mmarco/kenzo
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Updated Dockerfile & Jupyter notebooks.

Browse Source
This commit is contained in:
Gerd Heber 2017-10-08 20:11:31 -05:00
parent 7fbca6b38d
commit adcd323909
23 changed files with 6403 additions and 7675 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

72
Dockerfile
View File

@ -1,52 +1,46 @@
FROM jupyter/notebook:stable
MAINTAINER gheber <gheber@hdfgroup.org>
# original Dockerfile from https://github.com/melhadad/cl-jupyter-docker
RUN apt-get update
FROM python:3.6
RUN DEBIAN_FRONTEND=noninteractive apt-get -y install wget unzip
ENV HOME /root
# LaTeX (missing bits)
# -----------------------
# zeromq with libsodium for encrypted communication
# https://github.com/ogomezm/zeromq-container
# MAINTAINER Oscar Gómez
RUN DEBIAN_FRONTEND=noninteractive apt-get install texlive-generic-recommended
RUN apt-get update && apt-get install -y git build-essential libtool autoconf automake pkg-config unzip libkrb5-dev curl wget pandoc texlive-generic-recommended texlive-xetex
RUN cd /tmp && git clone git://github.com/jedisct1/libsodium.git && cd libsodium && git checkout e2a30a && ./autogen.sh && ./configure && make check && make install && ldconfig
RUN cd /tmp && git clone --depth 1 git://github.com/zeromq/libzmq.git && cd libzmq && ./autogen.sh && ./configure && make
# RUN cd /tmp/libzmq && make check
# SBCL
RUN cd /tmp/libzmq && make install && ldconfig
RUN rm /tmp/* -rf
RUN wget -nv http://downloads.sourceforge.net/project/sbcl/sbcl/1.3.11/sbcl-1.3.11-x86-64-linux-binary.tar.bz2 \
&& tar -jxvf sbcl-1.3.11-x86-64-linux-binary.tar.bz2 \
&& cd sbcl-1.3.11-x86-64-linux \
&& sh install.sh
# -----------------------
# sbcl with quicklist
RUN wget http://prdownloads.sourceforge.net/sbcl/sbcl-1.4.0-x86-64-linux-binary.tar.bz2 -O /tmp/sbcl.tar.bz2 && \
mkdir /tmp/sbcl && \
tar jxvf /tmp/sbcl.tar.bz2 --strip-components=1 -C /tmp/sbcl/ && \
cd /tmp/sbcl && \
sh install.sh && \
cd /tmp \
rm -rf /tmp/sbcl/
# Quicklisp
WORKDIR /tmp/
RUN wget http://beta.quicklisp.org/quicklisp.lisp
RUN wget -nv https://beta.quicklisp.org/quicklisp.lisp \
&& sbcl --load quicklisp.lisp --non-interactive --eval "(quicklisp-quickstart:install)"
RUN sbcl --non-interactive --load quicklisp.lisp --eval "(quicklisp-quickstart:install)" --eval "(setq ql-util::*do-not-prompt* t)" --eval "(ql:add-to-init-file)"
RUN echo '#-quicklisp' >> /root/.sbclrc
RUN echo '(let ((quicklisp-init (merge-pathnames "quicklisp/setup.lisp"' >> /root/.sbclrc
RUN echo ' (user-homedir-pathname))))' >> /root/.sbclrc
RUN echo ' (when (probe-file quicklisp-init)' >> /root/.sbclrc
RUN echo ' (load quicklisp-init)))' >> /root/.sbclrc
RUN echo '(push #p"/workspace/" asdf:*central-registry*)' >> /root/.sbclrc
RUN sbcl --non-interactive --eval '(ql:quickload "alexandria")' --eval '(ql:quickload "trivial-features")' --eval '(ql:quickload "babel")' --eval '(ql:quickload "kenzo")'
# -----------------------
# cl-jupyter
RUN pip3 install ipython
RUN pip3 install jupyter
RUN wget -nv https://github.com/fredokun/cl-jupyter/archive/master.zip \
&& unzip master.zip \
&& mv cl-jupyter-master /root \
&& python3 /root/cl-jupyter-master/install-cl-jupyter.py \
&& sbcl --load /root/cl-jupyter-master/cl-jupyter.lisp --non-interactive
WORKDIR /root
RUN cd /root && git clone https://github.com/fredokun/cl-jupyter.git && cd cl-jupyter && python3 ./install-cl-jupyter.py && sbcl --load ./cl-jupyter.lisp
RUN ln -s /root/cl-jupyter-master/src /root/quicklisp/local-projects/cl-jupyter
# Kenzo
RUN wget https://github.com/gheber/kenzo/archive/master.zip \
&& unzip master.zip -d /root/quicklisp/local-projects && rm master.zip
RUN mv /root/quicklisp/local-projects/kenzo-master /root/quicklisp/local-projects/kenzo
RUN echo '(ql:quickload :cl-jupyter)' >> /root/.sbclrc
RUN echo '(ql:quickload :kenzo)' >> /root/.sbclrc
RUN echo '(use-package :cat :cl-jupyter-user)' >> /root/.sbclrc
RUN echo '(cat:cat-init)' >> /root/.sbclrc
RUN sbcl --eval "(require 'asdf)"
EXPOSE 8888
CMD jupyter notebook --allow-root --no-browser --NotebookApp.token='' --ip '*' --port 8888

752
examples/00_Overview.ipynb
View File

File diff suppressed because it is too large Load Diff

551
examples/01_Chain_Complexes.ipynb
View File

File diff suppressed because one or more lines are too long

619
examples/02_Objects_with_effective_homology.ipynb
View File

File diff suppressed because it is too large Load Diff

1000
examples/03_The_Homology_module.ipynb
View File

File diff suppressed because one or more lines are too long

253
examples/04_Tensor_product_of_chain_complexes.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -54,10 +86,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -65,7 +95,7 @@
"<TnPr A B>"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -76,10 +106,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -91,7 +119,6 @@
"1. GNRT1: A\n",
"2. DEGR2: 2\n",
"3. GNRT2: B\n",
"\n",
"> "
]
},
@ -101,7 +128,7 @@
"NIL"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -112,10 +139,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -123,7 +148,7 @@
"T"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -134,10 +159,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
@ -145,7 +168,7 @@
"NIL"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -156,10 +179,8 @@
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
@ -167,7 +188,7 @@
"T"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@ -178,10 +199,8 @@
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
@ -200,7 +219,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@ -211,10 +230,8 @@
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
@ -222,7 +239,7 @@
"NIL"
]
},
"execution_count": 7,
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@ -233,10 +250,8 @@
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
@ -255,7 +270,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 8,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@ -297,10 +312,8 @@
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -316,7 +329,7 @@
"NIL"
]
},
"execution_count": 9,
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@ -327,10 +340,8 @@
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
@ -338,7 +349,7 @@
"CDELTA"
]
},
"execution_count": 10,
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@ -369,10 +380,8 @@
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
@ -380,7 +389,7 @@
"[K1 Chain-Complex]"
]
},
"execution_count": 11,
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@ -391,10 +400,8 @@
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
@ -402,7 +409,7 @@
"((0 1) (0 2) (1 2))"
]
},
"execution_count": 12,
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@ -413,10 +420,8 @@
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
@ -424,7 +429,7 @@
"[K3 Chain-Complex]"
]
},
"execution_count": 13,
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@ -442,10 +447,8 @@
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
@ -453,7 +456,7 @@
"(<TnPr (0) (0)> <TnPr (0) (1)> <TnPr (0) (2)> <TnPr (1) (0)> <TnPr (1) (1)> <TnPr (1) (2)> <TnPr (2) (0)> <TnPr (2) (1)> <TnPr (2) (2)>)"
]
},
"execution_count": 14,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@ -464,10 +467,8 @@
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
@ -475,7 +476,7 @@
"(<TnPr (0) (0 1)> <TnPr (0) (0 2)> <TnPr (0) (1 2)> <TnPr (1) (0 1)> <TnPr (1) (0 2)> <TnPr (1) (1 2)> <TnPr (2) (0 1)> <TnPr (2) (0 2)> <TnPr (2) (1 2)> <TnPr (0 1) (0)> ...)"
]
},
"execution_count": 15,
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@ -486,10 +487,8 @@
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
@ -497,7 +496,7 @@
"(<TnPr (0) (0 1 2)> <TnPr (1) (0 1 2)> <TnPr (2) (0 1 2)> <TnPr (0 1) (0 1)> <TnPr (0 1) (0 2)> <TnPr (0 1) (1 2)> <TnPr (0 2) (0 1)> <TnPr (0 2) (0 2)> <TnPr (0 2) (1 2)> <TnPr (1 2) (0 1)> ...)"
]
},
"execution_count": 16,
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@ -508,10 +507,8 @@
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
@ -519,7 +516,7 @@
"(<TnPr (0 1) (0 1 2)> <TnPr (0 2) (0 1 2)> <TnPr (1 2) (0 1 2)> <TnPr (0 1 2) (0 1)> <TnPr (0 1 2) (0 2)> <TnPr (0 1 2) (1 2)>)"
]
},
"execution_count": 17,
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@ -530,10 +527,8 @@
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
@ -541,7 +536,7 @@
"(<TnPr (0 1 2) (0 1 2)>)"
]
},
"execution_count": 18,
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@ -561,18 +556,16 @@
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"#<FUNCTION (LAMBDA (DGR GNR) :IN \"/root/cl-jupyter-master/cl-jupyter.lisp\") {1005B3B8EB}>"
"#<FUNCTION (LAMBDA (DGR GNR) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {100222C5BB}>"
]
},
"execution_count": 19,
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@ -586,10 +579,8 @@
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
@ -597,7 +588,7 @@
"[K5 Chain-Complex]"
]
},
"execution_count": 20,
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@ -612,10 +603,8 @@
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
@ -623,7 +612,7 @@
"(30 31 32 33 34 35 36 37 38 39)"
]
},
"execution_count": 21,
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@ -634,10 +623,8 @@
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
@ -645,7 +632,7 @@
"[K7 Chain-Complex]"
]
},
"execution_count": 22,
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@ -656,10 +643,8 @@
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
@ -672,7 +657,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 23,
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@ -683,10 +668,8 @@
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
@ -700,7 +683,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 24,
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@ -711,10 +694,8 @@
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
@ -735,7 +716,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 25,
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@ -746,10 +727,8 @@
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
@ -762,7 +741,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 26,
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@ -773,10 +752,8 @@
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
@ -786,7 +763,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 27,
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@ -866,5 +843,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

322
examples/05_Coalgebras_and_cobars.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -173,10 +205,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -184,7 +214,7 @@
"[K1 Simplicial-Set]"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -215,10 +245,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
@ -226,7 +254,7 @@
":EQUAL"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -237,10 +265,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -250,7 +276,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -261,10 +287,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
@ -278,7 +302,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -296,10 +320,8 @@
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
@ -307,7 +329,7 @@
"[K6 Chain-Complex]"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@ -318,10 +340,8 @@
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
@ -329,7 +349,7 @@
"<<AlLp>>"
]
},
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@ -340,10 +360,8 @@
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
@ -351,7 +369,7 @@
"<<AlLp[2 (0 1 2 3)]>>"
]
},
"execution_count": 7,
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@ -362,10 +380,8 @@
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
@ -373,7 +389,7 @@
"<<AlLp[2 (1 2 3 4)]>>"
]
},
"execution_count": 8,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@ -384,10 +400,8 @@
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
@ -395,7 +409,7 @@
":LESS"
]
},
"execution_count": 9,
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@ -406,10 +420,8 @@
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
@ -423,7 +435,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 10,
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@ -434,10 +446,8 @@
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
@ -447,7 +457,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 11,
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@ -458,10 +468,8 @@
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
@ -469,7 +477,7 @@
"<<AlLp[3 (0 1 2 3 4)][3 (1 3 5 7 9)]>>"
]
},
"execution_count": 12,
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@ -480,10 +488,8 @@
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
@ -503,7 +509,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 13,
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@ -514,10 +520,8 @@
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
@ -527,7 +531,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 14,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@ -538,10 +542,8 @@
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
@ -549,7 +551,7 @@
"<<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>"
]
},
"execution_count": 15,
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@ -560,10 +562,8 @@
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
@ -584,7 +584,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 16,
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@ -595,10 +595,8 @@
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
@ -608,7 +606,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 17,
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@ -660,10 +658,8 @@
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
@ -675,7 +671,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 18,
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@ -686,10 +682,8 @@
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
@ -701,7 +695,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 19,
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@ -712,10 +706,8 @@
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
@ -728,7 +720,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 20,
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@ -739,10 +731,8 @@
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
@ -750,7 +740,7 @@
"[K8 Morphism (degree -1): K6 -> K6]"
]
},
"execution_count": 21,
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@ -761,10 +751,8 @@
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
@ -772,7 +760,7 @@
"<<AlLp[2 (0 1 2 3)]>>"
]
},
"execution_count": 22,
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@ -783,10 +771,8 @@
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
@ -796,7 +782,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 23,
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@ -807,10 +793,8 @@
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
@ -818,7 +802,7 @@
"<<AlLp[3 (0 1 2 3 4)][3 (1 3 5 7 9)]>>"
]
},
"execution_count": 24,
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@ -829,10 +813,8 @@
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
@ -844,7 +826,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 25,
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@ -855,10 +837,8 @@
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
@ -868,7 +848,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 26,
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@ -879,10 +859,8 @@
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
@ -890,7 +868,7 @@
"<<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>"
]
},
"execution_count": 27,
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@ -901,10 +879,8 @@
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
@ -919,7 +895,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 28,
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@ -930,10 +906,8 @@
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
@ -943,7 +917,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 29,
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@ -988,10 +962,8 @@
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
@ -999,7 +971,7 @@
"[K9 Chain-Complex]"
]
},
"execution_count": 30,
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@ -1010,10 +982,8 @@
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
@ -1021,7 +991,7 @@
"<<AlLp[3 (0 1 2 3 4)][3 (1 3 5 7 9)]>>"
]
},
"execution_count": 31,
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
@ -1032,10 +1002,8 @@
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
@ -1056,7 +1024,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 32,
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
@ -1067,10 +1035,8 @@
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
@ -1080,7 +1046,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 33,
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@ -1091,10 +1057,8 @@
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
@ -1102,7 +1066,7 @@
"<<AlLp[3 (0 1 4 5 6)][4 (2 3 4 5 6 8)][4 (0 4 5 6 7 8)]>>"
]
},
"execution_count": 34,
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@ -1113,10 +1077,8 @@
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
@ -1137,7 +1099,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 35,
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@ -1148,10 +1110,8 @@
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
@ -1161,7 +1121,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 36,
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
@ -1213,5 +1173,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

287
examples/06_Algebras_and_bars.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -88,10 +120,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -99,7 +129,7 @@
"TRIVIAL-ALGEBRA"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -129,10 +159,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
@ -140,7 +168,7 @@
"[K1 Simplicial-Set]"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -164,10 +192,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -175,7 +201,7 @@
"[K1 Algebra]"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -193,10 +219,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
@ -204,7 +228,7 @@
"[K1 Algebra]"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -215,18 +239,16 @@
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"The object is a STANDARD-OBJECT of type CAT::ALGEBRA.\n",
"0. CMPR: #<FUNCTION (LAMBDA (GSM1 GSM2) :IN \"/root/cl-jupyter-master/cl-jupyter.lisp\") {100537E00B}>\n",
"The object is a STANDARD-OBJECT of type ALGEBRA.\n",
"0. CMPR: #<FUNCTION (LAMBDA (GSM1 GSM2) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {1001AEC60B}>\n",
"1. BASIS: :LOCALLY-EFFECTIVE\n",
"2. BSGN: (0)\n",
"3. DFFR: [K2 Morphism (degree -1): K1 -> K1]\n",
@ -235,7 +257,6 @@
"6. IDNM: 1\n",
"7. ORGN: (SIMPLE-DELTAB2)\n",
"8. APRD: [K6 Morphism (degree 0): K3 -> K1]\n",
"\n",
"> "
]
},
@ -245,7 +266,7 @@
"NIL"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@ -263,37 +284,10 @@
"Let us test now the product in this trivial algebra:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"----------------------------------------------------------------------{CMBN 3}\n",
"<1 * (1 2 3 4)>\n",
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(aprd smp-deltab2 3 (tnpr 0 '(0) 3 '(1 2 3 4)))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -310,15 +304,36 @@
}
],
"source": [
"(aprd smp-deltab2 3 (tnpr 3 '(1 2 3 4) 0 '(0)))"
"(aprd smp-deltab2 3 (tnpr 0 '(0) 3 '(1 2 3 4)))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"----------------------------------------------------------------------{CMBN 3}\n",
"<1 * (1 2 3 4)>\n",
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(aprd smp-deltab2 3 (tnpr 3 '(1 2 3 4) 0 '(0)))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
@ -328,7 +343,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 8,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@ -388,34 +403,10 @@
"from elements of an algebra (or a chain complex)."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<<Abar[2 A][3 B][5 C]>>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(abar 2 'a 3 'b 5 'c)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -429,15 +420,33 @@
}
],
"source": [
"(abar '(2 a 3 b 5 c))"
"(abar 2 'a 3 'b 5 'c)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<<Abar[2 A][3 B][5 C]>>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(abar '(2 a 3 b 5 c))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
@ -445,7 +454,7 @@
"<<Abar>>"
]
},
"execution_count": 11,
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@ -517,18 +526,16 @@
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"#<CLOSURE (FLET CAT::RSLT :IN BAR-CMPR) {1005C307DB}>"
"#<CLOSURE (FLET RSLT :IN BAR-CMPR) {10022131CB}>"
]
},
"execution_count": 12,
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@ -539,10 +546,8 @@
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
@ -550,7 +555,7 @@
":EQUAL"
]
},
"execution_count": 13,
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@ -561,10 +566,8 @@
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
@ -572,7 +575,7 @@
":LESS"
]
},
"execution_count": 14,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@ -583,10 +586,8 @@
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
@ -594,7 +595,7 @@
":EQUAL"
]
},
"execution_count": 15,
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@ -612,18 +613,16 @@
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"#<FUNCTION (LAMBDA (DEGR) :IN \"/root/cl-jupyter-master/cl-jupyter.lisp\") {1005DEE0FB}>"
"#<FUNCTION (LAMBDA (DEGR) :IN \"/root/cl-jupyter/cl-jupyter.lisp\") {100238964B}>"
]
},
"execution_count": 16,
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@ -635,10 +634,8 @@
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
@ -646,7 +643,7 @@
"(A5)"
]
},
"execution_count": 17,
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@ -664,18 +661,16 @@
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"#<CLOSURE (FLET CAT::RSLT :IN BAR-BASIS) {1005EAF78B}>"
"#<CLOSURE (FLET RSLT :IN BAR-BASIS) {1002416CEB}>"
]
},
"execution_count": 18,
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@ -686,10 +681,8 @@
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -711,7 +704,7 @@
"NIL"
]
},
"execution_count": 19,
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@ -730,10 +723,8 @@
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
@ -741,7 +732,7 @@
"[K7 Chain-Complex]"
]
},
"execution_count": 20,
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@ -752,10 +743,8 @@
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
@ -774,7 +763,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 21,
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@ -785,10 +774,8 @@
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
@ -798,7 +785,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 22,
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@ -906,5 +893,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

2136
examples/07_Simplicial_Sets.ipynb
View File

File diff suppressed because one or more lines are too long

122
examples/08_Simplicial_morphisms.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -54,10 +86,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -65,7 +95,7 @@
"[K1 Simplicial-Set]"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -76,10 +106,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
@ -87,7 +115,7 @@
"[K6 Simplicial-Morphism K1 -> K1]"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -103,10 +131,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -114,7 +140,7 @@
"<AbSm - 7>"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -125,10 +151,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
@ -136,7 +160,7 @@
"<AbSm 0 1>"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -147,10 +171,8 @@
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
@ -161,7 +183,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@ -179,10 +201,8 @@
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
@ -190,7 +210,7 @@
"[K7 Simplicial-Morphism K1 -> K1]"
]
},
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@ -206,10 +226,8 @@
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
@ -217,7 +235,7 @@
"<AbSm - 1>"
]
},
"execution_count": 7,
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@ -228,10 +246,8 @@
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
@ -239,7 +255,7 @@
"<AbSm 1-0 1>"
]
},
"execution_count": 8,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@ -250,10 +266,8 @@
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
@ -261,7 +275,7 @@
"<AbSm 0 1>"
]
},
"execution_count": 9,
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@ -272,10 +286,8 @@
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
@ -283,7 +295,7 @@
"<AbSm 2-1-0 1>"
]
},
"execution_count": 10,
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@ -294,10 +306,8 @@
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
@ -307,7 +317,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 11,
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@ -343,5 +353,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

685
examples/09_The_Eilenberg-Zilber_module.ipynb
View File

File diff suppressed because one or more lines are too long

154
examples/10_Programming_the_Kan_theory.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -71,10 +103,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -82,7 +112,7 @@
"DKFLL"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -111,10 +141,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
@ -122,7 +150,7 @@
"[K1 Simplicial-Set]"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -133,10 +161,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -144,7 +170,7 @@
"[K1 Kan-Simplicial-Set]"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -155,10 +181,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
@ -166,7 +190,7 @@
"<AbSm 0 1>"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -175,34 +199,10 @@
"(kfll d 0 1 (list (absm 0 1)))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<AbSm - 7>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(kfll d 0 2 (list (absm 0 5) (absm 0 3)))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -216,15 +216,13 @@
}
],
"source": [
"(kfll d 1 2 (list (absm 0 6) (absm 0 3)))"
"(kfll d 0 2 (list (absm 0 5) (absm 0 3)))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -238,20 +236,18 @@
}
],
"source": [
"(kfll d 2 2 (list (absm 0 6) (absm 0 5)))"
"(kfll d 1 2 (list (absm 0 6) (absm 0 3)))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<AbSm 1 3>"
"<AbSm - 7>"
]
},
"execution_count": 8,
@ -260,15 +256,13 @@
}
],
"source": [
"(kfll d 0 2 (list (absm 0 3) (absm 0 3)))"
"(kfll d 2 2 (list (absm 0 6) (absm 0 5)))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -282,20 +276,18 @@
}
],
"source": [
"(kfll d 1 2 (list (absm 1 2) (absm 0 3)))"
"(kfll d 0 2 (list (absm 0 3) (absm 0 3)))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"T"
"<AbSm 1 3>"
]
},
"execution_count": 10,
@ -304,15 +296,13 @@
}
],
"source": [
"(check-hat d 1 2 (list (absm 1 2) (absm 0 3)))"
"(kfll d 1 2 (list (absm 1 2) (absm 0 3)))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -326,15 +316,33 @@
}
],
"source": [
"(check-hat d 0 1 (list (absm 0 1)))"
"(check-hat d 1 2 (list (absm 1 2) (absm 0 3)))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"T"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(check-hat d 0 1 (list (absm 0 1)))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -350,7 +358,7 @@
"NIL"
]
},
"execution_count": 12,
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@ -388,5 +396,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

556
examples/11_Simplicial_Groups.ipynb
View File

File diff suppressed because it is too large Load Diff

972
examples/12_Fibrations.ipynb
View File

File diff suppressed because it is too large Load Diff

315
examples/13_Loop_Spaces.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -145,10 +177,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -156,7 +186,7 @@
"<<Loop>>"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -167,10 +197,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
@ -178,7 +206,7 @@
"<<Loop[A\\2][4-2 B\\-3][3-2 C]>>"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -189,10 +217,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -200,7 +226,7 @@
"<<Loop[A\\2][4-2 B\\-3][3-2 C][A\\3]>>"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -211,10 +237,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
@ -222,7 +246,7 @@
"<<Loop[2-1-0 P\\2][5-4-3-2-1 Q\\5]>>"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -242,10 +266,8 @@
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
@ -253,7 +275,7 @@
"[K1 Simplicial-Set]"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@ -264,10 +286,8 @@
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -277,7 +297,7 @@
"\n",
"Dimension = 0:\n",
"\n",
" Vertices : (*)\n",
" Vertices : (*)\n",
"\n",
"Dimension = 1:\n",
"\n",
@ -285,15 +305,15 @@
"\n",
"Dimension = 3:\n",
"\n",
" Simplex : M3\n",
" Simplex : M3\n",
"\n",
" Faces : (<AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *>)\n",
" Faces : (<AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *> <AbSm 1-0 *>)\n",
"\n",
"Dimension = 4:\n",
"\n",
" Simplex : N4\n",
" Simplex : N4\n",
"\n",
" Faces : (<AbSm - M3> <AbSm 2-1-0 *> <AbSm - M3> <AbSm 2-1-0 *> <AbSm 2-1-0 *>)"
" Faces : (<AbSm - M3> <AbSm 2-1-0 *> <AbSm - M3> <AbSm 2-1-0 *> <AbSm 2-1-0 *>)"
]
},
{
@ -302,7 +322,7 @@
"NIL"
]
},
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@ -320,10 +340,8 @@
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
@ -331,7 +349,7 @@
"[K6 Simplicial-Group]"
]
},
"execution_count": 7,
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@ -342,10 +360,8 @@
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
@ -353,7 +369,7 @@
"<AbSm 2-1-0 <<Loop>>>"
]
},
"execution_count": 8,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@ -364,10 +380,8 @@
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
@ -375,7 +389,7 @@
"<AbSm - <<Loop[M3\\2]>>>"
]
},
"execution_count": 9,
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@ -386,10 +400,8 @@
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
@ -397,7 +409,7 @@
"<AbSm 1-0 <<Loop>>>"
]
},
"execution_count": 10,
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@ -408,10 +420,8 @@
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
@ -419,7 +429,7 @@
"<AbSm - <<Loop[N4\\2]>>>"
]
},
"execution_count": 11,
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@ -430,10 +440,8 @@
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
@ -441,7 +449,7 @@
"<AbSm 0 <<Loop>>>"
]
},
"execution_count": 12,
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@ -459,10 +467,8 @@
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -471,7 +477,7 @@
"\n",
"The object is a STANDARD-OBJECT of type SIMPLICIAL-SET.\n",
"0. CMPR: #<FUNCTION S-CMPR>\n",
"1. BASIS: #<CLOSURE (FLET CAT::RSLT :IN CAT::FINITE-SS-BASIS) {10057E9E6B}>\n",
"1. BASIS: #<CLOSURE (FLET RSLT :IN FINITE-SS-BASIS) {1001EE2CFB}>\n",
"2. BSGN: *\n",
"3. DFFR: [K19 Morphism (degree -1): K18 -> K18]\n",
"4. GRMD: [K18 Simplicial-Set]\n",
@ -479,8 +485,7 @@
"6. IDNM: 18\n",
"7. ORGN: (BUILD-FINITE-SS (* 2 S2 (* * *) 3 S3 (S2 S2 S2 S2)))\n",
"8. CPRD: [K22 Morphism (degree 0): K18 -> K20]\n",
"9. FACE: #<CLOSURE (FLET CAT::RSLT :IN CAT::FINITE-SS-FACE) {10057E9E8B}>\n",
"\n",
"9. FACE: #<CLOSURE (FLET RSLT :IN FINITE-SS-FACE) {1001EE2D1B}>\n",
"> \n",
"Checking the 0-simplices...\n",
"Checking the 1-simplices...\n",
@ -494,7 +499,7 @@
"[K18 Simplicial-Set]"
]
},
"execution_count": 13,
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@ -507,10 +512,8 @@
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
@ -518,7 +521,7 @@
"[K23 Simplicial-Group]"
]
},
"execution_count": 14,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@ -529,10 +532,8 @@
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
@ -540,7 +541,7 @@
"<AbSm - <<Loop>>>"
]
},
"execution_count": 15,
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@ -549,34 +550,10 @@
"(face o-ss2 0 1 (loop3 0 's2 1))"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<AbSm - <<Loop[S2\\2]>>>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(face o-ss2 0 2 (loop3 0 's3 2))"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -590,15 +567,13 @@
}
],
"source": [
"(face o-ss2 1 2 (loop3 0 's3 2))"
"(face o-ss2 0 2 (loop3 0 's3 2))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
@ -618,9 +593,27 @@
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<AbSm - <<Loop[S2\\2]>>>"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(face o-ss2 1 2 (loop3 0 's3 2))"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
@ -628,7 +621,7 @@
"[K40 Simplicial-Group]"
]
},
"execution_count": 19,
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@ -639,10 +632,8 @@
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
@ -650,7 +641,7 @@
"<AbSm 1-0 <<Loop>>>"
]
},
"execution_count": 20,
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@ -661,10 +652,8 @@
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
@ -672,7 +661,7 @@
"<AbSm 0 <<Loop[7\\3]>>>"
]
},
"execution_count": 21,
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@ -683,10 +672,8 @@
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
@ -694,7 +681,7 @@
"<AbSm - <<Loop[1 7\\3][0 7\\3][1-0 3\\-1][1-0 5][1-0 3\\-1][1-0 5][1-0 3\\-1][1-0 5]>>>"
]
},
"execution_count": 22,
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@ -705,10 +692,8 @@
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
@ -716,7 +701,7 @@
"<AbSm - <<Loop[7\\3][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5][0 3\\-1][0 5]>>>"
]
},
"execution_count": 23,
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@ -734,10 +719,8 @@
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
@ -747,7 +730,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 24,
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@ -767,10 +750,8 @@
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
@ -778,7 +759,7 @@
"[K52 Simplicial-Set]"
]
},
"execution_count": 25,
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
@ -789,10 +770,8 @@
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -811,7 +790,7 @@
"NIL"
]
},
"execution_count": 26,
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
@ -822,10 +801,8 @@
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
@ -833,7 +810,7 @@
"[K57 Simplicial-Group]"
]
},
"execution_count": 27,
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
@ -844,10 +821,8 @@
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
@ -860,7 +835,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 28,
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
@ -871,10 +846,8 @@
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
@ -882,7 +855,7 @@
"[K74 Chain-Complex]"
]
},
"execution_count": 29,
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
@ -893,10 +866,8 @@
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
@ -910,7 +881,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 30,
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
@ -944,5 +915,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

