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*, for multiple of ideal of numerical semigroup 7.1-17
+, for defining ideal of numerical semigroup 7.1-1
    for ideals of numerical semigroup 7.1-16
    translation of ideal of numerical semigroup 7.1-20
-, for ideals of numerical semigroup 7.1-18
\/, quotient of numerical semigroup 5.2-2
\[ \], for ideals of numerical semigroups 7.1-13
    for numerical semigroups 3.1-7
\in, membership for good ideal 12.4-5
    membership for good semigroup 12.2-1
    membership test for numerical semigroup 2.2-7
    membership test in affine semigroup 11.1-8
    membership test in ideal of numerical semigroup 7.1-10
\{ \}, for ideals of numerical semigroups 7.1-14
    for numerical semigroups 3.1-8
AddSpecialGapOfNumericalSemigroup 5.1-2
AdjacentCatenaryDegreeOfSetOfFactorizations 9.3-2
AdjustmentOfNumericalSemigroup 9.2-16
AffineSemigroup, by equations 11.1-2
    by generators 11.1-1
    by inequalities 11.1-3
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 3.1-13
    for numerical semigroup with respect to integer 3.1-15
    for numerical semigroup with respect to multiplicity 3.1-14
AperyListOfIdealOfNumericalSemigroupWRTElement 7.2-11
AperyListOfNumericalSemigroup 3.1-14
AperyListOfNumericalSemigroupAsGraph 3.1-16
AperyListOfNumericalSemigroupWRTElement 3.1-13
AperyListOfNumericalSemigroupWRTInteger 3.1-15
AperyTableOfNumericalSemigroup 7.2-12
ApplyPatternToIdeal 7.3-5
ApplyPatternToNumericalSemigroup 7.3-6
ArfCharactersOfArfNumericalSemigroup 8.2-3
ArfClosure, of good semigroup 12.3-2
    of numerical semigroup 8.2-2
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
    of numerical semigroup 4.1-3
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 7.1-23
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 3.1-19
CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber 6.2-3
Conductor, for good semigroup 12.2-2
    for ideal of numerical semigroup 7.1-8
    for numerical Semigroup 3.1-21
ConductorOfGoodSemigroup 12.2-2
ConductorOfIdealOfNumericalSemigroup 7.1-8
ConductorOfNumericalSemigroup 3.1-21
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 3.1-25
Difference, for ideals of numerical semigroups 7.1-19
    for numerical semigroups 5.2-4
DifferenceOfIdealsOfNumericalSemigroup 7.1-19
DifferenceOfNumericalSemigroups 5.2-4
DivisorsOfElementInNumericalSemigroup 9.6-2
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
ElasticityOfAffineSemigroup 11.4-2
ElasticityOfFactorizationsElementWRTNumericalSemigroup 9.2-3
ElasticityOfNumericalSemigroup 9.2-4
ElementNumber_IdealOfNumericalSemigroup 7.1-11
ElementNumber_NumericalSemigroup 3.1-10
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 3.1-20
FrobeniusNumberOfNumericalSemigroup 3.1-20
FundamentalGaps, for numerical semigroup 3.1-31
FundamentalGapsOfNumericalSemigroup 3.1-31
Gaps, for numerical semigroup 3.1-24
GapsOfNumericalSemigroup 3.1-24
Generators, for affine semigroup 11.1-4
    for ideal of numerical semigroup 7.1-4
    for numerical semigroup 3.1-2
GeneratorsKahlerDifferentials 10.2-9
GeneratorsModule_Global 10.2-8
GeneratorsOfAffineSemigroup 11.1-4
GeneratorsOfIdealOfNumericalSemigroup 7.1-4
GeneratorsOfKernelCongruence 11.3-1
GeneratorsOfNumericalSemigroup 3.1-2
Genus, for numerical semigroup 3.1-30
GenusOfNumericalSemigroup 3.1-30
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
HasseDiagramOfAperyListOfNumericalSemigroup 14.1-4
HasseDiagramOfBettiElementsOfNumericalSemigroup 14.1-3
HasseDiagramOfNumericalSemigroup 14.1-2
HilbertBasisOfSystemOfHomogeneousEquations 11.1-10
HilbertBasisOfSystemOfHomogeneousInequalities 11.1-11
HilbertFunctionOfIdealOfNumericalSemigroup 7.2-1
HilbertSeriesOfNumericalSemigroup 10.1-4
Holes, for numerical semigroup 3.1-28
HolesOfNumericalSemigroup 3.1-28
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 7.1-21
    for numerical semigroups 5.2-1
IntersectionIdealsOfNumericalSemigroup 7.1-21
IntersectionOfNumericalSemigroups 5.2-1
IrreducibleMaximalElementsOfGoodSemigroup 12.2-7
IrreducibleNumericalSemigroupsWithFrobeniusNumber 6.1-5
IsACompleteIntersectionNumericalSemigroup 6.2-2
IsAcute, for numerical semigroups 3.1-27
IsAcuteNumericalSemigroup 3.1-27
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 7.1-24
IsCanonicalIdealOfNumericalSemigroup 7.1-24
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
    for numerical semigroups 4.2-2
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 3.1-26
IsOrdinaryNumericalSemigroup 3.1-26
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
    for numerical semigroups 6.1-2
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
Iterator, for ideals of numerical semigroups 7.1-15
    for numerical semigroups 3.1-12
KunzCoordinatesOfNumericalSemigroup 3.1-17
KunzPolytope 3.1-18
LatticePathAssociatedToNumericalSemigroup 3.1-29
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 7.1-22
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
    for ideal of numerical semigroup 7.1-3
    for numerical semigroup 3.1-2
MinimalGeneratingSystemOfIdealOfNumericalSemigroup 7.1-3
MinimalGeneratingSystemOfNumericalSemigroup 3.1-2
MinimalGenerators 12.2-10
    for affine semigroup 11.1-5
    for ideal of numerical semigroup 7.1-3
    for numerical semigroup 3.1-2
MinimalGoodGeneratingSystemOfGoodIdeal 12.4-4
MinimalGoodGeneratingSystemOfGoodSemigroup 12.2-9
MinimalMEDGeneratingSystemOfMEDNumericalSemigroup 8.1-3
MinimalPresentation, for affine semigroup 11.3-4
    for numerical semigroups 4.1-1
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 7.1-17
MultipleOfNumericalSemigroup 5.2-3
Multiplicity, for numerical semigroup 3.1-1
MultiplicityOfNumericalSemigroup 3.1-1
MultiplicitySequenceOfNumericalSemigroup 7.2-9
NextElementOfNumericalSemigroup 3.1-9
NumberElement_IdealOfNumericalSemigroup 7.1-12
NumberElement_NumericalSemigroup 3.1-11
NumericalDuplication 5.2-5
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
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 3.1-22
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
SetDotNSEngine 14.1-10
ShadedSetOfElementInAffineSemigroup 11.3-6
ShadedSetOfElementInNumericalSemigroup 4.1-5
SimpleForcedIntegersForPseudoFrobenius 5.6-2
SmallElements, for good ideal 12.4-6
    for good semigroup 12.2-3
    for ideal of numerical semigroup 7.1-7
    for numerical semigroup 3.1-4
SmallElementsOfGoodIdeal 12.4-6
SmallElementsOfGoodSemigroup 12.2-3
SmallElementsOfIdealOfNumericalSemigroup 7.1-7
SmallElementsOfNumericalSemigroup 3.1-4
SpecialGaps, for numerical semigroup 3.1-32
SpecialGapsOfNumericalSemigroup 3.1-32
StarClosureOfIdealOfNumericalSemigroup 7.2-13
SubtractIdealsOfNumericalSemigroup 7.1-18
SumIdealsOfNumericalSemigroup 7.1-16
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 7.1-20
TruncatedWilfNumberOfNumericalSemigroup 3.2-2
TypeOfNumericalSemigroup 3.1-23
TypeSequenceOfNumericalSemigroup 7.1-25
WilfNumber, for numerical semigroup 3.2-1
WilfNumberOfNumericalSemigroup 3.2-1

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