\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\citation{hap}
\citation{cryst}
\citation{cryst}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{Introduction}}{4}{chapter.1}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{Abstract and Notation}}{4}{section.1.1}\protected@file@percent }
\@writefile{brf}{\backcite{hap}{{4}{1.1}{section.1.1}}}
\@writefile{brf}{\backcite{cryst}{{4}{1.1}{section.1.1}}}
\@writefile{brf}{\backcite{cryst}{{4}{1.1}{section.1.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.1}\textcolor {Chapter }{The natural action of crystallographic groups}}{4}{subsection.1.1.1}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {1.2}\textcolor {Chapter }{Requirements}}{5}{section.1.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.1}\textcolor {Chapter }{Recommendation concerning polymake}}{5}{subsection.1.2.1}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {1.3}\textcolor {Chapter }{Global Variables}}{5}{section.1.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}\textcolor {Chapter }{InfoHAPcryst}}{5}{subsection.1.3.1}\protected@file@percent }
\newlabel{InfoHAPcryst}{{1.3.1}{5}{\textcolor {Chapter }{InfoHAPcryst}}{subsection.1.3.1}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{Bits and Pieces}}{6}{chapter.2}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{Matrices and Vectors}}{6}{section.2.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}\textcolor {Chapter }{SignRat}}{6}{subsection.2.1.1}\protected@file@percent }
\newlabel{SignRat}{{2.1.1}{6}{\textcolor {Chapter }{SignRat}}{subsection.2.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.2}\textcolor {Chapter }{VectorModOne}}{6}{subsection.2.1.2}\protected@file@percent }
\newlabel{VectorModOne}{{2.1.2}{6}{\textcolor {Chapter }{VectorModOne}}{subsection.2.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.3}\textcolor {Chapter }{IsSquareMat}}{6}{subsection.2.1.3}\protected@file@percent }
\newlabel{IsSquareMat}{{2.1.3}{6}{\textcolor {Chapter }{IsSquareMat}}{subsection.2.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.4}\textcolor {Chapter }{DimensionSquareMat}}{6}{subsection.2.1.4}\protected@file@percent }
\newlabel{DimensionSquareMat}{{2.1.4}{6}{\textcolor {Chapter }{DimensionSquareMat}}{subsection.2.1.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{Affine Matrices OnRight}}{7}{section.2.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}\textcolor {Chapter }{LinearPartOfAffineMatOnRight}}{7}{subsection.2.2.1}\protected@file@percent }
\newlabel{LinearPartOfAffineMatOnRight}{{2.2.1}{7}{\textcolor {Chapter }{LinearPartOfAffineMatOnRight}}{subsection.2.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}\textcolor {Chapter }{BasisChangeAffineMatOnRight}}{7}{subsection.2.2.2}\protected@file@percent }
\newlabel{BasisChangeAffineMatOnRight}{{2.2.2}{7}{\textcolor {Chapter }{BasisChangeAffineMatOnRight}}{subsection.2.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}\textcolor {Chapter }{TranslationOnRightFromVector}}{7}{subsection.2.2.3}\protected@file@percent }
\newlabel{TranslationOnRightFromVector}{{2.2.3}{7}{\textcolor {Chapter }{TranslationOnRightFromVector}}{subsection.2.2.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{Geometry}}{8}{section.2.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}\textcolor {Chapter }{GramianOfAverageScalarProductFromFiniteMatrixGroup}}{8}{subsection.2.3.1}\protected@file@percent }
\newlabel{GramianOfAverageScalarProductFromFiniteMatrixGroup}{{2.3.1}{8}{\textcolor {Chapter }{GramianOfAverageScalarProductFromFiniteMatrixGroup}}{subsection.2.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}\textcolor {Chapter }{Inequalities}}{8}{subsection.2.3.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.3}\textcolor {Chapter }{BisectorInequalityFromPointPair}}{8}{subsection.2.3.3}\protected@file@percent }
