Index
  
  ActionOnRespectedPartition, for a tame rcwa group 3.4-2 
  AllElementsOfCTZWithGivenModulus 3.1-9 
  AssignGlobals 7. 
  balanced, definition 2.4 
  Ball, for group, element and radius 3.3-9 
      for group, point and radius 3.3-9 
      for group, point, radius and action 3.3-9 
      for monoid, element and radius 4.2-2 
      for monoid, point, radius and action 4.2-2 
  class-wise translating, definition 2.4  5.1 
  ClassPairs, m 2.2-3 
  ClassReflection, cl 2.2-2 
      r, m 2.2-2 
  ClassRotation, cl, u 2.2-4 
      cl, u; for Z x Z 5.2-3 
      r, L, u; for Z x Z 5.2-3 
      r, m, u 2.2-4 
  ClassShift, cl 2.2-1 
      cl, k; for Z x Z 5.2-4 
      r, L, k; for Z x Z 5.2-4 
      r, m 2.2-1 
  ClassTransposition, cl1, cl2 2.2-3 
      cl1, cl2 (for Z x Z) 5.2-2 
      r1, L1, r2, L2 (for Z x Z) 5.2-2 
      r1, m1, r2, m2 2.2-3 
  ClassWiseConstantOn 2.4-3 
      for rcwa mappings of Z x Z 5.3 
  ClassWiseOrderPreservingOn 2.4-3 
      for rcwa mappings of Z x Z 5.3 
  ClassWiseOrderReversingOn 2.4-3 
      for rcwa mappings of Z x Z 5.3 
  Coefficients, of an rcwa mapping 2.3 
      of an rcwa mapping of Z x Z 5.3 
  Collatz mapping 1. 
  Collatz conjecture 1. 
  CollatzLikeMappingByOrbitTree, for rcwa group, root point and range of radii 3.3-13 
  CommonRightInverse, of two injective rcwa mappings 2.7-2 
  ComputeCycleLength, for an rcwa permutation and a point 3.3-6 
  CT, subgroup of CT(Z) 3.1-9 
      the group generated by all class transpositions of a ring 3.1-9 
  CT, the group generated by all class transpositions of Z x Z 5.4 
  CycleRepresentativesAndLengths, for rcwa permutation and set of seed points 3.3-7 
  CyclesOnFiniteOrbit 3.3-4 
  DecreasingOn, for an rcwa mapping 2.8-3 
  DensityOfSetOfFixedPoints, of an rcwa mapping 2.3 
  DensityOfSupport, of an rcwa mapping 2.3 
  DerivedSubgroup, of an rcwa group 3.2-1 
  Determinant, of an rcwa mapping of Z 2.4-4 
  DirectProduct, for rcwa groups over Z 3.1-2 
  Display, for an rcwa group 3.1-7 
      for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
      for an rcwa monoid 4.1 
  DistanceToNextSmallerPointInOrbit 3.3-2 
  Div, for an rcwa group 3.1-7 
      for an rcwa mapping 2.4 
  divisor, definition 2.1 
  Divisor, of an rcwa group 3.1-7 
      of an rcwa group over Z x Z 5.4 
      of an rcwa mapping 2.4 
      of an rcwa mapping of Z x Z 5.3 
  DrawGrid, P, yrange, xrange, filename 5.4-2 
      U, yrange, xrange, filename 5.4-2 
  DrawOrbitPicture, for rcwa groups over Z x Z 5.4-1 
  DrawOrbitPicture, G, p0, bound, h, w, colored, palette, filename 3.3-3 
  EpimorphismFromFpGroup, for an rcwa group and a search radius 3.2-2 
      for rcwa group, search radius and bound on number of affine parts 3.2-2 
  Exponent, of an rcwa group 3.2-1 
  ExtRepOfObj 2.10-1 
      for a class transposition 2.2-3 
  Factorization, for an rcwa permutation of Z 2.5-1 
  FactorizationIntoCSCRCT, for an rcwa permutation of Z 2.5-1 
  FactorizationOnConnectedComponents, for an rcwa mapping and a modulus 2.8-6 
  FixedPointsOfAffinePartialMappings, for an rcwa mapping 2.4-2 
  FixedResidueClasses, for rcwa group and bound on modulus 3.3-8 
      for rcwa mapping and bound on modulus 3.3-8 
  GluckTaylorInvariant, of a trajectory 2.8-10 
  Group 3.1 
  GroupByGenerators 3.1 
  GroupByResidueClasses, the group `permuting a given list of residue classes' 3.1-5 
  GroupWithGenerators 3.1 
  GrowthFunctionOfOrbit, for an rcwa group orbit and bounds on radius and sphere size 3.3-2 
      for an rcwa group, a point and bounds on radius and sphere size 3.3-2 
  GuessedDivergence, of an rcwa mapping 2.8-12 
  Image, of an rcwa mapping 2.3 
  ImageDensity, of an rcwa mapping 2.7-3 
  IncreasingOn, for an rcwa mapping 2.8-3 
  Index, for rcwa groups 3.2-1 
  Induction, for an rcwa monoid, by an injective rcwa mapping 4.1-1 
  Induction, of an rcwa group, by an injective rcwa mapping 3.1-7 
      of an rcwa mapping, by an injective rcwa mapping 3.1-7 
  InfoRCWA 9.5-1 
  InjectiveAsMappingFrom, for an rcwa mapping 2.7-3 
  integral, definition 2.4 
  IntegralConjugate, of a tame rcwa group 3.4-2 
      of a tame rcwa permutation 3.4-2 
  IntegralizingConjugator, of a tame rcwa group 3.4-2 
      of a tame rcwa permutation 3.4-2 
  IsBalanced, for an rcwa mapping 2.4 
      for an rcwa mapping of Z x Z 5.3 
  IsBijective, for an rcwa mapping 2.3 
      for an rcwa mapping of Z x Z 5.3 
  IsClassReflection, for an rcwa mapping 2.2-4 
  IsClassRotation, for an rcwa mapping 2.2-4 
      for an rcwa mapping of Z x Z 5.2-4 
  IsClassShift, for an rcwa mapping 2.2-4 
      for an rcwa mapping of Z x Z 5.2-4 
  IsClassTransposition, for an rcwa mapping 2.2-4 
      for an rcwa mapping of Z x Z 5.2-4 
  IsClassWiseOrderPreserving, for an rcwa group 3.1-7 
      for an rcwa mapping 2.4 
      for an rcwa mapping of Z x Z 5.3 
      for an rcwa monoid 4.2 
  IsClassWiseTranslating, for an rcwa group 3.1-7 
      for an rcwa group over Z x Z 5.4 
      for an rcwa mapping 2.4 
  IsConjugate, for elements of CT(R) 3.2-1 
      for elements of RCWA(R) 3.2-1 
  IsGeneralizedClassTransposition, for an rcwa mapping 2.2-4 
  IsInjective, for an rcwa mapping 2.3 
      for an rcwa mapping of Z x Z 5.3 
  IsIntegral, for an rcwa group 3.1-7 
      for an rcwa group over Z x Z 5.4 
      for an rcwa mapping 2.4 
      for an rcwa mapping of Z x Z 5.3 
      for an rcwa monoid 4.2 
  IsNaturalCT 3.6-1 
  IsNaturalRCWA 3.6-1 
  IsomorphismMatrixGroup, for an rcwa group 3.2-1 
  IsomorphismPermGroup, for a finite rcwa group 3.2-1 
  IsomorphismRcwaGroup, for a group 3.1-1 
      for a group, over a given ring 3.1-1 
      for GL(2,Z) and a residue class 5.4-1 
      for SL(2,Z) and a residue class 5.4-1 
  IsOne, for an rcwa mapping of Z x Z 5.3 
  IsPerfect, for an rcwa group 3.2-1 
  IsPrimeSwitch, for an rcwa mapping 2.5-2 
  IsRcwaGroup 3.6-1 
  IsRcwaGroupOverGFqx 3.6-1 
  IsRcwaGroupOverZ 3.6-1 
  IsRcwaGroupOverZ_pi 3.6-1 
  IsRcwaGroupOverZOrZ_pi 3.6-1 
  IsRcwaMapping 2.10-1 
  IsRcwaMappingOfGFqx 2.10-1 
  IsRcwaMappingOfZ 2.10-1 
  IsRcwaMappingOfZ_pi 2.10-1 
  IsRcwaMappingOfZOrZ_pi 2.10-1 
  IsRcwaMappingStandardRep 2.10-1 
  IsSignPreserving, for an rcwa group 3.1-7 
      for an rcwa mapping 2.4 
      for an rcwa monoid 4.2 
  IsSolvable, for an rcwa group 3.2-1 
  IsSubset, for two rcwa monoids 4.2 
  IsSurjective, for an rcwa mapping 2.3 
      for an rcwa mapping of Z x Z 5.3 
  IsTame, for an rcwa group 3.2-1 
      for an rcwa group over Z x Z 5.4 
      for an rcwa mapping 2.3 
      for an rcwa mapping of Z x Z 5.3 
      for an rcwa monoid 4.2 
  IsTransitive, for an rcwa group, on its underlying ring 3.3 
  IsTransitiveOnNonnegativeIntegersInSupport, for an rcwa group over Z 3.3 
  IsZero, for an rcwa mapping of Z x Z 5.3 
  KernelOfActionOnRespectedPartition, for a tame rcwa group 3.4-2 
  LargestSourcesOfAffineMappings, for an rcwa mapping 2.4-1 
  LaTeXAndXDVI, for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
  LaTeXStringRcwaMapping, for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
  LikelyContractionCentre, of an rcwa mapping 2.8-11 
  LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions, both databases 6.2-2 
      small database 6.2-1 
  LoadDatabaseOfGroupsGeneratedBy4ClassTranspositions 6.2-3 
  LoadDatabaseOfNonbalancedProductsOfClassTranspositions 6.3-2 
  LoadDatabaseOfProductsOf2ClassTranspositions 6.3-1 
  LoadRCWAExamples 6.1-1 
  LoadRCWAExamples 7. 
  LocalizedRcwaMapping, for an rcwa mapping of Z and a prime 2.2-6 
  Loops, of an rcwa mapping 2.8-9 
  maximal shift, definition 2.4 
  MaximalShift, of an rcwa mapping of Z 2.4 
  MergerExtension, for finite permutation groups 3.1-4 
  Mirrored 3.1-9 
  mKnot, for an odd integer 2.5-3 
  Mod, for an rcwa group 3.1-7 
      for an rcwa mapping 2.3 
  modulus, definition 2.1 
  Modulus, of an rcwa group 3.1-7 
      of an rcwa group over Z x Z 5.4 
      of an rcwa mapping 2.3 
      of an rcwa mapping of Z x Z 5.3 
      of an rcwa monoid 4.2 
  ModulusOfRcwaMonoid, for an rcwa group 3.1-7 
  Monoid 4.1 
  MonoidByGenerators 4.1 
  MovedPoints, of an rcwa group 3.3 
      of an rcwa mapping 2.3 
      of an rcwa mapping of Z x Z 5.3 
  Mult, for an rcwa group 3.1-7 
      for an rcwa mapping 2.4 
  multiplier, definition 2.1 
  Multiplier, of an rcwa group 3.1-7 
      of an rcwa group over Z x Z 5.4 
      of an rcwa mapping 2.4 
      of an rcwa mapping of Z x Z 5.3 
  Multpk, for an rcwa mapping, a prime and an exponent 2.4-3 
  Multpk, for rcwa mapping of Z x Z, prime and exponent 5.3 
  NrClassPairs, m 2.2-3 
  NrConjugacyClassesOfRCWAZOfOrder 3.1-8 
  NrConjugacyClassesOfCTZOfOrder 3.1-9 
  NrElementsOfCTZWithGivenModulus 3.1-9 
  ObjByExtRep 2.10-1 
  One, for an rcwa mapping of Z x Z 5.3 
  Orbit, for an rcwa group and a point 3.3-1 
      for an rcwa group and a set 3.3-1 
  OrbitLengthBound 3.2-1 
  OrbitsModulo, for an rcwa group and a modulus 3.3-11 
  OrbitsModulo, for an rcwa mapping and a modulus 2.8-5 
  Order, of an rcwa mapping of Z x Z 5.3 
      of an rcwa permutation 2.3 
  PermutationOpNC, g, P, OnPoints 3.4-1 
  PreImage, of a residue class union under an rcwa mapping 2.3 
      of a set of ring elements under an rcwa mapping 2.3 
  PreImageElm, of a ring element under an rcwa mapping 2.3 
  PreImagesElm, of a ring element under an rcwa mapping 2.3 
  PreImagesRepresentative, for an epi. from a free group to an rcwa group 3.2-3 
  PreImagesRepresentatives, for an epi. from a free group to an rcwa group 3.2-3 
  prime set, definition 5.1 
  PrimeSet, of an rcwa group 3.1-7 
      of an rcwa mapping 2.4 
      of an rcwa mapping of Z x Z 5.3 
      of an rcwa monoid 4.2 
  PrimeSwitch, p 2.5-2 
      p, cl 2.5-2 
      p, k 2.5-2 
      p, r, m 2.5-2 
  Print, for an rcwa group 3.1-7 
      for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
      for an rcwa monoid 4.1 
  ProjectionsToCoordinates, for an rcwa mapping of Z x Z 5.3-1 
  ProjectionsToInvariantUnionsOfResidueClasses, for rcwa group and modulus 3.3-11 
  Random, CT(R) 3.5 
      RCWA(R) 3.5 
  RankOfKernelOfActionOnRespectedPartition, for a tame rcwa group 3.4-2 
  RCWA, the group formed by all rcwa permutations of a ring 3.1-8 
  RCWA, the group formed by all rcwa permutations of Z x Z 5.4 
  Rcwa, the monoid formed by all rcwa mappings of a ring 4.1-1 
  Rcwa, the monoid formed by all rcwa permutations of Z x Z 5.4 
  rcwa group, class-wise order-preserving 3.1-7 
      class-wise translating 3.1-7 
      coercion 2.3 
      conjugacy problem 3.2-1 
      definition 2.1 
      divisor 3.1-7 
      integral 3.1-7 
      membership test 3.2-1 
      modulus 3.1-7 
      multiplier 3.1-7 
      prime set 3.1-7 
      sign-preserving 3.1-7 
      tame 2.1 
      wild 2.1 
  rcwa mapping, arithmetic operations 2.3 
      balanced 2.4 
      class-wise order-preserving 2.4 
      class-wise translating 2.4  5.1 
      coercion 2.3 
      definition 2.1 
      divisor 2.1 
      images under 2.3 
      integral 2.4 
      maximal shift 2.4 
      modulus 2.1  5.1 
      multiplier 2.1 
      of Z x Z, definition 5.1 
      prime set 2.4 
      sign-preserving 2.4 
      sparse representation 2.9 
      tame 2.1 
      transition graph 2.8-4 
      wild 2.1 
  rcwa monoid, class-wise order-preserving 4.2 
      definition 4. 
      integral 4.2 
      modulus 4.2 
      prime set 4.2 
      sign-preserving 4.2 
      tame 4.2 
      wild 4.2 
  rcwa monoids, membership test 4.2 
  RCWABuildManual 9.3-1 
  RCWAInfo 9.5-1 
  RcwaMapping, by arithmetical expression 2.2-5 
      by finite field size, modulus and list of coefficients 2.2-5 
      by list of coefficients 2.2-5 
  RcwaMapping, by list of coefficients, sparse representation 2.9 
  RcwaMapping, by modulus and list of values 2.2-5 
      by permutation and range 2.2-5 
      by residue class cycles 2.2-5 
      by ring = Z x Z, modulus and coefficients 5.2-1 
      by ring and list of coefficients 2.2-5 
      by ring, modulus and list of coefficients 2.2-5 
      by set of non-invertible primes and list of coefficients 2.2-5 
      by two partitions of a ring into residue classes 2.2-5 
      by two partitions of Z x Z into residue classes 5.2-1 
      of Z x Z, by projections to coordinates 5.2-1 
      of Z x Z, by residue class cycles 5.2-1 
  RcwaMappingsFamily, of a ring 2.10-2 
  RCWATestAll 9.4-2 
  RCWATestExamples 9.4-3 
  RCWATestInstall 9.4-1 
  RepresentativeAction, for RCWA(R) and 2 partitions of R into residue classes 3.3-12 
      G, source, destination, action 3.3-10 
  RepresentativeActionPreImage, G, source, destination, action, F 3.3-10 
  RespectedPartition, of a tame rcwa group 3.4-1 
      of a tame rcwa permutation 3.4-1 
  RespectsPartition, for an rcwa group 3.4-1 
      for an rcwa permutation 3.4-1 
  RestrictedBall, G, g, r, modulusbound 3.3-9 
  RestrictedPerm, for an rcwa permutation and a residue class union 2.3 
  Restriction, for an rcwa monoid, by an injective rcwa mapping 4.1-1 
  Restriction, of an rcwa group, by an injective rcwa mapping 3.1-6 
      of an rcwa mapping, by an injective rcwa mapping 3.1-6 
  RightInverse, of an injective rcwa mapping 2.7-1 
  Root, k-th root of an rcwa mapping 2.6-1 
  RotationFactor, of a class rotation 2.2-4 
      of a class rotation of Z x Z 5.2-3 
  SemilocalizedRcwaMapping, for an rcwa mapping of Z and a set of primes 2.2-6 
  ShiftsDownOn 2.4-3 
  ShiftsUpOn 2.4-3 
  ShortCycles, for rcwa perm. of Z x Z, set of points and max. length 5.3 
  ShortCycles, for rcwa permutation and bound on length 3.3-4 
      for rcwa permutation, set of points and bound on length 3.3-4 
      for rcwa permutation, set of points and bounds on length and points 3.3-4 
  ShortOrbits, for rcwa group, set of points and bound on length 3.3-4 
      for rcwa group, set of points and bounds on length and points 3.3-4 
      for rcwa monoid, set of points and bound on length 4.2-1 
  ShortResidueClassCycles, for rcwa permutation and bounds on modulus and length 3.3-5 
  ShortResidueClassOrbits, for rcwa group and bounds on modulus and length 3.3-5 
  Sign, of an rcwa permutation of Z 2.4-5 
  sign-preserving, definition 2.4 
  SimplifiedCertificate, for a transitivity certificate of an rcwa groups over Z 3.3 
  Sinks, of an rcwa mapping 2.8-8 
  Size, for an rcwa group 3.2-1 
      for an rcwa group over Z x Z 5.4 
      for an rcwa monoid 4.2 
  SmallGeneratingSet 3.1-7 
  Sources, of an rcwa mapping 2.8-8 
  SparseRep, of an rcwa mapping 2.9-1 
  SparseRepresentation, of an rcwa mapping 2.9-1 
  SplittedClassTransposition, for a class transposition and a number of factors 2.2-3 
      for a class transposition of Z x Z 5.2-2 
  StandardRep, of an rcwa mapping 2.9-1 
  StandardRepresentation, of an rcwa mapping 2.9-1 
  String, for an rcwa group 3.1-7 
      for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
      for an rcwa monoid 4.1 
  StructureDescription, for an rcwa group 3.2-1 
  Support, of an rcwa group 3.3 
      of an rcwa mapping 2.3 
      of an rcwa mapping of Z x Z 5.3 
      of an rcwa monoid 4.2 
  tame, rcwa group 2.1 
      rcwa mapping 2.1 
  Trajectory, for rcwa mapping, starting point, length 2.8-1 
      for rcwa mapping, starting point, length, coeff.-spec. 2.8-2 
      for rcwa mapping, starting point, length, modulus 2.8-1 
      for rcwa mapping, starting point, set of end points 2.8-1 
      for rcwa mapping, starting point, set of end points, coeff.-spec. 2.8-2 
      for rcwa mapping, starting point, set of end points, modulus 2.8-1 
  Trajectory, for rcwa mappings of Z x Z 5.3 
  TransitionGraph, for an rcwa mapping and a modulus 2.8-4 
  TransitionMatrix, for an rcwa mapping and a modulus 2.8-7 
  TransitivityCertificate, for an rcwa group over Z and a search limit 3.3 
  TransposedClasses, of a class transposition 2.2-3 
      of a class transposition of Z x Z 5.2-2 
  TryIsTransitiveOnNonnegativeIntegersInSupport, for an rcwa group over Z and a search limit 3.3 
  TryToComputeTransitivityCertificate, for an rcwa group over Z and a search limit 3.3 
  View, for an rcwa group 3.1-7 
      for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
      for an rcwa monoid 4.1 
  wild, rcwa group 2.1 
      rcwa mapping 2.1 
  WreathProduct, for an rcwa group over Z and a permutation group 3.1-3 
      for an rcwa group over Z and the infinite cyclic group 3.1-3 
  Zero, for an rcwa mapping of Z x Z 5.3 
  
  
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