Equations over Polyhedral Semirings
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912078893154304 |
|---|---|
| author | Manjunath, Madhusudan |
| author_facet | Manjunath, Madhusudan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equations over Polyhedral Semirings Manjunath, Madhusudan Algebraic Geometry Combinatorics 14T10, 15A80, 16Y60, 14M25, 52B20 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. |
| title | Equations over Polyhedral Semirings |
| topic | Algebraic Geometry Combinatorics 14T10, 15A80, 16Y60, 14M25, 52B20 |
| url | https://arxiv.org/abs/2410.15426 |