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.

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  1. Frellesvig, Hjalte; Gasparotto, Federico; Laporta, Stefano; Mandal, Manoj K.; Mastrolia, Pierpaolo; Mattiazzi, Luca; Mizera, Sebastian: Decomposition of Feynman integrals by multivariate intersection numbers (2021)
  2. Heinrich, Gudrun: Collider physics at the precision frontier (2021)
  3. Bendle, Dominik; Böhm, Janko; Decker, Wolfram; Georgoudis, Alessandro; Pfreundt, Franz-Josef; Rahn, Mirko; Wasser, Pascal; Zhang, Yang: Integration-by-parts reductions of Feynman integrals using singular and GPI-space (2020)
  4. Capatti, Zeno; Hirschi, Valentin; Kermanschah, Dario; Pelloni, Andrea; Ruijl, Ben: Numerical loop-tree duality: contour deformation and subtraction (2020)
  5. Caron-Huot, Simon; Chicherin, Dmitry; Henn, Johannes; Zhang, Yang; Zoia, Simone: Multi-Regge limit of the two-loop five-point amplitudes in (\mathcalN= 4) super Yang-Mills and (\mathcalN= 8) supergravity (2020)
  6. Martijn Hidding: DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions (2020) arXiv
  7. Smirnov, A. V.; Smirnov, V. A.: How to choose master integrals (2020)
  8. Abreu, Samuel; Dixon, Lance J.; Herrmann, Enrico; Page, Ben; Zeng, Mao: The two-loop five-point amplitude in $ \mathcalN=8$ supergravity (2019)
  9. Abreu, Samuel; Page, Ben; Zeng, Mao: Differential equations from unitarity cuts: nonplanar hexa-box integrals (2019)
  10. Ahmed, Taushif; Dhani, Prasanna K.: Two-loop doubly massive four-point amplitude involving a half-BPS and Konishi operator (2019)
  11. Artz, Johannes; Harlander, Robert V.; Lange, Fabian; Neumann, Tobias; Prausa, Mario: Results and techniques for higher order calculations within the gradient-flow formalism (2019)
  12. Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu; Peraro, Tiziano: Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case (2019)
  13. Bern, Zvi; Cheung, Clifford; Roiban, Radu; Shen, Chia-Hsien; Solon, Mikhail P.; Zeng, Mao: Black hole binary dynamics from the double copy and effective theory (2019)
  14. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  15. De Laurentis, Giuseppe; Maître, Daniel: Extracting analytical one-loop amplitudes from numerical evaluations (2019)
  16. Frellesvig, Hjalte; Gasparotto, Federico; Laporta, Stefano; Mandal, Manoj K.; Mastrolia, Pierpaolo; Mattiazzi, Luca; Mizera, Sebastian: Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019)
  17. Hidding, Martijn; Moriello, Francesco: All orders structure and efficient computation of linearly reducible elliptic Feynman integrals (2019)
  18. Mastrolia, Pierpaolo; Mizera, Sebastian: Feynman integrals and intersection theory (2019)
  19. Böhm, Janko; Georgoudis, Alessandro; Larsen, Kasper J.; Schönemann, Hans; Zhang, Yang: Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections (2018)