TSpreadIdeals : Index

• countTLexMon -- give the cardinality of the smallest initial t-lex segment containing a given monomial
• countTLexMon(...,FixedMax=>...) -- optional boolean argument for tNextMon
• countTLexMon(RingElement,ZZ) -- give the cardinality of the smallest initial t-lex segment containing a given monomial
• countTStronglyStableMon -- give the cardinality of the t-strongly stable set generated by a given monomial
• countTStronglyStableMon(RingElement,ZZ) -- give the cardinality of the t-strongly stable set generated by a given monomial
• FixedMax -- optional boolean argument for tNextMon
• fTVector -- compute the ft-vector of a given t-spread ideal of a polynomial ring
• fTVector(Ideal,ZZ) -- compute the ft-vector of a given t-spread ideal of a polynomial ring
• initialDegree -- return the initial degree of a given graded ideal
• initialDegree(Ideal) -- return the initial degree of a given graded ideal
• initialIdeal -- return the initial ideal of a given ideal
• initialIdeal(Ideal) -- return the initial ideal of a given ideal
• isFTVector -- whether a given list of nonnegative integers is the ft-vector of a t-strongly stable ideal of a given polynomial ring
• isFTVector(Ring,List,ZZ) -- whether a given list of nonnegative integers is the ft-vector of a t-strongly stable ideal of a given polynomial ring
• isTLexIdeal -- whether a given t-spread ideal is t-spread lex
• isTLexIdeal(Ideal,ZZ) -- whether a given t-spread ideal is t-spread lex
• isTLexSeg -- whether a set of t-spread monomials is a t-lex segment
• isTLexSeg(List,ZZ) -- whether a set of t-spread monomials is a t-lex segment
• isTSpread -- whether a monomial, a list of monomials or a monomial ideal is t-spread
• isTSpread(Ideal,ZZ) -- whether a monomial, a list of monomials or a monomial ideal is t-spread
• isTSpread(List,ZZ) -- whether a monomial, a list of monomials or a monomial ideal is t-spread
• isTSpread(RingElement,ZZ) -- whether a monomial, a list of monomials or a monomial ideal is t-spread
• isTStronglyStableIdeal -- whether a given t-spread ideal is t-strongly stable
• isTStronglyStableIdeal(Ideal,ZZ) -- whether a given t-spread ideal is t-strongly stable
• isTStronglyStableSeg -- whether the given list of t-spread monomials is a t-strongly stable segment
• isTStronglyStableSeg(List,ZZ) -- whether the given list of t-spread monomials is a t-strongly stable segment
• MaxInd -- optional integer argument for tLastMon
• minimalBettiNumbers -- return the minimal Betti numbers of the quotient ring corresponding to a given graded ideal
• minimalBettiNumbers(Ideal) -- return the minimal Betti numbers of the quotient ring corresponding to a given graded ideal
• minimalBettiNumbersIdeal -- return the minimal Betti numbers of a given graded ideal
• minimalBettiNumbersIdeal(Ideal) -- return the minimal Betti numbers of a given graded ideal
• Shift -- optional boolean argument for tMacaulayExpansion
• solveBinomialExpansion -- compute the sum of a binomial expansion
• solveBinomialExpansion(List) -- compute the sum of a binomial expansion
• tExtremalBettiCorners -- give the corners of the extremal Betti numbers of a given t-strongly stable ideal
• tExtremalBettiCorners(Ideal,ZZ) -- give the corners of the extremal Betti numbers of a given t-strongly stable ideal
• tExtremalBettiMonomials -- give the list of the t-spread basic monomials related to the given extremal Betti numbers configuration
• tExtremalBettiMonomials(Ring,List,List,ZZ) -- give the list of the t-spread basic monomials related to the given extremal Betti numbers configuration
• tLastMon -- give the last t-spread monomial of the Borel shadow a given t-spread monomial
• tLastMon(...,MaxInd=>...) -- optional integer argument for tLastMon
• tLastMon(RingElement,ZZ,ZZ) -- give the last t-spread monomial of the Borel shadow a given t-spread monomial
• tLexIdeal -- returns the t-spread lex ideal with a given ft-vector or with the same ft-vector of a given t-strongly stable ideal
• tLexIdeal(Ideal,ZZ) -- returns the t-spread lex ideal with a given ft-vector or with the same ft-vector of a given t-strongly stable ideal
• tLexIdeal(Ring,List,ZZ) -- returns the t-spread lex ideal with a given ft-vector or with the same ft-vector of a given t-strongly stable ideal
• tLexMon -- give the smallest initial t-lex segment containing a given monomial
• tLexMon(RingElement,ZZ) -- give the smallest initial t-lex segment containing a given monomial
• tLexSeg -- give the t-lex segment with given extremes
• tLexSeg(RingElement,RingElement,ZZ) -- give the t-lex segment with given extremes
• tMacaulayExpansion -- compute the t-Macaulay expansion of a positive integer
• tMacaulayExpansion(...,Shift=>...) -- optional boolean argument for tMacaulayExpansion
• tMacaulayExpansion(ZZ,ZZ,ZZ,ZZ) -- compute the t-Macaulay expansion of a positive integer
• tNextMon -- give the t-lex successor of a given t-spread monomial
• tNextMon(...,FixedMax=>...) -- optional boolean argument for tNextMon
• tNextMon(RingElement,ZZ) -- give the t-lex successor of a given t-spread monomial
• tPascalIdeal -- give the Pascal ideal of t-spread monomials of a given polynomial ring
• tPascalIdeal(Ring,ZZ) -- give the Pascal ideal of t-spread monomials of a given polynomial ring
• tShadow -- give the t-spread shadow of a given t-spread monomial or a given list of t-spread monomials
• tShadow(List,ZZ) -- give the t-spread shadow of a given t-spread monomial or a given list of t-spread monomials
• tShadow(RingElement,ZZ) -- give the t-spread shadow of a given t-spread monomial or a given list of t-spread monomials
• tSpreadIdeal -- give the ideal generated by the t-spread monomials which are among the generators of a given ideal
• tSpreadIdeal(Ideal,ZZ) -- give the ideal generated by the t-spread monomials which are among the generators of a given ideal
• TSpreadIdeals -- A package for working with t-spread ideals of polynomial rings
• tSpreadList -- give the set of all t-spread monomials of a given list
• tSpreadList(List,ZZ) -- give the set of all t-spread monomials of a given list
• tStronglyStableIdeal -- give the smallest t-strongly stable ideal containing a given t-spread ideal
• tStronglyStableIdeal(Ideal,ZZ) -- give the smallest t-strongly stable ideal containing a given t-spread ideal
• tStronglyStableMon -- give the t-strongly stable set generated by a given monomial
• tStronglyStableMon(RingElement,ZZ) -- give the t-strongly stable set generated by a given monomial
• tStronglyStableSeg -- give the t-strongly stable segment with the given extremes
• tStronglyStableSeg(RingElement,RingElement,ZZ) -- give the t-strongly stable segment with the given extremes
• tVeroneseIdeal -- give the Veronese ideal of t-spread monomials of a given degree
• tVeroneseIdeal(Ring,ZZ,ZZ) -- give the Veronese ideal of t-spread monomials of a given degree
• tVeroneseSet -- give the Veronese set of t-spread monomials of a given degree
• tVeroneseSet(Ring,ZZ,ZZ) -- give the Veronese set of t-spread monomials of a given degree