Azurite: An algebraic geometry based package for finding bases of loop integrals. For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. We introduce the package {sc Azurite} ({f A ZUR}ich-bred method for finding master {f I}n{f TE}grals), which efficiently finds a basis of this vector space. It constructs the needed integration-by-parts (IBP) identities on a set of generalized-unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems {sc Singular} and {sc Mathematica}. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts.

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  1. 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)
  2. Abreu, Samuel; Dixon, Lance J.; Herrmann, Enrico; Page, Ben; Zeng, Mao: The two-loop five-point amplitude in $ \mathcalN=8$ supergravity (2019)
  3. Abreu, Samuel; Page, Ben; Zeng, Mao: Differential equations from unitarity cuts: nonplanar hexa-box integrals (2019)
  4. Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu; Peraro, Tiziano: Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case (2019)
  5. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  6. 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)
  7. Mastrolia, Pierpaolo; Mizera, Sebastian: Feynman integrals and intersection theory (2019)
  8. Boels, Rutger H.; Luo, Hui: A minimal approach to the scattering of physical massless bosons (2018)
  9. 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)
  10. Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.; Papathanasiou, Georgios: The double pentaladder integral to all orders (2018)
  11. Bern, Zvi; Enciso, Michael; Parra-Martinez, Julio; Zeng, Mao: Manifesting enhanced cancellations in supergravity: integrands versus integrals (2017)
  12. Bosma, Jorrit; Sogaard, Mads; Zhang, Yang: Maximal cuts in arbitrary dimension (2017)
  13. Frellesvig, Hjalte; Papadopoulos, Costas G.: Cuts of Feynman integrals in Baikov representation (2017)
  14. Gituliar, Oleksandr; Magerya, Vitaly: Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form (2017)
  15. Kalmykov, Mikhail Yu.; Kniehl, Bernd A.: Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation (2017)
  16. Zeng, Mao: Differential equations on unitarity cut surfaces (2017)
  17. Alessandro Georgoudis, Kasper J. Larsen, Yang Zhang: Azurite: An algebraic geometry based package for finding bases of loop integrals (2016) arXiv