Questions tagged [tropical-geometry]
For questions about tropical geometry, piece-wise linear functions with integer slopes, tropical degenerations and applications of tropical geometry, max-plus algebra, and tropical semifields.
7 questions
65
votes
5
answers
18k
views
Why tropical geometry?
Tropical geometry can be described as "algebraic geometry" over the semifield $\mathbb{T}$ of tropical numbers. As a set, $\mathbb{T}=\mathbb{R}\cup \{ -\infty\}$; this is endowed with addition being ...
40
votes
5
answers
4k
views
How should one approach tropical mathematics?
Let me preface this by saying that my background is pretty meagre (i.e. solid undergrad). However, a few months ago I came across Litvinov - The Maslov dequantization, idempotent and tropical ...
34
votes
4
answers
2k
views
How is tropicalization like taking the classical limit?
There is a folk — I can't call it a theorem — "fact" that the mathematical relationship between Complex and Tropical geometry is analogous to the physical relationship between Quantum and ...
- 54.6k
7
votes
4
answers
1k
views
Origin of tropical mathematics
On Wikipedia, it is claimed without a source that Imre Simon founded tropical mathematics.
The first work of his I was able to find on the subject is Limited subsets of a free monoid which uses the ...
- 211
6
votes
1
answer
1k
views
Is there any "fundamental" distinction between min-plus, max-plus, min-product, and max-product algebras?
In the paper Faster Algorithms for Max-Product Message Passing by McAuley and Caetano (see e.g. here or here), several statements are made which seem mathematically questionable to me.
For ...
- 2,680
4
votes
0
answers
206
views
History of tropical mathematics
This is a follow-up to this question about the origin of tropical mathematics.
Are there any articles, websites or books which deal with the history of tropical mathematics?
I have been trying to find ...
- 211
2
votes
1
answer
296
views
Can we have "tropical polynomials" with arbitrary real powers?
I am referring to the definition of a tropical polynomial given on page 8 (top of section 3) here in this review, https://arxiv.org/pdf/math/0306366.pdf. I understand that here the notion of a ...
- 2,246