‣ IsGradedAssociatedRingNumericalSemigroupBuchsbaum( S ) | ( function ) |
S is a numerical semigroup.
Returns true if the graded ring associated to K[[S]] is Buchsbaum, and false otherwise. This test is the implementation of the algorithm given in [DMV09].
gap> s:=NumericalSemigroup(30, 35, 42, 47, 148, 153, 157, 169, 181, 193); <Numerical semigroup with 10 generators> gap> IsGradedAssociatedRingNumericalSemigroupBuchsbaum(s); true
‣ IsMpureNumericalSemigroup( S ) | ( function ) |
S is a numerical semigroup.
Test for the M-Purity of the numerical semigroup S S. This test is based on [Bry10].
gap> s:=NumericalSemigroup(30, 35, 42, 47, 148, 153, 157, 169, 181, 193); <Numerical semigroup with 10 generators> gap> IsMpureNumericalSemigroup(s); false gap> s:=NumericalSemigroup(4,6,11); <Numerical semigroup with 3 generators> gap> IsMpureNumericalSemigroup(s); true
‣ IsPureNumericalSemigroup( S ) | ( function ) |
S is a numerical semigroup.
Test for the purity of the numerical semigroup S S. This test is based on [Bry10].
gap> s:=NumericalSemigroup(30, 35, 42, 47, 148, 153, 157, 169, 181, 193); <Numerical semigroup with 10 generators> gap> IsPureNumericalSemigroup(s); false gap> s:=NumericalSemigroup(4,6,11); <Numerical semigroup with 3 generators> gap> IsPureNumericalSemigroup(s); true
‣ IsGradedAssociatedRingNumericalSemigroupGorenstein( S ) | ( function ) |
S is a numerical semigroup.
Returns true if the graded ring associated to K[[S]] is Gorenstein, and false otherwise. This test is the implementation of the algorithm given in [DMS11].
gap> s:=NumericalSemigroup(30, 35, 42, 47, 148, 153, 157, 169, 181, 193); <Numerical semigroup with 10 generators> gap> IsGradedAssociatedRingNumericalSemigroupGorenstein(s); false gap> s:=NumericalSemigroup(4,6,11); <Numerical semigroup with 3 generators> gap> IsGradedAssociatedRingNumericalSemigroupGorenstein(s); true
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