Factorizations of tropical and sign polynomials

Agudelo, Alexander; Lorscheid, Oliver

doi:10.1016/j.indag.2021.04.005

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Factorizations of tropical and sign polynomials

MPS-Authors

/persons/resource/persons262003

Agudelo, Alexander
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons235726

Lorscheid, Oliver
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1016/j.indag.2021.04.005
(Publisher version)

https://doi.org/10.48550/arXiv.2005.12882
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

Agudelo-Lorscheid_Factorizations of tropical and sign polynomials_2021.pdf
(Publisher version), 338KB

Supplementary Material (public)

There is no public supplementary material available

Citation

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.

Cite as: https://hdl.handle.net/21.11116/0000-0008-FD2B-C

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.