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- W2949918018 abstract "We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees were much larger, e.g., 248832 (for just the non-degenerate roots) via a famous general result of Khovanski. Our bound is sharp, allows real exponents, allows degeneracies, and extends to certain systems of n-variate fewnomials, giving improvements over earlier bounds by a factor exponential in the number of monomials. We also derive analogous sharpened bounds on the number of connected components of the real zero set of a single n-variate m-nomial." @default.
- W2949918018 created "2019-06-27" @default.
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- W2949918018 date "2002-12-12" @default.
- W2949918018 modified "2023-09-27" @default.
- W2949918018 title "Counting Real Connected Components of Trinomial Curve Intersections and m-nomial Hypersurfaces" @default.
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