*, for multiple of ideal of numerical semigroup 7.1-12 +, for defining ideal of numerical semigroup 7.1-1 -, for ideals of numerical semigroup 7.1-13 \/, quotient of numerical semigroup 5.2-2 \in, membership for good ideal 12.4-5 AddSpecialGapOfNumericalSemigroup 5.1-2 AdjacentCatenaryDegreeOfSetOfFactorizations 9.3-2 AdjustmentOfNumericalSemigroup 9.2-16 AffineSemigroup, by equations 11.1-2 AffineSemigroupByEquations 11.1-2 AffineSemigroupByGenerators 11.1-1 AffineSemigroupByInequalities 11.1-3 AlmostSymmetricNumericalSemigroupsFromIrreducible 6.3-1 AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber 6.3-3 AmalgamationOfNumericalSemigroups 12.1-3 AmbientGoodSemigroupOfGoodIdeal 12.4-3 AmbientNumericalSemigroupOfIdeal 7.1-5 AnIrreducibleNumericalSemigroupWithFrobeniusNumber 6.1-4 ANumericalSemigroupWithPseudoFrobeniusNumbers 5.6-4 AperyList, for numerical semigroup with respect to element 3.1-7 AperyListOfIdealOfNumericalSemigroupWRTElement 7.2-11 AperyListOfNumericalSemigroup 3.1-8 AperyListOfNumericalSemigroupAsGraph 3.1-10 AperyListOfNumericalSemigroupWRTElement 3.1-7 AperyListOfNumericalSemigroupWRTInteger 3.1-9 AperyTableOfNumericalSemigroup 7.2-12 ApplyPatternToIdeal 7.3-5 ApplyPatternToNumericalSemigroup 7.3-6 ArfCharactersOfArfNumericalSemigroup 8.2-3 ArfClosure, of good semigroup 12.3-2 ArfGoodSemigroupClosure 12.3-2 ArfNumericalSemigroupClosure 8.2-2 ArfNumericalSemigroupsWithFrobeniusNumber 8.2-4 ArfNumericalSemigroupsWithFrobeniusNumberUpTo 8.2-5 ArfNumericalSemigroupsWithGenus 8.2-6 ArfNumericalSemigroupsWithGenusAndFrobeniusNumber 8.2-8 ArfNumericalSemigroupsWithGenusUpTo 8.2-7 AsAffineSemigroup 11.1-6 AsGluingOfNumericalSemigroups 6.2-1 AsIdealOfNumericalSemigroup 7.3-3 AsymptoticRatliffRushNumberOfIdealOfNumericalSemigroup 7.2-8 BasisOfGroupGivenByEquations 11.1-13 BelongsToAffineSemigroup 11.1-8 BelongsToGoodIdeal 12.4-5 BelongsToGoodSemigroup 12.2-1 BelongsToHomogenizationOfNumericalSemigroup 9.5-1 BelongsToIdealOfNumericalSemigroup 7.1-10 BelongsToNumericalSemigroup 2.2-7 BettiElements, of affine semigroup 11.3-5 BettiElementsOfAffineSemigroup 11.3-5 BettiElementsOfNumericalSemigroup 4.1-3 BezoutSequence A.1-1 BlowUpIdealOfNumericalSemigroup 7.2-2 BlowUpOfNumericalSemigroup 7.2-4 BoundForConductorOfImageOfPattern 7.3-4 BuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup 7.4-4 CanonicalBasisOfKernelCongruence 11.3-2 CanonicalIdealOfGoodSemigroup 12.4-7 CanonicalIdealOfNumericalSemigroup 7.1-18 CartesianProductOfNumericalSemigroups 12.1-4 CatenaryDegreeOfAffineSemigroup 11.4-4 CatenaryDegreeOfElementInNumericalSemigroup 9.3-5 CatenaryDegreeOfNumericalSemigroup 9.3-7 CatenaryDegreeOfSetOfFactorizations 9.3-1 CeilingOfRational A.1-3 CocycleOfNumericalSemigroupWRTElement 3.1-13 CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber 6.2-3 Conductor, for good semigroup 12.2-2 ConductorOfGoodSemigroup 12.2-2 ConductorOfIdealOfNumericalSemigroup 7.1-8 ConductorOfNumericalSemigroup 3.1-15 CurveAssociatedToDeltaSequence 10.2-4 DecomposeIntoIrreducibles, for numerical semigroup 6.1-6 DeltaSequencesWithFrobeniusNumber 10.2-3 DeltaSetListUpToElementWRTNumericalSemigroup 9.2-9 DeltaSetOfAffineSemigroup 11.4-3 DeltaSetOfFactorizationsElementWRTNumericalSemigroup 9.2-6 DeltaSetOfNumericalSemigroup 9.2-11 DeltaSetOfSetOfIntegers 9.2-5 DeltaSetPeriodicityBoundForNumericalSemigroup 9.2-7 DeltaSetPeriodicityStartForNumericalSemigroup 9.2-8 DeltaSetUnionUpToElementWRTNumericalSemigroup 9.2-10 DenumerantOfElementInNumericalSemigroup 9.1-6 DesertsOfNumericalSemigroup 3.1-19 Difference, for ideals of numerical semigroups 7.1-14 DifferenceOfIdealsOfNumericalSemigroup 7.1-14 DifferenceOfNumericalSemigroups 5.2-4 DivisorsOfElementInNumericalSemigroup 9.6-2 ElasticityOfAffineSemigroup 11.4-2 ElasticityOfFactorizationsElementWRTNumericalSemigroup 9.2-3 ElasticityOfNumericalSemigroup 9.2-4 EliahouNumber, for numerical semigroup 3.2-2 EliahouSlicesOfNumericalSemigroup 3.2-4 EmbeddingDimension, for numerical semigroup 3.1-3 EmbeddingDimensionOfNumericalSemigroup 3.1-3 EqualCatenaryDegreeOfAffineSemigroup 11.4-5 EqualCatenaryDegreeOfNumericalSemigroup 9.3-9 EqualCatenaryDegreeOfSetOfFactorizations 9.3-3 EqualPrimitiveElementsOfNumericalSemigroup 9.3-8 EquationsOfGroupGeneratedBy 11.1-12 FactorizationsElementListWRTNumericalSemigroup 9.1-3 FactorizationsElementWRTNumericalSemigroup 9.1-2 FactorizationsInHomogenizationOfNumericalSemigroup 9.5-2 FactorizationsIntegerWRTList 9.1-1 FactorizationsVectorWRTList 11.4-1 FengRaoDistance 9.7-1 FengRaoNumber 9.7-2 FirstElementsOfNumericalSemigroup 3.1-5 ForcedIntegersForPseudoFrobenius 5.6-1 FreeNumericalSemigroupsWithFrobeniusNumber 6.2-5 FrobeniusNumber, for numerical semigroup 3.1-14 FrobeniusNumberOfNumericalSemigroup 3.1-14 FundamentalGaps, for numerical semigroup 3.1-25 FundamentalGapsOfNumericalSemigroup 3.1-25 Gaps, for numerical semigroup 3.1-18 GapsOfNumericalSemigroup 3.1-18 Generators, for affine semigroup 11.1-4 GeneratorsKahlerDifferentials 10.2-9 GeneratorsModule_Global 10.2-8 GeneratorsOfAffineSemigroup 11.1-4 GeneratorsOfIdealOfNumericalSemigroup 7.1-4 GeneratorsOfKernelCongruence 11.3-1 GeneratorsOfNumericalSemigroup 3.1-2 Genus, for numerical semigroup 3.1-24 GenusOfNumericalSemigroup 3.1-24 GluingOfAffineSemigroups 11.2-1 GoodGeneratingSystemOfGoodIdeal 12.4-2 GoodIdeal 12.4-1 GoodSemigroup 12.1-5 GoodSemigroupByMaximalElements 12.2-8 GoodSemigroupBySmallElements 12.2-5 GraeffePolynomial 10.1-5 GraphAssociatedToElementInNumericalSemigroup 4.1-2 GraverBasis 11.3-3 HilbertBasisOfSystemOfHomogeneousEquations 11.1-10 HilbertBasisOfSystemOfHomogeneousInequalities 11.1-11 HilbertFunctionOfIdealOfNumericalSemigroup 7.2-1 HilbertSeriesOfNumericalSemigroup 10.1-4 Holes, for numerical semigroup 3.1-22 HolesOfNumericalSemigroup 3.1-22 HomogeneousBettiElementsOfNumericalSemigroup 9.5-3 HomogeneousCatenaryDegreeOfAffineSemigroup 11.4-6 HomogeneousCatenaryDegreeOfNumericalSemigroup 9.5-4 IdealOfNumericalSemigroup 7.1-1 InductiveNumericalSemigroup 5.2-6 Intersection, for ideals of numerical semigroups 7.1-16 IntersectionIdealsOfNumericalSemigroup 7.1-16 IntersectionOfNumericalSemigroups 5.2-1 IrreducibleMaximalElementsOfGoodSemigroup 12.2-7 IrreducibleNumericalSemigroupsWithFrobeniusNumber 6.1-5 IsACompleteIntersectionNumericalSemigroup 6.2-2 IsAcute, for numerical semigroups 3.1-21 IsAcuteNumericalSemigroup 3.1-21 IsAdditiveNumericalSemigroup 9.2-17 IsAdmissiblePattern 7.3-1 IsAdmittedPatternByIdeal 7.3-7 IsAdmittedPatternByNumericalSemigroup 7.3-8 IsAffineSemigroup 11.1-7 IsAffineSemigroupByEquations 11.1-7 IsAffineSemigroupByGenerators 11.1-7 IsAffineSemigroupByInequalities 11.1-7 IsAlmostSymmetric 6.3-2 IsAlmostSymmetricNumericalSemigroup 6.3-2 IsAperyListOfNumericalSemigroup 2.2-4 IsAperySetAlphaRectangular 6.2-12 IsAperySetBetaRectangular 6.2-11 IsAperySetGammaRectangular 6.2-10 IsArf 8.2-1 IsArfNumericalSemigroup 8.2-1 IsBezoutSequence A.1-2 IsCanonicalIdeal 7.1-19 IsCanonicalIdealOfNumericalSemigroup 7.1-19 IsCompleteIntersection 6.2-2 IsCyclotomicNumericalSemigroup 10.1-8 IsCyclotomicPolynomial 10.1-6 IsDeltaSequence 10.2-2 IsFree 6.2-4 IsFreeNumericalSemigroup 6.2-4 IsFull 11.1-9 IsFullAffineSemigroup 11.1-9 IsGeneric, for affine semigroups 11.3-7 IsGenericAffineSemigroup 11.3-7 IsGenericNumericalSemigroup 4.2-2 IsGoodSemigroup 12.1-1 IsGradedAssociatedRingNumericalSemigroupBuchsbaum 7.4-2 IsGradedAssociatedRingNumericalSemigroupCI 7.4-8 IsGradedAssociatedRingNumericalSemigroupCM 7.4-1 IsGradedAssociatedRingNumericalSemigroupGorenstein 7.4-7 IsIdealOfNumericalSemigroup 7.1-2 IsIntegral 7.1-6 IsIntegralIdealOfNumericalSemigroup 7.1-6 IsIrreducible, for numerical semigroups 6.1-1 IsIrreducibleNumericalSemigroup 6.1-1 IsKroneckerPolynomial 10.1-7 IsListOfIntegersNS A.2-2 IsMED 8.1-1 IsMEDNumericalSemigroup 8.1-1 IsModularNumericalSemigroup 2.2-1 IsMonomialNumericalSemigroup 10.2-10 IsMpure 7.4-5 IsMpureNumericalSemigroup 7.4-5 IsNumericalSemigroup 2.2-1 IsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity 6.2-8 IsNumericalSemigroupByAperyList 2.2-1 IsNumericalSemigroupByFundamentalGaps 2.2-1 IsNumericalSemigroupByGaps 2.2-1 IsNumericalSemigroupByGenerators 2.2-1 IsNumericalSemigroupByInterval 2.2-1 IsNumericalSemigroupByMinimalGenerators 2.2-1 IsNumericalSemigroupByOpenInterval 2.2-1 IsNumericalSemigroupBySmallElements 2.2-1 IsNumericalSemigroupBySubAdditiveFunction 2.2-1 IsNumericalSemigroupPolynomial 10.1-2 IsOrdinary, for numerical semigroups 3.1-20 IsOrdinaryNumericalSemigroup 3.1-20 IsProportionallyModularNumericalSemigroup 2.2-1 IsPseudoSymmetric, for numerical semigroups 6.1-3 IsPseudoSymmetricNumericalSemigroup 6.1-3 IsPure 7.4-6 IsPureNumericalSemigroup 7.4-6 IsSaturated 8.3-1 IsSaturatedNumericalSemigroup 8.3-1 IsSelfReciprocalUnivariatePolynomial 10.1-9 IsStronglyAdmissiblePattern 7.3-2 IsSubsemigroupOfNumericalSemigroup 2.2-5 IsSubset 2.2-6 IsSuperSymmetricNumericalSemigroup 9.2-18 IsSymmetric, for good semigroups 12.3-1 IsSymmetricGoodSemigroup 12.3-1 IsSymmetricNumericalSemigroup 6.1-2 IsTelescopic 6.2-6 IsTelescopicNumericalSemigroup 6.2-6 IsUniquelyPresented 4.2-1 IsUniquelyPresentedAffineSemigroup 11.3-8 IsUniquelyPresentedNumericalSemigroup 4.2-1 KunzCoordinatesOfNumericalSemigroup 3.1-11 KunzPolytope 3.1-12 LatticePathAssociatedToNumericalSemigroup 3.1-23 LengthsOfFactorizationsElementWRTNumericalSemigroup 9.2-2 LengthsOfFactorizationsIntegerWRTList 9.2-1 LipmanSemigroup 7.2-5 LShapesOfNumericalSemigroup 9.1-5 MaximalDenumerantOfElementInNumericalSemigroup 9.2-13 MaximalDenumerantOfNumericalSemigroup 9.2-15 MaximalDenumerantOfSetOfFactorizations 9.2-14 MaximalElementsOfGoodSemigroup 12.2-6 MaximalIdealOfNumericalSemigroup 7.1-17 MaximumDegreeOfElementWRTNumericalSemigroup 9.2-12 MEDClosure, for numerical semigroups 8.1-2 MEDNumericalSemigroupClosure 8.1-2 MicroInvariantsOfNumericalSemigroup 7.2-10 MinimalArfGeneratingSystemOfArfNumericalSemigroup 8.2-3 MinimalGeneratingSystem, for affine semigroup 11.1-5 MinimalGeneratingSystemOfIdealOfNumericalSemigroup 7.1-3 MinimalGeneratingSystemOfNumericalSemigroup 3.1-2 MinimalGenerators 12.2-10 MinimalGoodGeneratingSystemOfGoodIdeal 12.4-4 MinimalGoodGeneratingSystemOfGoodSemigroup 12.2-9 MinimalMEDGeneratingSystemOfMEDNumericalSemigroup 8.1-3 MinimalPresentation, for affine semigroup 11.3-4 MinimalPresentationOfAffineSemigroup 11.3-4 MinimalPresentationOfNumericalSemigroup 4.1-1 Minimum, minimum of ideal of numerical semigroup 7.1-9 ModularNumericalSemigroup 2.1-8 MoebiusFunctionAssociatedToNumericalSemigroup 9.6-1 MonotoneCatenaryDegreeOfAffineSemigroup 11.4-7 MonotoneCatenaryDegreeOfNumericalSemigroup 9.3-11 MonotoneCatenaryDegreeOfSetOfFactorizations 9.3-4 MonotonePrimitiveElementsOfNumericalSemigroup 9.3-10 MultipleOfIdealOfNumericalSemigroup 7.1-12 MultipleOfNumericalSemigroup 5.2-3 Multiplicity, for numerical semigroup 3.1-1 MultiplicityOfNumericalSemigroup 3.1-1 MultiplicitySequenceOfNumericalSemigroup 7.2-9 NumericalDuplication 5.2-5 NumericalSemigroup, by (closed) interval 2.1-10 NumericalSemigroupByAffineMap 2.1-7 NumericalSemigroupByAperyList 2.1-3 NumericalSemigroupByFundamentalGaps 2.1-6 NumericalSemigroupByGaps 2.1-5 NumericalSemigroupByGenerators 2.1-1 NumericalSemigroupByInterval 2.1-10 NumericalSemigroupByOpenInterval 2.1-11 NumericalSemigroupBySmallElements 2.1-4 NumericalSemigroupBySubAdditiveFunction 2.1-2 NumericalSemigroupDuplication 12.1-2 NumericalSemigroupFromNumericalSemigroupPolynomial 10.1-3 NumericalSemigroupPolynomial 10.1-1 NumericalSemigroupsPlanarSingularityWithFrobeniusNumber 6.2-9 NumericalSemigroupsWithFrobeniusNumber 5.4-1 NumericalSemigroupsWithGenus 5.5-1 NumericalSemigroupsWithPseudoFrobeniusNumbers 5.6-3 NumericalSemigroupWithRandomElementsAndFrobenius B.1-6 NumSgpsUse4ti2 13.1-1 NumSgpsUse4ti2gap 13.1-2 NumSgpsUseNormalize 13.1-3 NumSgpsUseSingular 13.1-4 NumSgpsUseSingularGradedModules 13.1-6 NumSgpsUseSingularInterface 13.1-5 OmegaPrimalityOfAffineSemigroup 11.4-10 OmegaPrimalityOfElementInAffineSemigroup 11.4-9 OmegaPrimalityOfElementInNumericalSemigroup 9.4-1 OmegaPrimalityOfElementListInNumericalSemigroup 9.4-2 OmegaPrimalityOfNumericalSemigroup 9.4-3 OverSemigroupsNumericalSemigroup 5.3-1 PrimitiveElementsOfAffineSemigroup 11.3-9 PrimitiveElementsOfNumericalSemigroup 4.1-4 ProfileOfNumericalSemigroup 3.2-3 ProportionallyModularNumericalSemigroup 2.1-9 PseudoFrobeniusOfNumericalSemigroup 3.1-16 QuotientOfNumericalSemigroup 5.2-2 RandomListForNS B.1-2 RandomListRepresentingSubAdditiveFunction B.1-5 RandomModularNumericalSemigroup B.1-3 RandomNumericalSemigroup B.1-1 RandomProportionallyModularNumericalSemigroup B.1-4 RatliffRushClosureOfIdealOfNumericalSemigroup 7.2-7 RatliffRushNumberOfIdealOfNumericalSemigroup 7.2-6 RClassesOfSetOfFactorizations 9.1-4 ReductionNumber, for ideals of numerical semigroups 7.2-3 ReductionNumberIdealNumericalSemigroup 7.2-3 RemoveMinimalGeneratorFromNumericalSemigroup 5.1-1 RepresentsGapsOfNumericalSemigroup 2.2-3 RepresentsPeriodicSubAdditiveFunction A.2-1 RepresentsSmallElementsOfGoodSemigroup 12.2-4 RepresentsSmallElementsOfNumericalSemigroup 2.2-2 RthElementOfNumericalSemigroup 3.1-6 SaturatedClosure, for numerical semigroups 8.3-2 SaturatedNumericalSemigroupClosure 8.3-2 SaturatedNumericalSemigroupsWithFrobeniusNumber 8.3-3 SemigroupOfValuesOfCurve_Global 10.2-7 SemigroupOfValuesOfCurve_Local 10.2-6 SemigroupOfValuesOfPlaneCurve 10.2-5 SemigroupOfValuesOfPlaneCurveWithSinglePlaceAtInfinity 10.2-1 ShadedSetOfElementInAffineSemigroup 11.3-6 ShadedSetOfElementInNumericalSemigroup 4.1-5 SimpleForcedIntegersForPseudoFrobenius 5.6-2 SmallElements, for good ideal 12.4-6 SmallElementsOfGoodIdeal 12.4-6 SmallElementsOfGoodSemigroup 12.2-3 SmallElementsOfIdealOfNumericalSemigroup 7.1-7 SmallElementsOfNumericalSemigroup 3.1-4 SpecialGaps, for numerical semigroup 3.1-26 SpecialGapsOfNumericalSemigroup 3.1-26 StarClosureOfIdealOfNumericalSemigroup 7.2-13 SubtractIdealsOfNumericalSemigroup 7.1-13 SumIdealsOfNumericalSemigroup 7.1-11 TameDegreeOfAffineSemigroup 11.4-8 TameDegreeOfElementInNumericalSemigroup 9.3-13 TameDegreeOfNumericalSemigroup 9.3-12 TameDegreeOfSetOfFactorizations 9.3-6 TelescopicNumericalSemigroupsWithFrobeniusNumber 6.2-7 TorsionOfAssociatedGradedRingNumericalSemigroup 7.4-3 TranslationOfIdealOfNumericalSemigroup 7.1-15 TruncatedWilfNumberOfNumericalSemigroup 3.2-2 TypeOfNumericalSemigroup 3.1-17 TypeSequenceOfNumericalSemigroup 7.1-20 WilfNumber, for numerical semigroup 3.2-1 WilfNumberOfNumericalSemigroup 3.2-1
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