Fall 2014

Descartes' Rule of Signs for Polynomial Systems Supported on Circuits

Wednesday, October 15th, 2014 11:35 am12:00 pm

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Calvin Lab Auditorium

Descartes’ rule of signs bounds the number of positive roots of an univariate polynomial by the number of sign changes between consecutive coefficients. In particular, this produces a sharp bound depending on the number of monomials. Generalizing Descartes’ rule of signs or the corresponding sharp bound to the multivariable case is a challenging problem. In this talk, I will present a generalization of Descartes’ rule of signs for the number of positive solutions of any system of n real polynomial equations in n variables with at most n+2 monomials. This is a joint work with Alicia Dickenstein.