Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Description of polygonal regions by polynomials of bounded degree   We show that every (possibly unbounded) convex polygon $P$ in $R^2$ with $m$
edges can be represented by inequalities $p_1 \ge 0,...,p_n \ge 0,$ where the
$p_i$'s are products of at most $k$ affine functions each vanishing on an edge
of $P$ and $n=n(m,k)$ satisfies $s(m,k) \le n(m,k) \le (1+\epsilon_m) s(m,k)$
with $s(m,k):=\max \{m/k,\log_2 m\}$ and $\epsilon_m \to 0$ as $m \to \infty$.
This choice of $n$ is asymptotically best possible. An analogous result on
representing the interior of $P$ in the form $p_1 > 0,..., p_n > 0$ is also
given. For $k \le m/\log_2 m$ these statements remain valid for representations
with arbitrary polynomials of degree not exceeding $k$.

26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess