# PolynomialFactorizationByRecursion(R, E, VarSet, S)¶

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.