MultivariateSquareFree(E, OV, R, P)ΒΆ

multsqfr.spad line 1

Author : P.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation Af + Bg = h and its generalization to n polynomials over an integral domain and the package MultivariateLifting for the “multivariate” lifting.

check: (List Record(factor: SparseUnivariatePolynomial R, exponent: Integer), List Record(factor: SparseUnivariatePolynomial R, exponent: Integer)) -> Boolean
check should be local
coefChoose: (Integer, Factored P) -> P
coefChoose should be local
compdegd: List Record(factor: SparseUnivariatePolynomial R, exponent: Integer) -> 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: Integer), ctpol: R)
intChoose should be local
lift: (SparseUnivariatePolynomial P, SparseUnivariatePolynomial R, SparseUnivariatePolynomial R, P, List OV, List NonNegativeInteger, List 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: Integer))
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.
squareFreePrim: P -> Factored P
squareFreePrim(p) compute the square free decomposition of a primitive multivariate polynomial p.
univcase: (P, OV) -> Factored P
univcase should be local