Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiring isomorphisms between rational function semifields of tropical
  curves induce isomorphisms between tropical curves   We prove that a semiring isomorphism between the rational function semifields
of two tropical curves induces an expansive map between those tropical curves.
This semiring isomorphism and the expansive map respect zeros and poles of
rational functions with their degrees. As a corollary, we show that the
automorphism group of a tropical curve is isomorphic to the
$\boldsymbol{T}$-algebra automorphism group of its rational function semifield,
where $\boldsymbol{T} := (\boldsymbol{R} \cup \{ -\infty \},
\operatorname{max}, +)$ is the tropical semifield. Finally, we describe all
semiring automorphisms of rational function semifields of all tropical curves.

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The categories of this paper are: cs
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th