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# kan

## including double coset rewriting systems

1.34

13 March 2022

Anne Heyworth

Chris Wensley
Email: c.d.wensley@bangor.ac.uk
Homepage: https://github.com/cdwensley
Address:
Dr. C.D. Wensley
School of Computer Science
Bangor University
Dean Street
Bangor
Gwynedd LL57 1UT
UK

### Abstract

Kan is a GAP package 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 last author at c.d.wensley@bangor.ac.uk or submit an issue at the GitHub repository https://github.com/gap-packages/kan/issues/.

### Copyright

© 1996-2022 Anne Heyworth and Chris Wensley

The Kan package 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 using the GAPDoc [LN17] and AutoDoc [GH17] packages.

The procedure used to produce new releases uses the package GitHubPagesForGAP [Hor17] and the package ReleaseTools.

### Contents

1 Introduction
2 Double Coset Rewriting Systems
2.1 Rewriting Systems
2.1-1 KnuthBendixRewritingSystem
2.1-2 NextWord
2.2 Example 2 -- free product of two cyclic groups
2.2-1 DoubleCosetRewritingSystem
2.2-2 DisplayAsString
2.2-3 WordAcceptorOfReducedRws
2.3 Example 3 -- the trefoil group
2.3-1 PartialDoubleCosetRewritingSystem
2.4 Example 4 -- an infinite rewriting system
2.4-1 KBMagRewritingSystem
2.4-2 DCrules
2.4-3 WordToString
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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