Finding linear dependencies in integrationbyparts equations: A Monte Carlo approach
Abstract
The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multiloop calculations. It is also a major bottleneck in terms of running time and memory consumption. It involves solving a large set of linear equations where many of the equations are linearly dependent. We propose a simple algorithm that eliminates all linearly dependent equations from a given system, reducing the time and space requirements of a subsequent run of Laporta's algorithm.
 Publication:

Computer Physics Communications
 Pub Date:
 May 2014
 DOI:
 10.1016/j.cpc.2014.01.017
 arXiv:
 arXiv:1309.7287
 Bibcode:
 2014CoPhC.185.1473K
 Keywords:

 Feynman diagram reduction;
 Laporta algorithm;
 Redundancy;
 Dependent systems of linear equations;
 Monte Carlo;
 Homomorphic images;
 High Energy Physics  Phenomenology;
 Computer Science  Symbolic Computation;
 Physics  Computational Physics;
 J.2
 EPrint:
 8 pages, 1 figure. Added references. Some minor additions