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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.

Restrictions:
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.

References:
[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.