Optimal Descartes' Rule of Signs for Circuits

Abstract

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.

21 pages, 5 figures. We improved the proof of Theorem 2.4 by adding Proposition 2.7

References in corpus (1)

• Lower bounds for positive roots and regions of multistationarity in chemical reaction networks

Cited by in corpus (1)

• Counting Real Roots in Polynomial-Time for Systems Supported on Circuits