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associated primes
associatedPrimes
-- find associated primes
associatedPrimes(...,CodimensionLimit=>...)
-- find associated primes
associatedPrimes(...,MinimalGenerators=>...)
-- find associated primes
associatedPrimes(...,Strategy=>...)
-- find associated primes
associatedPrimes(Ideal)
-- find associated primes
associatedPrimes(Module)
-- find associated primes
associatedPrimes(Ring)
-- find associated primes
EisenbudHunekeVasconcelos
GTZ
Hybrid
Increment
-- find a primary component corresponding to an associated prime
irreducibleDecomposition
-- express a monomial ideal as an intersection of irreducible monomial ideals
irreducibleDecomposition(MonomialIdeal)
-- express a monomial ideal as an intersection of irreducible monomial ideals
isPrimary
-- determine whether a submodule is primary
isPrimary(...,Strategy=>...)
-- determine whether a submodule is primary
isPrimary(Ideal)
-- determine whether a submodule is primary
isPrimary(Ideal,Ideal)
-- determine whether a submodule is primary
isPrimary(Module,Module)
-- determine whether a submodule is primary
kernelOfLocalization
-- the kernel of the localization map
kernelOfLocalization(Module,Ideal)
-- the kernel of the localization map
localize
-- localize an ideal at a prime ideal
localize(...,Strategy=>...)
-- localize an ideal at a prime ideal
localize(Ideal,Ideal)
-- localize an ideal at a prime ideal
primary decomposition
primaryComponent
-- find a primary component corresponding to an associated prime
primaryComponent(...,Increment=>...)
-- find a primary component corresponding to an associated prime
primaryComponent(...,Strategy=>...)
-- find a primary component corresponding to an associated prime
primaryComponent(Ideal,Ideal)
-- find a primary component corresponding to an associated prime
PrimaryDecomposition
-- primary decomposition and associated primes routines for ideals and modules
primaryDecomposition
-- irredundant primary decomposition of an ideal
primaryDecomposition(...,MinimalGenerators=>...)
-- irredundant primary decomposition of an ideal
primaryDecomposition(...,Strategy=>...)
primaryDecomposition(Ideal)
-- irredundant primary decomposition of an ideal
primaryDecomposition(Module)
-- irredundant primary decomposition of a module
primaryDecomposition(Ring)
-- irredundant primary decomposition of a module
regSeqInIdeal
-- a regular sequence contained in an ideal
regSeqInIdeal(...,Strategy=>...)
-- a regular sequence contained in an ideal
regSeqInIdeal(Ideal)
-- a regular sequence contained in an ideal
regSeqInIdeal(Ideal,ZZ)
-- a regular sequence contained in an ideal
regSeqInIdeal(Ideal,ZZ,ZZ,ZZ)
-- a regular sequence contained in an ideal
removeLowestDimension
-- remove components of lowest dimension
removeLowestDimension(Ideal)
-- remove components of lowest dimension
removeLowestDimension(Module)
-- remove components of lowest dimension
ShimoyamaYokoyama
strategies for computing primary decomposition
topComponents
-- compute top dimensional component of an ideal or module
topComponents(Ideal)
-- compute top dimensional component of an ideal or module
topComponents(Module)
-- compute top dimensional component of an ideal or module