TSpreadIdeals : Table of Contents

• TSpreadIdeals -- A package for working with t-spread ideals of polynomial rings

  • tLastMon -- give the last t-spread monomial of the Borel shadow a given t-spread monomial
  • tPascalIdeal -- give the Pascal ideal of t-spread monomials of a given polynomial ring
  • tSpreadList -- give the set of all t-spread monomials of a given list
  • tSpreadIdeal -- give the ideal generated by the t-spread monomials which are among the generators of a given ideal
  • isTSpread -- whether a monomial, a list of monomials or a monomial ideal is t-spread
  • tShadow -- give the t-spread shadow of a given t-spread monomial or a given list of t-spread monomials
  • tNextMon -- give the t-lex successor of a given t-spread monomial
  • tLexSeg -- give the t-lex segment with given extremes
  • isTLexSeg -- whether a set of t-spread monomials is a t-lex segment
  • tLexMon -- give the smallest initial t-lex segment containing a given monomial
  • countTLexMon -- give the cardinality of the smallest initial t-lex segment containing a given monomial
  • tVeroneseSet -- give the Veronese set of t-spread monomials of a given degree
  • tVeroneseIdeal -- give the Veronese ideal of t-spread monomials of a given degree
  • isTLexIdeal -- whether a given t-spread ideal is t-spread lex
  • tStronglyStableSeg -- give the t-strongly stable segment with the given extremes
  • isTStronglyStableSeg -- whether the given list of t-spread monomials is a t-strongly stable segment
  • tStronglyStableMon -- give the t-strongly stable set generated by a given monomial
  • countTStronglyStableMon -- give the cardinality of the t-strongly stable set generated by a given monomial
  • tStronglyStableIdeal -- give the smallest t-strongly stable ideal containing a given t-spread ideal
  • isTStronglyStableIdeal -- whether a given t-spread ideal is t-strongly stable
  • tMacaulayExpansion -- compute the t-Macaulay expansion of a positive integer
  • fTVector -- compute the ft-vector of a given t-spread ideal of a polynomial ring
  • isFTVector -- wheter a given list of nonnegative intengers is the ft-vector of a t-strongly stable ideal of a given polynomial ring
  • 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
  • tExtremalBettiCorners -- 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
  • solveBinomialExpansion -- compute the sum of a binomial expansion
  • initialDegree -- return the initial degree of a given graded ideal
  • initialIdeal -- return the initial ideal of a given ideal
  • minimalBettiNumbers -- 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
  • Shift -- optional boolean argument for tMacaulayExpansion
  • FixedMax -- optional boolean argument for tNextMon
  • MaxInd -- optional integer argument for tLastMon