GAP (NumericalSgps) - Index

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### Index

`*`, for multiple of ideal of affine semigroup 11.5-9
for multiple of ideal of numerical semigroup 7.1-22
`+`, 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
`-`, for ideals of numerical semigroup 7.1-23
`\/`, quotient of numerical semigroup 5.2-2
`\[ \]`, for ideals of numerical semigroups 7.1-18
for numerical semigroups 3.1-8
`\in`, 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
`\{ \}`, for ideals of numerical semigroups 7.1-19
for numerical semigroups 3.1-9
`AbsoluteIrreduciblesOfGoodSemigroup` 12.5-8
`AddSpecialGapOfAffineSemigroup` 11.1-13
`AddSpecialGapOfNumericalSemigroup` 5.1-2
`AdjacentCatenaryDegreeOfSetOfFactorizations` 9.3-2
`Adjustment` 9.2-17
`AdjustmentOfNumericalSemigroup` 9.2-17
`AffineSemigroup`, 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
`AffineSemigroupByEquations` 11.1-2
`AffineSemigroupByGaps` 11.1-5
`AffineSemigroupByGenerators` 11.1-1
`AffineSemigroupByInequalities` 11.1-3
`AffineSemigroupByPMInequality` 11.1-4
`AllMinimalRelationsOfNumericalSemigroup` 4.1-5
`AlmostSymmetricNumericalSemigroupsFromIrreducible` 6.3-1
`AlmostSymmetricNumericalSemigroupsFromIrreducibleAndGivenType` 6.3-2
`AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber` 6.3-4
`AlmostSymmetricNumericalSemigroupsWithFrobeniusNumberAndType` 6.3-5
`AmalgamationOfNumericalSemigroups` 12.1-3
`AmbientAffineSemigroupOfIdeal` 11.5-5
`AmbientGoodSemigroupOfGoodIdeal` 12.5-3
`AmbientNumericalSemigroupOfIdeal` 7.1-5
`AnIrreducibleNumericalSemigroupWithFrobeniusNumber` 6.1-4
`ANumericalSemigroupWithPseudoFrobeniusNumbers` 5.6-4
`AperyList`, 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
`AperyListOfIdealOfNumericalSemigroupWRTElement` 7.3-12
`AperyListOfNumericalSemigroup` 3.1-17
`AperyListOfNumericalSemigroupAsGraph` 3.1-19
`AperyListOfNumericalSemigroupWRTElement` 3.1-16
`AperyListOfNumericalSemigroupWRTInteger` 3.1-18
`AperySetOfGoodSemigroup` 12.2-15
`AperyTable` 7.3-14
`AperyTableOfNumericalSemigroup` 7.3-14
`ApplyPatternToIdeal` 7.4-5
`ApplyPatternToNumericalSemigroup` 7.4-6
`ArfCharactersOfArfNumericalSemigroup` 8.2-3
`ArfClosure`, of good semigroup 12.4-1
of numerical semigroup 8.2-2
`ArfGoodSemigroupClosure` 12.4-1
`ArfNumericalSemigroupClosure` 8.2-2
`ArfNumericalSemigroupsWithFrobeniusNumber` 8.2-4
`ArfNumericalSemigroupsWithFrobeniusNumberUpTo` 8.2-5
`ArfNumericalSemigroupsWithGenus` 8.2-6
`ArfNumericalSemigroupsWithGenusAndFrobeniusNumber` 8.2-8
`ArfNumericalSemigroupsWithGenusUpTo` 8.2-7
`ArfOverSemigroups` 8.2-10
`ArfSpecialGaps` 8.2-9
`AsAffineSemigroup` 11.1-14
`AsGluingOfNumericalSemigroups` 6.2-1
`AsIdealOfNumericalSemigroup` 7.4-3
`AsNumericalDuplication` 5.2-5
`AsymptoticRatliffRushNumber` 7.3-9
`AsymptoticRatliffRushNumberOfIdealOfNumericalSemigroup` 7.3-9
`BasisOfGroupGivenByEquations` 11.1-21
`BelongsToAffineSemigroup` 11.1-16
`BelongsToGoodIdeal` 12.5-5
`BelongsToGoodSemigroup` 12.2-1
`BelongsToHomogenizationOfNumericalSemigroup` 9.5-1
`BelongsToIdealOfAffineSemigroup` 11.5-7
`BelongsToIdealOfNumericalSemigroup` 7.1-15
`BelongsToNumericalSemigroup` 2.2-7
`BettiElements`, of affine semigroup 11.3-7
of numerical semigroup 4.1-3
`BettiElementsOfAffineSemigroup` 11.3-7
`BettiElementsOfNumericalSemigroup` 4.1-3
`BezoutSequence` A.1-1
`BinomialIdealOfNumericalSemigroup` 4.2-1
`BlowUp`, for ideals of numerical semigroups 7.3-3
for numerical semigroups 7.3-5
`BlowUpIdealOfNumericalSemigroup` 7.3-3
`BlowUpOfNumericalSemigroup` 7.3-5
`BoundForConductorOfImageOfPattern` 7.4-4
`BuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup` 7.5-4
`CanonicalBasisOfKernelCongruence` 11.3-4
`CanonicalIdeal`, for numerical semigroups 7.1-29
`CanonicalIdealOfGoodSemigroup` 12.5-7
`CanonicalIdealOfNumericalSemigroup` 7.1-29
`CartesianProductOfNumericalSemigroups` 12.1-4
`CatenaryDegree`, 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
`CatenaryDegreeOfAffineSemigroup` 11.4-6
`CatenaryDegreeOfElementInNumericalSemigroup` 9.3-5
`CatenaryDegreeOfNumericalSemigroup` 9.3-7
`CatenaryDegreeOfSetOfFactorizations` 9.3-1
`CeilingOfRational` A.1-3
`CircuitsOfKernelCongruence` 11.3-1
`CocycleOfNumericalSemigroupWRTElement` 3.1-22
`CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber` 6.2-3
`Conductor`, for good semigroups 12.2-2
for ideal of numerical semigroup 7.1-10
for numerical Semigroup 3.1-24
`ConductorOfGoodSemigroup` 12.2-2
`ConductorOfIdealOfNumericalSemigroup` 7.1-10
`ConductorOfNumericalSemigroup` 3.1-24
`CurveAssociatedToDeltaSequence` 10.2-4
`CyclotomicExponentSequence` 10.1-9
`DecomposeIntegralIdealIntoIrreducibles` 7.2-2
`DecomposeIntoArfIrreducibles` 8.2-12
`DecomposeIntoIrreducibles`, for numerical semigroup 6.1-7
`DegreesOffEqualPrimitiveElementsOfNumericalSemigroup` 9.3-8
`DegreesOfMonotonePrimitiveElementsOfNumericalSemigroup` 9.3-10
`DegreesOfPrimitiveElementsOfAffineSemigroup` 11.3-11
`DegreesOfPrimitiveElementsOfNumericalSemigroup` 4.1-6
`DeltaSequencesWithFrobeniusNumber` 10.2-3
`DeltaSet`, 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
`DeltaSetListUpToElementWRTNumericalSemigroup` 9.2-9
`DeltaSetOfAffineSemigroup` 11.4-5
`DeltaSetOfFactorizationsElementWRTNumericalSemigroup` 9.2-6
`DeltaSetOfNumericalSemigroup` 9.2-11
`DeltaSetOfSetOfIntegers` 9.2-5
`DeltaSetPeriodicityBoundForNumericalSemigroup` 9.2-7
`DeltaSetPeriodicityStartForNumericalSemigroup` 9.2-8
`DeltaSetUnionUpToElementWRTNumericalSemigroup` 9.2-10
`DenumerantFunction` 9.1-8
`DenumerantIdeal`, 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
`DenumerantOfElementInNumericalSemigroup` 9.1-7
`Deserts` 3.1-29
`DesertsOfNumericalSemigroup` 3.1-29
`Difference`, for ideals of numerical semigroups 7.1-24
for numerical semigroups 3.1-15
`DifferenceOfIdealsOfNumericalSemigroup` 7.1-24
`DifferenceOfNumericalSemigroups` 3.1-15
`DilatationOfNumericalSemigroup` 5.2-7
`DivisorsOfElementInNumericalSemigroup` 9.6-3
`DotBinaryRelation` 14.1-1
`DotEliahouGraph` 14.1-9
`DotFactorizationGraph` 14.1-8
`DotOverSemigroupsNumericalSemigroup` 14.1-6
`DotRosalesGraph`, for affine semigroup 14.1-7
for numerical semigroup 14.1-7
`DotSplash` 14.1-11
`DotTreeOfGluingsOfNumericalSemigroup` 14.1-5
`Elasticity`, 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
`ElasticityOfAffineSemigroup` 11.4-4
`ElasticityOfFactorizationsElementWRTAffineSemigroup` 11.4-3
`ElasticityOfFactorizationsElementWRTNumericalSemigroup` 9.2-3
`ElasticityOfNumericalSemigroup` 9.2-4
`ElementNumber_IdealOfNumericalSemigroup` 7.1-16
`ElementNumber_NumericalSemigroup` 3.1-11
`ElementsUpTo` 3.1-7
`EliahouNumber`, for numerical semigroup 3.2-2
`EliahouSlicesOfNumericalSemigroup` 3.2-4
`EmbeddingDimension`, for numerical semigroup 3.1-3
`EmbeddingDimensionOfNumericalSemigroup` 3.1-3
`EqualCatenaryDegreeOfAffineSemigroup` 11.4-7
`EqualCatenaryDegreeOfNumericalSemigroup` 9.3-9
`EqualCatenaryDegreeOfSetOfFactorizations` 9.3-3
`EquationsOfGroupGeneratedBy` 11.1-20
`Factorizations` 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
`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` 3.1-6
`ForcedIntegersForPseudoFrobenius` 5.6-1
`FreeNumericalSemigroupsWithFrobeniusNumber` 6.2-5
`FrobeniusNumber`, for ideal of numerical semigroup 7.1-11
for numerical semigroup 3.1-23
`FrobeniusNumberOfIdealOfNumericalSemigroup` 7.1-11
`FrobeniusNumberOfNumericalSemigroup` 3.1-23
`FundamentalGaps`, for numerical semigroup 3.1-35
`FundamentalGapsOfNumericalSemigroup` 3.1-35
`Gaps`, for affine semigroup 11.1-6
for numerical semigroup 3.1-27
`GapsOfNumericalSemigroup` 3.1-27
`Generators`, 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
`GeneratorsKahlerDifferentials` 10.2-9
`GeneratorsModule_Global` 10.2-8
`GeneratorsOfAffineSemigroup` 11.1-10
`GeneratorsOfIdealOfNumericalSemigroup` 7.1-4
`GeneratorsOfKernelCongruence` 11.3-3
`GeneratorsOfNumericalSemigroup` 3.1-2
`Genus`, for affine semigroup 11.1-7
for good semigroup 12.2-13
for numerical semigroup 3.1-34
`GenusOfGoodSemigroup` 12.2-13
`GenusOfNumericalSemigroup` 3.1-34
`GluingOfAffineSemigroups` 11.2-1
`GoodGeneratingSystemOfGoodIdeal` 12.5-2
`GoodIdeal` 12.5-1
`GoodSemigroup` 12.1-5
`GoodSemigroupByMaximalElements` 12.2-10
`GoodSemigroupBySmallElements` 12.2-7
`GraeffePolynomial` 10.1-5
`GraphAssociatedToElementInNumericalSemigroup` 4.1-2
`GraverBasis` 11.3-5
`HasseDiagramOfAperyListOfNumericalSemigroup` 14.1-4
`HasseDiagramOfBettiElementsOfNumericalSemigroup` 14.1-3
`HasseDiagramOfNumericalSemigroup` 14.1-2
`HilbertBasisOfSystemOfHomogeneousEquations` 11.1-18
`HilbertBasisOfSystemOfHomogeneousInequalities` 11.1-19
`HilbertFunction` 7.3-2
`HilbertFunctionOfIdealOfNumericalSemigroup` 7.3-1
`HilbertSeriesOfNumericalSemigroup` 10.1-4
`Holes`, for numerical semigroup 3.1-32
`HolesOfNumericalSemigroup` 3.1-32
`HomogeneousBettiElementsOfNumericalSemigroup` 9.5-3
`HomogeneousCatenaryDegreeOfAffineSemigroup` 11.4-8
`HomogeneousCatenaryDegreeOfNumericalSemigroup` 9.5-4
`IdealByDivisorClosedSet` 7.1-8
`IdealOfAffineSemigroup` 11.5-1
`IdealOfNumericalSemigroup` 7.1-1
`InductiveNumericalSemigroup` 5.2-6
`Intersection`, for ideals of affine semigroups 11.5-12
for ideals of numerical semigroups 7.1-27
for numerical semigroups 5.2-1
`IntersectionIdealsOfAffineSemigroup` 11.5-12
`IntersectionIdealsOfNumericalSemigroup` 7.1-27
`IntersectionOfNumericalSemigroups` 5.2-1
`IrreducibleMaximalElementsOfGoodSemigroup` 12.2-9
`IrreducibleNumericalSemigroupsWithFrobeniusNumber` 6.1-5
`IrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity` 6.1-6
`IrreducibleZComponents` 7.2-1
`IsACompleteIntersectionNumericalSemigroup` 6.2-2
`IsAcute`, for numerical semigroups 3.1-31
`IsAcuteNumericalSemigroup` 3.1-31
`IsAdditiveNumericalSemigroup` 9.2-13
`IsAdmissiblePattern` 7.4-1
`IsAdmittedPatternByIdeal` 7.4-7
`IsAdmittedPatternByNumericalSemigroup` 7.4-8
`IsAffineSemigroup` 11.1-15
`IsAffineSemigroupByEquations` 11.1-15
`IsAffineSemigroupByGenerators` 11.1-15
`IsAffineSemigroupByInequalities` 11.1-15
`IsAlmostCanonicalIdeal` 7.1-31
`IsAlmostSymmetric` 6.3-3
`IsAlmostSymmetricNumericalSemigroup` 6.3-3
`IsAperyListOfNumericalSemigroup` 2.2-4
`IsAperySetAlphaRectangular` 6.2-13
`IsAperySetBetaRectangular` 6.2-12
`IsAperySetGammaRectangular` 6.2-11
`IsArf` 8.2-1
`IsArfIrreducible` 8.2-11
`IsArfNumericalSemigroup` 8.2-1
`IsBezoutSequence` A.1-2
`IsCanonicalIdeal` 7.1-30
`IsCanonicalIdealOfNumericalSemigroup` 7.1-30
`IsComplementOfIntegralIdeal` 7.1-7
`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` 11.1-17
`IsFullAffineSemigroup` 11.1-17
`IsGeneralizedAlmostSymmetric` 6.4-4
`IsGeneralizedGorenstein` 6.4-1
`IsGeneric`, for affine semigroups 11.3-9
for numerical semigroups 4.3-2
`IsGenericAffineSemigroup` 11.3-9
`IsGenericNumericalSemigroup` 4.3-2
`IsGoodSemigroup` 12.1-1
`IsGradedAssociatedRingNumericalSemigroupBuchsbaum` 7.5-2
`IsGradedAssociatedRingNumericalSemigroupCI` 7.5-6
`IsGradedAssociatedRingNumericalSemigroupCM` 7.5-1
`IsGradedAssociatedRingNumericalSemigroupGorenstein` 7.5-5
`IsHomogeneousNumericalSemigroup` 9.8-3
`IsIdealOfAffineSemigroup` 11.5-2
`IsIdealOfNumericalSemigroup` 7.1-2
`IsIntegral`, for ideal of numerical semigroup 7.1-6
for ideals of affine semigroups 11.5-6
`IsIntegralIdealOfAffineSemigroup` 11.5-6
`IsIntegralIdealOfNumericalSemigroup` 7.1-6
`IsIrreducible`, for numerical semigroups 6.1-1
`IsIrreducibleNumericalSemigroup` 6.1-1
`IsKroneckerPolynomial` 10.1-7
`IsListOfIntegersNS` A.2-2
`IsLocal`, for good semigroups 12.2-4
`IsMED` 8.1-1
`IsMEDNumericalSemigroup` 8.1-1
`IsMinimalRelationOfNumericalSemigroup` 4.1-4
`IsModularNumericalSemigroup` 2.2-1
`IsMonomialNumericalSemigroup` 10.2-10
`IsMpure` 9.8-2
`IsMpureNumericalSemigroup` 9.8-2
`IsNearlyGorenstein` 6.4-2
`IsNumericalSemigroup` 2.2-1
`IsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity` 6.2-9
`IsNumericalSemigroupByAperyList` 2.2-1
`IsNumericalSemigroupByFundamentalGaps` 2.2-1
`IsNumericalSemigroupByGaps` 2.2-1
`IsNumericalSemigroupByGenerators` 2.2-1
`IsNumericalSemigroupByInterval` 2.2-1
`IsNumericalSemigroupByOpenInterval` 2.2-1
`IsNumericalSemigroupBySmallElements` 2.2-1
`IsNumericalSemigroupBySubAdditiveFunction` 2.2-1
`IsNumericalSemigroupPolynomial` 10.1-2
`IsOrdinary`, for numerical semigroups 3.1-30
`IsOrdinaryNumericalSemigroup` 3.1-30
`IsProportionallyModularNumericalSemigroup` 2.2-1
`IsPseudoSymmetric`, for numerical semigroups 6.1-3
`IsPseudoSymmetricNumericalSemigroup` 6.1-3
`IsPure` 9.8-1
`IsPureNumericalSemigroup` 9.8-1
`IsSaturated` 8.3-1
`IsSaturatedNumericalSemigroup` 8.3-1
`IsSelfReciprocalUnivariatePolynomial` 10.1-11
`IsStronglyAdmissiblePattern` 7.4-2
`IsSubsemigroupOfNumericalSemigroup` 2.2-5
`IsSubset` 2.2-6
`IsSuperSymmetricNumericalSemigroup` 9.8-4
`IsSymmetric`, for good semigroups 12.3-1
for numerical semigroups 6.1-2
`IsSymmetricGoodSemigroup` 12.3-1
`IsSymmetricNumericalSemigroup` 6.1-2
`IsTelescopic` 6.2-6
`IsTelescopicNumericalSemigroup` 6.2-6
`IsUniquelyPresented`, for affine semigroups 11.3-10
for numerical semigroups 4.3-1
`IsUniquelyPresentedAffineSemigroup` 11.3-10
`IsUniquelyPresentedNumericalSemigroup` 4.3-1
`IsUniversallyFree` 6.2-8
`IsUniversallyFreeNumericalSemigroup` 6.2-8
`Iterator`, for ideals of numerical semigroups 7.1-20
for numerical semigroups 3.1-14
`KunzCoordinates`, for a numerical semigroup and (optionally) an integer 3.1-20
`KunzCoordinatesOfNumericalSemigroup` 3.1-20
`KunzPolytope` 3.1-21
`LatticePathAssociatedToNumericalSemigroup` 3.1-33
`LegendrianGenericNumericalSemigroup` 10.3-1
`Length`, for good semigroup 12.2-14
for numerical semigroup 3.1-5
`LengthOfGoodSemigroup` 12.2-14
`LengthsOfFactorizationsElementWRTNumericalSemigroup` 9.2-2
`LengthsOfFactorizationsIntegerWRTList` 9.2-1
`LipmanSemigroup` 7.3-6
`LShapes` 9.1-5
`LShapesOfNumericalSemigroup` 9.1-5
`MaximalDenumerant` 9.2-16
for a numerical semigroup and one of its elements 9.2-14
for element in numerical semigroup 9.2-14
`MaximalDenumerantOfElementInNumericalSemigroup` 9.2-14
`MaximalDenumerantOfNumericalSemigroup` 9.2-16
`MaximalDenumerantOfSetOfFactorizations` 9.2-15
`MaximalElementsOfGoodSemigroup` 12.2-8
`MaximalIdeal`, for affine semigroups 11.5-13
for numerical semigroups 7.1-28
`MaximalIdealOfNumericalSemigroup` 7.1-28
`MaximumDegree` 9.2-12
`MaximumDegreeOfElementWRTNumericalSemigroup` 9.2-12
`MEDClosure` 8.1-2
`MEDNumericalSemigroupClosure` 8.1-2
`MicroInvariants` 7.3-11
`MicroInvariantsOfNumericalSemigroup` 7.3-11
`MinimalArfGeneratingSystemOfArfNumericalSemigroup` 8.2-3
`MinimalGeneratingSystem`, for affine semigroup 11.1-11
for ideal of numerical semigroup 7.1-3
for numerical semigroup 3.1-2
`MinimalGeneratingSystemOfIdealOfNumericalSemigroup` 7.1-3
`MinimalGeneratingSystemOfNumericalSemigroup` 3.1-2
`MinimalGenerators`, 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
`MinimalGoodGeneratingSystemOfGoodIdeal` 12.5-4
`MinimalGoodGeneratingSystemOfGoodSemigroup` 12.2-11
`MinimalGoodGenerators` 12.2-11
`MinimalMEDGeneratingSystemOfMEDNumericalSemigroup` 8.1-3
`MinimalPresentation`, for affine semigroup 11.3-6
for numerical semigroups 4.1-1
`MinimalPresentationOfAffineSemigroup` 11.3-6
`MinimalPresentationOfNumericalSemigroup` 4.1-1
`Minimum`, minimum of ideal of numerical semigroup 7.1-14
`ModularNumericalSemigroup` 2.1-8
`MoebiusFunction` 9.6-2
`MoebiusFunctionAssociatedToNumericalSemigroup` 9.6-1
`MonotoneCatenaryDegreeOfAffineSemigroup` 11.4-9
`MonotoneCatenaryDegreeOfNumericalSemigroup` 9.3-11
`MonotoneCatenaryDegreeOfSetOfFactorizations` 9.3-4
`MultipleOfIdealOfAffineSemigroup` 11.5-9
`MultipleOfIdealOfNumericalSemigroup` 7.1-22
`MultipleOfNumericalSemigroup` 5.2-3
`Multiplicity`, for good semigroups 12.2-3
for numerical semigroup 3.1-1
`MultiplicityOfNumericalSemigroup` 3.1-1
`MultiplicitySequence` 7.3-10
`MultiplicitySequenceOfNumericalSemigroup` 7.3-10
`NearlyGorensteinVectors` 6.4-3
`NextElementOfNumericalSemigroup` 3.1-10
`NumberElement_IdealOfNumericalSemigroup` 7.1-17
`NumberElement_NumericalSemigroup` 3.1-13
`NumericalDuplication` 5.2-4
`NumericalSemigroup`, 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
`NumericalSemigroupByAffineMap` 2.1-7
`NumericalSemigroupByAperyList` 2.1-3
`NumericalSemigroupByFundamentalGaps` 2.1-6
`NumericalSemigroupByGaps` 2.1-5
`NumericalSemigroupByGenerators` 2.1-1
`NumericalSemigroupByInterval` 2.1-10
`NumericalSemigroupByNuSequence` 9.6-4
`NumericalSemigroupByOpenInterval` 2.1-11
`NumericalSemigroupBySmallElements` 2.1-4
`NumericalSemigroupBySubAdditiveFunction` 2.1-2
`NumericalSemigroupByTauSequence` 9.6-5
`NumericalSemigroupDuplication` 12.1-2
`NumericalSemigroupFromNumericalSemigroupPolynomial` 10.1-3
`NumericalSemigroupPolynomial` 10.1-1
`NumericalSemigroupsPlanarSingularityWithFrobeniusNumber` 6.2-10
`NumericalSemigroupsWithFrobeniusNumber` 5.4-3
`NumericalSemigroupsWithFrobeniusNumberAndMultiplicity` 5.4-2
`NumericalSemigroupsWithFrobeniusNumberFG` 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
`NumSgpsUseSingularInterface` 13.1-5
`OmegaPrimality`, 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
`OmegaPrimalityOfAffineSemigroup` 11.4-12
`OmegaPrimalityOfElementInAffineSemigroup` 11.4-11
`OmegaPrimalityOfElementInNumericalSemigroup` 9.4-1
`OmegaPrimalityOfElementListInNumericalSemigroup` 9.4-2
`OmegaPrimalityOfNumericalSemigroup` 9.4-3
`OverSemigroups`, of a numerical semigroup 5.3-1
`OverSemigroupsNumericalSemigroup` 5.3-1
`PrimitiveRelationsOfKernelCongruence` 11.3-2
`ProfileOfNumericalSemigroup` 3.2-3
`ProjectionOfAGoodSemigroup` 12.2-12
`ProportionallyModularNumericalSemigroup` 2.1-9
`PseudoFrobenius` 3.1-25
for affine semigroup 11.1-8
for ideal of numerical semigroup 7.1-12
`PseudoFrobeniusOfIdealOfNumericalSemigroup`, for ideal of numerical semigroup 7.1-12
`PseudoFrobeniusOfNumericalSemigroup` 3.1-25
`QuotientOfNumericalSemigroup` 5.2-2
`RandomAffineSemigroup` B.2-2
`RandomAffineSemigroupWithGenusAndDimension` B.2-1
`RandomFullAffineSemigroup` B.2-3
`RandomGoodSemigroupWithFixedMultiplicity` B.3-1
`RandomListForNS` B.1-2
`RandomListRepresentingSubAdditiveFunction` B.1-5
`RandomModularNumericalSemigroup` B.1-3
`RandomNumericalSemigroup` B.1-1
`RandomNumericalSemigroupWithGenus` B.1-7
`RandomProportionallyModularNumericalSemigroup` B.1-4
`RatliffRushClosure` 7.3-8
`RatliffRushClosureOfIdealOfNumericalSemigroup` 7.3-8
`RatliffRushNumber` 7.3-7
`RatliffRushNumberOfIdealOfNumericalSemigroup` 7.3-7
`RClassesOfSetOfFactorizations` 9.1-4
`ReductionNumber`, for ideals of numerical semigroups 7.3-4
`ReductionNumberIdealNumericalSemigroup` 7.3-4
`RemoveMinimalGeneratorFromAffineSemigroup` 11.1-12
`RemoveMinimalGeneratorFromNumericalSemigroup` 5.1-1
`RepresentsGapsOfNumericalSemigroup` 2.2-3
`RepresentsPeriodicSubAdditiveFunction` A.2-1
`RepresentsSmallElementsOfGoodSemigroup` 12.2-6
`RepresentsSmallElementsOfNumericalSemigroup` 2.2-2
`RFMatrices` 9.1-6
`RthElementOfNumericalSemigroup` 3.1-12
`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
`SetDotNSEngine` 14.1-10
`ShadedSetOfElementInAffineSemigroup` 11.3-8
`ShadedSetOfElementInNumericalSemigroup` 4.1-7
`SimpleForcedIntegersForPseudoFrobenius` 5.6-2
`SmallElements`, 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
`SmallElementsOfGoodIdeal` 12.5-6
`SmallElementsOfGoodSemigroup` 12.2-5
`SmallElementsOfIdealOfNumericalSemigroup` 7.1-9
`SmallElementsOfNumericalSemigroup` 3.1-4
`SpecialGaps`, for affine semigroup 11.1-9
for numerical semigroup 3.1-36
`SpecialGapsOfNumericalSemigroup` 3.1-36
`StarClosureOfIdealOfNumericalSemigroup` 7.3-15
`StratifiedAperySetOfGoodSemigroup` 12.2-16
`SubtractIdealsOfNumericalSemigroup` 7.1-23
`SumIdealsOfAffinSemigroup` 11.5-8
`SumIdealsOfNumericalSemigroup` 7.1-21
`TameDegree`, 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
`TameDegreeOfAffineSemigroup` 11.4-10
`TameDegreeOfElementInNumericalSemigroup` 9.3-13
`TameDegreeOfNumericalSemigroup` 9.3-12
`TameDegreeOfSetOfFactorizations` 9.3-6
`TelescopicNumericalSemigroupsWithFrobeniusNumber` 6.2-7
`TorsionOfAssociatedGradedRingNumericalSemigroup` 7.5-3
`TraceIdeal`, for numerical semigroups 7.1-32
`TraceIdealOfNumericalSemigroup` 7.1-32
`TracksOfGoodSemigroup` 12.5-9
`TranslationOfIdealOfAffineSemigroup` 11.5-10
`TranslationOfIdealOfNumericalSemigroup` 7.1-25
`TruncatedWilfNumberOfNumericalSemigroup` 3.2-2
`Type`, for ideal of numerical semigroup 7.1-13
of a numerical semigroup 3.1-26
`TypeOfNumericalSemigroup` 3.1-26
`TypeSequence`, for numerical semigroups 7.1-33
`TypeSequenceOfNumericalSemigroup` 7.1-33
`Union`, for ideals of affine semigroup 11.5-11
for ideals of numerical semigroup 7.1-26
`UnionIdealsOfAffineSemigroup` 11.5-11
`Weight`, for numerical semigroup 3.1-28
`WilfNumber`, for numerical semigroup 3.2-1
`WilfNumberOfNumericalSemigroup` 3.2-1
`WittCoefficients` 10.1-10

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