RandomMonomialIdeals : Index

• bettiStats -- statistics on Betti tables of a sample of monomial ideals or list of objects
• bettiStats(...,CountPure=>...) -- optional input to show the number of objects in the list whose Betti tables are pure
• bettiStats(...,IncludeZeroIdeals=>...) -- optional input to choose whether zero ideals should be included
• bettiStats(...,SaveBettis=>...) -- optional input to store all Betti tables computed
• bettiStats(...,Verbose=>...) -- optional input to request verbose feedback
• bettiStats(List) -- 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
• borelFixedStats(...,Verbose=>...) -- optional input to request verbose feedback
• borelFixedStats(List) -- 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
• CMStats(...,Verbose=>...) -- optional input to request verbose feedback
• CMStats(List) -- 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(...,ShowTally=>...) -- optional input to choose if the tally is to be returned
• degStats(...,Verbose=>...) -- optional input to request verbose feedback
• degStats(List) -- statistics on the degrees of a list of objects
• dimStats -- statistics on the Krull dimension of a list of objects
• dimStats(...,ShowTally=>...) -- optional input to choose if the tally is to be returned
• dimStats(...,Verbose=>...) -- optional input to request verbose feedback
• dimStats(List) -- 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
• getData(Sample) -- get the underlying samples
• Histogram -- a summary statistic for a list of objects
• idealsFromGeneratingSets -- creates ideals from sets of monomials
• idealsFromGeneratingSets(...,IncludeZeroIdeals=>...) -- optional input to choose whether zero ideals should be included
• idealsFromGeneratingSets(...,Verbose=>...) -- optional input to request verbose feedback
• idealsFromGeneratingSets(List) -- 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
• mingenStats(...,ShowTally=>...) -- optional input to choose if the tally is to be returned
• mingenStats(...,Verbose=>...) -- optional input to request verbose feedback
• mingenStats(List) -- 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
• model(List,FunctionClosure,String) -- 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
• pdimStats(...,ShowTally=>...) -- optional input to choose if the tally is to be returned
• pdimStats(...,Verbose=>...) -- optional input to request verbose feedback
• pdimStats(List) -- statistics on projective dimension of a list of objects
• RandomMonomialIdeals -- A package for generating Erdos-Renyi-type random monomial ideals and variations
• randomMonomialIdeals -- generates random sets of monomial ideals
• randomMonomialIdeals(...,Coefficients=>...) -- optional input to choose the coefficients of the ambient polynomial ring
• randomMonomialIdeals(...,IncludeZeroIdeals=>...) -- optional input to choose whether zero ideals should be included
• randomMonomialIdeals(...,Strategy=>...) -- optional input to choose the strategy for generating the random monomial set
• randomMonomialIdeals(...,VariableName=>...) -- optional input to choose the indexed variable name for the polynomial ring
• randomMonomialIdeals(ZZ,ZZ,List,ZZ) -- generates random sets of monomial ideals
• randomMonomialIdeals(ZZ,ZZ,RR,ZZ) -- generates random sets of monomial ideals
• randomMonomialIdeals(ZZ,ZZ,ZZ,ZZ) -- generates random sets of monomial ideals
• randomMonomialSet -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSet(...,Coefficients=>...) -- optional input to choose the coefficients of the ambient polynomial ring
• randomMonomialSet(...,Strategy=>...) -- optional input to choose the strategy for generating the random monomial set
• randomMonomialSet(...,VariableName=>...) -- optional input to choose the indexed variable name for the polynomial ring
• randomMonomialSet(PolynomialRing,ZZ,List) -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSet(PolynomialRing,ZZ,RR) -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSet(PolynomialRing,ZZ,ZZ) -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSet(ZZ,ZZ,List) -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSet(ZZ,ZZ,RR) -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSet(ZZ,ZZ,ZZ) -- randomly generates a list of monomials in fixed number of variables up to a given degree
• randomMonomialSets -- randomly generates lists of monomials in fixed number of variables up to a given degree
• randomMonomialSets(...,Coefficients=>...) -- optional input to choose the coefficients of the ambient polynomial ring
• randomMonomialSets(...,Strategy=>...) -- optional input to choose the strategy for generating the random monomial set
• randomMonomialSets(...,VariableName=>...) -- optional input to choose the indexed variable name for the polynomial ring
• randomMonomialSets(PolynomialRing,ZZ,List,ZZ) -- randomly generates lists of monomials in fixed number of variables up to a given degree
• randomMonomialSets(PolynomialRing,ZZ,RR,ZZ) -- randomly generates lists of monomials in fixed number of variables up to a given degree
• randomMonomialSets(PolynomialRing,ZZ,ZZ,ZZ) -- randomly generates lists of monomials in fixed number of variables up to a given degree
• randomMonomialSets(ZZ,ZZ,List,ZZ) -- randomly generates lists of monomials in fixed number of variables up to a given degree
• randomMonomialSets(ZZ,ZZ,RR,ZZ) -- randomly generates lists of monomials in fixed number of variables up to a given degree
• randomMonomialSets(ZZ,ZZ,ZZ,ZZ) -- 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
• regStats(...,ShowTally=>...) -- optional input to choose if the tally is to be returned
• regStats(...,Verbose=>...) -- optional input to request verbose feedback
• regStats(List) -- 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(Model,ZZ) -- 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
• statistics(Sample,Function) -- 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
• writeSample(Sample,String) -- write sample data to a directory