AZURITE: An algebraic geometry based package for finding bases of loop integrals

作者：Georgoudis Alessandro; Larsen Kasper J; Zhang Yang^*

来源：Computer Physics Communications, 2017, 221: 203-215.

DOI：10.1016/j.cpc.2017.08.013

• Feynman diagrams
• Computational algebraic geometry
• Integration-by-parts identities

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 ZURich-bred method for finding master InTEgrals), 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.
Program summary
Program Title: AZURITE
Licensing provisions: GNU General Public License (GPL)
Programming language: Wolfram MATHEMATICA version 10.0 or higher
Supplementary material: A manual in the form of a MATHEMATICA notebook
Nature of problem: Determination o

• 出版日期2017-12