volume 30, issue 3, P379-414 2003
DOI: 10.1007/s00454-003-2834-8
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Abstract: In memory of Konstantin Alexandrovich Sevast 'yanov,1956-1984. Abstract. We prove that any pair of bivariate trinomials has at most five 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 bo…

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