\indexentry{FRMachineNC@\texttt {FRMachineNC}!family,free,listlist,list|hyperpage}{17} \indexentry{FRMachine@\texttt {FRMachine}![list,]list,list|hyperpage}{17} \indexentry{FRMachine@\texttt {FRMachine}!semigroup,list,list|hyperpage}{17} \indexentry{UnderlyingFRMachine@\texttt {UnderlyingFRMachine}|hyperpage}{18} \indexentry{AsGroupFRMachine@\texttt {AsGroupFRMachine}|hyperpage}{19} \indexentry{AsMonoidFRMachine@\texttt {AsMonoidFRMachine}|hyperpage}{19} \indexentry{AsSemigroupFRMachine@\texttt {AsSemigroupFRMachine}|hyperpage}{19} \indexentry{ChangeFRMachineBasis@\texttt {ChangeFRMachineBasis}|hyperpage}{20} \indexentry{StateSet@\texttt {StateSet}!FR machine|hyperpage}{21} \indexentry{GeneratorsOfFRMachine@\texttt {GeneratorsOfFRMachine}|hyperpage}{21} \indexentry{Output@\texttt {Output}!FR machine,state|hyperpage}{22} \indexentry{Output@\texttt {Output}!FR machine,state,letter|hyperpage}{22} \indexentry{Transition@\texttt {Transition}!FR machine,state,input|hyperpage}{22} \indexentry{WreathRecursion@\texttt {WreathRecursion}|hyperpage}{22} \indexentry{StructuralGroup@\texttt {StructuralGroup}|hyperpage}{23} \indexentry{StructuralMonoid@\texttt {StructuralMonoid}|hyperpage}{23} \indexentry{StructuralSemigroup@\texttt {StructuralSemigroup}|hyperpage}{23} \indexentry{+@\texttt {\texttt {\char 92\relax }+}|hyperpage}{23} \indexentry{*@\texttt {\texttt {\char 92\relax }*}|hyperpage}{24} \indexentry{TensorSumOp@\texttt {TensorSumOp}!FR Machines|hyperpage}{24} \indexentry{TensorProductOp@\texttt {TensorProductOp}!FR Machines|hyperpage}{24} \indexentry{DirectSumOp@\texttt {DirectSumOp}!FR Machines|hyperpage}{25} \indexentry{DirectProductOp@\texttt {DirectProductOp}!FR Machines|hyperpage}{25} \indexentry{TreeWreathProduct@\texttt {TreeWreathProduct}!FR machine|hyperpage}{26} \indexentry{SubFRMachine@\texttt {SubFRMachine}|hyperpage}{26} \indexentry{Minimized@\texttt {Minimized}!FR machine|hyperpage}{27} \indexentry{Correspondence@\texttt {Correspondence}!FR machine|hyperpage}{27} \indexentry{FRElementNC@\texttt {FRElementNC}!family,free,listlist,list,assocword|hyperpage}{28} \indexentry{FRElement@\texttt {FRElement}![list,]list,list,list|hyperpage}{29} \indexentry{FRElement@\texttt {FRElement}!semigroup,list,list,list|hyperpage}{29} \indexentry{FRElement@\texttt {FRElement}!machine/element,list|hyperpage}{30} \indexentry{ComposeElement@\texttt {ComposeElement}!elementcoll,perm|hyperpage}{30} \indexentry{VertexElement@\texttt {VertexElement}|hyperpage}{31} \indexentry{DiagonalElement@\texttt {DiagonalElement}|hyperpage}{31} \indexentry{AsGroupFRElement@\texttt {AsGroupFRElement}|hyperpage}{32} \indexentry{AsMonoidFRElement@\texttt {AsMonoidFRElement}|hyperpage}{32} \indexentry{AsSemigroupFRElement@\texttt {AsSemigroupFRElement}|hyperpage}{32} \indexentry{Output@\texttt {Output}!FR element|hyperpage}{33} \indexentry{Activity@\texttt {Activity}|hyperpage}{34} \indexentry{ActivityInt@\texttt {ActivityInt}|hyperpage}{34} \indexentry{ActivityTransformation@\texttt {ActivityTransformation}|hyperpage}{34} \indexentry{ActivityPerm@\texttt {ActivityPerm}|hyperpage}{34} \indexentry{Transition@\texttt {Transition}!FR element,input|hyperpage}{34} \indexentry{Portrait@\texttt {Portrait}|hyperpage}{35} \indexentry{PortraitInt@\texttt {PortraitInt}|hyperpage}{35} \indexentry{DecompositionOfFRElement@\texttt {DecompositionOfFRElement}|hyperpage}{35} \indexentry{StateSet@\texttt {StateSet}!FR element|hyperpage}{35} \indexentry{State@\texttt {State}|hyperpage}{36} \indexentry{States@\texttt {States}|hyperpage}{36} \indexentry{FixedStates@\texttt {FixedStates}|hyperpage}{37} \indexentry{LimitStates@\texttt {LimitStates}|hyperpage}{37} \indexentry{IsFiniteStateFRElement@\texttt {IsFiniteStateFRElement}|hyperpage}{37} \indexentry{IsFiniteStateFRMachine@\texttt {IsFiniteStateFRMachine}|hyperpage}{37} \indexentry{InitialState@\texttt {InitialState}|hyperpage}{38} \indexentry{^@\texttt {\texttt {\char 92\relax }\texttt {\char 94\relax }}!POW|hyperpage}{38} \indexentry{*@\texttt {\texttt {\char 92\relax }*}!PROD|hyperpage}{39} \indexentry{[]@\texttt {\texttt {\char 92\relax }[\texttt {\char 92\relax }]}!ELMLIST|hyperpage}{39} \indexentry{{}@\texttt {\texttt {\char 92\relax }\texttt {\char 123\relax }\texttt {\char 92\relax }\texttt {\char 125\relax }}!ELMSLIST|hyperpage}{39} \indexentry{MealyMachine@\texttt {MealyMachine}![list,]listlist,list|hyperpage}{40} \indexentry{MealyElement@\texttt {MealyElement}![list,]listlist,list,int|hyperpage}{40} \indexentry{MealyMachine@\texttt {MealyMachine}!domain,domain,function,function|hyperpage}{41} \indexentry{MealyElement@\texttt {MealyElement}!domain,domain,function,function,obj|hyperpage}{41} \indexentry{MealyMachineNC@\texttt {MealyMachineNC}!family,listlist,list|hyperpage}{42} \indexentry{MealyElementNC@\texttt {MealyElementNC}!family,listlist,list,int|hyperpage}{42} \indexentry{AllMealyMachines@\texttt {AllMealyMachines}|hyperpage}{42} \indexentry{Draw@\texttt {Draw}|hyperpage}{43} \indexentry{Minimized@\texttt {Minimized}!Mealy machine|hyperpage}{44} \indexentry{DualMachine@\texttt {DualMachine}|hyperpage}{44} \indexentry{IsReversible@\texttt {IsReversible}|hyperpage}{45} \indexentry{IsMinimized@\texttt {IsMinimized}|hyperpage}{45} \indexentry{AlphabetInvolution@\texttt {AlphabetInvolution}|hyperpage}{45} \indexentry{IsBireversible@\texttt {IsBireversible}|hyperpage}{46} \indexentry{StateGrowth@\texttt {StateGrowth}|hyperpage}{46} \indexentry{Degree@\texttt {Degree}!FR element|hyperpage}{46} \indexentry{DegreeOfFRMachine@\texttt {DegreeOfFRMachine}|hyperpage}{46} \indexentry{DegreeOfFRElement@\texttt {DegreeOfFRElement}|hyperpage}{46} \indexentry{IsFinitaryFRElement@\texttt {IsFinitaryFRElement}|hyperpage}{47} \indexentry{IsFinitaryFRMachine@\texttt {IsFinitaryFRMachine}|hyperpage}{47} \indexentry{Depth@\texttt {Depth}!FR element|hyperpage}{47} \indexentry{DepthOfFRMachine@\texttt {DepthOfFRMachine}|hyperpage}{47} \indexentry{DepthOfFRElement@\texttt {DepthOfFRElement}|hyperpage}{47} \indexentry{IsBoundedFRElement@\texttt {IsBoundedFRElement}|hyperpage}{47} \indexentry{IsBoundedFRMachine@\texttt {IsBoundedFRMachine}|hyperpage}{47} \indexentry{IsPolynomialGrowthFRElement@\texttt {IsPolynomialGrowthFRElement}|hyperpage}{48} \indexentry{IsPolynomialGrowthFRMachine@\texttt {IsPolynomialGrowthFRMachine}|hyperpage}{48} \indexentry{Signatures@\texttt {Signatures}|hyperpage}{48} \indexentry{VertexTransformationsFRMachine@\texttt {VertexTransformationsFRMachine}|hyperpage}{49} \indexentry{VertexTransformationsFRElement@\texttt {VertexTransformationsFRElement}|hyperpage}{49} \indexentry{FixedRay@\texttt {FixedRay}!FR element|hyperpage}{49} \indexentry{IsLevelTransitive@\texttt {IsLevelTransitive}!FR element|hyperpage}{49} \indexentry{AsMealyMachine@\texttt {AsMealyMachine}!FR machine|hyperpage}{50} \indexentry{AsMealyMachine@\texttt {AsMealyMachine}!List|hyperpage}{50} \indexentry{AsMealyElement@\texttt {AsMealyElement}|hyperpage}{51} \indexentry{AsIntMealyMachine@\texttt {AsIntMealyMachine}|hyperpage}{51} \indexentry{AsIntMealyElement@\texttt {AsIntMealyElement}|hyperpage}{51} \indexentry{TopElement@\texttt {TopElement}|hyperpage}{52} \indexentry{ConfinalityClasses@\texttt {ConfinalityClasses}|hyperpage}{52} \indexentry{IsWeaklyFinitaryFRElement@\texttt {IsWeaklyFinitaryFRElement}|hyperpage}{52} \indexentry{Germs@\texttt {Germs}|hyperpage}{53} \indexentry{NormOfBoundedFRElement@\texttt {NormOfBoundedFRElement}|hyperpage}{53} \indexentry{HasOpenSetConditionFRElement@\texttt {HasOpenSetConditionFRElement}|hyperpage}{53} \indexentry{LimitMachine@\texttt {LimitMachine}|hyperpage}{53} \indexentry{NucleusMachine@\texttt {NucleusMachine}!FR machine|hyperpage}{54} \indexentry{GuessMealyElement@\texttt {GuessMealyElement}|hyperpage}{54} \indexentry{VectorMachine@\texttt {VectorMachine}|hyperpage}{56} \indexentry{VectorElement@\texttt {VectorElement}|hyperpage}{56} \indexentry{VectorMachineNC@\texttt {VectorMachineNC}|hyperpage}{56} \indexentry{VectorElementNC@\texttt {VectorElementNC}|hyperpage}{56} \indexentry{AlgebraMachine@\texttt {AlgebraMachine}|hyperpage}{57} \indexentry{AlgebraElement@\texttt {AlgebraElement}|hyperpage}{57} \indexentry{AlgebraMachineNC@\texttt {AlgebraMachineNC}|hyperpage}{57} \indexentry{AlgebraElementNC@\texttt {AlgebraElementNC}|hyperpage}{57} \indexentry{Transition@\texttt {Transition}!Linear machine|hyperpage}{58} \indexentry{Transitions@\texttt {Transitions}|hyperpage}{58} \indexentry{NestedMatrixState@\texttt {NestedMatrixState}|hyperpage}{59} \indexentry{NestedMatrixCoefficient@\texttt {NestedMatrixCoefficient}|hyperpage}{59} \indexentry{ActivitySparse@\texttt {ActivitySparse}|hyperpage}{59} \indexentry{Activities@\texttt {Activities}|hyperpage}{60} \indexentry{IsConvergent@\texttt {IsConvergent}|hyperpage}{60} \indexentry{TransposedFRElement@\texttt {TransposedFRElement}|hyperpage}{60} \indexentry{IsSymmetricFRElement@\texttt {IsSymmetricFRElement}|hyperpage}{60} \indexentry{IsAntisymmetricFRElement@\texttt {IsAntisymmetricFRElement}|hyperpage}{60} \indexentry{IsLowerTriangularFRElement@\texttt {IsLowerTriangularFRElement}|hyperpage}{60} \indexentry{IsUpperTriangularFRElement@\texttt {IsUpperTriangularFRElement}|hyperpage}{60} \indexentry{IsDiagonalFRElement@\texttt {IsDiagonalFRElement}|hyperpage}{60} \indexentry{LDUDecompositionFRElement@\texttt {LDUDecompositionFRElement}|hyperpage}{61} \indexentry{GuessVectorElement@\texttt {GuessVectorElement}|hyperpage}{62} \indexentry{AsLinearMachine@\texttt {AsLinearMachine}|hyperpage}{62} \indexentry{AsLinearElement@\texttt {AsLinearElement}|hyperpage}{62} \indexentry{AsVectorMachine@\texttt {AsVectorMachine}|hyperpage}{63} \indexentry{AsVectorElement@\texttt {AsVectorElement}|hyperpage}{63} \indexentry{AsAlgebraMachine@\texttt {AsAlgebraMachine}|hyperpage}{63} \indexentry{AsAlgebraElement@\texttt {AsAlgebraElement}|hyperpage}{63} \indexentry{AsVectorMachine@\texttt {AsVectorMachine}!Linear machine|hyperpage}{64} \indexentry{AsVectorElement@\texttt {AsVectorElement}!Linear machine|hyperpage}{64} \indexentry{AsAlgebraMachine@\texttt {AsAlgebraMachine}!Linear machine|hyperpage}{64} \indexentry{AsAlgebraElement@\texttt {AsAlgebraElement}!Linear machine|hyperpage}{64} \indexentry{FRGroup@\texttt {FRGroup}|hyperpage}{65} \indexentry{FRMonoid@\texttt {FRMonoid}|hyperpage}{65} \indexentry{FRSemigroup@\texttt {FRSemigroup}|hyperpage}{65} \indexentry{SCGroup@\texttt {SCGroup}|hyperpage}{67} \indexentry{SCGroupNC@\texttt {SCGroupNC}|hyperpage}{67} \indexentry{SCMonoid@\texttt {SCMonoid}|hyperpage}{67} \indexentry{SCMonoidNC@\texttt {SCMonoidNC}|hyperpage}{67} \indexentry{SCSemigroup@\texttt {SCSemigroup}|hyperpage}{67} \indexentry{SCSemigroupNC@\texttt {SCSemigroupNC}|hyperpage}{67} \indexentry{Correspondence@\texttt {Correspondence}!FR semigroup|hyperpage}{68} \indexentry{FullSCGroup@\texttt {FullSCGroup}|hyperpage}{68} \indexentry{FullSCMonoid@\texttt {FullSCMonoid}|hyperpage}{68} \indexentry{FullSCSemigroup@\texttt {FullSCSemigroup}|hyperpage}{68} \indexentry{FRMachineFRGroup@\texttt {FRMachineFRGroup}|hyperpage}{69} \indexentry{FRMachineFRMonoid@\texttt {FRMachineFRMonoid}|hyperpage}{69} \indexentry{FRMachineFRSemigroup@\texttt {FRMachineFRSemigroup}|hyperpage}{69} \indexentry{MealyMachineFRGroup@\texttt {MealyMachineFRGroup}|hyperpage}{69} \indexentry{MealyMachineFRMonoid@\texttt {MealyMachineFRMonoid}|hyperpage}{69} \indexentry{MealyMachineFRSemigroup@\texttt {MealyMachineFRSemigroup}|hyperpage}{69} \indexentry{IsomorphismFRGroup@\texttt {IsomorphismFRGroup}|hyperpage}{70} \indexentry{IsomorphismFRMonoid@\texttt {IsomorphismFRMonoid}|hyperpage}{70} \indexentry{IsomorphismFRSemigroup@\texttt {IsomorphismFRSemigroup}|hyperpage}{70} \indexentry{IsomorphismMealyGroup@\texttt {IsomorphismMealyGroup}|hyperpage}{71} \indexentry{IsomorphismMealyMonoid@\texttt {IsomorphismMealyMonoid}|hyperpage}{71} \indexentry{IsomorphismMealySemigroup@\texttt {IsomorphismMealySemigroup}|hyperpage}{71} \indexentry{FRGroupByVirtualEndomorphism@\texttt {FRGroupByVirtualEndomorphism}|hyperpage}{72} \indexentry{TreeWreathProduct@\texttt {TreeWreathProduct}!FR group|hyperpage}{73} \indexentry{WeaklyBranchedEmbedding@\texttt {WeaklyBranchedEmbedding}|hyperpage}{73} \indexentry{PermGroup@\texttt {PermGroup}|hyperpage}{73} \indexentry{EpimorphismPermGroup@\texttt {EpimorphismPermGroup}|hyperpage}{73} \indexentry{PcGroup@\texttt {PcGroup}|hyperpage}{74} \indexentry{EpimorphismPcGroup@\texttt {EpimorphismPcGroup}|hyperpage}{74} \indexentry{TransMonoid@\texttt {TransMonoid}|hyperpage}{75} \indexentry{TransformationMonoid@\texttt {TransformationMonoid}|hyperpage}{75} \indexentry{EpimorphismTransMonoid@\texttt {EpimorphismTransMonoid}|hyperpage}{75} \indexentry{EpimorphismTransformationMonoid@\texttt {EpimorphismTransformationMonoid}|hyperpage}{75} \indexentry{TransSemigroup@\texttt {TransSemigroup}|hyperpage}{75} \indexentry{TransformationSemigroup@\texttt {TransformationSemigroup}|hyperpage}{75} \indexentry{EpimorphismTransSemigroup@\texttt {EpimorphismTransSemigroup}|hyperpage}{75} \indexentry{EpimorphismTransformationSemigroup@\texttt {EpimorphismTransformationSemigroup}|hyperpage}{75} \indexentry{EpimorphismGermGroup@\texttt {EpimorphismGermGroup}|hyperpage}{76} \indexentry{EpimorphismGermGroup@\texttt {EpimorphismGermGroup}!EGG0|hyperpage}{76} \indexentry{StabilizerImage@\texttt {StabilizerImage}|hyperpage}{76} \indexentry{LevelStabilizer@\texttt {LevelStabilizer}|hyperpage}{77} \indexentry{IsStateClosedFRSemigroup@\texttt {IsStateClosedFRSemigroup}|hyperpage}{77} \indexentry{StateClosure@\texttt {StateClosure}|hyperpage}{78} \indexentry{IsRecurrentFRSemigroup@\texttt {IsRecurrentFRSemigroup}|hyperpage}{78} \indexentry{IsLevelTransitive@\texttt {IsLevelTransitive}!FR group|hyperpage}{78} \indexentry{IsInfinitelyTransitive@\texttt {IsInfinitelyTransitive}|hyperpage}{79} \indexentry{IsFinitaryFRSemigroup@\texttt {IsFinitaryFRSemigroup}|hyperpage}{79} \indexentry{IsWeaklyFinitaryFRSemigroup@\texttt {IsWeaklyFinitaryFRSemigroup}|hyperpage}{79} \indexentry{IsBoundedFRSemigroup@\texttt {IsBoundedFRSemigroup}|hyperpage}{79} \indexentry{IsPolynomialGrowthFRSemigroup@\texttt {IsPolynomialGrowthFRSemigroup}|hyperpage}{79} \indexentry{IsFiniteStateFRSemigroup@\texttt {IsFiniteStateFRSemigroup}|hyperpage}{79} \indexentry{Degree@\texttt {Degree}!FR semigroup|hyperpage}{79} \indexentry{DegreeOfFRSemigroup@\texttt {DegreeOfFRSemigroup}|hyperpage}{79} \indexentry{Depth@\texttt {Depth}!FR semigroup|hyperpage}{79} \indexentry{DepthOfFRSemigroup@\texttt {DepthOfFRSemigroup}|hyperpage}{79} \indexentry{HasOpenSetConditionFRSemigroup@\texttt {HasOpenSetConditionFRSemigroup}|hyperpage}{80} \indexentry{IsContracting@\texttt {IsContracting}|hyperpage}{80} \indexentry{NucleusOfFRSemigroup@\texttt {NucleusOfFRSemigroup}|hyperpage}{80} \indexentry{NucleusMachine@\texttt {NucleusMachine}!FR semigroup|hyperpage}{81} \indexentry{BranchingSubgroup@\texttt {BranchingSubgroup}|hyperpage}{81} \indexentry{FindBranchingSubgroup@\texttt {FindBranchingSubgroup}|hyperpage}{81} \indexentry{IsBranched@\texttt {IsBranched}!FR group|hyperpage}{82} \indexentry{IsBranchingSubgroup@\texttt {IsBranchingSubgroup}!FR semigroup|hyperpage}{82} \indexentry{TopVertexTransformations@\texttt {TopVertexTransformations}|hyperpage}{82} \indexentry{VertexTransformations@\texttt {VertexTransformations}!FR semigroup|hyperpage}{83} \indexentry{VirtualEndomorphism@\texttt {VirtualEndomorphism}|hyperpage}{83} \indexentry{EpimorphismFromFpGroup@\texttt {EpimorphismFromFpGroup}|hyperpage}{84} \indexentry{IsomorphismSubgroupFpGroup@\texttt {IsomorphismSubgroupFpGroup}|hyperpage}{84} \indexentry{AsSubgroupFpGroup@\texttt {AsSubgroupFpGroup}|hyperpage}{84} \indexentry{IsomorphismLpGroup@\texttt {IsomorphismLpGroup}|hyperpage}{84} \indexentry{AsLpGroup@\texttt {AsLpGroup}|hyperpage}{84} \indexentry{IsTorsionGroup@\texttt {IsTorsionGroup}|hyperpage}{85} \indexentry{IsTorsionFreeGroup@\texttt {IsTorsionFreeGroup}|hyperpage}{85} \indexentry{IsAmenableGroup@\texttt {IsAmenableGroup}|hyperpage}{86} \indexentry{IsVirtuallySimpleGroup@\texttt {IsVirtuallySimpleGroup}|hyperpage}{86} \indexentry{IsResiduallyFinite@\texttt {IsResiduallyFinite}|hyperpage}{86} \indexentry{IsSQUniversal@\texttt {IsSQUniversal}|hyperpage}{86} \indexentry{IsJustInfinite@\texttt {IsJustInfinite}|hyperpage}{86} \indexentry{FRAlgebra@\texttt {FRAlgebra}|hyperpage}{88} \indexentry{FRAlgebraWithOne@\texttt {FRAlgebraWithOne}|hyperpage}{88} \indexentry{SCAlgebra@\texttt {SCAlgebra}|hyperpage}{89} \indexentry{SCAlgebraWithOne@\texttt {SCAlgebraWithOne}|hyperpage}{89} \indexentry{SCAlgebraNC@\texttt {SCAlgebraNC}|hyperpage}{89} \indexentry{SCAlgebraWithOneNC@\texttt {SCAlgebraWithOneNC}|hyperpage}{89} \indexentry{BranchingIdeal@\texttt {BranchingIdeal}|hyperpage}{89} \indexentry{MatrixQuotient@\texttt {MatrixQuotient}|hyperpage}{89} \indexentry{EpimorphismMatrixQuotient@\texttt {EpimorphismMatrixQuotient}|hyperpage}{89} \indexentry{ThinnedAlgebra@\texttt {ThinnedAlgebra}|hyperpage}{90} \indexentry{ThinnedAlgebraWithOne@\texttt {ThinnedAlgebraWithOne}|hyperpage}{90} \indexentry{Nillity@\texttt {Nillity}|hyperpage}{90} \indexentry{IMGFRMachine@\texttt {IMGFRMachine}!FR machine|hyperpage}{91} \indexentry{IMGRelator@\texttt {IMGRelator}|hyperpage}{91} \indexentry{Mating@\texttt {Mating}|hyperpage}{92} \indexentry{PolynomialFRMachine@\texttt {PolynomialFRMachine}|hyperpage}{92} \indexentry{PolynomialIMGMachine@\texttt {PolynomialIMGMachine}|hyperpage}{92} \indexentry{PolynomialMealyMachine@\texttt {PolynomialMealyMachine}|hyperpage}{92} \indexentry{DBRationalIMGGroup@\texttt {DBRationalIMGGroup}|hyperpage}{93} \indexentry{ValueRational@\texttt {ValueRational}|hyperpage}{94} \indexentry{CriticalValuesQuadraticRational@\texttt {CriticalValuesQuadraticRational}|hyperpage}{94} \indexentry{CanonicalQuadraticRational@\texttt {CanonicalQuadraticRational}|hyperpage}{94} \indexentry{PostCriticalMachine@\texttt {PostCriticalMachine}|hyperpage}{95} \indexentry{RationalFunction@\texttt {RationalFunction}|hyperpage}{95} \indexentry{IMGFRMachine@\texttt {IMGFRMachine}!rational function|hyperpage}{96} \indexentry{FullBinaryGroup@\texttt {FullBinaryGroup}|hyperpage}{97} \indexentry{FiniteDepthBinaryGroup@\texttt {FiniteDepthBinaryGroup}|hyperpage}{97} \indexentry{FinitaryBinaryGroup@\texttt {FinitaryBinaryGroup}|hyperpage}{97} \indexentry{BoundedBinaryGroup@\texttt {BoundedBinaryGroup}|hyperpage}{97} \indexentry{PolynomialGrowthBinaryGroup@\texttt {PolynomialGrowthBinaryGroup}|hyperpage}{97} \indexentry{FiniteStateBinaryGroup@\texttt {FiniteStateBinaryGroup}|hyperpage}{97} \indexentry{BinaryKneadingGroup@\texttt {BinaryKneadingGroup}|hyperpage}{97} \indexentry{BinaryKneadingMachine@\texttt {BinaryKneadingMachine}|hyperpage}{97} \indexentry{BasilicaGroup@\texttt {BasilicaGroup}|hyperpage}{98} \indexentry{AddingGroup@\texttt {AddingGroup}|hyperpage}{98} \indexentry{AddingMachine@\texttt {AddingMachine}|hyperpage}{98} \indexentry{AddingElement@\texttt {AddingElement}|hyperpage}{98} \indexentry{BinaryAddingGroup@\texttt {BinaryAddingGroup}|hyperpage}{99} \indexentry{BinaryAddingMachine@\texttt {BinaryAddingMachine}|hyperpage}{99} \indexentry{BinaryAddingElement@\texttt {BinaryAddingElement}|hyperpage}{99} \indexentry{MixerGroup@\texttt {MixerGroup}|hyperpage}{99} \indexentry{MixerMachine@\texttt {MixerMachine}|hyperpage}{99} \indexentry{SunicGroup@\texttt {SunicGroup}|hyperpage}{100} \indexentry{Sunicmachine@\texttt {Sunicmachine}|hyperpage}{100} \indexentry{GrigorchukMachines@\texttt {GrigorchukMachines}|hyperpage}{100} \indexentry{GrigorchukGroups@\texttt {GrigorchukGroups}|hyperpage}{100} \indexentry{GrigorchukMachine@\texttt {GrigorchukMachine}|hyperpage}{101} \indexentry{GrigorchukGroup@\texttt {GrigorchukGroup}|hyperpage}{101} \indexentry{GrigorchukOverGroup@\texttt {GrigorchukOverGroup}|hyperpage}{101} \indexentry{GrigorchukEvilTwin@\texttt {GrigorchukEvilTwin}|hyperpage}{101} \indexentry{BrunnerSidkiVieiraGroup@\texttt {BrunnerSidkiVieiraGroup}|hyperpage}{102} \indexentry{BrunnerSidkiVieiraMachine@\texttt {BrunnerSidkiVieiraMachine}|hyperpage}{102} \indexentry{AleshinGroups@\texttt {AleshinGroups}|hyperpage}{102} \indexentry{AleshinMachines@\texttt {AleshinMachines}|hyperpage}{102} \indexentry{AleshinGroup@\texttt {AleshinGroup}|hyperpage}{102} \indexentry{AleshinMachine@\texttt {AleshinMachine}|hyperpage}{102} \indexentry{BabyAleshinGroup@\texttt {BabyAleshinGroup}|hyperpage}{103} \indexentry{BabyAleshinMachine@\texttt {BabyAleshinMachine}|hyperpage}{103} \indexentry{SidkiFreeGroup@\texttt {SidkiFreeGroup}|hyperpage}{103} \indexentry{GuptaSidkiGroups@\texttt {GuptaSidkiGroups}|hyperpage}{103} \indexentry{GeneralizedGuptaSidkiGroups@\texttt {GeneralizedGuptaSidkiGroups}|hyperpage}{103} \indexentry{GuptaSidkiMachines@\texttt {GuptaSidkiMachines}|hyperpage}{103} \indexentry{GuptaSidkiGroup@\texttt {GuptaSidkiGroup}|hyperpage}{104} \indexentry{GuptaSidkiMachine@\texttt {GuptaSidkiMachine}|hyperpage}{104} \indexentry{NeumannGroup@\texttt {NeumannGroup}|hyperpage}{104} \indexentry{NeumannMachine@\texttt {NeumannMachine}|hyperpage}{104} \indexentry{FabrykowskiGuptaGroup@\texttt {FabrykowskiGuptaGroup}|hyperpage}{104} \indexentry{FabrykowskiGuptaGroups@\texttt {FabrykowskiGuptaGroups}|hyperpage}{104} \indexentry{OtherSpinalGroup@\texttt {OtherSpinalGroup}|hyperpage}{104} \indexentry{GammaPQMachine@\texttt {GammaPQMachine}|hyperpage}{104} \indexentry{GammaPQGroup@\texttt {GammaPQGroup}|hyperpage}{104} \indexentry{HanoiGroup@\texttt {HanoiGroup}|hyperpage}{105} \indexentry{DahmaniGroup@\texttt {DahmaniGroup}|hyperpage}{105} \indexentry{MamaghaniGroup@\texttt {MamaghaniGroup}|hyperpage}{105} \indexentry{WeierstrassGroup@\texttt {WeierstrassGroup}|hyperpage}{105} \indexentry{FRAffineGroup@\texttt {FRAffineGroup}|hyperpage}{106} \indexentry{CayleyGroup@\texttt {CayleyGroup}|hyperpage}{107} \indexentry{CayleyMachine@\texttt {CayleyMachine}|hyperpage}{107} \indexentry{LamplighterGroup@\texttt {LamplighterGroup}|hyperpage}{107} \indexentry{I2Machine@\texttt {I2Machine}|hyperpage}{108} \indexentry{I2Monoid@\texttt {I2Monoid}|hyperpage}{108} \indexentry{I4Machine@\texttt {I4Machine}|hyperpage}{108} \indexentry{I4Monoid@\texttt {I4Monoid}|hyperpage}{108} \indexentry{PSZAlgebra@\texttt {PSZAlgebra}|hyperpage}{108} \indexentry{GrigorchukThinnedAlgebra@\texttt {GrigorchukThinnedAlgebra}|hyperpage}{109} \indexentry{GuptaSidkiThinnedAlgebra@\texttt {GuptaSidkiThinnedAlgebra}|hyperpage}{109} \indexentry{SidkiFreeAlgebra@\texttt {SidkiFreeAlgebra}|hyperpage}{109} \indexentry{VHStructure@\texttt {VHStructure}|hyperpage}{113} \indexentry{IsVHGroup@\texttt {IsVHGroup}|hyperpage}{113} \indexentry{VerticalAction@\texttt {VerticalAction}|hyperpage}{113} \indexentry{HorizontalAction@\texttt {HorizontalAction}|hyperpage}{113} \indexentry{VHGroup@\texttt {VHGroup}|hyperpage}{113} \indexentry{IsIrreducibleVHGroup@\texttt {IsIrreducibleVHGroup}|hyperpage}{113} \indexentry{MaximalSimpleSubgroup@\texttt {MaximalSimpleSubgroup}|hyperpage}{114} \indexentry{FRMFamily@\texttt {FRMFamily}|hyperpage}{115} \indexentry{FREFamily@\texttt {FREFamily}|hyperpage}{115} \indexentry{AlphabetOfFRObject@\texttt {AlphabetOfFRObject}|hyperpage}{115} \indexentry{AsPermutation@\texttt {AsPermutation}!FR object|hyperpage}{116} \indexentry{AsTransformation@\texttt {AsTransformation}!FR object|hyperpage}{116} \indexentry{IsGroupFRMachine@\texttt {IsGroupFRMachine}|hyperpage}{116} \indexentry{IsMonoidFRMachine@\texttt {IsMonoidFRMachine}|hyperpage}{116} \indexentry{IsSemigroupFRMachine@\texttt {IsSemigroupFRMachine}|hyperpage}{116} \indexentry{IsFRMachineStrRep@\texttt {IsFRMachineStrRep}|hyperpage}{116} \indexentry{IsMealyMachine@\texttt {IsMealyMachine}|hyperpage}{116} \indexentry{IsMealyElement@\texttt {IsMealyElement}|hyperpage}{117} \indexentry{IsMealyMachineIntRep@\texttt {IsMealyMachineIntRep}|hyperpage}{117} \indexentry{IsMealyMachineDomainRep@\texttt {IsMealyMachineDomainRep}|hyperpage}{117} \indexentry{IsVectorFRMachineRep@\texttt {IsVectorFRMachineRep}|hyperpage}{117} \indexentry{IsAlgebraFRMachineRep@\texttt {IsAlgebraFRMachineRep}|hyperpage}{117} \indexentry{IsLinearFRMachine@\texttt {IsLinearFRMachine}|hyperpage}{117} \indexentry{IsLinearFRElement@\texttt {IsLinearFRElement}|hyperpage}{118} \indexentry{IsFRElement@\texttt {IsFRElement}|hyperpage}{118} \indexentry{IsFRObject@\texttt {IsFRObject}|hyperpage}{118} \indexentry{IsFRMachine@\texttt {IsFRMachine}|hyperpage}{118} \indexentry{IsInvertible@\texttt {IsInvertible}|hyperpage}{118} \indexentry{IsFRGroup@\texttt {IsFRGroup}|hyperpage}{119} \indexentry{IsFRMonoid@\texttt {IsFRMonoid}|hyperpage}{119} \indexentry{IsFRSemigroup@\texttt {IsFRSemigroup}|hyperpage}{119} \indexentry{IsFRAlgebra@\texttt {IsFRAlgebra}|hyperpage}{119} \indexentry{IsFRAlgebraWithOne@\texttt {IsFRAlgebraWithOne}|hyperpage}{119} \indexentry{FRMachineRWS@\texttt {FRMachineRWS}|hyperpage}{119} \indexentry{maybe@\texttt {maybe}|hyperpage}{123} \indexentry{ReturnMaybe@\texttt {ReturnMaybe}|hyperpage}{123} \indexentry{TensorSum@\texttt {TensorSum}|hyperpage}{123} \indexentry{TensorProductX@\texttt {TensorProductX}|hyperpage}{123} \indexentry{DirectSum@\texttt {DirectSum}|hyperpage}{123} \indexentry{PeriodicList@\texttt {PeriodicList}|hyperpage}{124} \indexentry{PeriodicList@\texttt {PeriodicList}!period, looping point|hyperpage}{124} \indexentry{PeriodicList@\texttt {PeriodicList}!list, function|hyperpage}{124} \indexentry{CompressedPeriodicList@\texttt {CompressedPeriodicList}|hyperpage}{124} \indexentry{CompressedPeriodicList@\texttt {CompressedPeriodicList}!period, looping point|hyperpage}{124} \indexentry{PrePeriod@\texttt {PrePeriod}|hyperpage}{124} \indexentry{Period@\texttt {Period}|hyperpage}{124} \indexentry{CompressPeriodicList@\texttt {CompressPeriodicList}|hyperpage}{124} \indexentry{IsConfinal@\texttt {IsConfinal}|hyperpage}{125} \indexentry{ConfinalityClass@\texttt {ConfinalityClass}|hyperpage}{125} \indexentry{LargestCommonPrefix@\texttt {LargestCommonPrefix}|hyperpage}{125} \indexentry{WordGrowth@\texttt {WordGrowth}|hyperpage}{125} \indexentry{OrbitGrowth@\texttt {OrbitGrowth}|hyperpage}{125} \indexentry{Ball@\texttt {Ball}|hyperpage}{125} \indexentry{Sphere@\texttt {Sphere}|hyperpage}{125} \indexentry{ShortGroupRelations@\texttt {ShortGroupRelations}|hyperpage}{127} \indexentry{ShortMonoidRelations@\texttt {ShortMonoidRelations}|hyperpage}{127} \indexentry{ShortGroupWordInSet@\texttt {ShortGroupWordInSet}|hyperpage}{128} \indexentry{ShortMonoidWordInSet@\texttt {ShortMonoidWordInSet}|hyperpage}{128} \indexentry{ShortSemigroupWordInSet@\texttt {ShortSemigroupWordInSet}|hyperpage}{128} \indexentry{SurfaceBraidFpGroup@\texttt {SurfaceBraidFpGroup}|hyperpage}{128} \indexentry{PureSurfaceBraidFpGroup@\texttt {PureSurfaceBraidFpGroup}|hyperpage}{128} \indexentry{CharneyBraidFpGroup@\texttt {CharneyBraidFpGroup}|hyperpage}{128} \indexentry{ArtinRepresentation@\texttt {ArtinRepresentation}|hyperpage}{129} \indexentry{StringByInt@\texttt {StringByInt}|hyperpage}{129} \indexentry{PositionTower@\texttt {PositionTower}|hyperpage}{129} \indexentry{CoefficientsInAbelianExtension@\texttt {CoefficientsInAbelianExtension}|hyperpage}{129} \indexentry{MagmaEndomorphismByImagesNC@\texttt {MagmaEndomorphismByImagesNC}|hyperpage}{129} \indexentry{MagmaHomomorphismByImagesNC@\texttt {MagmaHomomorphismByImagesNC}|hyperpage}{129} \indexentry{NewFIFO@\texttt {NewFIFO}|hyperpage}{130} \indexentry{Add@\texttt {Add}!FIFO|hyperpage}{130} \indexentry{Append@\texttt {Append}!FIFO|hyperpage}{130} \indexentry{ProductIdeal@\texttt {ProductIdeal}|hyperpage}{130} \indexentry{ProductBOIIdeal@\texttt {ProductBOIIdeal}|hyperpage}{130} \indexentry{DimensionSeries@\texttt {DimensionSeries}|hyperpage}{130} \indexentry{Trans@\texttt {Trans}|hyperpage}{131} \indexentry{InfoFR@\texttt {InfoFR}|hyperpage}{131} \indexentry{FRSEARCH@\texttt {FR{\textunderscore }SEARCH}|hyperpage}{132}