Kira-A Feynman integral reduction program

In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals appearing in quantum field theoretic calculations to a set of master integrals. We extend existing approaches by using an additional algorithm based on modular arithmetic to remove linearly dependent equations from the system of equations arising from integration-by-parts and Lorentz identities. Furthermore, the algebraic manipulations required in the back substitution are optimized. We describe in detail the implementation as well as the usage of the program. In addition, we show benchmarks for concrete examples and compare the performance to Reduze 2 and FIRE 5. In our benchmarks we find that Kira is highly competitive with these existing tools. Program summary Program title: Kira Program Files doi : http://dx. doi .org/10.17632/v3cmsnfrnn.1 Licensing provisions: GPLv3 Programming language: C++ External routines/libraries used: Fermat [1], gateToFermat [2], GiNaC [3,4], yaml-cpp [5], zlib [6] and SQLite3 [7] Nature of problem: The reduction of Feynman integrals to master integrals leads in general to a system of equations which contains redundant, i.e. linearly dependent, equations. In particular, for multi-scale problems, the algebraic manipulation of these redundant equations can lead to a substantial increase in runtime and memory consumption without affecting the results. Solution method: The program identifies linearly dependent relations based on modular arithmetic with the help of an algorithm presented in Ref. [8]. Afterwards the program brings a linearly independent system of equations in a triangular form. Furthermore, the algebraic manipulations required in the back substitution are optimized. Restrictions: the CPU time and the available RAM References: [1] R. H. Lewis, Computer Algebra System Fermat, https://home.bway.net/lewis/. [2] M. Tentioukov, gateToFermat, http://science.sander.su/FLink.htm. [3] C. W. Bauer, A. Frink, and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comput. 33 (2000) 1, arXiv:cs/0004015 [cs-sc]. [4] J. Vollinga, GiNaC: Symbolic computation with C++, Nucl. Instrum. Meth. A559 (2006) 282-284, arXiv: hep-ph/0510057 [hep-ph]. [5] YAML, YAML Aint Markup Language, http://yaml.org . [6] J.-L. Gailly and M. Adler, ZLIB, http://zlib.net . [7] SQLite, SQLite3, version: 3.14.2, https://www.sqlite.org . [8] P. Kant, Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach, Comput. Phys. Commun. 185 (2014) 1473-1476, arXiv:1309.7287 [hep-ph]. (C) 2018 Elsevier B.V. All rights reserved.