manual.six

C intro.tex 1. Introduction
S 1.1. Short math background
S 1.2. Installation instructions
S 1.3. Quick example
C groups.tex 2. Properties and operations with groups and semigroups
S 2.1. Creation of groups and semigroups
F 2.1. AutomatonGroup
F 2.1. AutomatonGroup
F 2.1. AutomatonGroup
F 2.1. AutomatonSemigroup
F 2.1. AutomatonSemigroup
F 2.1. AutomatonSemigroup
F 2.1. SelfSimilarGroup
F 2.1. SelfSimilarGroup
F 2.1. SelfSimilarGroup
F 2.1. SelfSimilarSemigroup
F 2.1. SelfSimilarSemigroup
F 2.1. SelfSimilarSemigroup
F 2.1. IsTreeAutomorphismGroup
F 2.1. IsAutomGroup
F 2.1. IsAutomatonGroup
F 2.1. IsSelfSimGroup
F 2.1. IsSelfSimilarGroup
S 2.2. Basic properties of groups and semigroups
F 2.2. TopDegreeOfTree
F 2.2. DegreeOfTree
F 2.2. IsFractal
F 2.2. IsFractalByWords
F 2.2. IsSphericallyTransitive![treehomsg]
F 2.2. ContainsSphericallyTransitiveElement
F 2.2. IsTransitiveOnLevel![treehomsg]
F 2.2. IsSelfSimilar
F 2.2. IsContracting
F 2.2. IsNoncontracting
F 2.2. IsGeneratedByAutomatonOfPolynomialGrowth
F 2.2. IsGeneratedByBoundedAutomaton
F 2.2. PolynomialDegreeOfGrowthOfUnderlyingAutomaton
F 2.2. IsOfSubexponentialGrowth
F 2.2. IsAmenable
F 2.2. UnderlyingAutomaton
F 2.2. AutomatonList![automsg]
F 2.2. RecurList![selfsimsg]
S 2.3. Operations with groups and semigroups
F 2.3. PermGroupOnLevel
F 2.3. TransformationSemigroupOnLevel
F 2.3. StabilizerOfLevel
F 2.3. StabilizerOfFirstLevel
F 2.3. StabilizerOfVertex
F 2.3. FixesLevel
F 2.3. FixesVertex
F 2.3. Projection
F 2.3. ProjectionNC
F 2.3. ProjStab
F 2.3. FindGroupRelations
F 2.3. FindGroupRelations
F 2.3. FindSemigroupRelations
F 2.3. FindSemigroupRelations
F 2.3. Iterator
F 2.3. FindElement
F 2.3. FindElements
F 2.3. FindElementOfInfiniteOrder
F 2.3. FindElementsOfInfiniteOrder
F 2.3. SphericallyTransitiveElement
F 2.3. Growth
F 2.3. ListOfElements
F 2.3. FindNucleus
F 2.3. LevelOfFaithfulAction
F 2.3. LevelOfFaithfulAction
F 2.3. IsomorphismPermGroup
F 2.3. IsomorphismPermGroup
F 2.3. Random
F 2.3. MarkovOperator
F 2.3. MihailovaSystem![automgroup]
F 2.3. AbelImage
F 2.3. DiagonalPower
F 2.3. MultAutomAlphabet
F 2.3. UnderlyingAutomFamily
S 2.4. Self-similar groups and semigroups defined by the wreath recursion
F 2.4. IsFiniteState![selfsimsg]
F 2.4. IsomorphicAutomGroup
F 2.4. IsomorphicAutomSemigroup
F 2.4. UnderlyingAutomatonGroup
F 2.4. UnderlyingAutomatonSemigroup
F 2.4. MonomorphismToAutomatonGroup
F 2.4. MonomorphismToAutomatonSemigroup
S 2.5. Contracting groups
F 2.5. GroupNucleus
F 2.5. GeneratingSetWithNucleus
F 2.5. GeneratingSetWithNucleusAutom
F 2.5. ContractingLevel
F 2.5. ContractingTable
F 2.5. UseContraction
F 2.5. DoNotUseContraction
S 2.6. Rewriting Systems
F 2.6. AG_UseRewritingSystem
F 2.6. AG_AddRelators
F 2.6. AG_UpdateRewritingSystem
F 2.6. AG_RewritingSystemRules
C elements.tex 3. Properties and operations with group and semigroup elements
S 3.1. Creation of tree automorphisms and homomorphisms
F 3.1. TreeAutomorphism
F 3.1. TreeHomomorphism
F 3.1. Representative
F 3.1. Representative
S 3.2. Properties and attributes of tree automorphisms and homomorphisms
F 3.2. IsSphericallyTransitive![treehom]
F 3.2. IsTransitiveOnLevel![treehom]
F 3.2. IsOne
F 3.2. IsOneContr
F 3.2. Order
F 3.2. OrderUsingSections
F 3.2. Perm
F 3.2. PermOnLevel
F 3.2. PermOnLevelAsMatrix
F 3.2. TransformationOnLevel
F 3.2. TransformationOnFirstLevel
F 3.2. TransformationOnLevelAsMatrix
F 3.2. Word
S 3.3. Operations with tree automorphisms and homomorphisms
F 3.3. product!for tree homomorphisms
F 3.3. action!of tree homomorphism on letter
F 3.3. action!of tree homomorphism on vertex
F 3.3. Section![treehom]
F 3.3. Sections
F 3.3. Decompose
F 3.3. in
F 3.3. OrbitOfVertex
F 3.3. PrintOrbitOfVertex
F 3.3. PermActionOnLevel
S 3.4. Elements of groups and semigroups defined by wreath recursion
F 3.4. IsFiniteState![selfsim]
F 3.4. AllSections
S 3.5. Elements of contracting groups
F 3.5. AutomPortrait
F 3.5. AutomPortraitBoundary
F 3.5. AutomPortraitDepth
C autom.tex 4. Noninitial automata
S 4.1. Definition
F 4.1. MealyAutomaton
F 4.1. MealyAutomaton
F 4.1. MealyAutomaton
F 4.1. MealyAutomaton
F 4.1. MealyAutomaton
F 4.1. MealyAutomaton
F 4.1. IsMealyAutomaton
F 4.1. NumberOfStates
F 4.1. SizeOfAlphabet
F 4.1. AutomatonList![automaton]
S 4.2. Tools
F 4.2. IsTrivial
F 4.2. IsInvertible
F 4.2. MinimizationOfAutomaton
F 4.2. MinimizationOfAutomatonTrack
F 4.2. IsOfPolynomialGrowth
F 4.2. IsBounded
F 4.2. PolynomialDegreeOfGrowth
F 4.2. AdjacencyMatrix
F 4.2. IsAcyclic
F 4.2. DualAutomaton
F 4.2. InverseAutomaton
F 4.2. IsBireversible
F 4.2. IsReversible
F 4.2. IsIRAutomaton
F 4.2. MDReduction
F 4.2. IsMDTrivial
F 4.2. IsMDReduced
F 4.2. DisjointUnion
F 4.2. product!for noninitial automata
F 4.2. SubautomatonWithStates
F 4.2. AutomatonNucleus
F 4.2. AreEquivalentAutomata
C misc.tex 5. Miscellaneous
S 5.1. Converters to and from FR package
F 5.1. FR2AutomGrp
F 5.1. AutomGrp2FR
S 5.2. Trees
F 5.2. NumberOfVertex
F 5.2. VertexNumber
S 5.3. Some predefined groups
F 5.3. GrigorchukGroup
F 5.3. UniversalGrigorchukGroup
F 5.3. Basilica
F 5.3. Lamplighter
F 5.3. AddingMachine
F 5.3. InfiniteDihedral
F 5.3. AleshinGroup
F 5.3. Bellaterra
F 5.3. SushchanskyGroup
F 5.3. Hanoi3
F 5.3. Hanoi4
F 5.3. GuptaSidki3Group
F 5.3. GuptaFabrikowskiGroup
F 5.3. BartholdiGrigorchukGroup
F 5.3. GrigorchukErschlerGroup
F 5.3. BartholdiNonunifExponGroup
F 5.3. IMG_z2plusI
F 5.3. Airplane
F 5.3. Rabbit
F 5.3. TwoStateSemigroupOfIntermediateGrowth
F 5.3. UniversalD_omega