Equations over Polyhedral Semirings
Algebraic Geometry
2024-10-22 v1 Combinatorics
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.
Cite
@article{arxiv.2410.15426,
title = {Equations over Polyhedral Semirings},
author = {Madhusudan Manjunath},
journal= {arXiv preprint arXiv:2410.15426},
year = {2024}
}