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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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   HAPcryst – An extension of the GAP package HAP for crystallographic groups

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                               ( Version 0.1.11 )

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                                   Marc Röder

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  Marc Röder

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      Email:    mailto:marc_roeder(at)web.de

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  Address: Marc Röder, Department of Mathematics, NUI Galway, Irleland

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  -------------------------------------------------------

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  Abstract

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  -------------------------------------------------------

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  Copyright

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  © 2007 Marc Röder.

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  This  package  is  distributed  under  the  terms  of the GNU General Public

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  License  version  2 or later (at your convenience). See the file LICENSE.txt

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  or http://www.gnu.org/copyleft/gpl.html

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  -------------------------------------------------------

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  Acknowledgements

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  This work was supported by Marie Curie Grant No. MTKD-CT-2006-042685

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  -------------------------------------------------------

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  Contents (HAPcryst)

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  1 Introduction

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    1.1 Abstract and Notation

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      1.1-1 The natural action of crystallographic groups

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    1.2 Requirements

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      1.2-1 Recommendation concerning polymake

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    1.3 Global Variables

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      1.3-1 InfoHAPcryst

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  2 Bits and Pieces

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    2.1 Matrices and Vectors

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      2.1-1 SignRat

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      2.1-2 VectorModOne

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      2.1-3 IsSquareMat

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      2.1-4 DimensionSquareMat

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    2.2 Affine Matrices OnRight

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      2.2-1 LinearPartOfAffineMatOnRight

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      2.2-2 BasisChangeAffineMatOnRight

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      2.2-3 TranslationOnRightFromVector

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    2.3 Geometry

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      2.3-1 GramianOfAverageScalarProductFromFiniteMatrixGroup

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      2.3-2 Inequalities

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      2.3-3 BisectorInequalityFromPointPair

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      2.3-4 WhichSideOfHyperplane

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      2.3-5 RelativePositionPointAndPolygon

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    2.4 Space Groups

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      2.4-1 PointGroupRepresentatives

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  3 Algorithms of Orbit-Stabilizer Type

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    3.1 Orbit Stabilizer for Crystallographic Groups

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      3.1-1 OrbitStabilizerInUnitCubeOnRight

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      3.1-2 OrbitStabilizerInUnitCubeOnRightOnSets

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      3.1-3 OrbitPartInVertexSetsStandardSpaceGroup

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      3.1-4 OrbitPartInFacesStandardSpaceGroup

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      3.1-5 OrbitPartAndRepresentativesInFacesStandardSpaceGroup

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      3.1-6 StabilizerOnSetsStandardSpaceGroup

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      3.1-7 RepresentativeActionOnRightOnSets

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      3.1-8 Getting other orbit parts

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      3.1-9 ShiftedOrbitPart

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      3.1-10 TranslationsToOneCubeAroundCenter

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      3.1-11 TranslationsToBox

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  4 Resolutions of Crystallographic Groups

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    4.1 Fundamental Domains

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      4.1-1 FundamentalDomainStandardSpaceGroup

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      4.1-2 FundamentalDomainBieberbachGroup

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      4.1-3 FundamentalDomainFromGeneralPointAndOrbitPartGeometric

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      4.1-4 IsFundamentalDomainStandardSpaceGroup

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      4.1-5 IsFundamentalDomainBieberbachGroup

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    4.2 Face Lattice and Resolution

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      4.2-1 ResolutionBieberbachGroup

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      4.2-2 FaceLatticeAndBoundaryBieberbachGroup

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      4.2-3 ResolutionFromFLandBoundary

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