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LexIdeals : Index
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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