  
  
  [1XIndex[101X
  
  [2XActionOnRespectedPartition[102X, for a tame rcwa group 3.4-2 
  [10XAllElementsOfCTZWithGivenModulus[110X 3.1-9 
  [10XAssignGlobals[110X 7. 
  balanced, definition 2.4 
  [2XBall[102X, 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 
  [10XClassPairs[110X, m 2.2-3 
  [2XClassReflection[102X, cl 2.2-2 
      r, m 2.2-2 
  [2XClassRotation[102X, 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 
  [2XClassShift[102X, 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 
  [2XClassTransposition[102X, 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 
  [10XClassWiseConstantOn[110X 2.4-3 
      for rcwa mappings of Z x Z 5.3 
  [10XClassWiseOrderPreservingOn[110X 2.4-3 
      for rcwa mappings of Z x Z 5.3 
  [10XClassWiseOrderReversingOn[110X 2.4-3 
      for rcwa mappings of Z x Z 5.3 
  [10XCoefficients[110X, of an rcwa mapping 2.3 
      of an rcwa mapping of Z x Z 5.3 
  Collatz mapping 1. 
  Collatz conjecture 1. 
  [2XCollatzLikeMappingByOrbitTree[102X, for rcwa group, root point and range of radii 3.3-13 
  [2XCommonRightInverse[102X, of two injective rcwa mappings 2.7-2 
  [2XComputeCycleLength[102X, for an rcwa permutation and a point 3.3-6 
  [2XCT[102X, subgroup of CT(Z) 3.1-9 
      the group generated by all class transpositions of a ring 3.1-9 
  [10XCT[110X, the group generated by all class transpositions of Z x Z 5.4 
  [2XCTCSCRSplit[102X, for an rcwa permutation of Z 2.5-1 
  [2XCycleRepresentativesAndLengths[102X, for rcwa permutation and set of seed points 3.3-7 
  [10XCyclesOnFiniteOrbit[110X 3.3-4 
  [2XDecreasingOn[102X, for an rcwa mapping 2.8-3 
  [10XDensityOfSetOfFixedPoints[110X, of an rcwa mapping 2.3 
  [10XDensityOfSupport[110X, of an rcwa mapping 2.3 
  [10XDerivedSubgroup[110X, of an rcwa group 3.2-1 
  [2XDeterminant[102X, of an rcwa mapping of Z 2.4-4 
  [2XDirectProduct[102X, for rcwa groups over Z 3.1-2 
  [10XDisplay[110X, 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 
  [10XDistanceToNextSmallerPointInOrbit[110X 3.3-2 
  [10XDiv[110X, for an rcwa group 3.1-7 
      for an rcwa mapping 2.4 
  divisor, definition 2.1 
  [10XDivisor[110X, 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 
  [2XDrawGrid[102X, P, yrange, xrange, filename 5.4-2 
      U, yrange, xrange, filename 5.4-2 
  [10XDrawOrbitPicture[110X, for rcwa groups over Z x Z 5.4-1 
  [2XDrawOrbitPicture[102X, G, p0, bound, h, w, colored, palette, filename 3.3-3 
  [2XEpimorphismFromFpGroup[102X, 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 
  [10XExponent[110X, of an rcwa group 3.2-1 
  [10XExtRepOfObj[110X 2.10-1 
      for a class transposition 2.2-3 
  [2XFactorization[102X, for an rcwa permutation of Z 2.5-2 
  [2XFactorizationIntoCSCRCT[102X, for an rcwa permutation of Z 2.5-2 
  [2XFactorizationOnConnectedComponents[102X, for an rcwa mapping and a modulus 2.8-6 
  [2XFixedPointsOfAffinePartialMappings[102X, for an rcwa mapping 2.4-2 
  [2XFixedResidueClasses[102X, for rcwa group and bound on modulus 3.3-8 
      for rcwa mapping and bound on modulus 3.3-8 
  [2XGluckTaylorInvariant[102X, of a trajectory 2.8-10 
  [10XGroup[110X 3.1 
  [10XGroupByGenerators[110X 3.1 
  [2XGroupByResidueClasses[102X, the group `permuting a given list of residue classes' 3.1-5 
  [10XGroupWithGenerators[110X 3.1 
  [2XGrowthFunctionOfOrbit[102X, 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 
  [2XGuessedDivergence[102X, of an rcwa mapping 2.8-12 
  [10XImage[110X, of an rcwa mapping 2.3 
  [2XImageDensity[102X, of an rcwa mapping 2.7-3 
  [2XIncreasingOn[102X, for an rcwa mapping 2.8-3 
  [10XIndex[110X, for rcwa groups 3.2-1 
  [10XInduction[110X, for an rcwa monoid, by an injective rcwa mapping 4.1-1 
  [2XInduction[102X, of an rcwa group, by an injective rcwa mapping 3.1-7 
      of an rcwa mapping, by an injective rcwa mapping 3.1-7 
  [2XInfoRCWA[102X 9.5-1 
  [10XInjectiveAsMappingFrom[110X, for an rcwa mapping 2.7-3 
  integral, definition 2.4 
  [10XIntegralConjugate[110X, of a tame rcwa group 3.4-2 
      of a tame rcwa permutation 3.4-2 
  [10XIntegralizingConjugator[110X, of a tame rcwa group 3.4-2 
      of a tame rcwa permutation 3.4-2 
  [10XIsBalanced[110X, for an rcwa mapping 2.4 
      for an rcwa mapping of Z x Z 5.3 
  [10XIsBijective[110X, for an rcwa mapping 2.3 
      for an rcwa mapping of Z x Z 5.3 
  [10XIsClassReflection[110X, for an rcwa mapping 2.2-4 
  [10XIsClassRotation[110X, for an rcwa mapping 2.2-4 
      for an rcwa mapping of Z x Z 5.2-4 
  [10XIsClassShift[110X, for an rcwa mapping 2.2-4 
      for an rcwa mapping of Z x Z 5.2-4 
  [10XIsClassTransposition[110X, for an rcwa mapping 2.2-4 
      for an rcwa mapping of Z x Z 5.2-4 
  [10XIsClassWiseOrderPreserving[110X, 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 
  [10XIsClassWiseTranslating[110X, for an rcwa group 3.1-7 
      for an rcwa group over Z x Z 5.4 
      for an rcwa mapping 2.4 
  [10XIsConjugate[110X, for elements of CT(R) 3.2-1 
      for elements of RCWA(R) 3.2-1 
  [10XIsGeneralizedClassTransposition[110X, for an rcwa mapping 2.2-4 
  [10XIsInjective[110X, for an rcwa mapping 2.3 
      for an rcwa mapping of Z x Z 5.3 
  [10XIsIntegral[110X, 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 
  [10XIsNaturalCT[110X 3.6-1 
  [10XIsNaturalRCWA[110X 3.6-1 
  [10XIsomorphismMatrixGroup[110X, for an rcwa group 3.2-1 
  [10XIsomorphismPermGroup[110X, for a finite rcwa group 3.2-1 
  [2XIsomorphismRcwaGroup[102X, 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 
  [10XIsOne[110X, for an rcwa mapping of Z x Z 5.3 
  [10XIsPerfect[110X, for an rcwa group 3.2-1 
  [10XIsPrimeSwitch[110X, for an rcwa mapping 2.5-3 
  [2XIsRcwaGroup[102X 3.6-1 
  [2XIsRcwaGroupOverGFqx[102X 3.6-1 
  [2XIsRcwaGroupOverZ[102X 3.6-1 
  [2XIsRcwaGroupOverZ_pi[102X 3.6-1 
  [10XIsRcwaGroupOverZOrZ_pi[110X 3.6-1 
  [2XIsRcwaMapping[102X 2.10-1 
  [2XIsRcwaMappingOfGFqx[102X 2.10-1 
  [2XIsRcwaMappingOfZ[102X 2.10-1 
  [2XIsRcwaMappingOfZ_pi[102X 2.10-1 
  [10XIsRcwaMappingOfZOrZ_pi[110X 2.10-1 
  [10XIsRcwaMappingStandardRep[110X 2.10-1 
  [10XIsSignPreserving[110X, for an rcwa group 3.1-7 
      for an rcwa mapping 2.4 
      for an rcwa monoid 4.2 
  [10XIsSolvable[110X, for an rcwa group 3.2-1 
  [10XIsSubset[110X, for two rcwa monoids 4.2 
  [10XIsSurjective[110X, for an rcwa mapping 2.3 
      for an rcwa mapping of Z x Z 5.3 
  [10XIsTame[110X, 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 
  [10XIsTransitive[110X, for an rcwa group, on its underlying ring 3.3 
  [10XIsTransitiveOnNonnegativeIntegersInSupport[110X, for an rcwa group over Z 3.3 
  [10XIsZero[110X, for an rcwa mapping of Z x Z 5.3 
  [2XKernelOfActionOnRespectedPartition[102X, for a tame rcwa group 3.4-2 
  [2XLargestSourcesOfAffineMappings[102X, for an rcwa mapping 2.4-1 
  [10XLaTeXAndXDVI[110X, for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
  [10XLaTeXStringRcwaMapping[110X, for an rcwa mapping 2.2-6 
      for an rcwa mapping of Z x Z 5.3 
  [2XLikelyContractionCentre[102X, of an rcwa mapping 2.8-11 
  [2XLoadDatabaseOfGroupsGeneratedBy3ClassTranspositions[102X, both databases 6.2-2 
      small database 6.2-1 
  [2XLoadDatabaseOfGroupsGeneratedBy4ClassTranspositions[102X 6.2-3 
  [2XLoadDatabaseOfNonbalancedProductsOfClassTranspositions[102X 6.3-2 
  [2XLoadDatabaseOfProductsOf2ClassTranspositions[102X 6.3-1 
  [2XLoadRCWAExamples[102X 6.1-1 
  [10XLoadRCWAExamples[110X 7. 
  [2XLocalizedRcwaMapping[102X, for an rcwa mapping of Z and a prime 2.2-6 
  [2XLoops[102X, of an rcwa mapping 2.8-9 
  maximal shift, definition 2.4 
  [10XMaximalShift[110X, of an rcwa mapping of Z 2.4 
  [2XMergerExtension[102X, for finite permutation groups 3.1-4 
  [10XMirrored[110X 3.1-9 
  [2XmKnot[102X, for an odd integer 2.5-4 
  [10XMod[110X, for an rcwa group 3.1-7 
      for an rcwa mapping 2.3 
  modulus, definition 2.1 
  [10XModulus[110X, 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 
  [10XModulusOfRcwaMonoid[110X, for an rcwa group 3.1-7 
  [10XMonoid[110X 4.1 
  [10XMonoidByGenerators[110X 4.1 
  [10XMovedPoints[110X, of an rcwa group 3.3 
      of an rcwa mapping 2.3 
      of an rcwa mapping of Z x Z 5.3 
  [10XMult[110X, for an rcwa group 3.1-7 
      for an rcwa mapping 2.4 
  multiplier, definition 2.1 
  [10XMultiplier[110X, 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 
  [2XMultpk[102X, for an rcwa mapping, a prime and an exponent 2.4-3 
  [10XMultpk[110X, for rcwa mapping of Z x Z, prime and exponent 5.3 
  [10XNrClassPairs[110X, m 2.2-3 
  [10XNrConjugacyClassesOfRCWAZOfOrder[110X 3.1-8 
  [10XNrConjugacyClassesOfCTZOfOrder[110X 3.1-9 
  [10XNrElementsOfCTZWithGivenModulus[110X 3.1-9 
  [10XObjByExtRep[110X 2.10-1 
  [10XOne[110X, for an rcwa mapping of Z x Z 5.3 
  [2XOrbit[102X, for an rcwa group and a point 3.3-1 
      for an rcwa group and a set 3.3-1 
  [10XOrbitLengthBound[110X 3.2-1 
  [10XOrbitsModulo[110X, for an rcwa group and a modulus 3.3-11 
  [2XOrbitsModulo[102X, for an rcwa mapping and a modulus 2.8-5 
  [10XOrder[110X, of an rcwa mapping of Z x Z 5.3 
      of an rcwa permutation 2.3 
  [10XPermutationOpNC[110X, g, P, OnPoints 3.4-1 
  [10XPreImage[110X, of a residue class union under an rcwa mapping 2.3 
      of a set of ring elements under an rcwa mapping 2.3 
  [10XPreImageElm[110X, of a ring element under an rcwa mapping 2.3 
  [10XPreImagesElm[110X, of a ring element under an rcwa mapping 2.3 
  [2XPreImagesRepresentative[102X, for an epi. from a free group to an rcwa group 3.2-3 
  [10XPreImagesRepresentatives[110X, for an epi. from a free group to an rcwa group 3.2-3 
  prime set, definition 5.1 
  [10XPrimeSet[110X, 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 
  [2XPrimeSwitch[102X, p 2.5-3 
      p, cl 2.5-3 
      p, k 2.5-3 
      p, r, m 2.5-3 
  [10XPrint[110X, 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 
  [2XProjectionsToCoordinates[102X, for an rcwa mapping of Z x Z 5.3-1 
  [2XProjectionsToInvariantUnionsOfResidueClasses[102X, for rcwa group and modulus 3.3-11 
  [10XRandom[110X, CT(R) 3.5 
      RCWA(R) 3.5 
  [2XRankOfKernelOfActionOnRespectedPartition[102X, for a tame rcwa group 3.4-2 
  [2XRCWA[102X, the group formed by all rcwa permutations of a ring 3.1-8 
  [10XRCWA[110X, the group formed by all rcwa permutations of Z x Z 5.4 
  [2XRcwa[102X, the monoid formed by all rcwa mappings of a ring 4.1-1 
  [10XRcwa[110X, 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 
  [10Xrcwa monoids[110X, membership test 4.2 
  [2XRCWABuildManual[102X 9.3-1 
  [10XRCWAInfo[110X 9.5-1 
  [2XRcwaMapping[102X, 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 
  [10XRcwaMapping[110X, by list of coefficients, sparse representation 2.9 
  [2XRcwaMapping[102X, 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 
  [2XRcwaMappingsFamily[102X, of a ring 2.10-2 
  [2XRCWATestAll[102X 9.4-2 
  [2XRCWATestExamples[102X 9.4-3 
