  
  
  [1XIndex[101X
  
  [2X*[102X, for multiple of ideal of affine semigroup 11.5-9 
      for multiple of ideal of numerical semigroup 7.1-22 
  [2X+[102X, for defining ideal of affine semigroup 11.5-1 
      for defining ideal of numerical semigroup 7.1-1 
      for ideals of affine semigroup 11.5-8 
      for ideals of numerical semigroup 7.1-21 
      translation of ideal of affine semigroup 11.5-10 
      translation of ideal of numerical semigroup 7.1-25 
  [2X-[102X, for ideals of numerical semigroup 7.1-23 
  [2X\/[102X, quotient of numerical semigroup 5.2-2 
  [2X\[ \][102X, for ideals of numerical semigroups 7.1-18 
      for numerical semigroups 3.1-8 
  [2X\in[102X, membership for good ideal 12.5-5 
      membership for good semigroup 12.2-1 
      membership test for numerical semigroup 2.2-7 
      membership test in affine semigroup 11.1-16 
      membership test in ideal of affine semigroup 11.5-7 
      membership test in ideal of numerical semigroup 7.1-15 
  [2X\{ \}[102X, for ideals of numerical semigroups 7.1-19 
      for numerical semigroups 3.1-9 
  [2XAbsoluteIrreduciblesOfGoodSemigroup[102X 12.5-8 
  [2XAddSpecialGapOfAffineSemigroup[102X 11.1-13 
  [2XAddSpecialGapOfNumericalSemigroup[102X 5.1-2 
  [2XAdjacentCatenaryDegreeOfSetOfFactorizations[102X 9.3-2 
  [2XAdjustment[102X 9.2-17 
  [2XAdjustmentOfNumericalSemigroup[102X 9.2-17 
  [2XAffineSemigroup[102X, by equations 11.1-2 
      by gaps 11.1-5 
      by generators 11.1-1 
      by inequalities 11.1-3 
      by pminequality 11.1-4 
  [2XAffineSemigroupByEquations[102X 11.1-2 
  [2XAffineSemigroupByGaps[102X 11.1-5 
  [2XAffineSemigroupByGenerators[102X 11.1-1 
  [2XAffineSemigroupByInequalities[102X 11.1-3 
  [2XAffineSemigroupByPMInequality[102X 11.1-4 
  [2XAllMinimalRelationsOfNumericalSemigroup[102X 4.1-5 
  [2XAlmostSymmetricNumericalSemigroupsFromIrreducible[102X 6.3-1 
  [2XAlmostSymmetricNumericalSemigroupsFromIrreducibleAndGivenType[102X 6.3-2 
  [2XAlmostSymmetricNumericalSemigroupsWithFrobeniusNumber[102X 6.3-4 
  [2XAlmostSymmetricNumericalSemigroupsWithFrobeniusNumberAndType[102X 6.3-5 
  [2XAmalgamationOfNumericalSemigroups[102X 12.1-3 
  [2XAmbientAffineSemigroupOfIdeal[102X 11.5-5 
  [2XAmbientGoodSemigroupOfGoodIdeal[102X 12.5-3 
  [2XAmbientNumericalSemigroupOfIdeal[102X 7.1-5 
  [2XAnIrreducibleNumericalSemigroupWithFrobeniusNumber[102X 6.1-4 
  [2XANumericalSemigroupWithPseudoFrobeniusNumbers[102X 5.6-4 
  [2XAperyList[102X, for ideals of numerical semigroups with respect to element 7.3-12 
      for ideals of numerical semigroups with respect to multiplicity 7.3-13 
      for numerical semigroup with respect to element 3.1-16 
      for numerical semigroup with respect to integer 3.1-18 
      for numerical semigroup with respect to multiplicity 3.1-17 
  [2XAperyListOfIdealOfNumericalSemigroupWRTElement[102X 7.3-12 
  [2XAperyListOfNumericalSemigroup[102X 3.1-17 
  [2XAperyListOfNumericalSemigroupAsGraph[102X 3.1-19 
  [2XAperyListOfNumericalSemigroupWRTElement[102X 3.1-16 
  [2XAperyListOfNumericalSemigroupWRTInteger[102X 3.1-18 
  [2XAperySetOfGoodSemigroup[102X 12.2-15 
  [2XAperyTable[102X 7.3-14 
  [2XAperyTableOfNumericalSemigroup[102X 7.3-14 
  [2XApplyPatternToIdeal[102X 7.4-5 
  [2XApplyPatternToNumericalSemigroup[102X 7.4-6 
  [2XArfCharactersOfArfNumericalSemigroup[102X 8.2-3 
  [2XArfClosure[102X, of good semigroup 12.4-1 
      of numerical semigroup 8.2-2 
  [2XArfGoodSemigroupClosure[102X 12.4-1 
  [2XArfNumericalSemigroupClosure[102X 8.2-2 
  [2XArfNumericalSemigroupsWithFrobeniusNumber[102X 8.2-4 
  [2XArfNumericalSemigroupsWithFrobeniusNumberUpTo[102X 8.2-5 
  [2XArfNumericalSemigroupsWithGenus[102X 8.2-6 
  [2XArfNumericalSemigroupsWithGenusAndFrobeniusNumber[102X 8.2-8 
  [2XArfNumericalSemigroupsWithGenusUpTo[102X 8.2-7 
  [2XArfOverSemigroups[102X 8.2-10 
  [2XArfSpecialGaps[102X 8.2-9 
  [2XAsAffineSemigroup[102X 11.1-14 
  [2XAsGluingOfNumericalSemigroups[102X 6.2-1 
  [2XAsIdealOfNumericalSemigroup[102X 7.4-3 
  [2XAsNumericalDuplication[102X 5.2-5 
  [2XAsymptoticRatliffRushNumber[102X 7.3-9 
  [2XAsymptoticRatliffRushNumberOfIdealOfNumericalSemigroup[102X 7.3-9 
  [2XBasisOfGroupGivenByEquations[102X 11.1-21 
  [2XBelongsToAffineSemigroup[102X 11.1-16 
  [2XBelongsToGoodIdeal[102X 12.5-5 
  [2XBelongsToGoodSemigroup[102X 12.2-1 
  [2XBelongsToHomogenizationOfNumericalSemigroup[102X 9.5-1 
  [2XBelongsToIdealOfAffineSemigroup[102X 11.5-7 
  [2XBelongsToIdealOfNumericalSemigroup[102X 7.1-15 
  [2XBelongsToNumericalSemigroup[102X 2.2-7 
  [2XBettiElements[102X, of affine semigroup 11.3-7 
      of numerical semigroup 4.1-3 
  [2XBettiElementsOfAffineSemigroup[102X 11.3-7 
  [2XBettiElementsOfNumericalSemigroup[102X 4.1-3 
  [2XBezoutSequence[102X A.1-1 
  [2XBinomialIdealOfNumericalSemigroup[102X 4.2-1 
  [2XBlowUp[102X, for ideals of numerical semigroups 7.3-3 
      for numerical semigroups 7.3-5 
  [2XBlowUpIdealOfNumericalSemigroup[102X 7.3-3 
  [2XBlowUpOfNumericalSemigroup[102X 7.3-5 
  [2XBoundForConductorOfImageOfPattern[102X 7.4-4 
  [2XBuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup[102X 7.5-4 
  [2XCanonicalBasisOfKernelCongruence[102X 11.3-4 
  [2XCanonicalIdeal[102X, for numerical semigroups 7.1-29 
  [2XCanonicalIdealOfGoodSemigroup[102X 12.5-7 
  [2XCanonicalIdealOfNumericalSemigroup[102X 7.1-29 
  [2XCartesianProductOfNumericalSemigroups[102X 12.1-4 
  [2XCatenaryDegree[102X, for a numerical semigroup and one of its elements 9.3-5 
      for affine semigroups 11.4-6 
      for element in a numerical semigroup 9.3-5 
      for numerical semigroups 9.3-7 
      for sets of factorizations 9.3-1 
  [2XCatenaryDegreeOfAffineSemigroup[102X 11.4-6 
  [2XCatenaryDegreeOfElementInNumericalSemigroup[102X 9.3-5 
  [2XCatenaryDegreeOfNumericalSemigroup[102X 9.3-7 
  [2XCatenaryDegreeOfSetOfFactorizations[102X 9.3-1 
  [2XCeilingOfRational[102X A.1-3 
  [2XCircuitsOfKernelCongruence[102X 11.3-1 
  [2XCocycleOfNumericalSemigroupWRTElement[102X 3.1-22 
  [2XCompleteIntersectionNumericalSemigroupsWithFrobeniusNumber[102X 6.2-3 
  [2XConductor[102X, for good semigroups 12.2-2 
      for ideal of numerical semigroup 7.1-10 
      for numerical Semigroup 3.1-24 
  [2XConductorOfGoodSemigroup[102X 12.2-2 
  [2XConductorOfIdealOfNumericalSemigroup[102X 7.1-10 
  [2XConductorOfNumericalSemigroup[102X 3.1-24 
  [2XCurveAssociatedToDeltaSequence[102X 10.2-4 
  [2XCyclotomicExponentSequence[102X 10.1-9 
  [2XDecomposeIntegralIdealIntoIrreducibles[102X 7.2-2 
  [2XDecomposeIntoArfIrreducibles[102X 8.2-12 
  [2XDecomposeIntoIrreducibles[102X, for numerical semigroup 6.1-7 
  [2XDegreesOffEqualPrimitiveElementsOfNumericalSemigroup[102X 9.3-8 
  [2XDegreesOfMonotonePrimitiveElementsOfNumericalSemigroup[102X 9.3-10 
  [2XDegreesOfPrimitiveElementsOfAffineSemigroup[102X 11.3-11 
  [2XDegreesOfPrimitiveElementsOfNumericalSemigroup[102X 4.1-6 
  [2XDeltaSequencesWithFrobeniusNumber[102X 10.2-3 
  [2XDeltaSet[102X, for a numerical semigroup 9.2-11 
      for a set of integers 9.2-5 
      for an affine semigroup 11.4-5 
      for the factorizations in a numerical semigroup of one of its elements 9.2-6 
      for the factorizations of an element in a numerical semigroup 9.2-6 
  [2XDeltaSetListUpToElementWRTNumericalSemigroup[102X 9.2-9 
  [2XDeltaSetOfAffineSemigroup[102X 11.4-5 
  [2XDeltaSetOfFactorizationsElementWRTNumericalSemigroup[102X 9.2-6 
  [2XDeltaSetOfNumericalSemigroup[102X 9.2-11 
  [2XDeltaSetOfSetOfIntegers[102X 9.2-5 
  [2XDeltaSetPeriodicityBoundForNumericalSemigroup[102X 9.2-7 
  [2XDeltaSetPeriodicityStartForNumericalSemigroup[102X 9.2-8 
  [2XDeltaSetUnionUpToElementWRTNumericalSemigroup[102X 9.2-10 
  [2XDenumerantFunction[102X 9.1-8 
  [2XDenumerantIdeal[102X, denumerant ideal of a given number of factorizations in a numerical semigroup 9.1-9 
      denumerant ideal of semigroup with respect to a number of factorizations 9.1-9 
  [2XDenumerantOfElementInNumericalSemigroup[102X 9.1-7 
  [2XDeserts[102X 3.1-29 
  [2XDesertsOfNumericalSemigroup[102X 3.1-29 
  [2XDifference[102X, for ideals of numerical semigroups 7.1-24 
      for numerical semigroups 3.1-15 
  [2XDifferenceOfIdealsOfNumericalSemigroup[102X 7.1-24 
  [2XDifferenceOfNumericalSemigroups[102X 3.1-15 
  [2XDilatationOfNumericalSemigroup[102X 5.2-7 
  [2XDivisorsOfElementInNumericalSemigroup[102X 9.6-3 
  [2XDotBinaryRelation[102X 14.1-1 
  [2XDotEliahouGraph[102X 14.1-9 
  [2XDotFactorizationGraph[102X 14.1-8 
  [2XDotOverSemigroupsNumericalSemigroup[102X 14.1-6 
  [2XDotRosalesGraph[102X, for affine semigroup 14.1-7 
      for numerical semigroup 14.1-7 
  [2XDotSplash[102X 14.1-11 
  [2XDotTreeOfGluingsOfNumericalSemigroup[102X 14.1-5 
  [2XElasticity[102X, for affine semigroups 11.4-4 
      for numerical semigroups 9.2-4 
      for the factorizations in a numerical semigroup of one of its elements 9.2-3 
      for the factorizations in an affine semigroup of one of its elements 11.4-3 
      for the factorizations of an element in a numerical semigroup 9.2-3 
      for the factorizations of an element in an affine semigroup 11.4-3 
  [2XElasticityOfAffineSemigroup[102X 11.4-4 
  [2XElasticityOfFactorizationsElementWRTAffineSemigroup[102X 11.4-3 
  [2XElasticityOfFactorizationsElementWRTNumericalSemigroup[102X 9.2-3 
  [2XElasticityOfNumericalSemigroup[102X 9.2-4 
  [2XElementNumber_IdealOfNumericalSemigroup[102X 7.1-16 
  [2XElementNumber_NumericalSemigroup[102X 3.1-11 
  [2XElementsUpTo[102X 3.1-7 
  [2XEliahouNumber[102X, for numerical semigroup 3.2-2 
  [2XEliahouSlicesOfNumericalSemigroup[102X 3.2-4 
  [2XEmbeddingDimension[102X, for numerical semigroup 3.1-3 
  [2XEmbeddingDimensionOfNumericalSemigroup[102X 3.1-3 
  [2XEqualCatenaryDegreeOfAffineSemigroup[102X 11.4-7 
  [2XEqualCatenaryDegreeOfNumericalSemigroup[102X 9.3-9 
  [2XEqualCatenaryDegreeOfSetOfFactorizations[102X 9.3-3 
  [2XEquationsOfGroupGeneratedBy[102X 11.1-20 
  [2XFactorizations[102X 11.4-2 
      for a numerical semigroup and one of its elements 9.1-2 
      for an element in a numerical semigroup 9.1-2 
      for an element in an affine semigroup 11.4-2 
  [2XFactorizationsElementListWRTNumericalSemigroup[102X 9.1-3 
  [2XFactorizationsElementWRTNumericalSemigroup[102X 9.1-2 
  [2XFactorizationsInHomogenizationOfNumericalSemigroup[102X 9.5-2 
  [2XFactorizationsIntegerWRTList[102X 9.1-1 
  [2XFactorizationsVectorWRTList[102X 11.4-1 
  [2XFengRaoDistance[102X 9.7-1 
  [2XFengRaoNumber[102X 9.7-2 
  [2XFirstElementsOfNumericalSemigroup[102X 3.1-6 
  [2XForcedIntegersForPseudoFrobenius[102X 5.6-1 
  [2XFreeNumericalSemigroupsWithFrobeniusNumber[102X 6.2-5 
  [2XFrobeniusNumber[102X, for ideal of numerical semigroup 7.1-11 
      for numerical semigroup 3.1-23 
  [2XFrobeniusNumberOfIdealOfNumericalSemigroup[102X 7.1-11 
  [2XFrobeniusNumberOfNumericalSemigroup[102X 3.1-23 
  [2XFundamentalGaps[102X, for numerical semigroup 3.1-35 
  [2XFundamentalGapsOfNumericalSemigroup[102X 3.1-35 
  [2XGaps[102X, for affine semigroup 11.1-6 
      for numerical semigroup 3.1-27 
  [2XGapsOfNumericalSemigroup[102X 3.1-27 
  [2XGenerators[102X, for affine semigroup 11.1-10 
      for ideal of an affine semigroup 11.5-4 
      for ideal of numerical semigroup 7.1-4 
      for numerical semigroup 3.1-2 
  [2XGeneratorsKahlerDifferentials[102X 10.2-9 
  [2XGeneratorsModule_Global[102X 10.2-8 
  [2XGeneratorsOfAffineSemigroup[102X 11.1-10 
  [2XGeneratorsOfIdealOfNumericalSemigroup[102X 7.1-4 
  [2XGeneratorsOfKernelCongruence[102X 11.3-3 
  [2XGeneratorsOfNumericalSemigroup[102X 3.1-2 
  [2XGenus[102X, for affine semigroup 11.1-7 
      for good semigroup 12.2-13 
      for numerical semigroup 3.1-34 
  [2XGenusOfGoodSemigroup[102X 12.2-13 
  [2XGenusOfNumericalSemigroup[102X 3.1-34 
  [2XGluingOfAffineSemigroups[102X 11.2-1 
  [2XGoodGeneratingSystemOfGoodIdeal[102X 12.5-2 
  [2XGoodIdeal[102X 12.5-1 
  [2XGoodSemigroup[102X 12.1-5 
  [2XGoodSemigroupByMaximalElements[102X 12.2-10 
  [2XGoodSemigroupBySmallElements[102X 12.2-7 
  [2XGraeffePolynomial[102X 10.1-5 
  [2XGraphAssociatedToElementInNumericalSemigroup[102X 4.1-2 
  [2XGraverBasis[102X 11.3-5 
  [2XHasseDiagramOfAperyListOfNumericalSemigroup[102X 14.1-4 
  [2XHasseDiagramOfBettiElementsOfNumericalSemigroup[102X 14.1-3 
  [2XHasseDiagramOfNumericalSemigroup[102X 14.1-2 
  [2XHilbertBasisOfSystemOfHomogeneousEquations[102X 11.1-18 
  [2XHilbertBasisOfSystemOfHomogeneousInequalities[102X 11.1-19 
  [2XHilbertFunction[102X 7.3-2 
  [2XHilbertFunctionOfIdealOfNumericalSemigroup[102X 7.3-1 
  [2XHilbertSeriesOfNumericalSemigroup[102X 10.1-4 
  [2XHoles[102X, for numerical semigroup 3.1-32 
  [2XHolesOfNumericalSemigroup[102X 3.1-32 
  [2XHomogeneousBettiElementsOfNumericalSemigroup[102X 9.5-3 
  [2XHomogeneousCatenaryDegreeOfAffineSemigroup[102X 11.4-8 
  [2XHomogeneousCatenaryDegreeOfNumericalSemigroup[102X 9.5-4 
  [2XIdealByDivisorClosedSet[102X 7.1-8 
  [2XIdealOfAffineSemigroup[102X 11.5-1 
  [2XIdealOfNumericalSemigroup[102X 7.1-1 
  [2XInductiveNumericalSemigroup[102X 5.2-6 
  [2XIntersection[102X, for ideals of affine semigroups 11.5-12 
      for ideals of numerical semigroups 7.1-27 
      for numerical semigroups 5.2-1 
  [2XIntersectionIdealsOfAffineSemigroup[102X 11.5-12 
  [2XIntersectionIdealsOfNumericalSemigroup[102X 7.1-27 
  [2XIntersectionOfNumericalSemigroups[102X 5.2-1 
  [2XIrreducibleMaximalElementsOfGoodSemigroup[102X 12.2-9 
  [2XIrreducibleNumericalSemigroupsWithFrobeniusNumber[102X 6.1-5 
  [2XIrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity[102X 6.1-6 
  [2XIrreducibleZComponents[102X 7.2-1 
  [2XIsACompleteIntersectionNumericalSemigroup[102X 6.2-2 
  [2XIsAcute[102X, for numerical semigroups 3.1-31 
  [2XIsAcuteNumericalSemigroup[102X 3.1-31 
  [2XIsAdditiveNumericalSemigroup[102X 9.2-13 
  [2XIsAdmissiblePattern[102X 7.4-1 
  [2XIsAdmittedPatternByIdeal[102X 7.4-7 
  [2XIsAdmittedPatternByNumericalSemigroup[102X 7.4-8 
  [2XIsAffineSemigroup[102X 11.1-15 
  [2XIsAffineSemigroupByEquations[102X 11.1-15 
  [2XIsAffineSemigroupByGenerators[102X 11.1-15 
  [2XIsAffineSemigroupByInequalities[102X 11.1-15 
  [2XIsAlmostCanonicalIdeal[102X 7.1-31 
  [2XIsAlmostSymmetric[102X 6.3-3 
  [2XIsAlmostSymmetricNumericalSemigroup[102X 6.3-3 
  [2XIsAperyListOfNumericalSemigroup[102X 2.2-4 
  [2XIsAperySetAlphaRectangular[102X 6.2-13 
  [2XIsAperySetBetaRectangular[102X 6.2-12 
  [2XIsAperySetGammaRectangular[102X 6.2-11 
  [2XIsArf[102X 8.2-1 
  [2XIsArfIrreducible[102X 8.2-11 
  [2XIsArfNumericalSemigroup[102X 8.2-1 
  [2XIsBezoutSequence[102X A.1-2 
  [2XIsCanonicalIdeal[102X 7.1-30 
  [2XIsCanonicalIdealOfNumericalSemigroup[102X 7.1-30 
  [2XIsComplementOfIntegralIdeal[102X 7.1-7 
  [2XIsCompleteIntersection[102X 6.2-2 
  [2XIsCyclotomicNumericalSemigroup[102X 10.1-8 
  [2XIsCyclotomicPolynomial[102X 10.1-6 
  [2XIsDeltaSequence[102X 10.2-2 
  [2XIsFree[102X 6.2-4 
  [2XIsFreeNumericalSemigroup[102X 6.2-4 
  [2XIsFull[102X 11.1-17 
  [2XIsFullAffineSemigroup[102X 11.1-17 
  [2XIsGeneralizedAlmostSymmetric[102X 6.4-4 
  [2XIsGeneralizedGorenstein[102X 6.4-1 
  [2XIsGeneric[102X, for affine semigroups 11.3-9 
      for numerical semigroups 4.3-2 
  [2XIsGenericAffineSemigroup[102X 11.3-9 
  [2XIsGenericNumericalSemigroup[102X 4.3-2 
  [2XIsGoodSemigroup[102X 12.1-1 
  [2XIsGradedAssociatedRingNumericalSemigroupBuchsbaum[102X 7.5-2 
  [2XIsGradedAssociatedRingNumericalSemigroupCI[102X 7.5-6 
  [2XIsGradedAssociatedRingNumericalSemigroupCM[102X 7.5-1 
  [2XIsGradedAssociatedRingNumericalSemigroupGorenstein[102X 7.5-5 
  [2XIsHomogeneousNumericalSemigroup[102X 9.8-3 
  [2XIsIdealOfAffineSemigroup[102X 11.5-2 
  [2XIsIdealOfNumericalSemigroup[102X 7.1-2 
  [2XIsIntegral[102X, for ideal of numerical semigroup 7.1-6 
      for ideals of affine semigroups 11.5-6 
  [2XIsIntegralIdealOfAffineSemigroup[102X 11.5-6 
  [2XIsIntegralIdealOfNumericalSemigroup[102X 7.1-6 
  [2XIsIrreducible[102X, for numerical semigroups 6.1-1 
  [2XIsIrreducibleNumericalSemigroup[102X 6.1-1 
  [2XIsKroneckerPolynomial[102X 10.1-7 
  [2XIsListOfIntegersNS[102X A.2-2 
  [2XIsLocal[102X, for good semigroups 12.2-4 
  [2XIsMED[102X 8.1-1 
  [2XIsMEDNumericalSemigroup[102X 8.1-1 
  [2XIsMinimalRelationOfNumericalSemigroup[102X 4.1-4 
  [2XIsModularNumericalSemigroup[102X 2.2-1 
  [2XIsMonomialNumericalSemigroup[102X 10.2-10 
  [2XIsMpure[102X 9.8-2 
  [2XIsMpureNumericalSemigroup[102X 9.8-2 
  [2XIsNearlyGorenstein[102X 6.4-2 
  [2XIsNumericalSemigroup[102X 2.2-1 
  [2XIsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity[102X 6.2-9 
  [2XIsNumericalSemigroupByAperyList[102X 2.2-1 
  [2XIsNumericalSemigroupByFundamentalGaps[102X 2.2-1 
  [2XIsNumericalSemigroupByGaps[102X 2.2-1 
  [2XIsNumericalSemigroupByGenerators[102X 2.2-1 
  [2XIsNumericalSemigroupByInterval[102X 2.2-1 
  [2XIsNumericalSemigroupByOpenInterval[102X 2.2-1 
  [2XIsNumericalSemigroupBySmallElements[102X 2.2-1 
  [2XIsNumericalSemigroupBySubAdditiveFunction[102X 2.2-1 
  [2XIsNumericalSemigroupPolynomial[102X 10.1-2 
  [2XIsOrdinary[102X, for numerical semigroups 3.1-30 
  [2XIsOrdinaryNumericalSemigroup[102X 3.1-30 
  [2XIsProportionallyModularNumericalSemigroup[102X 2.2-1 
  [2XIsPseudoSymmetric[102X, for numerical semigroups 6.1-3 
  [2XIsPseudoSymmetricNumericalSemigroup[102X 6.1-3 
  [2XIsPure[102X 9.8-1 
  [2XIsPureNumericalSemigroup[102X 9.8-1 
  [2XIsSaturated[102X 8.3-1 
  [2XIsSaturatedNumericalSemigroup[102X 8.3-1 
  [2XIsSelfReciprocalUnivariatePolynomial[102X 10.1-11 
  [2XIsStronglyAdmissiblePattern[102X 7.4-2 
  [2XIsSubsemigroupOfNumericalSemigroup[102X 2.2-5 
  [2XIsSubset[102X 2.2-6 
  [2XIsSuperSymmetricNumericalSemigroup[102X 9.8-4 
  [2XIsSymmetric[102X, for good semigroups 12.3-1 
      for numerical semigroups 6.1-2 
  [2XIsSymmetricGoodSemigroup[102X 12.3-1 
  [2XIsSymmetricNumericalSemigroup[102X 6.1-2 
  [2XIsTelescopic[102X 6.2-6 
  [2XIsTelescopicNumericalSemigroup[102X 6.2-6 
  [2XIsUniquelyPresented[102X, for affine semigroups 11.3-10 
      for numerical semigroups 4.3-1 
