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# kan

## A package for Induced Category Actions

Version 0.95

October 2007

Anne Heyworth
e-mail: anne.heyworth@googlemail.com

Chris Wensley
e-mail: c.d.wensley@bangor.ac.uk
WWW: http://www.informatics.bangor.ac.uk/~cwensley/
Address:
School of Computer Science, Bangor University,
Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.

### Abstract

The kan package was originally implemented in 1997 using the GAP 3 language, to compute induced actions of categories, when the first author was studying for a Ph.D. in Bangor.

This version only provides functions for the computation of normal forms of representatives of double cosets of finitely presented groups,

Bug reports, suggestions and comments are, of course, welcome. Please contact the second author at c.d.wensley@bangor.ac.uk.

### Copyright

© 2005-2007 by Anne Heyworth and Chris Wensley

We adopt the copyright regulations of GAP as detailed in the copyright notice in the GAP manual.

### Contents

1. Introduction
2. Double Coset Rewriting Systems
2.1 Rewriting Systems
2.1-1 KnuthBendixRewritingSystem
2.2 Example 1 -- free product of two cyclic groups
2.2-1 DoubleCosetRewritingSystem
2.2-2 WordAcceptorOfReducedRws
2.2-3 SFAtoRatExp
2.3 Example 2 -- the trefoil group
2.3-1 PartialDoubleCosetRewritingSystem
2.4 Example 3 -- an infinite rewriting system
2.4-1 KBMagRewritingSystem
2.4-2 DCrules
2.4-3 NextWord
3. Development History
3.1 Versions of the package
3.2 What needs doing next?
3.2-1 DoubleCosetsAutomaton
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