Descartes' rule of signs, Newton polygons, and polynomials over hyperfields
arXiv:1811.04966 · doi:10.1016/j.jalgebra.2020.10.024
Abstract
We develop a theory of multiplicities of roots for polynomials over hyperfields and use this to provide a unified and conceptual proof of both Descartes' rule of signs and Newton's "polygon rule".
21 pages. v2: Revised the exposition and organization of the paper, corrected some minor typos. v3: Revised according to referee report, added new references. v4: Corrected a typo pointed out by Michaël Bensimhoun