Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Billiard algebra, integrable line congruences, and double reflection
  nets
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph