The number of real roots of a bivariate polynomial on a line

2007/02/28 by Martin Avendano, Avendano, Martin
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0702891

6 pages, no figures

arxiv created 2007/02/28 · arxiv updated 2009/12/01

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.

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