fmpz_mpoly_factor_irred_zassenhaus, fmpz_mpoly_factor_irred_wang, fmpz_mpoly_factor_irred_zippel

Set fac to the irreducible factors of A, which must be squarefree, primitive with respect to each variable and have positive leading coefficient, in a lex context with at least two variables. lcA is the leading coefficient of A in x_0 and lcAfac a squarefree factorisation of it, irreducible if lcAfac_irred is nonzero. Z collects the degrees of the factors of univariate images and can prove irreducibility early.

The Wang version evaluates x_1, \ldots at 0 and, if allow_shift is nonzero, then at random points of growing size, distributes the leading coefficient with fmpz_mpoly_factor_lcc_wang or fmpz_mpoly_factor_lcc_kaltofen, and lifts the factors one variable at a time with fmpz_mpoly_hlift. The Zippel version lifts modulo a prime with sparse Hensel lifting and then p-adically. The Zassenhaus version lifts without leading coefficient information and recombines subsets of the lifted factors. Return 1 on success, 0 if the method failed (another method or point may succeed), and -1 on an exceptional failure such as exponents that no longer fit one word.