\begin{theindex} \item \texttt {ActionOnRespectedPartition} \subitem for a tame rcwa group, \hyperpage{45} \item \texttt{AllProducts}, \hyperpage{108} \indexspace \item \texttt{balanced} \subitem definition, \hyperpage{17} \item \texttt {Ball} \subitem for group, element and radius, \hyperpage{41} \subitem for group, point, radius and action, \hyperpage{41} \subitem for monoid, element and radius, \hyperpage{51} \subitem for monoid, point, radius and action, \hyperpage{51} \indexspace \item \texttt{ClassPairs} \subitem m, \hyperpage{46} \subitem R, m, \hyperpage{46} \item \texttt {ClassReflection} \subitem cl, \hyperpage{10} \subitem r, m, \hyperpage{10} \item \texttt {ClassRotation} \subitem cl, u, \hyperpage{12} \subitem r, m, u, \hyperpage{12} \item \texttt {ClassShift} \subitem cl, \hyperpage{10} \subitem r, m, \hyperpage{10} \item \texttt {ClassTransposition} \subitem cl1, cl2, \hyperpage{11} \subitem r1, m1, r2, m2, \hyperpage{11} \item \texttt{ClassWiseConstantOn}, \hyperpage{19} \item \texttt{ClassWiseOrderPreservingOn}, \hyperpage{19} \item \texttt{ClassWiseOrderReversingOn}, \hyperpage{19} \item \texttt{Coefficients} \subitem of an rcwa mapping, \hyperpage{17} \item Collatz conjecture, \hyperpage{6} \item Collatz mapping, \hyperpage{6} \item \texttt {CommonRightInverse} \subitem of two injective rcwa mappings, \hyperpage{23} \item \texttt {CT} \subitem the group generated by all class transpositions of a ring, \hyperpage{31} \indexspace \item \texttt {DecreasingOn} \subitem for an rcwa mapping, \hyperpage{25} \item \texttt{DerivedSubgroup} \subitem of an rcwa group, \hyperpage{36} \item \texttt {Determinant} \subitem of an rcwa mapping of Z, \hyperpage{19} \item \texttt{DifferencesList}, \hyperpage{108} \item \texttt {DirectProduct} \subitem for rcwa groups over Z, \hyperpage{32} \item \texttt{Display} \subitem for an rcwa group, \hyperpage{30} \subitem for an rcwa mapping, \hyperpage{14} \subitem for an rcwa monoid, \hyperpage{48} \item \texttt{Div} \subitem for an rcwa group, \hyperpage{33} \subitem for an rcwa mapping, \hyperpage{17} \item \texttt{Divisor} \subitem of an rcwa group, \hyperpage{33} \subitem of an rcwa mapping, \hyperpage{17} \item divisor \subitem definition, \hyperpage{8} \item \texttt {DrawOrbitPicture} \subitem G, p0, r, h, w, colored, palette, filename, \hyperpage{40} \indexspace \item \texttt{EpimorphismByGenerators} \subitem for two groups, \hyperpage{108} \item \texttt {EpimorphismFromFpGroup} \subitem for an rcwa group and a search radius, \hyperpage{37} \item \texttt{EquivalenceClasses} \subitem for a list and a function computing a class invariant, \hyperpage{108} \subitem for a list and a function describing an equivalence relation, \hyperpage{108} \item \texttt{Exponent} \subitem of an rcwa group, \hyperpage{36} \item \texttt{ExtRepOfObj}, \hyperpage{29} \indexspace \item \texttt {Factorization} \subitem for an rcwa permutation of Z, \hyperpage{20} \item \texttt {FactorizationIntoCSCRCT} \subitem for an rcwa permutation of Z, \hyperpage{20} \item \texttt {FactorizationOnConnectedComponents} \subitem for an rcwa mapping and a modulus, \hyperpage{26} \item \texttt {FixedPointsOfAffinePartialMappings} \subitem for an rcwa mapping, \hyperpage{18} \item \texttt{FloatQuotients}, \hyperpage{108} \indexspace \item \texttt{GeneratorsAndInverses} \subitem for a group, \hyperpage{108} \item \texttt {GluckTaylorInvariant} \subitem of a trajectory, \hyperpage{27} \item \texttt{Group}, \hyperpage{30} \item \texttt{GroupByGenerators}, \hyperpage{30} \item \texttt{GroupWithGenerators}, \hyperpage{30} \item \texttt {GuessedDivergence} \subitem of an rcwa mapping, \hyperpage{28} \indexspace \item \texttt{Image} \subitem of an rcwa mapping, \hyperpage{15} \item \texttt {ImageDensity} \subitem of an rcwa mapping, \hyperpage{23} \item \texttt {IncreasingOn} \subitem for an rcwa mapping, \hyperpage{25} \item \texttt{Index} \subitem for rcwa groups, \hyperpage{36} \item \texttt {Induction} \subitem of an rcwa group, by an injective rcwa mapping, \hyperpage{33} \subitem of an rcwa mapping, by an injective rcwa mapping, \hyperpage{33} \item \texttt{Induction} \subitem for an rcwa monoid, by an injective rcwa mapping, \hyperpage{49} \item \texttt {InfoRCWA}, \hyperpage{106} \item \texttt{InjectiveAsMappingFrom} \subitem for an rcwa mapping, \hyperpage{24} \item integral \subitem definition, \hyperpage{17} \item \texttt{IntegralConjugate} \subitem of a tame rcwa group, \hyperpage{45} \subitem of a tame rcwa permutation, \hyperpage{45} \item \texttt{IntegralizingConjugator} \subitem of a tame rcwa group, \hyperpage{45} \subitem of a tame rcwa permutation, \hyperpage{45} \item \texttt{IsBalanced} \subitem for an rcwa mapping, \hyperpage{17} \item \texttt{IsBijective} \subitem for an rcwa mapping, \hyperpage{15} \item \texttt{IsClassReflection} \subitem for an rcwa mapping, \hyperpage{12} \item \texttt{IsClassRotation} \subitem for an rcwa mapping, \hyperpage{12} \item \texttt{IsClassShift} \subitem for an rcwa mapping, \hyperpage{12} \item \texttt{IsClassTransposition} \subitem for an rcwa mapping, \hyperpage{12} \item \texttt{IsClassWiseOrderPreserving} \subitem for an rcwa group, \hyperpage{33} \subitem for an rcwa mapping, \hyperpage{17} \subitem for an rcwa monoid, \hyperpage{49} \item \texttt{IsConjugate} \subitem for elements of CT(R), \hyperpage{36} \subitem for elements of RCWA(R), \hyperpage{36} \item \texttt{IsGeneralizedClassTransposition} \subitem for an rcwa mapping, \hyperpage{12} \item \texttt{IsInjective} \subitem for an rcwa mapping, \hyperpage{15} \item \texttt{IsIntegral} \subitem for an rcwa group, \hyperpage{33} \subitem for an rcwa mapping, \hyperpage{17} \subitem for an rcwa monoid, \hyperpage{49} \item \texttt{IsNaturalCT}, \hyperpage{47} \item \texttt{IsNaturalRCWA}, \hyperpage{47} \item \texttt{IsomorphismMatrixGroup} \subitem for an rcwa group, \hyperpage{36} \item \texttt{IsomorphismPermGroup} \subitem for a finite rcwa group, \hyperpage{35} \item \texttt {IsomorphismRcwaGroup} \subitem for a group, \hyperpage{31} \subitem for a group, over a given ring, \hyperpage{31} \item \texttt{IsPerfect} \subitem for an rcwa group, \hyperpage{36} \item \texttt{IsPrimeSwitch} \subitem for an rcwa mapping, \hyperpage{21} \item \texttt {IsRcwaGroup}, \hyperpage{47} \item \texttt {IsRcwaGroupOverGFqx}, \hyperpage{47} \item \texttt {IsRcwaGroupOverZ}, \hyperpage{47} \item \texttt{IsRcwaGroupOverZOrZ{\textunderscore}pi}, \hyperpage{47} \item \texttt {IsRcwaGroupOverZ{\textunderscore }pi}, \hyperpage{47} \item \texttt {IsRcwaMapping}, \hyperpage{29} \item \texttt {IsRcwaMappingOfGFqx}, \hyperpage{29} \item \texttt {IsRcwaMappingOfZ}, \hyperpage{29} \item \texttt{IsRcwaMappingOfZOrZ{\textunderscore}pi}, \hyperpage{29} \item \texttt {IsRcwaMappingOfZ{\textunderscore }pi}, \hyperpage{29} \item \texttt{IsRcwaMappingStandardRep}, \hyperpage{29} \item \texttt{IsSignPreserving} \subitem for an rcwa group, \hyperpage{33} \subitem for an rcwa mapping, \hyperpage{17} \subitem for an rcwa monoid, \hyperpage{49} \item \texttt{IsSolvable} \subitem for an rcwa group, \hyperpage{36} \item \texttt{IsSubset} \subitem for two rcwa monoids, \hyperpage{49} \item \texttt{IsSurjective} \subitem for an rcwa mapping, \hyperpage{15} \item \texttt{IsTame} \subitem for an rcwa group, \hyperpage{36} \subitem for an rcwa mapping, \hyperpage{15} \subitem for an rcwa monoid, \hyperpage{49} \item \texttt{IsTransitive} \subitem for an rcwa group, on its underlying ring, \hyperpage{39} \indexspace \item \texttt {KernelOfActionOnRespectedPartition} \subitem for a tame rcwa group, \hyperpage{45} \indexspace \item \texttt {LargestSourcesOfAffineMappings} \subitem for an rcwa mapping, \hyperpage{18} \item \texttt{LaTeX} \subitem for an rcwa mapping, \hyperpage{14} \item \texttt{LaTeXAndXDVI} \subitem for an rcwa mapping, \hyperpage{15} \item \texttt{LaTeXObj} \subitem for an rcwa mapping, \hyperpage{14} \item \texttt {LikelyContractionCentre} \subitem of an rcwa mapping, \hyperpage{28} \item \texttt{ListOfPowers}, \hyperpage{108} \item \texttt {LocalizedRcwaMapping} \subitem for an rcwa mapping of Z and a prime, \hyperpage{14} \item \texttt {Loops} \subitem of an rcwa mapping, \hyperpage{27} \indexspace \item \texttt {mKnot} \subitem for an odd integer, \hyperpage{22} \item \texttt{Mod} \subitem for an rcwa group, \hyperpage{33} \subitem for an rcwa mapping, \hyperpage{17} \item \texttt{Modulus} \subitem of an rcwa group, \hyperpage{33} \subitem of an rcwa mapping, \hyperpage{17} \subitem of an rcwa monoid, \hyperpage{49} \item modulus \subitem definition, \hyperpage{8} \item \texttt{ModulusOfRcwaMonoid} \subitem for an rcwa group, \hyperpage{33} \item \texttt{Monoid}, \hyperpage{48} \item \texttt{MonoidByGenerators}, \hyperpage{48} \item \texttt{MovedPoints} \subitem of an rcwa group, \hyperpage{39} \subitem of an rcwa mapping, \hyperpage{16} \item \texttt{Mult} \subitem for an rcwa group, \hyperpage{33} \subitem for an rcwa mapping, \hyperpage{17} \item \texttt{Multiplier} \subitem of an rcwa group, \hyperpage{33} \subitem of an rcwa mapping, \hyperpage{17} \item multiplier \subitem definition, \hyperpage{8} \item \texttt {Multpk} \subitem for an rcwa mapping, a prime and an exponent, \hyperpage{19} \indexspace \item \texttt{Name} \subitem for cs / cr / ct, \hyperpage{12} \item \texttt{NrConjugacyClassesOfRCWAZOfOrder}, \hyperpage{36} \indexspace \item \texttt{ObjByExtRep}, \hyperpage{29} \item \texttt {Orbit} \subitem for an rcwa group and a point, \hyperpage{39} \subitem for an rcwa group and a set, \hyperpage{39} \item \texttt {OrbitsModulo} \subitem for an rcwa mapping and a modulus, \hyperpage{26} \item \texttt{OrbitsModulo} \subitem for an rcwa group and a modulus, \hyperpage{43} \item \texttt{Order} \subitem of an rcwa permutation, \hyperpage{15} \indexspace \item \texttt{PermutationOpNC} \subitem g, P, OnPoints, \hyperpage{44} \item \texttt{PreImage} \subitem of a residue class union under an rcwa mapping, \hyperpage{16} \subitem of a set of ring elements under an rcwa mapping, \hyperpage{16} \item \texttt{PreImageElm} \subitem of a ring element under an rcwa mapping, \hyperpage{16} \item \texttt{PreImagesElm} \subitem of a ring element under an rcwa mapping, \hyperpage{16} \item \texttt {PreImagesRepresentative} \subitem for an epi. from a free group to an rcwa group, \hyperpage{38} \item \texttt{PreImagesRepresentatives} \subitem for an epi. from a free group to an rcwa group, \hyperpage{38} \item \texttt{PrimeSet} \subitem of an rcwa group, \hyperpage{33} \subitem of an rcwa mapping, \hyperpage{17} \subitem of an rcwa monoid, \hyperpage{49} \item \texttt {PrimeSwitch} \subitem p, \hyperpage{21} \subitem p, k, \hyperpage{21} \item \texttt{Print} \subitem for an rcwa group, \hyperpage{30} \subitem for an rcwa mapping, \hyperpage{14} \subitem for an rcwa monoid, \hyperpage{48} \item \texttt {Projections} \subitem for an rcwa group and a modulus, \hyperpage{43} \indexspace \item \texttt{Random} \subitem CT(R), \hyperpage{46} \subitem RCWA(R), \hyperpage{46} \item \texttt {RCWA} \subitem the group of all rcwa permutations of a ring, \hyperpage{30} \item \texttt {Rcwa} \subitem the monoid of all rcwa mappings of a ring, \hyperpage{49} \item rcwa group \subitem class-wise order-preserving, \hyperpage{33} \subitem coercion, \hyperpage{17} \subitem conjugacy problem, \hyperpage{36} \subitem definition, \hyperpage{8} \subitem divisor, \hyperpage{33} \subitem integral, \hyperpage{33} \subitem membership test, \hyperpage{35} \subitem modulus, \hyperpage{33} \subitem multiplier, \hyperpage{33} \subitem prime set, \hyperpage{33} \subitem tame, \hyperpage{8} \subitem wild, \hyperpage{8} \item rcwa mapping \subitem arithmetic operations, \hyperpage{15} \subitem balanced, \hyperpage{17} \subitem class-wise order-preserving, \hyperpage{17} \subitem coercion, \hyperpage{17} \subitem definition, \hyperpage{8} \subitem divisor, \hyperpage{8} \subitem images under, \hyperpage{16} \subitem integral, \hyperpage{17} \subitem modulus, \hyperpage{8} \subitem multiplier, \hyperpage{8} \subitem prime set, \hyperpage{17} \subitem tame, \hyperpage{8} \subitem transition graph, \hyperpage{25} \subitem wild, \hyperpage{8} \item rcwa monoid \subitem class-wise order-preserving, \hyperpage{49} \subitem definition, \hyperpage{48} \subitem integral, \hyperpage{49} \subitem modulus, \hyperpage{49} \subitem prime set, \hyperpage{49} \subitem sign-preserving, \hyperpage{49} \subitem tame, \hyperpage{49} \subitem wild, \hyperpage{49} \item \texttt{rcwa monoids} \subitem membership test, \hyperpage{49} \item \texttt {RCWABuildManual}, \hyperpage{107} \item \texttt{RCWAInfo}, \hyperpage{106} \item \texttt {RcwaMapping} \subitem by finite field size, modulus and list of coefficients, \hyperpage{13} \subitem by list of coefficients, \hyperpage{13} \subitem by modulus and list of values, \hyperpage{13} \subitem by permutation and range, \hyperpage{13} \subitem by residue class cycles, \hyperpage{13} \subitem by ring and list of coefficients, \hyperpage{13} \subitem by ring, modulus and list of coefficients, \hyperpage{13} \subitem by set of noninvertible primes and list of coefficients, \hyperpage{13} \subitem by two partitions of a ring into residue classes, \hyperpage{13} \item \texttt {RcwaMappingsFamily} \subitem of a ring, \hyperpage{29} \item \texttt {RCWATest}, \hyperpage{106} \item \texttt{ReadFromBitmapPicture} \subitem filename, \hyperpage{107} \item \texttt {RepresentativeAction} \subitem for RCWA(R) and 2 partitions of R into residue classes, \hyperpage{43} \subitem G, source, destination, action, \hyperpage{41} \item \texttt{RepresentativeActionPreImage} \subitem G, source, destination, action, F, \hyperpage{41} \item \texttt {RespectedPartition} \subitem of a tame rcwa group, \hyperpage{44} \subitem of a tame rcwa permutation, \hyperpage{44} \item \texttt{RespectedPartitionLong} \subitem for a tame rcwa group, \hyperpage{44} \subitem for a tame rcwa permutation, \hyperpage{44} \item \texttt{RespectedPartitionShort} \subitem for a tame rcwa group, \hyperpage{44} \subitem for a tame rcwa permutation, \hyperpage{44} \item \texttt{RespectsPartition} \subitem for an rcwa group, \hyperpage{44} \subitem for an rcwa permutation, \hyperpage{44} \item \texttt{RestrictedPerm} \subitem for an rcwa permutation and a residue class union, \hyperpage{16} \item \texttt {Restriction} \subitem of an rcwa group, by an injective rcwa mapping, \hyperpage{33} \subitem of an rcwa mapping, by an injective rcwa mapping, \hyperpage{33} \item \texttt{Restriction} \subitem for an rcwa monoid, by an injective rcwa mapping, \hyperpage{49} \item \texttt {RightInverse} \subitem of an injective rcwa mapping, \hyperpage{23} \item \texttt {Root} \subitem k-th root of an rcwa mapping, \hyperpage{22} \item \texttt{RotationFactor} \subitem of a class rotation, \hyperpage{12} \item \texttt {RunDemonstration} \subitem filename, \hyperpage{107} \indexspace \item \texttt {SaveAsBitmapPicture} \subitem picture, filename, \hyperpage{107} \item \texttt {SemilocalizedRcwaMapping} \subitem for an rcwa mapping of Z and a set of primes, \hyperpage{14} \item \texttt {ShortCycles} \subitem for rcwa permutation and bound on length, \hyperpage{40} \subitem for rcwa permutation, set of points and bound on length, \hyperpage{40} \item \texttt {ShortOrbits} \subitem for rcwa group, set of points and bound on length, \hyperpage{40} \subitem for rcwa monoid, set of points and bound on length, \hyperpage{50} \item \texttt {Sign} \subitem of an rcwa permutation of Z, \hyperpage{20} \item \texttt {Sinks} \subitem of an rcwa mapping, \hyperpage{27} \item \texttt{Size} \subitem for an rcwa group, \hyperpage{35} \subitem for an rcwa monoid, \hyperpage{49} \item \texttt {Sources} \subitem of an rcwa mapping, \hyperpage{27} \item \texttt{SplittedClassTransposition} \subitem for a class transposition and a number of factors, \hyperpage{11} \item \texttt{String} \subitem for an rcwa group, \hyperpage{30} \subitem for an rcwa mapping, \hyperpage{14} \subitem for an rcwa monoid, \hyperpage{48} \item \texttt {StructureDescription} \subitem for an rcwa group, \hyperpage{34} \item \texttt{Support} \subitem of an rcwa group, \hyperpage{39} \subitem of an rcwa mapping, \hyperpage{16} \subitem of an rcwa monoid, \hyperpage{49} \indexspace \item tame \subitem rcwa group, \hyperpage{8} \subitem rcwa mapping, \hyperpage{8} \item \texttt {Trajectory} \subitem for rcwa mapping, starting point, length, \hyperpage{24} \subitem for rcwa mapping, starting point, length, coeff.-spec., \hyperpage{24} \subitem for rcwa mapping, starting point, length, modulus, \hyperpage{24} \subitem for rcwa mapping, starting point, set of end points, \hyperpage{24} \subitem for rcwa mapping, starting point, set of end points, coeff.-spec., \hyperpage{24} \subitem for rcwa mapping, starting point, set of end points, modulus, \hyperpage{24} \item \texttt {TransitionGraph} \subitem for an rcwa mapping and a modulus, \hyperpage{25} \item \texttt {TransitionMatrix} \subitem for an rcwa mapping and a modulus, \hyperpage{26} \item \texttt{TransposedClasses} \subitem of a class transposition, \hyperpage{11} \indexspace \item \texttt{View} \subitem for an rcwa group, \hyperpage{30} \subitem for an rcwa mapping, \hyperpage{14} \subitem for an rcwa monoid, \hyperpage{48} \indexspace \item wild \subitem rcwa group, \hyperpage{8} \subitem rcwa mapping, \hyperpage{8} \item \texttt {WreathProduct} \subitem for an rcwa group over Z and a permutation group, \hyperpage{32} \subitem for an rcwa group over Z and the infinite cyclic group, \hyperpage{32} \end{theindex}