Approximate bivariate factorization: a geometric viewpoint

We briefly present and analyze, from a geometric viewpoint, strategies for designing algorithms to factor bivariate approximate polynomials in   [x, y]. Given a composite polynomial, stably square-free, satisfying a genericity hypothesis, we describe the effect of a perturbation on the roots of its discriminant with respect to one variable, and the perturbation of the corresponding monodromy action on a smooth fiber. A novel geometric approach is presented, based on guided projection in the parameter space and continuation method above randomly chosen loops, to reconstruct from a perturbed polynomial a nearby composite polynomial and its irreducible factors. An algorithm and its ingredients are described. Categories and Subject Descriptors

• Type: Conference
• Year: 2007
• Where: ISSAC
• Authors: André Galligo, Mark van Hoeij
• Keywords: Bivariate Approximate Polynomials, Composite Polynomial, ISSAC 2007, Nearby Composite Polynomial