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.