Optimal Descartes' Rule of Signs for Circuits
Algebraic Geometry
2022-05-27 v2 Symbolic Computation
Abstract
We present an optimal version of Descartes' rule of signs to bound the number of positive real roots of a sparse system of polynomial equations in n variables with n+2 monomials. This sharp upper bound is given in terms of the sign variation of a sequence associated to the exponents and the coefficients of the system.
Keywords
Cite
@article{arxiv.2010.09165,
title = {Optimal Descartes' Rule of Signs for Circuits},
author = {Frédéric Bihan and Alicia Dickenstein and Jens Forsgård},
journal= {arXiv preprint arXiv:2010.09165},
year = {2022}
}
Comments
21 pages, 5 figures. We improved the proof of Theorem 2.4 by adding Proposition 2.7