Sign conditions for the existence of at least one positive solution of a sparse polynomial system
Algebraic Geometry
2020-09-16 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1908.05503,
title = {Sign conditions for the existence of at least one positive solution of a sparse polynomial system},
author = {Frédéric Bihan and Alicia Dickenstein and Magalí Giaroli},
journal= {arXiv preprint arXiv:1908.05503},
year = {2020}
}
Comments
27 pages. Final version with mathematical improvements in Sections 3 and 6, plus several clarifications