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.

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64 votes
5 answers
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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
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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 ...
Theo Johnson-Freyd's user avatar
7 votes
4 answers
924 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 ...
Oussema's user avatar
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4 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 ...
Chill2Macht's user avatar
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4 votes
0 answers
189 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 ...
Oussema's user avatar
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2 votes
1 answer
278 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 ...
gradstudent's user avatar
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