Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A new family of ideals with the doubly exponential ideal membership
  property
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th