954
examples/14_Disk_pasting_and_suspension.ipynb
View File

File diff suppressed because it is too large Load Diff

1268
examples/15_Loop_spaces_fibrations.ipynb
View File

File diff suppressed because it is too large Load Diff

632
examples/16_Eilenberg-Moore_spectral_sequence_I.ipynb
View File

File diff suppressed because it is too large Load Diff

316
examples/17_Classifying_Spaces.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -117,10 +149,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -128,7 +158,7 @@
"<<GBar<0 A><1 B>>>"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -139,10 +169,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
@ -150,7 +178,7 @@
"<<GBar<- 3><1-0 0><0 0><- 0>>>"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -161,10 +189,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -172,7 +198,7 @@
"<<GBar<- <<Loop[1-0 M2][2 N3]>>><- <<Loop[N3]>>><- <<Loop[M2]>>><- <<Loop>>>>>"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -193,10 +219,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
@ -204,7 +228,7 @@
"[K6 Simplicial-Group]"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -215,18 +239,16 @@
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"#<CLOSURE (FLET CAT::RSLT :IN CLASSIFYING-SPACE-FACE) {1002FB5DBB}>"
"#<CLOSURE (FLET RSLT :IN CLASSIFYING-SPACE-FACE) {1001CE47FB}>"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@ -237,10 +259,8 @@
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -260,7 +280,7 @@
"NIL"
]
},
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@ -278,10 +298,8 @@
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
@ -289,7 +307,7 @@
"[K30 Abelian-Simplicial-Group]"
]
},
"execution_count": 7,
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@ -300,10 +318,8 @@
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
@ -311,7 +327,7 @@
"(CLASSIFYING-SPACE [K18 Abelian-Simplicial-Group])"
]
},
"execution_count": 8,
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
@ -322,10 +338,8 @@
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
@ -333,7 +347,7 @@
"<<GBar<- 3><- 2><- 1><- 0>>>"
]
},
"execution_count": 9,
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@ -344,10 +358,8 @@
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
@ -358,7 +370,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 10,
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@ -369,10 +381,8 @@
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
@ -382,7 +392,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 11,
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@ -393,10 +403,8 @@
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
@ -409,7 +417,7 @@
"------------------------------------------------------------------------------\n"
]
},
"execution_count": 12,
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@ -420,10 +428,8 @@
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -443,7 +449,7 @@
"NIL"
]
},
"execution_count": 13,
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@ -462,10 +468,8 @@
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
@ -473,7 +477,7 @@
"[K54 Abelian-Simplicial-Group]"
]
},
"execution_count": 14,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@ -484,10 +488,8 @@
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
@ -495,7 +497,7 @@
"<AbSm 2-1-0 <<GBar>>>"
]
},
"execution_count": 15,
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@ -507,10 +509,8 @@
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
@ -518,7 +518,7 @@
"<AbSm - <<GBar<- (1 2)><0 NIL><- NIL>>>>"
]
},
"execution_count": 16,
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@ -530,10 +530,8 @@
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
@ -541,7 +539,7 @@
"<AbSm - <<GBar<- (1 -1)><- (3)><- NIL>>>>"
]
},
"execution_count": 17,
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@ -553,10 +551,8 @@
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
@ -564,7 +560,7 @@
"<AbSm - <<GBar<- (-1 -2)><0 NIL><- NIL>>>>"
]
},
"execution_count": 18,
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@ -575,10 +571,8 @@
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
@ -586,7 +580,7 @@
"<AbSm - <<GBar<- (1 2)><0 NIL><- NIL>>>>"
]
},
"execution_count": 19,
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@ -604,10 +598,8 @@
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -623,7 +615,7 @@
"NIL"
]
},
"execution_count": 20,
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
@ -634,10 +626,8 @@
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
@ -645,7 +635,7 @@
"[K25 Abelian-Simplicial-Group]"
]
},
"execution_count": 21,
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
@ -656,10 +646,8 @@
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -670,7 +658,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n",
"<<Abar>> \n",
"End of computing.\n",
@ -690,7 +678,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 1.\n",
@ -709,7 +697,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 2.\n",
@ -720,7 +708,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 3) :\n",
"<<Abar[3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -734,14 +722,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 3.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 3) :\n",
"<<Abar[3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -761,7 +749,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 4.\n",
@ -772,7 +760,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 5) :\n",
"<<Abar[5 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n",
@ -786,14 +774,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 5.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 5) :\n",
"<<Abar[5 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n",
@ -803,7 +791,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -819,14 +807,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 6.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -836,7 +824,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 7) :\n",
"<<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n",
@ -850,14 +838,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 7.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 7) :\n",
"<<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n",
@ -867,13 +855,13 @@
"Rank of the source-module : 2.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/2 (dimension 8) :\n",
"<<Abar[3 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 2/2 (dimension 8) :\n",
"<<Abar[5 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -889,20 +877,20 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 8.\n",
"Rank of the source-module : 2.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/2 (dimension 8) :\n",
"<<Abar[3 <<Abar[2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 2/2 (dimension 8) :\n",
"<<Abar[5 <<Abar[2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -912,13 +900,13 @@
"Rank of the source-module : 2.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/2 (dimension 9) :\n",
"<<Abar[9 <<Abar[2 S1][2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 2/2 (dimension 9) :\n",
"<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -934,20 +922,20 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 9.\n",
"Rank of the source-module : 2.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/2 (dimension 9) :\n",
"<<Abar[9 <<Abar[2 S1][2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 2/2 (dimension 9) :\n",
"<<Abar[3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -957,19 +945,19 @@
"Rank of the source-module : 3.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/3 (dimension 10) :\n",
"<<Abar[3 <<Abar[2 S1]>>][7 <<Abar[2 S1][2 S1][2 S1]>>]>> \n",
"End of computing.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 2/3 (dimension 10) :\n",
"<<Abar[5 <<Abar[2 S1][2 S1]>>][5 <<Abar[2 S1][2 S1]>>]>> \n",
"End of computing.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 3/3 (dimension 10) :\n",
"<<Abar[7 <<Abar[2 S1][2 S1][2 S1]>>][3 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -985,7 +973,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n"
]
},
@ -995,7 +983,7 @@
"NIL"
]
},
"execution_count": 22,
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
@ -1006,10 +994,8 @@
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
@ -1017,7 +1003,7 @@
"[K342 Abelian-Simplicial-Group]"
]
},
"execution_count": 23,
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
@ -1028,10 +1014,8 @@
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -1042,7 +1026,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n",
"<<Abar>> \n",
"End of computing.\n",
@ -1062,7 +1046,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 1.\n",
@ -1081,7 +1065,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 2.\n",
@ -1100,7 +1084,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 3.\n",
@ -1119,7 +1103,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 4.\n",
@ -1130,7 +1114,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 5) :\n",
"<<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>]>> \n",
"End of computing.\n",
@ -1144,14 +1128,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 5.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 5) :\n",
"<<Abar[5 <<Abar[4 <<Abar[3 <<Abar[2 1]>>]>>]>>]>> \n",
"End of computing.\n",
@ -1161,7 +1145,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[6 <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>]>> \n",
"End of computing.\n",
@ -1177,14 +1161,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 6.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[6 <<Abar[5 <<Abar[4 <<Abar[3 2]>>]>>]>>]>> \n",
"End of computing.\n",
@ -1194,13 +1178,13 @@
"Rank of the source-module : 2.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 1/2 (dimension 7) :\n",
"<<Abar[7 <<Abar[6 <<Abar[5 <<Abar[4 3]>>]>>]>>]>> \n",
"End of computing.\n",
"\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"Computing the boundary of the generator 2/2 (dimension 7) :\n",
"<<Abar[7 <<Abar[6 <<Abar[5 <<Abar[2 1][2 1]>>]>>]>>]>> \n",
"End of computing.\n",
@ -1214,7 +1198,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-09-15, 15h 27m 10s.\n",
";; Clock -> 2017-10-08, 12h 28m 49s.\n",
"\n"
]
},
@ -1224,7 +1208,7 @@
"NIL"
]
},
"execution_count": 24,
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
@ -1258,5 +1242,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

