# Questions tagged [tropical-geometry]

For questions related to tropical geometry.

59 questions
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### Tropical algebra and tropical determinate

We know that a determinant of the matrix is the sum of permutation of the elements Multiplied by "(-1)" number of times equal to changes of matrix rows. Why the signal is not important in defining the ...
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### Add conditionals to plot in sage

I am trying to implement an algorithm which plots a tropical curve given a tropical polynomial $P(x,y)$. So for instance the graph of $P(x,y)=x+y+0$ should be a union of three half rays, starting at ...
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### definition of tropicalization map

I'm fairly new to the whole topic of tropicalization and I'm having trouble to even understand the following introductory definition: [General setting: Let $K$ be a field which is complete with ...
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### Min-Plus Algebra (Operation Question)

I was reading about distance matrices, and they discuss a concept known as min-plus algebra. I am unsure if the operator + means addition in this context, and also unsure what operation goes in the ...
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### Algorithm to find the convex polyhedron

In the context of my research, I've encountered the problem described below. I wonder if this is a standard problem in convex optimization or linear programming and would appreciate any comments. I ...
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### What is 'identifying restricted Boltzmann machine'?

Currently, I am going through Geometry of the Restricted Boltzmann Machine by Cueto et al. In this paper (in the abstract, multiple places in Section 1, etc.), the authors use the concept of the ...
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### Explain the Zero Tension Condition of a Tropical Curve $\mathcal{H}(x)$

Right now I am studying tropical mathematics and I just arrived at a statement that I'm having trouble understanding. Here's how its stated: For a tropic polynomial in two variables. $p$, the ...
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### A question about the solutions of $x+y-1$

Let us try and tropicalize $f(x,y)=x+y-1$. Ley $X=V(f)\subset G_m^2$. SO $X$ is $\Bbb{P}^1$ minus $3$ points. How is this? I understand that $(G_m)^2$ is a torus in two variables. I suppose $V(f)$ ...
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### Is there some notation and name for this norm?

Given a field $K$ with an absolute value (you may imagine $\mathbb{R},\mathbb{C}$ or a $p$-adic field), I wonder if there is some notation and name (like $\|\|_\infty$ for the infinite [or supremum, ...
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### “No cone of this fan contains a nonzero linear space”

On page 393 of this paper, Speyer and Sturmfels produce a quotient of a particular geometric object (which happens to be a polyhedral fan), and claim that, as in the question title, "no cone in this ...
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### Riemann-Hurwitz formula generalization in higher dimension

In "Basic algebraic geometry 2", Shafarevich finds a relation between the Euler characteristic and the genus of the curve. At page 139 he says that there's no analogue for varieties of dimension \$>...
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### Subjects or recent progress in Tropical geometry or similar suitable for undergraduate investigation

I'm worried this might not be fitting for this forum, but it's basically a literature and reference request. I'm looking to do a project in algebra where we are supposed to research some topic (...
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### Hodge Bundles on Tropical Spaces

I am not sure that this question even makes sense, which I suppose is part of the questions itself. In any case, I attended a talk recently wherin there was some discussion about a "tropical ...
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### How Max plus algebra is different from conventional algebra?

Here I have some basic questions about max-plus algebra. How this is useful? Why we need to define a different algebra? What aspects are highlighted in this which were untouched in conventional ...