m at h . C O ] 9 A ug 2 00 0 Descartes ’ Rule for Trinomials in the Plane and Beyond ∗
نویسنده
چکیده
We prove that any pair of bivariate trinomials has at most 16 roots in the positive quadrant, assuming there are only finitely many roots there. The best previous upper bound independent of the polynomial degrees (following from a general result of Khovanski with stronger non-degeneracy hypotheses) was 248,832. Our proof allows real exponents and extends to certain systems of n-variate fewnomials.
منابع مشابه
Descartes’ Rule for Trinomials in the Plane and Beyond
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 counted only non-degenerate roots and even then gave much larger bounds, e.g., 248832 via a famous general result of Khovanski. Our bound is sharp, allows real exponents, and extends to certain systems of n-variate fewnomials....
متن کاملDescartes’ Rule for Trinomials in the Plane and Beyond
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 counted only non-degenerate roots and even then gave much larger bounds, e.g., 248832 via a famous general result of Khovanski. Our bound is sharp, allows real exponents, and extends to certain systems of n-variate fewnomials,...
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تاریخ انتشار 2008