  
  
                                     [1X[5XIdRel[105X[101X
  
  
                    [1XA package for Identities among Relators[101X
  
  
                                  Version 2.34
  
  
                                   20/10/2016
  
  
                                 Anne Heyworth
  
                                 Chris Wensley
  
  
  
  Chris Wensley
      Email:    [7Xmailto:c.d.wensley@bangor.ac.uk[107X
      Homepage: [7Xhttp://pages.bangor.ac.uk/~mas023/[107X
      Address:  [33X[0;14YSchool of Computer Science, Bangor University,[133X
                [33X[0;14YDean Street, Bangor, Gwynedd, LL57 1UT, U.K.[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe  [5XIdRel[105X  package  was  originally  implemented  in  1999, using the [5XGAP[105X 3
  language, when the first author was studying for a Ph.D. in Bangor.[133X
  
  [33X[0;0YThis  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[133X
  
  [30X    [33X[0;6Yrewriting and logged rewriting: a self-contained implementation of the
        Knuth-Bendix  process  using the monoid presentation associated to the
        group presentation;[133X
  
  [30X    [33X[0;6Ymonoid polynomials: an implementation of the monoid ring;[133X
  
  [30X    [33X[0;6Ymodule  polynomials:  an  implementation of the right module over this
        monoid generated by the relators.[133X
  
  [30X    [33X[0;6YY-sequences:  used  as  a  [13Xrewriting[113X way of representing elements of a
        free  crossed  module  (products  of  conjugates of group relators and
        inverse relators).[133X
  
  [33X[0;0Y[5XIdRel[105X became an accepted [5XGAP[105X package in May 2015.[133X
  
  [33X[0;0YBug reports, suggestions and comments are, of course, welcome. Please submit
  an  issue  at [7Xhttps://github.com/gap-packages/idrel/issues/[107X or send an email
  to the second author at [7Xmailto:c.d.wensley@bangor.ac.uk[107X.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 1999-2016 Anne Heyworth and Chris Wensley[133X
  
  [33X[0;0Y[5XIdRel[105X  is  free software; you can redistribute it and/or modify it under the
  terms        of       the       GNU       General       Public       License
  ([7Xhttp://www.fsf.org/licenses/gpl.html[107X)  as  published  by  the Free Software
  Foundation;  either  version 2 of the License, or (at your option) any later
  version.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThis  documentation  was  prepared  with  the [5XGAPDoc[105X package [LN12] of Frank
  Lübeck and Max Neunhöffer.[133X
  
  [33X[0;0YThe  procedure  used  to  mount  new  releases  on  GitHub uses the packages
  [5XGitHubPagesForGAP[105X [Hor14] and [5XReleaseTools[105X of Max Horn.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (IdRel)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YRewriting Systems[133X
    2.1 [33X[0;0YIdentity Y-sequences[133X
    2.2 [33X[0;0YMonoid Presentations of FpGroups[133X
      2.2-1 FreeRelatorGroup
      2.2-2 MonoidPresentationFpGroup
    2.3 [33X[0;0YRewriting systems for FpGroups[133X
      2.3-1 RewritingSystemFpGroup
      2.3-2 OnePassReduceWord
      2.3-3 OnePassKB
    2.4 [33X[0;0YEnumerating elements[133X
      2.4-1 ElementsOfMonoidPresentation
  3 [33X[0;0YLogged Rewriting Systems[133X
    3.1 [33X[0;0YLogged Knuth-Bendix Completion[133X
      3.1-1 LoggedOnePassKB
      3.1-2 LoggedKnuthBendix
    3.2 [33X[0;0YLogged reduction of a word[133X
      3.2-1 LoggedReduceWordKB
      3.2-2 LoggedRewritingSystemFpGroup
  4 [33X[0;0YMonoid Polynomials[133X
    4.1 [33X[0;0YConstruction of monoid polynomials[133X
      4.1-1 MonoidPolyFromCoeffsWords
    4.2 [33X[0;0YComponents of a polynomial[133X
      4.2-1 Terms
      4.2-2 Monic
      4.2-3 AddTermMonoidPoly
    4.3 [33X[0;0YMonoid Polynomial Operations[133X
      4.3-1 Length
    4.4 [33X[0;0YReduction of a Monoid Polynomial[133X
      4.4-1 ReduceMonoidPoly
  5 [33X[0;0YModule Polynomials[133X
    5.1 [33X[0;0YConstruction of module polynomials[133X
      5.1-1 ModulePoly
    5.2 [33X[0;0YComponents of a module polynomial[133X
      5.2-1 Terms
    5.3 [33X[0;0YModule Polynomial Operations[133X
      5.3-1 AddTermModulePoly
    5.4 [33X[0;0YIdentities among relators[133X
      5.4-1 IdentityYSequences
      5.4-2 RootIdentities
  
  
  [32X
