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

Matthew Baker; Oliver Lorscheid

doi:10.1016/j.jalgebra.2020.10.024

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

Matthew Baker^*, Oliver Lorscheid^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

13 Citations (Scopus)

20 Downloads (Pure)

Abstract

In this note, 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”.

Original language	English
Pages (from-to)	416-441
Number of pages	26
Journal	Journal of algebra
Volume	569
DOIs	https://doi.org/10.1016/j.jalgebra.2020.10.024
Publication status	Published - Mar-2021
Externally published	Yes

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

abstract = "In this note, 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”.",

author = "Matthew Baker and Oliver Lorscheid",

year = "2021",

month = mar,

doi = "10.1016/j.jalgebra.2020.10.024",

language = "English",

volume = "569",

pages = "416--441",

journal = "Journal of algebra",

issn = "0021-8693",

publisher = "ACADEMIC PRESS INC ELSEVIER SCIENCE",

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TY - JOUR

T1 - Descartes' rule of signs, Newton polygons, and polynomials over hyperfields

AU - Baker, Matthew

AU - Lorscheid, Oliver

PY - 2021/3

Y1 - 2021/3

N2 - In this note, 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”.

AB - In this note, 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”.

U2 - 10.1016/j.jalgebra.2020.10.024

DO - 10.1016/j.jalgebra.2020.10.024

M3 - Article

SN - 0021-8693

VL - 569

SP - 416

EP - 441

JO - Journal of algebra

JF - Journal of algebra

ER -

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

Abstract

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