  
  
                                     [1X[5XIdRel[0X[0X
  
  
                    [1XA package for Identities among Relators[0X
  
  
                                  Version 2.03
  
  
                                  October 2007
  
  
                                 Anne Heyworth
  
                                 Chris Wensley
  
  
  
  Anne Heyworth
      Email:    [7Xmailto:anne.heyworth@googlemail.com[0X
  Chris Wensley
      Email:    [7Xmailto:c.d.wensley@bangor.ac.uk[0X
      Homepage: [7Xhttp://www.informatics.bangor.ac.uk/~cwensley/[0X
      Address:  School of Computer Science, Bangor University,
                Dean Street, Bangor, Gwynedd, LL57 1UT, U.K.
  
  
  
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  [1XAbstract[0X
  The  [5XIdRel[0X  package  was  originally  implemented  in  1999, using the [5XGAP[0X 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 relations 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[0X 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[0X.
  
  
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  [1XCopyright[0X
  © 2005-2007 by Anne Heyworth and Chris Wensley
  
  We  adopt  the  copyright  regulations  of  [5XGAP[0X as detailed in the copyright
  notice in the [5XGAP[0X manual.
  
  
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  [1XContent (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
      5.2-2 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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