Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The degree of $\text{SO}(n)$   We provide a closed formula for the degree of $\text{SO}(n)$ over an
algebraically closed field of characteristic zero. In addition, we describe
symbolic and numerical techniques which can also be used to compute the degree
of $\text{SO}(n)$ for small values of $n$. As an application of our results, we
give a formula for the number of critical points of a low-rank semidefinite
programming optimization problem. Finally, we provide some evidence for a
conjecture regarding the real locus of $\text{SO}(n)$.

14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio