%0 Journal Article
%T The number of real roots of a bivariate polynomial on a line
%A Martin Avendano
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0702891v1