Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ring of conditions for affine space   The exponential sum (ES) is a linear combination of characters of an additive
group $\mathbb C^n$. The exponential analytic set (EAS) is a set of common
zeroes of a finite tuple of ESs. We consider ES and EAS as an analogs of
Laurent polynomial and of algebraic variety in complex torus
$(\mathbb{C}\setminus0)^n$. Respectively we construct the ring of conditions
for $\mathbb C^n$ as an analog of the ring of conditions for
$(\mathbb{C}\setminus0)^n$. The construction of this ring is based on the
definition of associated to EAS algebraic subvariety of some multidimensional
torus and on the applying tropical algebraic geometry to this subvariety. Just
as in the case of a torus, the ring of conditions is generated by
hypersurfaces. This preprint is an extended summary of the article proposed to
"Izvestiya: Mathematics".

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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex