Optimal Descartes' Rule of Signs for Circuits

10/19/2020

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by   Frédéric Bihan, et al.

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We present an optimal version of Descartes' rule of signs to bound the number of positive real roots of a sparse system of polynomial equations in n variables with n+2 monomials. This sharp upper bound is given in terms of the sign variation of a sequence associated to the exponents and the coefficients of the system.