# Tagged Questions

For questions related to tropical geometry.

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### Software Plotting Tropical Curves

I'm an undergrad student and currently working on my paper focusing on Tropical Math. Can anyone suggest for any software that could plot tropical curves easily? Help please!
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### The standard tropical lines - Pointwise valuation

Let $K$ be an algebraically closed field with valuation, and its value group $\Gamma_\text{val}^n$ is dense in $\mathbb{R}$. Consider the polynomial $f(x,y)=x+y+1.$ It can easy by shown that the ...
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### The Variety X(K) as a subset of the analytification of X

I am working with Sam Payne's artical Analytification is the limit of all tropicalizations, and because of my limited understanding of analytification it gives me some difficulties. The article: ...
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### Tropicalization of a line in the projective plane P^2

Lets assume that our field $K$ is the Puiseux series. I have been working with tropicalization from the book "Introduction to tropical geometry" link : https://homepages.warwick.ac.uk/staff/D....
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Assume a unidirectional, unweighted network generated according to a degree distribution. Each node is given a value between 0 and 1 called threshold $\phi$. We topple some nodes, the neighbours will ...
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### Non-convex subdivisions of newton polygon of a tropical plane curve

This is probably an elementary question, but how come the Newton polygon of a tropical plane curve can't have non-convex subdivisions? Or can it?
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### Weighted and Generic vector

I am writing a project about tropicalization of toric varieties and in my work I come up with 2 expressions I do not know the meaning of. A weighted vector This is an example of where it is used. ...
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### Convex Hull given set of planes.

If I have some finite amount of planes, for example $$z_1=2x, \\ z_2=2y, \\ z_3=3+x+y, \\ z_4= 2+x, \\ z_5=2+y \\ z_6 =3$$ And I wish to find the convex hull in order to ...
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### Zeros of a Tropical polynomial

Consider the Tropical semiring $(\mathbb{R}\cup\{-\infty\},\max,+)$. We define $x$ as a zero of a tropical polynomial $f(x)$ if $f$ attains its maximum twice at point $x$ in its linear parts. Why is ...
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### Minimal equations defining a linear subspace (or: how I forgot linear algebra).

I have a question that may be trivial, but I just can't find the answer in the internet (nor in my head). Given a linear vector subspace of dimension $d$ and given its Plücker coordinates I can ...
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### Motivation for the study of amoebas.

What was the primary motivation for the study of the amoebas?
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### Tropical versus max-plus

Is the max-plus algebra an example of tropical mathematics or is it an independent structure? How can we turn a max-plus algebra into tropical geometry or viceversa-if possible?
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### What is the link of the origin of a polyhedral fan?

I am trying to understand the article http://arxiv.org/abs/0804.3651 by David Helm and Eric Katz. There the link of the origin of a polyhedral fan is mentioned. I googled and only found definitions ...
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### Transition functions of toric projective bundle (Proposition in [Cox, Toric Varieties])

My reference: David Cox's "Toric Varieties" My question is the proof of Proposition 7.3.3. Proposition 7.3.3. The cones {$\sigma_i$ | $\sigma \in \Sigma$, $i = 0,\dots,r$} and their faces form ...
The Structure Theorem of Tropical geometry states that "Let $X$ be an irreducible $d$-dimensional subvariety of $\mathbb T^n$ . Then $\operatorname{trop}(X)$ is the support of a balanced weighted \$Γ_{...