Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polar Varieties and Efficient Real Elimination   Let $S_0$ be a smooth and compact real variety given by a reduced regular
sequence of polynomials $f_1, ..., f_p$. This paper is devoted to the
algorithmic problem of finding {\em efficiently} a representative point for
each connected component of $S_0$ . For this purpose we exhibit explicit
polynomial equations that describe the generic polar varieties of $S_0$. This
leads to a procedure which solves our algorithmic problem in time that is
polynomial in the (extrinsic) description length of the input equations $f_1,
>..., f_p$ and in a suitably introduced, intrinsic geometric parameter, called
the {\em degree} of the real interpretation of the given equation system $f_1,
>..., f_p$.

1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph