Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithms for Checking Rational Roots of $b$-functions and their
  Applications   Bernstein-Sato polynomial of a hypersurface is an important object with
numerous applications. It is known, that it is complicated to obtain it
computationally, as a number of open questions and challenges indicate. In this
paper we propose a family of algorithms called \texttt{checkRoot} for optimized
check of whether a given rational number is a root of Bernstein-Sato polynomial
and the computations of its multiplicity. This algorithms are used in the new
approach to compute the whole global or local Bernstein-Sato polynomial and
$b$-function of a holonomic ideal with respect to weights. They are applied in
numerous situations, where there is a possibility to compute an upper bound for
the polynomial. Namely, it can be achieved by means of embedded resolution, for
topologically equivalent singularities or using the formula of A'Campo and
spectral numbers. We also present approaches to the logarithmic comparison
problem and the intersection homology D-module. Several applications are
presented as well as solutions to some challenges which were intractable with
the classical methods. One of the main applications consists of computing of a
stratification of affine space with the local $b$-function being constant on
each stratum. Notably, the algorithm we propose does not employ primary
decomposition. Also we apply our results for the computation of Bernstein-Sato
polynomials for varieties. The methods from this paper have been implemented in
{\sc Singular:Plural} as libraries {\tt dmod.lib} and {\tt bfun.lib}. All the
examples from the paper have been computed with this implementation.

15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys