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\begin{document}
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\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
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-----
\vskip 0.20cm
Institut Fourier \\
Grenoble, France \\
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-----
\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 (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.
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\input {kenovrvw}
\tableofcontents
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\input {ccdoc}
\input {ccehdoc}
\input {homlgdoc.tex}
\input {tprdoc}
\input {coaldoc.tex}
\input {aldoc.tex}
\input {ssdoc}
\input {smmrdoc.tex}
\input {ezdoc.tex}
\input {kandoc}
\input {smgrdoc.tex}
\input {fibrdoc.tex}
\input {lopspdoc}
\input {dspspdoc.tex}
\input {lptwdoc.tex}
\input {emspdoc1.tex}
\input {classydoc.tex}
\input {serredoc.tex}
\input {cstwdoc.tex}
\input {emspdoc2.tex}
\input {whithdoc.tex}
\addcontentsline{toc}{chapter}{Index}
\printindex
\end{document}