Abstract only

Abstract

We investigate the problem of computing the sparsest multiple of a given univariate polynomial. Over the rational numbers we exhibit algorithms for when the target sparsity is two (i.e., the existence of a binomial multiple), as well as some cases when the target multiple has greater (constant) sparsity. Over finite fields, we tie the cost of finding a binomial multiple (of low degree) to order-finding in the multiplicative group of a finite field, as well as presenting similar, but more limited results for general sparsit.