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Fixed LaTeX conversion error.

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gheber 2016-03-25 07:23:58 -05:00
parent 259e152ad6
commit 0b93e50198
1 changed files with 74 additions and 74 deletions
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examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb
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@ -44,12 +44,12 @@
"- ${\\check{\\cal C}}_*({\\cal G})$, module on ${\\cal C}_*({\\cal G})$, with a \"trivial\" product $${\\check{\\cal C}}_*({\\cal G})\\otimes{\\cal C}_*({\\cal G}) \\stackrel {\\check{\\Pi}}{\\longrightarrow} {\\check{\\cal C}}_*({\\cal G})$$ defined by $$\\sigma \\otimes \\tau \\longmapsto \\sigma . \\varepsilon(\\tau),$$ where $\\varepsilon$ is the traditional augmentation of ${\\cal C}_*({\\cal G})$.\n", "- ${\\check{\\cal C}}_*({\\cal G})$, module on ${\\cal C}_*({\\cal G})$, with a \"trivial\" product $${\\check{\\cal C}}_*({\\cal G})\\otimes{\\cal C}_*({\\cal G}) \\stackrel {\\check{\\Pi}}{\\longrightarrow} {\\check{\\cal C}}_*({\\cal G})$$ defined by $$\\sigma \\otimes \\tau \\longmapsto \\sigma . \\varepsilon(\\tau),$$ where $\\varepsilon$ is the traditional augmentation of ${\\cal C}_*({\\cal G})$.\n",
"\n", "\n",
"Now, we consider the set of the followings Bars (where $u$ means *\"untwisted\"* and $t$ *\"twisted\"*):\n", "Now, we consider the set of the followings Bars (where $u$ means *\"untwisted\"* and $t$ *\"twisted\"*):\n",
"\\begin{aligned}\n", "$$\\begin{aligned}\n",
"{\\rm Hat}_{uu} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z}),\\\\\n", "{\\rm Hat}_{uu} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z}),\\\\\n",
"{\\rm Hat}_{ut} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\cal C}_*({\\cal G}),\\mathbb{Z}),\\\\\n", "{\\rm Hat}_{ut} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes {\\cal C}_*({\\cal G}),\\mathbb{Z}),\\\\\n",
"{\\rm Hat}_{tu} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t{\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z}),\\\\\n", "{\\rm Hat}_{tu} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t{\\check{\\cal C}}_*({\\cal G}),\\mathbb{Z}),\\\\\n",
"{\\rm Hat}_{tt} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}).\n", "{\\rm Hat}_{tt} &=& Bar^{{\\cal C}_*({\\cal G})}({\\cal C}_*(\\bar{\\cal W}{\\cal G})\\otimes_t {\\cal C}_*({\\cal G}),\\mathbb{Z}).\n",
"\\end{aligned}\n", "\\end{aligned}$$\n",
"\n", "\n",
"One may always say that ${\\rm Hat}_{ut}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_r$ ($r$: right) induced by the discrepancy between the products in ${\\check{\\cal C}}_*({\\cal G})$ and ${\\cal C}_*({\\cal G})$ and that ${\\rm Hat}_{tu}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_l$ ($l$: left) induced by the twisted tensor product $\\otimes_t$. After that,\n", "One may always say that ${\\rm Hat}_{ut}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_r$ ($r$: right) induced by the discrepancy between the products in ${\\check{\\cal C}}_*({\\cal G})$ and ${\\cal C}_*({\\cal G})$ and that ${\\rm Hat}_{tu}$ is obtained from ${\\rm Hat}_{uu}$ by a perturbation $\\delta_l$ ($l$: left) induced by the twisted tensor product $\\otimes_t$. After that,\n",
"${\\rm Hat}_{tt}$ is obtained from ${\\rm Hat}_{tu}$ by the perturbation $\\delta_r$ as well as, by commutativity, from ${\\rm Hat}_{ut}$ by the perturbation $\\delta_l$.\n", "${\\rm Hat}_{tt}$ is obtained from ${\\rm Hat}_{tu}$ by the perturbation $\\delta_r$ as well as, by commutativity, from ${\\rm Hat}_{ut}$ by the perturbation $\\delta_l$.\n",
@ -198,7 +198,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n",
"* \n", "* \n",
"End of computing.\n", "End of computing.\n",
@ -208,7 +208,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n",
"CAT::S1 \n", "CAT::S1 \n",
"End of computing.\n", "End of computing.\n",
@ -224,14 +224,14 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 1.\n", "Computing boundary-matrix in dimension 1.\n",
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n",
"CAT::S1 \n", "CAT::S1 \n",
"End of computing.\n", "End of computing.\n",
@ -251,7 +251,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 2.\n", "Computing boundary-matrix in dimension 2.\n",
@ -270,7 +270,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 3.\n", "Computing boundary-matrix in dimension 3.\n",
@ -289,7 +289,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 4.\n", "Computing boundary-matrix in dimension 4.\n",
@ -308,7 +308,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 5.\n", "Computing boundary-matrix in dimension 5.\n",
@ -327,7 +327,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 6.\n", "Computing boundary-matrix in dimension 6.\n",
@ -346,7 +346,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 7.\n", "Computing boundary-matrix in dimension 7.\n",
@ -365,7 +365,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 8.\n", "Computing boundary-matrix in dimension 8.\n",
@ -384,7 +384,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 9.\n", "Computing boundary-matrix in dimension 9.\n",
@ -403,7 +403,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 12m 52s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n" "\n"
] ]
}, },
@ -460,7 +460,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n",
"<<Abar>> \n", "<<Abar>> \n",
"End of computing.\n", "End of computing.\n",
@ -480,7 +480,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 1.\n", "Computing boundary-matrix in dimension 1.\n",
@ -491,7 +491,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 2) :\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n",
"<<Abar[2 S1]>> \n", "<<Abar[2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -505,14 +505,14 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 2.\n", "Computing boundary-matrix in dimension 2.\n",
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 2) :\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n",
"<<Abar[2 S1]>> \n", "<<Abar[2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -532,7 +532,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 3.\n", "Computing boundary-matrix in dimension 3.\n",
@ -543,7 +543,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 4) :\n", "Computing the boundary of the generator 1/1 (dimension 4) :\n",
"<<Abar[2 S1][2 S1]>> \n", "<<Abar[2 S1][2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -557,14 +557,14 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 4.\n", "Computing boundary-matrix in dimension 4.\n",
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 4) :\n", "Computing the boundary of the generator 1/1 (dimension 4) :\n",
"<<Abar[2 S1][2 S1]>> \n", "<<Abar[2 S1][2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -584,7 +584,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 5.\n", "Computing boundary-matrix in dimension 5.\n",
@ -595,7 +595,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n", "Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[2 S1][2 S1][2 S1]>> \n", "<<Abar[2 S1][2 S1][2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -609,14 +609,14 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 6.\n", "Computing boundary-matrix in dimension 6.\n",
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n", "Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[2 S1][2 S1][2 S1]>> \n", "<<Abar[2 S1][2 S1][2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -636,7 +636,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 7.\n", "Computing boundary-matrix in dimension 7.\n",
@ -647,7 +647,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 8) :\n", "Computing the boundary of the generator 1/1 (dimension 8) :\n",
"<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n", "<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -661,14 +661,14 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 8.\n", "Computing boundary-matrix in dimension 8.\n",
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 8) :\n", "Computing the boundary of the generator 1/1 (dimension 8) :\n",
"<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n", "<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -688,7 +688,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 9.\n", "Computing boundary-matrix in dimension 9.\n",
@ -699,7 +699,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"Computing the boundary of the generator 1/1 (dimension 10) :\n", "Computing the boundary of the generator 1/1 (dimension 10) :\n",
"<<Abar[2 S1][2 S1][2 S1][2 S1][2 S1]>> \n", "<<Abar[2 S1][2 S1][2 S1][2 S1][2 S1]>> \n",
"End of computing.\n", "End of computing.\n",
@ -713,7 +713,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 28s.\n", ";; Clock -> 2016-03-25, 12h 22m 29s.\n",
"\n" "\n"
] ]
}, },
@ -770,7 +770,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n",
"<<AlLp>> \n", "<<AlLp>> \n",
"End of computing.\n", "End of computing.\n",
@ -780,7 +780,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n",
"<<AlLp[1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -796,14 +796,14 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 1.\n", "Computing boundary-matrix in dimension 1.\n",
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n",
"<<AlLp[1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -813,7 +813,7 @@
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/1 (dimension 2) :\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -829,14 +829,14 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 2.\n", "Computing boundary-matrix in dimension 2.\n",
"Rank of the source-module : 1.\n", "Rank of the source-module : 1.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/1 (dimension 2) :\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -846,13 +846,13 @@
"Rank of the source-module : 2.\n", "Rank of the source-module : 2.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/2 (dimension 3) :\n", "Computing the boundary of the generator 1/2 (dimension 3) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 2/2 (dimension 3) :\n", "Computing the boundary of the generator 2/2 (dimension 3) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -866,20 +866,20 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 3.\n", "Computing boundary-matrix in dimension 3.\n",
"Rank of the source-module : 2.\n", "Rank of the source-module : 2.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/2 (dimension 3) :\n", "Computing the boundary of the generator 1/2 (dimension 3) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 2/2 (dimension 3) :\n", "Computing the boundary of the generator 2/2 (dimension 3) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -889,19 +889,19 @@
"Rank of the source-module : 3.\n", "Rank of the source-module : 3.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/3 (dimension 4) :\n", "Computing the boundary of the generator 1/3 (dimension 4) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 2/3 (dimension 4) :\n", "Computing the boundary of the generator 2/3 (dimension 4) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 3/3 (dimension 4) :\n", "Computing the boundary of the generator 3/3 (dimension 4) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -915,26 +915,26 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 4.\n", "Computing boundary-matrix in dimension 4.\n",
"Rank of the source-module : 3.\n", "Rank of the source-module : 3.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/3 (dimension 4) :\n", "Computing the boundary of the generator 1/3 (dimension 4) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 2/3 (dimension 4) :\n", "Computing the boundary of the generator 2/3 (dimension 4) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 3/3 (dimension 4) :\n", "Computing the boundary of the generator 3/3 (dimension 4) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -944,31 +944,31 @@
"Rank of the source-module : 5.\n", "Rank of the source-module : 5.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/5 (dimension 5) :\n", "Computing the boundary of the generator 1/5 (dimension 5) :\n",
"<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n", "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 2/5 (dimension 5) :\n", "Computing the boundary of the generator 2/5 (dimension 5) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 3/5 (dimension 5) :\n", "Computing the boundary of the generator 3/5 (dimension 5) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 4/5 (dimension 5) :\n", "Computing the boundary of the generator 4/5 (dimension 5) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 5/5 (dimension 5) :\n", "Computing the boundary of the generator 5/5 (dimension 5) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -982,38 +982,38 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"\n", "\n",
"\n", "\n",
"Computing boundary-matrix in dimension 5.\n", "Computing boundary-matrix in dimension 5.\n",
"Rank of the source-module : 5.\n", "Rank of the source-module : 5.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/5 (dimension 5) :\n", "Computing the boundary of the generator 1/5 (dimension 5) :\n",
"<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n", "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 2/5 (dimension 5) :\n", "Computing the boundary of the generator 2/5 (dimension 5) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 3/5 (dimension 5) :\n", "Computing the boundary of the generator 3/5 (dimension 5) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 4/5 (dimension 5) :\n", "Computing the boundary of the generator 4/5 (dimension 5) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 5/5 (dimension 5) :\n", "Computing the boundary of the generator 5/5 (dimension 5) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -1023,49 +1023,49 @@
"Rank of the source-module : 8.\n", "Rank of the source-module : 8.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 1/8 (dimension 6) :\n", "Computing the boundary of the generator 1/8 (dimension 6) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 2/8 (dimension 6) :\n", "Computing the boundary of the generator 2/8 (dimension 6) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 3/8 (dimension 6) :\n", "Computing the boundary of the generator 3/8 (dimension 6) :\n",
"<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 4/8 (dimension 6) :\n", "Computing the boundary of the generator 4/8 (dimension 6) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 5/8 (dimension 6) :\n", "Computing the boundary of the generator 5/8 (dimension 6) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 58s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 6/8 (dimension 6) :\n", "Computing the boundary of the generator 6/8 (dimension 6) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 59s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 7/8 (dimension 6) :\n", "Computing the boundary of the generator 7/8 (dimension 6) :\n",
"<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
"\n", "\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 59s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"Computing the boundary of the generator 8/8 (dimension 6) :\n", "Computing the boundary of the generator 8/8 (dimension 6) :\n",
"<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n", "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n", "End of computing.\n",
@ -1079,7 +1079,7 @@
"\n", "\n",
"---done---\n", "---done---\n",
"\n", "\n",
";; Clock -> 2016-03-25, 12h 13m 59s.\n", ";; Clock -> 2016-03-25, 12h 22m 30s.\n",
"\n" "\n"
] ]
}, },