Automatic Integral Reduction for Higher Order Perturbative Calculations. We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of intermediate expressions relatively small throughout the calculation. The program requires modest input information from the user and can be used for generic calculations in perturbation theory.

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  1. Heinrich, Gudrun: Collider physics at the precision frontier (2021)
  2. Capatti, Zeno; Hirschi, Valentin; Kermanschah, Dario; Pelloni, Andrea; Ruijl, Ben: Numerical loop-tree duality: contour deformation and subtraction (2020)
  3. Smirnov, A. V.; Smirnov, V. A.: How to choose master integrals (2020)
  4. Abreu, Samuel; Page, Ben; Zeng, Mao: Differential equations from unitarity cuts: nonplanar hexa-box integrals (2019)
  5. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  6. Boels, Rutger H.; Huber, Tobias; Yang, Gang: The Sudakov form factor at four loops in maximal super Yang-Mills theory (2018)
  7. 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)
  8. Herzog, Franz; Ruijl, Ben: The (R^\ast)-operation for Feynman graphs with generic numerators (2017)
  9. Meyer, Christoph: Transforming differential equations of multi-loop Feynman integrals into canonical form (2017)
  10. Boels, Rutger H.; Kniehl, Bernd A.; Yang, Gang: Master integrals for the four-loop Sudakov form factor (2016)
  11. Ahmed, Taushif; Gehrmann, Thomas; Mathews, Prakash; Rana, Narayan; Ravindran, V.: Pseudo-scalar form factors at three loops in QCD (2015)
  12. Georgoudis, Alessandro; Zhang, Yang: Two-loop integral reduction from elliptic and hyperelliptic curves (2015)
  13. Ruijl, B.; Ueda, T.; Vermaseren, J. A. M.: The diamond rule for multi-loop Feynman diagrams (2015)
  14. Smirnov, A. V.: FIRE5: a C++ implementation of Feynman integral REduction (2015)
  15. Tancredi, Lorenzo: Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations (2015)
  16. Caron-Huot, Simon; Henn, Johannes M.: Iterative structure of finite loop integrals (2014)
  17. Kant, Philipp: Finding linear dependencies in integration-by-parts equations: a Monte Carlo approach (2014)
  18. Henn, Johannes M.; Smirnov, Alexander V.; Smirnov, Vladimir A.: Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation (2013)
  19. Smirnov, A. V.; Smirnov, V. A.: FIRE4, LiteRed and accompanying tools to solve integration by parts relations (2013)
  20. Anastasiou, Charalampos; Herzog, Franz; Lazopoulos, Achilleas: The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD (2012)

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