\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-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}{References}{21}{chapter*.4}%
\contentsline {chapter}{Index}{22}{section*.5}%
