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# 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