Descartes' Rule of Signs for Polynomial Systems supported on Circuits

01/21/2016

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by   Frédéric Bihan, et al.

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We give a multivariate version of Descartes' rule of signs to bound the number of positive real roots of a system of polynomial equations in n variables with n+2 monomials, in terms of the sign variation of a sequence associated both to the exponent vectors and the given coefficients. We show that our bound is sharp and is related to the signature of the circuit.