\indexentry{NumericalSemigroup@\texttt  {NumericalSemigroup}|hyperpage}{9}
\indexentry{ModularNumericalSemigroup@\texttt  {ModularNumericalSemigroup}|hyperpage}{10}
\indexentry{ProportionallyModularNumericalSemigroup@\texttt  {ProportionallyModularNumericalSemigroup}|hyperpage}{10}
\indexentry{NumericalSemigroupByGenerators@\texttt  {NumericalSemigroupByGenerators}|hyperpage}{11}
\indexentry{NumericalSemigroupByMinimalGenerators@\texttt  {NumericalSemigroupByMinimalGenerators}|hyperpage}{11}
\indexentry{NumericalSemigroupByMinimalGeneratorsNC@\texttt  {NumericalSemigroupByMinimalGeneratorsNC}|hyperpage}{11}
\indexentry{NumericalSemigroupByInterval@\texttt  {NumericalSemigroupByInterval}|hyperpage}{11}
\indexentry{NumericalSemigroupByOpenInterval@\texttt  {NumericalSemigroupByOpenInterval}|hyperpage}{11}
\indexentry{NumericalSemigroupBySubAdditiveFunction@\texttt  {NumericalSemigroupBySubAdditiveFunction}|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}{11}
\indexentry{IsNumericalSemigroupByGenerators@\texttt  {IsNumericalSemigroupByGenerators}|hyperpage}{11}
\indexentry{IsNumericalSemigroupByMinimalGenerators@\texttt  {IsNumericalSemigroupByMinimalGenerators}|hyperpage}{11}
\indexentry{IsNumericalSemigroupByInterval@\texttt  {IsNumericalSemigroupByInterval}|hyperpage}{11}
\indexentry{IsNumericalSemigroupByOpenInterval@\texttt  {IsNumericalSemigroupByOpenInterval}|hyperpage}{11}
\indexentry{IsNumericalSemigroupBySubAdditiveFunction@\texttt  {IsNumerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {Sub}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Function}|hyperpage}{11}
\indexentry{IsNumericalSemigroupByAperyList@\texttt  {IsNumericalSemigroupByAperyList}|hyperpage}{11}
\indexentry{IsNumericalSemigroupBySmallElements@\texttt  {IsNumericalSemigroupBySmallElements}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByGaps@\texttt  {IsNumericalSemigroupByGaps}|hyperpage}{12}
\indexentry{IsNumericalSemigroupByFundamentalGaps@\texttt  {IsNumericalSemigroupByFundamentalGaps}|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}{12}
\indexentry{IsAperyListOfNumericalSemigroup@\texttt  {IsAperyListOfNumericalSemigroup}|hyperpage}{13}
\indexentry{IsSubsemigroupOfNumericalSemigroup@\texttt  {IsSubsemigroupOfNumericalSemigroup}|hyperpage}{13}
\indexentry{BelongsToNumericalSemigroup@\texttt  {BelongsToNumericalSemigroup}|hyperpage}{13}
\indexentry{MultiplicityOfNumericalSemigroup@\texttt  {MultiplicityOfNumericalSemigroup}|hyperpage}{15}
\indexentry{GeneratorsOfNumericalSemigroup@\texttt  {GeneratorsOfNumericalSemigroup}|hyperpage}{15}
\indexentry{GeneratorsOfNumericalSemigroupNC@\texttt  {GeneratorsOfNumericalSemigroupNC}|hyperpage}{15}
\indexentry{MinimalGeneratingSystemOfNumericalSemigroup@\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generating}\discretionary {-}{}{}\texttt  {System}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{15}
\indexentry{SmallElementsOfNumericalSemigroup@\texttt  {SmallElementsOfNumericalSemigroup}|hyperpage}{16}
\indexentry{FirstElementsOfNumericalSemigroup@\texttt  {FirstElementsOfNumericalSemigroup}|hyperpage}{16}
\indexentry{AperyListOfNumericalSemigroupWRTElement@\texttt  {AperyListOfNumericalSemigroupWRTElement}|hyperpage}{16}
\indexentry{DrawAperyListOfNumericalSemigroup@\texttt  {DrawAperyListOfNumericalSemigroup}|hyperpage}{16}
\indexentry{AperyListOfNumericalSemigroupAsGraph@\texttt  {AperyListOfNumericalSemigroupAsGraph}|hyperpage}{17}
\indexentry{FrobeniusNumberOfNumericalSemigroup@\texttt  {FrobeniusNumberOfNumericalSemigroup}|hyperpage}{17}
\indexentry{FrobeniusNumber@\texttt  {FrobeniusNumber}|hyperpage}{17}
\indexentry{PseudoFrobeniusOfNumericalSemigroup@\texttt  {PseudoFrobeniusOfNumericalSemigroup}|hyperpage}{17}
\indexentry{GapsOfNumericalSemigroup@\texttt  {GapsOfNumericalSemigroup}|hyperpage}{18}
\indexentry{FundamentalGapsOfNumericalSemigroup@\texttt  {FundamentalGapsOfNumericalSemigroup}|hyperpage}{18}
\indexentry{SpecialGapsOfNumericalSemigroup@\texttt  {SpecialGapsOfNumericalSemigroup}|hyperpage}{18}
\indexentry{FortenTruncatedNCForNumericalSemigroups@\texttt  {FortenTruncatedNCForNumericalSemigroups}|hyperpage}{19}
\indexentry{MinimalPresentationOfNumericalSemigroup@\texttt  {MinimalPresentationOfNumericalSemigroup}|hyperpage}{19}
\indexentry{GraphAssociatedToElementInNumericalSemigroup@\texttt  {Graph}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {In}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{20}
\indexentry{RemoveMinimalGeneratorFromNumericalSemigroup@\texttt  {Remove}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Generator}\discretionary {-}{}{}\texttt  {From}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{21}
\indexentry{AddSpecialGapOfNumericalSemigroup@\texttt  {AddSpecialGapOfNumericalSemigroup}|hyperpage}{21}
\indexentry{IntersectionOfNumericalSemigroups@\texttt  {IntersectionOfNumericalSemigroups}|hyperpage}{22}
\indexentry{QuotientOfNumericalSemigroup@\texttt  {QuotientOfNumericalSemigroup}|hyperpage}{22}
\indexentry{OverSemigroupsNumericalSemigroup@\texttt  {OverSemigroupsNumericalSemigroup}|hyperpage}{23}
\indexentry{NumericalSemigroupsWithFrobeniusNumber@\texttt  {NumericalSemigroupsWithFrobeniusNumber}|hyperpage}{23}
\indexentry{NumericalSemigroupsWithGenus@\texttt  {NumericalSemigroupsWithGenus}|hyperpage}{23}
\indexentry{IsIrreducibleNumericalSemigroup@\texttt  {IsIrreducibleNumericalSemigroup}|hyperpage}{25}
\indexentry{IsSymmetricNumericalSemigroup@\texttt  {IsSymmetricNumericalSemigroup}|hyperpage}{26}
\indexentry{IsPseudoSymmetricNumericalSemigroup@\texttt  {IsPseudoSymmetricNumericalSemigroup}|hyperpage}{26}
\indexentry{AnIrreducibleNumericalSemigroupWithFrobeniusNumber@\texttt  {AnIrreducible}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{26}
\indexentry{IrreducibleNumericalSemigroupsWithFrobeniusNumber@\texttt  {Irreducible}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroups}\discretionary {-}{}{}\texttt  {With}\discretionary {-}{}{}\texttt  {Frobenius}\discretionary {-}{}{}\texttt  {Number}|hyperpage}{26}
\indexentry{DecomposeIntoIrreducibles@\texttt  {DecomposeIntoIrreducibles}|hyperpage}{27}
\indexentry{IdealOfNumericalSemigroup@\texttt  {IdealOfNumericalSemigroup}|hyperpage}{28}
\indexentry{IsIdealOfNumericalSemigroup@\texttt  {IsIdealOfNumericalSemigroup}|hyperpage}{28}
\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}{29}
\indexentry{GeneratorsOfIdealOfNumericalSemigroup@\texttt  {GeneratorsOfIdealOfNumericalSemigroup}|hyperpage}{29}
\indexentry{GeneratorsOfIdealOfNumericalSemigroupNC@\texttt  {GeneratorsOfIdealOfNumericalSemigroupNC}|hyperpage}{29}
\indexentry{AmbientNumericalSemigroupOfIdeal@\texttt  {AmbientNumericalSemigroupOfIdeal}|hyperpage}{29}
\indexentry{SmallElementsOfIdealOfNumericalSemigroup@\texttt  {SmallElementsOfIdealOfNumericalSemigroup}|hyperpage}{30}
\indexentry{BelongsToIdealOfNumericalSemigroup@\texttt  {BelongsToIdealOfNumericalSemigroup}|hyperpage}{30}
\indexentry{SumIdealsOfNumericalSemigroup@\texttt  {SumIdealsOfNumericalSemigroup}|hyperpage}{31}
\indexentry{MultipleOfIdealOfNumericalSemigroup@\texttt  {MultipleOfIdealOfNumericalSemigroup}|hyperpage}{31}
\indexentry{SubtractIdealsOfNumericalSemigroup@\texttt  {SubtractIdealsOfNumericalSemigroup}|hyperpage}{31}
\indexentry{DifferenceOfIdealsOfNumericalSemigroup@\texttt  {DifferenceOfIdealsOfNumericalSemigroup}|hyperpage}{32}
\indexentry{TranslationOfIdealOfNumericalSemigroup@\texttt  {TranslationOfIdealOfNumericalSemigroup}|hyperpage}{32}
\indexentry{HilbertFunctionOfIdealOfNumericalSemigroup@\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Function}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ideal}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{33}
\indexentry{BlowUpIdealOfNumericalSemigroup@\texttt  {BlowUpIdealOfNumericalSemigroup}|hyperpage}{33}
\indexentry{ReductionNumberIdealNumericalSemigroup@\texttt  {ReductionNumberIdealNumericalSemigroup}|hyperpage}{33}
\indexentry{MaximalIdealOfNumericalSemigroup@\texttt  {MaximalIdealOfNumericalSemigroup}|hyperpage}{34}
\indexentry{BlowUpOfNumericalSemigroup@\texttt  {BlowUpOfNumericalSemigroup}|hyperpage}{34}
\indexentry{MicroInvariantsOfNumericalSemigroup@\texttt  {MicroInvariantsOfNumericalSemigroup}|hyperpage}{34}
\indexentry{IsGradedAssociatedRingNumericalSemigroupCM@\texttt  {IsGraded}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {SemigroupCM}|hyperpage}{35}
\indexentry{CanonicalIdealOfNumericalSemigroup@\texttt  {CanonicalIdealOfNumericalSemigroup}|hyperpage}{35}
\indexentry{IntersectionIdealsOfNumericalSemigroup@\texttt  {IntersectionIdealsOfNumericalSemigroup}|hyperpage}{36}
\indexentry{IsMonomialNumericalSemigroup@\texttt  {IsMonomialNumericalSemigroup}|hyperpage}{36}
\indexentry{IsMEDNumericalSemigroup@\texttt  {IsMEDNumericalSemigroup}|hyperpage}{37}
\indexentry{MEDNumericalSemigroupClosure@\texttt  {MEDNumericalSemigroupClosure}|hyperpage}{38}
\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}{38}
\indexentry{IsArfNumericalSemigroup@\texttt  {IsArfNumericalSemigroup}|hyperpage}{38}
\indexentry{ArfNumericalSemigroupClosure@\texttt  {ArfNumericalSemigroupClosure}|hyperpage}{39}
\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}{39}
\indexentry{FactorizationsElementWRTNumericalSemigroup@\texttt  {Factorizations}\discretionary {-}{}{}\texttt  {Element}\discretionary {-}{}{}\texttt  {W}\discretionary {-}{}{}\texttt  {R}\discretionary {-}{}{}\texttt  {T}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{40}
\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}{41}
\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}{41}
\indexentry{ElasticityOfNumericalSemigroup@\texttt  {ElasticityOfNumericalSemigroup}|hyperpage}{41}
\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}{41}
\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}{42}
\indexentry{CatenaryDegreeOfNumericalSemigroup@\texttt  {CatenaryDegreeOfNumericalSemigroup}|hyperpage}{42}
\indexentry{CatenaryDegreeOfElementNS@\texttt  {CatenaryDegreeOfElementNS}|hyperpage}{42}
\indexentry{TameDegreeOfNumericalSemigroup@\texttt  {TameDegreeOfNumericalSemigroup}|hyperpage}{42}
\indexentry{BezoutSequence@\texttt  {BezoutSequence}|hyperpage}{43}
\indexentry{IsBezoutSequence@\texttt  {IsBezoutSequence}|hyperpage}{43}
\indexentry{CeilingOfRational@\texttt  {CeilingOfRational}|hyperpage}{44}
\indexentry{RepresentsPeriodicSubAdditiveFunction@\texttt  {RepresentsPeriodicSubAdditiveFunction}|hyperpage}{44}
\indexentry{RandomNumericalSemigroup@\texttt  {RandomNumericalSemigroup}|hyperpage}{45}
\indexentry{RandomListForNS@\texttt  {RandomListForNS}|hyperpage}{45}
\indexentry{RandomModularNumericalSemigroup@\texttt  {RandomModularNumericalSemigroup}|hyperpage}{45}
\indexentry{RandomProportionallyModularNumericalSemigroup@\texttt  {Random}\discretionary {-}{}{}\texttt  {Proportionally}\discretionary {-}{}{}\texttt  {Modular}\discretionary {-}{}{}\texttt  {Numerical}\discretionary {-}{}{}\texttt  {Semigroup}|hyperpage}{46}
\indexentry{RandomListRepresentingSubAdditiveFunction@\texttt  {Random}\discretionary {-}{}{}\texttt  {List}\discretionary {-}{}{}\texttt  {Representing}\discretionary {-}{}{}\texttt  {Sub}\discretionary {-}{}{}\texttt  {Additive}\discretionary {-}{}{}\texttt  {Function}|hyperpage}{46}
\indexentry{XNumericalSemigroup@\texttt  {XNumericalSemigroup}|hyperpage}{47}