GAP (Kan) - Chapter 1: Introduction

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### 1. Introduction

The kan package started out as part of Anne Heyworth's thesis [H99]}, and was designed to compute induced actions of categories (see also [BH00]).

This version of kan only provides functions for the computation of normal forms of representatives of double cosets of finitely presented groups, and is made available in support of the paper [BG+06]. Existing methods for computing double cosets in GAP are described in [L91].

The package is loaded into GAP with the command

    gap> LoadPackage( "kan" );

This version of kan has been prepared for GAP~4.4.6. Some of the functions in the automata share package are used to compute word acceptors and regular expressions for the languages they accept.

The kbmag share package is also used to compute a word acceptor of a group `G` when `G` has no finite rewriting system. If kbmag is not available (the user is not on a UNIX system, or the C-programs have not been compiled), the file `dckbmag.gi` will not be read, so methods for the functions detailed in section 2.4.1 will not be available.

The information parameter `InfoKan` takes default value `0`. When raised to a higher value, additional information is printed out.

The following test file (assuming the user is in the `kan` directory) runs all the manual examples.

    gap> ReadTest("tst/kan_manual.tst");
    + setting AssertionLevel to 0 to avoid recursion in Automata
    + Testing all example commands in the Kan manual
    + GAP4stones: 6
    true

(If kbmag is not loaded then a collection of error lines for Example 3 will be printed out.)

Please send bug reports, suggestions and other comments to the second author.

The kan package is subject to the GAP copyright regulations as detailed in the copyright notice in the GAP manual.

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