  
  
     [1X[5XHap Programming[0X – An experimental framework for objectifying the data[0X
                               [1Xstructures of Hap[0X
  
  
                     ( development version of 02.12.2008 )
  
  
                                   Marc Röder
  
  
  
  Marc Röder
      Email:    [7Xmailto:marc.roeder(at)nuigalway.ie[0X
  
  
  Address: Marc Röder, Department of Mathematics, NUI Galway, Irleland
  
  
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  [1XAbstract[0X
  This   extension  does  not  change  the  behaviour  of  Hap  and  is  fully
  backwards-compatible. It is not a part of Hap and there is no guarantee that
  it will at any point be supported by Hap. Use at your own risk.
  
  
  -------------------------------------------------------
  [1XCopyright[0X
  © 2007 Marc Röder.
  
  This  package  is  distributed  under  the  terms  of the GNU General Public
  License  version  2 or later (at your convenience). See the file [11XLICENSE.txt[0X
  or [7Xhttp://www.gnu.org/copyleft/gpl.html[0X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[0X
  This work was supported by Marie Curie Grant No. MTKD-CT-2006-042685
  
  
  -------------------------------------------------------
  
  
  [1XContent (HAPprog)[0X
  
  1. Resolutions in Hap
    1.1 The Standard Representation [9XHapResolutionRep[0X
    1.2 The [9XHapLargeGroupResolutionRep[0X Representation
  2. Accessing and Manipulating Resolutions
    2.1 Representation-Independent Access Methods
      2.1-1 StrongestValidRepresentationForLetter
      2.1-2 StrongestValidRepresentationForWord
      2.1-3 PositionInGroupOfResolution
      2.1-4 IsValidGroupInt
      2.1-5 GroupElementFromPosition
      2.1-6 MultiplyGroupElts
      2.1-7 MultiplyFreeZGLetterWithGroupElt
      2.1-8 MultiplyFreeZGWordWithGroupElt
      2.1-9 BoundaryOfFreeZGLetter
      2.1-10 BoundaryOfFreeZGWord
    2.2 Converting Between Representations
      2.2-1 ConvertStandardLetter
      2.2-2 ConvertStandardWord
      2.2-3 ConvertLetterToStandardRep
      2.2-4 ConvertWordToStandardRep
    2.3 Special Methods for [9XHapResolutionRep[0X
      2.3-1 IsFreeZGLetter
      2.3-2 IsFreeZGWord
      2.3-3 MultiplyGroupEltsNC
      2.3-4 MultiplyFreeZGLetterWithGroupEltNC
      2.3-5 MultiplyFreeZGWordWithGroupEltNC
      2.3-6 BoundaryOfFreeZGLetterNC
      2.3-7 BoundaryOfFreeZGWordNC
    2.4 The [9XHapLargeGroupResolutionRep[0X Representation
      2.4-1 GroupRingOfResolution
      2.4-2 MultiplyGroupElts_LargeGroupRep
      2.4-3 IsFreeZGLetterNoTermCheck_LargeGroupRep
      2.4-4 IsFreeZGWordNoTermCheck_LargeGroupRep
      2.4-5 IsFreeZGLetter_LargeGroupRep
      2.4-6 IsFreeZGWord_LargeGroupRep
      2.4-7 MultiplyFreeZGLetterWithGroupElt_LargeGroupRep
      2.4-8 MultiplyFreeZGWordWithGroupElt_LargeGroupRep
      2.4-9 GeneratorsOfModuleOfResolution_LargeGroupRep
      2.4-10 BoundaryOfGenerator_LargeGroupRep
      2.4-11 BoundaryOfFreeZGLetterNC_LargeGroupRep
      2.4-12 BoundaryOfFreeZGWord_LargeGroupRep
  3. Contracting Homotopies
    3.1 The [9XPartialContractingHomotopy[0X Data Type
      3.1-1 ResolutionOfContractingHomotopy
      3.1-2 PartialContractingHomotopyLookup
  
  
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