Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algorithm to approximate reals by rationals of the form a/b^2   The papers shows an algorithm to search for approximations of reals to
rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn