From 4f2d59002ac04006484d271a12dd7dac5b11cb50 Mon Sep 17 00:00:00 2001 From: Gerd Heber Date: Fri, 21 Aug 2015 19:38:16 -0500 Subject: [PATCH] Added Chapter 3 examples. --- examples/Chapter3.ipynb | 2415 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 2415 insertions(+) create mode 100644 examples/Chapter3.ipynb diff --git a/examples/Chapter3.ipynb b/examples/Chapter3.ipynb new file mode 100644 index 0000000..0e1c204 --- /dev/null +++ b/examples/Chapter3.ipynb @@ -0,0 +1,2415 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3\n", + "# The Homology Module\n", + "## Example" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(\"kenzo\")" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(ql:quickload \"kenzo\")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:cat-init)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K1 Chain-Complex]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def diabolo (cat:build-chcm\n", + " :cmpr #'cat:s-cmpr\n", + " :basis #'(lambda (dmn)\n", + " (case dmn\n", + " (0 '(s0 s1 s2 s3 s4 s5))\n", + " (1 '(s01 s02 s12 s23 s34 s35 s45))\n", + " (2 '(s345))\n", + " (otherwise nil)))\n", + " :bsgn 's0\n", + " :intr-dffr #'(lambda (dmn gnr)\n", + " (unless (<= 0 dmn 2)\n", + " (error \"Incorrect dimension for diabolo-dp.\"))\n", + " (case dmn\n", + " (0 (cat:cmbn -1)) ; Note the null combination of degree -1\n", + " (1 (case gnr\n", + " (s01 (cat:cmbn 0 -1 's0 1 's1))\n", + " (s02 (cat:cmbn 0 -1 's0 1 's2))\n", + " (s12 (cat:cmbn 0 -1 's1 1 's2))\n", + " (s23 (cat:cmbn 0 -1 's2 1 's3))\n", + " (s34 (cat:cmbn 0 -1 's3 1 's4))\n", + " (s35 (cat:cmbn 0 -1 's3 1 's5))\n", + " (s45 (cat:cmbn 0 -1 's4 1 's5))))\n", + " (2 (case gnr\n", + " (s345 (cat:cmbn 1 1 's34 -1 's35 1 's45))))\n", + " (otherwise (error \"Bad generator for complex diabolo\"))))\n", + " :strt :GNRT\n", + " :orgn '(diabolo-for-example)))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 0.\n", + "Rank of the source-module : 6.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/6 (dimension 0) :\n", + "S0 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/6 (dimension 0) :\n", + "S1 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/6 (dimension 0) :\n", + "S2 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/6 (dimension 0) :\n", + "S3 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/6 (dimension 0) :\n", + "S4 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/6 (dimension 0) :\n", + "S5 \n", + "End of computing.\n", + "\n", + "\n", + "Computing boundary-matrix in dimension 1.\n", + "Rank of the source-module : 7.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/7 (dimension 1) :\n", + "S01 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/7 (dimension 1) :\n", + "S02 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/7 (dimension 1) :\n", + "S12 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/7 (dimension 1) :\n", + "S23 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/7 (dimension 1) :\n", + "S34 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/7 (dimension 1) :\n", + "S35 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/7 (dimension 1) :\n", + "S45 \n", + "End of computing.\n", + "\n", + "\n", + "\n", + "\n", + "Homology in dimension 0 :\n", + "\n", + "\n", + "Component Z\n", + "\n", + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:chcm-homology diabolo 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 1.\n", + "Rank of the source-module : 7.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/7 (dimension 1) :\n", + "S01 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/7 (dimension 1) :\n", + "S02 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/7 (dimension 1) :\n", + "S12 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/7 (dimension 1) :\n", + "S23 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/7 (dimension 1) :\n", + "S34 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/7 (dimension 1) :\n", + "S35 \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/7 (dimension 1) :\n", + "S45 \n", + "End of computing.\n", + "\n", + "\n", + "Computing boundary-matrix in dimension 2.\n", + "Rank of the source-module : 1.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/1 (dimension 2) :\n", + "S345 \n", + "End of computing.\n", + "\n", + "\n", + "\n", + "\n", + "Homology in dimension 1 :\n", + "\n", + "\n", + "Component Z\n", + "\n", + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:chcm-homology diabolo 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 2.\n", + "Rank of the source-module : 1.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/1 (dimension 2) :\n", + "S345 \n", + "End of computing.\n", + "\n", + "\n", + "Computing boundary-matrix in dimension 3.\n", + "Rank of the source-module : 0.\n", + "\n", + "\n", + "\n", + "\n", + "Homology in dimension 2 :\n", + "\n", + "\n", + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:chcm-homology diabolo 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "#" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def duncehat-basis #'(lambda (dmn)\n", + " (case dmn\n", + " (0 '((0) (1) (2) (3) (4) (5) (6) (7)))\n", + " (1 '((0 1) (0 2) (0 3)\n", + " (0 4) (0 5) (0 6)\n", + " (0 7) (1 2) (1 3)\n", + " (1 4) (1 5) (1 6)\n", + " (1 7) (2 3) (2 4)\n", + " (2 6) (2 7) (3 4)\n", + " (3 5) (4 5) (4 6)\n", + " (5 6) (5 7) (6 7)))\n", + " (2 '((0 1 5) (0 1 6) (0 1 7)\n", + " (0 2 3) (0 2 4) (0 2 6)\n", + " (0 3 4) (0 5 7) (1 2 3)\n", + " (1 2 4) (1 2 7) (1 3 5)\n", + " (1 4 6) (2 6 7) (3 4 5)\n", + " (4 5 6) (5 6 7)))\n", + " (otherwise nil))))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "#" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def duncehat-df #'(lambda (dmn gnr)\n", + " (case dmn\n", + " (0 (cat:cmbn -1))\n", + " (1 (cat:cmbn 0 -1 (list (first gnr)) 1 (rest gnr)))\n", + " (2 (cat:cmbn 1 1 (list (first gnr) (second gnr))\n", + " -1 (list (first gnr) (third gnr))\n", + " 1 (rest gnr)))\n", + " (otherwise nil))))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K3 Chain-Complex]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def duncehat (cat:build-chcm :cmpr #'cat:l-cmpr\n", + " :basis duncehat-basis\n", + " :bsgn '(0)\n", + " :intr-dffr duncehat-df\n", + " :strt :gnrt\n", + " :orgn '(dunce hat)))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 0.\n", + "Rank of the source-module : 8.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/8 (dimension 0) :\n", + "(0) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/8 (dimension 0) :\n", + "(1) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/8 (dimension 0) :\n", + "(2) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/8 (dimension 0) :\n", + "(3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/8 (dimension 0) :\n", + "(4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/8 (dimension 0) :\n", + "(5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/8 (dimension 0) :\n", + "(6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 8/8 (dimension 0) :\n", + "(7) \n", + "End of computing.\n", + "\n", + "\n", + "Computing boundary-matrix in dimension 1.\n", + "Rank of the source-module : 24.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/24 (dimension 1) :\n", + "(0 1) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/24 (dimension 1) :\n", + "(0 2) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/24 (dimension 1) :\n", + "(0 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/24 (dimension 1) :\n", + "(0 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/24 (dimension 1) :\n", + "(0 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/24 (dimension 1) :\n", + "(0 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/24 (dimension 1) :\n", + "(0 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 8/24 (dimension 1) :\n", + "(1 2) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 9/24 (dimension 1) :\n", + "(1 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 10/24 (dimension 1) :\n", + "(1 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 11/24 (dimension 1) :\n", + "(1 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 12/24 (dimension 1) :\n", + "(1 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 13/24 (dimension 1) :\n", + "(1 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 14/24 (dimension 1) :\n", + "(2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 15/24 (dimension 1) :\n", + "(2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 16/24 (dimension 1) :\n", + "(2 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 