Approximate polynomial gcd: Small degree and small height perturbations

Authors:
Joachim von zur Gathen;Maurice Mignotte;Igor E. Shparlinski
Affiliations:
B-IT, Universität Bonn, 53113 Bonn, Germany;Département de Mathématiques, Université Louis Pasteur, 7 rue René Descartes, F-67084 Strasbourg cedex, France;Department of Computing, Macquarie University, NSW 2109, Australia
Venue:
Journal of Symbolic Computation
Year:
2010

Citing 5
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Abstract

We consider the following computational problem: we are given two coprime univariate polynomials f"0 and f"1 over a ring R and want to find whether after a small perturbation we can achieve a large gcd. We solve this problem in polynomial time for two notions of ''large'' (and ''small''): large degree (when R=F is an arbitrary field, in the generic case when f"0 and f"1 have a so-called normal degree sequence), and large height (when R=Z). Our work adds to the existing notions of ''approximate gcd''.