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[Licence| Download | New Version Template] aepw_v2_0.tar.gz(39108 Kbytes)
Manuscript Title: FIRE5: a C++ implementation of Feynman Integral REduction
Authors: A.V. Smirnov
Program title: FIRE5
Catalogue identifier: AEPW_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 189(2015)182
Programming language: Wolfram Mathematica 6.0 or higher, C++.
Computer: Starting from a desktop PC.
Operating system: Linux 64bit, Mac OS X 10.6 or higher 64bit.
Has the code been vectorised or parallelized?: Yes
RAM: Depends on the complexity of the problem
Keywords: Feynman diagrams, Multiloop Feynman integrals, Dimensional regularization, Computer algebra.
PACS: 02.70.Wz, 03.70.+k, 11.10.-z.
Classification: 4.4, 4.8, 5, 20.

External routines: Wolfram Mathematica [1], Snappy [2], KyotoCabinet [3], Fermat [4], LiteRed [5].

Does the new version supersede the previous version?: Yes

Nature of problem:
Reducing Feynman integrals to master integrals can be treated as a task to solve a huge system of sparse linear equations with polynomial coefficients.

Solution method:
Since the matrix of equations is very specific, none of standard methods of solving linear equations can be applied efficiently. The program approaches solving those equations with a special version of Gauss elimination. The data preparation and result analysis is performed in Wolfram Mathematica [1], but the main reduction procedure is written in C++; FIRE compresses data with the use of the Snappy [2] library, stores it on disk with the use of the KyotoCabinet [3] database engine, and performs algebraic simplifications with the Fermat [4] program. The external package LiteRed [5] can be used to produce additional rules for reduction.

Reasons for new version:
The Mathematica version of FIRE is too slow to perform reduction where it is needed in the current state of Elementary Particle Physics. Hence the most time-consuming part of FIRE was rewritten in C++.

Summary of revisions:
FIRE5 is a major update of FIRE4 - the reduction was completely rewritten (now in C++ instead of Wolfram Mathematica), gaining a huge speed advantage. Apart from that, FIRE is made backward-compatible with the previouis versions.

The complexity of the problem is mostly restricted by CPU time required to perform the reduction of integrals and the available RAM. The program has the following limits: maximal number of indices = 21, maximal number of positive indices = 15, maximal number of non-trivial sectors = 128 x 256 - 3 = 32765 (global symmetries decrease the number of sectors, indices that cannot be positive do not double the number of sectors).

Additional comments:
Additional information may be found at http://science.sander.su.

Running time:
Depends on the complexity of the problem.

[1] http://www.wolfram.com/mathematica/, commercial algebraic software;
[2] http://code.google.com/p/snappy/, open source;
[3] http://fallabs.com/kyotocabinet/, open source;
[4] https://home.bway.net/lewis/, free-ware with some restrictions for organizations;
[5] http://www.inp.nsk.su/~lee/programs/LiteRed/, open source.