Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Inside factorial monoids and the cale monoid of a single Diophantine
  equation
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom