# Finding linear dependencies in integration-by-parts equations: A Monte Carlo approach

## Description

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) 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... Title of program: ICE - the IBP Chooser of Equations Catalogue Id: AESF_v1_0 Nature of problem Find linear dependencies in a system of linear equations with multivariate polynomial coefficients. To be used on Integration-By-Parts identities before running Laporta's Algorithm. Versions of this program held in the CPC repository in Mendeley Data AESF_v1_0; ICE - the IBP Chooser of Equations; 10.1016/j.cpc.2014.01.017