Improved dense multivariate polynomial factorization algorithms

Authors:
Grégoire Lecerf
Affiliations:
Laboratoire de Mathématiques, UMR 8100 CNRS, Université de Versailles Saint-Quentin-en-Yvelines, 45 avenue des États-Unis, 78035 Versailles, France
Venue:
Journal of Symbolic Computation
Year:
2007

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Abstract

We present new deterministic and probabilistic algorithms that reduce the factorization of dense polynomials from several variables to one variable. The deterministic algorithm runs in sub-quadratic time in the dense size of the input polynomial, and the probabilistic algorithm is softly optimal when the number of variables is at least three. We also investigate the reduction from several to two variables and improve the quantitative version of Bertini's irreducibility theorem.