_RELATIVE·························6fcaab
9832 00000000008852e8··0000000000000008·R_X86_64_RELATIVE·························6fcaae9832 00000000008852e8··0000000000000008·R_X86_64_RELATIVE·························6fcaae
9833 00000000008852f0··0000000000000008·R_X86_64_RELATIVE·························6fad5f9833 00000000008852f0··0000000000000008·R_X86_64_RELATIVE·························6fad5f
9834 00000000008852f8··0000000000000008·R_X86_64_RELATIVE·························6fa1b59834 00000000008852f8··0000000000000008·R_X86_64_RELATIVE·························6fa1b5
9835 0000000000885300··0000000000000008·R_X86_64_RELATIVE·························6fcc489835 0000000000885300··0000000000000008·R_X86_64_RELATIVE·························6fcc48
9836 0000000000885308··0000000000000008·R_X86_64_RELATIVE·························6fb9eb9836 0000000000885308··0000000000000008·R_X86_64_RELATIVE·························6fb9eb
9837 0000000000885310··0000000000000008·R_X86_64_RELATIVE·························6fd5f59837 0000000000885310··0000000000000008·R_X86_64_RELATIVE·························6fd5f2
9838 0000000000885318··0000000000000008·R_X86_64_RELATIVE·························6fb6d19838 0000000000885318··0000000000000008·R_X86_64_RELATIVE·························6fb6d1
9839 0000000000885320··0000000000000008·R_X86_64_RELATIVE·························6fb5779839 0000000000885320··0000000000000008·R_X86_64_RELATIVE·························6fb577
9840 0000000000885328··0000000000000008·R_X86_64_RELATIVE·························6fcab19840 0000000000885328··0000000000000008·R_X86_64_RELATIVE·························6fcab1
9841 0000000000885330··0000000000000008·R_X86_64_RELATIVE·························6fd2639841 0000000000885330··0000000000000008·R_X86_64_RELATIVE·························6fd260
9842 0000000000885338··0000000000000008·R_X86_64_RELATIVE·························6fceba9842 0000000000885338··0000000000000008·R_X86_64_RELATIVE·························6fceba
9843 0000000000885340··0000000000000008·R_X86_64_RELATIVE·························6fbb1b9843 0000000000885340··0000000000000008·R_X86_64_RELATIVE·························6fbb1b
9844 0000000000885348··0000000000000008·R_X86_64_RELATIVE·························6fc2cc9844 0000000000885348··0000000000000008·R_X86_64_RELATIVE·························6fc2cc
9845 0000000000885350··0000000000000008·R_X86_64_RELATIVE·························6fc3839845 0000000000885350··0000000000000008·R_X86_64_RELATIVE·························6fc383
9846 0000000000885358··0000000000000008·R_X86_64_RELATIVE·························6fad609846 0000000000885358··0000000000000008·R_X86_64_RELATIVE·························6fad60
9847 0000000000885360··0000000000000008·R_X86_64_RELATIVE·························6fad609847 0000000000885360··0000000000000008·R_X86_64_RELATIVE·························6fad60
9848 0000000000885368··0000000000000008·R_X86_64_RELATIVE·························6fad609848 0000000000885368··0000000000000008·R_X86_64_RELATIVE·························6fad60
Offset 9854, 15 lines modifiedOffset 9854, 15 lines modified
9854 0000000000885398··0000000000000008·R_X86_64_RELATIVE·························6fcae89854 0000000000885398··0000000000000008·R_X86_64_RELATIVE·························6fcae8
9855 00000000008853a0··0000000000000008·R_X86_64_RELATIVE·························6fcb2a9855 00000000008853a0··0000000000000008·R_X86_64_RELATIVE·························6fcb2a
9856 00000000008853a8··0000000000000008·R_X86_64_RELATIVE·························6fb6b79856 00000000008853a8··0000000000000008·R_X86_64_RELATIVE·························6fb6b7
9857 00000000008853b0··0000000000000008·R_X86_64_RELATIVE·························6fc96f9857 00000000008853b0··0000000000000008·R_X86_64_RELATIVE·························6fc96f
9858 00000000008853b8··0000000000000008·R_X86_64_RELATIVE·························6fcb099858 00000000008853b8··0000000000000008·R_X86_64_RELATIVE·························6fcb09
9859 00000000008853c0··0000000000000008·R_X86_64_RELATIVE·························6fcab39859 00000000008853c0··0000000000000008·R_X86_64_RELATIVE·························6fcab3
9860 00000000008853c8··0000000000000008·R_X86_64_RELATIVE·························6faee39860 00000000008853c8··0000000000000008·R_X86_64_RELATIVE·························6faee3
9861 00000000008853d0··0000000000000008·R_X86_64_RELATIVE·························6fd24a9861 00000000008853d0··0000000000000008·R_X86_64_RELATIVE·························6fd247
9862 00000000008853d8··0000000000000008·R_X86_64_RELATIVE·························6fca6f9862 00000000008853d8··0000000000000008·R_X86_64_RELATIVE·························6fca6f
9863 00000000008853e0··0000000000000008·R_X86_64_RELATIVE·························6fcb979863 00000000008853e0··0000000000000008·R_X86_64_RELATIVE·························6fcb97
9864 00000000008853e8··0000000000000008·R_X86_64_RELATIVE·························6fcab59864 00000000008853e8··0000000000000008·R_X86_64_RELATIVE·························6fcab5
9865 00000000008853f0··0000000000000008·R_X86_64_RELATIVE·························6fcb8b9865 00000000008853f0··0000000000000008·R_X86_64_RELATIVE·························6fcb8b
9866 00000000008853f8··0000000000000008·R_X86_64_RELATIVE·························6fb6c79866 00000000008853f8··0000000000000008·R_X86_64_RELATIVE·························6fb6c7
9867 0000000000885400··0000000000000008·R_X86_64_RELATIVE·························6fcae19867 0000000000885400··0000000000000008·R_X86_64_RELATIVE·························6fcae1
9868 0000000000885408··0000000000000008·R_X86_64_RELATIVE·························6fcae49868 0000000000885408··0000000000000008·R_X86_64_RELATIVE·························6fcae4
Offset 9992, 26 lines modifiedOffset 9992, 26 lines modified
9992 00000000008857f8··0000000000000008·R_X86_64_RELATIVE·························6fbcdf9992 00000000008857f8··0000000000000008·R_X86_64_RELATIVE·························6fbcdf
9993 0000000000885800··0000000000000008·R_X86_64_RELATIVE·························6fcaeb9993 0000000000885800··0000000000000008·R_X86_64_RELATIVE·························6fcaeb
9994 0000000000885808··0000000000000008·R_X86_64_RELATIVE·························6fc9549994 0000000000885808··0000000000000008·R_X86_64_RELATIVE·························6fc954
9995 0000000000885810··0000000000000008·R_X86_64_RELATIVE·························6fcb0f9995 0000000000885810··0000000000000008·R_X86_64_RELATIVE·························6fcb0f
9996 0000000000885818··0000000000000008·R_X86_64_RELATIVE·························6fcab69996 0000000000885818··0000000000000008·R_X86_64_RELATIVE·························6fcab6
9997 0000000000885820··0000000000000008·R_X86_64_RELATIVE·························6fcaf19997 0000000000885820··0000000000000008·R_X86_64_RELATIVE·························6fcaf1
9998 0000000000885828··0000000000000008·R_X86_64_RELATIVE·························6fcedb9998 0000000000885828··0000000000000008·R_X86_64_RELATIVE·························6fcedb
9999 0000000000885830··0000000000000008·R_X86_64_RELATIVE·························6fd5f59999 0000000000885830··0000000000000008·R_X86_64_RELATIVE·························6fd5f2
10000 0000000000885838··0000000000000008·R_X86_64_RELATIVE·························6fb5d810000 0000000000885838··0000000000000008·R_X86_64_RELATIVE·························6fb5d8
10001 0000000000885840··0000000000000008·R_X86_64_RELATIVE·························6fd24a10001 0000000000885840··0000000000000008·R_X86_64_RELATIVE·························6fd247
10002 0000000000885848··0000000000000008·R_X86_64_RELATIVE·························6fd25110002 0000000000885848··0000000000000008·R_X86_64_RELATIVE·························6fd24e
10003 0000000000885850··0000000000000008·R_X86_64_RELATIVE·························6fb6d110003 0000000000885850··0000000000000008·R_X86_64_RELATIVE·························6fb6d1
10004 0000000000885858··0000000000000008·R_X86_64_RELATIVE·························6fb1ae10004 0000000000885858··0000000000000008·R_X86_64_RELATIVE·························6fb1ae
10005 0000000000885860··0000000000000008·R_X86_64_RELATIVE·························6fb57710005 0000000000885860··0000000000000008·R_X86_64_RELATIVE·························6fb577
10006 0000000000885868··0000000000000008·R_X86_64_RELATIVE·························6fb9f310006 0000000000885868··0000000000000008·R_X86_64_RELATIVE·························6fb9f3
10007 0000000000885870··0000000000000008·R_X86_64_RELATIVE·························6fcab110007 0000000000885870··0000000000000008·R_X86_64_RELATIVE·························6fcab1
10008 0000000000885878··0000000000000008·R_X86_64_RELATIVE·························6fce1d10008 0000000000885878··0000000000000008·R_X86_64_RELATIVE·························6fce1d
10009 0000000000885880··0000000000000008·R_X86_64_RELATIVE·························6fd26310009 0000000000885880··0000000000000008·R_X86_64_RELATIVE·························6fd260
10010 0000000000885888··0000000000000008·R_X86_64_RELATIVE·························6fd23e10010 0000000000885888··0000000000000008·R_X86_64_RELATIVE·························6fd23b
10011 0000000000885890··0000000000000008·R_X86_64_RELATIVE·························6fcb0610011 0000000000885890··0000000000000008·R_X86_64_RELATIVE·························6fcb06
10012 0000000000885898··0000000000000008·R_X86_64_RELATIVE·························6fcd3410012 0000000000885898··0000000000000008·R_X86_64_RELATIVE·························6fcd34
10013 00000000008858a0··0000000000000008·R_X86_64_RELATIVE·························6fcd4710013 00000000008858a0··0000000000000008·R_X86_64_RELATIVE·························6fcd47
10014 00000000008858a8··0000000000000008·R_X86_64_RELATIVE·························6fcd5510014 00000000008858a8··0000000000000008·R_X86_64_RELATIVE·························6fcd55
10015 00000000008858b0··0000000000000008·R_X86_64_RELATIVE·························6fcd6910015 00000000008858b0··0000000000000008·R_X86_64_RELATIVE·························6fcd69
10016 00000000008858b8··0000000000000008·R_X86_64_RELATIVE·························6fcd6f10016 00000000008858b8··0000000000000008·R_X86_64_RELATIVE·························6fcd6f
10017 00000000008858c0··0000000000000008·R_X86_64_RELATIVE·························6fad6010017 00000000008858c0··0000000000000008·R_X86_64_RELATIVE·························6fad60
Offset 10019, 36 lines modifiedOffset 10019, 36 lines modified
10019 00000000008859c8··0000000000000008·R_X86_64_RELATIVE·························6fced810019 00000000008859c8··0000000000000008·R_X86_64_RELATIVE·························6fced8
10020 00000000008859e0··0000000000000008·R_X86_64_RELATIVE·························885a2010020 00000000008859e0··0000000000000008·R_X86_64_RELATIVE·························885a20
10021 0000000000885a20··0000000000000008·R_X86_64_RELATIVE·························6fcedd10021 0000000000885a20··0000000000000008·R_X86_64_RELATIVE·························6fcedd
10022 0000000000885a28··0000000000000008·R_X86_64_RELATIVE·························56728010022 0000000000885a28··0000000000000008·R_X86_64_RELATIVE·························567280
10023 0000000000885a38··0000000000000008·R_X86_64_RELATIVE·························6fcee410023 0000000000885a38··0000000000000008·R_X86_64_RELATIVE·························6fcee4
10024 0000000000885a70··0000000000000008·R_X86_64_RELATIVE·························71ab0010024 0000000000885a70··0000000000000008·R_X86_64_RELATIVE·························71ab00
10025 0000000000885a78··0000000000000008·R_X86_64_RELATIVE·························71ab2810025 0000000000885a78··0000000000000008·R_X86_64_RELATIVE·························71ab28
10026 0000000000885a80··0000000000000008·R_X86_64_RELATIVE·························6fd61b10026 0000000000885a80··0000000000000008·R_X86_64_RELATIVE·························6fd618
10027 0000000000885a88··0000000000000008·R_X86_64_RELATIVE·························6fd33610027 0000000000885a88··0000000000000008·R_X86_64_RELATIVE·························6fd333
10028 0000000000885a90··0000000000000008·R_X86_64_RELATIVE·························6fd42310028 0000000000885a90··0000000000000008·R_X86_64_RELATIVE·························6fd420
10029 0000000000885a98··0000000000000008·R_X86_64_RELATIVE·························71a33010029 0000000000885a98··0000000000000008·R_X86_64_RELATIVE·························71a330
10030 0000000000885aa0··0000000000000008·R_X86_64_RELATIVE·························71ab5010030 0000000000885aa0··0000000000000008·R_X86_64_RELATIVE·························71ab50
Max diff block lines reached; 2593/16570 bytes (15.65%) of diff not shown.
821 B
readelf --wide --notes {}
    
Offset 1, 12 lines modifiedOffset 1, 12 lines modified
  
1 Displaying·notes·found·in:·.note.gnu.property1 Displaying·notes·found·in:·.note.gnu.property
2 ··Owner················Data·size·»  Description2 ··Owner················Data·size·»  Description
3 ··GNU··················0x00000010»  NT_GNU_PROPERTY_TYPE_0»    ······Properties:·x86·ISA·needed:·x86-64-baseline3 ··GNU··················0x00000010»  NT_GNU_PROPERTY_TYPE_0»    ······Properties:·x86·ISA·needed:·x86-64-baseline
  
4 Displaying·notes·found·in:·.note.gnu.build-id4 Displaying·notes·found·in:·.note.gnu.build-id
5 ··Owner················Data·size·»  Description5 ··Owner················Data·size·»  Description
6 ··GNU··················0x00000014»  NT_GNU_BUILD_ID·(unique·build·ID·bitstring)»   ····Build·ID:·a58afbeef2e278d168cbad374f8659e91501e9236 ··GNU··················0x00000014»  NT_GNU_BUILD_ID·(unique·build·ID·bitstring)»   ····Build·ID:·fc6d061c5f071055b88eaeaf0bd3f74d0b63f1ef
  
7 Displaying·notes·found·in:·.note.ABI-tag7 Displaying·notes·found·in:·.note.ABI-tag
8 ··Owner················Data·size·»  Description8 ··Owner················Data·size·»  Description
9 ··GNU··················0x00000010»  NT_GNU_ABI_TAG·(ABI·version·tag)»     ····OS:·Linux,·ABI:·3.2.09 ··GNU··················0x00000010»  NT_GNU_ABI_TAG·(ABI·version·tag)»     ····OS:·Linux,·ABI:·3.2.0
527 B
strings --all --bytes=8 {}
    
Offset 1, 8 lines modifiedOffset 1, 8 lines modified
1 #/lib64/ld-linux-x86-64.so.21 /lib64/ld-linux-x86-64.so.2
2 __gmon_start__2 __gmon_start__
3 _ITM_deregisterTMCloneTable3 _ITM_deregisterTMCloneTable
4 _ITM_registerTMCloneTable4 _ITM_registerTMCloneTable
5 cblas_dscal5 cblas_dscal
6 cblas_dtrsm6 cblas_dtrsm
7 cblas_sscal7 cblas_sscal
8 cblas_dgemm8 cblas_dgemm
Offset 12796, 15 lines modifiedOffset 12796, 15 lines modified
12796 errorreturn12796 errorreturn
12797 evaluate_backtrace12797 evaluate_backtrace
12798 evaluate_profiling12798 evaluate_profiling
12799 lastCode12799 lastCode
12800 tryEvalSuccess12800 tryEvalSuccess
12801 gcc·14.2.012801 gcc·14.2.0
12802 x86_64-Linux-Debian-1312802 x86_64-Linux-Debian-13
12803 6.1.0-37-cloud-amd6412803 6.12.22+bpo-amd64
12804 m2-compile-node12804 m2-compile-node
12805 %d.%d.%d12805 %d.%d.%d
12806 not·present12806 not·present
12807 x86_64-pc-linux-gnu12807 x86_64-pc-linux-gnu
12808 1.25.06-bin12808 1.25.06-bin
12809 whichway12809 whichway
12810 sortlist12810 sortlist
250 KB
objdump --line-numbers --disassemble --demangle --reloc --no-show-raw-insn --section=.text {}
    
Offset 72904, 15 lines modifiedOffset 72904, 15 lines modified
72904 »       endbr6472904 »       endbr64
72905 »       push···%rbp72905 »       push···%rbp
72906 »       mov····$0x10,%edi72906 »       mov····$0x10,%edi
72907 »       push···%rbx72907 »       push···%rbx
72908 »       push···%rax72908 »       push···%rax
72909 »       call···5c0d0·<__cxa_allocate_exception@plt>72909 »       call···5c0d0·<__cxa_allocate_exception@plt>
72910 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1)72910 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1)
72911 »       lea····0x6673aa(%rip),%rsi········72911 »       lea····0x6673a7(%rip),%rsi········
72912 »       mov····%rax,%rdi72912 »       mov····%rax,%rdi
72913 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:4072913 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40
72914 »       mov····%rax,%rbx72914 »       mov····%rax,%rbx
72915 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1)72915 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1)
72916 »       call···59850·<std::runtime_error::runtime_error(char·const*)@plt>72916 »       call···59850·<std::runtime_error::runtime_error(char·const*)@plt>
72917 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·2)72917 ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·2)
72918 »       mov····0x7ef0f6(%rip),%rdx········72918 »       mov····0x7ef0f6(%rip),%rdx········
Offset 72971, 15 lines modifiedOffset 72971, 15 lines modified
72971 /usr/include/c++/14/bits/basic_string.h:203272971 /usr/include/c++/14/bits/basic_string.h:2032
72972 »       push···%rax72972 »       push···%rax
72973 std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::_M_check(unsigned·long,·char·const*)·const:72973 std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::_M_check(unsigned·long,·char·const*)·const:
72974 /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1)72974 /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1)
72975 »       mov····%rsi,%rdx72975 »       mov····%rsi,%rdx
72976 »       lea····0x67f0e1(%rip),%rdi········72976 »       lea····0x67f0e1(%rip),%rdi········
72977 »       xor····%eax,%eax72977 »       xor····%eax,%eax
72978 »       lea····0x6672ff(%rip),%rsi········72978 »       lea····0x6672fc(%rip),%rsi········
72979 »       call···593e0·<std::__throw_out_of_range_fmt(char·const*,·...)@plt>72979 »       call···593e0·<std::__throw_out_of_range_fmt(char·const*,·...)@plt>
72980 std::basic_ostream<char,·std::char_traits<char>·>&·std::endl<char,·std::char_traits<char>·>(std::basic_ostream<char,·std::char_traits<char>·>&):72980 std::basic_ostream<char,·std::char_traits<char>·>&·std::endl<char,·std::char_traits<char>·>(std::basic_ostream<char,·std::char_traits<char>·>&):
72981 /usr/include/c++/14/ostream:74472981 /usr/include/c++/14/ostream:744
72982 »       push···%rbp72982 »       push···%rbp
72983 »       push···%rbx72983 »       push···%rbx
72984 »       push···%rdx72984 »       push···%rdx
72985 /usr/include/c++/14/ostream:74572985 /usr/include/c++/14/ostream:745
Offset 133383, 15 lines modifiedOffset 133383, 15 lines modified
133383 »       mov····0xbaa500(%rip),%rdi········133383 »       mov····0xbaa500(%rip),%rdi········
133384 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63133384 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63
133385 »       movw···$0x7,(%rbx)133385 »       movw···$0x7,(%rbx)
133386 »       movl···$0x2,0x4(%rbx)133386 »       movl···$0x2,0x4(%rbx)
133387 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59133387 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59
133388 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133388 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
133389 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133389 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133390 »       lea····0x63732b(%rip),%rdi········133390 »       lea····0x637328(%rip),%rdi········
133391 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)133391 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)
133392 »       mov····%rax,0x8(%rbx)133392 »       mov····%rax,0x8(%rbx)
133393 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133393 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133394 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>133394 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>
133395 »       mov····%rax,%rdi133395 »       mov····%rax,%rdi
133396 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)133396 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)
133397 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133397 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
Offset 133427, 15 lines modifiedOffset 133427, 15 lines modified
133427 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:82133427 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:82
133428 »       shr····$0x10,%r9d133428 »       shr····$0x10,%r9d
133429 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:85133429 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:85
133430 »       cmp····$0xff,%eax133430 »       cmp····$0xff,%eax
133431 »       je·····c6d5a·<std::runtime_error::~runtime_error()@plt+0x693f2>133431 »       je·····c6d5a·<std::runtime_error::~runtime_error()@plt+0x693f2>
133432 /usr/include/x86_64-linux-gnu/bits/stdio2.h:68·(discriminator·1)133432 /usr/include/x86_64-linux-gnu/bits/stdio2.h:68·(discriminator·1)
133433 »       push···%rax133433 »       push···%rax
133434 »       lea····0x6372ca(%rip),%r8········133434 »       lea····0x6372c7(%rip),%r8········
133435 »       push···%rdx133435 »       push···%rdx
133436 »       lea····0xbaa53f(%rip),%rbx········133436 »       lea····0xbaa53f(%rip),%rbx········
133437 »       mov····$0x1,%edx133437 »       mov····$0x1,%edx
133438 »       mov····$0x28,%ecx133438 »       mov····$0x28,%ecx
133439 »       xor····%eax,%eax133439 »       xor····%eax,%eax
133440 »       mov····$0x28,%esi133440 »       mov····$0x28,%esi
133441 »       mov····%rbx,%rdi133441 »       mov····%rbx,%rdi
Offset 133464, 15 lines modifiedOffset 133464, 15 lines modified
133464 »       test···%rax,%rax133464 »       test···%rax,%rax
133465 »       je·····c6d6d·<std::runtime_error::~runtime_error()@plt+0x69405>133465 »       je·····c6d6d·<std::runtime_error::~runtime_error()@plt+0x69405>
133466 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:160133466 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:160
133467 »       mov····0x58(%rsp),%r14133467 »       mov····0x58(%rsp),%r14
133468 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59133468 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59
133469 »       mov····0xbaa408(%rip),%rdi········133469 »       mov····0xbaa408(%rip),%rdi········
133470 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133470 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133471 »       lea····0x63726d(%rip),%rbx········133471 »       lea····0x63726a(%rip),%rbx········
133472 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:160133472 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:160
133473 »       movw···$0x7,(%r14)133473 »       movw···$0x7,(%r14)
133474 »       movl···$0x2,0x4(%r14)133474 »       movl···$0x2,0x4(%r14)
133475 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59133475 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59
133476 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133476 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
133477 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133477 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133478 »       mov····%rbx,%rdi133478 »       mov····%rbx,%rdi
Offset 133499, 15 lines modifiedOffset 133499, 15 lines modified
133499 »       mov····0xbaa3aa(%rip),%rdi········133499 »       mov····0xbaa3aa(%rip),%rdi········
133500 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63133500 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63
133501 »       movw···$0x7,(%r15)133501 »       movw···$0x7,(%r15)
133502 »       movl···$0x2,0x4(%r15)133502 »       movl···$0x2,0x4(%r15)
133503 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59133503 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59
133504 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133504 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
133505 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)133505 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)
133506 »       lea····0x637210(%rip),%rdi········133506 »       lea····0x63720d(%rip),%rdi········
133507 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)133507 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)
133508 »       mov····%rax,0x8(%r15)133508 »       mov····%rax,0x8(%r15)
133509 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)133509 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)
133510 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>133510 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>
133511 »       mov····%rax,%rdi133511 »       mov····%rax,%rdi
133512 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·2)133512 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·2)
133513 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133513 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
Offset 133527, 15 lines modifiedOffset 133527, 15 lines modified
133527 »       mov····0xbaa34f(%rip),%rdi········133527 »       mov····0xbaa34f(%rip),%rdi········
133528 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:168133528 ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:168
133529 »       movw···$0x7,(%r14)133529 »       movw···$0x7,(%r14)
133530 »       movl···$0x2,0x4(%r14)133530 »       movl···$0x2,0x4(%r14)
133531 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59133531 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59
133532 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133532 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
133533 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133533 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133534 »       lea····0x6371c3(%rip),%rdi········133534 »       lea····0x6371c0(%rip),%rdi········
133535 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)133535 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)
133536 »       mov····%rax,0x8(%r14)133536 »       mov····%rax,0x8(%r14)
133537 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133537 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133538 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>133538 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>
133539 »       mov····%rax,%rdi133539 »       mov····%rax,%rdi
133540 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)133540 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)
133541 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133541 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
Offset 133555, 15 lines modifiedOffset 133555, 15 lines modified
133555 »       mov····0xbaa2f4(%rip),%rdi········133555 »       mov····0xbaa2f4(%rip),%rdi········
133556 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63133556 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63
133557 »       movw···$0x7,(%r15)133557 »       movw···$0x7,(%r15)
133558 »       movl···$0x2,0x4(%r15)133558 »       movl···$0x2,0x4(%r15)
133559 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59133559 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59
133560 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133560 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
133561 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133561 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133562 »       lea····0x637176(%rip),%rdi········133562 »       lea····0x637173(%rip),%rdi········
133563 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)133563 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1)
133564 »       mov····%rax,0x8(%r15)133564 »       mov····%rax,0x8(%r15)
133565 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62133565 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62
133566 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>133566 »       call···567760·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe940>
133567 »       mov····%rax,%rdi133567 »       mov····%rax,%rdi
133568 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)133568 ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1)
133569 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>133569 »       call···592150·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x39330>
Max diff block lines reached; 250029/256181 bytes (97.60%) of diff not shown.
11.0 KB
readelf --wide --decompress --hex-dump=.rodata {}
    
Offset 788, 90 lines modifiedOffset 788, 90 lines modified
788 ··0x006fd110·74726163·65006576·616c7561·74655f70·trace.evaluate_p788 ··0x006fd110·74726163·65006576·616c7561·74655f70·trace.evaluate_p
789 ··0x006fd120·726f6669·6c696e67·006c6173·74436f64·rofiling.lastCod789 ··0x006fd120·726f6669·6c696e67·006c6173·74436f64·rofiling.lastCod
790 ··0x006fd130·65007472·79457661·6c537563·63657373·e.tryEvalSuccess790 ··0x006fd130·65007472·79457661·6c537563·63657373·e.tryEvalSuccess
791 ··0x006fd140·00312e32·352e3036·00342e34·2e310067·.1.25.06.4.4.1.g791 ··0x006fd140·00312e32·352e3036·00342e34·2e310067·.1.25.06.4.4.1.g
792 ··0x006fd150·63632031·342e322e·30007838·365f3634·cc·14.2.0.x86_64792 ··0x006fd150·63632031·342e322e·30007838·365f3634·cc·14.2.0.x86_64
793 ··0x006fd160·00783836·5f36342d·4c696e75·782d4465·.x86_64-Linux-De793 ··0x006fd160·00783836·5f36342d·4c696e75·782d4465·.x86_64-Linux-De
794 ··0x006fd170·6269616e·2d313300·4c696e75·7800362e·bian-13.Linux.6.794 ··0x006fd170·6269616e·2d313300·4c696e75·7800362e·bian-13.Linux.6.
795 ··0x006fd180·312e302d·33372d63·6c6f7564·2d616d64·1.0-37-cloud-amd795 ··0x006fd180·31322e32·322b6270·6f2d616d·64363400·12.22+bpo-amd64.
796 ··0x006fd190·3634006d·322d636f·6d70696c·652d6e6f·64.m2-compile-no796 ··0x006fd190·6d322d63·6f6d7069·6c652d6e·6f646500·m2-compile-node.
797 ··0x006fd1a0·64650025·642e2564·2e256400·6e6f7420·de.%d.%d.%d.not·797 ··0x006fd1a0·25642e25·642e2564·006e6f74·20707265·%d.%d.%d.not·pre
798 ··0x006fd1b0·70726573·656e7400·322e352e·3000352e·present.2.5.0.5.798 ··0x006fd1b0·73656e74·00322e35·2e300035·2e352e30·sent.2.5.0.5.5.0
799 ··0x006fd1c0·352e3000·332e322e·3100332e·31332e34·5.0.3.2.1.3.13.4 
800 ··0x006fd1d0·00332e31·302e3400·31312e35·2e310033·.3.10.4.11.5.1.3799 ··0x006fd1c0·00332e32·2e310033·2e31332e·3400332e·.3.2.1.3.13.4.3.
 800 ··0x006fd1d0·31302e34·0031312e·352e3100·332e312e·10.4.11.5.1.3.1.
801 ··0x006fd1e0·2e312e30·00315f38·3300382e·3200342e·.1.0.1_83.8.2.4.801 ··0x006fd1e0·3000315f·38330038·2e320034·2e322e32·0.1_83.8.2.4.2.2
802 ··0x006fd1f0·322e3200·312e352e·34003230·32322e31·2.2.1.5.4.2022.1802 ··0x006fd1f0·00312e35·2e340032·3032322e·3100332e·.1.5.4.2022.1.3.
803 ··0x006fd200·00332e34·2e300033·2e342e38·004d3200·.3.4.0.3.4.8.M2.803 ··0x006fd200·342e3000·332e342e·38004d32·00783836·4.0.3.4.8.M2.x86
804 ··0x006fd210·7838365f·36342d70·632d6c69·6e75782d·x86_64-pc-linux-804 ··0x006fd210·5f36342d·70632d6c·696e7578·2d676e75·_64-pc-linux-gnu
805 ··0x006fd220·676e7500·312e3235·2e30362d·62696e00·gnu.1.25.06-bin.805 ··0x006fd220·00312e32·352e3036·2d62696e·004d3254·.1.25.06-bin.M2T
806 ··0x006fd230·4d325461·736b0077·68696368·77617900·M2Task.whichway.806 ··0x006fd230·61736b00·77686963·68776179·00736f72·ask.whichway.sor
807 ··0x006fd240·736f7274·6c697374·00257000·68616473·sortlist.%p.hads807 ··0x006fd240·746c6973·74002570·00686164·73657100·tlist.%p.hadseq.
808 ··0x006fd250·65710064·65657073·65710064·65657069·eq.deepseq.deepi808 ··0x006fd250·64656570·73657100·64656570·696e6465·deepseq.deepinde
809 ··0x006fd260·6e646578·00726573·65747661·72730077·ndex.resetvars.w809 ··0x006fd260·78007265·73657476·61727300·77726170·x.resetvars.wrap
810 ··0x006fd270·72617070·6564204d·61636175·6c617932·rapped·Macaulay2810 ··0x006fd270·70656420·4d616361·756c6179·32206675·ped·Macaulay2·fu
811 ··0x006fd280·2066756e·6374696f·6e007465·73740062··function.test.b811 ··0x006fd280·6e637469·6f6e0074·65737400·62617369·nction.test.basi
812 ··0x006fd290·61736963·5f737472·696e673a·3a696e73·asic_string::ins812 ··0x006fd290·635f7374·72696e67·3a3a696e·73657274·c_string::insert
813 ··0x006fd2a0·65727400·4f766572·666c6f77·20457272·ert.Overflow·Err813 ··0x006fd2a0·004f7665·72666c6f·77204572·726f7200·.Overflow·Error.
814 ··0x006fd2b0·6f720063·6272743c·2531253e·28253125·or.cbrt<%1%>(%1%814 ··0x006fd2b0·63627274·3c253125·3e282531·2529006c·cbrt<%1%>(%1%).l
815 ··0x006fd2c0·29006c67·616d6d61·3c253125·3e00626f·).lgamma<%1%>.bo815 ··0x006fd2c0·67616d6d·613c2531·253e0062·6f6f7374·gamma<%1%>.boost
816 ··0x006fd2d0·6f73743a·3a6d6174·683a3a65·78706d31·ost::math::expm1816 ··0x006fd2d0·3a3a6d61·74683a3a·6578706d·313c2531·::math::expm1<%1
817 ··0x006fd2e0·3c253125·3e282531·2529006e·756d6572·<%1%>(%1%).numer817 ··0x006fd2e0·253e2825·31252900·6e756d65·72696320·%>(%1%).numeric·
818 ··0x006fd2f0·6963206f·76657266·6c6f7700·626f6f73·ic·overflow.boos818 ··0x006fd2f0·6f766572·666c6f77·00626f6f·73743a3a·overflow.boost::
819 ··0x006fd300·743a3a6d·6174683a·3a6c6f67·31703c25·t::math::log1p<%819 ··0x006fd300·6d617468·3a3a6c6f·6731703c·2531253e·math::log1p<%1%>
820 ··0x006fd310·31253e28·25312529·00457661·6c756174·1%>(%1%).Evaluat820 ··0x006fd310·28253125·29004576·616c7561·74696f6e·(%1%).Evaluation
821 ··0x006fd320·696f6e20·6f66206c·67616d6d·61206174·ion·of·lgamma·at 
822 ··0x006fd330·20253125·2e00626f·6f73743a·3a6d6174··%1%..boost::mat 
823 ··0x006fd340·683a3a6c·67616d6d·613c2531·253e2825·h::lgamma<%1%>(% 
824 ··0x006fd350·31252900·6f706572·61746f72·3d00556e·1%).operator=.Un 
825 ··0x006fd360·61626c65·20746f20·70617273·65207374·able·to·parse·st 
826 ··0x006fd370·72696e67·20220045·76616c75·6174696f·ring·".Evaluatio 
827 ··0x006fd380·6e206f66·20746761·6d6d6120·61742025·n·of·tgamma·at·%821 ··0x006fd320·206f6620·6c67616d·6d612061·74202531··of·lgamma·at·%1
828 ··0x006fd390·31252e00·626f6f73·743a3a6d·6174683a·1%..boost::math: 
829 ··0x006fd3a0·3a697472·756e633c·2531253e·28253125·:itrunc<%1%>(%1% 
830 ··0x006fd3b0·29002061·6e642078·203d2025·31250062·).·and·x·=·%1%.b 
831 ··0x006fd3c0·6f6f7374·3a3a6d61·74683a3a·7a657461·oost::math::zeta 
832 ··0x006fd3d0·3c253125·3e282531·25290062·6f6f7374·<%1%>(%1%).boost 
833 ··0x006fd3e0·3a3a6d61·74683a3a·6572665f·696e763c·::math::erf_inv< 
834 ··0x006fd3f0·2531253e·0067616d·6d615f71·3c253125·%1%>.gamma_q<%1% 
835 ··0x006fd400·3e282531·252c2025·31252900·67616d6d·>(%1%,·%1%).gamm 
836 ··0x006fd410·615f703c·2531253e·28253125·2c202531·a_p<%1%>(%1%,·%1 
837 ··0x006fd420·25290062·6f6f7374·3a3a6d61·74683a3a·%).boost::math::822 ··0x006fd330·252e0062·6f6f7374·3a3a6d61·74683a3a·%..boost::math::
 823 ··0x006fd340·6c67616d·6d613c25·31253e28·25312529·lgamma<%1%>(%1%)
 824 ··0x006fd350·006f7065·7261746f·723d0055·6e61626c·.operator=.Unabl
 825 ··0x006fd360·6520746f·20706172·73652073·7472696e·e·to·parse·strin
 826 ··0x006fd370·67202200·4576616c·75617469·6f6e206f·g·".Evaluation·o
 827 ··0x006fd380·66207467·616d6d61·20617420·2531252e·f·tgamma·at·%1%.
 828 ··0x006fd390·00626f6f·73743a3a·6d617468·3a3a6974·.boost::math::it
 829 ··0x006fd3a0·72756e63·3c253125·3e282531·25290020·runc<%1%>(%1%).·
 830 ··0x006fd3b0·616e6420·78203d20·25312500·626f6f73·and·x·=·%1%.boos
 831 ··0x006fd3c0·743a3a6d·6174683a·3a7a6574·613c2531·t::math::zeta<%1
 832 ··0x006fd3d0·253e2825·31252900·626f6f73·743a3a6d·%>(%1%).boost::m
 833 ··0x006fd3e0·6174683a·3a657266·5f696e76·3c253125·ath::erf_inv<%1%
 834 ··0x006fd3f0·3e006761·6d6d615f·713c2531·253e2825·>.gamma_q<%1%>(%
 835 ··0x006fd400·31252c20·25312529·0067616d·6d615f70·1%,·%1%).gamma_p
 836 ··0x006fd410·3c253125·3e282531·252c2025·31252900·<%1%>(%1%,·%1%).
 837 ··0x006fd420·626f6f73·743a3a6d·6174683a·3a7a6574·boost::math::zet
838 ··0x006fd430·7a657461·3c253125·3e003234·00313230·zeta<%1%>.24.120838 ··0x006fd430·613c2531·253e0032·34003132·30003732·a<%1%>.24.120.72
839 ··0x006fd440·00373230·00353034·30003430·33323000·.720.5040.40320. 
840 ··0x006fd450·33363238·38300033·36323838·30300033·362880.3628800.3 
841 ··0x006fd460·39393136·38303000·34373930·30313630·9916800.47900160839 ··0x006fd440·30003530·34300034·30333230·00333632·0.5040.40320.362
 840 ··0x006fd450·38383000·33363238·38303000·33393931·880.3628800.3991
 841 ··0x006fd460·36383030·00343739·30303136·30300036·6800.479001600.6
842 ··0x006fd470·30003632·32373032·30383030·00383731·0.6227020800.871842 ··0x006fd470·32323730·32303830·30003837·31373832·227020800.871782
843 ··0x006fd480·37383239·31323030·00313330·37363734·78291200.1307674843 ··0x006fd480·39313230·30003133·30373637·34333638·91200.1307674368
844 ··0x006fd490·33363830·30300032·30393232·37383938·368000.209227898844 ··0x006fd490·30303000·32303932·32373839·38383830·000.209227898880
845 ··0x006fd4a0·38383030·30003335·35363837·34323830·88000.3556874280845 ··0x006fd4a0·30300033·35353638·37343238·30393630·00.3556874280960
846 ··0x006fd4b0·39363030·30003634·30323337·33373035·96000.6402373705846 ··0x006fd4b0·30300036·34303233·37333730·35373238·00.6402373705728
847 ··0x006fd4c0·37323830·30300031·32313634·35313030·728000.121645100 
848 ··0x006fd4d0·34303838·33323030·30003234·33323930·408832000.243290847 ··0x006fd4c0·30303000·31323136·34353130·30343038·000.121645100408
 848 ··0x006fd4d0·38333230·30300032·34333239·30323030·832000.243290200
849 ··0x006fd4e0·32303038·31373636·34303030·30003531·2008176640000.51849 ··0x006fd4e0·38313736·36343030·30300035·31303930·8176640000.51090
850 ··0x006fd4f0·30393039·34323137·31373039·34343030·0909421717094400850 ··0x006fd4f0·39343231·37313730·39343430·30303000·942171709440000.
851 ··0x006fd500·30300031·31323430·30303732·37373737·00.1124000727777851 ··0x006fd500·31313234·30303037·32373737·37363037·1124000727777607
852 ··0x006fd510·36303736·38303030·30003235·38353230·607680000.258520852 ··0x006fd510·36383030·30300032·35383532·30313637·680000.258520167
853 ··0x006fd520·31363733·38383834·39373636·34303030·1673888497664000853 ··0x006fd520·33383838·34393736·36343030·30300036·38884976640000.6
854 ··0x006fd530·30003632·30343438·34303137·33333233·0.62044840173323854 ··0x006fd530·32303434·38343031·37333332·33393433·2044840173323943
855 ··0x006fd540·39343339·33363030·30300031·35353131·9439360000.15511855 ··0x006fd540·39333630·30303000·31353531·31323130·9360000.15511210
856 ··0x006fd550·32313030·34333333·30393835·39383430·2100433309859840856 ··0x006fd550·30343333·33303938·35393834·30303030·0433309859840000
857 ··0x006fd560·30303030·30003430·33323931·34363131·00000.4032914611857 ··0x006fd560·30300034·30333239·31343631·31323636·00.4032914611266
858 ··0x006fd570·32363630·35363335·35383430·30303030·2660563558400000858 ··0x006fd570·30353633·35353834·30303030·30300031·05635584000000.1
859 ··0x006fd580·30003130·38383838·36393435·30343138·0.10888869450418859 ··0x006fd580·30383838·38363934·35303431·38333532·0888869450418352
860 ··0x006fd590·33353231·36303736·38303030·30303000·352160768000000.860 ··0x006fd590·31363037·36383030·30303030·00666c6f·160768000000.flo
861 ··0x006fd5a0·666c6f61·745f7072·696f723c·2531253e·float_prior<%1%>861 ··0x006fd5a0·61745f70·72696f72·3c253125·3e282531·at_prior<%1%>(%1
862 ··0x006fd5b0·28253125·2900666c·6f61745f·6e657874·(%1%).float_next862 ··0x006fd5b0·25290066·6c6f6174·5f6e6578·743c2531·%).float_next<%1
863 ··0x006fd5c0·3c253125·3e282531·25290062·61736963·<%1%>(%1%).basic863 ··0x006fd5c0·253e2825·31252900·62617369·635f7374·%>(%1%).basic_st
864 ··0x006fd5d0·5f737472·696e673a·3a726570·6c616365·_string::replace864 ··0x006fd5d0·72696e67·3a3a7265·706c6163·6500652b·ring::replace.e+
865 ··0x006fd5e0·00652b30·3000302e·002d696e·66002b69·.e+00.0..-inf.+i865 ··0x006fd5e0·30300030·2e002d69·6e66002b·696e6600·00.0..-inf.+inf.
866 ··0x006fd5f0·6e66006e·616e002d·30004361·75736520·nf.nan.-0.Cause·866 ··0x006fd5f0·6e616e00·2d300043·61757365·20756e6b·nan.-0.Cause·unk
867 ··0x006fd600·756e6b6e·6f776e00·4572726f·7220696e·unknown.Error·in867 ··0x006fd600·6e6f776e·00457272·6f722069·6e206675·nown.Error·in·fu
868 ··0x006fd610·2066756e·6374696f·6e200062·6f6f7374··function·.boost868 ··0x006fd610·6e637469·6f6e2000·626f6f73·743a3a6d·nction·.boost::m
869 ··0x006fd620·3a3a6d61·74683a3a·7467616d·6d613c25·::math::tgamma<%869 ··0x006fd620·6174683a·3a746761·6d6d613c·2531253e·ath::tgamma<%1%>
870 ··0x006fd630·31253e28·25312529·00000000·00000000·1%>(%1%)........870 ··0x006fd630·28253125·29000000·00000000·00000000·(%1%)...........
871 ··0x006fd640·01000000·00000000·00000000·00000000·................871 ··0x006fd640·01000000·00000000·00000000·00000000·................
872 ··0x006fd650·30303031·30323033·30343035·30363037·0001020304050607872 ··0x006fd650·30303031·30323033·30343035·30363037·0001020304050607
873 ··0x006fd660·30383039·31303131·31323133·31343135·0809101112131415873 ··0x006fd660·30383039·31303131·31323133·31343135·0809101112131415
874 ··0x006fd670·31363137·31383139·32303231·32323233·1617181920212223874 ··0x006fd670·31363137·31383139·32303231·32323233·1617181920212223
875 ··0x006fd680·32343235·32363237·32383239·33303331·2425262728293031875 ··0x006fd680·32343235·32363237·32383239·33303331·2425262728293031
876 ··0x006fd690·33323333·33343335·33363337·33383339·3233343536373839876 ··0x006fd690·33323333·33343335·33363337·33383339·3233343536373839
877 ··0x006fd6a0·34303431·34323433·34343435·34363437·4041424344454647877 ··0x006fd6a0·34303431·34323433·34343435·34363437·4041424344454647
2.88 KB
readelf --wide --decompress --hex-dump=.data.rel.ro {}
    
Offset 1834, 28 lines modifiedOffset 1834, 28 lines modified
1834 ··0x008744b0·e84d7100·00000000·004f7100·00000000·.Mq......Oq.....1834 ··0x008744b0·e84d7100·00000000·004f7100·00000000·.Mq......Oq.....
1835 ··0x008744c0·404f7100·00000000·22ca6f00·00000000·@Oq.....".o.....1835 ··0x008744c0·404f7100·00000000·22ca6f00·00000000·@Oq.....".o.....
1836 ··0x008744d0·c8218800·00000000·50218800·00000000·.!......P!......1836 ··0x008744d0·c8218800·00000000·50218800·00000000·.!......P!......
1837 ··0x008744e0·40228800·00000000·d8208800·00000000·@".......·......1837 ··0x008744e0·40228800·00000000·d8208800·00000000·@".......·......
1838 ··0x008744f0·80437200·00000000·30ee5700·00000000·.Cr.....0.W.....1838 ··0x008744f0·80437200·00000000·30ee5700·00000000·.Cr.....0.W.....
1839 ··0x00874500·50ee5700·00000000·101b5800·00000000·P.W.......X.....1839 ··0x00874500·50ee5700·00000000·101b5800·00000000·P.W.......X.....
1840 ··0x00874510·00000000·00000000·00000000·00000000·................1840 ··0x00874510·00000000·00000000·00000000·00000000·................
1841 ··0x00874520·c8d16f00·00000000·c8d16f00·00000000·..o.......o.....1841 ··0x00874520·c5d16f00·00000000·c5d16f00·00000000·..o.......o.....
1842 ··0x00874530·f2d16f00·00000000·47d16f00·00000000·..o.....G.o.....1842 ··0x00874530·efd16f00·00000000·47d16f00·00000000·..o.....G.o.....
1843 ··0x00874540·3ad46f00·00000000·3dd46f00·00000000·:.o.....=.o.....1843 ··0x00874540·37d46f00·00000000·3ad46f00·00000000·7.o.....:.o.....
1844 ··0x00874550·41d46f00·00000000·45d46f00·00000000·A.o.....E.o.....1844 ··0x00874550·3ed46f00·00000000·42d46f00·00000000·>.o.....B.o.....
1845 ··0x00874560·4ad46f00·00000000·50d46f00·00000000·J.o.....P.o.....1845 ··0x00874560·47d46f00·00000000·4dd46f00·00000000·G.o.....M.o.....
1846 ··0x00874570·57d46f00·00000000·5fd46f00·00000000·W.o....._.o.....1846 ··0x00874570·54d46f00·00000000·5cd46f00·00000000·T.o.....\.o.....
1847 ··0x00874580·68d46f00·00000000·72d46f00·00000000·h.o.....r.o.....1847 ··0x00874580·65d46f00·00000000·6fd46f00·00000000·e.o.....o.o.....
1848 ··0x00874590·7dd46f00·00000000·89d46f00·00000000·}.o.......o.....1848 ··0x00874590·7ad46f00·00000000·86d46f00·00000000·z.o.......o.....
1849 ··0x008745a0·97d46f00·00000000·a6d46f00·00000000·..o.......o.....1849 ··0x008745a0·94d46f00·00000000·a3d46f00·00000000·..o.......o.....
1850 ··0x008745b0·b6d46f00·00000000·c7d46f00·00000000·..o.......o.....1850 ··0x008745b0·b3d46f00·00000000·c4d46f00·00000000·..o.......o.....
1851 ··0x008745c0·dad46f00·00000000·eed46f00·00000000·..o.......o.....1851 ··0x008745c0·d7d46f00·00000000·ebd46f00·00000000·..o.......o.....
1852 ··0x008745d0·03d56f00·00000000·1ad56f00·00000000·..o.......o.....1852 ··0x008745d0·00d56f00·00000000·17d56f00·00000000·..o.......o.....
1853 ··0x008745e0·32d56f00·00000000·4bd56f00·00000000·2.o.....K.o.....1853 ··0x008745e0·2fd56f00·00000000·48d56f00·00000000·/.o.....H.o.....
1854 ··0x008745f0·66d56f00·00000000·82d56f00·00000000·f.o.......o.....1854 ··0x008745f0·63d56f00·00000000·7fd56f00·00000000·c.o.......o.....
1855 ··0x00874600·a0ab7100·00000000·c0ab7100·00000000·..q.......q.....1855 ··0x00874600·a0ab7100·00000000·c0ab7100·00000000·..q.......q.....
1856 ··0x00874610·e0ab7100·00000000·08ac7100·00000000·..q.......q.....1856 ··0x00874610·e0ab7100·00000000·08ac7100·00000000·..q.......q.....
1857 ··0x00874620·30ac7100·00000000·58ac7100·00000000·0.q.....X.q.....1857 ··0x00874620·30ac7100·00000000·58ac7100·00000000·0.q.....X.q.....
1858 ··0x00874630·80ac7100·00000000·a8ac7100·00000000·..q.......q.....1858 ··0x00874630·80ac7100·00000000·a8ac7100·00000000·..q.......q.....
1859 ··0x00874640·d8ac7100·00000000·08ad7100·00000000·..q.......q.....1859 ··0x00874640·d8ac7100·00000000·08ad7100·00000000·..q.......q.....
1860 ··0x00874650·38ad7100·00000000·68ad7100·00000000·8.q.....h.q.....1860 ··0x00874650·38ad7100·00000000·68ad7100·00000000·8.q.....h.q.....
1861 ··0x00874660·98ad7100·00000000·d0ad7100·00000000·..q.......q.....1861 ··0x00874660·98ad7100·00000000·d0ad7100·00000000·..q.......q.....
5.78 KB
readelf --wide --decompress --hex-dump=.data {}
    
Offset 40, 32 lines modifiedOffset 40, 32 lines modified
40 ··0x00885250·9aca6f00·00000000·5bae6f00·00000000·..o.....[.o.....40 ··0x00885250·9aca6f00·00000000·5bae6f00·00000000·..o.....[.o.....
41 ··0x00885260·4db36f00·00000000·d8a86f00·00000000·M.o.......o.....41 ··0x00885260·4db36f00·00000000·d8a86f00·00000000·M.o.......o.....
42 ··0x00885270·17c26f00·00000000·9cca6f00·00000000·..o.......o.....42 ··0x00885270·17c26f00·00000000·9cca6f00·00000000·..o.......o.....
43 ··0x00885280·9eca6f00·00000000·05b06f00·00000000·..o.......o.....43 ··0x00885280·9eca6f00·00000000·05b06f00·00000000·..o.......o.....
44 ··0x00885290·32ae6f00·00000000·7da26f00·00000000·2.o.....}.o.....44 ··0x00885290·32ae6f00·00000000·7da26f00·00000000·2.o.....}.o.....
45 ··0x008852a0·99c66f00·00000000·a0ca6f00·00000000·..o.......o.....45 ··0x008852a0·99c66f00·00000000·a0ca6f00·00000000·..o.......o.....
46 ··0x008852b0·53cb6f00·00000000·15b66f00·00000000·S.o.......o.....46 ··0x008852b0·53cb6f00·00000000·15b66f00·00000000·S.o.......o.....
47 ··0x008852c0·5fb56f00·00000000·ccd26f00·00000000·_.o.......o.....47 ··0x008852c0·5fb56f00·00000000·c9d26f00·00000000·_.o.......o.....
48 ··0x008852d0·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....48 ··0x008852d0·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....
49 ··0x008852e0·abca6f00·00000000·aeca6f00·00000000·..o.......o.....49 ··0x008852e0·abca6f00·00000000·aeca6f00·00000000·..o.......o.....
50 ··0x008852f0·5fad6f00·00000000·b5a16f00·00000000·_.o.......o.....50 ··0x008852f0·5fad6f00·00000000·b5a16f00·00000000·_.o.......o.....
51 ··0x00885300·48cc6f00·00000000·ebb96f00·00000000·H.o.......o.....51 ··0x00885300·48cc6f00·00000000·ebb96f00·00000000·H.o.......o.....
52 ··0x00885310·f5d56f00·00000000·d1b66f00·00000000·..o.......o.....52 ··0x00885310·f2d56f00·00000000·d1b66f00·00000000·..o.......o.....
53 ··0x00885320·77b56f00·00000000·b1ca6f00·00000000·w.o.......o.....53 ··0x00885320·77b56f00·00000000·b1ca6f00·00000000·w.o.......o.....
54 ··0x00885330·63d26f00·00000000·bace6f00·00000000·c.o.......o.....54 ··0x00885330·60d26f00·00000000·bace6f00·00000000·`.o.......o.....
55 ··0x00885340·1bbb6f00·00000000·ccc26f00·00000000·..o.......o.....55 ··0x00885340·1bbb6f00·00000000·ccc26f00·00000000·..o.......o.....
56 ··0x00885350·83c36f00·00000000·60ad6f00·00000000·..o.....`.o.....56 ··0x00885350·83c36f00·00000000·60ad6f00·00000000·..o.....`.o.....
57 ··0x00885360·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....57 ··0x00885360·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....
58 ··0x00885370·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....58 ··0x00885370·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....
59 ··0x00885380·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....59 ··0x00885380·60ad6f00·00000000·60ad6f00·00000000·`.o.....`.o.....
60 ··0x00885390·60ad6f00·00000000·e8ca6f00·00000000·`.o.......o.....60 ··0x00885390·60ad6f00·00000000·e8ca6f00·00000000·`.o.......o.....
61 ··0x008853a0·2acb6f00·00000000·b7b66f00·00000000·*.o.......o.....61 ··0x008853a0·2acb6f00·00000000·b7b66f00·00000000·*.o.......o.....
62 ··0x008853b0·6fc96f00·00000000·09cb6f00·00000000·o.o.......o.....62 ··0x008853b0·6fc96f00·00000000·09cb6f00·00000000·o.o.......o.....
63 ··0x008853c0·b3ca6f00·00000000·e3ae6f00·00000000·..o.......o.....63 ··0x008853c0·b3ca6f00·00000000·e3ae6f00·00000000·..o.......o.....
64 ··0x008853d0·4ad26f00·00000000·6fca6f00·00000000·J.o.....o.o.....64 ··0x008853d0·47d26f00·00000000·6fca6f00·00000000·G.o.....o.o.....
65 ··0x008853e0·97cb6f00·00000000·b5ca6f00·00000000·..o.......o.....65 ··0x008853e0·97cb6f00·00000000·b5ca6f00·00000000·..o.......o.....
66 ··0x008853f0·8bcb6f00·00000000·c7b66f00·00000000·..o.......o.....66 ··0x008853f0·8bcb6f00·00000000·c7b66f00·00000000·..o.......o.....
67 ··0x00885400·e1ca6f00·00000000·e4ca6f00·00000000·..o.......o.....67 ··0x00885400·e1ca6f00·00000000·e4ca6f00·00000000·..o.......o.....
68 ··0x00885410·e7ca6f00·00000000·79cd6f00·00000000·..o.....y.o.....68 ··0x00885410·e7ca6f00·00000000·79cd6f00·00000000·..o.....y.o.....
69 ··0x00885420·eaca6f00·00000000·edca6f00·00000000·..o.......o.....69 ··0x00885420·eaca6f00·00000000·edca6f00·00000000·..o.......o.....
70 ··0x00885430·81a86f00·00000000·f0ca6f00·00000000·..o.......o.....70 ··0x00885430·81a86f00·00000000·f0ca6f00·00000000·..o.......o.....
71 ··0x00885440·ecb36f00·00000000·2da26f00·00000000·..o.....-.o.....71 ··0x00885440·ecb36f00·00000000·2da26f00·00000000·..o.....-.o.....
Offset 127, 20 lines modifiedOffset 127, 20 lines modified
127 ··0x008857c0·27cd6f00·00000000·48cc6f00·00000000·'.o.....H.o.....127 ··0x008857c0·27cd6f00·00000000·48cc6f00·00000000·'.o.....H.o.....
128 ··0x008857d0·53cb6f00·00000000·bace6f00·00000000·S.o.......o.....128 ··0x008857d0·53cb6f00·00000000·bace6f00·00000000·S.o.......o.....
129 ··0x008857e0·0fa66f00·00000000·83c36f00·00000000·..o.......o.....129 ··0x008857e0·0fa66f00·00000000·83c36f00·00000000·..o.......o.....
130 ··0x008857f0·ebb96f00·00000000·dfbc6f00·00000000·..o.......o.....130 ··0x008857f0·ebb96f00·00000000·dfbc6f00·00000000·..o.......o.....
131 ··0x00885800·ebca6f00·00000000·54c96f00·00000000·..o.....T.o.....131 ··0x00885800·ebca6f00·00000000·54c96f00·00000000·..o.....T.o.....
132 ··0x00885810·0fcb6f00·00000000·b6ca6f00·00000000·..o.......o.....132 ··0x00885810·0fcb6f00·00000000·b6ca6f00·00000000·..o.......o.....
133 ··0x00885820·f1ca6f00·00000000·dbce6f00·00000000·..o.......o.....133 ··0x00885820·f1ca6f00·00000000·dbce6f00·00000000·..o.......o.....
134 ··0x00885830·f5d56f00·00000000·d8b56f00·00000000·..o.......o.....134 ··0x00885830·f2d56f00·00000000·d8b56f00·00000000·..o.......o.....
135 ··0x00885840·4ad26f00·00000000·51d26f00·00000000·J.o.....Q.o.....135 ··0x00885840·47d26f00·00000000·4ed26f00·00000000·G.o.....N.o.....
136 ··0x00885850·d1b66f00·00000000·aeb16f00·00000000·..o.......o.....136 ··0x00885850·d1b66f00·00000000·aeb16f00·00000000·..o.......o.....
137 ··0x00885860·77b56f00·00000000·f3b96f00·00000000·w.o.......o.....137 ··0x00885860·77b56f00·00000000·f3b96f00·00000000·w.o.......o.....
138 ··0x00885870·b1ca6f00·00000000·1dce6f00·00000000·..o.......o.....138 ··0x00885870·b1ca6f00·00000000·1dce6f00·00000000·..o.......o.....
139 ··0x00885880·63d26f00·00000000·3ed26f00·00000000·c.o.....>.o.....139 ··0x00885880·60d26f00·00000000·3bd26f00·00000000·`.o.....;.o.....
140 ··0x00885890·06cb6f00·00000000·34cd6f00·00000000·..o.....4.o.....140 ··0x00885890·06cb6f00·00000000·34cd6f00·00000000·..o.....4.o.....
141 ··0x008858a0·47cd6f00·00000000·55cd6f00·00000000·G.o.....U.o.....141 ··0x008858a0·47cd6f00·00000000·55cd6f00·00000000·G.o.....U.o.....
142 ··0x008858b0·69cd6f00·00000000·6fcd6f00·00000000·i.o.....o.o.....142 ··0x008858b0·69cd6f00·00000000·6fcd6f00·00000000·i.o.....o.o.....
143 ··0x008858c0·60ad6f00·00000000·00000000·00000000·`.o.............143 ··0x008858c0·60ad6f00·00000000·00000000·00000000·`.o.............
144 ··0x008858d0·25733a25·643a2065·72726f72·3a202573·%s:%d:·error:·%s144 ··0x008858d0·25733a25·643a2065·72726f72·3a202573·%s:%d:·error:·%s
145 ··0x008858e0·00000000·00000000·00000000·00000000·................145 ··0x008858e0·00000000·00000000·00000000·00000000·................
146 ··0x008858f0·25733a25·643a2564·3a206572·726f723a·%s:%d:%d:·error:146 ··0x008858f0·25733a25·643a2564·3a206572·726f723a·%s:%d:%d:·error:
Offset 164, 22 lines modifiedOffset 164, 22 lines modified
164 ··0x00885a10·00000000·00000000·00000000·00000000·................164 ··0x00885a10·00000000·00000000·00000000·00000000·................
165 ··0x00885a20·ddce6f00·00000000·80725600·00000000·..o......rV.....165 ··0x00885a20·ddce6f00·00000000·80725600·00000000·..o......rV.....
166 ··0x00885a30·01000000·00000000·e4ce6f00·00000000·..........o.....166 ··0x00885a30·01000000·00000000·e4ce6f00·00000000·..........o.....
167 ··0x00885a40·00000000·00000000·00000000·00000000·................167 ··0x00885a40·00000000·00000000·00000000·00000000·................
168 ··0x00885a50·00000000·00000000·00000000·00000000·................168 ··0x00885a50·00000000·00000000·00000000·00000000·................
169 ··0x00885a60·0a000000·00000000·64636261·00000000·........dcba....169 ··0x00885a60·0a000000·00000000·64636261·00000000·........dcba....
170 ··0x00885a70·00ab7100·00000000·28ab7100·00000000·..q.....(.q.....170 ··0x00885a70·00ab7100·00000000·28ab7100·00000000·..q.....(.q.....
171 ··0x00885a80·1bd66f00·00000000·36d36f00·00000000·..o.....6.o.....171 ··0x00885a80·18d66f00·00000000·33d36f00·00000000·..o.....3.o.....
172 ··0x00885a90·23d46f00·00000000·30a37100·00000000·#.o.....0.q.....172 ··0x00885a90·20d46f00·00000000·30a37100·00000000··.o.....0.q.....
173 ··0x00885aa0·50ab7100·00000000·78ab7100·00000000·P.q.....x.q.....173 ··0x00885aa0·50ab7100·00000000·78ab7100·00000000·P.q.....x.q.....
174 ··0x00885ab0·d8c67100·00000000·28ab7100·00000000·..q.....(.q.....174 ··0x00885ab0·d8c67100·00000000·28ab7100·00000000·..q.....(.q.....
175 ··0x00885ac0·18c77100·00000000·18c77100·00000000·..q.......q.....175 ··0x00885ac0·18c77100·00000000·18c77100·00000000·..q.......q.....
176 ··0x00885ad0·a0d56f00·00000000·b6d56f00·00000000·..o.......o.....176 ··0x00885ad0·9dd56f00·00000000·b3d56f00·00000000·..o.......o.....
177 ··0x00885ae0·40c77100·00000000·1bd66f00·00000000·@.q.......o.....177 ··0x00885ae0·40c77100·00000000·18d66f00·00000000·@.q.......o.....
178 ··0x00885af0·36d36f00·00000000·c0a97100·00000000·6.o.......q.....178 ··0x00885af0·33d36f00·00000000·c0a97100·00000000·3.o.......q.....
179 ··0x00885b00·68c77100·00000000·90c77100·00000000·h.q.......q.....179 ··0x00885b00·68c77100·00000000·90c77100·00000000·h.q.......q.....
180 ··0x00885b10·b8c77100·00000000·18c77100·00000000·..q.......q.....180 ··0x00885b10·b8c77100·00000000·18c77100·00000000·..q.......q.....
181 ··0x00885b20·50ab7100·00000000·fcd26f00·00000000·P.q.......o.....181 ··0x00885b20·50ab7100·00000000·f9d26f00·00000000·P.q.......o.....
182 ··0x00885b30·18c77100·00000000·90c77100·00000000·..q.......q.....182 ··0x00885b30·18c77100·00000000·90c77100·00000000·..q.......q.....
183 ··0x00885b40·e8c77100·00000000·03000000·14000000·..q.............183 ··0x00885b40·e8c77100·00000000·03000000·14000000·..q.............
184 ··0x00885b50·58238800·00000000·00000000·00000000·X#..............184 ··0x00885b50·58238800·00000000·00000000·00000000·X#..............
  
866 B
error from `readelf --wide --decompress --hex-dump=.gnu_debuglink {}`: readelf: Error: Unable to find program interpreter name readelf: Error: no .dynamic section in the dynamic segment
    
Offset 1, 7 lines modifiedOffset 1, 7 lines modified
  
1 Hex·dump·of·section·'.gnu_debuglink':1 Hex·dump·of·section·'.gnu_debuglink':
2 ··0x00000000·38616662·65656632·65323738·64313638·8afbeef2e278d168 
3 ··0x00000010·63626164·33373466·38363539·65393135·cbad374f8659e9152 ··0x00000000·36643036·31633566·30373130·35356238·6d061c5f071055b8
 3 ··0x00000010·38656165·61663062·64336637·34643062·8eaeaf0bd3f74d0b
4 ··0x00000020·30316539·32332e64·65627567·00000000·01e923.debug....4 ··0x00000020·36336631·65662e64·65627567·00000000·63f1ef.debug....
5 ··0x00000030·7e5e9489····························~^..5 ··0x00000030·19320722····························.2."
  
482 MB
macaulay2-dbgsym_1.25.06+ds-2_amd64.deb
367 B
file list
    
Offset 1, 3 lines modifiedOffset 1, 3 lines modified
1 -rw-r--r--···0········0········0········4·2025-06-02·16:39:21.000000·debian-binary1 -rw-r--r--···0········0········0········4·2025-06-02·16:39:21.000000·debian-binary
2 -rw-r--r--···0········0········0······532·2025-06-02·16:39:21.000000·control.tar.xz2 -rw-r--r--···0········0········0······532·2025-06-02·16:39:21.000000·control.tar.xz
3 -rw-r--r--···0········0········0·49716384·2025-06-02·16:39:21.000000·data.tar.xz3 -rw-r--r--···0········0········0·49712960·2025-06-02·16:39:21.000000·data.tar.xz
636 B
control.tar.xz
608 B
control.tar
360 B
./control
    
Offset 5, 8 lines modifiedOffset 5, 8 lines modified
5 Architecture:·amd645 Architecture:·amd64
6 Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org>6 Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org>
7 Installed-Size:·524237 Installed-Size:·52423
8 Depends:·macaulay2·(=·1.25.06+ds-2)8 Depends:·macaulay2·(=·1.25.06+ds-2)
9 Section:·debug9 Section:·debug
10 Priority:·optional10 Priority:·optional
11 Description:·debug·symbols·for·macaulay211 Description:·debug·symbols·for·macaulay2
12 Build-Ids:·a58afbeef2e278d168cbad374f8659e91501e92312 Build-Ids:·fc6d061c5f071055b88eaeaf0bd3f74d0b63f1ef
226 B
./md5sums
30.0 B
./md5sums
Files differ
178 B
line order
    
Offset 1, 1 lines modifiedOffset 1, 1 lines modified
1 usr/lib/debug/.build-id/a5/8afbeef2e278d168cbad374f8659e91501e923.debug1 usr/lib/debug/.build-id/fc/6d061c5f071055b88eaeaf0bd3f74d0b63f1ef.debug
482 MB
data.tar.xz
482 MB
data.tar
1.38 KB
file list
    
Offset 1, 10 lines modifiedOffset 1, 10 lines modified
1 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./1 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./
2 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/2 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/
3 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/3 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/
4 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/debug/4 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/debug/
5 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/debug/.build-id/5 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/debug/.build-id/
6 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/debug/.build-id/a5/6 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/lib/debug/.build-id/fc/
7 -rw-r--r--···0·root·········(0)·root·········(0)·53669912·2025-06-02·16:39:21.000000·./usr/lib/debug/.build-id/a5/8afbeef2e278d168cbad374f8659e91501e923.debug7 -rw-r--r--···0·root·········(0)·root·········(0)·53670424·2025-06-02·16:39:21.000000·./usr/lib/debug/.build-id/fc/6d061c5f071055b88eaeaf0bd3f74d0b63f1ef.debug
8 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/8 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/
9 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/doc/9 drwxr-xr-x···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/doc/
10 lrwxrwxrwx···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/doc/macaulay2-dbgsym·->·macaulay210 lrwxrwxrwx···0·root·········(0)·root·········(0)········0·2025-06-02·16:39:21.000000·./usr/share/doc/macaulay2-dbgsym·->·macaulay2
482 MB
./usr/lib/debug/.build-id/a5/8afbeef2e278d168cbad374f8659e91501e923.debug vs.
./usr/lib/debug/.build-id/fc/6d061c5f071055b88eaeaf0bd3f74d0b63f1ef.debug
File has been modified after NT_GNU_BUILD_ID has been applied. Files 97% similar despite different names
989 B
readelf --wide --file-header {}
error from `readelf --wide --file-header {}`: readelf: Error: Unable to find program interpreter name
    
Offset 6, 15 lines modifiedOffset 6, 15 lines modified
6 ··OS/ABI:····························UNIX·-·GNU6 ··OS/ABI:····························UNIX·-·GNU
7 ··ABI·Version:·······················07 ··ABI·Version:·······················0
8 ··Type:······························DYN·(Shared·object·file)8 ··Type:······························DYN·(Shared·object·file)
9 ··Machine:···························Advanced·Micro·Devices·X86-649 ··Machine:···························Advanced·Micro·Devices·X86-64
10 ··Version:···························0x110 ··Version:···························0x1
11 ··Entry·point·address:···············0xf19f011 ··Entry·point·address:···············0xf19f0
12 ··Start·of·program·headers:··········64·(bytes·into·file)12 ··Start·of·program·headers:··········64·(bytes·into·file)
13 ··Start·of·section·headers:··········53667224·(bytes·into·file)13 ··Start·of·section·headers:··········53667736·(bytes·into·file)
14 ··Flags:·····························0x014 ··Flags:·····························0x0
15 ··Size·of·this·header:···············64·(bytes)15 ··Size·of·this·header:···············64·(bytes)
16 ··Size·of·program·headers:···········56·(bytes)16 ··Size·of·program·headers:···········56·(bytes)
17 ··Number·of·program·headers:·········1517 ··Number·of·program·headers:·········15
18 ··Size·of·section·headers:···········64·(bytes)18 ··Size·of·section·headers:···········64·(bytes)
19 ··Number·of·section·headers:·········4219 ··Number·of·section·headers:·········42
20 ··Section·header·string·table·index:·4120 ··Section·header·string·table·index:·41
3.61 KB
readelf --wide --sections {}
error from `readelf --wide --sections {}`: readelf: Error: Unable to find program interpreter name
    
Offset 1, 8 lines modifiedOffset 1, 8 lines modified
1 There·are·42·section·headers,·starting·at·offset·0x332e598:1 There·are·42·section·headers,·starting·at·offset·0x332e798:
  
2 Section·Headers:2 Section·Headers:
3 ··[Nr]·Name··············Type············Address··········Off····Size···ES·Flg·Lk·Inf·Al3 ··[Nr]·Name··············Type············Address··········Off····Size···ES·Flg·Lk·Inf·Al
4 ··[·0]···················NULL············0000000000000000·000000·000000·00······0···0··04 ··[·0]···················NULL············0000000000000000·000000·000000·00······0···0··0
5 ··[·1]·.note.gnu.property·NOTE············0000000000000388·000388·000020·00···A··0···0··85 ··[·1]·.note.gnu.property·NOTE············0000000000000388·000388·000020·00···A··0···0··8
6 ··[·2]·.note.gnu.build-id·NOTE············00000000000003a8·0003a8·000024·00···A··0···0··46 ··[·2]·.note.gnu.build-id·NOTE············00000000000003a8·0003a8·000024·00···A··0···0··4
7 ··[·3]·.interp···········NOBITS··········00000000000003cc·0003cc·00001c·00···A··0···0··17 ··[·3]·.interp···········NOBITS··········00000000000003cc·0003cc·00001c·00···A··0···0··1
Offset 29, 23 lines modifiedOffset 29, 23 lines modified
29 ··[24]·.data.rel.ro······NOBITS··········000000000086d240·172ec0·015488·00··WA··0···0·3229 ··[24]·.data.rel.ro······NOBITS··········000000000086d240·172ec0·015488·00··WA··0···0·32
30 ··[25]·.dynamic··········NOBITS··········00000000008826c8·172ec0·0003d0·10··WA··6···0··830 ··[25]·.dynamic··········NOBITS··········00000000008826c8·172ec0·0003d0·10··WA··6···0··8
31 ··[26]·.got··············NOBITS··········0000000000882a98·172ec0·002560·08··WA··0···0··831 ··[26]·.got··············NOBITS··········0000000000882a98·172ec0·002560·08··WA··0···0··8
32 ··[27]·.data·············NOBITS··········0000000000885000·172ec0·000b60·00··WA··0···0·3232 ··[27]·.data·············NOBITS··········0000000000885000·172ec0·000b60·00··WA··0···0·32
33 ··[28]·.bss··············NOBITS··········0000000000885b80·172ec0·3f0080·00··WA··0···0·6433 ··[28]·.bss··············NOBITS··········0000000000885b80·172ec0·3f0080·00··WA··0···0·64
34 ··[29]·.comment··········PROGBITS········0000000000000000·1729f0·00001f·01··MS··0···0··134 ··[29]·.comment··········PROGBITS········0000000000000000·1729f0·00001f·01··MS··0···0··1
35 ··[30]·.debug_aranges····PROGBITS········0000000000000000·172a10·009b2c·00···C··0···0··835 ··[30]·.debug_aranges····PROGBITS········0000000000000000·172a10·009b2c·00···C··0···0··8
36 ··[31]·.debug_info·······PROGBITS········0000000000000000·17c540·1b5fd6f·00···C··0···0··836 ··[31]·.debug_info·······PROGBITS········0000000000000000·17c540·1b5ffa3·00···C··0···0··8
37 ··[32]·.debug_abbrev·····PROGBITS········0000000000000000·1cdc2b0·03bba9·00···C··0···0··837 ··[32]·.debug_abbrev·····PROGBITS········0000000000000000·1cdc4e8·03bba9·00···C··0···0··8
38 ··[33]·.debug_line·······PROGBITS········0000000000000000·1d17e60·2a48ac·00···C··0···0··838 ··[33]·.debug_line·······PROGBITS········0000000000000000·1d18098·2a48ac·00···C··0···0··8
39 ··[34]·.debug_str········PROGBITS········0000000000000000·1fbc710·8fef14·01·MSC··0···0··839 ··[34]·.debug_str········PROGBITS········0000000000000000·1fbc948·8fef24·01·MSC··0···0··8
40 ··[35]·.debug_line_str···PROGBITS········0000000000000000·28bb628·0036a6·01·MSC··0···0··840 ··[35]·.debug_line_str···PROGBITS········0000000000000000·28bb870·0036a6·01·MSC··0···0··8
41 ··[36]·.debug_loclists···PROGBITS········0000000000000000·28becd0·5cf225·00···C··0···0··841 ··[36]·.debug_loclists···PROGBITS········0000000000000000·28bef18·5cf21f·00···C··0···0··8
42 ··[37]·.debug_macro······PROGBITS········0000000000000000·2e8def8·0e4799·00···C··0···0··842 ··[37]·.debug_macro······PROGBITS········0000000000000000·2e8e138·0e475c·00···C··0···0··8
43 ··[38]·.debug_rnglists···PROGBITS········0000000000000000·2f72698·148bbc·00···C··0···0··843 ··[38]·.debug_rnglists···PROGBITS········0000000000000000·2f72898·148bbc·00···C··0···0··8
44 ··[39]·.symtab···········SYMTAB··········0000000000000000·30bb258·090a08·18·····40·8787··844 ··[39]·.symtab···········SYMTAB··········0000000000000000·30bb458·090a08·18·····40·8787··8
45 ··[40]·.strtab···········STRTAB··········0000000000000000·314bc60·1e2782·00······0···0··145 ··[40]·.strtab···········STRTAB··········0000000000000000·314be60·1e2782·00······0···0··1
46 ··[41]·.shstrtab·········STRTAB··········0000000000000000·332e3e2·0001b3·00······0···0··146 ··[41]·.shstrtab·········STRTAB··········0000000000000000·332e5e2·0001b3·00······0···0··1
47 Key·to·Flags:47 Key·to·Flags:
48 ··W·(write),·A·(alloc),·X·(execute),·M·(merge),·S·(strings),·I·(info),48 ··W·(write),·A·(alloc),·X·(execute),·M·(merge),·S·(strings),·I·(info),
49 ··L·(link·order),·O·(extra·OS·processing·required),·G·(group),·T·(TLS),49 ··L·(link·order),·O·(extra·OS·processing·required),·G·(group),·T·(TLS),
50 ··C·(compressed),·x·(unknown),·o·(OS·specific),·E·(exclude),50 ··C·(compressed),·x·(unknown),·o·(OS·specific),·E·(exclude),
51 ··R·(retain),·D·(mbind),·l·(large),·p·(processor·specific)51 ··R·(retain),·D·(mbind),·l·(large),·p·(processor·specific)
915 B
readelf --wide --notes {}
error from `readelf --wide --notes {}`: readelf: Error: Unable to find program interpreter name
    
Offset 1, 12 lines modifiedOffset 1, 12 lines modified
  
1 Displaying·notes·found·in:·.note.gnu.property1 Displaying·notes·found·in:·.note.gnu.property
2 ··Owner················Data·size·»  Description2 ··Owner················Data·size·»  Description
3 ··GNU··················0x00000010»  NT_GNU_PROPERTY_TYPE_0»    ······Properties:·x86·ISA·needed:·x86-64-baseline3 ··GNU··················0x00000010»  NT_GNU_PROPERTY_TYPE_0»    ······Properties:·x86·ISA·needed:·x86-64-baseline
  
4 Displaying·notes·found·in:·.note.gnu.build-id4 Displaying·notes·found·in:·.note.gnu.build-id
5 ··Owner················Data·size·»  Description5 ··Owner················Data·size·»  Description
6 ··GNU··················0x00000014»  NT_GNU_BUILD_ID·(unique·build·ID·bitstring)»   ····Build·ID:·a58afbeef2e278d168cbad374f8659e91501e9236 ··GNU··················0x00000014»  NT_GNU_BUILD_ID·(unique·build·ID·bitstring)»   ····Build·ID:·fc6d061c5f071055b88eaeaf0bd3f74d0b63f1ef
  
7 Displaying·notes·found·in:·.note.ABI-tag7 Displaying·notes·found·in:·.note.ABI-tag
8 ··Owner················Data·size·»  Description8 ··Owner················Data·size·»  Description
9 ··GNU··················0x00000010»  NT_GNU_ABI_TAG·(ABI·version·tag)»     ····OS:·Linux,·ABI:·3.2.09 ··GNU··················0x00000010»  NT_GNU_ABI_TAG·(ABI·version·tag)»     ····OS:·Linux,·ABI:·3.2.0
268 MB
readelf --wide --debug-dump=info {}
Max HTML report size reached
1.29 KB
readelf --wide --debug-dump=macro {}
error from `readelf --wide --debug-dump=macro {}`: readelf: Error: Unable to find program interpreter name
    
Offset 11714, 15 lines modifiedOffset 11714, 15 lines modified
11714 ·DW_MACRO_define_strp·-·lineno·:·310·macro·:·PACKAGE_BUGREPORT·"https://github.com/Macaulay2/M2/issues"11714 ·DW_MACRO_define_strp·-·lineno·:·310·macro·:·PACKAGE_BUGREPORT·"https://github.com/Macaulay2/M2/issues"
11715 ·DW_MACRO_define_strp·-·lineno·:·313·macro·:·PACKAGE_NAME·"Macaulay2"11715 ·DW_MACRO_define_strp·-·lineno·:·313·macro·:·PACKAGE_NAME·"Macaulay2"
11716 ·DW_MACRO_define_strp·-·lineno·:·316·macro·:·PACKAGE_STRING·"Macaulay2·1.25.06"11716 ·DW_MACRO_define_strp·-·lineno·:·316·macro·:·PACKAGE_STRING·"Macaulay2·1.25.06"
11717 ·DW_MACRO_define_strp·-·lineno·:·319·macro·:·PACKAGE_TARNAME·"Macaulay2"11717 ·DW_MACRO_define_strp·-·lineno·:·319·macro·:·PACKAGE_TARNAME·"Macaulay2"
11718 ·DW_MACRO_define_strp·-·lineno·:·322·macro·:·PACKAGE_URL·"https://macaulay2.com/"11718 ·DW_MACRO_define_strp·-·lineno·:·322·macro·:·PACKAGE_URL·"https://macaulay2.com/"
11719 ·DW_MACRO_define_strp·-·lineno·:·325·macro·:·PACKAGE_VERSION·"1.25.06"11719 ·DW_MACRO_define_strp·-·lineno·:·325·macro·:·PACKAGE_VERSION·"1.25.06"
11720 ·DW_MACRO_define_strp·-·lineno·:·328·macro·:·PROFILING·011720 ·DW_MACRO_define_strp·-·lineno·:·328·macro·:·PROFILING·0
11721 ·DW_MACRO_define_strp·-·lineno·:·331·macro·:·REL·"6.1.0-37-cloud-amd64"11721 ·DW_MACRO_define_strp·-·lineno·:·331·macro·:·REL·"6.12.22+bpo-amd64"
11722 ·DW_MACRO_define_strp·-·lineno·:·334·macro·:·SIZEOF_INT_P·811722 ·DW_MACRO_define_strp·-·lineno·:·334·macro·:·SIZEOF_INT_P·8
11723 ·DW_MACRO_define_strp·-·lineno·:·337·macro·:·SIZEOF_LONG·811723 ·DW_MACRO_define_strp·-·lineno·:·337·macro·:·SIZEOF_LONG·8
11724 ·DW_MACRO_define_strp·-·lineno·:·350·macro·:·STDC_HEADERS·111724 ·DW_MACRO_define_strp·-·lineno·:·350·macro·:·STDC_HEADERS·1
11725 ·DW_MACRO_define_strp·-·lineno·:·356·macro·:·WITH_NEWLINE_CR·011725 ·DW_MACRO_define_strp·-·lineno·:·356·macro·:·WITH_NEWLINE_CR·0
11726 ·DW_MACRO_define_strp·-·lineno·:·359·macro·:·WITH_NEWLINE_CRLF·011726 ·DW_MACRO_define_strp·-·lineno·:·359·macro·:·WITH_NEWLINE_CRLF·0
11727 ·DW_MACRO_define_strp·-·lineno·:·362·macro·:·WITH_PYTHON·111727 ·DW_MACRO_define_strp·-·lineno·:·362·macro·:·WITH_PYTHON·1
11728 ·DW_MACRO_define_strp·-·lineno·:·365·macro·:·WITH_TBB·111728 ·DW_MACRO_define_strp·-·lineno·:·365·macro·:·WITH_TBB·1
8.61 KB
readelf --wide --debug-dump=loc {}
error from `readelf --wide --debug-dump=loc {}`: readelf: Error: Unable to find program interpreter name
    
Offset 2680159, 15 lines modifiedOffset 2680159, 15 lines modified
2680159 ····00795e8e·v000000000000001·v000000000000000·views·at·00795e8c·for:2680159 ····00795e8e·v000000000000001·v000000000000000·views·at·00795e8c·for:
2680160 ·············00000000002d0d3d·00000000002d0d5b·(DW_OP_reg6·(rbp))2680160 ·············00000000002d0d3d·00000000002d0d5b·(DW_OP_reg6·(rbp))
2680161 ····00795e9a·<End·of·list>2680161 ····00795e9a·<End·of·list>
  
2680162 ····00795e9b·v000000000000001·v000000000000000·location·view·pair2680162 ····00795e9b·v000000000000001·v000000000000000·location·view·pair
  
2680163 ····00795e9d·v000000000000001·v000000000000000·views·at·00795e9b·for:2680163 ····00795e9d·v000000000000001·v000000000000000·views·at·00795e9b·for:
2680164 ·············00000000002d0d3d·00000000002d0d5b·(DW_OP_addr:·6fd1c8;·DW_OP_stack_value)2680164 ·············00000000002d0d3d·00000000002d0d5b·(DW_OP_addr:·6fd1c5;·DW_OP_stack_value)
2680165 ····00795eb2·<End·of·list>2680165 ····00795eb2·<End·of·list>
  
2680166 ····00795eb3·v000000000000002·v000000000000001·location·view·pair2680166 ····00795eb3·v000000000000002·v000000000000001·location·view·pair
  
2680167 ····00795eb5·v000000000000002·v000000000000001·views·at·00795eb3·for:2680167 ····00795eb5·v000000000000002·v000000000000001·views·at·00795eb3·for:
2680168 ·············00000000002d0df4·00000000002d0e05·(DW_OP_reg6·(rbp))2680168 ·············00000000002d0df4·00000000002d0e05·(DW_OP_reg6·(rbp))
2680169 ····00795ec1·<End·of·list>2680169 ····00795ec1·<End·of·list>
Offset 2750869, 15 lines modifiedOffset 2750869, 15 lines modified
2750869 ····007ca626·v000000000000001·v000000000000001·views·at·007ca624·for:2750869 ····007ca626·v000000000000001·v000000000000001·views·at·007ca624·for:
2750870 ·············00000000002e4678·00000000002e4687·(DW_OP_reg3·(rbx))2750870 ·············00000000002e4678·00000000002e4687·(DW_OP_reg3·(rbx))
2750871 ····007ca632·<End·of·list>2750871 ····007ca632·<End·of·list>
  
2750872 ····007ca633·v000000000000001·v000000000000001·location·view·pair2750872 ····007ca633·v000000000000001·v000000000000001·location·view·pair
  
2750873 ····007ca635·v000000000000001·v000000000000001·views·at·007ca633·for:2750873 ····007ca635·v000000000000001·v000000000000001·views·at·007ca633·for:
2750874 ·············00000000002e4678·00000000002e4687·(DW_OP_addr:·6fd263;·DW_OP_stack_value)2750874 ·············00000000002e4678·00000000002e4687·(DW_OP_addr:·6fd260;·DW_OP_stack_value)
2750875 ····007ca64a·<End·of·list>2750875 ····007ca64a·<End·of·list>
  
2750876 ····007ca64b·v000000000000001·v000000000000001·location·view·pair2750876 ····007ca64b·v000000000000001·v000000000000001·location·view·pair
  
2750877 ····007ca64d·v000000000000001·v000000000000001·views·at·007ca64b·for:2750877 ····007ca64d·v000000000000001·v000000000000001·views·at·007ca64b·for:
2750878 ·············00000000002e4687·00000000002e4693·(DW_OP_reg3·(rbx))2750878 ·············00000000002e4687·00000000002e4693·(DW_OP_reg3·(rbx))
2750879 ····007ca659·<End·of·list>2750879 ····007ca659·<End·of·list>
Offset 3299076, 15 lines modifiedOffset 3299076, 15 lines modified
3299076 ····00964ec3·v000000000000001·v000000000000001·views·at·00964ec1·for:3299076 ····00964ec3·v000000000000001·v000000000000001·views·at·00964ec1·for:
3299077 ·············000000000037ead4·000000000037eae3·(DW_OP_reg6·(rbp))3299077 ·············000000000037ead4·000000000037eae3·(DW_OP_reg6·(rbp))
3299078 ····00964ecf·<End·of·list>3299078 ····00964ecf·<End·of·list>
  
3299079 ····00964ed0·v000000000000001·v000000000000001·location·view·pair3299079 ····00964ed0·v000000000000001·v000000000000001·location·view·pair
  
3299080 ····00964ed2·v000000000000001·v000000000000001·views·at·00964ed0·for:3299080 ····00964ed2·v000000000000001·v000000000000001·views·at·00964ed0·for:
3299081 ·············000000000037ead4·000000000037eae3·(DW_OP_addr:·6fd2cc;·DW_OP_stack_value)3299081 ·············000000000037ead4·000000000037eae3·(DW_OP_addr:·6fd2c9;·DW_OP_stack_value)
3299082 ····00964ee7·<End·of·list>3299082 ····00964ee7·<End·of·list>
  
3299083 ····00964ee8·v000000000000001·v000000000000000·location·view·pair3299083 ····00964ee8·v000000000000001·v000000000000000·location·view·pair
3299084 ····00964eea·v000000000000000·v000000000000000·location·view·pair3299084 ····00964eea·v000000000000000·v000000000000000·location·view·pair
3299085 ····00964eec·v000000000000000·v000000000000000·location·view·pair3299085 ····00964eec·v000000000000000·v000000000000000·location·view·pair
  
3299086 ····00964eee·000000000037eb4f·(base·address)3299086 ····00964eee·000000000037eb4f·(base·address)
Offset 3326938, 15 lines modifiedOffset 3326938, 15 lines modified
3326938 ····0097a92c·v000000000000001·v000000000000001·views·at·0097a92a·for:3326938 ····0097a92c·v000000000000001·v000000000000001·views·at·0097a92a·for:
3326939 ·············0000000000386b33·0000000000386b42·(DW_OP_reg6·(rbp))3326939 ·············0000000000386b33·0000000000386b42·(DW_OP_reg6·(rbp))
3326940 ····0097a938·<End·of·list>3326940 ····0097a938·<End·of·list>
  
3326941 ····0097a939·v000000000000001·v000000000000001·location·view·pair3326941 ····0097a939·v000000000000001·v000000000000001·location·view·pair
  
3326942 ····0097a93b·v000000000000001·v000000000000001·views·at·0097a939·for:3326942 ····0097a93b·v000000000000001·v000000000000001·views·at·0097a939·for:
3326943 ·············0000000000386b33·0000000000386b42·(DW_OP_addr:·6fd2cc;·DW_OP_stack_value)3326943 ·············0000000000386b33·0000000000386b42·(DW_OP_addr:·6fd2c9;·DW_OP_stack_value)
3326944 ····0097a950·<End·of·list>3326944 ····0097a950·<End·of·list>
  
3326945 ····0097a951·v000000000000001·v000000000000000·location·view·pair3326945 ····0097a951·v000000000000001·v000000000000000·location·view·pair
3326946 ····0097a953·v000000000000000·v000000000000000·location·view·pair3326946 ····0097a953·v000000000000000·v000000000000000·location·view·pair
3326947 ····0097a955·v000000000000000·v000000000000000·location·view·pair3326947 ····0097a955·v000000000000000·v000000000000000·location·view·pair
  
3326948 ····0097a957·0000000000386baf·(base·address)3326948 ····0097a957·0000000000386baf·(base·address)
Offset 3614899, 15 lines modifiedOffset 3614899, 15 lines modified
3614899 ····00a54c63·v000000000000001·v000000000000001·views·at·00a54c61·for:3614899 ····00a54c63·v000000000000001·v000000000000001·views·at·00a54c61·for:
3614900 ·············00000000003c41ac·00000000003c41bb·(DW_OP_reg6·(rbp))3614900 ·············00000000003c41ac·00000000003c41bb·(DW_OP_reg6·(rbp))
3614901 ····00a54c6f·<End·of·list>3614901 ····00a54c6f·<End·of·list>
  
3614902 ····00a54c70·v000000000000001·v000000000000001·location·view·pair3614902 ····00a54c70·v000000000000001·v000000000000001·location·view·pair
  
3614903 ····00a54c72·v000000000000001·v000000000000001·views·at·00a54c70·for:3614903 ····00a54c72·v000000000000001·v000000000000001·views·at·00a54c70·for:
3614904 ·············00000000003c41ac·00000000003c41bb·(DW_OP_addr:·6fd2cc;·DW_OP_stack_value)3614904 ·············00000000003c41ac·00000000003c41bb·(DW_OP_addr:·6fd2c9;·DW_OP_stack_value)
3614905 ····00a54c87·<End·of·list>3614905 ····00a54c87·<End·of·list>
  
3614906 ····00a54c88·v000000000000001·v000000000000000·location·view·pair3614906 ····00a54c88·v000000000000001·v000000000000000·location·view·pair
  
3614907 ····00a54c8a·v000000000000001·v000000000000000·views·at·00a54c88·for:3614907 ····00a54c8a·v000000000000001·v000000000000000·views·at·00a54c88·for:
3614908 ·············00000000003c4214·00000000003c421f·(DW_OP_reg6·(rbp))3614908 ·············00000000003c4214·00000000003c421f·(DW_OP_reg6·(rbp))
3614909 ····00a54c96·<End·of·list>3614909 ····00a54c96·<End·of·list>
Offset 3701783, 15 lines modifiedOffset 3701783, 15 lines modified
3701783 ····00a95cba·v000000000000001·v000000000000000·views·at·00a95cb8·for:3701783 ····00a95cba·v000000000000001·v000000000000000·views·at·00a95cb8·for:
3701784 ·············00000000003d996c·00000000003d9973·(DW_OP_reg6·(rbp))3701784 ·············00000000003d996c·00000000003d9973·(DW_OP_reg6·(rbp))
3701785 ····00a95cc6·<End·of·list>3701785 ····00a95cc6·<End·of·list>
  
3701786 ····00a95cc7·v000000000000001·v000000000000000·location·view·pair3701786 ····00a95cc7·v000000000000001·v000000000000000·location·view·pair
  
3701787 ····00a95cc9·v000000000000001·v000000000000000·views·at·00a95cc7·for:3701787 ····00a95cc9·v000000000000001·v000000000000000·views·at·00a95cc7·for:
3701788 ·············00000000003d996c·00000000003d9973·(DW_OP_addr:·6fd1c8;·DW_OP_stack_value)3701788 ·············00000000003d996c·00000000003d9973·(DW_OP_addr:·6fd1c5;·DW_OP_stack_value)
3701789 ····00a95cde·<End·of·list>3701789 ····00a95cde·<End·of·list>
  
3701790 ····00a95cdf·v000000000000000·v000000000000000·location·view·pair3701790 ····00a95cdf·v000000000000000·v000000000000000·location·view·pair
3701791 ····00a95ce1·v000000000000000·v000000000000000·location·view·pair3701791 ····00a95ce1·v000000000000000·v000000000000000·location·view·pair
3701792 ····00a95ce3·v000000000000000·v000000000000000·location·view·pair3701792 ····00a95ce3·v000000000000000·v000000000000000·location·view·pair
  
3701793 ····00a95ce5·00000000003d9ea0·(base·address)3701793 ····00a95ce5·00000000003d9ea0·(base·address)
Offset 3703159, 15 lines modifiedOffset 3703159, 15 lines modified
3703159 ····00a96bce·v000000000000000·v000000000000000·views·at·00a96bcc·for:3703159 ····00a96bce·v000000000000000·v000000000000000·views·at·00a96bcc·for:
3703160 ·············00000000003d9109·00000000003d9118·(DW_OP_reg6·(rbp))3703160 ·············00000000003d9109·00000000003d9118·(DW_OP_reg6·(rbp))
3703161 ····00a96bda·<End·of·list>3703161 ····00a96bda·<End·of·list>
  
3703162 ····00a96bdb·v000000000000000·v000000000000000·location·view·pair3703162 ····00a96bdb·v000000000000000·v000000000000000·location·view·pair
  
3703163 ····00a96bdd·v000000000000000·v000000000000000·views·at·00a96bdb·for:3703163 ····00a96bdd·v000000000000000·v000000000000000·views·at·00a96bdb·for:
3703164 ·············00000000003d9109·00000000003d9118·(DW_OP_addr:·6fd1c8;·DW_OP_stack_value)3703164 ·············00000000003d9109·00000000003d9118·(DW_OP_addr:·6fd1c5;·DW_OP_stack_value)
3703165 ····00a96bf2·<End·of·list>3703165 ····00a96bf2·<End·of·list>
  
3703166 ····00a96bf3·v000000000000000·v000000000000000·location·view·pair3703166 ····00a96bf3·v000000000000000·v000000000000000·location·view·pair
3703167 ····00a96bf5·v000000000000000·v000000000000000·location·view·pair3703167 ····00a96bf5·v000000000000000·v000000000000000·location·view·pair
3703168 ····00a96bf7·v000000000000000·v000000000000000·location·view·pair3703168 ····00a96bf7·v000000000000000·v000000000000000·location·view·pair
  
3703169 ····00a96bf9·00000000003d9154·(base·address)3703169 ····00a96bf9·00000000003d9154·(base·address)
Offset 3723424, 15 lines modifiedOffset 3723424, 15 lines modified
3723424 ····00aa5f91·v000000000000001·v000000000000001·views·at·00aa5f8f·for:3723424 ····00aa5f91·v000000000000001·v000000000000001·views·at·00aa5f8f·for:
3723425 ·············00000000003de1d6·00000000003de1f3·(DW_OP_fbreg:·-152)3723425 ·············00000000003de1d6·00000000003de1f3·(DW_OP_fbreg:·-152)
3723426 ····00aa5f9f·<End·of·list>3723426 ····00aa5f9f·<End·of·list>
  
3723427 ····00aa5fa0·v000000000000001·v000000000000001·location·view·pair3723427 ····00aa5fa0·v000000000000001·v000000000000001·location·view·pair
  
3723428 ····00aa5fa2·v000000000000001·v000000000000001·views·at·00aa5fa0·for:3723428 ····00aa5fa2·v000000000000001·v000000000000001·views·at·00aa5fa0·for:
3723429 ·············00000000003de1d6·00000000003de1f3·(DW_OP_addr:·6fd1c8;·DW_OP_stack_value)3723429 ·············00000000003de1d6·00000000003de1f3·(DW_OP_addr:·6fd1c5;·DW_OP_stack_value)
3723430 ····00aa5fb7·<End·of·list>3723430 ····00aa5fb7·<End·of·list>
  
3723431 ····00aa5fb8·v000000000000000·v000000000000000·location·view·pair3723431 ····00aa5fb8·v000000000000000·v000000000000000·location·view·pair
3723432 ····00aa5fba·v000000000000000·v000000000000000·location·view·pair3723432 ····00aa5fba·v000000000000000·v000000000000000·location·view·pair
3723433 ····00aa5fbc·v000000000000000·v000000000000000·location·view·pair3723433 ····00aa5fbc·v000000000000000·v000000000000000·location·view·pair
3723434 ····00aa5fbe·v000000000000000·v000000000000000·location·view·pair3723434 ····00aa5fbe·v000000000000000·v000000000000000·location·view·pair
3723435 ····00aa5fc0·v000000000000000·v000000000000000·location·view·pair3723435 ····00aa5fc0·v000000000000000·v000000000000000·location·view·pair
Max diff block lines reached; 2225/8644 bytes (25.74%) of diff not shown.
169 KB
strings --all --bytes=8 {}
    
Offset 2, 6397 lines modifiedOffset 2, 6569 lines modified
2 yI*E6*MjE2U62 yI*E6*MjE2U6
3 ph8o82\03 ph8o82\0
4 0|c?l}wN4 0|c?l}wN
5 9i8%\M8-5 9i8%\M8-
6 ph8o82\06 ph8o82\0
7 \482868185837 \48286818583
8 ~^lpbp:@8 ~^lpbp:@
9 8o"TsN(r 
10 ]Bh»    $$@· 
11 h-'Ek9:? 
12 EJ]Lu2z' 
13 ZQs;JzZ4 
14 Z7)'Z6)3 
15 1-~a<$ia| 
16 lr;p.'%` 
17 pfyuIyus5uW 
18 ··roR:m· 
19 8Bd`X#g]! 
20 xZM:O'N,b 
21 q!^'e%(. 
22 JPn9<1tZh 
23 IKwzxM(Q9 };3;;;[fv
 10 hQmdka8(
 11 @CJCmt^L#mn^Lc
 12 V9ArJ_@G(c
 13 .'@lk~·W
 14 XM~5FZ,e
 15 -]&F[\&F
 16 3a^.->?&
 17 u6Q\,@Kq
 18 Il;IHfH9
 19 [-%y:[gll
 20 13vI,$iI
 21 er~Snq8h*
 22 g,NokYN/kYc
 23 <vhsT~8o
 24 2_`ihy~~
 25 ;aM1:aMq:a
 26 |1gDp^%h
 27 RJe%8.pf
 28 Q^y<9lzX
 29 IBu(&k?S
 30 {,q2J18Z
24 f7S&'Eo^431 f7S&'Do^45
25 !>.H{P-| 
26 "^@/&b3< 
27 tFyE)uKP 
28 rW\N[<{3E5 
29 ).jz,FF1 
30 n&CM;"|@ 
31 P[067q1hU#Z 
32 ]$Z+S<Dk 
33 +]CQ?[rR 
34 N"Y3v2p],v 
35 kkYl·25g 
36 XP»     W/ChI 
37 eQ9(j*u3 
38 Ge>:H!Su 
39 9a%NhZMb 
40 10weNc/{# 
41 wD{e_,lVm' 
42 fdt01?=mc{ 
43 6}P'~J}l 
44 8p5>EDaP 
45 zZui-k4> 
46 ?\;IK$#Q 
47 TE=*luWpGPW2b 
48 IIH1luAP 
49 :CP1A)HOK 
50 ch>c|h>w 
51 ,/CDeM1w 
52 TL'wp|1[W 
53 X<R2^B9h 
54 498C#8eC 
55 ·~U{Gkk# 
56 |780Y8:8 
57 ZDJ6PR6- 
58 <iBJ_b9i 
59 #ox9QKMK 
60 <5xF0}\! 
61 xCs(·/Gp 
62 /Jp<InEO 
63 W1)!-4eq 
64 [S|SO@1Y 
65 SB»     LV$lNx! 
66 zDg|}5R»#aH 
67 l1#tn($b^ 
68 tF-fy\(oB 
69 ,.mQtzAf 
70 fe2u@giXg 
71 z-Ya9$]. 
72 Ei<l,2&\tD 
73 8K`*.6lD 
74 Ex%N]"}w: 
75 >>'KsKVAs 
76 jlI·#j,K 
77 /Cq$fx621 
78 hl|r<d!J 
79 ag1^8K`W%l1 
80 z!:?aiz8Tv 
81 H4NH4NO4.L 
82 SV)!op3. 
83 s'ja_4^1 
84 :·C05uwD 
85 PRU-(MqP 
86 Ns.TstH%t:' 
87 tw!·DkSV32 [wZ@%zZKNFZ^_
 33 RX+H1!_b0[
 34 oX4S>Q6]
 35 _<SMsTv(fV
 36 X<R(·E43
 37 bPq[zHsGJC
 38 v5[`D4*nST
 39 /w4.U4.mZU
 40 l3@}3Y#F}
 41 Xl0B,ekf
 42 2qHIEq7ew
 43 al)YFuNR
 44 i<»     [QiU?
 45 -@95";:aa»      ?
 46 h{]&jI» H
 47 A~a1p2cS
 48 LR|2+9OM
 49 tk}eukrEo
 50 9C))$3·h
 51 0loQAa*@y"
 52 EH_!\Rdg
Max diff block lines reached; 170598/172508 bytes (98.89%) of diff not shown.
213 MB
readelf --wide --decompress --string-dump=.debug_str {}
Max HTML report size reached