\indexentry{NumericalSemigroup@\texttt  {NumericalSemigroup}|hyperpage}{9}
\indexentry{ModularNumericalSemigroup@\texttt  {ModularNumericalSemigroup}|hyperpage}{10}
\indexentry{ProportionallyModularNumericalSemigroup@\texttt  {Proportionally}\discretionary {-}{}{}\texttt  {Modular}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{11}
\indexentry{NumericalSemigroupByGenerators@\texttt  {NumericalSemigroupByGenerators}|hyperpage}{11}
\indexentry{NumericalSemigroupByMinimalGenerators@\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generators}|hyperpage}{11}
\indexentry{NumericalSemigroupByMinimalGeneratorsNC@\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {GeneratorsNC}|hyperpage}{11}
\indexentry{NumericalSemigroupByInterval@\texttt  {NumericalSemigroupByInterval}|hyperpage}{11}
\indexentry{NumericalSemigroupByOpenInterval@\texttt  {NumericalSemigroupByOpenInterval}|hyperpage}{11}
\indexentry{NumericalSemigroupBySubAdditiveFunction@\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Sub}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Function}|hyperpage}{11}
\indexentry{NumericalSemigroupByAperyList@\texttt  {NumericalSemigroupByAperyList}|hyperpage}{11}
\indexentry{NumericalSemigroupBySmallElements@\texttt  {NumericalSemigroupBySmallElements}|hyperpage}{11}
\indexentry{NumericalSemigroupByGaps@\texttt  {NumericalSemigroupByGaps}|hyperpage}{11}
\indexentry{NumericalSemigroupByFundamentalGaps@\texttt  {NumericalSemigroupByFundamentalGaps}|hyperpage}{11}
\indexentry{IsNumericalSemigroup@\texttt  {IsNumericalSemigroup}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByGenerators@\texttt  {IsNumericalSemigroupByGenerators}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByMinimalGenerators@\texttt  {IsNumerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generators}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByInterval@\texttt  {IsNumericalSemigroupByInterval}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByOpenInterval@\texttt  {IsNumericalSemigroupByOpenInterval}|hyperpage}{12}
\indexentry{IsNumericalSemigroupBySubAdditiveFunction@\texttt  {IsNumerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Sub}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Function}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByAperyList@\texttt  {IsNumericalSemigroupByAperyList}|hyperpage}{12}
\indexentry{IsNumericalSemigroupBySmallElements@\texttt  {IsNumericalSemigroupBySmallElements}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByGaps@\texttt  {IsNumericalSemigroupByGaps}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByFundamentalGaps@\texttt  {IsNumerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Fundamental}\discretionary {-}{}{}\texttt  {Gaps}|hyperpage}{12}
\indexentry{IsProportionallyModularNumericalSemigroup@\texttt  {IsProportionally}\discretionary {-}{}{}\texttt  {Modular}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{12}
\indexentry{IsModularNumericalSemigroup@\texttt  {IsModularNumericalSemigroup}|hyperpage}{12}
\indexentry{RepresentsSmallElementsOfNumericalSemigroup@\texttt  {Represents}\discretionary {-}{}{}\texttt  {Small}\discretionary {-}{}{}\texttt  {Elements}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{12}
\indexentry{RepresentsGapsOfNumericalSemigroup@\texttt  {RepresentsGapsOfNumericalSemigroup}|hyperpage}{13}
\indexentry{IsAperyListOfNumericalSemigroup@\texttt  {IsAperyListOfNumericalSemigroup}|hyperpage}{13}
\indexentry{IsSubsemigroupOfNumericalSemigroup@\texttt  {IsSubsemigroupOfNumericalSemigroup}|hyperpage}{13}
\indexentry{BelongsToNumericalSemigroup@\texttt  {BelongsToNumericalSemigroup}|hyperpage}{14}
\indexentry{MultiplicityOfNumericalSemigroup@\texttt  {MultiplicityOfNumericalSemigroup}|hyperpage}{15}
\indexentry{GeneratorsOfNumericalSemigroup@\texttt  {GeneratorsOfNumericalSemigroup}|hyperpage}{15}
\indexentry{MinimalGeneratingSystemOfNumericalSemigroup@\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generating}\discretionary {-}{}{}\texttt  {System}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{15}
\indexentry{MinimalGeneratingSystem@\texttt  {MinimalGeneratingSystem}|hyperpage}{15}
\indexentry{EmbeddingDimensionOfNumericalSemigroup@\texttt  {Embedding}\discretionary {-}{}{}\texttt  {Dimension}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{16}
\indexentry{SmallElementsOfNumericalSemigroup@\texttt  {SmallElementsOfNumericalSemigroup}|hyperpage}{16}
\indexentry{SmallElements@\texttt  {SmallElements}|hyperpage}{16}
\indexentry{FirstElementsOfNumericalSemigroup@\texttt  {FirstElementsOfNumericalSemigroup}|hyperpage}{16}
\indexentry{AperyListOfNumericalSemigroupWRTElement@\texttt  {Apery}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Element}|hyperpage}{16}
\indexentry{AperyListOfNumericalSemigroup@\texttt  {AperyListOfNumericalSemigroup}|hyperpage}{17}
\indexentry{AperyListOfNumericalSemigroupWRTInteger@\texttt  {Apery}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Integer}|hyperpage}{17}
\indexentry{AperyListOfNumericalSemigroupAsGraph@\texttt  {Apery}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {As}\discretionary {-}{}{}\texttt  {Graph}|hyperpage}{17}
\indexentry{KunzCoordinatesOfNumericalSemigroup@\texttt  {KunzCoordinatesOfNumericalSemigroup}|hyperpage}{18}
\indexentry{KunzPolytope@\texttt  {KunzPolytope}|hyperpage}{18}
\indexentry{FrobeniusNumberOfNumericalSemigroup@\texttt  {FrobeniusNumberOfNumericalSemigroup}|hyperpage}{18}
\indexentry{FrobeniusNumber@\texttt  {FrobeniusNumber}|hyperpage}{19}
\indexentry{ConductorOfNumericalSemigroup@\texttt  {ConductorOfNumericalSemigroup}|hyperpage}{19}
\indexentry{PseudoFrobeniusOfNumericalSemigroup@\texttt  {PseudoFrobeniusOfNumericalSemigroup}|hyperpage}{19}
\indexentry{TypeOfNumericalSemigroup@\texttt  {TypeOfNumericalSemigroup}|hyperpage}{19}
\indexentry{GapsOfNumericalSemigroup@\texttt  {GapsOfNumericalSemigroup}|hyperpage}{19}
\indexentry{GenusOfNumericalSemigroup@\texttt  {GenusOfNumericalSemigroup}|hyperpage}{20}
\indexentry{FundamentalGapsOfNumericalSemigroup@\texttt  {FundamentalGapsOfNumericalSemigroup}|hyperpage}{20}
\indexentry{SpecialGapsOfNumericalSemigroup@\texttt  {SpecialGapsOfNumericalSemigroup}|hyperpage}{20}
\indexentry{MinimalPresentationOfNumericalSemigroup@\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Presentation}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{21}
\indexentry{GraphAssociatedToElementInNumericalSemigroup@\texttt  {Graph}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{21}
\indexentry{BettiElementsOfNumericalSemigroup@\texttt  {BettiElementsOfNumericalSemigroup}|hyperpage}{22}
\indexentry{PrimitiveElementsOfNumericalSemigroup@\texttt  {Primitive}\discretionary {-}{}{}\texttt  {Elements}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{22}
\indexentry{ShadedSetOfElementInNumericalSemigroup@\texttt  {Shaded}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{22}
\indexentry{IsUniquelyPresentedNumericalSemigroup@\texttt  {IsUniquely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{23}
\indexentry{IsGenericNumericalSemigroup@\texttt  {IsGenericNumericalSemigroup}|hyperpage}{23}
\indexentry{RemoveMinimalGeneratorFromNumericalSemigroup@\texttt  {Remove}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generator}\discretionary {-}{}{}\texttt  {From}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{24}
\indexentry{AddSpecialGapOfNumericalSemigroup@\texttt  {AddSpecialGapOfNumericalSemigroup}|hyperpage}{24}
\indexentry{IntersectionOfNumericalSemigroups@\texttt  {IntersectionOfNumericalSemigroups}|hyperpage}{25}
\indexentry{QuotientOfNumericalSemigroup@\texttt  {QuotientOfNumericalSemigroup}|hyperpage}{25}
\indexentry{OverSemigroupsNumericalSemigroup@\texttt  {OverSemigroupsNumericalSemigroup}|hyperpage}{26}
\indexentry{NumericalSemigroupsWithFrobeniusNumber@\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{26}
\indexentry{NumericalSemigroupsWithGenus@\texttt  {NumericalSemigroupsWithGenus}|hyperpage}{27}
\indexentry{ForcedIntegersForPseudoFrobenius@\texttt  {ForcedIntegersForPseudoFrobenius}|hyperpage}{27}
\indexentry{SimpleForcedIntegersForPseudoFrobenius@\texttt  {Simple}\discretionary {-}{}{}\texttt  {Forced}\discretionary {-}{}{}\texttt  {Integers}\discretionary {-}{}{}\texttt  {For}\discretionary {-}{}{}\texttt  {Pseudo}\discretionary {-}{}{}\texttt  {Frobenius}|hyperpage}{28}
\indexentry{NumericalSemigroupsWithPseudoFrobeniusNumbers@\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Pseudo}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Numbers}|hyperpage}{28}
\indexentry{RandomNumericalSemigroupWithPseudoFrobeniusNumbers@\texttt  {Random}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Pseudo}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Numbers}|hyperpage}{29}
\indexentry{IsIrreducibleNumericalSemigroup@\texttt  {IsIrreducibleNumericalSemigroup}|hyperpage}{30}
\indexentry{IsSymmetricNumericalSemigroup@\texttt  {IsSymmetricNumericalSemigroup}|hyperpage}{31}
\indexentry{IsPseudoSymmetricNumericalSemigroup@\texttt  {IsPseudoSymmetricNumericalSemigroup}|hyperpage}{31}
\indexentry{AnIrreducibleNumericalSemigroupWithFrobeniusNumber@\texttt  {AnIrreducible}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{31}
\indexentry{IrreducibleNumericalSemigroupsWithFrobeniusNumber@\texttt  {Irreducible}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{31}
\indexentry{DecomposeIntoIrreducibles@\texttt  {DecomposeIntoIrreducibles}|hyperpage}{31}
\indexentry{AsGluingOfNumericalSemigroups@\texttt  {AsGluingOfNumericalSemigroups}|hyperpage}{32}
\indexentry{IsACompleteIntersectionNumericalSemigroup@\texttt  {IsA}\discretionary {-}{}{}\texttt  {Complete}\discretionary {-}{}{}\texttt  {Intersection}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{32}
\indexentry{CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber@\texttt  {Complete}\discretionary {-}{}{}\texttt  {Intersection}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{33}
\indexentry{IsFreeNumericalSemigroup@\texttt  {IsFreeNumericalSemigroup}|hyperpage}{33}
\indexentry{FreeNumericalSemigroupsWithFrobeniusNumber@\texttt  {Free}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{33}
\indexentry{IsTelescopicNumericalSemigroup@\texttt  {IsTelescopicNumericalSemigroup}|hyperpage}{33}
\indexentry{TelescopicNumericalSemigroupsWithFrobeniusNumber@\texttt  {Telescopic}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{34}
\indexentry{IsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity@\texttt  {IsNumerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {Irreducible}\discretionary {-}{}{}\texttt  {Planar}\discretionary {-}{}{}\texttt  {Curve}\discretionary {-}{}{}\texttt  {Singularity}|hyperpage}{34}
\indexentry{NumericalSemigroupsAssociatedIrreduciblePlanarCurveSingularityWithFrobeniusNumber@\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {Irreducible}\discretionary {-}{}{}\texttt  {Planar}\discretionary {-}{}{}\texttt  {Curve}\discretionary {-}{}{}\texttt  {Singularity}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{34}
\indexentry{AlmostSymmetricNumericalSemigroupsFromIrreducible@\texttt  {Almost}\discretionary {-}{}{}\texttt  {Symmetric}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {From}\discretionary {-}{}{}\texttt  {Irreducible}|hyperpage}{35}
\indexentry{IsAlmostSymmetricNumericalSemigroup@\texttt  {IsAlmostSymmetricNumericalSemigroup}|hyperpage}{35}
\indexentry{AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber@\texttt  {Almost}\discretionary {-}{}{}\texttt  {Symmetric}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{35}
\indexentry{IdealOfNumericalSemigroup@\texttt  {IdealOfNumericalSemigroup}|hyperpage}{36}
\indexentry{IsIdealOfNumericalSemigroup@\texttt  {IsIdealOfNumericalSemigroup}|hyperpage}{36}
\indexentry{MinimalGeneratingSystemOfIdealOfNumericalSemigroup@\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generating}\discretionary {-}{}{}\texttt  {System}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{37}
\indexentry{MinimalGeneratingSystem@\texttt  {MinimalGeneratingSystem}|hyperpage}{37}
\indexentry{GeneratorsOfIdealOfNumericalSemigroup@\texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{37}
\indexentry{GeneratorsOfIdealOfNumericalSemigroupNC@\texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {SemigroupNC}|hyperpage}{37}
\indexentry{AmbientNumericalSemigroupOfIdeal@\texttt  {AmbientNumericalSemigroupOfIdeal}|hyperpage}{37}
\indexentry{SmallElementsOfIdealOfNumericalSemigroup@\texttt  {Small}\discretionary {-}{}{}\texttt  {Elements}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{38}
\indexentry{SmallElements@\texttt  {SmallElements}|hyperpage}{38}
\indexentry{BelongsToIdealOfNumericalSemigroup@\texttt  {BelongsToIdealOfNumericalSemigroup}|hyperpage}{38}
\indexentry{SumIdealsOfNumericalSemigroup@\texttt  {SumIdealsOfNumericalSemigroup}|hyperpage}{38}
\indexentry{MultipleOfIdealOfNumericalSemigroup@\texttt  {MultipleOfIdealOfNumericalSemigroup}|hyperpage}{39}
\indexentry{SubtractIdealsOfNumericalSemigroup@\texttt  {SubtractIdealsOfNumericalSemigroup}|hyperpage}{39}
\indexentry{DifferenceOfIdealsOfNumericalSemigroup@\texttt  {Difference}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideals}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{39}
\indexentry{TranslationOfIdealOfNumericalSemigroup@\texttt  {Translation}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{40}
\indexentry{IntersectionIdealsOfNumericalSemigroup@\texttt  {Intersection}\discretionary {-}{}{}\texttt  {Ideals}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{40}
\indexentry{MaximalIdealOfNumericalSemigroup@\texttt  {MaximalIdealOfNumericalSemigroup}|hyperpage}{40}
\indexentry{CanonicalIdealOfNumericalSemigroup@\texttt  {CanonicalIdealOfNumericalSemigroup}|hyperpage}{41}
\indexentry{HilbertFunctionOfIdealOfNumericalSemigroup@\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Function}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{41}
\indexentry{BlowUpIdealOfNumericalSemigroup@\texttt  {BlowUpIdealOfNumericalSemigroup}|hyperpage}{41}
\indexentry{ReductionNumberIdealNumericalSemigroup@\texttt  {Reduction}\discretionary {-}{}{}\texttt  {Number}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{41}
\indexentry{BlowUpOfNumericalSemigroup@\texttt  {BlowUpOfNumericalSemigroup}|hyperpage}{42}
\indexentry{MicroInvariantsOfNumericalSemigroup@\texttt  {MicroInvariantsOfNumericalSemigroup}|hyperpage}{42}
\indexentry{IsGradedAssociatedRingNumericalSemigroupCM@\texttt  {IsGraded}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {SemigroupCM}|hyperpage}{42}
\indexentry{IsMonomialNumericalSemigroup@\texttt  {IsMonomialNumericalSemigroup}|hyperpage}{43}
\indexentry{AperyListOfIdealOfNumericalSemigroupWRTElement@\texttt  {Apery}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Element}|hyperpage}{43}
\indexentry{AperyTableOfNumericalSemigroup@\texttt  {AperyTableOfNumericalSemigroup}|hyperpage}{44}
\indexentry{StarClosureOfIdealOfNumericalSemigroup@\texttt  {Star}\discretionary {-}{}{}\texttt  {Closure}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{44}
\indexentry{IsMEDNumericalSemigroup@\texttt  {IsMEDNumericalSemigroup}|hyperpage}{45}
\indexentry{MEDNumericalSemigroupClosure@\texttt  {MEDNumericalSemigroupClosure}|hyperpage}{46}
\indexentry{MinimalMEDGeneratingSystemOfMEDNumericalSemigroup@\texttt  {Minimal}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {D}\discretionary {-}{}{}\texttt  {Generating}\discretionary {-}{}{}\texttt  {System}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {M}\discretionary {-}{}{}\texttt  {E}\discretionary {-}{}{}\texttt  {D}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{46}
\indexentry{IsArfNumericalSemigroup@\texttt  {IsArfNumericalSemigroup}|hyperpage}{46}
\indexentry{ArfNumericalSemigroupClosure@\texttt  {ArfNumericalSemigroupClosure}|hyperpage}{47}
\indexentry{MinimalArfGeneratingSystemOfArfNumericalSemigroup@\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Arf}\discretionary {-}{}{}\texttt  {Generating}\discretionary {-}{}{}\texttt  {System}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Arf}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{47}
\indexentry{ArfNumericalSemigroupsWithFrobeniusNumber@\texttt  {Arf}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{47}
\indexentry{IsSaturatedNumericalSemigroup@\texttt  {IsSaturatedNumericalSemigroup}|hyperpage}{48}
\indexentry{SaturatedNumericalSemigroupClosure@\texttt  {SaturatedNumericalSemigroupClosure}|hyperpage}{48}
\indexentry{SaturatedNumericalSemigroupsWithFrobeniusNumber@\texttt  {Saturated}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{48}
\indexentry{FactorizationsIntegerWRTList@\texttt  {FactorizationsIntegerWRTList}|hyperpage}{49}
\indexentry{FactorizationsElementWRTNumericalSemigroup@\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{50}
\indexentry{RClassesOfSetOfFactorizations@\texttt  {RClassesOfSetOfFactorizations}|hyperpage}{50}
\indexentry{LShapesOfNumericalSemigroup@\texttt  {LShapesOfNumericalSemigroup}|hyperpage}{50}
\indexentry{DenumerantOfElementInNumericalSemigroup@\texttt  {Denumerant}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{51}
\indexentry{LengthsOfFactorizationsIntegerWRTList@\texttt  {Lengths}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {Integer}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {List}|hyperpage}{51}
\indexentry{LengthsOfFactorizationsElementWRTNumericalSemigroup@\texttt  {Lengths}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{51}
\indexentry{ElasticityOfFactorizationsElementWRTNumericalSemigroup@\texttt  {Elasticity}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{51}
\indexentry{ElasticityOfNumericalSemigroup@\texttt  {ElasticityOfNumericalSemigroup}|hyperpage}{52}
\indexentry{DeltaSetOfSetOfIntegers@\texttt  {DeltaSetOfSetOfIntegers}|hyperpage}{52}
\indexentry{DeltaSetOfFactorizationsElementWRTNumericalSemigroup@\texttt  {Delta}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{52}
\indexentry{MaximumDegreeOfElementWRTNumericalSemigroup@\texttt  {Maximum}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{52}
\indexentry{MaximalDenumerantOfElementInNumericalSemigroup@\texttt  {Maximal}\discretionary {-}{}{}\texttt  {Denumerant}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{53}
\indexentry{MaximalDenumerantOfSetOfFactorizations@\texttt  {Maximal}\discretionary {-}{}{}\texttt  {Denumerant}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}|hyperpage}{53}
\indexentry{MaximalDenumerantOfNumericalSemigroup@\texttt  {Maximal}\discretionary {-}{}{}\texttt  {Denumerant}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{53}
\indexentry{AdjustmentOfNumericalSemigroup@\texttt  {AdjustmentOfNumericalSemigroup}|hyperpage}{53}
\indexentry{IsAdditiveNumericalSemigroup@\texttt  {IsAdditiveNumericalSemigroup}|hyperpage}{54}
\indexentry{IsSuperSymmetricNumericalSemigroup@\texttt  {IsSuperSymmetricNumericalSemigroup}|hyperpage}{54}
\indexentry{CatenaryDegreeOfSetOfFactorizations@\texttt  {CatenaryDegreeOfSetOfFactorizations}|hyperpage}{54}
\indexentry{AdjacentCatenaryDegreeOfSetOfFactorizations@\texttt  {Adjacent}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}|hyperpage}{55}
\indexentry{EqualCatenaryDegreeOfSetOfFactorizations@\texttt  {Equal}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}|hyperpage}{55}
\indexentry{MonotoneCatenaryDegreeOfSetOfFactorizations@\texttt  {Monotone}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Factorizations}|hyperpage}{55}
\indexentry{CatenaryDegreeOfElementInNumericalSemigroup@\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{56}
\indexentry{TameDegreeOfSetOfFactorizations@\texttt  {TameDegreeOfSetOfFactorizations}|hyperpage}{56}
\indexentry{CatenaryDegreeOfNumericalSemigroup@\texttt  {CatenaryDegreeOfNumericalSemigroup}|hyperpage}{56}
\indexentry{EqualPrimitiveElementsOfNumericalSemigroup@\texttt  {Equal}\discretionary {-}{}{}\texttt  {Primitive}\discretionary {-}{}{}\texttt  {Elements}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{56}
\indexentry{EqualCatenaryDegreeOfNumericalSemigroup@\texttt  {Equal}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{57}
\indexentry{MonotonePrimitiveElementsOfNumericalSemigroup@\texttt  {Monotone}\discretionary {-}{}{}\texttt  {Primitive}\discretionary {-}{}{}\texttt  {Elements}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{57}
\indexentry{MonotoneCatenaryDegreeOfNumericalSemigroup@\texttt  {Monotone}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{57}
\indexentry{TameDegreeOfNumericalSemigroup@\texttt  {TameDegreeOfNumericalSemigroup}|hyperpage}{57}
\indexentry{TameDegreeOfElementInNumericalSemigroup@\texttt  {Tame}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{58}
\indexentry{OmegaPrimalityOfElementInNumericalSemigroup@\texttt  {Omega}\discretionary {-}{}{}\texttt  {Primality}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{58}
\indexentry{OmegaPrimalityOfNumericalSemigroup@\texttt  {OmegaPrimalityOfNumericalSemigroup}|hyperpage}{58}
\indexentry{BelongsToHomogenizationOfNumericalSemigroup@\texttt  {Belongs}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {Homogenization}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{59}
\indexentry{FactorizationsInHomogenizationOfNumericalSemigroup@\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Homogenization}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{59}
\indexentry{HomogeneousBettiElementsOfNumericalSemigroup@\texttt  {Homogeneous}\discretionary {-}{}{}\texttt  {Betti}\discretionary {-}{}{}\texttt  {Elements}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{59}
\indexentry{HomogeneousCatenaryDegreeOfNumericalSemigroup@\texttt  {Homogeneous}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{60}
\indexentry{MoebiusFunctionAssociatedToNumericalSemigroup@\texttt  {Moebius}\discretionary {-}{}{}\texttt  {Function}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{60}
\indexentry{NumericalSemigroupPolynomial@\texttt  {NumericalSemigroupPolynomial}|hyperpage}{61}
\indexentry{HilbertSeriesOfNumericalSemigroup@\texttt  {HilbertSeriesOfNumericalSemigroup}|hyperpage}{61}
\indexentry{GraeffePolynomial@\texttt  {GraeffePolynomial}|hyperpage}{61}
\indexentry{IsCyclotomicPolynomial@\texttt  {IsCyclotomicPolynomial}|hyperpage}{62}
\indexentry{IsKroneckerPolynomial@\texttt  {IsKroneckerPolynomial}|hyperpage}{62}
\indexentry{IsCyclotomicNumericalSemigroup@\texttt  {IsCyclotomicNumericalSemigroup}|hyperpage}{62}
\indexentry{IsSelfReciprocalUnivariatePolynomial@\texttt  {IsSelf}\discretionary {-}{}{}\texttt  {Reciprocal}\discretionary {-}{}{}\texttt  {Univariate}\discretionary {-}{}{}\texttt  {Polynomial}|hyperpage}{63}
\indexentry{SemigroupOfValuesOfPlaneCurveWithSinglePlaceAtInfinity@\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Values}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Plane}\discretionary {-}{}{}\texttt  {Curve}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Single}\discretionary {-}{}{}\texttt  {Place}\discretionary {-}{}{}\texttt  {At}\discretionary {-}{}{}\texttt  {Infinity}|hyperpage}{63}
\indexentry{IsDeltaSequence@\texttt  {IsDeltaSequence}|hyperpage}{63}
\indexentry{DeltaSequencesWithFrobeniusNumber@\texttt  {DeltaSequencesWithFrobeniusNumber}|hyperpage}{64}
\indexentry{CurveAssociatedToDeltaSequence@\texttt  {CurveAssociatedToDeltaSequence}|hyperpage}{64}
\indexentry{SemigroupOfValuesOfCurveLocal@\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Values}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Curve{\textunderscore }}\discretionary {-}{}{}\texttt  {Local}|hyperpage}{64}
\indexentry{SemigroupOfValuesOfCurveGlobal@\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Values}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Curve{\textunderscore }}\discretionary {-}{}{}\texttt  {Global}|hyperpage}{65}
\indexentry{NumSgpsUse4ti2@\texttt  {NumSgpsUse4ti2}|hyperpage}{66}
\indexentry{NumSgpsUse4ti2gap@\texttt  {NumSgpsUse4ti2gap}|hyperpage}{66}
\indexentry{NumSgpsUseNormalize@\texttt  {NumSgpsUseNormalize}|hyperpage}{66}
\indexentry{NumSgpsUseSingular@\texttt  {NumSgpsUseSingular}|hyperpage}{67}
\indexentry{NumSgpsUseSingularInterface@\texttt  {NumSgpsUseSingularInterface}|hyperpage}{67}
\indexentry{NumSgpsUseSingularGradedModules@\texttt  {NumSgpsUseSingularGradedModules}|hyperpage}{67}
\indexentry{AffineSemigroup@\texttt  {AffineSemigroup}|hyperpage}{67}
\indexentry{AsAffineSemigroup@\texttt  {AsAffineSemigroup}|hyperpage}{68}
\indexentry{IsAffineSemigroup@\texttt  {IsAffineSemigroup}|hyperpage}{68}
\indexentry{IsAffineSemigroupByGenerators@\texttt  {IsAffineSemigroupByGenerators}|hyperpage}{68}
\indexentry{IsAffineSemigroupByMinimalGenerators@\texttt  {IsAffine}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generators}|hyperpage}{68}
\indexentry{IsAffineSemigroupByEquations@\texttt  {IsAffineSemigroupByEquations}|hyperpage}{68}
\indexentry{IsAffineSemigroupByInequalities@\texttt  {IsAffineSemigroupByInequalities}|hyperpage}{68}
\indexentry{BelongsToAffineSemigroup@\texttt  {BelongsToAffineSemigroup}|hyperpage}{69}
\indexentry{IsFullAffineSemigroup@\texttt  {IsFullAffineSemigroup}|hyperpage}{69}
\indexentry{HilbertBasisOfSystemOfHomogeneousEquations@\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Basis}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {System}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Homogeneous}\discretionary {-}{}{}\texttt  {Equations}|hyperpage}{69}
\indexentry{HilbertBasisOfSystemOfHomogeneousInequalities@\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Basis}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {System}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Homogeneous}\discretionary {-}{}{}\texttt  {Inequalities}|hyperpage}{70}
\indexentry{EquationsOfGroupGeneratedBy@\texttt  {EquationsOfGroupGeneratedBy}|hyperpage}{70}
\indexentry{BasisOfGroupGivenByEquations@\texttt  {BasisOfGroupGivenByEquations}|hyperpage}{70}
\indexentry{GluingOfAffineSemigroups@\texttt  {GluingOfAffineSemigroups}|hyperpage}{71}
\indexentry{GeneratorsOfKernelCongruence@\texttt  {GeneratorsOfKernelCongruence}|hyperpage}{71}
\indexentry{MinimalPresentationOfAffineSemigroup@\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Presentation}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Affine}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{71}
\indexentry{BettiElementsOfAffineSemigroup@\texttt  {BettiElementsOfAffineSemigroup}|hyperpage}{72}
\indexentry{ShadedSetOfElementInAffineSemigroup@\texttt  {ShadedSetOfElementInAffineSemigroup}|hyperpage}{72}
\indexentry{IsGenericAffineSemigroup@\texttt  {IsGenericAffineSemigroup}|hyperpage}{72}
\indexentry{IsUniquelyPresentedAffineSemigroup@\texttt  {IsUniquelyPresentedAffineSemigroup}|hyperpage}{72}
\indexentry{PrimitiveElementsOfAffineSemigroup@\texttt  {PrimitiveElementsOfAffineSemigroup}|hyperpage}{72}
\indexentry{FactorizationsVectorWRTList@\texttt  {FactorizationsVectorWRTList}|hyperpage}{73}
\indexentry{ElasticityOfAffineSemigroup@\texttt  {ElasticityOfAffineSemigroup}|hyperpage}{73}
\indexentry{CatenaryDegreeOfAffineSemigroup@\texttt  {CatenaryDegreeOfAffineSemigroup}|hyperpage}{73}
\indexentry{EqualCatenaryDegreeOfAffineSemigroup@\texttt  {Equal}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Affine}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{74}
\indexentry{HomogeneousCatenaryDegreeOfAffineSemigroup@\texttt  {Homogeneous}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Affine}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{74}
\indexentry{MonotoneCatenaryDegreeOfAffineSemigroup@\texttt  {Monotone}\discretionary {-}{}{}\texttt  {Catenary}\discretionary {-}{}{}\texttt  {Degree}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Affine}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{74}
\indexentry{TameDegreeOfAffineSemigroup@\texttt  {TameDegreeOfAffineSemigroup}|hyperpage}{74}
\indexentry{OmegaPrimalityOfElementInAffineSemigroup@\texttt  {Omega}\discretionary {-}{}{}\texttt  {Primality}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Affine}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{75}
\indexentry{OmegaPrimalityOfAffineSemigroup@\texttt  {OmegaPrimalityOfAffineSemigroup}|hyperpage}{75}
\indexentry{BezoutSequence@\texttt  {BezoutSequence}|hyperpage}{76}
\indexentry{IsBezoutSequence@\texttt  {IsBezoutSequence}|hyperpage}{76}
\indexentry{CeilingOfRational@\texttt  {CeilingOfRational}|hyperpage}{77}
\indexentry{RepresentsPeriodicSubAdditiveFunction@\texttt  {Represents}\discretionary {-}{}{}\texttt  {Periodic}\discretionary {-}{}{}\texttt  {Sub}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Function}|hyperpage}{77}
\indexentry{IsListOfIntegersNS@\texttt  {IsListOfIntegersNS}|hyperpage}{77}
\indexentry{RandomNumericalSemigroup@\texttt  {RandomNumericalSemigroup}|hyperpage}{78}
\indexentry{RandomListForNS@\texttt  {RandomListForNS}|hyperpage}{78}
\indexentry{RandomModularNumericalSemigroup@\texttt  {RandomModularNumericalSemigroup}|hyperpage}{78}
\indexentry{RandomProportionallyModularNumericalSemigroup@\texttt  {Random}\discretionary {-}{}{}\texttt  {Proportionally}\discretionary {-}{}{}\texttt  {Modular}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{79}
\indexentry{RandomListRepresentingSubAdditiveFunction@\texttt  {Random}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {Representing}\discretionary {-}{}{}\texttt  {Sub}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Function}|hyperpage}{79}
\indexentry{IsGradedAssociatedRingNumericalSemigroupBuchsbaum@\texttt  {IsGraded}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {Buchsbaum}|hyperpage}{80}
\indexentry{IsMpureNumericalSemigroup@\texttt  {IsMpureNumericalSemigroup}|hyperpage}{80}
\indexentry{IsPureNumericalSemigroup@\texttt  {IsPureNumericalSemigroup}|hyperpage}{80}
\indexentry{IsGradedAssociatedRingNumericalSemigroupGorenstein@\texttt  {IsGraded}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {Gorenstein}|hyperpage}{81}
\indexentry{IsGradedAssociatedRingNumericalSemigroupCI@\texttt  {IsGraded}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {SemigroupCI}|hyperpage}{81}
\indexentry{IsAperySetGammaRectangular@\texttt  {IsAperySetGammaRectangular}|hyperpage}{81}
\indexentry{IsAperySetBetaRectangular@\texttt  {IsAperySetBetaRectangular}|hyperpage}{82}
\indexentry{IsAperySetAlphaRectangular@\texttt  {IsAperySetAlphaRectangular}|hyperpage}{82}
\indexentry{TypeSequenceOfNumericalSemigroup@\texttt  {TypeSequenceOfNumericalSemigroup}|hyperpage}{82}
\indexentry{OmegaPrimalityOfElementListInNumericalSemigroup@\texttt  {Omega}\discretionary {-}{}{}\texttt  {Primality}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{83}
\indexentry{FactorizationsElementListWRTNumericalSemigroup@\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{83}
\indexentry{DeltaSetPeriodicityBoundForNumericalSemigroup@\texttt  {Delta}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Periodicity}\discretionary {-}{}{}\texttt  {Bound}\discretionary {-}{}{}\texttt  {For}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{84}
\indexentry{DeltaSetPeriodicityStartForNumericalSemigroup@\texttt  {Delta}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Periodicity}\discretionary {-}{}{}\texttt  {Start}\discretionary {-}{}{}\texttt  {For}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{84}
\indexentry{DeltaSetListUpToElementWRTNumericalSemigroup@\texttt  {Delta}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {Up}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{84}
\indexentry{DeltaSetUnionUpToElementWRTNumericalSemigroup@\texttt  {Delta}\discretionary {-}{}{}\texttt  {Set}\discretionary {-}{}{}\texttt  {Union}\discretionary {-}{}{}\texttt  {Up}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{84}
\indexentry{DeltaSetOfNumericalSemigroup@\texttt  {DeltaSetOfNumericalSemigroup}|hyperpage}{85}
