On factorization of multivariate polynomials over algebraic number and function fields

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.

• Type: Conference
• Year: 2009
• Where: ISSAC
• Authors: Seyed Mohammad Mahdi Javadi, Michael B. Monagan
• Keywords: Algorithm, Algorithm Uses Hensel, ISSAC 2009, Mathematics, P-adic Lifting Algorithm