[1X[5XIdRel[0m[1X[0m [1XA package for Identities among Relators[0m Version 2.05 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 [5XIdRel[0m package was originally implemented in 1999, using the [5XGAP[0m 3 language, when the first author was studying for a Ph.D. in Bangor. This package is designed to compute a minimal set of generators for the module of the identities among relators of a group presentation. It does this using -- rewriting and logged rewriting: a self-contained implementation of the Knuth-Bendix process using the monoid presentation associated to the group presentation; -- monoid polynomials: an implementation of the monoid ring; -- module polynomials: an implementation of the right module over this monoid generated by the relators. -- Y-sequences: used as a [13Xrewriting[0m way of representing elements of a free crossed module (products of conjugates of group relators and inverse relators). 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 [5Xidrel[0m package is released under the GNU General Public License (GPL). This file is part of [5Xidrel[0m, though as documentation it is released under the GNU Free Documentation License (see [7Xhttp://www.gnu.org/licenses/licenses.html#FDL[0m). [5Xidrel[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. [5Xidrel[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 [5Xidrel[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 (IdRel)[0X 1 Introduction 2 Rewriting Systems 2.1 Identity Y-sequences 2.2 Monoid Presentations of FpGroups 2.2-1 FreeRelatorGroup 2.2-2 MonoidPresentationFpGroup 2.3 Rewriting systems for FpGroups 2.3-1 RewritingSystemFpGroup 2.3-2 OnePassReduceWord 2.3-3 OnePassKB 2.4 Enumerating elements 2.4-1 ElementsOfMonoidPresentation 3 Logged Rewriting Systems 3.1 Logged Knuth-Bendix Completion 3.1-1 LoggedOnePassKB 3.1-2 LoggedKnuthBendix 3.2 Logged reduction of a word 3.2-1 LoggedReduceWordKB 3.2-2 LoggedRewritingSystemFpGroup 4 Monoid Polynomials 4.1 Construction of monoid polynomials 4.1-1 MonoidPolyFromCoeffsWords 4.2 Components of a polynomial 4.2-1 Terms 4.2-2 Monic 4.2-3 AddTermMonoidPoly 4.3 Monoid Polynomial Operations 4.3-1 Length 4.4 Reduction of a Monoid Polynomial 4.4-1 ReduceMonoidPoly 5 Module Polynomials 5.1 Construction of module polynomials 5.1-1 ModulePoly 5.2 Components of a module polynomial 5.2-1 Terms 5.3 Module Polynomial Operations 5.3-1 AddTermModulePoly 5.4 Identities among relators 5.4-1 IdentityYSequences 5.4-2 RootIdentities -------------------------------------------------------