\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{Introduction}}{4}{chapter.1}%
\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{Abstract and Notation}}{4}{section.1.1}%
\contentsline {subsection}{\numberline {1.1.1}\textcolor {Chapter }{The natural action of crystallographic groups}}{4}{subsection.1.1.1}%
\contentsline {section}{\numberline {1.2}\textcolor {Chapter }{Requirements}}{5}{section.1.2}%
\contentsline {subsection}{\numberline {1.2.1}\textcolor {Chapter }{Recommendation concerning polymake}}{5}{subsection.1.2.1}%
\contentsline {section}{\numberline {1.3}\textcolor {Chapter }{Global Variables}}{5}{section.1.3}%
\contentsline {subsection}{\numberline {1.3.1}\textcolor {Chapter }{InfoHAPcryst}}{5}{subsection.1.3.1}%
\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{Bits and Pieces}}{6}{chapter.2}%
\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{Matrices and Vectors}}{6}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}\textcolor {Chapter }{SignRat}}{6}{subsection.2.1.1}%
\contentsline {subsection}{\numberline {2.1.2}\textcolor {Chapter }{VectorModOne}}{6}{subsection.2.1.2}%
\contentsline {subsection}{\numberline {2.1.3}\textcolor {Chapter }{IsSquareMat}}{6}{subsection.2.1.3}%
\contentsline {subsection}{\numberline {2.1.4}\textcolor {Chapter }{DimensionSquareMat}}{6}{subsection.2.1.4}%
\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{Affine Matrices OnRight}}{7}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}\textcolor {Chapter }{LinearPartOfAffineMatOnRight}}{7}{subsection.2.2.1}%
\contentsline {subsection}{\numberline {2.2.2}\textcolor {Chapter }{BasisChangeAffineMatOnRight}}{7}{subsection.2.2.2}%
\contentsline {subsection}{\numberline {2.2.3}\textcolor {Chapter }{TranslationOnRightFromVector}}{7}{subsection.2.2.3}%
\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{Geometry}}{8}{section.2.3}%
\contentsline {subsection}{\numberline {2.3.1}\textcolor {Chapter }{GramianOfAverageScalarProductFromFiniteMatrixGroup}}{8}{subsection.2.3.1}%
\contentsline {subsection}{\numberline {2.3.2}\textcolor {Chapter }{Inequalities}}{8}{subsection.2.3.2}%
\contentsline {subsection}{\numberline {2.3.3}\textcolor {Chapter }{BisectorInequalityFromPointPair}}{8}{subsection.2.3.3}%
\contentsline {subsection}{\numberline {2.3.4}\textcolor {Chapter }{WhichSideOfHyperplane}}{8}{subsection.2.3.4}%
\contentsline {subsection}{\numberline {2.3.5}\textcolor {Chapter }{RelativePositionPointAndPolygon}}{9}{subsection.2.3.5}%
\contentsline {section}{\numberline {2.4}\textcolor {Chapter }{Space Groups}}{9}{section.2.4}%
\contentsline {subsection}{\numberline {2.4.1}\textcolor {Chapter }{PointGroupRepresentatives}}{9}{subsection.2.4.1}%
\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Algorithms of Orbit\texttt {\symbol {45}}Stabilizer Type}}{10}{chapter.3}%
\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{Orbit Stabilizer for Crystallographic Groups}}{10}{section.3.1}%
\contentsline {subsection}{\numberline {3.1.1}\textcolor {Chapter }{OrbitStabilizerInUnitCubeOnRight}}{10}{subsection.3.1.1}%
\contentsline {subsection}{\numberline {3.1.2}\textcolor {Chapter }{OrbitStabilizerInUnitCubeOnRightOnSets}}{11}{subsection.3.1.2}%
\contentsline {subsection}{\numberline {3.1.3}\textcolor {Chapter }{OrbitPartInVertexSetsStandardSpaceGroup}}{11}{subsection.3.1.3}%
\contentsline {subsection}{\numberline {3.1.4}\textcolor {Chapter }{OrbitPartInFacesStandardSpaceGroup}}{12}{subsection.3.1.4}%
\contentsline {subsection}{\numberline {3.1.5}\textcolor {Chapter }{OrbitPartAndRepresentativesInFacesStandardSpaceGroup}}{12}{subsection.3.1.5}%
\contentsline {subsection}{\numberline {3.1.6}\textcolor {Chapter }{StabilizerOnSetsStandardSpaceGroup}}{12}{subsection.3.1.6}%
\contentsline {subsection}{\numberline {3.1.7}\textcolor {Chapter }{RepresentativeActionOnRightOnSets}}{13}{subsection.3.1.7}%
\contentsline {subsection}{\numberline {3.1.8}\textcolor {Chapter }{Getting other orbit parts}}{13}{subsection.3.1.8}%
\contentsline {subsection}{\numberline {3.1.9}\textcolor {Chapter }{ShiftedOrbitPart}}{13}{subsection.3.1.9}%
\contentsline {subsection}{\numberline {3.1.10}\textcolor {Chapter }{TranslationsToOneCubeAroundCenter}}{13}{subsection.3.1.10}%
\contentsline {subsection}{\numberline {3.1.11}\textcolor {Chapter }{TranslationsToBox}}{13}{subsection.3.1.11}%
\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{Resolutions of Crystallographic Groups}}{15}{chapter.4}%
\contentsline {section}{\numberline {4.1}\textcolor {Chapter }{Fundamental Domains}}{15}{section.4.1}%
\contentsline {subsection}{\numberline {4.1.1}\textcolor {Chapter }{FundamentalDomainStandardSpaceGroup}}{15}{subsection.4.1.1}%
\contentsline {subsection}{\numberline {4.1.2}\textcolor {Chapter }{FundamentalDomainBieberbachGroup}}{15}{subsection.4.1.2}%
\contentsline {subsection}{\numberline {4.1.3}\textcolor {Chapter }{FundamentalDomainFromGeneralPointAndOrbitPartGeometric}}{17}{subsection.4.1.3}%
\contentsline {subsection}{\numberline {4.1.4}\textcolor {Chapter }{IsFundamentalDomainStandardSpaceGroup}}{17}{subsection.4.1.4}%
\contentsline {subsection}{\numberline {4.1.5}\textcolor {Chapter }{IsFundamentalDomainBieberbachGroup}}{17}{subsection.4.1.5}%
\contentsline {section}{\numberline {4.2}\textcolor {Chapter }{Face Lattice and Resolution}}{18}{section.4.2}%
\contentsline {subsection}{\numberline {4.2.1}\textcolor {Chapter }{ResolutionBieberbachGroup}}{18}{subsection.4.2.1}%
\contentsline {subsection}{\numberline {4.2.2}\textcolor {Chapter }{FaceLatticeAndBoundaryBieberbachGroup}}{18}{subsection.4.2.2}%
\contentsline {subsection}{\numberline {4.2.3}\textcolor {Chapter }{ResolutionFromFLandBoundary}}{19}{subsection.4.2.3}%
\contentsline {chapter}{\numberline {A}\textcolor {Chapter }{Resolutions in Hap}}{21}{appendix.A}%
\contentsline {section}{\numberline {A.1}\textcolor {Chapter }{The Standard Representation \texttt {HapResolutionRep}}}{21}{section.A.1}%
\contentsline {section}{\numberline {A.2}\textcolor {Chapter }{The \texttt {HapLargeGroupResolutionRep} Representation}}{22}{section.A.2}%
\contentsline {chapter}{\numberline {B}\textcolor {Chapter }{Accessing and Manipulating Resolutions}}{23}{appendix.B}%
\contentsline {section}{\numberline {B.1}\textcolor {Chapter }{Representation\texttt {\symbol {45}}Independent Access Methods}}{23}{section.B.1}%
\contentsline {subsection}{\numberline {B.1.1}\textcolor {Chapter }{StrongestValidRepresentationForLetter}}{23}{subsection.B.1.1}%
\contentsline {subsection}{\numberline {B.1.2}\textcolor {Chapter }{StrongestValidRepresentationForWord}}{23}{subsection.B.1.2}%
\contentsline {subsection}{\numberline {B.1.3}\textcolor {Chapter }{PositionInGroupOfResolution}}{23}{subsection.B.1.3}%
\contentsline {subsection}{\numberline {B.1.4}\textcolor {Chapter }{IsValidGroupInt}}{24}{subsection.B.1.4}%
\contentsline {subsection}{\numberline {B.1.5}\textcolor {Chapter }{GroupElementFromPosition}}{24}{subsection.B.1.5}%
\contentsline {subsection}{\numberline {B.1.6}\textcolor {Chapter }{MultiplyGroupElts}}{24}{subsection.B.1.6}%
\contentsline {subsection}{\numberline {B.1.7}\textcolor {Chapter }{MultiplyFreeZGLetterWithGroupElt}}{24}{subsection.B.1.7}%
\contentsline {subsection}{\numberline {B.1.8}\textcolor {Chapter }{MultiplyFreeZGWordWithGroupElt}}{24}{subsection.B.1.8}%
\contentsline {subsection}{\numberline {B.1.9}\textcolor {Chapter }{BoundaryOfFreeZGLetter}}{24}{subsection.B.1.9}%
\contentsline {subsection}{\numberline {B.1.10}\textcolor {Chapter }{BoundaryOfFreeZGWord}}{25}{subsection.B.1.10}%
\contentsline {section}{\numberline {B.2}\textcolor {Chapter }{Converting Between Representations}}{25}{section.B.2}%
