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Introduction

Since its first version, EAT has been designed to determine homology groups which couldn't be reached by using alternative methods of computation (even theoretic and non-algorithmic methods).

But the aim of the implementors is now to expand the application field of the system and to make easier the use of the program for a larger community of algebraic topologists. For this, a 240 pages long user guide has been written which contains in particular many examples, ranging from elementary surfaces to sophisticated operations on iterated loop spaces.

EAT can deal with the following mathematical structures:

and their corresponding versions with effective homology (roughly speaking, an object with effective homology is a structure on which an algorithm to compute its homology groups can be applied, see [4]).

The operations which have been implemented in the current version of EAT are:

and the corresponding operations on objects with effective homology (in particular, the construction of a loop space with effective homology involves the implementation of an effective version of the Eilenberg-Moore spectral sequence, see [1]).

The examples in the user guide cover:

EAT is organised in a tree of eleven (Common Lisp) modules: This set of modules enables the topologist to work on a computer with the objects and operators which are the matter of his papers and textbooks, in a way which is very close to its usual practice.

A new version of the system is currently under development and could be available in 1998.