Descartes’ Rule of Signs for Polynomial Systems Supported on Circuits
Frédéric Bihan, Alicia Dickenstein · International Mathematics Research Notices · 2016
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.