Azurite swMATH ID: 20252 Software Authors: Alessandro Georgoudis, Kasper J. Larsen, Yang Zhang Description: 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. Homepage: https://arxiv.org/abs/1612.04252 Related Software: Reduze; LiteRed; FIRE; Fuchsia; Kira; FIRE5; epsilon; CutTools; SINGULAR; DiffExp; AIR; Fermat; pySecDec; GitHub; FiniteFlow; Axodraw; JaxoDraw; Mathematica; RationalizeRoots; HyperInt Cited in: 23 Publications all top 5 Cited by 59 Authors 5 Zhang, Yang 4 Zeng, Mao 3 Abreu, Samuel 3 Georgoudis, Alessandro 3 Page, Ben 2 Böhm, Janko 2 Chen, Jiaqi 2 Dixon, Lance J. 2 Frellesvig, Hjalte 2 Jiang, Xuhang 2 Larsen, Kasper J. 2 Mastrolia, Pierpaolo 2 Mizera, Sebastian 2 Xu, Xiaofeng 2 Yang, Li Lin 1 Badger, Simon D. 1 Bendle, Dominik 1 Bern, Zvi 1 Bitoun, Thomas 1 Boels, Rutger H. 1 Bogner, Christian 1 Bosma, Jorrit 1 Brønnum-Hansen, Christian 1 Caron-Huot, Simon 1 Decker, Wolfram 1 Dlapa, Christoph 1 Enciso, Michael 1 Gasparotto, Federico 1 Gituliar, Oleksandr 1 Hartanto, Heribertus Bayu 1 Heinrich, Gudrun 1 Herrmann, Enrico 1 Ita, Harald 1 Kalmykov, Mikhail Yu. 1 Klausen, René Pascal 1 Kniehl, Bernd A. 1 Laporta, Stefano 1 Li, Xiaodi 1 Luo, Hui 1 Ma, Chichuan 1 Magerya, Vitaly 1 Maierhöfer, P. 1 Mandal, Manoj K. 1 Mattiazzi, Luca 1 McLeod, Andrew J. 1 Panzer, Erik 1 Papadopoulos, Costas G. 1 Papathanasiou, Georgios 1 Parra-Martinez, Julio 1 Peraro, Tiziano 1 Pfreundt, Franz-Josef 1 Rahn, Mirko 1 Schönemann, Hans 1 Søgaard, Mads 1 Tschernow, Wladimir 1 Usovitsch, J. 1 Uwer, Peter 1 von Hippel, Matt 1 Wasser, Pascal Cited in 5 Serials 17 Journal of High Energy Physics 3 Computer Physics Communications 1 Letters in Mathematical Physics 1 Physics Letters. B 1 Physics Reports all top 5 Cited in 9 Fields 23 Quantum theory (81-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Operator theory (47-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year