## Approximate Bivariate Factorization, a Geometric Viewpoint (2007)

Citations: | 8 - 1 self |

### BibTeX

@MISC{Galligo07approximatebivariate,

author = {Andre Galligo and et al.},

title = { Approximate Bivariate Factorization, a Geometric Viewpoint},

year = {2007}

}

### OpenURL

### Abstract

We briefly present and analyze, from a geometric viewpoint, strategies for designing algorithms to factor bivariate approximate polynomials in C[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.