PolynomialFactorizationByRecursion(R, E, VarSet, S)

pfbr.spad line 1 [edit on github]

• R : PolynomialFactorizationExplicit
• E : OrderedAbelianMonoidSup
• VarSet : OrderedSet
• S : PolynomialCategory(R, E, VarSet)

PolynomialFactorizationByRecursion(R, E, VarSet, S) is used for factorization of sparse univariate polynomials over a domain S of multivariate polynomials over R.

bivariateSLPEBR : (List(SparseUnivariatePolynomial(S)), SparseUnivariatePolynomial(S), VarSet) -> Union(List(SparseUnivariatePolynomial(S)), "failed")

bivariateSLPEBR(lp, p, v) implements the bivariate case of solveLinearPolynomialEquationByRecursion; its implementation depends on R

factorByRecursion : SparseUnivariatePolynomial(S) -> Factored(SparseUnivariatePolynomial(S))

factorByRecursion(p) factors polynomial p. This function performs the recursion step for factorPolynomial, as defined in PolynomialFactorizationExplicit category (see factorPolynomial)

factorSquareFreeByRecursion : SparseUnivariatePolynomial(S) -> Factored(SparseUnivariatePolynomial(S))

factorSquareFreeByRecursion(p) returns the square free factorization of p. This functions performs the recursion step for factorSquareFreePolynomial, as defined in PolynomialFactorizationExplicit category (see factorSquareFreePolynomial).

randomR : Integer -> R

randomR produces a random element of R

solveLinearPolynomialEquationByRecursion : (List(SparseUnivariatePolynomial(S)), SparseUnivariatePolynomial(S)) -> Union(List(SparseUnivariatePolynomial(S)), "failed")

solveLinearPolynomialEquationByRecursion([p1, ..., pn], p) returns the list of polynomials [q1, ..., qn] such that sum qi/pi = p / prod pi, a recursion step for solveLinearPolynomialEquation as defined in PolynomialFactorizationExplicit category (see solveLinearPolynomialEquation). If no such list of qi exists, then "failed" is returned.