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MonomialAlgebras : Table of Contents
MonomialAlgebras
-- Decompose a monomial algebra as a module over a subalgebra.
adjoinPurePowers
-- adjoin semigroup elements corresponding to pure powers of variables
affineAlgebra
-- Define a monomial algebra
binomialIdeal
-- Compute the ideal of a monomial algebra
codimMA
-- Codimension of a monomial algebra.
CoefficientField
-- Option to set the coefficient field.
decomposeHomogeneousMA
-- Decomposition of one monomial algebra over a subalgebra
decomposeHomogeneousMA(...,Verbose=>...)
-- Option to print intermediate results.
decomposeMonomialAlgebra
-- Decomposition of one monomial algebra over a subalgebra
decomposeMonomialAlgebra(...,Verbose=>...)
-- Option to print intermediate results.
Decomposition
-- Optional argument of regularityMA to specify the decomposition.
degreeMA
-- Degree of a monomial algebra.
degreeMA(...,Verbose=>...)
-- Option to print intermediate results.
degrees(MonomialAlgebra)
-- Generators of the degree monoid
Diagrams
-- Diagrams illustrating the tests
findGeneratorsOfSubalgebra
-- Find submonoid corresponding to the convex hull.
findMonomialSubalgebra
-- Find monomial subalgebra corresponding to the convex hull.
homogenizeSemigroup
-- Homogenize generators of a semigroup.
isBuchsbaumMA
-- Test whether a simplicial monomial algebra is Buchsbaum.
isCohenMacaulayMA
-- Test whether a simplicial monomial algebra is Cohen-Macaulay.
isGorensteinMA
-- Test whether a simplicial monomial algebra is Gorenstein.
isNormalMA
-- Test whether a simplicial monomial algebra is normal.
isSeminormalMA
-- Test whether a simplicial monomial algebra is seminormal.
isSimplicialMA
-- Test whether a monomial algebra is simplicial.
MonomialAlgebra
-- The class of all monomialAlgebras.
monomialAlgebra
-- Create a monomial algebra
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.
randomSemigroup
-- Generate random semigroups.
regularityMA
-- 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.