First experiments w/ Org version of the Handbook.
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\begin{center}
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\line(1,0){450}
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\end{center}
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The *Kenzo* program implements the general ideas of the second author about
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/Effective Homology/[fn:1], mainly around the Serre and Eilenberg-Moore
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spectral sequences. The first author (re-)discovered the importance of the
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/Basic Perturbation Lemma/ in these questions, already noted by Victor
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Guggenheim[fn:2] and this program directly implements and directly uses this
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"lemma" which should be called the /Fundamental Theorem of Algebraic Topology/.
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The first version of the program, called *EAT*, was written in 1989-90 by the
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first and the second authors. It has been demonstrated in several universities:
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France: Grenoble and Montpellier, Belgium: Louvain-la-Neuve, Italy: Genoa and
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Pisa, Sweden: Stockholm, Japan: Sapporo, Morioka, Urawa, Tokyo, Kyoto, Nara,
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Osaka and Hiroshima.
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In this *Kenzo* version, numerous improvements have been integrated in
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comparison with *EAT*.
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1. Standard CLOS (Common Lisp Object System) techniques.
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2. Use of Zermelo theorem about ordered sets (!): any set can be well ordered
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and this remark gives important new ideas to improve execution speed.
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3. Better memory management.
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4. Use of Szczarba's formulas instead of Shih's for implementing the twisted
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Eilenberg-Zilber theorem.
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5. New mathematical objects:
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- Serre spectral sequences.
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- Differential algebras.
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- Simplicial morphisms.
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- Kan simplicial sets.
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- Simplicial groups.
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- Fibrations.
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- Classifying spaces.
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In particular, using these tools, the first homotopy groups of /arbitrary/
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simplicial sets with effective homology, are now reachable.
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The present documentation is a joint work between the second and third authors.
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\begin{center}
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\line(1,0){450}
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\end{center}
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[fn:1] *Francis Sergeraert.* /The computability problem in algebraic topology./
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Advances in Mathematics, 1994, vol. 104, pp 1-29.
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[fn:2] *V.K.A.M. Guggenheim.* /On a perturbation theory for the homology of the
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loop space./ Journal of Pure and Applied Algebra, 1982, vol. 25, pp 197-205.
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#+TITLE: Kenzo - a Symbolic Software for Effective Homology Computation
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#+AUTHOR: Julio Rubio Garcia, Francis Sergeraert, Yvon Siret
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#+DATE: April 26, 1999
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#+BEGIN_SRC lisp :session cat :exports none :results silent
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(ql:quickload "kenzo")
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(use-package :cat)
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#+END_SRC
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#+INCLUDE: "Foreword.org"
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#+INCLUDE: "00_Overview.org"
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