Practical polynomial factoring in polynomial time

There are several algorithms for factoring in Z[x] which have a proven polynomial complexity bound such as Sch¨onhage of 1984, Belabas/Kl¨uners/van Hoeij/Steel of 2004, and vanHoeij/Novocin of 2009. While several other algorithms can claim to be comparable to the best algorithms in practice such as Zassenhaus on restricted inputs, van Hoeij of 2002, and Belabas of 2004. We present here the first algorithm for factoring polynomials in Z[x] which is both comparable to the best algorithms in practice and has a proven polynomial complexity bound. We show that the algorithm has a competitive runtime on many worst-case polynomials and can be made significantly faster on a wide class of common polynomials. Our algorithm makes its practical gains by requiring less Hensel lifting.

• Type: Journal
• Year: 2011
• Where: ISSAC
• Authors: William Hart, Mark van Hoeij, Andrew Novocin
• Keywords: Factoring Polynomials, ISSAC 2011, Mathematics, Polynomial Complexity, Zassenhaus