From d169572ae9cef48d4839865c77d9724b4130bb2c Mon Sep 17 00:00:00 2001 From: Gerd Heber Date: Mon, 28 Dec 2015 19:14:23 -0600 Subject: [PATCH] Updated introduction and formatting. --- examples/Overview.ipynb | 365 +++++++++++++++++++++------------------- 1 file changed, 191 insertions(+), 174 deletions(-) diff --git a/examples/Overview.ipynb b/examples/Overview.ipynb index 1377b46..1f7f575 100644 --- a/examples/Overview.ipynb +++ b/examples/Overview.ipynb @@ -13,7 +13,11 @@ "source": [ "In this overview we try to show, without entering in detailed explanations, various possibilities of $\\texttt{Kenzo}$ in algebraic topology.\n", "\n", - "Load the $\\texttt{Kenzo}$ software as follows:" + "The material is arranged in a sequence of cells. Cells marked with $\\texttt{In [*]}$ represent (editable) input expressions, which in a traditional REPL (Read-Evaluate-Print Loop) would be typed by the user. Cells marked with $\\texttt{Out [*]}$ represent the value of the correpsponding input expression. Note that if an input expression was not evaluated previously, the ouput cell might be missing. Finally, there might be additional, non-editable, diagnostic output printed between an input and output cell. This is a side-effect of the input form evaluation and can be ignored on first reading.\n", + "\n", + "### Getting off the Ground\n", + "\n", + "Load the $\\texttt{Kenzo}$ software by evaluating the follwing expression. When loaded successfully, the value of this form is a single string atom list $(\\texttt{\"kenzo\"})$." ] }, { @@ -23,6 +27,18 @@ "collapsed": false }, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "To load \"kenzo\":\n", + " Load 1 ASDF system:\n", + " kenzo\n", + "\n", + "; Loading \"kenzo\"\n", + "\n" + ] + }, { "data": { "text/plain": [ @@ -42,7 +58,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The main functionality of the $\\texttt{Kenzo}$ software is defined package in the $\\texttt{cat}$ Lisp package. Initialize the $\\texttt{cat}$ package as follows:" + "The main functionality of the $\\texttt{Kenzo}$ software is defined in a Lisp package called $\\texttt{cat}$. Initialize the software by calling the $\\texttt{cat-init}$ function of the $\\texttt{cat}$ package. Upon successful initialization this form evaluates to $\\texttt{NIL}$." ] }, { @@ -79,7 +95,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Print the $\\texttt{Kenzo}$ version as follows:" + "You can print the $\\texttt{Kenzo}$ version by calling the $\\texttt{kenzo-version}$ function:" ] }, { @@ -117,7 +133,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let us begin by the space $\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z}, 3)$ described as a simplicial set having only three non--degenerate simplices, namely in dimension $0$, $3$ and $4$. In the representation created by the software, the $0$--simplex (base point), 15 the $3$--simplex and the $4$--simplex are respectively labelled $\\texttt{\"*\"}$, $\\texttt{M3}$ and $\\texttt{N4}$. Two faces of the $4$-simplex $\\texttt{N4}$ are identified with the $3$-simplex $\\texttt{M3}$, the others being contracted on the base point. To create the simplicial set one types simply: " + "### $\\texttt{Kenzo}$ in Action\n", + "\n", + "Let us begin by the space $\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z}, 3)$ described as a simplicial set having only three non-degenerate simplices, namely in dimension $0$, $3$ and $4$. In the representation created by the software, the $0$-simplex (base point), the $3$-simplex and the $4$-simplex are respectively labelled $\\texttt{\"*\"}$, $\\texttt{M3}$ and $\\texttt{N4}$. Two faces of the $4$-simplex $\\texttt{N4}$ are identified with the $3$-simplex $\\texttt{M3}$, the others being contracted on the base point. To create the simplicial set one types simply: " ] }, { @@ -194,7 +212,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n", "* \n", "End of computing.\n", @@ -214,7 +232,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 1.\n", @@ -233,7 +251,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 2.\n", @@ -244,7 +262,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 3) :\n", "M3 \n", "End of computing.\n", @@ -258,14 +276,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 3.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 3) :\n", "M3 \n", "End of computing.\n", @@ -275,7 +293,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 4) :\n", "N4 \n", "End of computing.\n", @@ -291,14 +309,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 4.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 4) :\n", "N4 \n", "End of computing.\n", @@ -316,7 +334,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n" ] }, @@ -419,7 +437,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The number of elements of the basis is quite large (230). The user will note that the basis elements are formed by cartesian products of *degenerated simplices*. In the list, an element like $\\texttt{}$ means $\\eta_1\\eta_0\\mathrm{N4}\\times\\eta_5\\eta_3\\eta_2\\mathrm{M3}$.\n", + "As shown by the last command, the number of elements of the basis is quite large (230). The user will note that the basis elements are formed by cartesian products of *degenerated simplices*. In the list, an element like $\\texttt{}$ means $\\eta_1\\eta_0\\mathrm{N4}\\times\\eta_5\\eta_3\\eta_2\\mathrm{M3}$.\n", "\n", "We may construct also the tensor product $\\mathrm{m23}\\otimes\\mathrm{m23}$ from the underlying chain complex of the simplicial set $\\texttt{m23}$. This tensor product is a new chain complex and we see that the basis in dimension $6$ has only one element:" ] @@ -491,7 +509,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 0) :\n", " \n", "End of computing.