Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Manjunath, Madhusudan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404088643