MEGA 2007 Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th http://www.ricam.oeaw.ac.at/mega2007

Abstract

Title	New Complexity Bounds for Certain Real Fewnomial Zero Sets (extended abstract)
Keywords	lower bounds, upper bounds, diffeotopy, sparse, fewnomial, discriminant
Abstract	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^8) 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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