Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Solvability of a Lie algebra of vector fields implies their
  integrability by quadratures
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio