From 259e152ad6bc53ce06137dad404bb89c130b247d Mon Sep 17 00:00:00 2001
From: gheber <gheber@hdfgroup.org>
Date: Fri, 25 Mar 2016 07:17:35 -0500
Subject: [PATCH] First draft of Chapter 20.

---
 ...Eilenberg-Moore_spectral_sequence_II.ipynb | 945 +++++++++++++++++-
 1 file changed, 937 insertions(+), 8 deletions(-)

diff --git a/examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb b/examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb
index f0b8632..9cf2f9b 100644
--- a/examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb
+++ b/examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb
@@ -162,21 +162,950 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K1 Abelian-Simplicial-Group]"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(def kz1 (k-z-1))"
+   ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {
-    "collapsed": true
+    "collapsed": false
    },
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Computing boundary-matrix in dimension 0.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
+      "* \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 1.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
+      "CAT::S1 \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 0 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 1.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
+      "CAT::S1 \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 2.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 1 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 2.\n",
+      "Rank of the source-module : 0.\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---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 3.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 4.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 3 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 4.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 5.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 4 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 5.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 6.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 5 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 6.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 7.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 6 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 7.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 8.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 7 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 8.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 9.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 8 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 9.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 10.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 9 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 12m 52s.\n",
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(homology kz1 0 10)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K23 Abelian-Simplicial-Group]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(def bkz1 (classifying-space kz1))"
+   ]
+  },
+  {
+   "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 : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
+      "<<Abar>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 1.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 0 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\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 -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
+      "<<Abar[2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 1 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 2.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
+      "<<Abar[2 S1]>> \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",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 3.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 4.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
+      "<<Abar[2 S1][2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 3 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 4.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 4) :\n",
+      "<<Abar[2 S1][2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 5.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 4 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 5.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 6.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
+      "<<Abar[2 S1][2 S1][2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 5 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 6.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 6) :\n",
+      "<<Abar[2 S1][2 S1][2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 7.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 6 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 7.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 8.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
+      "<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 7 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 8.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 8) :\n",
+      "<<Abar[2 S1][2 S1][2 S1][2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 9.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 8 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 9.\n",
+      "Rank of the source-module : 0.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 10.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 10) :\n",
+      "<<Abar[2 S1][2 S1][2 S1][2 S1][2 S1]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 9 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 28s.\n",
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(homology bkz1 0 10)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K154 Simplicial-Group]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(def obkz1 (loop-space bkz1))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Computing boundary-matrix in dimension 0.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 0) :\n",
+      "<<AlLp>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 1.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 0 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 1.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 1) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 2.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 1 :\n",
+      "\n",
+      "\n",
+      "Component Z\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 2.\n",
+      "Rank of the source-module : 1.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/1 (dimension 2) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 3.\n",
+      "Rank of the source-module : 2.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 2 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 3.\n",
+      "Rank of the source-module : 2.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/2 (dimension 3) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 2/2 (dimension 3) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 4.\n",
+      "Rank of the source-module : 3.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/3 (dimension 4) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 2/3 (dimension 4) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 3/3 (dimension 4) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 3 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 4.\n",
+      "Rank of the source-module : 3.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/3 (dimension 4) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 2/3 (dimension 4) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 3/3 (dimension 4) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 5.\n",
+      "Rank of the source-module : 5.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/5 (dimension 5) :\n",
+      "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 2/5 (dimension 5) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 3/5 (dimension 5) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 4/5 (dimension 5) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 5/5 (dimension 5) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 4 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 5.\n",
+      "Rank of the source-module : 5.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/5 (dimension 5) :\n",
+      "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 2/5 (dimension 5) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 3/5 (dimension 5) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 4/5 (dimension 5) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 5/5 (dimension 5) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "Computing boundary-matrix in dimension 6.\n",
+      "Rank of the source-module : 8.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 1/8 (dimension 6) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 2/8 (dimension 6) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 3/8 (dimension 6) :\n",
+      "<<AlLp[5 <<Abar[2 S1][2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 4/8 (dimension 6) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 5/8 (dimension 6) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 58s.\n",
+      "Computing the boundary of the generator 6/8 (dimension 6) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 59s.\n",
+      "Computing the boundary of the generator 7/8 (dimension 6) :\n",
+      "<<AlLp[3 <<Abar[2 S1][2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 59s.\n",
+      "Computing the boundary of the generator 8/8 (dimension 6) :\n",
+      "<<AlLp[1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>][1 <<Abar[2 S1]>>]>> \n",
+      "End of computing.\n",
+      "\n",
+      "\n",
+      "\n",
+      "\n",
+      "Homology in dimension 5 :\n",
+      "\n",
+      "\n",
+      "\n",
+      "---done---\n",
+      "\n",
+      ";; Clock -> 2016-03-25, 12h 13m 59s.\n",
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(homology obkz1 0 6)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Lisp files concerned in this chapter\n",
+    "\n",
+    "`cs-space-efhm.lisp`, `searching-homology.lisp`."
+   ]
   }
  ],
  "metadata": {