FIRE5: A C++ implementation of Feynman Integral REduction

Abstract In this paper the C++ version of FIRE is presented — a powerful program performing Feynman integral reduction to master integrals. All previous versions used only Wolfram Mathematica , the current version mostly uses Wolfram Mathematica as a front-end. However, the most complicated part, the reduction itself can now be done by C++ , which significantly improves the performance and allows one to reduce Feynman integrals in previously impossible situations. Program summary Program title: FIRE5 Catalogue identifier: AEPW_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPW_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 681856 No. of bytes in distributed program, including test data, etc.: 40047357 Distribution format: tar.gz 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 vectorized or parallelized?: Yes RAM: Depends on the complexity of the problem 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 the 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 previous 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=128×256−3=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.