Approximate Polynomial gcd: Small Degree and Small Height Perturbations

  • Joachim von zur Gathen
  • Igor E. Shparlinski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4957)


We consider the following computational problem: we are given two coprime univariate polynomials f 0 and f 1 over a ring \(\mathcal{R}\) 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 \(\mathcal{R} = \mathbb{F}\) 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 \(\mathcal{R} =\mathbb{Z}\)).


Euclidean algorithm gcd approximate computation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Joachim von zur Gathen
    • 1
  • Igor E. Shparlinski
    • 2
  1. 1.B-ITUniversität BonnBonnGermany
  2. 2.Department of ComputingMacquarie UniversityAustralia

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