Approximate polynomial GCD: small degree and small height perturbations

• Autores: Joachim von zur Gathen, Maurice Mignotte, Igor E. Shparlinski
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 45, Nº 8, 2010, págs. 879-886
• Idioma: inglés
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• Resumen

  • We consider the following computational problem: we are given two coprime univariate polynomials f0 and f1 over a ring and want to find whether after a small perturbation we can achieve a large . We solve this problem in polynomial time for two notions of �large� (and �small�): large degree (when is an arbitrary field, in the generic case when f0 and f1 have a so-called normal degree sequence), and large height (when ). Our work adds to the existing notions of �approximate gcd�.