  [2XIsUniquelyPresentedAffineSemigroup[102X 11.3-10 
  [2XIsUniquelyPresentedNumericalSemigroup[102X 4.3-1 
  [2XIsUniversallyFree[102X 6.2-8 
  [2XIsUniversallyFreeNumericalSemigroup[102X 6.2-8 
  [2XIterator[102X, for ideals of numerical semigroups 7.1-20 
      for numerical semigroups 3.1-14 
  [2XKunzCoordinates[102X, for a numerical semigroup and (optionally) an integer 3.1-20 
  [2XKunzCoordinatesOfNumericalSemigroup[102X 3.1-20 
  [2XKunzPolytope[102X 3.1-21 
  [2XLatticePathAssociatedToNumericalSemigroup[102X 3.1-33 
  [2XLegendrianGenericNumericalSemigroup[102X 10.3-1 
  [2XLength[102X, for good semigroup 12.2-14 
      for numerical semigroup 3.1-5 
  [2XLengthOfGoodSemigroup[102X 12.2-14 
  [2XLengthsOfFactorizationsElementWRTNumericalSemigroup[102X 9.2-2 
  [2XLengthsOfFactorizationsIntegerWRTList[102X 9.2-1 
  [2XLipmanSemigroup[102X 7.3-6 
  [2XLShapes[102X 9.1-5 
  [2XLShapesOfNumericalSemigroup[102X 9.1-5 
  [2XMaximalDenumerant[102X 9.2-16 
      for a numerical semigroup and one of its elements 9.2-14 
      for element in numerical semigroup 9.2-14 
  [2XMaximalDenumerantOfElementInNumericalSemigroup[102X 9.2-14 
  [2XMaximalDenumerantOfNumericalSemigroup[102X 9.2-16 
  [2XMaximalDenumerantOfSetOfFactorizations[102X 9.2-15 
  [2XMaximalElementsOfGoodSemigroup[102X 12.2-8 
  [2XMaximalIdeal[102X, for affine semigroups 11.5-13 
      for numerical semigroups 7.1-28 
  [2XMaximalIdealOfNumericalSemigroup[102X 7.1-28 
  [2XMaximumDegree[102X 9.2-12 
  [2XMaximumDegreeOfElementWRTNumericalSemigroup[102X 9.2-12 
  [2XMEDClosure[102X 8.1-2 
  [2XMEDNumericalSemigroupClosure[102X 8.1-2 
  [2XMicroInvariants[102X 7.3-11 
  [2XMicroInvariantsOfNumericalSemigroup[102X 7.3-11 
  [2XMinimalArfGeneratingSystemOfArfNumericalSemigroup[102X 8.2-3 
  [2XMinimalGeneratingSystem[102X, for affine semigroup 11.1-11 
      for ideal of numerical semigroup 7.1-3 
      for numerical semigroup 3.1-2 
  [2XMinimalGeneratingSystemOfIdealOfNumericalSemigroup[102X 7.1-3 
  [2XMinimalGeneratingSystemOfNumericalSemigroup[102X 3.1-2 
  [2XMinimalGenerators[102X, for affine semigroup 11.1-11 
      for ideal of an affine semigroup 11.5-3 
      for ideal of numerical semigroup 7.1-3 
      for numerical semigroup 3.1-2 
  [2XMinimalGoodGeneratingSystemOfGoodIdeal[102X 12.5-4 
  [2XMinimalGoodGeneratingSystemOfGoodSemigroup[102X 12.2-11 
  [2XMinimalGoodGenerators[102X 12.2-11 
  [2XMinimalMEDGeneratingSystemOfMEDNumericalSemigroup[102X 8.1-3 
  [2XMinimalPresentation[102X, for affine semigroup 11.3-6 
      for numerical semigroups 4.1-1 
  [2XMinimalPresentationOfAffineSemigroup[102X 11.3-6 
  [2XMinimalPresentationOfNumericalSemigroup[102X 4.1-1 
  [2XMinimum[102X, minimum of ideal of numerical semigroup 7.1-14 
  [2XModularNumericalSemigroup[102X 2.1-8 
  [2XMoebiusFunction[102X 9.6-2 
  [2XMoebiusFunctionAssociatedToNumericalSemigroup[102X 9.6-1 
  [2XMonotoneCatenaryDegreeOfAffineSemigroup[102X 11.4-9 
  [2XMonotoneCatenaryDegreeOfNumericalSemigroup[102X 9.3-11 
  [2XMonotoneCatenaryDegreeOfSetOfFactorizations[102X 9.3-4 
  [2XMultipleOfIdealOfAffineSemigroup[102X 11.5-9 
  [2XMultipleOfIdealOfNumericalSemigroup[102X 7.1-22 
  [2XMultipleOfNumericalSemigroup[102X 5.2-3 
  [2XMultiplicity[102X, for good semigroups 12.2-3 
      for numerical semigroup 3.1-1 
  [2XMultiplicityOfNumericalSemigroup[102X 3.1-1 
  [2XMultiplicitySequence[102X 7.3-10 
  [2XMultiplicitySequenceOfNumericalSemigroup[102X 7.3-10 
  [2XNearlyGorensteinVectors[102X 6.4-3 
  [2XNextElementOfNumericalSemigroup[102X 3.1-10 
  [2XNumberElement_IdealOfNumericalSemigroup[102X 7.1-17 
  [2XNumberElement_NumericalSemigroup[102X 3.1-13 
  [2XNumericalDuplication[102X 5.2-4 
  [2XNumericalSemigroup[102X, by (closed) interval 2.1-10 
      by affine map 2.1-7 
      by Apery list 2.1-3 
      by fundamental gaps 2.1-6 
      by gaps 2.1-5 
      by generators 2.1-1 
      by modular condition 2.1-8 
      by open interval 2.1-11 
      by proportionally modular condition 2.1-9 
      by small elements 2.1-4 
      by subadditive function 2.1-2 
  [2XNumericalSemigroupByAffineMap[102X 2.1-7 
  [2XNumericalSemigroupByAperyList[102X 2.1-3 
  [2XNumericalSemigroupByFundamentalGaps[102X 2.1-6 
  [2XNumericalSemigroupByGaps[102X 2.1-5 
  [2XNumericalSemigroupByGenerators[102X 2.1-1 
  [2XNumericalSemigroupByInterval[102X 2.1-10 
  [2XNumericalSemigroupByNuSequence[102X 9.6-4 
  [2XNumericalSemigroupByOpenInterval[102X 2.1-11 
  [2XNumericalSemigroupBySmallElements[102X 2.1-4 
  [2XNumericalSemigroupBySubAdditiveFunction[102X 2.1-2 
  [2XNumericalSemigroupByTauSequence[102X 9.6-5 
  [2XNumericalSemigroupDuplication[102X 12.1-2 
  [2XNumericalSemigroupFromNumericalSemigroupPolynomial[102X 10.1-3 
  [2XNumericalSemigroupPolynomial[102X 10.1-1 
  [2XNumericalSemigroupsPlanarSingularityWithFrobeniusNumber[102X 6.2-10 
  [2XNumericalSemigroupsWithFrobeniusNumber[102X 5.4-3 
  [2XNumericalSemigroupsWithFrobeniusNumberAndMultiplicity[102X 5.4-2 
  [2XNumericalSemigroupsWithFrobeniusNumberFG[102X 5.4-1 
  [2XNumericalSemigroupsWithGenus[102X 5.5-1 
  [2XNumericalSemigroupsWithPseudoFrobeniusNumbers[102X 5.6-3 
  [2XNumericalSemigroupWithRandomElementsAndFrobenius[102X B.1-6 
  [2XNumSgpsUse4ti2[102X 13.1-1 
  [2XNumSgpsUse4ti2gap[102X 13.1-2 
  [2XNumSgpsUseNormalize[102X 13.1-3 
  [2XNumSgpsUseSingular[102X 13.1-4 
  [2XNumSgpsUseSingularInterface[102X 13.1-5 
  [2XOmegaPrimality[102X, for a numerical semigroup 9.4-3 
      for a numerical semigroup and one of its elements 9.4-1 
      for an affine semigroup 11.4-12 
      for an affine semigroup and one of its elements 11.4-11 
      for an element in a numerical semigroup 9.4-1 
      for an element in an affine semigroup 11.4-11 
  [2XOmegaPrimalityOfAffineSemigroup[102X 11.4-12 
  [2XOmegaPrimalityOfElementInAffineSemigroup[102X 11.4-11 
  [2XOmegaPrimalityOfElementInNumericalSemigroup[102X 9.4-1 
  [2XOmegaPrimalityOfElementListInNumericalSemigroup[102X 9.4-2 
  [2XOmegaPrimalityOfNumericalSemigroup[102X 9.4-3 
  [2XOverSemigroups[102X, of a numerical semigroup 5.3-1 
  [2XOverSemigroupsNumericalSemigroup[102X 5.3-1 
  [2XPrimitiveRelationsOfKernelCongruence[102X 11.3-2 
  [2XProfileOfNumericalSemigroup[102X 3.2-3 
  [2XProjectionOfAGoodSemigroup[102X 12.2-12 
  [2XProportionallyModularNumericalSemigroup[102X 2.1-9 
  [2XPseudoFrobenius[102X 3.1-25 
      for affine semigroup 11.1-8 
      for ideal of numerical semigroup 7.1-12 
  [2XPseudoFrobeniusOfIdealOfNumericalSemigroup[102X, for ideal of numerical semigroup 7.1-12 
  [2XPseudoFrobeniusOfNumericalSemigroup[102X 3.1-25 
  [2XQuotientOfNumericalSemigroup[102X 5.2-2 
  [2XRandomAffineSemigroup[102X B.2-2 
  [2XRandomAffineSemigroupWithGenusAndDimension[102X B.2-1 
  [2XRandomFullAffineSemigroup[102X B.2-3 
  [2XRandomGoodSemigroupWithFixedMultiplicity[102X B.3-1 
  [2XRandomListForNS[102X B.1-2 
  [2XRandomListRepresentingSubAdditiveFunction[102X B.1-5 
  [2XRandomModularNumericalSemigroup[102X B.1-3 
  [2XRandomNumericalSemigroup[102X B.1-1 
  [2XRandomNumericalSemigroupWithGenus[102X B.1-7 
  [2XRandomProportionallyModularNumericalSemigroup[102X B.1-4 
  [2XRatliffRushClosure[102X 7.3-8 
  [2XRatliffRushClosureOfIdealOfNumericalSemigroup[102X 7.3-8 
  [2XRatliffRushNumber[102X 7.3-7 
  [2XRatliffRushNumberOfIdealOfNumericalSemigroup[102X 7.3-7 
  [2XRClassesOfSetOfFactorizations[102X 9.1-4 
  [2XReductionNumber[102X, for ideals of numerical semigroups 7.3-4 
  [2XReductionNumberIdealNumericalSemigroup[102X 7.3-4 
  [2XRemoveMinimalGeneratorFromAffineSemigroup[102X 11.1-12 
  [2XRemoveMinimalGeneratorFromNumericalSemigroup[102X 5.1-1 
  [2XRepresentsGapsOfNumericalSemigroup[102X 2.2-3 
  [2XRepresentsPeriodicSubAdditiveFunction[102X A.2-1 
  [2XRepresentsSmallElementsOfGoodSemigroup[102X 12.2-6 
  [2XRepresentsSmallElementsOfNumericalSemigroup[102X 2.2-2 
  [2XRFMatrices[102X 9.1-6 
  [2XRthElementOfNumericalSemigroup[102X 3.1-12 
  [2XSaturatedClosure[102X, for numerical semigroups 8.3-2 
  [2XSaturatedNumericalSemigroupClosure[102X 8.3-2 
  [2XSaturatedNumericalSemigroupsWithFrobeniusNumber[102X 8.3-3 
  [2XSemigroupOfValuesOfCurve_Global[102X 10.2-7 
  [2XSemigroupOfValuesOfCurve_Local[102X 10.2-6 
  [2XSemigroupOfValuesOfPlaneCurve[102X 10.2-5 
  [2XSemigroupOfValuesOfPlaneCurveWithSinglePlaceAtInfinity[102X 10.2-1 
  [2XSetDotNSEngine[102X 14.1-10 
  [2XShadedSetOfElementInAffineSemigroup[102X 11.3-8 
  [2XShadedSetOfElementInNumericalSemigroup[102X 4.1-7 
  [2XSimpleForcedIntegersForPseudoFrobenius[102X 5.6-2 
  [2XSmallElements[102X, for good ideal 12.5-6 
      for good semigroup 12.2-5 
      for ideal of numerical semigroup 7.1-9 
      for numerical semigroup 3.1-4 
  [2XSmallElementsOfGoodIdeal[102X 12.5-6 
  [2XSmallElementsOfGoodSemigroup[102X 12.2-5 
  [2XSmallElementsOfIdealOfNumericalSemigroup[102X 7.1-9 
  [2XSmallElementsOfNumericalSemigroup[102X 3.1-4 
  [2XSpecialGaps[102X, for affine semigroup 11.1-9 
      for numerical semigroup 3.1-36 
  [2XSpecialGapsOfNumericalSemigroup[102X 3.1-36 
  [2XStarClosureOfIdealOfNumericalSemigroup[102X 7.3-15 
  [2XStratifiedAperySetOfGoodSemigroup[102X 12.2-16 
  [2XSubtractIdealsOfNumericalSemigroup[102X 7.1-23 
  [2XSumIdealsOfAffinSemigroup[102X 11.5-8 
  [2XSumIdealsOfNumericalSemigroup[102X 7.1-21 
  [2XTameDegree[102X, for affine semigroups 11.4-10 
      for element in numerical semigroups 9.3-13 
      for numerical semigroups 9.3-12 
      for numerical semigroups and one of its elements 9.3-13 
      for sets of factorizations 9.3-6 
  [2XTameDegreeOfAffineSemigroup[102X 11.4-10 
  [2XTameDegreeOfElementInNumericalSemigroup[102X 9.3-13 
  [2XTameDegreeOfNumericalSemigroup[102X 9.3-12 
  [2XTameDegreeOfSetOfFactorizations[102X 9.3-6 
  [2XTelescopicNumericalSemigroupsWithFrobeniusNumber[102X 6.2-7 
  [2XTorsionOfAssociatedGradedRingNumericalSemigroup[102X 7.5-3 
  [2XTraceIdeal[102X, for numerical semigroups 7.1-32 
  [2XTraceIdealOfNumericalSemigroup[102X 7.1-32 
  [2XTracksOfGoodSemigroup[102X 12.5-9 
  [2XTranslationOfIdealOfAffineSemigroup[102X 11.5-10 
  [2XTranslationOfIdealOfNumericalSemigroup[102X 7.1-25 
  [2XTruncatedWilfNumberOfNumericalSemigroup[102X 3.2-2 
  [2XType[102X, for ideal of numerical semigroup 7.1-13 
      of a numerical semigroup 3.1-26 
  [2XTypeOfNumericalSemigroup[102X 3.1-26 
  [2XTypeSequence[102X, for numerical semigroups 7.1-33 
  [2XTypeSequenceOfNumericalSemigroup[102X 7.1-33 
  [2XUnion[102X, for ideals of affine semigroup 11.5-11 
      for ideals of numerical semigroup 7.1-26 
  [2XUnionIdealsOfAffineSemigroup[102X 11.5-11 
  [2XWeight[102X, for numerical semigroup 3.1-28 
  [2XWilfNumber[102X, for numerical semigroup 3.2-1 
  [2XWilfNumberOfNumericalSemigroup[102X 3.2-1 
  [2XWittCoefficients[102X 10.1-10 
  
  
  -------------------------------------------------------
