RandomMonomialIdeals : Table of Contents

• RandomMonomialIdeals -- A package for generating Erdos-Renyi-type random monomial ideals and variations
• bettiStats -- statistics on Betti tables of a sample of monomial ideals or list of objects
• borelFixedStats -- fraction of Borel-fixed monomial ideals in the given list
• CMStats -- fraction of monomial ideals (or other objects) in the given list whose quotient ring is Cohen-Macaulay
• Coefficients -- optional input to choose the coefficients of the ambient polynomial ring
• CountPure -- optional input to show the number of objects in the list whose Betti tables are pure
• degStats -- statistics on the degrees of a list of objects
• degStats(...,Verbose=>...) -- optional input to request verbose feedback
• dimStats -- statistics on the Krull dimension of a list of objects
• ER -- model for sampling from Erdos-Renyi type distributions on monomials
• ER(PolynomialRing,ZZ,List) -- Graded Erdos-Renyi type distribution on monomials over (R,D,L)
• ER(PolynomialRing,ZZ,RR) -- Erdos-Renyi type distribution on monomials over (R,D,p)
• ER(PolynomialRing,ZZ,ZZ) -- Erdos-Renyi type distribution on monomials over (R,D,M)
• ER(ZZ,ZZ,List) -- Graded Erdos-Renyi type distribution on monomials over (n,D,L)
• ER(ZZ,ZZ,RR) -- Erdos-Renyi type distribution on monomials over (n,D,p)
• ER(ZZ,ZZ,ZZ) -- Erdos-Renyi type distribution on monomials over (n,D,M)
• Generate -- model construct function
• getData -- get the underlying samples
• Histogram -- a summary statistic for a list of objects
• idealsFromGeneratingSets -- creates ideals from sets of monomials
• IncludeZeroIdeals -- optional input to choose whether zero ideals should be included
• Mean -- a summary statistic for a list of objects
• mingenStats -- statistics on the minimal generators of a list of ideals: number and degree complexity
• Model -- a type used to store a statistical model and its parameters
• model -- creates a new model for random objects with a given list of parameters and generating function
• ModelName -- name of the model used to generate a given sample
• Parameters -- values of the model parameters that were used to generate a given sample
• pdimStats -- statistics on projective dimension of a list of objects
• randomMonomialIdeals -- generates random sets of monomial ideals
• randomMonomialSet -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSet(...,Strategy=>...) -- optional input to choose the strategy for generating the random monomial set
• randomMonomialSets -- randomly generates lists of monomials in fixed number of variables up to a given degree
• regStats -- statistics on the regularities of a list of objects
• Sample -- a type used to store a data sample from a statistical model
• sample -- generates a sample from the given model
• sample(String) -- creates an object of type Sample from a sample stored in a directory on disk
• SampleSize -- size of the random sample
• SaveBettis -- optional input to store all Betti tables computed
• ShowTally -- optional input to choose if the tally is to be returned
• statistics -- generate statistics for a sample
• StdDev -- a summary statistic for a list of objects
• VariableName -- optional input to choose the indexed variable name for the polynomial ring
• writeSample -- write sample data to a directory