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# Kan

## A package for Induced Category Actions

Version 1.25

18/02/2016

Anne Heyworth

Chris Wensley
Email: c.d.wensley@bangor.ac.uk
Homepage: http://pages.bangor.ac.uk/~mas023/
Address:
School of Computer Science, Bangor University,
Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.

### Abstract

The Kan package was originally implemented in 1996 using the GAP 3 language, to compute induced actions of categories, when the first author was studying for a Ph.D. in Bangor.

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

Kan became an accepted GAP package in May 2015.

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

### Copyright

© 1996-2016 Anne Heyworth and Chris Wensley

kan is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

### Acknowledgements

This documentation was prepared with the GAPDoc package of Frank Lübeck and Max Neunhöffer.

### 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
2.3 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
References
Index
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