diff --git a/examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb b/examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb index 8d53614..6324a63 100644 --- a/examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb +++ b/examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb @@ -8,8 +8,8 @@ "\n", "## Introduction\n", "\n", - "This chapter is devoted to the effective homology version of the spectral sequence of Eilenberg-Moore, in the particular case of loop spaces. More precisely, let $X$ be a **1-reduced** simplicial set with effective homology, the software `Kenzo` constructs a 0-reduced simplicial set $GX$ which is also with effective homology. In particular, if $X$ is $m$-reduced, this process may be iterated $m$ times, producing an effective homology version of $G^kX,\\,k\\leq m$. So, the software builds an object which contains a complete solution of the Adams problem about the iteration of the\n", - "cobar construction. The user is advised to consult the paper *Stable homotopy and iterated loop spaces, pp. 545* by **Gunnar Carlsson** and **R.James Milgram** in *Handbook of Algebraic Topology, pp 545* edited by *I.M.James, North-Holland, 1995*.\n", + "This chapter is devoted to the effective homology version of the spectral sequence of Eilenberg-Moore, in the particular case of loop spaces. More precisely, let $X$ be a **1-reduced** simplicial set with effective homology, the program `Kenzo` constructs a 0-reduced simplicial set $GX$ which is also with effective homology. In particular, if $X$ is $m$-reduced, this process may be iterated $m$ times, producing an effective homology version of $G^kX,\\,k\\leq m$. So, the program builds an object which contains a complete solution of the Adams problem about the iteration of the\n", + "cobar construction. The user is advised to consult the paper *Stable homotopy and iterated loop spaces, pp. 545* by **Gunnar Carlsson** and **R.James Milgram** in *Handbook of Algebraic Topology, pp 545* edited by *I.M.James, North-Holland, 1995*. The lovely underlying algorithm is due to Julio Rubio, see *A program computing the homology groups of loop spaces*, SIGSAM Bulletin, 1991, vol. 25, pp. 20-24.\n", "\n", "## The detailed construction\n", "\n", @@ -21,7 +21,7 @@ "{\\cal C}_*(X) & & EC_* \\cr\n", "\\end{aligned}\n", "$$\n", - "is provided, where the chain complex $EC_*$ is effective and must be considered as describing the homology of ${\\cal C}_*(X)$. This scheme includes the case where ${\\cal C}_*(X)$ is itself effective; without any other information, the program constructs automatically a trivial homotopy equivalence.\n", + "is provided, where the chain complex $EC_*$ is effective and must be considered as describing the homology of ${\\cal C}_*(X)$. This scheme includes the case where ${\\cal C}_*(X)$ is itself effective; in this case, without any other information, the program constructs automatically a trivial homotopy equivalence.\n", "\n", "Now, if we apply the *Cobar* functor to this homotopy equivalence we obtain the homotopy equivalence $H_R$:\n", "$$\n", @@ -46,9 +46,10 @@ "### Obtaining the left reduction $H_L$\n", "\n", "The homotopy equivalence $H_L$ is obtained by a sequence of intermediate constructions based mainly upon two applications of the basic perturbation lemma. We are led to consider the two following comodules:\n", - "- ${\\cal C}_*(X)$ comodule on itself, with the canonical coproduct.\n", + "\n", + "* ${\\cal C}_*(X)$ comodule on itself, with the canonical coproduct.\n", "$${\\cal C}_*(X)\\stackrel {\\Delta}{\\longrightarrow} {\\cal C}_*(X)\\otimes {\\cal C}_*(X).$$\n", - "- ${\\check{\\cal C}}_*(X)$, comodule on ${\\cal C}_*(X)$, with a \"trivial\" coproduct \n", + "* ${\\check{\\cal C}}_*(X)$, comodule on ${\\cal C}_*(X)$, with a \"trivial\" coproduct \n", "$${\\check{\\cal C}}_*(X) \\stackrel {\\check{\\Delta}}{\\longrightarrow} {\\cal C}_*(X)\\otimes{\\check{\\cal C}}_*(X),\\quad\n", "\\sigma \\rightarrow 1\\otimes\\sigma,\\,\\sigma \\in {\\check{\\cal C}}_*(X).$$\n", "\n", @@ -172,7 +173,7 @@ " (declare (type simplicial-set loop-space))\n", " (loop-space-efhm (second (orgn loop-space))))\n", "```\n", - "The lisp definition of the function `loop-space-efhm` shows clearly the possible recursivity of the process is *space* is itself a loop space.\n", + "The lisp definition of the function `loop-space-efhm` shows clearly the possible recursivity of the process if *space* is itself a loop space.\n", "```commonlisp\n", "(defun LOOP-SPACE-EFHM (space)\n", " (declare (type simplicial-set space))\n", @@ -247,7 +248,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n", "<> \n", "End of computing.\n", @@ -257,7 +258,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n", "<> \n", "End of computing.\n", @@ -273,14 +274,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 1.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n", "<> \n", "End of computing.\n", @@ -290,7 +291,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n", "<> \n", "End of computing.\n", @@ -306,14 +307,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 2.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n", "<> \n", "End of computing.\n", @@ -323,7 +324,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 3) :\n", "<> \n", "End of computing.\n", @@ -339,14 +340,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 3.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 3) :\n", "<> \n", "End of computing.\n", @@ -356,7 +357,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 4) :\n", "<> \n", "End of computing.\n", @@ -372,14 +373,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 4.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 4) :\n", "<> \n", "End of computing.\n", @@ -389,7 +390,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 5) :\n", "<> \n", "End of computing.\n", @@ -405,14 +406,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 5.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 5) :\n", "<> \n", "End of computing.\n", @@ -422,7 +423,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 6) :\n", "<> \n", "End of computing.\n", @@ -438,14 +439,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 6.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 6) :\n", "<> \n", "End of computing.\n", @@ -455,7 +456,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 7) :\n", "<> \n", "End of computing.\n", @@ -471,14 +472,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 7.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 7) :\n", "<> \n", "End of computing.\n", @@ -488,7 +489,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 8) :\n", "<> \n", "End of computing.\n", @@ -504,14 +505,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 8.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 8) :\n", "<> \n", "End of computing.\n", @@ -521,7 +522,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 9) :\n", "<> \n", "End of computing.\n", @@ -537,14 +538,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 9.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 9) :\n", "<> \n", "End of computing.\n", @@ -554,7 +555,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 10) :\n", "<> \n", "End of computing.\n", @@ -570,7 +571,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n" ] }, @@ -679,7 +680,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n", "<> \n", "End of computing.\n", @@ -689,7 +690,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n", "<>]>>]>> \n", "End of computing.\n", @@ -705,14 +706,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 1.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n", "<>]>>]>> \n", "End of computing.\n", @@ -722,7 +723,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n", "<>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -738,14 +739,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 2.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n", "<>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -755,13 +756,13 @@ "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/2 (dimension 3) :\n", "<>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 2/2 (dimension 3) :\n", "<>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -777,20 +778,20 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 3.\n", "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/2 (dimension 3) :\n", "<>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 2/2 (dimension 3) :\n", "<>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -800,25 +801,25 @@ "Rank of the source-module : 4.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/4 (dimension 4) :\n", "<>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 2/4 (dimension 4) :\n", "<>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 3/4 (dimension 4) :\n", "<>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 4/4 (dimension 4) :\n", "<>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -834,32 +835,32 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 4.\n", "Rank of the source-module : 4.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/4 (dimension 4) :\n", "<>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 2/4 (dimension 4) :\n", "<>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 3/4 (dimension 4) :\n", "<>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 4/4 (dimension 4) :\n", "<>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -869,43 +870,43 @@ "Rank of the source-module : 7.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/7 (dimension 5) :\n", "<>][2 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 2/7 (dimension 5) :\n", "<>]>>][4 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 3/7 (dimension 5) :\n", "<>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 4/7 (dimension 5) :\n", "<>]>>][1 <>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 5/7 (dimension 5) :\n", "<>]>>][3 <>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 6/7 (dimension 5) :\n", "<>][2 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 7/7 (dimension 5) :\n", "<>]>>][1 <>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -925,50 +926,50 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "\n", "\n", "Computing boundary-matrix in dimension 5.\n", "Rank of the source-module : 7.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/7 (dimension 5) :\n", "<>][2 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 2/7 (dimension 5) :\n", "<>]>>][4 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 3/7 (dimension 5) :\n", "<>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 4/7 (dimension 5) :\n", "<>]>>][1 <>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 5/7 (dimension 5) :\n", "<>]>>][3 <>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 6/7 (dimension 5) :\n", "<>][2 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 7/7 (dimension 5) :\n", "<>]>>][1 <>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -978,79 +979,79 @@ "Rank of the source-module : 13.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 19s.\n", "Computing the boundary of the generator 1/13 (dimension 6) :\n", "<>][5 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/13 (dimension 6) :\n", "<>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/13 (dimension 6) :\n", "<>]>>][5 <>][2 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/13 (dimension 6) :\n", "<>][2 <>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 5/13 (dimension 6) :\n", "<>][2 <>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 6/13 (dimension 6) :\n", "<>]>>][1 <>]>>][4 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 7/13 (dimension 6) :\n", "<>]>>][4 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 8/13 (dimension 6) :\n", "<>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 9/13 (dimension 6) :\n", "<>]>>][1 <>]>>][1 <>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 28s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 10/13 (dimension 6) :\n", "<>]>>][1 <>]>>][3 <>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 11/13 (dimension 6) :\n", "<>]>>][3 <>][2 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 12/13 (dimension 6) :\n", "<>][2 <>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 13/13 (dimension 6) :\n", "<>]>>][1 <>]>>][1 <>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", @@ -1070,7 +1071,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "\n" ] }, @@ -1149,7 +1150,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n", "<> \n", "End of computing.\n", @@ -1159,7 +1160,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n", "<>]>> \n", "End of computing.\n", @@ -1175,14 +1176,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "\n", "\n", "Computing boundary-matrix in dimension 1.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/1 (dimension 1) :\n", "<>]>> \n", "End of computing.\n", @@ -1192,13 +1193,13 @@ "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/2 (dimension 2) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/2 (dimension 2) :\n", "<>][1 <>]>> \n", "End of computing.\n", @@ -1214,20 +1215,20 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "\n", "\n", "Computing boundary-matrix in dimension 2.\n", "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/2 (dimension 2) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/2 (dimension 2) :\n", "<>][1 <>]>> \n", "End of computing.\n", @@ -1237,25 +1238,25 @@ "Rank of the source-module : 4.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/4 (dimension 3) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/4 (dimension 3) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/4 (dimension 3) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/4 (dimension 3) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1271,32 +1272,32 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "\n", "\n", "Computing boundary-matrix in dimension 3.\n", "Rank of the source-module : 4.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/4 (dimension 3) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/4 (dimension 3) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/4 (dimension 3) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/4 (dimension 3) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1306,55 +1307,55 @@ "Rank of the source-module : 9.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/9 (dimension 4) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/9 (dimension 4) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/9 (dimension 4) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/9 (dimension 4) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 5/9 (dimension 4) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 6/9 (dimension 4) :\n", "<>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 7/9 (dimension 4) :\n", "<>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 8/9 (dimension 4) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 9/9 (dimension 4) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1372,62 +1373,62 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "\n", "\n", "Computing boundary-matrix in dimension 4.\n", "Rank of the source-module : 9.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/9 (dimension 4) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/9 (dimension 4) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/9 (dimension 4) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/9 (dimension 4) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 5/9 (dimension 4) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 6/9 (dimension 4) :\n", "<>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 7/9 (dimension 4) :\n", "<>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 8/9 (dimension 4) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 9/9 (dimension 4) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1437,115 +1438,115 @@ "Rank of the source-module : 19.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/19 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/19 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/19 (dimension 5) :\n", "<>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/19 (dimension 5) :\n", "<>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 5/19 (dimension 5) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 6/19 (dimension 5) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 7/19 (dimension 5) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 8/19 (dimension 5) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 9/19 (dimension 5) :\n", "<>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 10/19 (dimension 5) :\n", "<>][2 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 11/19 (dimension 5) :\n", "<>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 12/19 (dimension 5) :\n", "<>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 13/19 (dimension 5) :\n", "<>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 14/19 (dimension 5) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 15/19 (dimension 5) :\n", "<>][1 <>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 16/19 (dimension 5) :\n", "<>][1 <>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 17/19 (dimension 5) :\n", "<>][2 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 18/19 (dimension 5) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 19/19 (dimension 5) :\n", "<>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1565,122 +1566,122 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "\n", "\n", "Computing boundary-matrix in dimension 5.\n", "Rank of the source-module : 19.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/19 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/19 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/19 (dimension 5) :\n", "<>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/19 (dimension 5) :\n", "<>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 5/19 (dimension 5) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 6/19 (dimension 5) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 7/19 (dimension 5) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 8/19 (dimension 5) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 9/19 (dimension 5) :\n", "<>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 10/19 (dimension 5) :\n", "<>][2 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 11/19 (dimension 5) :\n", "<>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 12/19 (dimension 5) :\n", "<>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 13/19 (dimension 5) :\n", "<>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 14/19 (dimension 5) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 15/19 (dimension 5) :\n", "<>][1 <>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 16/19 (dimension 5) :\n", "<>][1 <>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 17/19 (dimension 5) :\n", "<>][2 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 18/19 (dimension 5) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 19/19 (dimension 5) :\n", "<>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1690,247 +1691,247 @@ "Rank of the source-module : 41.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/41 (dimension 6) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 2/41 (dimension 6) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 3/41 (dimension 6) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 4/41 (dimension 6) :\n", "<>][5 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 5/41 (dimension 6) :\n", "<>][5 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 6/41 (dimension 6) :\n", "<>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 7/41 (dimension 6) :\n", "<>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 8/41 (dimension 6) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 9/41 (dimension 6) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 10/41 (dimension 6) :\n", "<>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 11/41 (dimension 6) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 12/41 (dimension 6) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 13/41 (dimension 6) :\n", "<>][1 <>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 14/41 (dimension 6) :\n", "<>][1 <>][4 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 15/41 (dimension 6) :\n", "<>][2 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 16/41 (dimension 6) :\n", "<>][3 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 17/41 (dimension 6) :\n", "<>][4 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 18/41 (dimension 6) :\n", "<>][4 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 19/41 (dimension 6) :\n", "<>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 20/41 (dimension 6) :\n", "<>][2 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 21/41 (dimension 6) :\n", "<>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 22/41 (dimension 6) :\n", "<>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 23/41 (dimension 6) :\n", "<>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 24/41 (dimension 6) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 25/41 (dimension 6) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 26/41 (dimension 6) :\n", "<>][1 <>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 27/41 (dimension 6) :\n", "<>][1 <>][2 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 28/41 (dimension 6) :\n", "<>][1 <>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 29/41 (dimension 6) :\n", "<>][2 <>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 30/41 (dimension 6) :\n", "<>][2 <>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 31/41 (dimension 6) :\n", "<>][3 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 32/41 (dimension 6) :\n", "<>][1 <>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 33/41 (dimension 6) :\n", "<>][1 <>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 34/41 (dimension 6) :\n", "<>][2 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 35/41 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 36/41 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>][2 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 37/41 (dimension 6) :\n", "<>][1 <>][1 <>][2 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 38/41 (dimension 6) :\n", "<>][1 <>][2 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 39/41 (dimension 6) :\n", "<>][2 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 40/41 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 41/41 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1952,7 +1953,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "\n" ] }, @@ -1977,9 +1978,9 @@ "source": [ "## The solution of the Adams and Carlsson problem\n", "\n", - "Let $X$ an $n$-reduced simplicial set which is not a suspension. The Adams and Carlsson problem (**Gunnar Carlsson, R.James Milgram.** *Stable homotopy and iterated loop spaces* in *Handbook of Algebraic Topology, pp 545* edited by *I.M.James, North-Holland, 1995*.) asks for a finite CW-complex modelizing the iterated loop space $\\Omega^n X$. We show in this section how the `Kenzo` program builds the relevant solution.\n", + "Let $X$ be an $n$-reduced simplicial set which is not a suspension. The Adams and Carlsson problem (**Gunnar Carlsson, R.James Milgram.** *Stable homotopy and iterated loop spaces* in *Handbook of Algebraic Topology, pp 545* edited by *I.M.James, North-Holland, 1995*.) asks for a finite CW-complex modelizing the iterated loop space $\\Omega^n X$. We show in this section how the `Kenzo` program builds the relevant solution.\n", "\n", - "Let us consider for instance the truncated projective space $X=P^\\infty \\mathbb{R}/ P^3 \\mathbb{R}$ (a non-suspended space) and let us build $\\Omega^3 X$." + "Let us consider for instance the stunted projective space $X=P^\\infty \\mathbb{R}/ P^3 \\mathbb{R}$ (a non-suspended space) and let us build $\\Omega^3 X$." ] }, { @@ -2031,7 +2032,7 @@ } ], "source": [ - "(def p4 (R-proj-space 4))" + "(def p4 (R-proj-space :infinity 4))" ] }, { @@ -2082,7 +2083,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The cellular homology of $\\Omega^3 X$ is now known through the symbol `ecc`. Note that 360 objects ($390-30$) have been built to get the final complex `ecc`. From the printing of the length of the basis in dimensions 0 to 5," + "The cellular homology of $\\Omega^3 X$ is now known through the symbol `ecc`. Note that 360 objects ($390-30$) have been built to get the final chain complex `ecc`. From the printing of the length of the basis in dimensions 0 to 5," ] }, { @@ -2143,199 +2144,199 @@ "Rank of the source-module : 33.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 20s.\n", "Computing the boundary of the generator 1/33 (dimension 5) :\n", "<>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 2/33 (dimension 5) :\n", "<>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 3/33 (dimension 5) :\n", "<>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 29s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 4/33 (dimension 5) :\n", "<>][4 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 5/33 (dimension 5) :\n", "<>][3 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 6/33 (dimension 5) :\n", "<>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 7/33 (dimension 5) :\n", "<>][2 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 8/33 (dimension 5) :\n", "<>]>>][4 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 9/33 (dimension 5) :\n", "<>]>>][4 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 10/33 (dimension 5) :\n", "<>]>>][4 <>][3 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 11/33 (dimension 5) :\n", "<>]>>][4 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 12/33 (dimension 5) :\n", "<>]>>][3 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 13/33 (dimension 5) :\n", "<>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 14/33 (dimension 5) :\n", "<>]>>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 15/33 (dimension 5) :\n", "<>][2 <>]>>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 16/33 (dimension 5) :\n", "<>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 17/33 (dimension 5) :\n", "<>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 18/33 (dimension 5) :\n", "<>][3 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 19/33 (dimension 5) :\n", "<>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 20/33 (dimension 5) :\n", "<>]>>][1 <>]>>][3 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 21/33 (dimension 5) :\n", "<>]>>][1 <>]>>][3 <>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 22/33 (dimension 5) :\n", "<>]>>][2 <>]>>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 23/33 (dimension 5) :\n", "<>]>>][3 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 24/33 (dimension 5) :\n", "<>]>>][3 <>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 25/33 (dimension 5) :\n", "<>]>>][1 <>]>>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 26/33 (dimension 5) :\n", "<>]>>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 27/33 (dimension 5) :\n", "<>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 28/33 (dimension 5) :\n", "<>][2 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 29/33 (dimension 5) :\n", "<>]>>][1 <>]>>][1 <>]>>][2 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 30/33 (dimension 5) :\n", "<>]>>][1 <>]>>][2 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 31/33 (dimension 5) :\n", "<>]>>][2 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 32/33 (dimension 5) :\n", "<>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2016-04-03, 8h 33m 30s.\n", + ";; Clock -> 2016-07-17, 16h 53m 21s.\n", "Computing the boundary of the generator 33/33 (dimension 5) :\n", "<>]>>][1 <>]>>][1 <>]>>][1 <>]>>][1 <>]>>]>> \n", "End of computing.\n",