Probabilistic algorithms for sparse polynomials

Abstract

In this paper we have tried to demonstrate how sparse techniques can be used to increase the effectiveness of the modular algorithms of Brown and Collins. These techniques can be used for an extremely wide class of problems and can applied to a number of different algorithms including Hensel's lemma. We believe this work has finally laid to rest the bad zero problem. Much of the work here is the direct result of discussion with Barry Trager and Joel Moses whose help we wish to acknowledge.