Kira swMATH ID: 34816 Software Authors: Maierhöfer, P.; Usovitsch, J.; Uwer, P. Description: Kira - A Feynman integral reduction program. n 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. Homepage: https://arxiv.org/abs/1705.05610 Source Code: https://gitlab.com/kira-pyred/kira Related Software: FIRE; Reduze; LiteRed; FIRE5; Azurite; pySecDec; GiNaC; Fuchsia; FIESTA; FireFly; epsilon; FORM; PolyLogTools; CANONICA; Mathematica; DiffExp; MultivariateApart; SecDec; AIR; FeynArts Cited in: 47 Documents all top 5 Cited by 125 Authors 4 Mastrolia, Pierpaolo 4 Weinzierl, Stefan 3 Abreu, Samuel 3 Caron-Huot, Simon 3 Frellesvig, Hjalte 3 Mandal, Manoj Kumar 3 Mizera, Sebastian 3 Page, Ben 3 Tancredi, Lorenzo 3 Zeng, Mao 3 Zhang, Yang 2 Baranowski, Daniel 2 Böhm, Janko 2 Czakon, Michał 2 Gasparotto, Federico 2 Georgoudis, Alessandro 2 Hidding, Martijn 2 Lange, Fabian 2 Laporta, Stefano 2 Long, Ming-Ming 2 Mattiazzi, Luca 2 Melnikov, Kirill 2 Panzer, Erik 2 Pokraka, Andrzej 1 Ahmed, Taushif 1 Artz, Johannes 1 Badger, Simon D. 1 Behring, Arnd 1 Belitsky, Andrei V. 1 Bendle, Dominik 1 Bern, Zvi 1 Bitoun, Thomas 1 Bogner, Christian 1 Bonciani, Roberto 1 Bonetti, Marco 1 Brønnum-Hansen, Christian 1 Brüser, Robin 1 Buccioni, Federico 1 Capatti, Zeno 1 Chaubey, Ekta 1 Chen, Jiaqi 1 Cheung, Clifford 1 Chicherin, Dmitry 1 Davies, Joshua 1 Davydychev, Andrei I. 1 De Laurentis, Giuseppe 1 Decker, Wolfram 1 Delto, Maximilian 1 Dhani, Prasanna K. 1 Dixon, Lance J. 1 Duhr, Claude 1 Eschment, Felix 1 Feng, Bo 1 Fieker, Claus 1 Han, Liang 1 Harlander, Robert V. 1 Hartanto, Heribertus Bayu 1 Heinrich, Gudrun 1 Henn, Johannes M. 1 Herrmann, Enrico 1 Hirschi, Valentin 1 Hönemann, Ina 1 Huber, Tobias 1 Ita, Harald 1 Jakobsen, Gustav Uhre 1 Jiang, Xuhang 1 Jiang, Yi 1 Kermanschah, Dario 1 Klappert, Jonas 1 Klausen, René Pascal 1 Klemm, Albrecht 1 Larsen, Kasper J. 1 Li, Tingfei 1 Li, Zhe 1 Ma, Chichuan 1 Ma, Wen-Gan 1 Ma, Yan-Qing 1 Maierhöfer, Philipp 1 Maître, Daniel 1 Mishima, Go 1 Mogull, Gustav 1 Moriello, Francesco 1 Müller, Hildegard 1 Nega, Christoph 1 Neumann, Tobias 1 Patil, Raj 1 Pelloni, Andrea 1 Peraro, Tiziano 1 Pfreundt, Franz-Josef 1 Piclum, Jan H. 1 Plefka, Jan Christoph 1 Pögel, Sebastian 1 Prausa, Mario 1 Rahn, Mirko 1 Rana, Narayan 1 Roiban, Radu 1 Ruijl, Ben 1 Sapeta, Sebastian 1 Sauer, Benjamin 1 Schellenberger, Tom ...and 25 more Authors all top 5 Cited in 6 Serials 38 Journal of High Energy Physics 4 Computer Physics Communications 2 Nuclear Physics. B 1 Letters in Mathematical Physics 1 Physics Reports 1 Unitext for Physics all top 5 Cited in 12 Fields 44 Quantum theory (81-XX) 4 Mechanics of particles and systems (70-XX) 4 Relativity and gravitational theory (83-XX) 3 Numerical analysis (65-XX) 2 Computer science (68-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year