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A quick introduction to this package
-- How to use this package
Alternative algorithm to compute the symbolic powers of a prime ideal in positive characteristic
assPrimesHeight
-- The heights of all associated primes
assPrimesHeight(Ideal)
-- The heights of all associated primes
asymptoticRegularity
-- approximates the asymptotic regularity
asymptoticRegularity(...,SampleSize=>...)
-- optional parameter used for approximating asymptotic invariants that are defined as limits.
asymptoticRegularity(Ideal)
-- approximates the asymptotic regularity
bigHeight
-- computes the big height of an ideal
bigHeight(Ideal)
-- computes the big height of an ideal
CIPrimes
-- compute the symbolic power by taking the intersection of the powers of the primary components
Computing symbolic powers of an ideal
containmentProblem
-- computes the smallest symbolic power contained in a power of an ideal.
containmentProblem(...,CIPrimes=>...)
-- compute the symbolic power by taking the intersection of the powers of the primary components
containmentProblem(...,InSymbolic=>...)
-- an optional parameter used in containmentProblem.
containmentProblem(...,UseMinimalPrimes=>...)
-- an option to only use minimal primes to calculate symbolic powers
containmentProblem(Ideal,ZZ)
-- computes the smallest symbolic power contained in a power of an ideal.
InSymbolic
-- an optional parameter used in containmentProblem.
isKonig
-- determines if a given square-free ideal is Konig.
isKonig(Ideal)
-- determines if a given square-free ideal is Konig.
isPacked
-- determines if a given square-free ideal is packed.
isPacked(Ideal)
-- determines if a given square-free ideal is packed.
isSymbolicEqualOrdinary
-- tests if symbolic power is equal to ordinary power
isSymbolicEqualOrdinary(Ideal,ZZ)
-- tests if symbolic power is equal to ordinary power
isSymbPowerContainedinPower
-- tests if the m-th symbolic power an ideal is contained the n-th power
isSymbPowerContainedinPower(...,CIPrimes=>...)
-- compute the symbolic power by taking the intersection of the powers of the primary components
isSymbPowerContainedinPower(...,UseMinimalPrimes=>...)
-- an option to only use minimal primes to calculate symbolic powers
isSymbPowerContainedinPower(Ideal,ZZ,ZZ)
-- tests if the m-th symbolic power an ideal is contained the n-th power
joinIdeals
-- Computes the join of the given ideals
joinIdeals(Ideal,Ideal)
-- Computes the join of the given ideals
lowerBoundResurgence
-- computes a lower bound for the resurgence of a given ideal.
lowerBoundResurgence(...,SampleSize=>...)
-- optional parameter used for approximating asymptotic invariants that are defined as limits.
lowerBoundResurgence(...,UseWaldschmidt=>...)
-- optional input for computing a lower bound for the resurgence of a given ideal.
lowerBoundResurgence(Ideal)
-- computes a lower bound for the resurgence of a given ideal.
minDegreeSymbPower
-- returns the minimal degree of a given symbolic power of an ideal.
minDegreeSymbPower(Ideal,ZZ)
-- returns the minimal degree of a given symbolic power of an ideal.
minimalPart
-- intersection of the minimal components
minimalPart(Ideal)
-- intersection of the minimal components
noPackedAllSubs
-- finds all substitutions of variables by 1 and/or 0 for which ideal is not Konig.
noPackedAllSubs(Ideal)
-- finds all substitutions of variables by 1 and/or 0 for which ideal is not Konig.
noPackedSub
-- finds a substitution of variables by 1 and/or 0 for which an ideal is not Konig.
noPackedSub(Ideal)
-- finds a substitution of variables by 1 and/or 0 for which an ideal is not Konig.
SampleSize
-- optional parameter used for approximating asymptotic invariants that are defined as limits.
squarefreeGens
-- returns all square-free monomials in a minimal generating set of the given ideal.
squarefreeGens(Ideal)
-- returns all square-free monomials in a minimal generating set of the given ideal.
squarefreeInCodim
-- finds square-fee monomials in ideal raised to the power of the codimension.
squarefreeInCodim(Ideal)
-- finds square-fee monomials in ideal raised to the power of the codimension.
Sullivant's algorithm for primes in a polynomial ring
symbolicDefect
-- computes the symbolic defect of an ideal
symbolicDefect(...,CIPrimes=>...)
-- compute the symbolic power by taking the intersection of the powers of the primary components
symbolicDefect(...,UseMinimalPrimes=>...)
-- an option to only use minimal primes to calculate symbolic powers
symbolicDefect(Ideal,ZZ)
-- computes the symbolic defect of an ideal
symbolicPolyhedron
-- computes the symbolic polyhedron for a monomial ideal.
symbolicPolyhedron(Ideal)
-- computes the symbolic polyhedron for a monomial ideal.
symbolicPolyhedron(MonomialIdeal)
-- computes the symbolic polyhedron for a monomial ideal.
symbolicPower
-- computes the symbolic power of an ideal.
symbolicPower(...,CIPrimes=>...)
-- compute the symbolic power by taking the intersection of the powers of the primary components
symbolicPower(...,UseMinimalPrimes=>...)
-- an option to only use minimal primes to calculate symbolic powers
symbolicPower(Ideal,ZZ)
-- computes the symbolic power of an ideal.
symbolicPowerJoin
-- computes the symbolic power of the prime ideal using join of ideals.
symbolicPowerJoin(Ideal,ZZ)
-- computes the symbolic power of the prime ideal using join of ideals.
SymbolicPowers
-- symbolic powers of ideals
symbPowerPrimePosChar
symbPowerPrimePosChar(Ideal,ZZ)
The Containment Problem
The Packing Problem
UseMinimalPrimes
-- an option to only use minimal primes to calculate symbolic powers
UseWaldschmidt
-- optional input for computing a lower bound for the resurgence of a given ideal.
waldschmidt
-- computes the Waldschmidt constant for a homogeneous ideal.
waldschmidt(...,SampleSize=>...)
-- optional parameter used for approximating asymptotic invariants that are defined as limits.
waldschmidt(Ideal)
-- computes the Waldschmidt constant for a homogeneous ideal.
waldschmidt(MonomialIdeal)
-- computes the Waldschmidt constant for a homogeneous ideal.