Improved dense multivariate polynomial factorization algorithms

We present new deterministic and probabilistic algorithms that reduce the factorization of dense polynomials from several 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. Key words: Polynomial factorization, Hensel lifting, Bertini’s irreducibility theorem.

• Type: Journal
• Year: 2007
• Where: JSC
• Authors: Grégoire Lecerf
• Keywords: Bertini’s Irreducibility, JSC 2007, Polynomial, Probabilistic Algorithm