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  Factorizations of tropical and sign polynomials

Agudelo, A., & Lorscheid, O. (2021). Factorizations of tropical and sign polynomials. Indagationes Mathematicae, 32(4), 797-812. doi:10.1016/j.indag.2021.04.005.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0008-FD2B-C Version Permalink: https://hdl.handle.net/21.11116/0000-000D-F86B-4
Genre: Journal Article

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This is an open access article distributed under the terms of the Creative Commons CC-BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. You are not required to obtain permission to reuse this article.
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 Creators:
Agudelo, Alexander1, Author           
Lorscheid, Oliver1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory
 Abstract: In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call `tropical polynomials' and `sign polynomials', respectively. We classify all irreducible polynomials in either case. We show that tropical polynomials factor uniquely into irreducible factors, but that unique factorization fails for sign polyomials. We describe
division algorithms for tropical and sign polynomials by linear terms that
correspond to roots of the polynomials.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2005.12882
DOI: 10.1016/j.indag.2021.04.005
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Title: Indagationes Mathematicae
  Abbreviation : Indag. Math.
Source Genre: Journal
 Creator(s):
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Publ. Info: Elsevier
Pages: - Volume / Issue: 32 (4) Sequence Number: - Start / End Page: 797 - 812 Identifier: -