[1X[5Xkan[0m[1X[0m [1XA package for Induced Category Actions[0m Version 0.97 November 2008 Anne Heyworth Chris Wensley Anne Heyworth Email: [7Xmailto:anne.heyworth@googlemail.com[0m Chris Wensley Email: [7Xmailto:c.d.wensley@bangor.ac.uk[0m Homepage: [7Xhttp://www.bangor.ac.uk/~mas023/[0m Address: School of Computer Science, Bangor University, Dean Street, Bangor, Gwynedd, LL57 1UT, U.K. ------------------------------------------------------- [1XAbstract[0m The [5Xkan[0m package was originally implemented in 1997 using the [5XGAP[0m 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 [7Xmailto:c.d.wensley@bangor.ac.uk[0m. ------------------------------------------------------- [1XCopyright[0m © 2005-2008 Anne Heyworth and Chris Wensley ------------------------------------------------------- [1XAcknowledgements[0m This [5Xkan[0m package is released under the GNU General Public License (GPL). This file is part of [5Xkan[0m, though as documentation it is released under the GNU Free Documentation License (see [7Xhttp://www.gnu.org/licenses/licenses.html#FDL[0m). [5Xkan[0m 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. [5Xkan[0m 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 [5Xkan[0m; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. For more details, see [7Xhttp://www.fsf.org/licenses/gpl.html[0m. This documentation was prepared with the [5XGAPDoc[0m package of Frank L\"ubeck and Max Neunh\"offer. ------------------------------------------------------- [1XContents (Kan)[0X 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 -------------------------------------------------------