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# kan

## A package for Induced Category Actions

Version 0.97

November 2008

Anne Heyworth
Email: anne.heyworth@googlemail.com

Chris Wensley
Email: c.d.wensley@bangor.ac.uk
Homepage: http://www.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 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 reduced 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

© 2005-2008 Anne Heyworth and Chris Wensley

### Acknowledgements

This kan package is released under the GNU General Public License (GPL). This file is part of kan, though as documentation it is released under the GNU Free Documentation License (see http://www.gnu.org/licenses/licenses.html#FDL).

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.

kan is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with kan; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.

For more details, see http://www.fsf.org/licenses/gpl.html.

This documentation was prepared with the GAPDoc package of Frank L\"ubeck and Max Neunh\"offer.

### 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
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