2416 lines
65 KiB
Plaintext
2416 lines
65 KiB
Plaintext
{
|
|
"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": [
|
|
"#<Anonymous Function #x302001DB640F>"
|
|
]
|
|
},
|
|
"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": [
|
|
"#<Anonymous Function #x302001DCAE4F>"
|
|
]
|
|
},
|
|
"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: #<STANDARD-CLASS CAT::SIMPLICIAL-SET>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT::SIMPLICIAL-SET #x302001B2688D>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<Compiled-function CAT::SPHERE-CMPR #x302001C19EFF>\n",
|
|
"CAT:BASIS: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT::SPHERE-BASIS) #x302001E3230F>\n",
|
|
"CAT:BSGN: *\n",
|
|
"CAT:DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
|
|
"CAT::GRMD: [K1 Simplicial-Set]\n",
|
|
"CAT:EFHM: #<Unbound>\n",
|
|
"CAT:IDNM: 1\n",
|
|
"CAT:ORGN: (CAT:SPHERE 2)\n",
|
|
"CAT:CPRD: [K5 Morphism (degree 0): K1 -> K3]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:SPHERE-FACE) #x302001E322AF>\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: #<STANDARD-CLASS CAT::SIMPLICIAL-SET>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT::SIMPLICIAL-SET #x302001B2688D>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<Compiled-function CAT::SPHERE-CMPR #x302001C19EFF>\n",
|
|
"CAT:BASIS: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT::SPHERE-BASIS) #x302001E3230F>\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: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:SPHERE-FACE) #x302001E322AF>\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: #<STANDARD-CLASS CAT:SIMPLICIAL-GROUP>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT:SIMPLICIAL-GROUP #x302001B4C3ED>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-CMPR) #x302001ED76CF>\n",
|
|
"CAT:BASIS: :LOCALLY-EFFECTIVE\n",
|
|
"CAT:BSGN: <<Loop>>\n",
|
|
"CAT:DFFR: [K11 Morphism (degree -1): K10 -> K10]\n",
|
|
"CAT::GRMD: [K10 Simplicial-Group]\n",
|
|
"CAT:EFHM: #<Unbound>\n",
|
|
"CAT:IDNM: 10\n",
|
|
"CAT:ORGN: (CAT:LOOP-SPACE [K1 Simplicial-Set])\n",
|
|
"CAT:APRD: #<Unbound>\n",
|
|
"CAT:CPRD: [K14 Morphism (degree 0): K10 -> K12]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-FACE) #x302001ED767F>\n",
|
|
"CAT:KFLL: #<Unbound>\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: #<STANDARD-CLASS CAT:SIMPLICIAL-GROUP>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT:SIMPLICIAL-GROUP #x302001B4C3ED>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-CMPR) #x302001D0426F>\n",
|
|
"CAT:BASIS: :LOCALLY-EFFECTIVE\n",
|
|
"CAT:BSGN: <<Loop>>\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: #<Unbound>\n",
|
|
"CAT:CPRD: [K14 Morphism (degree 0): K10 -> K12]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-FACE) #x302001D0421F>\n",
|
|
"CAT:KFLL: #<Unbound>\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: #<STANDARD-CLASS CAT::SIMPLICIAL-SET>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT::SIMPLICIAL-SET #x302001B2688D>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<Compiled-function CAT::SPHERE-CMPR #x302001C19EFF>\n",
|
|
"CAT:BASIS: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT::SPHERE-BASIS) #x302001DB506F>\n",
|
|
"CAT:BSGN: *\n",
|
|
"CAT:DFFR: [K120 Morphism (degree -1): K119 -> K119]\n",
|
|
"CAT::GRMD: [K119 Simplicial-Set]\n",
|
|
"CAT:EFHM: #<Unbound>\n",
|
|
"CAT:IDNM: 119\n",
|
|
"CAT:ORGN: (CAT:SPHERE 4)\n",
|
|
"CAT:CPRD: [K123 Morphism (degree 0): K119 -> K121]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:SPHERE-FACE) #x302001DB500F>\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: #<STANDARD-CLASS CAT:SIMPLICIAL-GROUP>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT:SIMPLICIAL-GROUP #x302001B4C3ED>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-CMPR) #x302001DF573F>\n",
