Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sweeping Algebraic Curves for Singular Solutions   Many problems give rise to polynomial systems. These systems often have
several parameters and we are interested to study how the solutions vary when
we change the values for the parameters. Using predictor-corrector methods we
track the solution paths. A point along a solution path is critical when the
Jacobian matrix is rank deficient. The simplest case of quadratic turning
points is well understood, but these methods no longer work for general types
of singularities. In order not to miss any singular solutions along a path we
propose to monitor the determinant of the Jacobian matrix. We examine the
operation range of deflation and relate the effectiveness of deflation to the
winding number. Computational experiments on systems coming from different
application fields are presented.

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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin