# Questions tagged [tropical-arithmetic]

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### Does tropicalization commute with composition?

Say we have two polynomials $$f = \sum d_n x^n, \quad g = \sum_n b_n x^n$$ that tropicalize to $$F = \max(d_n + nx), \quad G = \max(b_n + nx).$$ Can we say $f\circ g$ tropicalizes to $F\circ G$? ...
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### Proving equivalence of tropical polynomials

I am new to the world of tropical mathematics. I am wondering if there is an algorithm to prove the equivalence of two tropical polynomials (in the plus-min semiring let's say), say over multivaribles?...
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### Efficient computation of "discrete infimal convolution"

This question arises from an application to graphical models in probability theory, but I have abstracted that part out so only algebra remains. Let $\mathbb{R}$ denote standard field of real numbers ...
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### Algorithms for "Ideals" in polynomial algebras over the max-plus semi-ring

I'm a beginner in tropical geometry, and I'm running into the following question: In the usual polynomial ring over a field, one has algorithms (i.e. using a Groebner basis) for determining whether ...
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### Tropical homological algebra

Has anyone out there thought about homological algebra over the tropical semifield $\mathbb{T}$? For example, I'm interested in the Hochschild homology and cyclic homology of tropical algebras, if ...
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### Generalized Haar Measures and Semiring-Valued Integrals on Lie Groups

In an applied research problem I am currently working on, I am using non-commutative semiring convolution to formulate some interesting types of calculations on images and solid objects. For discrete ...
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### Tropical mathematics and enriched category theory

Is there a connection between tropical mathematics and the Lawvere enriched category theory approach to metric spaces? I guess I will give a partial answer to this below, but I mean can they be ...