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