Descartes' Rule of Signs for Polynomial Systems supported on Circuits

We give the first 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.

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Frédéric Bihan, Alicia Dickenstein
• Keywords: CORR 2016, Education