@article{b516974bc5d34ee1a4dca453b37e7a14,
title = "Factorizations of tropical and sign polynomials",
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 polynomials. We describe division algorithms for tropical and sign polynomials by linear terms that correspond to roots of the polynomials.",
keywords = "Division algorithm for polynomials, Factorization into irreducible elements, Hyperfields",
author = "Alexander Agudelo and Oliver Lorscheid",
note = "Funding Information: The authors thank Matt Baker for helpful discussions that led to the results of this paper. We thank Gunn Trevor and Liu Ziqi for correcting some wrong statements of an early draft of this text. We thank an anonymous referee for pointing out the existence of a (non-deterministic) division algorithm for polynomials over an arbitrary hyperfield. Publisher Copyright: {\textcopyright} 2021 The Author(s)",
year = "2021",
month = jul,
doi = "10.1016/j.indag.2021.04.005",
language = "English",
volume = "32",
pages = "797--812",
journal = "Indagationes Mathematicae",
issn = "0019-3577",
publisher = "ELSEVIER SCIENCE BV",
number = "4",
}