The number of real roots of a bivariate polynomial on a line
Algebraic Geometry
2007-05-23 v1
Abstract
We prove that a bivariate polynomial f with exactly t non-zero terms, restricted to a real line {y=ax+b}, either has at most 6t-4 zeroes or vanishes over the whole line. As a consequence, we derive an alternative algorithm to decide whether a linear polynomial divides a bivariate polynomial (with exactly t non-zero terms) over a real number field K within [ log(H(f)H(a)H(b)) [K:Q}] log(deg(f)) t]^{O(1)} bit operations.
Cite
@article{arxiv.math/0702891,
title = {The number of real roots of a bivariate polynomial on a line},
author = {Martin Avendano},
journal= {arXiv preprint arXiv:math/0702891},
year = {2007}
}
Comments
6 pages, no figures