17/24 (dimension 1) :\n", + "(2 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 18/24 (dimension 1) :\n", + "(3 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 19/24 (dimension 1) :\n", + "(3 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 20/24 (dimension 1) :\n", + "(4 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 21/24 (dimension 1) :\n", + "(4 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 22/24 (dimension 1) :\n", + "(5 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 23/24 (dimension 1) :\n", + "(5 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 24/24 (dimension 1) :\n", + "(6 7) \n", + "End of computing.\n", + "\n", + "\n", + "\n", + "\n", + "Homology in dimension 0 :\n", + "\n", + "\n", + "Component Z\n", + "\n", + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:chcm-homology duncehat 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 1.\n", + "Rank of the source-module : 24.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/24 (dimension 1) :\n", + "(0 1) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/24 (dimension 1) :\n", + "(0 2) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/24 (dimension 1) :\n", + "(0 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/24 (dimension 1) :\n", + "(0 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/24 (dimension 1) :\n", + "(0 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/24 (dimension 1) :\n", + "(0 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/24 (dimension 1) :\n", + "(0 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 8/24 (dimension 1) :\n", + "(1 2) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 9/24 (dimension 1) :\n", + "(1 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 10/24 (dimension 1) :\n", + "(1 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 11/24 (dimension 1) :\n", + "(1 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 12/24 (dimension 1) :\n", + "(1 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 13/24 (dimension 1) :\n", + "(1 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 14/24 (dimension 1) :\n", + "(2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 15/24 (dimension 1) :\n", + "(2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 16/24 (dimension 1) :\n", + "(2 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 17/24 (dimension 1) :\n", + "(2 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 18/24 (dimension 1) :\n", + "(3 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 19/24 (dimension 1) :\n", + "(3 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 20/24 (dimension 1) :\n", + "(4 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 21/24 (dimension 1) :\n", + "(4 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 22/24 (dimension 1) :\n", + "(5 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 23/24 (dimension 1) :\n", + "(5 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 24/24 (dimension 1) :\n", + "(6 7) \n", + "End of computing.\n", + "\n", + "\n", + "Computing boundary-matrix in dimension 2.\n", + "Rank of the source-module : 17.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/17 (dimension 2) :\n", + "(0 1 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/17 (dimension 2) :\n", + "(0 1 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/17 (dimension 2) :\n", + "(0 1 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/17 (dimension 2) :\n", + "(0 2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/17 (dimension 2) :\n", + "(0 2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/17 (dimension 2) :\n", + "(0 2 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/17 (dimension 2) :\n", + "(0 3 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 8/17 (dimension 2) :\n", + "(0 5 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 9/17 (dimension 2) :\n", + "(1 2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 10/17 (dimension 2) :\n", + "(1 2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 11/17 (dimension 2) :\n", + "(1 2 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 12/17 (dimension 2) :\n", + "(1 3 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 13/17 (dimension 2) :\n", + "(1 4 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 14/17 (dimension 2) :\n", + "(2 6 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 15/17 (dimension 2) :\n", + "(3 4 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 16/17 (dimension 2) :\n", + "(4 5 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 17/17 (dimension 2) :\n", + "(5 6 7) \n", + "End of computing.