  [2XRCWATestInstall[102X 9.4-1 
  [2XRepresentativeAction[102X, for RCWA(R) and 2 partitions of R into residue classes 3.3-12 
      G, source, destination, action 3.3-10 
  [10XRepresentativeActionPreImage[110X, G, source, destination, action, F 3.3-10 
  [2XRespectedPartition[102X, of a tame rcwa group 3.4-1 
      of a tame rcwa permutation 3.4-1 
  [10XRespectsPartition[110X, for an rcwa group 3.4-1 
      for an rcwa permutation 3.4-1 
  [10XRestrictedBall[110X, G, g, r, modulusbound 3.3-9 
  [10XRestrictedPerm[110X, for an rcwa permutation and a residue class union 2.3 
  [10XRestriction[110X, for an rcwa monoid, by an injective rcwa mapping 4.1-1 
  [2XRestriction[102X, of an rcwa group, by an injective rcwa mapping 3.1-6 
      of an rcwa mapping, by an injective rcwa mapping 3.1-6 
  [2XRightInverse[102X, of an injective rcwa mapping 2.7-1 
  [2XRoot[102X, k-th root of an rcwa mapping 2.6-1 
  [10XRotationFactor[110X, of a class rotation 2.2-4 
      of a class rotation of Z x Z 5.2-3 
  [2XSemilocalizedRcwaMapping[102X, for an rcwa mapping of Z and a set of primes 2.2-6 
  [10XShiftsDownOn[110X 2.4-3 
  [10XShiftsUpOn[110X 2.4-3 
  [10XShortCycles[110X, for rcwa perm. of Z x Z, set of points and max. length 5.3 
  [2XShortCycles[102X, 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 
  [2XShortOrbits[102X, 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 
  [2XShortResidueClassCycles[102X, for rcwa permutation and bounds on modulus and length 3.3-5 
  [2XShortResidueClassOrbits[102X, for rcwa group and bounds on modulus and length 3.3-5 
  [2XSign[102X, of an rcwa permutation of Z 2.4-5 
  sign-preserving, definition 2.4 
  [10XSimplifiedCertificate[110X, for a transitivity certificate of an rcwa groups over Z 3.3 
  [2XSinks[102X, of an rcwa mapping 2.8-8 
  [10XSize[110X, for an rcwa group 3.2-1 
      for an rcwa group over Z x Z 5.4 
      for an rcwa monoid 4.2 
  [10XSmallGeneratingSet[110X 3.1-7 
  [2XSources[102X, of an rcwa mapping 2.8-8 
  [2XSparseRep[102X, of an rcwa mapping 2.9-1 
  [2XSparseRepresentation[102X, of an rcwa mapping 2.9-1 
  [10XSplittedClassTransposition[110X, for a class transposition and a number of factors 2.2-3 
      for a class transposition of Z x Z 5.2-2 
  [2XStandardRep[102X, of an rcwa mapping 2.9-1 
  [2XStandardRepresentation[102X, of an rcwa mapping 2.9-1 
  [10XString[110X, 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 
  [2XStructureDescription[102X, for an rcwa group 3.2-1 
  [10XSupport[110X, 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 
  [2XTrajectory[102X, 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 
  [10XTrajectory[110X, for rcwa mappings of Z x Z 5.3 
  [2XTransitionGraph[102X, for an rcwa mapping and a modulus 2.8-4 
  [2XTransitionMatrix[102X, for an rcwa mapping and a modulus 2.8-7 
  [10XTransitivityCertificate[110X, for an rcwa group over Z and a search limit 3.3 
  [10XTransposedClasses[110X, of a class transposition 2.2-3 
      of a class transposition of Z x Z 5.2-2 
  [10XTryIsTransitiveOnNonnegativeIntegersInSupport[110X, for an rcwa group over Z and a search limit 3.3 
  [10XTryToComputeTransitivityCertificate[110X, for an rcwa group over Z and a search limit 3.3 
  [10XView[110X, 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 
  [2XWreathProduct[102X, 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 
  [10XZero[110X, for an rcwa mapping of Z x Z 5.3 
  
  
  -------------------------------------------------------
