On factorization of multivariate polynomials over algebraic number and function fields

Abstract

We present an efficient algorithm for factoring a multivariate polynomial f ∈ L[x1,...,xv] where L is an algebraic function field with k ≥0 parameters t1,...,tk and r ≥0 field extensions.Our algorithm uses Hensel lifting and extends the EEZ algorithm of Wang which was designed for factorization over Q. We also give a multivariate p-adic lifting algorithm which uses sparse interpolation. This enables us to avoid using poor bounds on the size of the integer coefficients in the factorization of f when using Hensel lifting. We have implemented our algorithm in Maple 13. We provide timings demonstrating the efficiency of our algorithm.