Finding linear dependencies in integration-by-parts 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 multi-loop 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
- E-Print:
- 8 pages, 1 figure. Added references. Some minor additions
