A Maple Program to Factor Multivariate Polynomials Given by Black Boxes

Let a be a polynomial in Z[x1,x2,…,xn]. Let α ∈ Zn and p be a large prime. Let B be a modular black box representation for a, that is, B : Zn × {p} → Zp such that B(α,p) outputs a(α) mod p. In our implementation B is a Maple procedure. We present a Maple program CMBBSHL which on input of B outputs the irreducible factorization Πri=1 feii of a(x1,…,xn) with high probability. Our program is a combination of Maple codes and C codes where the main programs are implemented in Maple and several subroutines are implemented in C for increased efficiency. We present (1) a description of the algorithm, (2) a demonstration of the software, (3) a timing benchmark, and (4) some implementation details.