Computing sparse multiples of polynomials
Symbolic Computation
2011-01-04 v2 Computational Complexity
Data Structures and Algorithms
Abstract
We consider the problem of finding a sparse multiple of a polynomial. Given f in F[x] of degree d over a field F, and a desired sparsity t, our goal is to determine if there exists a multiple h in F[x] of f such that h has at most t non-zero terms, and if so, to find such an h. When F=Q and t is constant, we give a polynomial-time algorithm in d and the size of coefficients in h. When F is a finite field, we show that the problem is at least as hard as determining the multiplicative order of elements in an extension field of F (a problem thought to have complexity similar to that of factoring integers), and this lower bound is tight when t=2.
Cite
@article{arxiv.1009.3214,
title = {Computing sparse multiples of polynomials},
author = {Mark Giesbrecht and Daniel S. Roche and Hrushikesh Tilak},
journal= {arXiv preprint arXiv:1009.3214},
year = {2011}
}
Comments
Extended abstract appears in Proc. ISAAC 2010, pp. 266-278, LNCS 6506