|
|
"CAT:BASIS: :LOCALLY-EFFECTIVE\n",
|
|
"CAT:BSGN: <<Loop>>\n",
|
|
"CAT:DFFR: [K137 Morphism (degree -1): K136 -> K136]\n",
|
|
"CAT::GRMD: [K136 Simplicial-Group]\n",
|
|
"CAT:EFHM: #<Unbound>\n",
|
|
"CAT:IDNM: 136\n",
|
|
"CAT:ORGN: (CAT:LOOP-SPACE [K124 Simplicial-Group])\n",
|
|
"CAT:APRD: #<Unbound>\n",
|
|
"CAT:CPRD: [K140 Morphism (degree 0): K136 -> K138]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-FACE) #x302001DF56EF>\n",
|
|
"CAT:KFLL: #<Unbound>\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: #<STANDARD-CLASS CAT:SIMPLICIAL-GROUP>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT:SIMPLICIAL-GROUP #x302001B4C3ED>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-CMPR) #x302001DFA6EF>\n",
|
|
"CAT:BASIS: :LOCALLY-EFFECTIVE\n",
|
|
"CAT:BSGN: <<Loop>>\n",
|
|
"CAT:DFFR: [K125 Morphism (degree -1): K124 -> K124]\n",
|
|
"CAT::GRMD: [K124 Simplicial-Group]\n",
|
|
"CAT:EFHM: #<Unbound>\n",
|
|
"CAT:IDNM: 124\n",
|
|
"CAT:ORGN: (CAT:LOOP-SPACE [K119 Simplicial-Set])\n",
|
|
"CAT:APRD: #<Unbound>\n",
|
|
"CAT:CPRD: [K128 Morphism (degree 0): K124 -> K126]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-FACE) #x302001DFA69F>\n",
|
|
"CAT:KFLL: #<Unbound>\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: #<STANDARD-CLASS CAT::SIMPLICIAL-SET>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT::SIMPLICIAL-SET #x302001B2688D>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<Compiled-function CAT::SPHERE-CMPR #x302001C19EFF>\n",
|
|
"CAT:BASIS: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT::SPHERE-BASIS) #x302001DB506F>\n",
|
|
"CAT:BSGN: *\n",
|
|
"CAT:DFFR: [K120 Morphism (degree -1): K119 -> K119]\n",
|
|
"CAT::GRMD: [K119 Simplicial-Set]\n",
|
|
"CAT:EFHM: #<Unbound>\n",
|
|
"CAT:IDNM: 119\n",
|
|
"CAT:ORGN: (CAT:SPHERE 4)\n",
|
|
"CAT:CPRD: [K123 Morphism (degree 0): K119 -> K121]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:SPHERE-FACE) #x302001DB500F>\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: #<STANDARD-CLASS CAT:SIMPLICIAL-GROUP>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT:SIMPLICIAL-GROUP #x302001B4C3ED>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-CMPR) #x302001D2179F>\n",
|
|
"CAT:BASIS: :LOCALLY-EFFECTIVE\n",
|
|
"CAT:BSGN: <<Loop>>\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: #<Unbound>\n",
|
|
"CAT:CPRD: [K128 Morphism (degree 0): K124 -> K126]\n",
|
|
"CAT:FACE: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:LOOP-SPACE-FACE) #x302001D2174F>\n",
|
|
"CAT:KFLL: #<Unbound>\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: #<STANDARD-CLASS CAT::SIMPLICIAL-SET>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT::SIMPLICIAL-SET #x302001B2688D>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<Compiled-function CAT::SPHERE-CMPR #x302001C19EFF>\n",
|
|
"CAT:BASIS: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT::SPHERE-BASIS) #x302001D1823F>\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: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:SPHERE-FACE) #x302001D181DF>\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: #<STANDARD-CLASS CAT::SIMPLICIAL-SET>\n",
|
|
"Wrapper: #<CCL::CLASS-WRAPPER CAT::SIMPLICIAL-SET #x302001B2688D>\n",
|
|
"Instance slots\n",
|
|
"CAT:CMPR: #<Compiled-function CAT::SPHERE-CMPR #x302001C19EFF>\n",
|
|
"CAT:BASIS: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT::SPHERE-BASIS) #x302001D1823F>\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: #<CCL:COMPILED-LEXICAL-CLOSURE (:INTERNAL\n",
|
|
" CAT::RSLT\n",
|
|
" CAT:SPHERE-FACE) #x302001D181DF>\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
|
|
}
|