Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Sum of Squares Decompositions of Polynomials over their Gradient Ideals
  with Rational Coefficients
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat