Sign conditions for the existence of at least one positive solution of a sparse polynomial system

A DICKENSTEIN

Congreso; MCA Session on Symb. and Numer. Comp w. Polynomials; 2021

We give sign conditions on the support and coefficients of a sparse system of d generalized polynomials in d variables that guarantee the existence of at least one positive real root, based on degree theory and Gale duality. In the case of integer exponents, we relate our sufficient conditions to algebraic conditions that emerged in the study of toric ideals. This is joint work with Frédéric Bihan and Magalí Giaroli.