Complexity issues in bivariate polynomial factorization

Many polynomial factorization algorithms rely on Hensel lifting and factor recombination. For bivariate polynomials we show that lifting the factors up to a precision linear in the total degree of the polynomial to be factored is sufficient to deduce the recombination by linear algebra, using trace recombination. Then, the total cost of the lifting and the recombination stage is subquadratic in the size of the dense representation of the input polynomial. Lifting is often the practical bottleneck of this method: we propose an algorithm based on a faster multi-moduli computation for univariate polynomials and show that it saves a constant factor compared to the classical multifactor lifting algorithm. Categories and Subject Descriptors F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; G.4 [Mathematics of Computing]: Mathematical Software General Terms Algorithm, Theory Keywords Computer algebra, polynomial factorization, Hensel lifting, multi-moduli, Tellegen,...

• Type: Conference
• Year: 2004
• Where: ISSAC
• Authors: Alin Bostan, Grégoire Lecerf, Bruno Salvy, Éric Schost, B. Wiebelt
• Keywords: Hensel Lifting, ISSAC 2004, Polynomial, Polynomial Factorization