\newlabel{BisectorInequalityFromPointPair}{{2.3.3}{8}{\textcolor {Chapter }{BisectorInequalityFromPointPair}}{subsection.2.3.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.4}\textcolor {Chapter }{WhichSideOfHyperplane}}{8}{subsection.2.3.4}\protected@file@percent }
\newlabel{WhichSideOfHyperplane}{{2.3.4}{8}{\textcolor {Chapter }{WhichSideOfHyperplane}}{subsection.2.3.4}{}}
\newlabel{WhichSideOfHyperplaneNC}{{2.3.4}{8}{\textcolor {Chapter }{WhichSideOfHyperplane}}{subsection.2.3.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.5}\textcolor {Chapter }{RelativePositionPointAndPolygon}}{9}{subsection.2.3.5}\protected@file@percent }
\newlabel{RelativePositionPointAndPolygon}{{2.3.5}{9}{\textcolor {Chapter }{RelativePositionPointAndPolygon}}{subsection.2.3.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.4}\textcolor {Chapter }{Space Groups}}{9}{section.2.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}\textcolor {Chapter }{PointGroupRepresentatives}}{9}{subsection.2.4.1}\protected@file@percent }
\newlabel{PointGroupRepresentatives}{{2.4.1}{9}{\textcolor {Chapter }{PointGroupRepresentatives}}{subsection.2.4.1}{}}
\newlabel{PointGroupRepresentatives}{{2.4.1}{9}{\textcolor {Chapter }{PointGroupRepresentatives}}{subsection.2.4.1}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Algorithms of Orbit-Stabilizer Type}}{10}{chapter.3}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{Orbit Stabilizer for Crystallographic Groups}}{10}{section.3.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}\textcolor {Chapter }{OrbitStabilizerInUnitCubeOnRight}}{10}{subsection.3.1.1}\protected@file@percent }
\newlabel{OrbitStabilizerInUnitCubeOnRight}{{3.1.1}{10}{\textcolor {Chapter }{OrbitStabilizerInUnitCubeOnRight}}{subsection.3.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}\textcolor {Chapter }{OrbitStabilizerInUnitCubeOnRightOnSets}}{11}{subsection.3.1.2}\protected@file@percent }
\newlabel{OrbitStabilizerInUnitCubeOnRightOnSets}{{3.1.2}{11}{\textcolor {Chapter }{OrbitStabilizerInUnitCubeOnRightOnSets}}{subsection.3.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.3}\textcolor {Chapter }{OrbitPartInVertexSetsStandardSpaceGroup}}{11}{subsection.3.1.3}\protected@file@percent }
\newlabel{OrbitPartInVertexSetsStandardSpaceGroup}{{3.1.3}{11}{\textcolor {Chapter }{OrbitPartInVertexSetsStandardSpaceGroup}}{subsection.3.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.4}\textcolor {Chapter }{OrbitPartInFacesStandardSpaceGroup}}{12}{subsection.3.1.4}\protected@file@percent }
\newlabel{OrbitPartInFacesStandardSpaceGroup}{{3.1.4}{12}{\textcolor {Chapter }{OrbitPartInFacesStandardSpaceGroup}}{subsection.3.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.5}\textcolor {Chapter }{OrbitPartAndRepresentativesInFacesStandardSpaceGroup}}{12}{subsection.3.1.5}\protected@file@percent }
\newlabel{OrbitPartAndRepresentativesInFacesStandardSpaceGroup}{{3.1.5}{12}{\textcolor {Chapter }{OrbitPartAndRepresentativesInFacesStandardSpaceGroup}}{subsection.3.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.6}\textcolor {Chapter }{StabilizerOnSetsStandardSpaceGroup}}{12}{subsection.3.1.6}\protected@file@percent }
\newlabel{StabilizerOnSetsStandardSpaceGroup}{{3.1.6}{12}{\textcolor {Chapter }{StabilizerOnSetsStandardSpaceGroup}}{subsection.3.1.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.7}\textcolor {Chapter }{RepresentativeActionOnRightOnSets}}{13}{subsection.3.1.7}\protected@file@percent }
\newlabel{RepresentativeActionOnRightOnSets}{{3.1.7}{13}{\textcolor {Chapter }{RepresentativeActionOnRightOnSets}}{subsection.3.1.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.8}\textcolor {Chapter }{Getting other orbit parts}}{13}{subsection.3.1.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.9}\textcolor {Chapter }{ShiftedOrbitPart}}{13}{subsection.3.1.9}\protected@file@percent }
\newlabel{ShiftedOrbitPart}{{3.1.9}{13}{\textcolor {Chapter }{ShiftedOrbitPart}}{subsection.3.1.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.10}\textcolor {Chapter }{TranslationsToOneCubeAroundCenter}}{13}{subsection.3.1.10}\protected@file@percent }
\newlabel{TranslationsToOneCubeAroundCenter}{{3.1.10}{13}{\textcolor {Chapter }{TranslationsToOneCubeAroundCenter}}{subsection.3.1.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.11}\textcolor {Chapter }{TranslationsToBox}}{13}{subsection.3.1.11}\protected@file@percent }
\newlabel{TranslationsToBox}{{3.1.11}{13}{\textcolor {Chapter }{TranslationsToBox}}{subsection.3.1.11}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{Resolutions of Crystallographic Groups}}{15}{chapter.4}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}\textcolor {Chapter }{Fundamental Domains}}{15}{section.4.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.1}\textcolor {Chapter }{FundamentalDomainStandardSpaceGroup}}{15}{subsection.4.1.1}\protected@file@percent }
\newlabel{FundamentalDomainStandardSpaceGroup}{{4.1.1}{15}{\textcolor {Chapter }{FundamentalDomainStandardSpaceGroup}}{subsection.4.1.1}{}}
\newlabel{FundamentalDomainStandardSpaceGroup}{{4.1.1}{15}{\textcolor {Chapter }{FundamentalDomainStandardSpaceGroup}}{subsection.4.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.2}\textcolor {Chapter }{FundamentalDomainBieberbachGroup}}{15}{subsection.4.1.2}\protected@file@percent }
\newlabel{FundamentalDomainBieberbachGroup}{{4.1.2}{15}{\textcolor {Chapter }{FundamentalDomainBieberbachGroup}}{subsection.4.1.2}{}}
\newlabel{FundamentalDomainBieberbachGroup}{{4.1.2}{15}{\textcolor {Chapter }{FundamentalDomainBieberbachGroup}}{subsection.4.1.2}{}}
\newlabel{ineqThreshold}{{4.1.2}{16}{\textcolor {Chapter }{FundamentalDomainBieberbachGroup}}{subsection.4.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.3}\textcolor {Chapter }{FundamentalDomainFromGeneralPointAndOrbitPartGeometric}}{17}{subsection.4.1.3}\protected@file@percent }
\newlabel{FundamentalDomainFromGeneralPointAndOrbitPartGeometric}{{4.1.3}{17}{\textcolor {Chapter }{FundamentalDomainFromGeneralPointAndOrbitPartGeometric}}{subsection.4.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.4}\textcolor {Chapter }{IsFundamentalDomainStandardSpaceGroup}}{17}{subsection.4.1.4}\protected@file@percent }
\newlabel{IsFundamentalDomainStandardSpaceGroup}{{4.1.4}{17}{\textcolor {Chapter }{IsFundamentalDomainStandardSpaceGroup}}{subsection.4.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.5}\textcolor {Chapter }{IsFundamentalDomainBieberbachGroup}}{17}{subsection.4.1.5}\protected@file@percent }
\newlabel{IsFundamentalDomainBieberbachGroup}{{4.1.5}{17}{\textcolor {Chapter }{IsFundamentalDomainBieberbachGroup}}{subsection.4.1.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}\textcolor {Chapter }{Face Lattice and Resolution}}{18}{section.4.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}\textcolor {Chapter }{ResolutionBieberbachGroup}}{18}{subsection.4.2.1}\protected@file@percent }
\newlabel{ResolutionBieberbachGroup}{{4.2.1}{18}{\textcolor {Chapter }{ResolutionBieberbachGroup}}{subsection.4.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}\textcolor {Chapter }{FaceLatticeAndBoundaryBieberbachGroup}}{18}{subsection.4.2.2}\protected@file@percent }
\newlabel{FaceLatticeAndBoundaryBieberbachGroup}{{4.2.2}{18}{\textcolor {Chapter }{FaceLatticeAndBoundaryBieberbachGroup}}{subsection.4.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.3}\textcolor {Chapter }{ResolutionFromFLandBoundary}}{19}{subsection.4.2.3}\protected@file@percent }
\newlabel{ResolutionFromFLandBoundary}{{4.2.3}{19}{\textcolor {Chapter }{ResolutionFromFLandBoundary}}{subsection.4.2.3}{}}
\bibstyle{alpha}
\bibdata{HAPcryst}
\bibcite{cryst}{EGN}
\bibcite{hap}{Ell}
\@writefile{toc}{\contentsline {chapter}{References}{21}{chapter*.4}\protected@file@percent }
\@writefile{toc}{\contentsline {chapter}{Index}{22}{section*.5}\protected@file@percent }
\gdef \@abspage@last{22}
