LexIdeals is a package for creating lexicographic ideals and lex-plus-powers (LPP) ideals. There are also several functions for use with the multiplicity conjectures of Herzog, Huneke, and Srinivasan.
cancelAll -- make all potentially possible cancellations in the graded free resolution of an ideal in a particular way
generateLPPs -- return all LPP ideals corresponding to a given Hilbert function
hilbertFunct -- return the Hilbert function of a quotient by a homogeneous ideal as a list
isCM -- test whether a polynomial ring modulo a homogeneous ideal is Cohen-Macaulay
isHF -- test whether a finite list is a Hilbert function of a polynomial ring modulo a homogeneous ideal
isLexIdeal -- determine whether an ideal is a lexicographic ideal
isLPP -- determine whether an ideal is an LPP ideal
lexIdeal -- produce an Artinian lexicographic ideal
LPP -- return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence
macaulayBound -- the bound on the growth of a Hilbert function from Macaulay's Theorem
macaulayLowerOperator -- the a_<d> operator used in Green's proof of Macaulay's Theorem
macaulayRep -- the Macaulay representation of an integer
multBounds -- determine whether the multiplicity of an ideal satisfies the upper and lower bounds from the conjectures of Herzog-Huneke-Srinivasan
multLowerBound -- determine whether the multiplicity of an ideal satisfies the lower bound of the Herzog-Huneke-Srinivasan conjecture
multUpperBound -- determine whether the multiplicity of an ideal satisfies the upper bound conjectured by Herzog-Huneke-Srinivasan
multUpperHF -- determine whether a particular sufficient condition is satisfied that implies the upper bound of the Herzog-Huneke-Srinivasan conjecture for all modules with a given Hilbert function
purePower -- determine whether a ring element is a pure power of a variable