Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear estimates for solutions of quadratic equations in free groups   We prove that in a free group the length of the value of each variable in a
minimal solution of a standard quadratic equation is bounded by $2s$ for
orientable equation and by $12s^4$ for non-orientable equation, where $s$ is
the sum of the lengths of the coefficients

32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con