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Journal Article

Factorizations of tropical and sign polynomials

MPS-Authors
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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;

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Citation

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


Cite as: http://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.