Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random points on an algebraic manifold   Consider the set of solutions to a system of polynomial equations in many
variables. An algebraic manifold is an open submanifold of such a set. We
introduce a new method for computing integrals and sampling from distributions
on algebraic manifolds. This method is based on intersecting with random linear
spaces. It produces i.i.d. samples, works in the presence of multiple connected
components, and is simple to implement. We present applications to
computational statistical physics and topological data analysis.

11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex