FIRE6: Feynman Integral REduction with modular arithmeticстатья

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[1] Smirnov A. V., Chukharev F. S. Fire6: Feynman integral reduction with modular arithmetic // Computer Physics Communications. — 2019. — P. 106877. FIRE is a program performing reduction of Feynman integrals to master integrals. The C++ version of FIRE was presented in 2014. There have been multiple changes and upgrades since then including the possibility to use multiple computers for one reduction task and to perform reduction with modular arithmetic. The goal of this paper is to present the current version of FIRE. Program summary Program title: FIRE, version 6 (FIRE6) Program files doi: Licensing provisions: GPLv2 Programming language: Wolfram Mathematica 6.0 or higher, C++ Supplementary material: The article, install instructions, External routines/libraries used: Wolfram Mathematica [1], Snappy [2], ZStandard [3], KyotoCabinet [4], Fermat [5], LiteRed [6] 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. In complex cases the direct reduction approach might fail, so the approach with modular arithmetic is used, where the reduction is performed multiple times with different values of variables over large prime number fields, afterwards the coefficients are reconstructed. The data preparation and result analysis are performed in Wolfram Mathematica [1], but the main reduction procedure is written in C++; FIRE compresses data with the use of the Snappy [2] or ZStandard [3] library, stores it on disk with the use of the KyotoCabinet [4] database engine, and performs algebraic simplifications with the Fermat [5] program. The external package LiteRed [6] can be used to produce additional rules for reduction. 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 = 22, 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). FIRE6 follows the C++11 standard, so requires gcc 4.8.1 or higher to be compiled, but works with the current gcc 7.3 as well. References: [1], commercial algebraic software; [2], open source; [3], open source; [4], open source; [5], free–ware with some restrictions for organizations; [6] lee/programs/LiteRed/, open source. [ DOI ]

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