\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Licensing}}{10}{chapter.1}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }FR package}}{11}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }A brief mathematical introduction}}{11}{section.2.1}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }An example session}}{12}{section.2.2}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Functionally recursive machines}}{16}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Types of machines}}{16}{section.3.1}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Products of machines}}{17}{section.3.2}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }Creators for \texttt {FRMachine}s}}{17}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}\leavevmode {\color {Chapter }FRMachineNC (family,free,listlist,list)}}{17}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}\leavevmode {\color {Chapter }FRMachine ([list,]list,list)}}{17}{subsection.3.3.2}
\contentsline {subsection}{\numberline {3.3.3}\leavevmode {\color {Chapter }UnderlyingFRMachine}}{18}{subsection.3.3.3}
\contentsline {subsection}{\numberline {3.3.4}\leavevmode {\color {Chapter }AsGroupFRMachine}}{19}{subsection.3.3.4}
\contentsline {subsection}{\numberline {3.3.5}\leavevmode {\color {Chapter }ChangeFRMachineBasis}}{20}{subsection.3.3.5}
\contentsline {section}{\numberline {3.4}\leavevmode {\color {Chapter }Attributes for \texttt {FRMachine}s}}{21}{section.3.4}
\contentsline {subsection}{\numberline {3.4.1}\leavevmode {\color {Chapter }StateSet (FR machine)}}{21}{subsection.3.4.1}
\contentsline {subsection}{\numberline {3.4.2}\leavevmode {\color {Chapter }GeneratorsOfFRMachine}}{21}{subsection.3.4.2}
\contentsline {subsection}{\numberline {3.4.3}\leavevmode {\color {Chapter }Output (FR machine,state)}}{22}{subsection.3.4.3}
\contentsline {subsection}{\numberline {3.4.4}\leavevmode {\color {Chapter }Transition (FR machine,state,input)}}{22}{subsection.3.4.4}
\contentsline {subsection}{\numberline {3.4.5}\leavevmode {\color {Chapter }WreathRecursion}}{22}{subsection.3.4.5}
\contentsline {section}{\numberline {3.5}\leavevmode {\color {Chapter }Operations for \texttt {FRMachine}s}}{23}{section.3.5}
\contentsline {subsection}{\numberline {3.5.1}\leavevmode {\color {Chapter }StructuralGroup}}{23}{subsection.3.5.1}
\contentsline {subsection}{\numberline {3.5.2}\leavevmode {\color {Chapter }\texttt {\char 92\relax }+}}{23}{subsection.3.5.2}
\contentsline {subsection}{\numberline {3.5.3}\leavevmode {\color {Chapter }\texttt {\char 92\relax }*}}{24}{subsection.3.5.3}
\contentsline {subsection}{\numberline {3.5.4}\leavevmode {\color {Chapter }TensorSumOp (FR Machines)}}{24}{subsection.3.5.4}
\contentsline {subsection}{\numberline {3.5.5}\leavevmode {\color {Chapter }TensorProductOp (FR Machines)}}{24}{subsection.3.5.5}
\contentsline {subsection}{\numberline {3.5.6}\leavevmode {\color {Chapter }DirectSumOp (FR Machines)}}{25}{subsection.3.5.6}
\contentsline {subsection}{\numberline {3.5.7}\leavevmode {\color {Chapter }DirectProductOp (FR Machines)}}{25}{subsection.3.5.7}
\contentsline {subsection}{\numberline {3.5.8}\leavevmode {\color {Chapter }TreeWreathProduct (FR machine)}}{26}{subsection.3.5.8}
\contentsline {subsection}{\numberline {3.5.9}\leavevmode {\color {Chapter }SubFRMachine}}{26}{subsection.3.5.9}
\contentsline {subsection}{\numberline {3.5.10}\leavevmode {\color {Chapter }Minimized (FR machine)}}{27}{subsection.3.5.10}
\contentsline {subsection}{\numberline {3.5.11}\leavevmode {\color {Chapter }Correspondence (FR machine)}}{27}{subsection.3.5.11}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Functionally recursive elements}}{28}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Creators for \texttt {FRElement}s}}{28}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color {Chapter }FRElementNC (family,free,listlist,list,assocword)}}{28}{subsection.4.1.1}
\contentsline {subsection}{\numberline {4.1.2}\leavevmode {\color {Chapter }FRElement ([list,]list,list,list)}}{29}{subsection.4.1.2}
\contentsline {subsection}{\numberline {4.1.3}\leavevmode {\color {Chapter }FRElement (machine/element,list)}}{30}{subsection.4.1.3}
\contentsline {subsection}{\numberline {4.1.4}\leavevmode {\color {Chapter }ComposeElement (elementcoll,perm)}}{30}{subsection.4.1.4}
\contentsline {subsection}{\numberline {4.1.5}\leavevmode {\color {Chapter }VertexElement}}{31}{subsection.4.1.5}
\contentsline {subsection}{\numberline {4.1.6}\leavevmode {\color {Chapter }DiagonalElement}}{31}{subsection.4.1.6}
\contentsline {subsection}{\numberline {4.1.7}\leavevmode {\color {Chapter }AsGroupFRElement}}{32}{subsection.4.1.7}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Operations and Attributes for \texttt {FRElement}s}}{33}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }Output (FR element)}}{33}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color {Chapter }Activity}}{34}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}\leavevmode {\color {Chapter }Transition (FR element,input)}}{34}{subsection.4.2.3}
\contentsline {subsection}{\numberline {4.2.4}\leavevmode {\color {Chapter }Portrait}}{35}{subsection.4.2.4}
\contentsline {subsection}{\numberline {4.2.5}\leavevmode {\color {Chapter }DecompositionOfFRElement}}{35}{subsection.4.2.5}
\contentsline {subsection}{\numberline {4.2.6}\leavevmode {\color {Chapter }StateSet (FR element)}}{35}{subsection.4.2.6}
\contentsline {subsection}{\numberline {4.2.7}\leavevmode {\color {Chapter }State}}{36}{subsection.4.2.7}
\contentsline {subsection}{\numberline {4.2.8}\leavevmode {\color {Chapter }States}}{36}{subsection.4.2.8}
\contentsline {subsection}{\numberline {4.2.9}\leavevmode {\color {Chapter }FixedStates}}{37}{subsection.4.2.9}
\contentsline {subsection}{\numberline {4.2.10}\leavevmode {\color {Chapter }LimitStates}}{37}{subsection.4.2.10}
\contentsline {subsection}{\numberline {4.2.11}\leavevmode {\color {Chapter }IsFiniteStateFRElement}}{37}{subsection.4.2.11}
\contentsline {subsection}{\numberline {4.2.12}\leavevmode {\color {Chapter }InitialState}}{38}{subsection.4.2.12}
\contentsline {subsection}{\numberline {4.2.13}\leavevmode {\color {Chapter }\texttt {\char 92\relax }\texttt {\char 94\relax } (POW)}}{38}{subsection.4.2.13}
\contentsline {subsection}{\numberline {4.2.14}\leavevmode {\color {Chapter }\texttt {\char 92\relax }* (PROD)}}{39}{subsection.4.2.14}
\contentsline {subsection}{\numberline {4.2.15}\leavevmode {\color {Chapter }\texttt {\char 92\relax }[\texttt {\char 92\relax }] (ELMLIST)}}{39}{subsection.4.2.15}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Mealy machines and elements}}{40}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter }Creators for \texttt {MealyMachine}s and \texttt {MealyElement}s}}{40}{section.5.1}
\contentsline {subsection}{\numberline {5.1.1}\leavevmode {\color {Chapter }MealyMachine ([list,]listlist,list)}}{40}{subsection.5.1.1}
\contentsline {subsection}{\numberline {5.1.2}\leavevmode {\color {Chapter }MealyMachine (domain,domain,function,function)}}{41}{subsection.5.1.2}
\contentsline {subsection}{\numberline {5.1.3}\leavevmode {\color {Chapter }MealyMachineNC (family,listlist,list)}}{42}{subsection.5.1.3}
\contentsline {subsection}{\numberline {5.1.4}\leavevmode {\color {Chapter }AllMealyMachines}}{42}{subsection.5.1.4}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter }Operations and Attributes for \texttt {MealyMachine}s and \texttt {MealyElement}s}}{43}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color {Chapter }Draw}}{43}{subsection.5.2.1}
\contentsline {subsection}{\numberline {5.2.2}\leavevmode {\color {Chapter }Minimized (Mealy machine)}}{44}{subsection.5.2.2}
\contentsline {subsection}{\numberline {5.2.3}\leavevmode {\color {Chapter }DualMachine}}{44}{subsection.5.2.3}
\contentsline {subsection}{\numberline {5.2.4}\leavevmode {\color {Chapter }IsReversible}}{45}{subsection.5.2.4}
\contentsline {subsection}{\numberline {5.2.5}\leavevmode {\color {Chapter }IsMinimized}}{45}{subsection.5.2.5}
\contentsline {subsection}{\numberline {5.2.6}\leavevmode {\color {Chapter }AlphabetInvolution}}{45}{subsection.5.2.6}
\contentsline {subsection}{\numberline {5.2.7}\leavevmode {\color {Chapter }IsBireversible}}{46}{subsection.5.2.7}
\contentsline {subsection}{\numberline {5.2.8}\leavevmode {\color {Chapter }StateGrowth}}{46}{subsection.5.2.8}
\contentsline {subsection}{\numberline {5.2.9}\leavevmode {\color {Chapter }Degree (FR element)}}{46}{subsection.5.2.9}
\contentsline {subsection}{\numberline {5.2.10}\leavevmode {\color {Chapter }IsFinitaryFRElement}}{47}{subsection.5.2.10}
\contentsline {subsection}{\numberline {5.2.11}\leavevmode {\color {Chapter }Depth (FR element)}}{47}{subsection.5.2.11}
\contentsline {subsection}{\numberline {5.2.12}\leavevmode {\color {Chapter }IsBoundedFRElement}}{47}{subsection.5.2.12}
\contentsline {subsection}{\numberline {5.2.13}\leavevmode {\color {Chapter }IsPolynomialGrowthFRElement}}{48}{subsection.5.2.13}
\contentsline {subsection}{\numberline {5.2.14}\leavevmode {\color {Chapter }Signatures}}{48}{subsection.5.2.14}
\contentsline {subsection}{\numberline {5.2.15}\leavevmode {\color {Chapter }VertexTransformationsFRMachine}}{49}{subsection.5.2.15}
\contentsline {subsection}{\numberline {5.2.16}\leavevmode {\color {Chapter }FixedRay (FR element)}}{49}{subsection.5.2.16}
\contentsline {subsection}{\numberline {5.2.17}\leavevmode {\color {Chapter }IsLevelTransitive (FR element)}}{49}{subsection.5.2.17}
\contentsline {subsection}{\numberline {5.2.18}\leavevmode {\color {Chapter }AsMealyMachine (FR machine)}}{50}{subsection.5.2.18}
\contentsline {subsection}{\numberline {5.2.19}\leavevmode {\color {Chapter }AsMealyMachine (List)}}{50}{subsection.5.2.19}
\contentsline {subsection}{\numberline {5.2.20}\leavevmode {\color {Chapter }AsMealyElement}}{51}{subsection.5.2.20}
\contentsline {subsection}{\numberline {5.2.21}\leavevmode {\color {Chapter }AsIntMealyMachine}}{51}{subsection.5.2.21}
\contentsline {subsection}{\numberline {5.2.22}\leavevmode {\color {Chapter }TopElement}}{52}{subsection.5.2.22}
\contentsline {subsection}{\numberline {5.2.23}\leavevmode {\color {Chapter }ConfinalityClasses}}{52}{subsection.5.2.23}
\contentsline {subsection}{\numberline {5.2.24}\leavevmode {\color {Chapter }Germs}}{53}{subsection.5.2.24}
\contentsline {subsection}{\numberline {5.2.25}\leavevmode {\color {Chapter }HasOpenSetConditionFRElement}}{53}{subsection.5.2.25}
\contentsline {subsection}{\numberline {5.2.26}\leavevmode {\color {Chapter }LimitMachine}}{53}{subsection.5.2.26}
\contentsline {subsection}{\numberline {5.2.27}\leavevmode {\color {Chapter }NucleusMachine (FR machine)}}{54}{subsection.5.2.27}
\contentsline {subsection}{\numberline {5.2.28}\leavevmode {\color {Chapter }GuessMealyElement}}{54}{subsection.5.2.28}
\contentsline {chapter}{\numberline {6}\leavevmode {\color {Chapter }Linear machines and elements}}{56}{chapter.6}
\contentsline {section}{\numberline {6.1}\leavevmode {\color {Chapter }Methods and operations for \texttt {LinearFRMachine}s and \texttt {LinearFRElement}s}}{56}{section.6.1}
\contentsline {subsection}{\numberline {6.1.1}\leavevmode {\color {Chapter }VectorMachine}}{56}{subsection.6.1.1}
\contentsline {subsection}{\numberline {6.1.2}\leavevmode {\color {Chapter }AlgebraMachine}}{57}{subsection.6.1.2}
\contentsline {subsection}{\numberline {6.1.3}\leavevmode {\color {Chapter }Transition (Linear machine)}}{58}{subsection.6.1.3}
\contentsline {subsection}{\numberline {6.1.4}\leavevmode {\color {Chapter }Transitions}}{58}{subsection.6.1.4}
\contentsline {subsection}{\numberline {6.1.5}\leavevmode {\color {Chapter }NestedMatrixState}}{59}{subsection.6.1.5}
\contentsline {subsection}{\numberline {6.1.6}\leavevmode {\color {Chapter }ActivitySparse}}{59}{subsection.6.1.6}
\contentsline {subsection}{\numberline {6.1.7}\leavevmode {\color {Chapter }Activities}}{60}{subsection.6.1.7}
\contentsline {subsection}{\numberline {6.1.8}\leavevmode {\color {Chapter }IsConvergent}}{60}{subsection.6.1.8}
\contentsline {subsection}{\numberline {6.1.9}\leavevmode {\color {Chapter }TransposedFRElement}}{60}{subsection.6.1.9}
\contentsline {subsection}{\numberline {6.1.10}\leavevmode {\color {Chapter }LDUDecompositionFRElement}}{61}{subsection.6.1.10}
\contentsline {subsection}{\numberline {6.1.11}\leavevmode {\color {Chapter }GuessVectorElement}}{62}{subsection.6.1.11}
\contentsline {subsection}{\numberline {6.1.12}\leavevmode {\color {Chapter }AsLinearMachine}}{62}{subsection.6.1.12}
\contentsline {subsection}{\numberline {6.1.13}\leavevmode {\color {Chapter }AsVectorMachine}}{63}{subsection.6.1.13}
\contentsline {subsection}{\numberline {6.1.14}\leavevmode {\color {Chapter }AsAlgebraMachine}}{63}{subsection.6.1.14}
\contentsline {subsection}{\numberline {6.1.15}\leavevmode {\color {Chapter }AsVectorMachine (Linear machine)}}{64}{subsection.6.1.15}
\contentsline {subsection}{\numberline {6.1.16}\leavevmode {\color {Chapter }AsAlgebraMachine (Linear machine)}}{64}{subsection.6.1.16}
\contentsline {chapter}{\numberline {7}\leavevmode {\color {Chapter }Self-similar groups, monoids and semigroups}}{65}{chapter.7}
\contentsline {section}{\numberline {7.1}\leavevmode {\color {Chapter }Creators for FR semigroups}}{65}{section.7.1}
\contentsline {subsection}{\numberline {7.1.1}\leavevmode {\color {Chapter }FRGroup}}{65}{subsection.7.1.1}
\contentsline {subsection}{\numberline {7.1.2}\leavevmode {\color {Chapter }SCGroup}}{67}{subsection.7.1.2}
\contentsline {subsection}{\numberline {7.1.3}\leavevmode {\color {Chapter }Correspondence (FR semigroup)}}{68}{subsection.7.1.3}
\contentsline {subsection}{\numberline {7.1.4}\leavevmode {\color {Chapter }FullSCGroup}}{68}{subsection.7.1.4}
\contentsline {subsection}{\numberline {7.1.5}\leavevmode {\color {Chapter }FRMachineFRGroup}}{69}{subsection.7.1.5}
\contentsline {subsection}{\numberline {7.1.6}\leavevmode {\color {Chapter }IsomorphismFRGroup}}{70}{subsection.7.1.6}
\contentsline {subsection}{\numberline {7.1.7}\leavevmode {\color {Chapter }IsomorphismMealyGroup}}{71}{subsection.7.1.7}
\contentsline {subsection}{\numberline {7.1.8}\leavevmode {\color {Chapter }FRGroupByVirtualEndomorphism}}{72}{subsection.7.1.8}
\contentsline {subsection}{\numberline {7.1.9}\leavevmode {\color {Chapter }TreeWreathProduct (FR group)}}{73}{subsection.7.1.9}
\contentsline {subsection}{\numberline {7.1.10}\leavevmode {\color {Chapter }WeaklyBranchedEmbedding}}{73}{subsection.7.1.10}
\contentsline {section}{\numberline {7.2}\leavevmode {\color {Chapter }Operations for FR semigroups}}{73}{section.7.2}
\contentsline {subsection}{\numberline {7.2.1}\leavevmode {\color {Chapter }PermGroup}}{73}{subsection.7.2.1}
\contentsline {subsection}{\numberline {7.2.2}\leavevmode {\color {Chapter }PcGroup}}{74}{subsection.7.2.2}
\contentsline {subsection}{\numberline {7.2.3}\leavevmode {\color {Chapter }TransMonoid}}{75}{subsection.7.2.3}
\contentsline {subsection}{\numberline {7.2.4}\leavevmode {\color {Chapter }TransSemigroup}}{75}{subsection.7.2.4}
\contentsline {subsection}{\numberline {7.2.5}\leavevmode {\color {Chapter }EpimorphismGermGroup}}{76}{subsection.7.2.5}
\contentsline {subsection}{\numberline {7.2.6}\leavevmode {\color {Chapter }StabilizerImage}}{76}{subsection.7.2.6}
\contentsline {subsection}{\numberline {7.2.7}\leavevmode {\color {Chapter }LevelStabilizer}}{77}{subsection.7.2.7}
\contentsline {subsection}{\numberline {7.2.8}\leavevmode {\color {Chapter }IsStateClosedFRSemigroup}}{77}{subsection.7.2.8}
\contentsline {subsection}{\numberline {7.2.9}\leavevmode {\color {Chapter }StateClosure}}{78}{subsection.7.2.9}
\contentsline {subsection}{\numberline {7.2.10}\leavevmode {\color {Chapter }IsRecurrentFRSemigroup}}{78}{subsection.7.2.10}
\contentsline {subsection}{\numberline {7.2.11}\leavevmode {\color {Chapter }IsLevelTransitive (FR group)}}{78}{subsection.7.2.11}
\contentsline {subsection}{\numberline {7.2.12}\leavevmode {\color {Chapter }IsInfinitelyTransitive}}{79}{subsection.7.2.12}
\contentsline {subsection}{\numberline {7.2.13}\leavevmode {\color {Chapter }IsFinitaryFRSemigroup}}{79}{subsection.7.2.13}
\contentsline {subsection}{\numberline {7.2.14}\leavevmode {\color {Chapter }Degree (FR semigroup)}}{79}{subsection.7.2.14}
\contentsline {subsection}{\numberline {7.2.15}\leavevmode {\color {Chapter }HasOpenSetConditionFRSemigroup}}{80}{subsection.7.2.15}
\contentsline {subsection}{\numberline {7.2.16}\leavevmode {\color {Chapter }IsContracting}}{80}{subsection.7.2.16}
\contentsline {subsection}{\numberline {7.2.17}\leavevmode {\color {Chapter }NucleusOfFRSemigroup}}{80}{subsection.7.2.17}
\contentsline {subsection}{\numberline {7.2.18}\leavevmode {\color {Chapter }NucleusMachine (FR semigroup)}}{81}{subsection.7.2.18}
\contentsline {subsection}{\numberline {7.2.19}\leavevmode {\color {Chapter }BranchingSubgroup}}{81}{subsection.7.2.19}
\contentsline {subsection}{\numberline {7.2.20}\leavevmode {\color {Chapter }FindBranchingSubgroup}}{81}{subsection.7.2.20}
\contentsline {subsection}{\numberline {7.2.21}\leavevmode {\color {Chapter }IsBranched (FR group)}}{82}{subsection.7.2.21}
\contentsline {subsection}{\numberline {7.2.22}\leavevmode {\color {Chapter }IsBranchingSubgroup (FR semigroup)}}{82}{subsection.7.2.22}
\contentsline {subsection}{\numberline {7.2.23}\leavevmode {\color {Chapter }TopVertexTransformations}}{82}{subsection.7.2.23}
\contentsline {subsection}{\numberline {7.2.24}\leavevmode {\color {Chapter }VertexTransformations (FR semigroup)}}{83}{subsection.7.2.24}
\contentsline {subsection}{\numberline {7.2.25}\leavevmode {\color {Chapter }VirtualEndomorphism}}{83}{subsection.7.2.25}
\contentsline {subsection}{\numberline {7.2.26}\leavevmode {\color {Chapter }EpimorphismFromFpGroup}}{84}{subsection.7.2.26}
\contentsline {subsection}{\numberline {7.2.27}\leavevmode {\color {Chapter }IsomorphismSubgroupFpGroup}}{84}{subsection.7.2.27}
\contentsline {section}{\numberline {7.3}\leavevmode {\color {Chapter }Properties for infinite groups}}{85}{section.7.3}
\contentsline {subsection}{\numberline {7.3.1}\leavevmode {\color {Chapter }IsTorsionGroup}}{85}{subsection.7.3.1}
\contentsline {subsection}{\numberline {7.3.2}\leavevmode {\color {Chapter }IsTorsionFreeGroup}}{85}{subsection.7.3.2}
\contentsline {subsection}{\numberline {7.3.3}\leavevmode {\color {Chapter }IsAmenableGroup}}{86}{subsection.7.3.3}
\contentsline {subsection}{\numberline {7.3.4}\leavevmode {\color {Chapter }IsVirtuallySimpleGroup}}{86}{subsection.7.3.4}
\contentsline {subsection}{\numberline {7.3.5}\leavevmode {\color {Chapter }IsResiduallyFinite}}{86}{subsection.7.3.5}
\contentsline {subsection}{\numberline {7.3.6}\leavevmode {\color {Chapter }IsSQUniversal}}{86}{subsection.7.3.6}
\contentsline {subsection}{\numberline {7.3.7}\leavevmode {\color {Chapter }IsJustInfinite}}{86}{subsection.7.3.7}
\contentsline {chapter}{\numberline {8}\leavevmode {\color {Chapter }Algebras}}{88}{chapter.8}
\contentsline {section}{\numberline {8.1}\leavevmode {\color {Chapter }Creators for FR algebras}}{88}{section.8.1}
\contentsline {subsection}{\numberline {8.1.1}\leavevmode {\color {Chapter }FRAlgebra}}{88}{subsection.8.1.1}
\contentsline {subsection}{\numberline {8.1.2}\leavevmode {\color {Chapter }SCAlgebra}}{89}{subsection.8.1.2}
\contentsline {subsection}{\numberline {8.1.3}\leavevmode {\color {Chapter }BranchingIdeal}}{89}{subsection.8.1.3}
\contentsline {section}{\numberline {8.2}\leavevmode {\color {Chapter }Operations for FR algebras}}{89}{section.8.2}
\contentsline {subsection}{\numberline {8.2.1}\leavevmode {\color {Chapter }MatrixQuotient}}{89}{subsection.8.2.1}
\contentsline {subsection}{\numberline {8.2.2}\leavevmode {\color {Chapter }ThinnedAlgebra}}{90}{subsection.8.2.2}
\contentsline {subsection}{\numberline {8.2.3}\leavevmode {\color {Chapter }Nillity}}{90}{subsection.8.2.3}
\contentsline {chapter}{\numberline {9}\leavevmode {\color {Chapter }Iterated monodromy groups}}{91}{chapter.9}
\contentsline {section}{\numberline {9.1}\leavevmode {\color {Chapter }Creators and operations for IMG FR machines}}{91}{section.9.1}
\contentsline {subsection}{\numberline {9.1.1}\leavevmode {\color {Chapter }IMGFRMachine (FR machine)}}{91}{subsection.9.1.1}
\contentsline {subsection}{\numberline {9.1.2}\leavevmode {\color {Chapter }IMGRelator}}{91}{subsection.9.1.2}
\contentsline {subsection}{\numberline {9.1.3}\leavevmode {\color {Chapter }Mating}}{92}{subsection.9.1.3}
\contentsline {subsection}{\numberline {9.1.4}\leavevmode {\color {Chapter }PolynomialFRMachine}}{92}{subsection.9.1.4}
\contentsline {subsection}{\numberline {9.1.5}\leavevmode {\color {Chapter }DBRationalIMGGroup}}{93}{subsection.9.1.5}
\contentsline {subsection}{\numberline {9.1.6}\leavevmode {\color {Chapter }ValueRational}}{94}{subsection.9.1.6}
\contentsline {subsection}{\numberline {9.1.7}\leavevmode {\color {Chapter }CriticalValuesQuadraticRational}}{94}{subsection.9.1.7}
\contentsline {subsection}{\numberline {9.1.8}\leavevmode {\color {Chapter }CanonicalQuadraticRational}}{94}{subsection.9.1.8}
\contentsline {subsection}{\numberline {9.1.9}\leavevmode {\color {Chapter }PostCriticalMachine}}{95}{subsection.9.1.9}
\contentsline {section}{\numberline {9.2}\leavevmode {\color {Chapter }Spiders}}{95}{section.9.2}
\contentsline {subsection}{\numberline {9.2.1}\leavevmode {\color {Chapter }RationalFunction}}{95}{subsection.9.2.1}
\contentsline {subsection}{\numberline {9.2.2}\leavevmode {\color {Chapter }IMGFRMachine (rational function)}}{96}{subsection.9.2.2}
\contentsline {chapter}{\numberline {10}\leavevmode {\color {Chapter }Examples}}{97}{chapter.10}
\contentsline {section}{\numberline {10.1}\leavevmode {\color {Chapter }Examples of groups}}{97}{section.10.1}
\contentsline {subsection}{\numberline {10.1.1}\leavevmode {\color {Chapter }FullBinaryGroup}}{97}{subsection.10.1.1}
\contentsline {subsection}{\numberline {10.1.2}\leavevmode {\color {Chapter }BinaryKneadingGroup}}{97}{subsection.10.1.2}
\contentsline {subsection}{\numberline {10.1.3}\leavevmode {\color {Chapter }BasilicaGroup}}{98}{subsection.10.1.3}
\contentsline {subsection}{\numberline {10.1.4}\leavevmode {\color {Chapter }AddingGroup}}{98}{subsection.10.1.4}
\contentsline {subsection}{\numberline {10.1.5}\leavevmode {\color {Chapter }BinaryAddingGroup}}{99}{subsection.10.1.5}
\contentsline {subsection}{\numberline {10.1.6}\leavevmode {\color {Chapter }MixerGroup}}{99}{subsection.10.1.6}
\contentsline {subsection}{\numberline {10.1.7}\leavevmode {\color {Chapter }SunicGroup}}{100}{subsection.10.1.7}
\contentsline {subsection}{\numberline {10.1.8}\leavevmode {\color {Chapter }GrigorchukMachines}}{100}{subsection.10.1.8}
\contentsline {subsection}{\numberline {10.1.9}\leavevmode {\color {Chapter }GrigorchukMachine}}{101}{subsection.10.1.9}
\contentsline {subsection}{\numberline {10.1.10}\leavevmode {\color {Chapter }GrigorchukOverGroup}}{101}{subsection.10.1.10}
\contentsline {subsection}{\numberline {10.1.11}\leavevmode {\color {Chapter }GrigorchukEvilTwin}}{101}{subsection.10.1.11}
\contentsline {subsection}{\numberline {10.1.12}\leavevmode {\color {Chapter }BrunnerSidkiVieiraGroup}}{102}{subsection.10.1.12}
\contentsline {subsection}{\numberline {10.1.13}\leavevmode {\color {Chapter }AleshinGroups}}{102}{subsection.10.1.13}
\contentsline {subsection}{\numberline {10.1.14}\leavevmode {\color {Chapter }AleshinGroup}}{102}{subsection.10.1.14}
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\contentsline {subsection}{\numberline {10.1.16}\leavevmode {\color {Chapter }SidkiFreeGroup}}{103}{subsection.10.1.16}
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\contentsline {subsection}{\numberline {10.1.18}\leavevmode {\color {Chapter }GuptaSidkiGroup}}{104}{subsection.10.1.18}
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\contentsline {subsection}{\numberline {10.1.28}\leavevmode {\color {Chapter }CayleyGroup}}{107}{subsection.10.1.28}
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\contentsline {subsection}{\numberline {10.2.2}\leavevmode {\color {Chapter }I4Machine}}{108}{subsection.10.2.2}
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\contentsline {subsection}{\numberline {10.3.2}\leavevmode {\color {Chapter }GrigorchukThinnedAlgebra}}{109}{subsection.10.3.2}
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\contentsline {subsection}{\numberline {10.3.4}\leavevmode {\color {Chapter }SidkiFreeAlgebra}}{109}{subsection.10.3.4}
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\contentsline {subsection}{\numberline {11.3.3}\leavevmode {\color {Chapter }Membership in semigroups}}{120}{subsection.11.3.3}
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\contentsline {subsection}{\numberline {12.2.1}\leavevmode {\color {Chapter }InfoFR}}{131}{subsection.12.2.1}
\contentsline {subsection}{\numberline {12.2.2}\leavevmode {\color {Chapter }FR{\textunderscore }SEARCH}}{132}{subsection.12.2.2}