\n", + "\n", + "\n", + "\n", + "\n", + "Homology in dimension 1 :\n", + "\n", + "\n", + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:chcm-homology duncehat 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 2.\n", + "Rank of the source-module : 17.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/17 (dimension 2) :\n", + "(0 1 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/17 (dimension 2) :\n", + "(0 1 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/17 (dimension 2) :\n", + "(0 1 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/17 (dimension 2) :\n", + "(0 2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/17 (dimension 2) :\n", + "(0 2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/17 (dimension 2) :\n", + "(0 2 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/17 (dimension 2) :\n", + "(0 3 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 8/17 (dimension 2) :\n", + "(0 5 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 9/17 (dimension 2) :\n", + "(1 2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 10/17 (dimension 2) :\n", + "(1 2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 11/17 (dimension 2) :\n", + "(1 2 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 12/17 (dimension 2) :\n", + "(1 3 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 13/17 (dimension 2) :\n", + "(1 4 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 14/17 (dimension 2) :\n", + "(2 6 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 15/17 (dimension 2) :\n", + "(3 4 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 16/17 (dimension 2) :\n", + "(4 5 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 17/17 (dimension 2) :\n", + "(5 6 7) \n", + "End of computing.\n", + "\n", + "\n", + "Computing boundary-matrix in dimension 3.\n", + "Rank of the source-module : 0.\n", + "\n", + "\n", + "\n", + "\n", + "Homology in dimension 2 :\n", + "\n", + "\n", + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:chcm-homology duncehat 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 1.\n", + "Rank of the source-module : 24.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/24 (dimension 1) :\n", + "(0 1) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/24 (dimension 1) :\n", + "(0 2) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/24 (dimension 1) :\n", + "(0 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/24 (dimension 1) :\n", + "(0 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/24 (dimension 1) :\n", + "(0 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/24 (dimension 1) :\n", + "(0 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/24 (dimension 1) :\n", + "(0 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 8/24 (dimension 1) :\n", + "(1 2) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 9/24 (dimension 1) :\n", + "(1 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 10/24 (dimension 1) :\n", + "(1 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 11/24 (dimension 1) :\n", + "(1 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 12/24 (dimension 1) :\n", + "(1 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 13/24 (dimension 1) :\n", + "(1 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 14/24 (dimension 1) :\n", + "(2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 15/24 (dimension 1) :\n", + "(2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 16/24 (dimension 1) :\n", + "(2 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 17/24 (dimension 1) :\n", + "(2 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 18/24 (dimension 1) :\n", + "(3 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 19/24 (dimension 1) :\n", + "(3 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 20/24 (dimension 1) :\n", + "(4 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 21/24 (dimension 1) :\n", + "(4 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 22/24 (dimension 1) :\n", + "(5 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 23/24 (dimension 1) :\n", + "(5 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 24/24 (dimension 1) :\n", + "(6 7) \n", + "End of computing.