{ "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)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(CAT:LOOP-SPACE [K124 Simplicial-Group])" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(cat:orgn (second (cat:orgn ooos4)))" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(CAT:LOOP-SPACE [K119 Simplicial-Set])" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(cat:orgn (second (cat:orgn (second (cat:orgn ooos4)))))" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(CAT:SPHERE 4)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(cat:orgn (second (cat:orgn (second (cat:orgn (second (cat:orgn ooos4)))))))" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[K136 Simplicial-Group]\n", "Class: #\n", "Wrapper: #\n", "Instance slots\n", "CAT:CMPR: #\n", "CAT:BASIS: :LOCALLY-EFFECTIVE\n", "CAT:BSGN: <>\n", "CAT:DFFR: [K137 Morphism (degree -1): K136 -> K136]\n", "CAT::GRMD: [K136 Simplicial-Group]\n", "CAT:EFHM: #\n", "CAT:IDNM: 136\n", "CAT:ORGN: (CAT:LOOP-SPACE [K124 Simplicial-Group])\n", "CAT:APRD: #\n", "CAT:CPRD: [K140 Morphism (degree 0): K136 -> K138]\n", "CAT:FACE: #\n", "CAT:KFLL: #\n", "CAT:GRML: [K146 Simplicial-Morphism K141 -> K136]\n", "CAT:GRIN: [K147 Simplicial-Morphism K136 -> K136]\n" ] }, { "data": { "text/plain": [ "NIL" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(describe (cat:smgr 136))" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[K124 Simplicial-Group]\n", "Class: #\n", "Wrapper: #\n", "Instance slots\n", "CAT:CMPR: #\n", "CAT:BASIS: :LOCALLY-EFFECTIVE\n", "CAT:BSGN: <>\n", "CAT:DFFR: [K125 Morphism (degree -1): K124 -> K124]\n", "CAT::GRMD: [K124 Simplicial-Group]\n", "CAT:EFHM: #\n", "CAT:IDNM: 124\n", "CAT:ORGN: (CAT:LOOP-SPACE [K119 Simplicial-Set])\n", "CAT:APRD: #\n", "CAT:CPRD: [K128 Morphism (degree 0): K124 -> K126]\n", "CAT:FACE: #\n", "CAT:KFLL: #\n", "CAT:GRML: [K134 Simplicial-Morphism K129 -> K124]\n", "CAT:GRIN: [K135 Simplicial-Morphism K124 -> K124]\n" ] }, { "data": { "text/plain": [ "NIL" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(describe (cat:smgr 124))" ] }, { "cell_type": "code", "execution_count": 36, "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": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(describe (cat:smst 119))" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[K522 Homotopy-Equivalence K148 <= K512 => K508]" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(cat:efhm ooos4)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[K124 Simplicial-Group]\n", "Class: #\n", "Wrapper: #\n", "Instance slots\n", "CAT:CMPR: #\n", "CAT:BASIS: :LOCALLY-EFFECTIVE\n", "CAT:BSGN: <>\n", "CAT:DFFR: [K125 Morphism (degree -1): K124 -> K124]\n", "CAT::GRMD: [K124 Simplicial-Group]\n", "CAT:EFHM: [K426 Homotopy-Equivalence K124 <= K416 => K329]\n", "CAT:IDNM: 124\n", "CAT:ORGN: (CAT:LOOP-SPACE [K119 Simplicial-Set])\n", "CAT:APRD: #\n", "CAT:CPRD: [K128 Morphism (degree 0): K124 -> K126]\n", "CAT:FACE: #\n", "CAT:KFLL: #\n", "CAT:GRML: [K134 Simplicial-Morphism K129 -> K124]\n", "CAT:GRIN: [K135 Simplicial-Morphism K124 -> K124]\n" ] }, { "data": { "text/plain": [ "NIL" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(describe (cat:smgr 124))" ] }, { "cell_type": "code", "execution_count": 39, "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: [K412 Homotopy-Equivalence K119 <= K119 => K119]\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": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(describe (cat:smst 119))" ] }, { "cell_type": "code", "execution_count": 40, "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: [K412 Homotopy-Equivalence K119 <= K119 => K119]\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": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(describe s4)" ] } ], "metadata": { "kernelspec": { "display_name": "CCL Lisp", "language": "lisp", "name": "lisp" }, "language_info": { "codemirror_mode": "text/x-common-lisp", "mimetype": "text/x-common-lisp", "name": "common-lisp", "pygments_lexer": "common-lisp", "version": "X3J13" } }, "nbformat": 4, "nbformat_minor": 0 }