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 Azurite (A ZUR ich-bred method for finding master I nTE 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 Singular and Mathematica. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts. In some cases, the basis obtained by Azurite may be slightly overcomplete.