\n", @@ -511,7 +529,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 1.\n", @@ -530,7 +548,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 2.\n", @@ -541,13 +559,13 @@ "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/2 (dimension 3) :\n", " \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/2 (dimension 3) :\n", " \n", "End of computing.\n", @@ -561,20 +579,20 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 3.\n", "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/2 (dimension 3) :\n", " \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/2 (dimension 3) :\n", " \n", "End of computing.\n", @@ -584,13 +602,13 @@ "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/2 (dimension 4) :\n", " \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/2 (dimension 4) :\n", " \n", "End of computing.\n", @@ -608,20 +626,20 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 4.\n", "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/2 (dimension 4) :\n", " \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/2 (dimension 4) :\n", " \n", "End of computing.\n", @@ -639,7 +657,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 5.\n", @@ -650,7 +668,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 6) :\n", " \n", "End of computing.\n", @@ -664,14 +682,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 6.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 6) :\n", " \n", "End of computing.\n", @@ -681,13 +699,13 @@ "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/2 (dimension 7) :\n", " \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/2 (dimension 7) :\n", " \n", "End of computing.\n", @@ -703,20 +721,20 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 7.\n", "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/2 (dimension 7) :\n", " \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/2 (dimension 7) :\n", " \n", "End of computing.\n", @@ -726,7 +744,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 8) :\n", " \n", "End of computing.\n", @@ -742,7 +760,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n" ] }, @@ -765,8 +783,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let us consider now the space $\\mathrm{K}(\\mathbb{Z}, 1)$. This is an Abelian simplicial group created in $\\texttt{Kenzo}$ by the function $\\texttt{k-z}$. In this simplicial group, a simplex in dimension $n$ \n", - "is mathematically represented by a sequence of integers, known as a *bar* object: $$ [a_1 \\mid a_2 \\mid \\ldots \\mid a_n].$$ \n", + "Let us consider now the space $\\mathrm{K}(\\mathbb{Z}, 1)$. This is an Abelian simplicial group created in $\\texttt{Kenzo}$ by the function $\\texttt{k-z}$. In this simplicial group, a simplex in dimension $n$ is mathematically represented by a sequence of integers, known as a *bar* object: $$ [a_1 \\mid a_2 \\mid \\ldots \\mid a_n].$$\n", "In $\\texttt{Kenzo}$, a non-degenerate simplex of $\\mathrm{K}(\\mathbb{Z}, 1)$ in dimension $n$ will be simply a list of $n$ non-null integers, for instance: $\\texttt{(2 3 4 5)}$. In dimension $0$, the only \n", "simplex is $\\texttt{NIL}$ (the base point)." ] @@ -912,13 +929,13 @@ "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/2 (dimension 4) :\n", "<> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/2 (dimension 4) :\n", "<> \n", "End of computing.\n", @@ -928,19 +945,19 @@ "Rank of the source-module : 3.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/3 (dimension 5) :\n", "<> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/3 (dimension 5) :\n", "<> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 3/3 (dimension 5) :\n", "<> \n", "End of computing.\n", @@ -956,7 +973,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n" ] }, @@ -1043,19 +1060,19 @@ "Rank of the source-module : 3.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/3 (dimension 4) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/3 (dimension 4) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 3/3 (dimension 4) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1065,31 +1082,31 @@ "Rank of the source-module : 5.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 25s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/5 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 26s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/5 (dimension 5) :\n", "<>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 3/5 (dimension 5) :\n", "<>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 4/5 (dimension 5) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 5/5 (dimension 5) :\n", "<>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1107,38 +1124,38 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 5.\n", "Rank of the source-module : 5.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/5 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/5 (dimension 5) :\n", "<>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 3/5 (dimension 5) :\n", "<>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 4/5 (dimension 5) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 5/5 (dimension 5) :\n", "<>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1148,49 +1165,49 @@ "Rank of the source-module : 8.