Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
401277 | Journal of Symbolic Computation | 2012 | 12 Pages |
Abstract
We consider the following computational problem: given a family of generic univariate polynomials f≔(f0,…,fs)f≔(f0,…,fs), construct an algorithm to find polynomial perturbations u≔(u0,…,us)u≔(u0,…,us) with “small” degrees such that the greater common divisor of the family of polynomials f+uf+u has a “large” degree.In this paper, we propose an algorithm which solves this problem in polynomial time under a generic condition generalizing the normal degree sequence for the case s=1s=1.
► We study the approximate gcd of several univariate polynomials. ► We propose an algorithm which computes this gcd in polynomial time. ► The algorithm is based on the gin and minimal syzygies of these polynomials.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Mohamed Elkadi, André Galligo, Thang Luu Ba,