HAPcryst – An extension of the GAP package HAP for crystallographic groups
  
  
                               ( Version 0.1.8 )
  
  
                                   Marc Röder
  
  
  
  Marc Röder
      Email:    mailto:marc_roeder(at)web.de
  
  
  Address: Marc Röder, Department of Mathematics, NUI Galway, Irleland
  
  
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  Abstract
  
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  Copyright
  © 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 LICENSE.txt
  or http://www.gnu.org/copyleft/gpl.html
  
  
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  Acknowledgements
  This work was supported by Marie Curie Grant No. MTKD-CT-2006-042685
  
  
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  Content (HAPcryst)
  
  1. Introduction
    1.1 Abstract and Notation
      1.1-1 The natural action of crystallographic groups
    1.2 Requirements
      1.2-1 Recommendation concerning polymake
    1.3 Global Variables
      1.3-1 InfoHAPcryst
  2. Bits and Pieces
    2.1 Matrices and Vectors
      2.1-1 SignRat
      2.1-2 VectorModOne
      2.1-3 IsSquareMat
      2.1-4 DimensionSquareMat
    2.2 Affine Matrices OnRight
      2.2-1 LinearPartOfAffineMatOnRight
      2.2-2 BasisChangeAffineMatOnRight
      2.2-3 TranslationOnRightFromVector
    2.3 Geometry
      2.3-1 GramianOfAverageScalarProductFromFiniteMatrixGroup
      2.3-2 Inequalities
      2.3-3 BisectorInequalityFromPointPair
      2.3-4 WhichSideOfHyperplane
      2.3-5 RelativePositionPointAndPolygon
    2.4 Space Groups
      2.4-1 PointGroupRepresentatives
  3. Algorithms of Orbit-Stabilizer Type
    3.1 Orbit Stabilizer for Crystallographic Groups
      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 Getting other orbit parts
      3.1-9 ShiftedOrbitPart
      3.1-10 TranslationsToOneCubeAroundCenter
      3.1-11 TranslationsToBox
  4. Resolutions of Crystallographic Groups
    4.1 Fundamental Domains
      4.1-1 FundamentalDomainStandardSpaceGroup
      4.1-2 FundamentalDomainBieberbachGroup
      4.1-3 FundamentalDomainFromGeneralPointAndOrbitPartGeometric
      4.1-4 IsFundamentalDomainStandardSpaceGroup
      4.1-5 IsFundamentalDomainBieberbachGroup
    4.2 Face Lattice and Resolution
      4.2-1 ResolutionBieberbachGroup
      4.2-2 FaceLatticeAndBoundaryBieberbachGroup
      4.2-3 ResolutionFromFLandBoundary
  
  
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