Factorizations of tropical and sign polynomials
Number Theory
2020-05-27 v1
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.
Cite
@article{arxiv.2005.12882,
title = {Factorizations of tropical and sign polynomials},
author = {Alexander Agudelo and Oliver Lorscheid},
journal= {arXiv preprint arXiv:2005.12882},
year = {2020}
}
Comments
14 pages