Practical polynomial factoring in polynomial time

Authors:
William Hart;Mark van Hoeij;Andrew Novocin
Affiliations:
University of Warwick, Coventry, United Kingdom;Florida State University, Tallahassee, FL, USA;CNRS, ENS Lyon, INRIA, UCBL, U. Lyon, Lyon, France
Venue:
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Year:
2011

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Abstract

State of the art factoring in Q[x] is dominated in theory by a combinatorial reconstruction problem while, excluding some rare polynomials, performance tends to be dominated by Hensel lifting. We present an algorithm which gives a practical improvement (less Hensel lifting) for these more common polynomials. In addition, factoring has suffered from a 25 year complexity gap because the best implementations are much faster in practice than their complexity bounds. We illustrate that this complexity gap can be closed by providing an implementation which is comparable to the best current implementations and for which competitive complexity results can be proved.