Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical primary decomposition   Consider an ideal $I \subset R = \bC[x_1,...,x_n]$ defining a complex affine
variety $X \subset \bC^n$. We describe the components associated to $I$ by
means of {\em numerical primary decomposition} (NPD).
  The method is based on the construction of {\em deflation ideal} $I^{(d)}$
that defines the {\em deflated variety} $\dXd$ in a complex space of higher
dimension. For every embedded component there exists $d$ and an isolated
component $\dYd$ of $\dId$ projecting onto $Y$. In turn, $\dYd$ can be
discovered by existing methods for prime decomposition, in particular, the {\em
numerical irreducible decomposition}, applied to $\dXd$.
  The concept of NPD gives a full description of the scheme $\Spec(R/I)$ by
representing each component with a {\em witness set}. We propose an algorithm
to produce a collection of witness sets that contains a NPD and that can be
used to solve the {\em ideal membership problem} for $I$.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga