论文信息 - Approximate polynomial GCD: Small degree and small height perturbations

Approximate polynomial GCD: Small degree and small height perturbations

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''.

Igor E. Shparlinski | Maurice Mignotte | Joachim von zur Gathen

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