Minimum volumes of tropical rational functions
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_ | 1866912047889907712 |
|---|---|
| author | Sukenaga, Masayuki |
| author_facet | Sukenaga, Masayuki |
| contents | When a tropical rational function φon R^n is given, we can represent it as φ=f-g with tropical polynomials f and g. We develop the duality theorem for tropical rational functions to define the volume of the pair (f, g). We show that when n=1, we can find a representation of φ(x) \neq -\infty as f(x)-g(x) with the pair (f, g) of minimum volume. The dual subdivision of f(x) \oplus (yg(x)) is unique up to translation, but when n=2 this is not true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimum volumes of tropical rational functions Sukenaga, Masayuki Algebraic Geometry When a tropical rational function φon R^n is given, we can represent it as φ=f-g with tropical polynomials f and g. We develop the duality theorem for tropical rational functions to define the volume of the pair (f, g). We show that when n=1, we can find a representation of φ(x) \neq -\infty as f(x)-g(x) with the pair (f, g) of minimum volume. The dual subdivision of f(x) \oplus (yg(x)) is unique up to translation, but when n=2 this is not true. |
| title | Minimum volumes of tropical rational functions |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.18348 |