Factorizations of tropical and sign polynomials

Agudelo, Alexander; Lorscheid, Oliver

doi:10.1016/j.indag.2021.04.005

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Factorizations of tropical and sign polynomials

MPG-Autoren

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

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

Externe Ressourcen

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

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

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Agudelo-Lorscheid_Factorizations of tropical and sign polynomials_2021.pdf
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Zitation

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.

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

Zusammenfassung

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.