Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic Nullstellensatz and Nonstandard Methods   In this study we find height bounds for polynomial rings over integral
domains. We apply nonstandard methods and hence our constants will be
ineffective. Then we find height bounds in the polynomial ring over algebraic
numbers to test primality of an ideal. Furthermore we consider unique
factorization domains and possible bounds for valuation rings and arithmetical
functions.

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The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg