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MonomialAlgebras : Index
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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 monomial 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 monomial 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.