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arXiv · 2005.12882

Factorizations of tropical and sign polynomials

Alexander Agudelo·Oliver Lorscheid
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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.

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Alexander Agudelo, Oliver Lorscheid. 2020-05-26. Factorizations of tropical and sign polynomials. https://arxiv.org/abs/2005.12882

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