IdealDecompositionPackage(vl)

idecomp.spad line 1 [edit on github]

• vl : List(Symbol)

This package provides functions for the primary decomposition of polynomial ideals over the rational numbers. The ideals are members of the PolynomialIdeal domain, and the polynomial generators are required to be from the DistributedMultivariatePolynomial domain.

contract : (PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer))), List(OrderedVariableList(vl))) -> PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer)))

contract(I, lvar) contracts the ideal I to the polynomial ring F[lvar].

primaryDecomp : PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer))) -> List(PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer))))

primaryDecomp(I) returns a list of primary ideals such that their intersection is the ideal I.

prime? : PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer))) -> Boolean

prime?(I) tests if the ideal I is prime.

radical : PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer))) -> PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer)))

radical(I) returns the radical of the ideal I.

zeroDimPrimary? : PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer))) -> Boolean

zeroDimPrimary?(I) tests if the ideal I is 0-dimensional primary.

zeroDimPrime? : PolynomialIdeal(Fraction(Integer), DirectProduct(#(vl), NonNegativeInteger), OrderedVariableList(vl), DistributedMultivariatePolynomial(vl, Fraction(Integer))) -> Boolean

zeroDimPrime?(I) tests if the ideal I is a 0-dimensional prime.