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 -- an option to 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 => ...) -- an option to 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 => ...) -- an option to 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 => ...) -- an option to 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 => ...) -- an option to 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.