\relax 
\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{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\@writefile{toc}{\contentsline {chapter}{\numberline {1}\leavevmode {\color  {Chapter }Introduction}}{6}{chapter.1}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{intro}{{1}{6}{\textcolor {Chapter }{Introduction}\relax }{chapter.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}\leavevmode {\color  {Chapter }Motivation for this package}}{6}{section.1.1}}
\newlabel{philosophy}{{1.1}{6}{\textcolor {Chapter }{Motivation for this package}\relax }{section.1.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {1.2}\leavevmode {\color  {Chapter }Overview over this manual}}{6}{section.1.2}}
\newlabel{overview}{{1.2}{6}{\textcolor {Chapter }{Overview over this manual}\relax }{section.1.2}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}\leavevmode {\color  {Chapter }Installation of the \textsf  {orb}-Package}}{7}{chapter.2}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{install}{{2}{7}{\textcolor {Chapter }{Installation of the \textsf {orb}-Package}\relax }{chapter.2}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}\leavevmode {\color  {Chapter }Basic orbit enumeration}}{8}{chapter.3}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{basic}{{3}{8}{\textcolor {Chapter }{Basic orbit enumeration}\relax }{chapter.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}\leavevmode {\color  {Chapter }Enumerating orbits}}{8}{section.3.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color  {Chapter }Orb}}{8}{subsection.3.1.1}}
\newlabel{Orb}{{3.1.1}{8}{\textcolor {Chapter }{Orb}\relax }{subsection.3.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}\leavevmode {\color  {Chapter }Enumerate}}{9}{subsection.3.1.2}}
\newlabel{Enumerate}{{3.1.2}{9}{\textcolor {Chapter }{Enumerate}\relax }{subsection.3.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.3}\leavevmode {\color  {Chapter }IsClosed}}{9}{subsection.3.1.3}}
\newlabel{IsClosed}{{3.1.3}{9}{\textcolor {Chapter }{IsClosed}\relax }{subsection.3.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.4}\leavevmode {\color  {Chapter }Options for orbits}}{10}{subsection.3.1.4}}
\newlabel{orboptions}{{3.1.4}{10}{\textcolor {Chapter }{Options for orbits}\relax }{subsection.3.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.5}\leavevmode {\color  {Chapter }Output components of orbits}}{13}{subsection.3.1.5}}
\newlabel{orboutputs}{{3.1.5}{13}{\textcolor {Chapter }{Output components of orbits}\relax }{subsection.3.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.6}\leavevmode {\color  {Chapter }StabWords (basic)}}{13}{subsection.3.1.6}}
\newlabel{StabWords:basic}{{3.1.6}{13}{\textcolor {Chapter }{StabWords (basic)}\relax }{subsection.3.1.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.7}\leavevmode {\color  {Chapter }PositionOfFound}}{13}{subsection.3.1.7}}
\newlabel{PositionOfFound}{{3.1.7}{13}{\textcolor {Chapter }{PositionOfFound}\relax }{subsection.3.1.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.8}\leavevmode {\color  {Chapter }DepthOfSchreierTree}}{14}{subsection.3.1.8}}
\newlabel{DepthOfSchreierTree}{{3.1.8}{14}{\textcolor {Chapter }{DepthOfSchreierTree}\relax }{subsection.3.1.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.9}\leavevmode {\color  {Chapter }ActionOnOrbit}}{14}{subsection.3.1.9}}
\newlabel{ActionOnOrbit}{{3.1.9}{14}{\textcolor {Chapter }{ActionOnOrbit}\relax }{subsection.3.1.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.10}\leavevmode {\color  {Chapter }OrbActionHomomorphism}}{14}{subsection.3.1.10}}
\newlabel{OrbActionHomomorphism}{{3.1.10}{14}{\textcolor {Chapter }{OrbActionHomomorphism}\relax }{subsection.3.1.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.11}\leavevmode {\color  {Chapter }TraceSchreierTreeForward}}{14}{subsection.3.1.11}}
\newlabel{TraceSchreierTreeForward}{{3.1.11}{14}{\textcolor {Chapter }{TraceSchreierTreeForward}\relax }{subsection.3.1.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.12}\leavevmode {\color  {Chapter }TraceSchreierTreeBack}}{14}{subsection.3.1.12}}
\newlabel{TraceSchreierTreeBack}{{3.1.12}{14}{\textcolor {Chapter }{TraceSchreierTreeBack}\relax }{subsection.3.1.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.13}\leavevmode {\color  {Chapter }ActWithWord}}{15}{subsection.3.1.13}}
\newlabel{ActWithWord}{{3.1.13}{15}{\textcolor {Chapter }{ActWithWord}\relax }{subsection.3.1.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.14}\leavevmode {\color  {Chapter }EvaluateWord}}{15}{subsection.3.1.14}}
\newlabel{EvaluateWord}{{3.1.14}{15}{\textcolor {Chapter }{EvaluateWord}\relax }{subsection.3.1.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.15}\leavevmode {\color  {Chapter }AddGeneratorsToOrbit}}{15}{subsection.3.1.15}}
\newlabel{AddGeneratorsToOrbit}{{3.1.15}{15}{\textcolor {Chapter }{AddGeneratorsToOrbit}\relax }{subsection.3.1.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.16}\leavevmode {\color  {Chapter }MakeSchreierTreeShallow}}{15}{subsection.3.1.16}}
\newlabel{MakeSchreierTreeShallow}{{3.1.16}{15}{\textcolor {Chapter }{MakeSchreierTreeShallow}\relax }{subsection.3.1.16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.17}\leavevmode {\color  {Chapter }FindSuborbits}}{15}{subsection.3.1.17}}
\newlabel{FindSuborbits}{{3.1.17}{15}{\textcolor {Chapter }{FindSuborbits}\relax }{subsection.3.1.17}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.18}\leavevmode {\color  {Chapter }OrbitIntersectionMatrix}}{16}{subsection.3.1.18}}
\newlabel{OrbitIntersectionMatrix}{{3.1.18}{16}{\textcolor {Chapter }{OrbitIntersectionMatrix}\relax }{subsection.3.1.18}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}\leavevmode {\color  {Chapter }Hashing techniques}}{17}{chapter.4}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{hash}{{4}{17}{\textcolor {Chapter }{Hashing techniques}\relax }{chapter.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}\leavevmode {\color  {Chapter }The idea of hashing}}{17}{section.4.1}}
\newlabel{hashidea}{{4.1}{17}{\textcolor {Chapter }{The idea of hashing}\relax }{section.4.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}\leavevmode {\color  {Chapter }Hash functions}}{17}{section.4.2}}
\newlabel{hashfunc}{{4.2}{17}{\textcolor {Chapter }{Hash functions}\relax }{section.4.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color  {Chapter }ChooseHashFunction}}{17}{subsection.4.2.1}}
\newlabel{ChooseHashFunction}{{4.2.1}{17}{\textcolor {Chapter }{ChooseHashFunction}\relax }{subsection.4.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color  {Chapter }ChooseHashFunction (gf2vec)}}{18}{subsection.4.2.2}}
\newlabel{ChooseHashFunction:gf2vec}{{4.2.2}{18}{\textcolor {Chapter }{ChooseHashFunction (gf2vec)}\relax }{subsection.4.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.3}\leavevmode {\color  {Chapter }ChooseHashFunction (8bitvec)}}{18}{subsection.4.2.3}}
\newlabel{ChooseHashFunction:8bitvec}{{4.2.3}{18}{\textcolor {Chapter }{ChooseHashFunction (8bitvec)}\relax }{subsection.4.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.4}\leavevmode {\color  {Chapter }ChooseHashFunction (gf2mat)}}{18}{subsection.4.2.4}}
\newlabel{ChooseHashFunction:gf2mat}{{4.2.4}{18}{\textcolor {Chapter }{ChooseHashFunction (gf2mat)}\relax }{subsection.4.2.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.5}\leavevmode {\color  {Chapter }ChooseHashFunction (8bitmat)}}{18}{subsection.4.2.5}}
\newlabel{ChooseHashFunction:8bitmat}{{4.2.5}{18}{\textcolor {Chapter }{ChooseHashFunction (8bitmat)}\relax }{subsection.4.2.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.6}\leavevmode {\color  {Chapter }ChooseHashFunction (int)}}{18}{subsection.4.2.6}}
\newlabel{ChooseHashFunction:int}{{4.2.6}{18}{\textcolor {Chapter }{ChooseHashFunction (int)}\relax }{subsection.4.2.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.7}\leavevmode {\color  {Chapter }ChooseHashFunction (perm)}}{19}{subsection.4.2.7}}
\newlabel{ChooseHashFunction:perm}{{4.2.7}{19}{\textcolor {Chapter }{ChooseHashFunction (perm)}\relax }{subsection.4.2.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.8}\leavevmode {\color  {Chapter }ChooseHashFunction (intlist)}}{19}{subsection.4.2.8}}
\newlabel{ChooseHashFunction:intlist}{{4.2.8}{19}{\textcolor {Chapter }{ChooseHashFunction (intlist)}\relax }{subsection.4.2.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.9}\leavevmode {\color  {Chapter }ChooseHashFunction (NBitsPcWord)}}{19}{subsection.4.2.9}}
\newlabel{ChooseHashFunction:NBitsPcWord}{{4.2.9}{19}{\textcolor {Chapter }{ChooseHashFunction (NBitsPcWord)}\relax }{subsection.4.2.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.10}\leavevmode {\color  {Chapter }ChooseHashFunction (IntLists)}}{19}{subsection.4.2.10}}
\newlabel{ChooseHashFunction:IntLists}{{4.2.10}{19}{\textcolor {Chapter }{ChooseHashFunction (IntLists)}\relax }{subsection.4.2.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.11}\leavevmode {\color  {Chapter }ChooseHashFunction (MatLists)}}{19}{subsection.4.2.11}}
\newlabel{ChooseHashFunction:MatLists}{{4.2.11}{19}{\textcolor {Chapter }{ChooseHashFunction (MatLists)}\relax }{subsection.4.2.11}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.3}\leavevmode {\color  {Chapter }Using hash tables}}{19}{section.4.3}}
\newlabel{hashtables}{{4.3}{19}{\textcolor {Chapter }{Using hash tables}\relax }{section.4.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color  {Chapter }NewHT}}{19}{subsection.4.3.1}}
\newlabel{NewHT}{{4.3.1}{19}{\textcolor {Chapter }{NewHT}\relax }{subsection.4.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color  {Chapter }AddHT}}{20}{subsection.4.3.2}}
\newlabel{AddHT}{{4.3.2}{20}{\textcolor {Chapter }{AddHT}\relax }{subsection.4.3.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.3}\leavevmode {\color  {Chapter }ValueHT}}{20}{subsection.4.3.3}}
\newlabel{ValueHT}{{4.3.3}{20}{\textcolor {Chapter }{ValueHT}\relax }{subsection.4.3.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.4}\leavevmode {\color  {Chapter }InitHT}}{20}{subsection.4.3.4}}
\newlabel{InitHT}{{4.3.4}{20}{\textcolor {Chapter }{InitHT}\relax }{subsection.4.3.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.5}\leavevmode {\color  {Chapter }GrowHT}}{20}{subsection.4.3.5}}
\newlabel{GrowHT}{{4.3.5}{20}{\textcolor {Chapter }{GrowHT}\relax }{subsection.4.3.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.4}\leavevmode {\color  {Chapter } The data structures for hash tables }}{21}{section.4.4}}
\newlabel{hashdata}{{4.4}{21}{\textcolor {Chapter }{ The data structures for hash tables }\relax }{section.4.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.1}\leavevmode {\color  {Chapter } Memory requirements }}{21}{subsection.4.4.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.2}\leavevmode {\color  {Chapter } Handling of collisions }}{21}{subsection.4.4.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.3}\leavevmode {\color  {Chapter } Efficiency }}{22}{subsection.4.4.3}}
\@writefile{toc}{\contentsline {chapter}{\numberline {5}\leavevmode {\color  {Chapter }Caching techniques}}{23}{chapter.5}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{cache}{{5}{23}{\textcolor {Chapter }{Caching techniques}\relax }{chapter.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.1}\leavevmode {\color  {Chapter }The idea of caching}}{23}{section.5.1}}
\newlabel{cacheidea}{{5.1}{23}{\textcolor {Chapter }{The idea of caching}\relax }{section.5.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.2}\leavevmode {\color  {Chapter }Using caches}}{23}{section.5.2}}
\newlabel{cacheusage}{{5.2}{23}{\textcolor {Chapter }{Using caches}\relax }{section.5.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color  {Chapter }LinkedListCache}}{23}{subsection.5.2.1}}
\newlabel{LinkedListCache}{{5.2.1}{23}{\textcolor {Chapter }{LinkedListCache}\relax }{subsection.5.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.2}\leavevmode {\color  {Chapter }CacheObject}}{23}{subsection.5.2.2}}
\newlabel{CacheObject}{{5.2.2}{23}{\textcolor {Chapter }{CacheObject}\relax }{subsection.5.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.3}\leavevmode {\color  {Chapter }ClearCache}}{24}{subsection.5.2.3}}
\newlabel{ClearCache}{{5.2.3}{24}{\textcolor {Chapter }{ClearCache}\relax }{subsection.5.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.4}\leavevmode {\color  {Chapter }UseCacheObject}}{24}{subsection.5.2.4}}
\newlabel{UseCacheObject}{{5.2.4}{24}{\textcolor {Chapter }{UseCacheObject}\relax }{subsection.5.2.4}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {6}\leavevmode {\color  {Chapter }Random elements}}{25}{chapter.6}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{random}{{6}{25}{\textcolor {Chapter }{Random elements}\relax }{chapter.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6.1}\leavevmode {\color  {Chapter }Randomizing mutable objects}}{25}{section.6.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.1}\leavevmode {\color  {Chapter }Randomize}}{25}{subsection.6.1.1}}
\newlabel{Randomize}{{6.1.1}{25}{\textcolor {Chapter }{Randomize}\relax }{subsection.6.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.2}\leavevmode {\color  {Chapter }MakeRandomVectors}}{25}{subsection.6.1.2}}
\newlabel{MakeRandomVectors}{{6.1.2}{25}{\textcolor {Chapter }{MakeRandomVectors}\relax }{subsection.6.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1.3}\leavevmode {\color  {Chapter }MakeRandomLines}}{25}{subsection.6.1.3}}
\newlabel{MakeRandomLines}{{6.1.3}{25}{\textcolor {Chapter }{MakeRandomLines}\relax }{subsection.6.1.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6.2}\leavevmode {\color  {Chapter }Product replacement}}{26}{section.6.2}}
\newlabel{prodrepl}{{6.2}{26}{\textcolor {Chapter }{Product replacement}\relax }{section.6.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2.1}\leavevmode {\color  {Chapter }ProductReplacer}}{26}{subsection.6.2.1}}
\newlabel{ProductReplacer}{{6.2.1}{26}{\textcolor {Chapter }{ProductReplacer}\relax }{subsection.6.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2.2}\leavevmode {\color  {Chapter }Next}}{27}{subsection.6.2.2}}
\newlabel{Next}{{6.2.2}{27}{\textcolor {Chapter }{Next}\relax }{subsection.6.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2.3}\leavevmode {\color  {Chapter }Reset}}{27}{subsection.6.2.3}}
\newlabel{Reset}{{6.2.3}{27}{\textcolor {Chapter }{Reset}\relax }{subsection.6.2.3}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {7}\leavevmode {\color  {Chapter }Searching in groups and orbits}}{28}{chapter.7}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{search}{{7}{28}{\textcolor {Chapter }{Searching in groups and orbits}\relax }{chapter.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7.1}\leavevmode {\color  {Chapter }Searching using orbit enumeration}}{28}{section.7.1}}
\@writefile{toc}{\contentsline {section}{\numberline {7.2}\leavevmode {\color  {Chapter }Random searches in groups}}{29}{section.7.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.1}\leavevmode {\color  {Chapter }RandomSearcher}}{29}{subsection.7.2.1}}
\newlabel{RandomSearcher}{{7.2.1}{29}{\textcolor {Chapter }{RandomSearcher}\relax }{subsection.7.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.2}\leavevmode {\color  {Chapter }Search}}{29}{subsection.7.2.2}}
\newlabel{Search}{{7.2.2}{29}{\textcolor {Chapter }{Search}\relax }{subsection.7.2.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7.3}\leavevmode {\color  {Chapter }The dihedral trick and applications}}{30}{section.7.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.1}\leavevmode {\color  {Chapter }FindInvolution}}{30}{subsection.7.3.1}}
\newlabel{FindInvolution}{{7.3.1}{30}{\textcolor {Chapter }{FindInvolution}\relax }{subsection.7.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.2}\leavevmode {\color  {Chapter }FindCentralisingElementOfInvolution}}{30}{subsection.7.3.2}}
\newlabel{FindCentralisingElementOfInvolution}{{7.3.2}{30}{\textcolor {Chapter }{FindCentralisingElementOfInvolution}\relax }{subsection.7.3.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3.3}\leavevmode {\color  {Chapter }FindInvolutionCentralizer}}{30}{subsection.7.3.3}}
\newlabel{FindInvolutionCentralizer}{{7.3.3}{30}{\textcolor {Chapter }{FindInvolutionCentralizer}\relax }{subsection.7.3.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7.4}\leavevmode {\color  {Chapter }Orbit statistics on vector spaces}}{30}{section.7.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.4.1}\leavevmode {\color  {Chapter }OrbitStatisticOnVectorSpace}}{30}{subsection.7.4.1}}
\newlabel{OrbitStatisticOnVectorSpace}{{7.4.1}{30}{\textcolor {Chapter }{OrbitStatisticOnVectorSpace}\relax }{subsection.7.4.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.4.2}\leavevmode {\color  {Chapter }OrbitStatisticOnVectorSpaceLines}}{31}{subsection.7.4.2}}
\newlabel{OrbitStatisticOnVectorSpaceLines}{{7.4.2}{31}{\textcolor {Chapter }{OrbitStatisticOnVectorSpaceLines}\relax }{subsection.7.4.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {7.5}\leavevmode {\color  {Chapter }Finding generating sets of subgroups}}{31}{section.7.5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.5.1}\leavevmode {\color  {Chapter }FindShortGeneratorsOfSubgroup}}{31}{subsection.7.5.1}}
\newlabel{FindShortGeneratorsOfSubgroup}{{7.5.1}{31}{\textcolor {Chapter }{FindShortGeneratorsOfSubgroup}\relax }{subsection.7.5.1}{}}
\citation{MNW}
\@writefile{toc}{\contentsline {chapter}{\numberline {8}\leavevmode {\color  {Chapter }Orbit enumeration by suborbits}}{32}{chapter.8}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{bysuborbit}{{8}{32}{\textcolor {Chapter }{Orbit enumeration by suborbits}\relax }{chapter.8}{}}
\@writefile{brf}{\backcite{MNW}{{32}{8}{chapter.8}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.1}\leavevmode {\color  {Chapter }\texttt  {OrbitBySuborbits} and its resulting objects}}{32}{section.8.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.1}\leavevmode {\color  {Chapter }OrbitBySuborbit}}{32}{subsection.8.1.1}}
\newlabel{OrbitBySuborbit}{{8.1.1}{32}{\textcolor {Chapter }{OrbitBySuborbit}\relax }{subsection.8.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.2}\leavevmode {\color  {Chapter }OrbitBySuborbitKnownSize}}{33}{subsection.8.1.2}}
\newlabel{OrbitBySuborbitKnownSize}{{8.1.2}{33}{\textcolor {Chapter }{OrbitBySuborbitKnownSize}\relax }{subsection.8.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.3}\leavevmode {\color  {Chapter }Size (fororb)}}{33}{subsection.8.1.3}}
\newlabel{Size:fororb}{{8.1.3}{33}{\textcolor {Chapter }{Size (fororb)}\relax }{subsection.8.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.4}\leavevmode {\color  {Chapter }Seed}}{33}{subsection.8.1.4}}
\newlabel{Seed}{{8.1.4}{33}{\textcolor {Chapter }{Seed}\relax }{subsection.8.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.5}\leavevmode {\color  {Chapter }SuborbitsDb}}{33}{subsection.8.1.5}}
\newlabel{SuborbitsDb}{{8.1.5}{33}{\textcolor {Chapter }{SuborbitsDb}\relax }{subsection.8.1.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.6}\leavevmode {\color  {Chapter }WordsToSuborbits}}{33}{subsection.8.1.6}}
\newlabel{WordsToSuborbits}{{8.1.6}{33}{\textcolor {Chapter }{WordsToSuborbits}\relax }{subsection.8.1.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.7}\leavevmode {\color  {Chapter }Memory (forob)}}{34}{subsection.8.1.7}}
\newlabel{Memory:forob}{{8.1.7}{34}{\textcolor {Chapter }{Memory (forob)}\relax }{subsection.8.1.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.8}\leavevmode {\color  {Chapter }Stabilizer (obso)}}{34}{subsection.8.1.8}}
\newlabel{Stabilizer:obso}{{8.1.8}{34}{\textcolor {Chapter }{Stabilizer (obso)}\relax }{subsection.8.1.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.9}\leavevmode {\color  {Chapter }StabWords}}{34}{subsection.8.1.9}}
\newlabel{StabWords}{{8.1.9}{34}{\textcolor {Chapter }{StabWords}\relax }{subsection.8.1.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.10}\leavevmode {\color  {Chapter }SavingFactor (fororb)}}{34}{subsection.8.1.10}}
\newlabel{SavingFactor:fororb}{{8.1.10}{34}{\textcolor {Chapter }{SavingFactor (fororb)}\relax }{subsection.8.1.10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.11}\leavevmode {\color  {Chapter }TotalLength (fordb)}}{35}{subsection.8.1.11}}
\newlabel{TotalLength:fordb}{{8.1.11}{35}{\textcolor {Chapter }{TotalLength (fordb)}\relax }{subsection.8.1.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.12}\leavevmode {\color  {Chapter }Representatives}}{35}{subsection.8.1.12}}
\newlabel{Representatives}{{8.1.12}{35}{\textcolor {Chapter }{Representatives}\relax }{subsection.8.1.12}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.13}\leavevmode {\color  {Chapter }SavingFactor (fordb)}}{35}{subsection.8.1.13}}
\newlabel{SavingFactor:fordb}{{8.1.13}{35}{\textcolor {Chapter }{SavingFactor (fordb)}\relax }{subsection.8.1.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1.14}\leavevmode {\color  {Chapter }OrigSeed}}{35}{subsection.8.1.14}}
\newlabel{OrigSeed}{{8.1.14}{35}{\textcolor {Chapter }{OrigSeed}\relax }{subsection.8.1.14}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8.2}\leavevmode {\color  {Chapter }Preparation functions for \texttt  {OrbitBySuborbit} (\ref  {OrbitBySuborbit})}}{35}{section.8.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2.1}\leavevmode {\color  {Chapter }OrbitBySuborbitBootstrapForVectors}}{35}{subsection.8.2.1}}
\newlabel{OrbitBySuborbitBootstrapForVectors}{{8.2.1}{35}{\textcolor {Chapter }{OrbitBySuborbitBootstrapForVectors}\relax }{subsection.8.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2.2}\leavevmode {\color  {Chapter }OrbitBySuborbitBootstrapForLines}}{36}{subsection.8.2.2}}
\newlabel{OrbitBySuborbitBootstrapForLines}{{8.2.2}{36}{\textcolor {Chapter }{OrbitBySuborbitBootstrapForLines}\relax }{subsection.8.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.2.3}\leavevmode {\color  {Chapter }OrbitBySuborbitBootstrapForSpaces}}{36}{subsection.8.2.3}}
\newlabel{OrbitBySuborbitBootstrapForSpaces}{{8.2.3}{36}{\textcolor {Chapter }{OrbitBySuborbitBootstrapForSpaces}\relax }{subsection.8.2.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8.3}\leavevmode {\color  {Chapter }Data structures for orbit-by-suborbits}}{36}{section.8.3}}
\newlabel{obsodatastrucs}{{8.3}{36}{\textcolor {Chapter }{Data structures for orbit-by-suborbits}\relax }{section.8.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.3.1}\leavevmode {\color  {Chapter }IsOrbitBySuborbitSetup}}{36}{subsection.8.3.1}}
\newlabel{IsOrbitBySuborbitSetup}{{8.3.1}{36}{\textcolor {Chapter }{IsOrbitBySuborbitSetup}\relax }{subsection.8.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.3.2}\leavevmode {\color  {Chapter }The global record \texttt  {ORB}}}{38}{subsection.8.3.2}}
\@writefile{toc}{\contentsline {section}{\numberline {8.4}\leavevmode {\color  {Chapter }Lists of orbit-by-suborbit objects}}{39}{section.8.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.1}\leavevmode {\color  {Chapter }InitOrbitBySuborbitList}}{39}{subsection.8.4.1}}
\newlabel{InitOrbitBySuborbitList}{{8.4.1}{39}{\textcolor {Chapter }{InitOrbitBySuborbitList}\relax }{subsection.8.4.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.2}\leavevmode {\color  {Chapter }IsVectorInOrbitBySuborbitList}}{39}{subsection.8.4.2}}
\newlabel{IsVectorInOrbitBySuborbitList}{{8.4.2}{39}{\textcolor {Chapter }{IsVectorInOrbitBySuborbitList}\relax }{subsection.8.4.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.3}\leavevmode {\color  {Chapter }OrbitsFromSeedsToOrbitList}}{40}{subsection.8.4.3}}
\newlabel{OrbitsFromSeedsToOrbitList}{{8.4.3}{40}{\textcolor {Chapter }{OrbitsFromSeedsToOrbitList}\relax }{subsection.8.4.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.4}\leavevmode {\color  {Chapter }VerifyDisjointness}}{40}{subsection.8.4.4}}
\newlabel{VerifyDisjointness}{{8.4.4}{40}{\textcolor {Chapter }{VerifyDisjointness}\relax }{subsection.8.4.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.5}\leavevmode {\color  {Chapter }Memory (forobsol)}}{40}{subsection.8.4.5}}
\newlabel{Memory:forobsol}{{8.4.5}{40}{\textcolor {Chapter }{Memory (forobsol)}\relax }{subsection.8.4.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.6}\leavevmode {\color  {Chapter }TotalLength (forobsol)}}{40}{subsection.8.4.6}}
\newlabel{TotalLength:forobsol}{{8.4.6}{40}{\textcolor {Chapter }{TotalLength (forobsol)}\relax }{subsection.8.4.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.7}\leavevmode {\color  {Chapter }Size (forobsol)}}{40}{subsection.8.4.7}}
\newlabel{Size:forobsol}{{8.4.7}{40}{\textcolor {Chapter }{Size (forobsol)}\relax }{subsection.8.4.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.4.8}\leavevmode {\color  {Chapter }SavingFactor (forobsol)}}{40}{subsection.8.4.8}}
\newlabel{SavingFactor:forobsol}{{8.4.8}{40}{\textcolor {Chapter }{SavingFactor (forobsol)}\relax }{subsection.8.4.8}{}}
\@writefile{toc}{\contentsline {chapter}{\numberline {9}\leavevmode {\color  {Chapter }Finding nice quotients}}{42}{chapter.9}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{quotfinder}{{9}{42}{\textcolor {Chapter }{Finding nice quotients}\relax }{chapter.9}{}}
\citation{MNW}
\citation{LongOrbits}
\citation{MueBMCo2}
\citation{MNW}
\@writefile{toc}{\contentsline {chapter}{\numberline {10}\leavevmode {\color  {Chapter }Examples}}{43}{chapter.10}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{examples}{{10}{43}{\textcolor {Chapter }{Examples}\relax }{chapter.10}{}}
\@writefile{brf}{\backcite{MNW}{{43}{10}{chapter.10}}}
\@writefile{brf}{\backcite{LongOrbits}{{43}{10}{chapter.10}}}
\@writefile{brf}{\backcite{MueBMCo2}{{43}{10}{chapter.10}}}
\@writefile{brf}{\backcite{MNW}{{43}{10}{chapter.10}}}
\@writefile{toc}{\contentsline {section}{\numberline {10.1}\leavevmode {\color  {Chapter }The Mathieu group $M_{{11}}$ acting in dimension $24$}}{43}{section.10.1}}
\newlabel{M11example}{{10.1}{43}{\textcolor {Chapter }{The Mathieu group $M_{{11}}$ acting in dimension $24$}\relax }{section.10.1}{}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{44}{10.1}{section.10.1}}}
\citation{Fi23mod2}
\@writefile{toc}{\contentsline {section}{\numberline {10.2}\leavevmode {\color  {Chapter }The Fischer group $Fi_{{23}}$ acting in dimension $1494$ }}{45}{section.10.2}}
\newlabel{Fi23example}{{10.2}{45}{\textcolor {Chapter }{The Fischer group $Fi_{{23}}$ acting in dimension $1494$ }\relax }{section.10.2}{}}
\@writefile{brf}{\backcite{CCN85}{{45}{10.2}{section.10.2}}}
\@writefile{brf}{\backcite{Fi23mod2}{{45}{10.2}{section.10.2}}}
\@writefile{toc}{\contentsline {section}{\numberline {10.3}\leavevmode {\color  {Chapter }The Conway group $Co_1$ acting in dimension $24$ }}{45}{section.10.3}}
\newlabel{Co1example}{{10.3}{45}{\textcolor {Chapter }{The Conway group $Co_1$ acting in dimension $24$ }\relax }{section.10.3}{}}
\citation{CCN85}
\citation{Jansen}
\citation{LongOrbits}
\@writefile{brf}{\backcite{CCN85}{{46}{10.3}{section.10.3}}}
\@writefile{brf}{\backcite{Jansen}{{46}{10.3}{section.10.3}}}
\@writefile{brf}{\backcite{LongOrbits}{{46}{10.3}{section.10.3}}}
\@writefile{toc}{\contentsline {section}{\numberline {10.4}\leavevmode {\color  {Chapter }The Baby Monster $B$ acting on its 2A involutions}}{46}{section.10.4}}
\newlabel{Borbit}{{10.4}{46}{\textcolor {Chapter }{The Baby Monster $B$ acting on its 2A involutions}\relax }{section.10.4}{}}
\citation{CCN85}
\citation{Jansen}
\citation{Wil96}
\citation{AGR}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{47}{10.4}{section.10.4}}}
\@writefile{brf}{\backcite{Jansen}{{47}{10.4}{section.10.4}}}
\@writefile{brf}{\backcite{Wil96}{{47}{10.4}{section.10.4}}}
\@writefile{brf}{\backcite{AGR}{{47}{10.4}{section.10.4}}}
\citation{Jansen}
\citation{AGR}
\@writefile{brf}{\backcite{CCN85}{{48}{10.4}{section.10.4}}}
\@writefile{brf}{\backcite{Jansen}{{48}{10.4}{section.10.4}}}
\@writefile{brf}{\backcite{AGR}{{48}{10.4}{section.10.4}}}
\citation{AGR}
\@writefile{brf}{\backcite{AGR}{{49}{10.4}{section.10.4}}}
\citation{AGR}
\@writefile{brf}{\backcite{AGR}{{50}{10.4}{section.10.4}}}
\bibstyle{alpha}
\bibdata{orb}
\bibcite{CCN85}{CCN{$^{+}$}85}
\bibcite{Fi23mod2}{HNN06}
\bibcite{Jansen}{Jan05}
\bibcite{LongOrbits}{Mal06}
\bibcite{MNW}{MNW07}
\bibcite{MueBMCo2}{M{\"u}l08}
\bibcite{AGR}{Wil}
\bibcite{Wil96}{Wil96}
