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

ported to LaTeX2e, added build instructions, removed old files

Browse Source
This commit is contained in:
Dima Pasechnik 2015-07-01 22:59:24 +01:00
parent b288a64669
commit 45cf053708
30 changed files with 35 additions and 347 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

7
doc/doc_src/README Normal file
View File

@ -0,0 +1,7 @@
To build docs, run
(xe)latex kendoc
makeindex kendoc
(xe)latex kendoc
Tested with texlive 2014

3
doc/doc_src/ccdoc.tex
View File

@ -53,7 +53,8 @@ for this purpose and we shall take as typical example the following simplicial
complex. complex.
% %
\vskip 0.50cm \vskip 0.50cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/diabolo.eps}} \centerline{\includegraphics{diabolo.eps}}
%\centerline{\psfig{figure=diabolo.eps}}
\vskip 0.50cm \vskip 0.50cm
% %
In this simplicial complex, called here {\em diabolo}, there are $3$ associated chain groups. In this simplicial complex, called here {\em diabolo}, there are $3$ associated chain groups.

135
doc/doc_src/chapitre-0.tex
View File

@ -1,135 +0,0 @@
\documentstyle[psfig,11pt]{report}
\pagestyle{headings}
\makeindex
\parindent=0mm
%\textwidth=6.0in
%\textheight=8.0in
%\oddsidemargin=-.35i
%\evensidemargin=-.35in
%\topmargin=-.50in
\input amssym.def
\input amssym.tex
\newtheorem{thr}{Theorem}
%\font\bb=msym10
\def\N{{\Bbb N}}
\def\Z{{\Bbb Z}}
\def\R{{\Bbb R}}
%
% macros pour les diagrammes rectangulaires
%
\def\hfl#1#2{\smash{\mathop{\hbox to 15mm{\rightarrowfill}}
\limits^{\scriptstyle#1}_{\scriptstyle#2}}}
%
\def\hflr#1#2{\smash{\mathop{\hbox to 15mm{\rightarrowfill}}
\limits^{\scriptstyle#1}_{\scriptstyle#2}}}
%
\def\hfll#1#2{\smash{\mathop{\hbox to 15mm{\leftarrowfill}}
\limits^{\scriptstyle#1}_{\scriptstyle#2}}}
%
\def\vfl#1#2{\llap{$\scriptstyle #1$}\left\downarrow
\vbox to 7mm{}\right.\rlap{$\scriptstyle #2$}}
%
\def\vflu#1#2{\llap{$\scriptstyle #1$}\left\uparrow
\vbox to 7mm{}\right.\rlap{$\scriptstyle #2$}}
%
\def\diagram#1{\def\normalbaselines{\baselineskip=0pt
\lineskip=10pt\lineskiplimit=1pt} \matrix{#1}}
%
% macro tvi pour les lignes verticales et horizontales dans un tableau
%
\def\tvi{\vrule height 12pt depth 5pt width 0pt}
\def\tv{\tvi\vrule}
\begin{document}
\pagenumbering{roman}
\begin{titlepage}
\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
\begin{center}
{\huge KENZO} \\
\ \\
{\Large a Symbolic Software} \\
for \\
{\Large Effective Homology Computation}
\vskip 0.5cm
-----
\vskip 0.5cm
Julio Rubio Garcia\\
Francis Sergeraert \\
Yvon Siret
\vskip 0.20cm
-----
\vskip 0.20cm
Institut Fourier \\
Grenoble, France \\
\vskip 0.20cm
-----
\vskip 0.20cm
\end{center}
\vskip 0.5cm
This document is a user guide for the
basic modules of the Effective Ho\-mo\-lo\-gy Software ({\bf Kenzo} Version 1998). \\
It is also available by anonymous ftp ({\bf ftp fourier.ujf-grenoble.fr})
in the directory {\bf /pub/KENZO}. \\
\vskip 0.5cm
\begin{center}
{\em \today} \\
\end{center}
\end{titlepage}
\vskip 1in
\centerline {FOREWORD}
\vskip 0.5in
The {\bf Kenzo} program implements the general ideas of the second author
about \emph{Effective Homology}\footnote{{\bf Francis Sergeraert.}
\emph{The computability problem in algebraic topology}.
Advances in Mathematics, 1994, vol. 104, pp 1-29.},
mainly around the Serre and Eilenberg--Moore spectral sequences.
The first author (re--) discovered the importance
of the \emph{Basic Perturbation Lemma} in these questions, already
noted by Victor Gugenheim\footnote{{\bf V.K.A.M. Gugenheim.}
\emph{On a perturbation theory for the homology of the loop space}.
Journal of Pure and Applied Algebra, 1982, vol. 25, pp 197-205.}
and this program directly
implements and directly uses this ``lemma'' which should be called the
\emph{Fundamental Theorem of Algebraic Topology}. The first version of the program,
called {\bf EAT}, was written in 1989-90 by the first and the second authors.
It has been demonstrated in several universities: France: Grenoble and
Montpellier, Belgium: Louvain-la-Neuve, Italy: Genoa and Pisa,
Sweden: Stockolm, Japan:
Sapporo, Morioka, Urawa, Tokyo, Kyoto, Nara, Osaka and Hiroshima.
\par
In this {\bf Kenzo} version, numerous improvements have been integrated in comparison with
{\bf EAT}.
\begin{enumerate}
\item Standard CLOS (Common Lisp Object System) techniques.
\item Use of the Zermelo theorem about ordered sets (!): any set can be
well ordered and this remark gives important new ideas to improve
execution speed.
\item Better memory management.
\item Use of Szczarba's formulas instead of Shih's for implementing the twisted
Eilenberg--Zilber theorem.
\item New mathematical objects:
\begin{itemize}
\item Serre spectral sequences.
\item Differentials algebras.
\item Simplicial morphisms.
\item Kan simplicial sets.
\item Simplicial groups.
\item Fibrations.
\item Classifying spaces.
\end{itemize}
In particular, using these tools, the first homotopy groups of {\em arbitrary}
simplicial sets with effective homology, are now reachable.
\end{enumerate}
\par
The present documentation is a joint work between the second and third authors.
\cleardoublepage
\input {kenovrvw}
%\tableofcontents
\cleardoublepage
\input kendoc.toc
\pagenumbering{arabic}
\begin{theindex}
\input kendoc.ind
\end{theindex}
\end{document}

