Approximate GCD of several univariate polynomials with small degree perturbations

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• 作者：Mohamed Elkadi ^{elkadi@math.unice.fr} ; André ; Galligo ^{galligo@math.unice.fr} ; Thang Luu Ba ^{tanglb@math.unice.fr}
• 关键词：GCD of univariate polynomials ; EEA ; Normal degree sequence ; Approximate computation ; Minimal syzygies ; 渭-basis ; Generic initial ideal ; Groebner basis
• 刊名：Journal of Symbolic Computation
• 出版年：2012
• 期刊代码：140_07477171
• 类别：cp
• 出版时间：April, 2012
• 卷：47
• 期：4
• 页码：410-421
• 文件大小：273 K

摘要

We consider the following computational problem: given a family of generic univariate polynomials , construct an algorithm to find polynomial perturbations with 鈥渟mall鈥?degrees such that the greater common divisor of the family of polynomials has a 鈥渓arge鈥?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 .