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### Index

`ActionOnRespectedPartition`, for a tame rcwa group 3.4-2
`AllProducts` 7.8
`balanced`, definition 2.4
`Ball`, for group, element and radius 3.3-4
`Ball`, for group, point, radius and action 3.3-4
`Ball`, for monoid, element and radius 4.2-2
`Ball`, for monoid, point, radius and action 4.2-2
`ClassPairs`, R, m 3.5
`ClassPairs`, m 3.5
`ClassReflection`, cl 2.2-2
`ClassReflection`, r, m 2.2-2
`ClassRotation`, cl, u 2.2-4
`ClassRotation`, r, m, u 2.2-4
`ClassShift`, cl 2.2-1
`ClassShift`, r, m 2.2-1
`ClassTransposition`, cl1, cl2 2.2-3
`ClassTransposition`, r1, m1, r2, m2 2.2-3
`ClassWiseConstantOn` 2.4-3
`ClassWiseOrderPreservingOn` 2.4-3
`ClassWiseOrderReversingOn` 2.4-3
`Coefficients`, of an rcwa mapping 2.3
Collatz conjecture 1.1
Collatz mapping 1.1
`CommonRightInverse`, of two injective rcwa mappings 2.7-2
`CT`, the group generated by all class transpositions of a ring 3.1-2
`DecreasingOn`, for an rcwa mapping 2.8-3
`DerivedSubgroup`, of an rcwa group 3.2-1
`Determinant`, of an rcwa mapping of Z 2.4-4
`DifferencesList` 7.8
`DirectProduct`, for rcwa groups over Z 3.1-4
`Display`, for an rcwa group 3.1
`Display`, for an rcwa mapping 2.2-6
`Display`, for an rcwa monoid 4.1
`Div`, for an rcwa group 3.1-7
`Div`, for an rcwa mapping 2.4
divisor, definition 2.1
`Divisor`, of an rcwa group 3.1-7
`Divisor`, of an rcwa mapping 2.4
`DrawOrbitPicture`, G, p0, r, h, w, colored, palette, filename 3.3-2
`EpimorphismByGenerators`, for two groups 7.8
`EpimorphismFromFpGroup`, for an rcwa group and a search radius 3.2-2
`EquivalenceClasses`, for a list and a function computing a class invariant 7.8
`EquivalenceClasses`, for a list and a function describing an equivalence relation 7.8
`Exponent`, of an rcwa group 3.2-1
`ExtRepOfObj` 2.9-1
`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
`FloatQuotients` 7.8
`GeneratorsAndInverses`, for a group 7.8
`GluckTaylorInvariant`, of a trajectory 2.8-10
`Group` 3.1
`GroupByGenerators` 3.1
`GroupWithGenerators` 3.1
`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
`Induction`, of an rcwa mapping, by an injective rcwa mapping 3.1-7
`InfoRCWA` 7.3-1
`InjectiveAsMappingFrom`, for an rcwa mapping 2.7-3
integral, definition 2.4
`IntegralConjugate`, of a tame rcwa group 3.4-2
`IntegralConjugate`, of a tame rcwa permutation 3.4-2
`IntegralizingConjugator`, of a tame rcwa group 3.4-2
`IntegralizingConjugator`, of a tame rcwa permutation 3.4-2
`IsBalanced`, for an rcwa mapping 2.4
`IsBijective`, for an rcwa mapping 2.3
`IsClassReflection`, for an rcwa mapping 2.2-4
`IsClassRotation`, for an rcwa mapping 2.2-4
`IsClassShift`, for an rcwa mapping 2.2-4
`IsClassTransposition`, for an rcwa mapping 2.2-4
`IsClassWiseOrderPreserving`, for an rcwa group 3.1-7
`IsClassWiseOrderPreserving`, for an rcwa mapping 2.4
`IsClassWiseOrderPreserving`, for an rcwa monoid 4.2
`IsConjugate`, for elements of CT(R) 3.2-1
`IsConjugate`, for elements of RCWA(R) 3.2-1
`IsGeneralizedClassTransposition`, for an rcwa mapping 2.2-4
`IsInjective`, for an rcwa mapping 2.3
`IsIntegral`, for an rcwa group 3.1-7
`IsIntegral`, for an rcwa mapping 2.4
`IsIntegral`, 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 3.1-3
`IsomorphismRcwaGroup`, for a group, over a given ring 3.1-3
`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` 2.9-1
`IsRcwaMappingOfGFqx` 2.9-1
`IsRcwaMappingOfZ` 2.9-1
`IsRcwaMappingOfZ_pi` 2.9-1
`IsRcwaMappingOfZOrZ_pi` 2.9-1
`IsRcwaMappingStandardRep` 2.9-1
`IsSignPreserving`, for an rcwa group 3.1-7
`IsSignPreserving`, for an rcwa mapping 2.4
`IsSignPreserving`, 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
`IsTame`, for an rcwa group 3.2-1
`IsTame`, for an rcwa mapping 2.3
`IsTame`, for an rcwa monoid 4.2
`IsTransitive`, for an rcwa group, on its underlying ring 3.3
`KernelOfActionOnRespectedPartition`, for a tame rcwa group 3.4-2
`LargestSourcesOfAffineMappings`, for an rcwa mapping 2.4-1
`LaTeX`, for an rcwa mapping 2.2-6
`LaTeXAndXDVI`, for an rcwa mapping 2.2-6
`LaTeXObj`, for an rcwa mapping 2.2-6
`LikelyContractionCentre`, of an rcwa mapping 2.8-11
`ListOfPowers` 7.8
`LocalizedRcwaMapping`, for an rcwa mapping of Z and a prime 2.2-6
`Loops`, of an rcwa mapping 2.8-9
`mKnot`, for an odd integer 2.5-3
`Mod`, for an rcwa group 3.1-7
`Mod`, for an rcwa mapping 2.3
modulus, definition 2.1
`Modulus`, of an rcwa group 3.1-7
`Modulus`, of an rcwa mapping 2.3
`Modulus`, 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
`MovedPoints`, of an rcwa mapping 2.3
`Mult`, for an rcwa group 3.1-7
`Mult`, for an rcwa mapping 2.4
multiplier, definition 2.1
`Multiplier`, of an rcwa group 3.1-7
`Multiplier`, of an rcwa mapping 2.4
`Multpk`, for an rcwa mapping, a prime and an exponent 2.4-3
`Name`, for cs / cr / ct 2.2-4
`NrConjugacyClassesOfRCWAZOfOrder` 3.2-1
`ObjByExtRep` 2.9-1
`Orbit`, for an rcwa group and a point 3.3-1
`Orbit`, for an rcwa group and a set 3.3-1
`OrbitsModulo`, for an rcwa group and a modulus 3.3-6
`OrbitsModulo`, for an rcwa mapping and a modulus 2.8-5
`Order`, 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
`PreImage`, 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
`PrimeSet`, of an rcwa group 3.1-7
`PrimeSet`, of an rcwa mapping 2.4
`PrimeSet`, of an rcwa monoid 4.2
`PrimeSwitch`, p 2.5-2
`PrimeSwitch`, p, k 2.5-2
`Print`, for an rcwa group 3.1
`Print`, for an rcwa mapping 2.2-6
`Print`, for an rcwa monoid 4.1
`Projections`, for an rcwa group and a modulus 3.3-6
`Random`, CT(R) 3.5
`Random`, RCWA(R) 3.5
`RCWA`, the group of all rcwa permutations of a ring 3.1-1
`Rcwa`, the monoid of all rcwa mappings of a ring 4.1-1
rcwa group, class-wise order-preserving 3.1-7
rcwa group, coercion 2.3
rcwa group, conjugacy problem 3.2-1
rcwa group, definition 2.1
rcwa group, divisor 3.1-7
rcwa group, integral 3.1-7
rcwa group, membership test 3.2-1
rcwa group, modulus 3.1-7
rcwa group, multiplier 3.1-7
rcwa group, prime set 3.1-7
rcwa group, tame 2.1
rcwa group, wild 2.1
rcwa mapping, arithmetic operations 2.3
rcwa mapping, balanced 2.4
rcwa mapping, class-wise order-preserving 2.4
rcwa mapping, coercion 2.3
rcwa mapping, definition 2.1
rcwa mapping, divisor 2.1
rcwa mapping, images under 2.3
rcwa mapping, integral 2.4
rcwa mapping, modulus 2.1
rcwa mapping, multiplier 2.1
rcwa mapping, prime set 2.4
rcwa mapping, tame 2.1
rcwa mapping, transition graph 2.8-4
rcwa mapping, wild 2.1
rcwa monoid, class-wise order-preserving 4.2
rcwa monoid, definition 4.
rcwa monoid, integral 4.2
rcwa monoid, modulus 4.2
rcwa monoid, prime set 4.2
rcwa monoid, sign-preserving 4.2
rcwa monoid, tame 4.2
rcwa monoid, wild 4.2
`rcwa monoids`, membership test 4.2
`RCWABuildManual` 7.5-1
`RCWAInfo` 7.3-1
`RcwaMapping`, by finite field size, modulus and list of coefficients 2.2-5
`RcwaMapping`, by list of coefficients 2.2-5
`RcwaMapping`, by modulus and list of values 2.2-5
`RcwaMapping`, by permutation and range 2.2-5
`RcwaMapping`, by residue class cycles 2.2-5
`RcwaMapping`, by ring and list of coefficients 2.2-5
`RcwaMapping`, by ring, modulus and list of coefficients 2.2-5
`RcwaMapping`, by set of noninvertible primes and list of coefficients 2.2-5
`RcwaMapping`, by two partitions of a ring into residue classes 2.2-5
`RcwaMappingsFamily`, of a ring 2.9-2
`RCWATest` 7.4-1
`ReadFromBitmapPicture`, filename 7.6-1
`RepresentativeAction`, G, source, destination, action 3.3-5
`RepresentativeAction`, for RCWA(R) and 2 partitions of R into residue classes 3.3-7
`RepresentativeActionPreImage`, G, source, destination, action, F 3.3-5
`RespectedPartition`, of a tame rcwa group 3.4-1
`RespectedPartition`, of a tame rcwa permutation 3.4-1
`RespectedPartitionLong`, for a tame rcwa group 3.4-1
`RespectedPartitionLong`, for a tame rcwa permutation 3.4-1
`RespectedPartitionShort`, for a tame rcwa group 3.4-1
`RespectedPartitionShort`, for a tame rcwa permutation 3.4-1
`RespectsPartition`, for an rcwa group 3.4-1
`RespectsPartition`, for an rcwa permutation 3.4-1
`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
`Restriction`, 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
`RunDemonstration`, filename 7.7-1
`SaveAsBitmapPicture`, picture, filename 7.6-1
`SemilocalizedRcwaMapping`, for an rcwa mapping of Z and a set of primes 2.2-6
`ShortCycles`, for rcwa permutation and bound on length 3.3-3
`ShortCycles`, for rcwa permutation, set of points and bound on length 3.3-3
`ShortOrbits`, for rcwa group, set of points and bound on length 3.3-3
`ShortOrbits`, for rcwa monoid, set of points and bound on length 4.2-1
`Sign`, of an rcwa permutation of Z 2.4-5
`Sinks`, of an rcwa mapping 2.8-8
`Size`, for an rcwa group 3.2-1
`Size`, for an rcwa monoid 4.2
`Sources`, of an rcwa mapping 2.8-8
`SplittedClassTransposition`, for a class transposition and a number of factors 2.2-3
`String`, for an rcwa group 3.1
`String`, for an rcwa mapping 2.2-6
`String`, for an rcwa monoid 4.1
`StructureDescription`, for an rcwa group 3.2-1
`Support`, of an rcwa group 3.3
`Support`, of an rcwa mapping 2.3
`Support`, of an rcwa monoid 4.2
tame, rcwa group 2.1
tame, rcwa mapping 2.1
`Trajectory`, for rcwa mapping, starting point, length 2.8-1
`Trajectory`, for rcwa mapping, starting point, length, coeff.-spec. 2.8-2
`Trajectory`, for rcwa mapping, starting point, length, modulus 2.8-1
`Trajectory`, for rcwa mapping, starting point, set of end points 2.8-1
`Trajectory`, for rcwa mapping, starting point, set of end points, coeff.-spec. 2.8-2
`Trajectory`, for rcwa mapping, starting point, set of end points, modulus 2.8-1
`TransitionGraph`, for an rcwa mapping and a modulus 2.8-4
`TransitionMatrix`, for an rcwa mapping and a modulus 2.8-7
`TransposedClasses`, of a class transposition 2.2-3
`View`, for an rcwa group 3.1
`View`, for an rcwa mapping 2.2-6
`View`, for an rcwa monoid 4.1
wild, rcwa group 2.1
wild, rcwa mapping 2.1
`WreathProduct`, for an rcwa group over Z and a permutation group 3.1-5
`WreathProduct`, for an rcwa group over Z and the infinite cyclic group 3.1-5

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