\contentsline {subsection}{\numberline {B.2.1}\textcolor {Chapter }{ConvertStandardLetter}}{25}{subsection.B.2.1}%
\contentsline {subsection}{\numberline {B.2.2}\textcolor {Chapter }{ConvertStandardWord}}{25}{subsection.B.2.2}%
\contentsline {subsection}{\numberline {B.2.3}\textcolor {Chapter }{ConvertLetterToStandardRep}}{25}{subsection.B.2.3}%
\contentsline {subsection}{\numberline {B.2.4}\textcolor {Chapter }{ConvertWordToStandardRep}}{25}{subsection.B.2.4}%
\contentsline {section}{\numberline {B.3}\textcolor {Chapter }{Special Methods for \texttt {HapResolutionRep}}}{26}{section.B.3}%
\contentsline {subsection}{\numberline {B.3.1}\textcolor {Chapter }{IsFreeZGLetter}}{26}{subsection.B.3.1}%
\contentsline {subsection}{\numberline {B.3.2}\textcolor {Chapter }{IsFreeZGWord}}{26}{subsection.B.3.2}%
\contentsline {subsection}{\numberline {B.3.3}\textcolor {Chapter }{MultiplyGroupEltsNC}}{26}{subsection.B.3.3}%
\contentsline {subsection}{\numberline {B.3.4}\textcolor {Chapter }{MultiplyFreeZGLetterWithGroupEltNC}}{26}{subsection.B.3.4}%
\contentsline {subsection}{\numberline {B.3.5}\textcolor {Chapter }{MultiplyFreeZGWordWithGroupEltNC}}{26}{subsection.B.3.5}%
\contentsline {subsection}{\numberline {B.3.6}\textcolor {Chapter }{BoundaryOfFreeZGLetterNC}}{26}{subsection.B.3.6}%
\contentsline {subsection}{\numberline {B.3.7}\textcolor {Chapter }{BoundaryOfFreeZGWordNC}}{27}{subsection.B.3.7}%
\contentsline {section}{\numberline {B.4}\textcolor {Chapter }{The \texttt {HapLargeGroupResolutionRep} Representation}}{27}{section.B.4}%
\contentsline {subsection}{\numberline {B.4.1}\textcolor {Chapter }{GroupRingOfResolution}}{27}{subsection.B.4.1}%
\contentsline {subsection}{\numberline {B.4.2}\textcolor {Chapter }{MultiplyGroupElts{\textunderscore }LargeGroupRep}}{27}{subsection.B.4.2}%
\contentsline {subsection}{\numberline {B.4.3}\textcolor {Chapter }{IsFreeZGLetterNoTermCheck{\textunderscore }LargeGroupRep}}{27}{subsection.B.4.3}%
\contentsline {subsection}{\numberline {B.4.4}\textcolor {Chapter }{IsFreeZGWordNoTermCheck{\textunderscore }LargeGroupRep}}{27}{subsection.B.4.4}%
\contentsline {subsection}{\numberline {B.4.5}\textcolor {Chapter }{IsFreeZGLetter{\textunderscore }LargeGroupRep}}{28}{subsection.B.4.5}%
\contentsline {subsection}{\numberline {B.4.6}\textcolor {Chapter }{IsFreeZGWord{\textunderscore }LargeGroupRep}}{28}{subsection.B.4.6}%
\contentsline {subsection}{\numberline {B.4.7}\textcolor {Chapter }{MultiplyFreeZGLetterWithGroupElt{\textunderscore }LargeGroupRep}}{28}{subsection.B.4.7}%
\contentsline {subsection}{\numberline {B.4.8}\textcolor {Chapter }{MultiplyFreeZGWordWithGroupElt{\textunderscore }LargeGroupRep}}{28}{subsection.B.4.8}%
\contentsline {subsection}{\numberline {B.4.9}\textcolor {Chapter }{GeneratorsOfModuleOfResolution{\textunderscore }LargeGroupRep}}{28}{subsection.B.4.9}%
\contentsline {subsection}{\numberline {B.4.10}\textcolor {Chapter }{BoundaryOfGenerator{\textunderscore }LargeGroupRep}}{28}{subsection.B.4.10}%
\contentsline {subsection}{\numberline {B.4.11}\textcolor {Chapter }{BoundaryOfFreeZGLetterNC{\textunderscore }LargeGroupRep}}{29}{subsection.B.4.11}%
\contentsline {subsection}{\numberline {B.4.12}\textcolor {Chapter }{BoundaryOfFreeZGWord{\textunderscore }LargeGroupRep}}{29}{subsection.B.4.12}%
\contentsline {chapter}{\numberline {C}\textcolor {Chapter }{Contracting Homotopies}}{30}{appendix.C}%
\contentsline {section}{\numberline {C.1}\textcolor {Chapter }{The \texttt {PartialContractingHomotopy} Data Type}}{30}{section.C.1}%
\contentsline {subsection}{\numberline {C.1.1}\textcolor {Chapter }{ResolutionOfContractingHomotopy}}{30}{subsection.C.1.1}%
\contentsline {subsection}{\numberline {C.1.2}\textcolor {Chapter }{PartialContractingHomotopyLookup}}{30}{subsection.C.1.2}%
\contentsline {chapter}{References}{32}{appendix*.4}%
\contentsline {chapter}{Index}{33}{section*.5}%