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/8 (dimension 6) :\n", "<>][5 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/8 (dimension 6) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 27s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 3/8 (dimension 6) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 28s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 4/8 (dimension 6) :\n", "<>][1 <>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 28s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 5/8 (dimension 6) :\n", "<>][1 <>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 29s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 6/8 (dimension 6) :\n", "<>][3 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 29s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 7/8 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 29s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 8/8 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1208,7 +1225,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n" ] }, @@ -1260,7 +1277,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the following instruction, we locate in the symbol $\\texttt{L1}$ the canonical generator of $\\pi_2 (\\Omega^1S^3)$, that is the $2$--simplex coming from the original sphere. In fact, the object created by the command $\\texttt{(loop3 0 's3 1)}$ is the \"word\" $S3^1$ belonging to the Kan simplicial version $G(S^3)$ (a simplicial group) of the loop space $\\Omega S^3$." + "In the following instruction, we locate in the symbol $\\texttt{L1}$ the canonical generator of $\\pi_2 (\\Omega^1S^3)$, that is the $2$-simplex coming from the original sphere. In fact, the object created by the command $\\texttt{(loop3 0 's3 1)}$ is the \"word\" $S3^1$ belonging to the Kan simplicial version $G(S^3)$ (a simplicial group) of the loop space $\\Omega S^3$." ] }, { @@ -1289,7 +1306,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let us consider also the $2$--degeneracy of the base point of the loop space. In the printed result, the user will recognize the degeneracy $\\eta_1\\eta_0$ of the null loop, base point of $\\Omega^1 S^3$: " + "Let us consider also the $2$-degeneracy of the base point of the loop space. In the printed result, the user will recognize the degeneracy $\\eta_1\\eta_0$ of the null loop, base point of $\\Omega^1 S^3$: " ] }, { @@ -1318,7 +1335,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We may build now a new space by pasting a disk $D3$ as indicated by the following call. It means that we \"paste\" to the space $\\texttt{os3}$ a $3$--simplex named $\\texttt{D3}$, the attaching map being described by the list of its faces in dimension $2$." + "We may build now a new space by pasting a disk $D3$ as indicated by the following call. It means that we \"paste\" to the space $\\texttt{os3}$ a $3$-simplex named $\\texttt{D3}$, the attaching map being described by the list of its faces in dimension $2$." ] }, { @@ -1367,7 +1384,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 2) :\n", "<> \n", "End of computing.\n", @@ -1377,7 +1394,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 3) :\n", " \n", "End of computing.\n", @@ -1393,14 +1410,14 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n", "\n", "Computing boundary-matrix in dimension 3.\n", "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 3) :\n", " \n", "End of computing.\n", @@ -1410,7 +1427,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/1 (dimension 4) :\n", "<> \n", "End of computing.\n", @@ -1424,7 +1441,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n" ] }, @@ -1488,85 +1505,85 @@ "Rank of the source-module : 14.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/14 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/14 (dimension 5) :\n", "<][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 3/14 (dimension 5) :\n", "<>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 4/14 (dimension 5) :\n", "<>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 5/14 (dimension 5) :\n", "<>][2 ][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 6/14 (dimension 5) :\n", "<>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 7/14 (dimension 5) :\n", "<][1 <>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 8/14 (dimension 5) :\n", "<][2 ][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 30s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 9/14 (dimension 5) :\n", "<>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 31s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 10/14 (dimension 5) :\n", "<>][1 <>][1 <>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 31s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 11/14 (dimension 5) :\n", "<>][1 <>][2 ][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 31s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 12/14 (dimension 5) :\n", "<>][2 ][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 31s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 13/14 (dimension 5) :\n", "<][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 31s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 14/14 (dimension 5) :\n", "<>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1576,157 +1593,157 @@ "Rank of the source-module : 26.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 31s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 1/26 (dimension 6) :\n", "<>][5 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 31s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 2/26 (dimension 6) :\n", "<>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 32s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 3/26 (dimension 6) :\n", "<>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 32s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 4/26 (dimension 6) :\n", "<>][2 ][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 32s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 5/26 (dimension 6) :\n", "<>][3 <>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 32s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 6/26 (dimension 6) :\n", "<][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 32s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 7/26 (dimension 6) :\n", "<][2 ][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 33s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 8/26 (dimension 6) :\n", "<][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 33s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 9/26 (dimension 6) :\n", "<>][1 <>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 33s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 10/26 (dimension 6) :\n", "<>][2 ][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 33s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 11/26 (dimension 6) :\n", "<>][1 <>][1 <>][3 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 33s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 12/26 (dimension 6) :\n", "<>][1 <>][2 ][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 33s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 13/26 (dimension 6) :\n", "<>][1 <>][3 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 34s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 14/26 (dimension 6) :\n", "<>][2 ][1 <>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 34s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 15/26 (dimension 6) :\n", "<>][2 ][2 ][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 34s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 16/26 (dimension 6) :\n", "<>][3 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 34s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 17/26 (dimension 6) :\n", "<][1 <>][1 <>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 34s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 18/26 (dimension 6) :\n", "<][1 <>][2 ][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 34s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 19/26 (dimension 6) :\n", "<][2 ][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 34s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 20/26 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 35s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 21/26 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>][2 ]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 35s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 22/26 (dimension 6) :\n", "<>][1 <>][1 <>][2 ][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 35s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 23/26 (dimension 6) :\n", "<>][1 <>][2 ][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 35s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 24/26 (dimension 6) :\n", "<>][2 ][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 35s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 25/26 (dimension 6) :\n", "<][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 35s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "Computing the boundary of the generator 26/26 (dimension 6) :\n", "<>][1 <>][1 <>][1 <>][1 <>][1 <>]>> \n", "End of computing.\n", @@ -1754,7 +1771,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 1s.\n", "\n" ] }, @@ -1777,7 +1794,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let us continue with the Kan theory. First, we check that $S^3$ is not of type Kan and that $\\Omega S^3$ is indeed of type Kan and a non--Abelian simplicial group." + "Let us continue with the Kan theory. First, we check that $S^3$ is not of type Kan and that $\\Omega S^3$ is indeed of type Kan and a non-Abelian simplicial group." ] }, { @@ -2063,7 +2080,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let ${\\cal G}$ be a simplicial group $0$--reduced. $\\Omega S^3$ is such a group. The software $\\texttt{Kenzo}$ allows the construction of the universal bundle $\\bar{\\cal W}{\\cal G}$, i.e. the classifying space of ${\\cal G}$. In our case, as $\\Omega S^3$ in non--Abelian, the result is not a simplicial group but only a simplicial set. We verify that the $H_4$ is null." + "Let ${\\cal G}$ be a simplicial group $0$-reduced. $\\Omega S^3$ is such a group. The software $\\texttt{Kenzo}$ allows the construction of the universal bundle $\\bar{\\cal W}{\\cal G}$, i.e. the classifying space of ${\\cal G}$. In our case, as $\\Omega S^3$ in non-Abelian, the result is not a simplicial group but only a simplicial set. We verify that the $H_4$ is null." ] }, { @@ -2130,7 +2147,7 @@ "Rank of the source-module : 1.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/1 (dimension 5) :\n", "<>]>> \n", "End of computing.\n", @@ -2144,7 +2161,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "\n" ] }, @@ -2167,7 +2184,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let us end this short overview with an example of computation of homotopy groups. The method used in $\\texttt{Kenzo}$ is the Whitehead tower. In this current version only the case where the first non--null homology group (in non--null dimension) is $\\mathbb{Z}$ or $\\mathbb{Z}/{2\\mathbb{Z}}$ can be processed; however if this homology group is a direct sum of several copies of $\\mathbb{Z}$ or $\\mathbb{Z}/{2 \\mathbb{Z}}$, then the corresponding stage of the Whitehead tower may also be constructed step by step.\n", + "Let us end this short overview with an example of computation of homotopy groups. The method used in $\\texttt{Kenzo}$ is the Whitehead tower. In this current version only the case where the first non-null homology group (in non-null dimension) is $\\mathbb{Z}$ or $\\mathbb{Z}/{2\\mathbb{Z}}$ can be processed; however if this homology group is a direct sum of several copies of $\\mathbb{Z}$ or $\\mathbb{Z}/{2 \\mathbb{Z}}$, then the corresponding stage of the Whitehead tower may also be constructed step by step.\n", "\n", "We take again $\\mathrm{Moore}(\\mathbb{Z}/2\\mathbb{Z}, 3)$ whose $H_3$ is $\\mathbb{Z}/2\\mathbb{Z}$. First the fundamental cohomology class is constructed:" ] @@ -2275,13 +2292,13 @@ "Rank of the source-module : 2.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/2 (dimension 3) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/2 (dimension 3) :\n", ">> \n", "End of computing.\n", @@ -2291,19 +2308,19 @@ "Rank of the source-module : 3.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/3 (dimension 4) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/3 (dimension 4) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 3/3 (dimension 4) :\n", ">> \n", "End of computing.\n", @@ -2317,26 +2334,26 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "\n", "\n", "Computing boundary-matrix in dimension 4.\n", "Rank of the source-module : 3.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/3 (dimension 4) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/3 (dimension 4) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 3/3 (dimension 4) :\n", ">> \n", "End of computing.\n", @@ -2346,25 +2363,25 @@ "Rank of the source-module : 4.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/4 (dimension 5) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/4 (dimension 5) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 3/4 (dimension 5) :\n", ">> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 4/4 (dimension 5) :\n", ">> \n", "End of computing.\n", @@ -2380,7 +2397,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "\n" ] }, @@ -2488,25 +2505,25 @@ "Rank of the source-module : 4.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/4 (dimension 4) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/4 (dimension 4) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 3/4 (dimension 4) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 4/4 (dimension 4) :\n", ">> <>> \n", "End of computing.\n", @@ -2516,43 +2533,43 @@ "Rank of the source-module : 7.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/7 (dimension 5) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/7 (dimension 5) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 3/7 (dimension 5) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 4/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 36s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 5/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 6/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 7/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", @@ -2566,50 +2583,50 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "\n", "\n", "Computing boundary-matrix in dimension 5.\n", "Rank of the source-module : 7.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/7 (dimension 5) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/7 (dimension 5) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 3/7 (dimension 5) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 4/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 5/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 6/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 7/7 (dimension 5) :\n", ">> <>> \n", "End of computing.\n", @@ -2619,85 +2636,85 @@ "Rank of the source-module : 14.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 1/14 (dimension 6) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 2/14 (dimension 6) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 37s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 3/14 (dimension 6) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 38s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 4/14 (dimension 6) :\n", ">> <>][3 <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 38s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 5/14 (dimension 6) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 38s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 6/14 (dimension 6) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 38s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 7/14 (dimension 6) :\n", ">> <>]>>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 38s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 8/14 (dimension 6) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 38s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 9/14 (dimension 6) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 38s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 10/14 (dimension 6) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 39s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 11/14 (dimension 6) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 39s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 12/14 (dimension 6) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 41s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 13/14 (dimension 6) :\n", ">> <>> \n", "End of computing.\n", "\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 42s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "Computing the boundary of the generator 14/14 (dimension 6) :\n", ">> <>> \n", "End of computing.\n", @@ -2713,7 +2730,7 @@ "\n", "---done---\n", "\n", - ";; Clock -> 2015-08-14, 21h 17m 43s.\n", + ";; Clock -> 2015-12-29, 1h 11m 2s.\n", "\n" ] }, @@ -2742,7 +2759,7 @@ ], "metadata": { "kernelspec": { - "display_name": "CCL Lisp", + "display_name": "SBCL Lisp", "language": "lisp", "name": "lisp" },