IdRel

A package for Identities among Relators

Version 2.02

June 2006

Anne Heyworth
e-mail: a.heyworth@mcs.le.ac.uk
Address:
University of Leicester.

Chris Wensley
e-mail: c.d.wensley@bangor.ac.uk
WWW: http://www.informatics.bangor.ac.uk/~cwensley/
Address:
School of Informatics, University of Wales Bangor,
Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.

Abstract

The IdRel package was originally implemented in 1999 using the GAP3 language, when the first author was studying for a Ph.D. in Bangor, and has since been converted to GAP4.

This package is designed to compute a minimal set of generators for the module of the identities among relations of a group presentation. It does this using

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

Copyright

(C) 1999-2006 by Anne Heyworth and Chris Wensley

We adopt the copyright regulations of GAP as detailed in the copyright notice in the GAP manual.

Contents

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
      5.2-2 ZeroModulePoly
      5.2-3 AddTermModulePoly
   5.3 Module Polynomial Operations
   5.4 Identities among relators
      5.4-1 IdentitiesAmongRelators
      5.4-2 RootIdentities




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