392
examples/18_Serre_spectral_sequence.ipynb
View File

File diff suppressed because it is too large Load Diff

690
examples/19_Simplicial_groups_fibration.ipynb
View File

File diff suppressed because it is too large Load Diff

230
examples/20_Eilenberg-Moore_spectral_sequence_II.ipynb
View File

@ -1,5 +1,37 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"To load \"kenzo\":\n",
" Load 1 ASDF system:\n",
" kenzo\n",
"; Loading \"kenzo\"\n",
"\n"
]
},
{
"data": {
"text/plain": [
"#<PACKAGE \"CAT\">"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(ql:quickload \"kenzo\")\n",
"(in-package :cat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
@ -162,10 +194,8 @@
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
@ -173,7 +203,7 @@
"[K1 Abelian-Simplicial-Group]"
]
},
"execution_count": 1,
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@ -184,10 +214,8 @@
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -198,7 +226,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n",
"* \n",
"End of computing.\n",
@ -208,9 +236,9 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n",
"CAT::S1 \n",
"S1 \n",
"End of computing.\n",
"\n",
"\n",
@ -224,16 +252,16 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 1.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n",
"CAT::S1 \n",
"S1 \n",
"End of computing.\n",
"\n",
"\n",
@ -251,7 +279,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 2.\n",
@ -270,7 +298,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 3.\n",
@ -289,7 +317,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 4.\n",
@ -308,7 +336,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 5.\n",
@ -327,7 +355,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 6.\n",
@ -346,7 +374,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 7.\n",
@ -365,7 +393,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 8.\n",
@ -384,7 +412,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 9.\n",
@ -403,7 +431,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n"
]
},
@ -413,7 +441,7 @@
"NIL"
]
},
"execution_count": 2,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@ -424,10 +452,8 @@
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
@ -435,7 +461,7 @@
"[K23 Abelian-Simplicial-Group]"
]
},
"execution_count": 3,
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@ -446,10 +472,8 @@
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -460,7 +484,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n",
"<<Abar>> \n",
"End of computing.\n",
@ -480,7 +504,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 1.\n",
@ -491,7 +515,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 2) :\n",
"<<Abar[2 S1]>> \n",
"End of computing.\n",
@ -505,14 +529,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 2.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 2) :\n",
"<<Abar[2 S1]>> \n",
"End of computing.\n",
@ -532,7 +556,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 3.\n",
@ -543,7 +567,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 4) :\n",
"<<Abar[2 S1][2 S1]>> \n",
"End of computing.\n",
@ -557,14 +581,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 4.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 4) :\n",
"<<Abar[2 S1][2 S1]>> \n",
"End of computing.\n",
@ -584,7 +608,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 5.\n",
@ -595,7 +619,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[2 S1][2 S1][2 S1]>> \n",
"End of computing.\n",
@ -609,14 +633,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 6.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 6) :\n",
"<<Abar[2 S1][2 S1][2 S1]>> \n",
"End of computing.\n",
@ -636,7 +660,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 7.\n",
@ -647,7 +671,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -661,14 +685,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 8.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -688,7 +712,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 9.\n",
@ -699,7 +723,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -713,7 +737,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 29s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n"
]
},
@ -723,7 +747,7 @@
"NIL"
]
},
"execution_count": 4,
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
@ -734,10 +758,8 @@
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
@ -745,7 +767,7 @@
"[K154 Simplicial-Group]"
]
},
"execution_count": 5,
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
@ -756,10 +778,8 @@
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
@ -770,7 +790,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 0) :\n",
"<<AlLp>> \n",
"End of computing.\n",
@ -780,7 +800,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n",
"<<AlLp[1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -796,14 +816,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 1.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"Computing the boundary of the generator 1/1 (dimension 1) :\n",
"<<AlLp[1 <<Abar[2 S1]>>]>> \n",
"End of computing.\n",
@ -813,7 +833,7 @@
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -829,14 +849,14 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 2.\n",
"Rank of the source-module : 1.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -846,13 +866,13 @@
"Rank of the source-module : 2.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -866,20 +886,20 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 3.\n",
"Rank of the source-module : 2.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -889,19 +909,19 @@
"Rank of the source-module : 3.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -915,26 +935,26 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 4.\n",
"Rank of the source-module : 3.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -944,31 +964,31 @@
"Rank of the source-module : 5.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -982,38 +1002,38 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\n",
"\n",
"\n",
"Computing boundary-matrix in dimension 5.\n",
"Rank of the source-module : 5.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -1023,49 +1043,49 @@
"Rank of the source-module : 8.\n",
"\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 7s.\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",
@ -1079,7 +1099,7 @@
"\n",
"---done---\n",
"\n",
";; Clock -> 2016-03-25, 12h 22m 30s.\n",
";; Clock -> 2017-10-08, 12h 33m 8s.\n",
"\n"
]
},
@ -1089,7 +1109,7 @@
"NIL"
]
},
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@ -1123,5 +1143,5 @@
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}

798
examples/21_Computing_homotopy_groups.ipynb
View File

File diff suppressed because it is too large Load Diff