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arXiv · 2410.15426

Equations over Polyhedral Semirings

Madhusudan Manjunath
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Abstract

We study the theory of equations in one variable over polyhedral semirings. The article revolves around a notion of solution to a polynomial equation over a polyhedral semiring. Our main results are a characterisation of local solutions in terms of the coefficients, a local-global principle, and the basics of multiplicity and discriminants. Our primary sources of motivation are tropical geometry and the theory of exceptional points in non-Hermitian physics.

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Madhusudan Manjunath. 2024-10-20. Equations over Polyhedral Semirings. https://arxiv.org/abs/2410.15426

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