New Complexity Bounds for Certain Real Fewnomial Zero Sets

Details New Complexity Bounds for Certain Real Fewnomial Zero Sets New Complexity Bounds for Certain Real Fewnomial Zero Sets

2007-09-15

arxiv.org/abs/0709.2405v1

Mathematics

Algebraic Geometry

8 pages, no figures. Extended abstract accepted and presented at MEGA (Effective Methods in Algebraic Geometry) 2007

Scientific paper

Consider real bivariate polynomials f and g, respectively having 3 and m monomial terms. We prove that for all m>=3, there are systems of the form (f,g) having exactly 2m-1 roots in the positive quadrant. Even examples with m=4 having 7 positive roots were unknown before this paper, so we detail an explicit example of this form. We also present an O(n^{11}) upper bound for the number of diffeotopy types of the real zero set of an n-variate polynomial with n+4 monomial terms.

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