Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connectivity in Semi-Algebraic Sets I   A semi-algebraic set is a subset of the real space defined by polynomial
equations and inequalities having real coefficients and is a union of finitely
many maximally connected components. We consider the problem of deciding
whether two given points in a semi-algebraic set are connected; that is,
whether the two points lie in the same connected component. In particular, we
consider the semi-algebraic set defined by f <> 0 where f is a given polynomial
with integer coefficients. The motivation comes from the observation that many
important or non-trivial problems in science and engineering can be often
reduced to that of connectivity. Due to its importance, there has been intense
research effort on the problem. We will describe a symbolic-numeric method
based on gradient ascent. The method will be described in two papers. The first
paper (the present one) will describe the symbolic part and the forthcoming
second paper will describe the numeric part. In the present paper, we give
proofs of correctness and termination for the symbolic part and illustrate the
efficacy of the method using several non-trivial examples.

26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex