Approximate polynomial gcd: small degree and small height perturbations

Authors:
Joachim Von Zur Gathen;Igor E. Shparlinski
Affiliations:
B-IT, Universität Bonn, Bonn, Germany;Department of Computing, Macquarie University, NSW, Australia
Venue:
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Year:
2008

Citing 2
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Abstract

We consider the following computational problem: we are given two coprime univariate polynomials f0 and f1 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 f0 and f1 have a so-called normal degree sequence), and large height (when R = Z).