  
  
                                   [1X HAPcryst [101X
  
  
                 [1X A HAP extension for crystallographic groups [101X
  
  
                                 Version 0.2.0
  
  
                                 24 March 2026
  
  
                                  Marc Roeder
  
  
  
  Marc Roeder
      Email:    [7Xmailto:roeder.marc@gmail.com[107X
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2007 Marc Röder.[133X
  
  [33X[0;0YThis  package  is  distributed  under  the  terms  of the GNU General Public
  License  version  2  or later (at your convenience). See the file [11XLICENSE[111X or
  [7Xhttps://www.gnu.org/copyleft/gpl.html[107X[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThis work was supported by Marie Curie Grant No. MTKD-CT-2006-042685[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (HAPcryst)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YAbstract and Notation[133X
      1.1-1 [33X[0;0YThe natural action of crystallographic groups[133X
    1.2 [33X[0;0YRequirements[133X
      1.2-1 [33X[0;0YRecommendation concerning polymake[133X
    1.3 [33X[0;0YGlobal Variables[133X
      1.3-1 InfoHAPcryst
  2 [33X[0;0YBits and Pieces[133X
    2.1 [33X[0;0YMatrices and Vectors[133X
      2.1-1 SignRat
      2.1-2 VectorModOne
      2.1-3 IsSquareMat
      2.1-4 DimensionSquareMat
    2.2 [33X[0;0YAffine Matrices OnRight[133X
      2.2-1 LinearPartOfAffineMatOnRight
      2.2-2 BasisChangeAffineMatOnRight
      2.2-3 TranslationOnRightFromVector
    2.3 [33X[0;0YGeometry[133X
      2.3-1 GramianOfAverageScalarProductFromFiniteMatrixGroup
      2.3-2 [33X[0;0YInequalities[133X
      2.3-3 BisectorInequalityFromPointPair
      2.3-4 WhichSideOfHyperplane
      2.3-5 RelativePositionPointAndPolygon
    2.4 [33X[0;0YSpace Groups[133X
      2.4-1 PointGroupRepresentatives
  3 [33X[0;0YAlgorithms of Orbit-Stabilizer Type[133X
    3.1 [33X[0;0YOrbit Stabilizer for Crystallographic Groups[133X
      3.1-1 OrbitStabilizerInUnitCubeOnRight
      3.1-2 OrbitStabilizerInUnitCubeOnRightOnSets
      3.1-3 OrbitPartInVertexSetsStandardSpaceGroup
      3.1-4 OrbitPartInFacesStandardSpaceGroup
      3.1-5 OrbitPartAndRepresentativesInFacesStandardSpaceGroup
      3.1-6 StabilizerOnSetsStandardSpaceGroup
      3.1-7 RepresentativeActionOnRightOnSets
      3.1-8 [33X[0;0YGetting other orbit parts[133X
      3.1-9 ShiftedOrbitPart
      3.1-10 TranslationsToOneCubeAroundCenter
      3.1-11 TranslationsToBox
  4 [33X[0;0YResolutions of Crystallographic Groups[133X
    4.1 [33X[0;0YFundamental Domains[133X
      4.1-1 FundamentalDomainStandardSpaceGroup
      4.1-2 FundamentalDomainBieberbachGroup
      4.1-3 FundamentalDomainFromGeneralPointAndOrbitPartGeometric
      4.1-4 IsFundamentalDomainStandardSpaceGroup
      4.1-5 IsFundamentalDomainBieberbachGroup
    4.2 [33X[0;0YFace Lattice and Resolution[133X
      4.2-1 ResolutionBieberbachGroup
      4.2-2 FaceLatticeAndBoundaryBieberbachGroup
      4.2-3 ResolutionFromFLandBoundary
  A [33X[0;0YResolutions in Hap[133X
    A.1 [33X[0;0YThe Standard Representation [9XHapResolutionRep[109X[133X
    A.2 [33X[0;0YThe [9XHapLargeGroupResolutionRep[109X Representation[133X
  B [33X[0;0YAccessing and Manipulating Resolutions[133X
    B.1 [33X[0;0YRepresentation-Independent Access Methods[133X
      B.1-1 StrongestValidRepresentationForLetter
      B.1-2 StrongestValidRepresentationForWord
      B.1-3 PositionInGroupOfResolution
      B.1-4 IsValidGroupInt
      B.1-5 GroupElementFromPosition
      B.1-6 MultiplyGroupElts
      B.1-7 MultiplyFreeZGLetterWithGroupElt
      B.1-8 MultiplyFreeZGWordWithGroupElt
      B.1-9 BoundaryOfFreeZGLetter
      B.1-10 BoundaryOfFreeZGWord
    B.2 [33X[0;0YConverting Between Representations[133X
      B.2-1 ConvertStandardLetter
      B.2-2 ConvertStandardWord
      B.2-3 ConvertLetterToStandardRep
      B.2-4 ConvertWordToStandardRep
    B.3 [33X[0;0YSpecial Methods for [9XHapResolutionRep[109X[133X
      B.3-1 IsFreeZGLetter
      B.3-2 IsFreeZGWord
      B.3-3 MultiplyGroupEltsNC
      B.3-4 MultiplyFreeZGLetterWithGroupEltNC
      B.3-5 MultiplyFreeZGWordWithGroupEltNC
      B.3-6 BoundaryOfFreeZGLetterNC
      B.3-7 BoundaryOfFreeZGWordNC
    B.4 [33X[0;0YThe [9XHapLargeGroupResolutionRep[109X Representation[133X
      B.4-1 GroupRingOfResolution
      B.4-2 MultiplyGroupElts_LargeGroupRep
      B.4-3 IsFreeZGLetterNoTermCheck_LargeGroupRep
      B.4-4 IsFreeZGWordNoTermCheck_LargeGroupRep
      B.4-5 IsFreeZGLetter_LargeGroupRep
      B.4-6 IsFreeZGWord_LargeGroupRep
      B.4-7 MultiplyFreeZGLetterWithGroupElt_LargeGroupRep
      B.4-8 MultiplyFreeZGWordWithGroupElt_LargeGroupRep
      B.4-9 GeneratorsOfModuleOfResolution_LargeGroupRep
      B.4-10 BoundaryOfGenerator_LargeGroupRep
      B.4-11 BoundaryOfFreeZGLetterNC_LargeGroupRep
      B.4-12 BoundaryOfFreeZGWord_LargeGroupRep
  C [33X[0;0YContracting Homotopies[133X
    C.1 [33X[0;0YThe [9XPartialContractingHomotopy[109X Data Type[133X
      C.1-1 ResolutionOfContractingHomotopy
      C.1-2 PartialContractingHomotopyLookup
  
  
  [32X
