Factoring bivariate lacunary polynomials without heights
Computational Complexity
2013-07-02 v3 Symbolic Computation
Abstract
We present an algorithm which computes the multilinear factors of bivariate lacunary polynomials. It is based on a new Gap Theorem which allows to test whether a polynomial of the form P(X,X+1) is identically zero in time polynomial in the number of terms of P(X,Y). The algorithm we obtain is more elementary than the one by Kaltofen and Koiran (ISSAC'05) since it relies on the valuation of polynomials of the previous form instead of the height of the coefficients. As a result, it can be used to find some linear factors of bivariate lacunary polynomials over a field of large finite characteristic in probabilistic polynomial time.
Keywords
Cite
@article{arxiv.1206.4224,
title = {Factoring bivariate lacunary polynomials without heights},
author = {Arkadev Chattopadhyay and Bruno Grenet and Pascal Koiran and Natacha Portier and Yann Strozecki},
journal= {arXiv preprint arXiv:1206.4224},
year = {2013}
}
Comments
25 pages, 1 appendix