Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Evaluation of Tensor Feynman Integrals in Euclidean Kinematics   For the investigation of higher order Feynman integrals, potentially with
tensor structure, it is highly desirable to have numerical methods and
automated tools for dedicated, but sufficiently 'simple' numerical approaches.
We elaborate two algorithms for this purpose which may be applied in the
Euclidean kinematical region and in d=4-2*epsilon dimensions. One method uses
Mellin-Barnes representations for the Feynman parameter representation of
multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica
package AMBRE has been extended for that purpose, and together with the
packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may
perform automatically a numerical evaluation of planar tensor Feynman
integrals. Alternatively, one may apply sector decomposition to planar and
non-planar multi-loop epsilon-expanded Feynman integrals with arbitrary tensor
rank. We automatized the preparations of Feynman integrals for an immediate
application of the package sector_decomposition (C. Bogner and S. Weinzierl) so
that one has to give only a proper definition of propagators and numerators.
The efficiency of the two implementations, based on Mellin-Barnes
representations and sector decompositions, is compared. The computational
packages are publicly available.

13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin