# 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(lp, p, v) implements the bivariate case of solveLinearPolynomialEquationByRecursion; its implementation depends on R
factorByRecursion(p) factors polynomial p. This function performs the recursion step for factorPolynomial, as defined in PolynomialFactorizationExplicit category (see factorPolynomial)
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 produces a random element of R
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.