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arXiv · 1811.04966

Descartes' rule of signs, Newton polygons, and polynomials over hyperfields

Matthew Baker·Oliver Lorscheid
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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".

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Matthew Baker, Oliver Lorscheid. 2018-11-12. Descartes' rule of signs, Newton polygons, and polynomials over hyperfields. https://doi.org/10.1016/j.jalgebra.2020.10.024

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