# LexIdeals : Index

• cancelAll -- make all potentially possible cancellations in the graded free resolution of an ideal
• cancelAll(Ideal) -- make all potentially possible cancellations in the graded free resolution of an ideal
• generateLPPs -- return all LPP ideals corresponding to a given Hilbert function
• generateLPPs(...,PrintIdeals=>...) -- print LPP ideals nicely on the screen
• generateLPPs(PolynomialRing,List) -- return all LPP ideals corresponding to a given Hilbert function
• hilbertFunct -- return the Hilbert function of a polynomial ring mod a homogeneous ideal as a list
• hilbertFunct(...,MaxDegree=>...) -- bound degree through which Hilbert function is computed
• hilbertFunct(Ideal) -- return the Hilbert function of a polynomial ring mod a homogeneous ideal as a list
• isCM -- test whether a polynomial ring modulo a homogeneous ideal is Cohen-Macaulay
• isCM(Ideal) -- test whether a polynomial ring modulo a homogeneous ideal is Cohen-Macaulay
• isHF -- is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal
• isHF(List) -- is a finite list a Hilbert function of a polynomial ring mod a homogeneous ideal
• isLexIdeal -- determine whether an ideal is a lexicographic ideal
• isLexIdeal(Ideal) -- determine whether an ideal is a lexicographic ideal
• isLPP -- determine whether an ideal is an LPP ideal
• isLPP(Ideal) -- determine whether an ideal is an LPP ideal
• isPurePower -- determine whether a ring element is a pure power of a variable
• isPurePower(RingElement) -- determine whether a ring element is a pure power of a variable
• lexIdeal -- produce a lexicographic ideal
• lexIdeal(Ideal) -- produce a lexicographic ideal
• lexIdeal(PolynomialRing,List) -- produce a lexicographic ideal
• lexIdeal(QuotientRing,List) -- produce a lexicographic ideal
• LexIdeals -- a package for working with lex ideals
• LPP -- return the lex-plus-powers (LPP) ideal corresponding to a given Hilbert function and power sequence
• LPP(PolynomialRing,List,List) -- 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
• macaulayBound(ZZ,ZZ) -- 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
• macaulayLowerOperator(ZZ,ZZ) -- the a_<d> operator used in Green's proof of Macaulay's Theorem
• macaulayRep -- the Macaulay representation of an integer
• macaulayRep(ZZ,ZZ) -- the Macaulay representation of an integer
• MaxDegree -- optional argument for hilbertFunct
• multBounds -- determine whether an ideal satisfies the upper and lower bounds of the multiplicity conjecture
• multBounds(Ideal) -- determine whether an ideal satisfies the upper and lower bounds of the multiplicity conjecture
• multLowerBound -- determine whether an ideal satisfies the lower bound of the multiplicity conjecture
• multLowerBound(Ideal) -- determine whether an ideal satisfies the lower bound of the multiplicity conjecture
• multUpperBound -- determine whether an ideal satisfies the upper bound of the multiplicity conjecture
• multUpperBound(Ideal) -- determine whether an ideal satisfies the upper bound of the multiplicity conjecture
• multUpperHF -- test a sufficient condition for the upper bound of the multiplicity conjecture
• multUpperHF(PolynomialRing,List) -- test a sufficient condition for the upper bound of the multiplicity conjecture
• PrintIdeals -- optional argument for generateLPPs