\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "\n", + "========== MATRIX 8 lines + 24 columns =====\n", + "L1=[C1=-1][C2=-1][C3=-1][C4=-1][C5=-1][C6=-1][C7=-1]\n", + "L2=[C1=1][C8=-1][C9=-1][C10=-1][C11=-1][C12=-1][C13=-1]\n", + "L3=[C2=1][C8=1][C14=-1][C15=-1][C16=-1][C17=-1]\n", + "L4=[C3=1][C9=1][C14=1][C18=-1][C19=-1]\n", + "L5=[C4=1][C10=1][C15=1][C18=1][C20=-1][C21=-1]\n", + "L6=[C5=1][C11=1][C19=1][C20=1][C22=-1][C23=-1]\n", + "L7=[C6=1][C12=1][C16=1][C21=1][C22=1][C24=-1]\n", + "L8=[C7=1][C13=1][C17=1][C23=1][C24=1]\n", + "========== END-MATRIX" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def mz (cat:chcm-mat duncehat 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 2.\n", + "Rank of the source-module : 17.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/17 (dimension 2) :\n", + "(0 1 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 2/17 (dimension 2) :\n", + "(0 1 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 3/17 (dimension 2) :\n", + "(0 1 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 4/17 (dimension 2) :\n", + "(0 2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 5/17 (dimension 2) :\n", + "(0 2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 6/17 (dimension 2) :\n", + "(0 2 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 7/17 (dimension 2) :\n", + "(0 3 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 8/17 (dimension 2) :\n", + "(0 5 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 9/17 (dimension 2) :\n", + "(1 2 3) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 10/17 (dimension 2) :\n", + "(1 2 4) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 11/17 (dimension 2) :\n", + "(1 2 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 12/17 (dimension 2) :\n", + "(1 3 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 13/17 (dimension 2) :\n", + "(1 4 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 14/17 (dimension 2) :\n", + "(2 6 7) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 15/17 (dimension 2) :\n", + "(3 4 5) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 16/17 (dimension 2) :\n", + "(4 5 6) \n", + "End of computing.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 17/17 (dimension 2) :\n", + "(5 6 7) \n", + "End of computing.\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "\n", + "========== MATRIX 24 lines + 17 columns =====\n", + "L1=[C1=1][C2=1][C3=1]\n", + "L2=[C4=1][C5=1][C6=1]\n", + "L3=[C4=-1][C7=1]\n", + "L4=[C5=-1][C7=-1]\n", + "L5=[C1=-1][C8=1]\n", + "L6=[C2=-1][C6=-1]\n", + "L7=[C3=-1][C8=-1]\n", + "L8=[C9=1][C10=1][C11=1]\n", + "L9=[C9=-1][C12=1]\n", + "L10=[C10=-1][C13=1]\n", + "L11=[C1=1][C12=-1]\n", + "L12=[C2=1][C13=-1]\n", + "L13=[C3=1][C11=-1]\n", + "L14=[C4=1][C9=1]\n", + "L15=[C5=1][C10=1]\n", + "L16=[C6=1][C14=1]\n", + "L17=[C11=1][C14=-1]\n", + "L18=[C7=1][C15=1]\n", + "L19=[C12=1][C15=-1]\n", + "L20=[C15=1][C16=1]\n", + "L21=[C13=1][C16=-1]\n", + "L22=[C16=1][C17=1]\n", + "L23=[C8=1][C17=-1]\n", + "L24=[C14=1][C17=1]\n", + "========== END-MATRIX" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def nb (cat:chcm-mat duncehat 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:homologie mz nb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3.2 The general method for computing homology\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "---done---" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:cat-init)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K1 Simplicial-Set]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def s2 (cat:sphere 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[K1 Simplicial-Set]\n", + "Class: #\n", + "Wrapper: #\n", + "Instance slots\n", + "CAT:CMPR: #\n", + "CAT:BASIS: #\n", + "CAT:BSGN: *\n", + "CAT:DFFR: [K2 Morphism (degree -1): K1 -> K1]\n", + "CAT::GRMD: [K1 Simplicial-Set]\n", + "CAT:EFHM: #\n", + "CAT:IDNM: 1\n", + "CAT:ORGN: (CAT:SPHERE 2)\n", + "CAT:CPRD: [K5 Morphism (degree 0): K1 -> K3]\n", + "CAT:FACE: #\n" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(describe s2)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Computing boundary-matrix in dimension 1.\n", + "Rank of the source-module : 0.\n", + "\n", + "\n", + "Computing boundary-matrix in dimension 2.\n", + "Rank of the source-module : 1.\n", + "\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "Computing the boundary of the generator 1/1 (dimension 2) :\n", + "S2 \n", + "End of computing.\n", + "\n", + "\n", + "\n", + "\n", + "Homology in dimension 1 :\n", + "\n", + "\n", + "\n", + "---done---\n", + "\n", + ";; Clock -> 2015-08-21, 19h 37m 14s.\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:homology s2 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[K1 Simplicial-Set]\n", + "Class: #\n", + "Wrapper: #\n", + "Instance slots\n", + "CAT:CMPR: #\n", + "CAT:BASIS: #\n", + "CAT:BSGN: *\n", + "CAT:DFFR: [K2 Morphism (degree -1): K1 -> K1]\n", + "CAT::GRMD: [K1 Simplicial-Set]\n", + "CAT:EFHM: [K9 Homotopy-Equivalence K1 <= K1 => K1]\n", + "CAT:IDNM: 1\n", + "CAT:ORGN: (CAT:SPHERE 2)\n", + "CAT:CPRD: [K5 Morphism (degree 0): K1 -> K3]\n", + "CAT:FACE: #\n" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(describe s2)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(CAT:TRIVIAL-HMEQ [K1 Simplicial-Set])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:orgn (cat:hmeq 9))" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K10 Simplicial-Group]" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def os2 (cat:loop-space s2))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[K10 Simplicial-Group]\n", + "Class: #\n", + "Wrapper: #\n", + "Instance slots\n", + "CAT:CMPR: #\n", + "CAT:BASIS: :LOCALLY-EFFECTIVE\n", + "CAT:BSGN: <>\n", + "CAT:DFFR: [K11 Morphism (degree -1): K10 -> K10]\n", + "CAT::GRMD: [K10 Simplicial-Group]\n", + "CAT:EFHM: #\n", + "CAT:IDNM: 10\n", + "CAT:ORGN: (CAT:LOOP-SPACE [K1 Simplicial-Set])\n", + "CAT:APRD: #\n", + "CAT:CPRD: [K14 Morphism (degree 0): K10 -> K12]\n", + "CAT:FACE: #\n", + "CAT:KFLL: #\n", + "CAT:GRML: [K20 Simplicial-Morphism K15 -> K10]\n", + "CAT:GRIN: [K21 Simplicial-Morphism K10 -> K10]\n" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(describe os2)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(CAT:LOOP-SPACE [K1 Simplicial-Set])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:orgn os2)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K118 Homotopy-Equivalence K10 <= K108 => K25]" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:efhm os2)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[K10 Simplicial-Group]\n", + "Class: #\n", + "Wrapper: #\n", + "Instance slots\n", + "CAT:CMPR: #\n", + "CAT:BASIS: :LOCALLY-EFFECTIVE\n", + "CAT:BSGN: <>\n", + "CAT:DFFR: [K11 Morphism (degree -1): K10 -> K10]\n", + "CAT::GRMD: [K10 Simplicial-Group]\n", + "CAT:EFHM: [K118 Homotopy-Equivalence K10 <= K108 => K25]\n", + "CAT:IDNM: 10\n", + "CAT:ORGN: (CAT:LOOP-SPACE [K1 Simplicial-Set])\n", + "CAT:APRD: #\n", + "CAT:CPRD: [K14 Morphism (degree 0): K10 -> K12]\n", + "CAT:FACE: #\n", + "CAT:KFLL: #\n", + "CAT:GRML: [K20 Simplicial-Morphism K15 -> K10]\n", + "CAT:GRIN: [K21 Simplicial-Morphism K10 -> K10]\n" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(describe os2)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K119 Simplicial-Set]" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def s4 (cat:sphere 4))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[K119 Simplicial-Set]\n", + "Class: #\n", + "Wrapper: #\n", + "Instance slots\n", + "CAT:CMPR: #\n", + "CAT:BASIS: #\n", + "CAT:BSGN: *\n", + "CAT:DFFR: [K120 Morphism (degree -1): K119 -> K119]\n", + "CAT::GRMD: [K119 Simplicial-Set]\n", + "CAT:EFHM: #\n", + "CAT:IDNM: 119\n", + "CAT:ORGN: (CAT:SPHERE 4)\n", + "CAT:CPRD: [K123 Morphism (degree 0): K119 -> K121]\n", + "CAT:FACE: #\n" + ] + }, + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(describe s4)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K148 Simplicial-Group]" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:def ooos4 (cat:loop-space (cat:loop-space (cat:loop-space s4))))" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(CAT:LOOP-SPACE [K136 Simplicial-Group])" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(cat:orgn ooos4)" + ] + }, + { + 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