MonomialAlgebras : Index
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adjoinPurePowers -- adjoin semigroup elements corresponding to pure powers of variables
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adjoinPurePowers(List) -- adjoin semigroup elements corresponding to pure powers of variables
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affineAlgebra -- Define a monomial algebra
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affineAlgebra(...,CoefficientField=>...) -- Option to set the coefficient field.
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affineAlgebra(List) -- Define a monomial algebra
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affineAlgebra(MonomialAlgebra) -- Define a monomial algebra
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affineAlgebra(PolynomialRing) -- Define a monomial algebra
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binomialIdeal -- Compute the ideal of a monomial algebra
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binomialIdeal(...,CoefficientField=>...) -- Option to set the coefficient field.
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binomialIdeal(List) -- Compute the ideal of a monomial algebra
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binomialIdeal(MonomialAlgebra) -- Compute the ideal of a monomial algebra
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binomialIdeal(PolynomialRing) -- Compute the ideal of a monomial algebra
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codimMA -- Codimension of a monomial algebra.
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codimMA(List) -- Codimension of a monomial algebra.
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codimMA(MonomialAlgebra) -- Codimension of a monomial algebra.
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codimMA(PolynomialRing) -- Codimension of a monomial algebra.
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CoefficientField -- Option to set the coefficient field.
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decomposeHomogeneousMA -- Decomposition of one monomial algebra over a subalgebra
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decomposeHomogeneousMA(...,CoefficientField=>...) -- Option to set the coefficient field.
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decomposeHomogeneousMA(...,ReturnMingens=>...) -- Option to return the minimal generating set B_A of K[B] as K[A]-module.
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decomposeHomogeneousMA(...,Verbose=>...) -- Option to print intermediate results.
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decomposeHomogeneousMA(List) -- Decomposition of one monomial algebra over a subalgebra
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decomposeHomogeneousMA(MonomialAlgebra) -- Decomposition of one monomial algebra over a subalgebra
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decomposeHomogeneousMA(PolynomialRing) -- Decomposition of one monomial algebra over a subalgebra
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decomposeHomogeneousMA(RingMap) -- Decomposition of one monomial algebra over a subalgebra
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decomposeMonomialAlgebra -- Decomposition of one monomial algebra over a subalgebra
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decomposeMonomialAlgebra(...,CoefficientField=>...) -- Option to set the coefficient field.
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decomposeMonomialAlgebra(...,ReturnMingens=>...) -- Option to return the minimal generating set B_A of K[B] as K[A]-module.
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decomposeMonomialAlgebra(...,Verbose=>...) -- Option to print intermediate results.
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decomposeMonomialAlgebra(List) -- Decomposition of one monomial algebra over a subalgebra
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decomposeMonomialAlgebra(List,List) -- Decomposition of one monomial algebra over a subalgebra
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decomposeMonomialAlgebra(MonomialAlgebra) -- Decomposition of one monomial algebra over a subalgebra
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decomposeMonomialAlgebra(PolynomialRing) -- Decomposition of one monomial algebra over a subalgebra
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decomposeMonomialAlgebra(RingMap) -- Decomposition of one monomial algebra over a subalgebra
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Decomposition -- Optional argument of regularityMA to specify the decomposition.
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degreeMA -- Degree of a monomial algebra.
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degreeMA(...,Verbose=>...) -- Option to print intermediate results.
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degreeMA(List) -- Degree of a monomial algebra.
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degreeMA(MonomialAlgebra) -- Degree of a monomial algebra.
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degreeMA(PolynomialRing) -- Degree of a monomial algebra.
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degrees(MonomialAlgebra) -- Generators of the degree monoid
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Diagrams -- Diagrams illustrating the tests
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findGeneratorsOfSubalgebra -- Find submonoid corresponding to the convex hull.
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findGeneratorsOfSubalgebra(List) -- Find submonoid corresponding to the convex hull.
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findMonomialSubalgebra -- Find monomial subalgebra corresponding to the convex hull.
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findMonomialSubalgebra(MonomialAlgebra) -- Find monomial subalgebra corresponding to the convex hull.
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findMonomialSubalgebra(PolynomialRing) -- Find monomial subalgebra corresponding to the convex hull.
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homogenizeSemigroup -- Homogenize generators of a semigroup.
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homogenizeSemigroup(List) -- Homogenize generators of a semigroup.
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isBuchsbaumMA -- Test whether a simplicial monomial algebra is Buchsbaum.
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isBuchsbaumMA(List) -- Test whether a simplicial monomial algebra is Buchsbaum.
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isBuchsbaumMA(MonomialAlgebra) -- Test whether a simplicial monomial algebra is Buchsbaum.
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isBuchsbaumMA(PolynomialRing) -- Test whether a simplicial monomial algebra is Buchsbaum.
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isCohenMacaulayMA -- Test whether a simplicial monomial algebra is Cohen-Macaulay.
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isCohenMacaulayMA(List) -- Test whether a simplicial monomial algebra is Cohen-Macaulay.
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isCohenMacaulayMA(MonomialAlgebra) -- Test whether a simplicial monomial algebra is Cohen-Macaulay.
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isCohenMacaulayMA(PolynomialRing) -- Test whether a simplicial monomial algebra is Cohen-Macaulay.
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isGorensteinMA -- Test whether a simplicial monomial algebra is Gorenstein.
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isGorensteinMA(List) -- Test whether a simplicial monomial algebra is Gorenstein.
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isGorensteinMA(MonomialAlgebra) -- Test whether a simplicial monomial algebra is Gorenstein.
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isGorensteinMA(PolynomialRing) -- Test whether a simplicial monomial algebra is Gorenstein.
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isNormalMA -- Test whether a simplicial monomial algebra is normal.
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isNormalMA(List) -- Test whether a simplicial monomial algebra is normal.
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isNormalMA(MonomialAlgebra) -- Test whether a simplicial monomial algebra is normal.
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isNormalMA(PolynomialRing) -- Test whether a simplicial monomial algebra is normal.
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isSeminormalMA -- Test whether a simplicial monomial algebra is seminormal.
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isSeminormalMA(List) -- Test whether a simplicial monomial algebra is seminormal.
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isSeminormalMA(MonomialAlgebra) -- Test whether a simplicial monomial algebra is seminormal.
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isSeminormalMA(PolynomialRing) -- Test whether a simplicial monomial algebra is seminormal.
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isSimplicialMA -- Test whether a monomial algebra is simplicial.
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isSimplicialMA(List) -- Test whether a monomial algebra is simplicial.
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isSimplicialMA(MonomialAlgebra) -- Test whether a monomial algebra is simplicial.
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isSimplicialMA(PolynomialRing) -- Test whether a monomial algebra is simplicial.
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MonomialAlgebra -- The class of all monomialAlgebras.
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monomialAlgebra -- Create a monomial algebra
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monomialAlgebra(...,CoefficientField=>...) -- Option to set the coefficient field.
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monomialAlgebra(List) -- Create a monomial algebra
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monomialAlgebra(PolynomialRing) -- Create a monomial algebra
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MonomialAlgebras -- Decompose a monomial algebra as a module over a subalgebra.
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net(MonomialAlgebra) -- Pretty print for monomial algebras
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Num -- Option of randomSemigroup and randomMonomialAlgebra to return a list of several semigroups.
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randomMonomialAlgebra -- Generate random monoimal algebra.
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randomMonomialAlgebra(...,Num=>...) -- Option of randomSemigroup and randomMonomialAlgebra to return a list of several semigroups.
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randomMonomialAlgebra(...,SetSeed=>...) -- Option to set the random seed for randomSemigroup and randomMonomialAlgebra.
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randomMonomialAlgebra(...,Simplicial=>...) -- Option of randomSemigroup and randomMonomialAlgebra to return a simplicial semigroup.
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randomMonomialAlgebra(ZZ,ZZ,ZZ) -- Generate random monoimal algebra.
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randomSemigroup -- Generate random semigroups.
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randomSemigroup(...,Num=>...) -- Option of randomSemigroup and randomMonomialAlgebra to return a list of several semigroups.
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randomSemigroup(...,SetSeed=>...) -- Option to set the random seed for randomSemigroup and randomMonomialAlgebra.
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randomSemigroup(...,Simplicial=>...) -- Option of randomSemigroup and randomMonomialAlgebra to return a simplicial semigroup.
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randomSemigroup(ZZ,ZZ,ZZ) -- Generate random semigroups.
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regularityMA -- Compute regularity from decomposition
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regularityMA(...,CoefficientField=>...) -- Option to set the coefficient field.
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regularityMA(...,Decomposition=>...) -- Optional argument of regularityMA to specify the decomposition.
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regularityMA(List) -- Compute regularity from decomposition
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regularityMA(MonomialAlgebra) -- Compute regularity from decomposition
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regularityMA(PolynomialRing) -- Compute regularity from decomposition
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ReturnMingens -- Option to return the minimal generating set B_A of K[B] as K[A]-module.
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ring(MonomialAlgebra) -- Multigraded polynomial ring associated to a monomial algebra
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SetSeed -- Option to set the random seed for randomSemigroup and randomMonomialAlgebra.
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Simplicial -- Option of randomSemigroup and randomMonomialAlgebra to return a simplicial semigroup.