MultivariateSquareFree(E, OV, R, P)

multsqfr.spad line 1 [edit on github]

• E: OrderedAbelianMonoidSup

• OV: OrderedSet

• R: EuclideanDomain

• P: PolynomialCategory(R, E, OV)

Author : P.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses modular reduction and the package MultivariateLifting for the “multivariate” lifting.

check: (List Record(factor: SparseUnivariatePolynomial R, exponent: NonNegativeInteger), List Record(factor: SparseUnivariatePolynomial R, exponent: NonNegativeInteger)) -> Boolean

check should be local

coefChoose: (Integer, P, List Record(factor: P, exponent: NonNegativeInteger)) -> P

coefChoose should be local

compdegd: List Record(factor: SparseUnivariatePolynomial R, exponent: NonNegativeInteger) -> Integer

compdegd should be local

consnewpol: (SparseUnivariatePolynomial P, SparseUnivariatePolynomial R, Integer) -> Record(pol: SparseUnivariatePolynomial P, polval: SparseUnivariatePolynomial R)

consnewpol should be local

intChoose: (SparseUnivariatePolynomial P, List OV, List List R) -> Record(upol: SparseUnivariatePolynomial R, Lval: List R, Lfact: List Record(factor: SparseUnivariatePolynomial R, exponent: NonNegativeInteger), ctpol: R)

intChoose should be local

lift: (SparseUnivariatePolynomial P, SparseUnivariatePolynomial R, SparseUnivariatePolynomial R, P, List OV, List NonNegativeInteger, List R, R) -> Union(List SparseUnivariatePolynomial P, failed)

lift should be local

myDegree: (SparseUnivariatePolynomial P, List OV, NonNegativeInteger) -> List NonNegativeInteger

myDegree should be local

normDeriv2: (SparseUnivariatePolynomial R, Integer) -> SparseUnivariatePolynomial R

normDeriv2 should be local

nsqfree: (SparseUnivariatePolynomial P, List OV, List List R) -> Record(unitPart: P, suPart: List Record(factor: SparseUnivariatePolynomial P, exponent: NonNegativeInteger))

nsqfree should be local

squareFree: P -> Factored P

squareFree(p) computes the square free decomposition of a multivariate polynomial p.

squareFree: SparseUnivariatePolynomial P -> Factored SparseUnivariatePolynomial P

squareFree(p) computes the square free decomposition of a multivariate polynomial p presented as a univariate polynomial with multivariate coefficients.

univcase: (P, OV) -> Factored P

univcase should be local