SymbolicPowers : Index

• 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.