On factorization of multivariate polynomials over algebraic number and function fields

Authors:
Seyed Mohammad Mahdi Javadi;Michael B. Monagan
Affiliations:
Simon Fraser University, Burnaby, BC, Canada;Simon Fraser University, Burnaby, BC, Canada
Venue:
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Year:
2009

Citing 6
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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.