7
doc/doc_src/chapitre-1.tex
View File

@ -1,7 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\input {ccdoc}
\end{document}

9
doc/doc_src/chapitre-10.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{184}
\setcounter{chapter}{9}
\input {kandoc}
\end{document}

9
doc/doc_src/chapitre-11.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{189}
\setcounter{chapter}{10}
\input {smgrdoc}
\end{document}

9
doc/doc_src/chapitre-12.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{208}
\setcounter{chapter}{11}
\input {fibrdoc}
\end{document}

9
doc/doc_src/chapitre-13.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{218}
\setcounter{chapter}{12}
\input {lopspdoc}
\end{document}

9
doc/doc_src/chapitre-14.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{228}
\setcounter{chapter}{13}
\input {dspspdoc}
\end{document}

9
doc/doc_src/chapitre-15.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{248}
\setcounter{chapter}{14}
\input {lptwdoc}
\end{document}

9
doc/doc_src/chapitre-16.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{280}
\setcounter{chapter}{15}
\input {emspdoc1}
\end{document}

9
doc/doc_src/chapitre-17.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{293}
\setcounter{chapter}{16}
\input {classydoc}
\end{document}

9
doc/doc_src/chapitre-18.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{301}
\setcounter{chapter}{17}
\input {serredoc}
\end{document}

9
doc/doc_src/chapitre-19.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{315}
\setcounter{chapter}{18}
\input {cstwdoc}
\end{document}

9
doc/doc_src/chapitre-2.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{30}
\setcounter{chapter}{1}
\input {ccehdoc}
\end{document}

9
doc/doc_src/chapitre-20.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{331}
\setcounter{chapter}{19}
\input {emspdoc2}
\end{document}

9
doc/doc_src/chapitre-21.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{340}
\setcounter{chapter}{20}
\input {whithdoc.tex}
\end{document}

9
doc/doc_src/chapitre-3.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{65}
\setcounter{chapter}{2}
\input {homlgdoc}
\end{document}

9
doc/doc_src/chapitre-4.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{77}
\setcounter{chapter}{3}
\input {tprdoc}
\end{document}

9
doc/doc_src/chapitre-5.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{86}
\setcounter{chapter}{4}
\input {coaldoc}
\end{document}

9
doc/doc_src/chapitre-6.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{101}
\setcounter{chapter}{5}
\input {aldoc}
\end{document}

9
doc/doc_src/chapitre-7.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{114}
\setcounter{chapter}{6}
\input {ssdoc}
\end{document}

9
doc/doc_src/chapitre-8.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{161}
\setcounter{chapter}{7}
\input {smmrdoc}
\end{document}

9
doc/doc_src/chapitre-9.tex
View File

@ -1,9 +0,0 @@
\documentstyle[psfig,11pt]{report}
\input {params}
\begin{document}
\pagenumbering{arabic}
\cleardoublepage
\setcounter{page}{166}
\setcounter{chapter}{8}
\input {ezdoc}
\end{document}

2
doc/doc_src/classydoc.tex
View File

@ -168,7 +168,7 @@ itself.
Let us begin by showing some examples of gbars built from various Let us begin by showing some examples of gbars built from various
initial simplicial groups. In the second statement, the initial simplicial group initial simplicial groups. In the second statement, the initial simplicial group
is $K({\Z}_2, 1)$, in the third, it is $\Omega({\em Moore}(2,2))$. We recall that is $K({\Z}_2, 1)$, in the third, it is $\Omega({\mathit Moore}(2,2))$. We recall that
in the call of the function {\tt gbar}, the degeneracy operators appear as integers, in the call of the function {\tt gbar}, the degeneracy operators appear as integers,
according to the general rule in {\tt Kenzo}, but the printed result shows in clear according to the general rule in {\tt Kenzo}, but the printed result shows in clear
the sequence of $\eta_i$'s. the sequence of $\eta_i$'s.

10
doc/doc_src/ezdoc.tex
View File

@ -63,8 +63,8 @@ $$d \circ \Phi + \Phi \circ d = Id - {\cal EML} \circ {\cal AW}.$$
{\leftskip=5mm {\leftskip=5mm
{\tt ez} {\em ssx ssy} \hfill {\em [Function]} \par} {\tt ez} {\em ssx ssy} \hfill {\em [Function]} \par}
{\leftskip=15mm {\leftskip=15mm
build the Eilenberg--Zilber reduction as shown by the following dia\-gram, where $X={\em ssx}$ build the Eilenberg--Zilber reduction as shown by the following dia\-gram, where $X={\mathit ssx}$
and $Y={\em ssy}$. and $Y={\mathit ssy}$.
$$ $$
\diagram{ \diagram{
{{\cal C}_*(X \times Y)} & \stackrel{\Phi}{\longrightarrow} & {}^s{{\cal C}_*(X \times Y)} \cr {{\cal C}_*(X \times Y)} & \stackrel{\Phi}{\longrightarrow} & {}^s{{\cal C}_*(X \times Y)} \cr
@ -81,7 +81,7 @@ $$
\subsection* {Examples} \subsection* {Examples}
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/eml1.eps}} \centerline{\includegraphics{eml1.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
As simplicial sets $X$ and $Y$, let us use two copies of $\Delta^{\N}$, that we may build As simplicial sets $X$ and $Y$, let us use two copies of $\Delta^{\N}$, that we may build
@ -149,7 +149,7 @@ CODE
\newpage \newpage
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/eml2.eps}} \centerline{\includegraphics{eml2.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
@ -357,7 +357,7 @@ $$\Phi((0\, 1), (2\, 3))= (\eta_1(2\, 3),\eta_0(0\, 1)).$$
This is illustrated by the following diagram (the 2-simplex is the shaded triangle). This is illustrated by the following diagram (the 2-simplex is the shaded triangle).
\vskip 0.50cm \vskip 0.50cm
% %
\centerline{\psfig{figure=/home/home/siret/Kenzo/eml3.eps}} \centerline{\includegraphics{eml3.eps}}
% %
\vskip 0.50cm \vskip 0.50cm
{\footnotesize\begin{verbatim} {\footnotesize\begin{verbatim}

4
doc/doc_src/homlgdoc.tex
View File

@ -99,7 +99,7 @@ well known {\em dunce hat}. We shall see later in the chapter {\tt Simplicial Se
much more elegant method to describe this object. much more elegant method to describe this object.
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/dunce.eps}} \centerline{\includegraphics{dunce.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
The diagram shows a permissible triangulation. For the generators, we have chosen lists The diagram shows a permissible triangulation. For the generators, we have chosen lists
@ -482,4 +482,4 @@ SIMPLICIAL-SET @ #x4191d2 = [K119 Simplicial-Set]
\subsection* {Lisp files concerned in this chapter} \subsection* {Lisp files concerned in this chapter}
{\tt homology-groups.lisp}, {\tt searching-homology}\par {\tt homology-groups.lisp}, {\tt searching-homology}\par
and files containing a {\tt search-efhm} method. and files containing a {\tt search-efhm} method.

14
doc/doc_src/kendoc.tex
View File

@ -1,4 +1,7 @@
\documentstyle[psfig,11pt]{report} \documentclass[11pt]{report}
\usepackage{makeidx}
\usepackage{graphics}
\usepackage{amssymb}
\pagestyle{headings} \pagestyle{headings}
\makeindex \makeindex
\parindent=0mm \parindent=0mm
@ -8,8 +11,6 @@
%\evensidemargin=-.35in %\evensidemargin=-.35in
%\topmargin=-.50in %\topmargin=-.50in
\input amssym.def
\input amssym.tex
\newtheorem{thr}{Theorem} \newtheorem{thr}{Theorem}
%\font\bb=msym10 %\font\bb=msym10
\def\N{{\Bbb N}} \def\N{{\Bbb N}}
@ -149,7 +150,8 @@ The present documentation is a joint work between the second and third authors.
\input {cstwdoc.tex} \input {cstwdoc.tex}
\input {emspdoc2.tex} \input {emspdoc2.tex}
\input {whithdoc.tex} \input {whithdoc.tex}
\begin{theindex} %\begin{theindex}
\input kendoc.ind %\input kendoc.ind
\end{theindex} %\end{theindex}
\printindex
\end{document} \end{document}

4
doc/doc_src/lopspdoc.tex
View File

@ -7,9 +7,9 @@ Consider the set ${\cal A}\times \lbrace +1, -1 \rbrace$ and
make, as long as there is no ambiguity, the identification $a_i= (a_i,1)$ and $a_i^{-1}= (a_i,-1)$ make, as long as there is no ambiguity, the identification $a_i= (a_i,1)$ and $a_i^{-1}= (a_i,-1)$
for all $a_i\in{\cal A}$. for all $a_i\in{\cal A}$.
\proclaim {Definition}. $a_i$ and its formal inverse $a_i^{-1}$ are {\em letters}. \paragraph{Definition}. $a_i$ and its formal inverse $a_i^{-1}$ are {\em letters}.
\proclaim {Definition}. A word is a {\em finite} sequence of letters, possibly repeated, \paragraph{Definition}. A word is a {\em finite} sequence of letters, possibly repeated,
without any pair of the form $a_ja_j^{-1}$ and $a_k^{-1}a_k$. The word is said {\em reduced}. without any pair of the form $a_ja_j^{-1}$ and $a_k^{-1}a_k$. The word is said {\em reduced}.
Now, let $\Z^{*{\cal A}}$ the set of {\em words} on $\cal A$. Now, let $\Z^{*{\cal A}}$ the set of {\em words} on $\cal A$.

16
doc/doc_src/ssdoc.tex
View File

@ -595,7 +595,7 @@ triangulation of the torus. As the faces are never degenerated, the description
is of simplified form. is of simplified form.
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/torus2.eps}} \centerline{\includegraphics{torus2.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
The vertices will be named {\tt v0}, {\tt v1}, ..., {\tt v6}, {\tt v0} being the base point. The edges The vertices will be named {\tt v0}, {\tt v1}, ..., {\tt v6}, {\tt v0} being the base point. The edges
@ -668,7 +668,7 @@ ones in the previous page and in the Homology chapter.
\newpage \newpage
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/cylinss.eps}} \centerline{\includegraphics{cylinss.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
@ -697,7 +697,7 @@ Homology in dimension 2 :
\newpage \newpage
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/moebiuss.eps}} \centerline{\includegraphics{moebiuss.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
{\footnotesize\begin{verbatim} {\footnotesize\begin{verbatim}
@ -725,7 +725,7 @@ Homology in dimension 2 :
\newpage \newpage
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/toruss.eps}} \centerline{\includegraphics{toruss.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
{\footnotesize\begin{verbatim} {\footnotesize\begin{verbatim}
@ -757,7 +757,7 @@ Component Z
\newpage \newpage
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/bottless.eps}} \centerline{\includegraphics{bottless.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
{\footnotesize\begin{verbatim} {\footnotesize\begin{verbatim}
@ -787,7 +787,7 @@ Homology in dimension 2 :
\newpage \newpage
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/ppss.eps}} \centerline{\includegraphics{ppss.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
{\footnotesize\begin{verbatim} {\footnotesize\begin{verbatim}
@ -819,7 +819,7 @@ by ``{\tt *}'' instead of the complete form {\tt (0 *)}.
\newpage \newpage
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/duncess.eps}} \centerline{\includegraphics{duncess.eps}}
\vskip 0.40cm \vskip 0.40cm
% %
{\footnotesize\begin{verbatim} {\footnotesize\begin{verbatim}
@ -1715,7 +1715,7 @@ up to dimension $2$ for a better understanding of the components of the product
\end{verbatim}} \end{verbatim}}
% %
\vskip 0.40cm \vskip 0.40cm
\centerline{\psfig{figure=/home/home/siret/Kenzo/ssquare.eps}} \centerline{\includegraphics{ssquare.eps}}
\vskip 0.40cm \vskip 0.40cm
% %