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Manuscript Title: Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach
Authors: Philipp Kant
Program title: ICE - the IBP Chooser of Equations
Catalogue identifier: AESF_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 185(2014)1473
Programming language: Haskell.
Computer: Any system that hosts the Haskell Platform.
Operating system: GNU/Linux, Windows, OS/X.
Keywords: Multiloop Calculation, Laporta Algorithm, Integration-By-Parts.
PACS: 12.38.Bx.
Classification: 4.4, 4.8, 5, 11.1.

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.

Solution method:
Map the system to a finite field and solve there, keeping track of the required equations.

Typically less than the restrictions imposed by the requirement of being able to process the output with Laporta's Algorithm.

Unusual features:
Complexity increases only very mildly with the number of kinematic invariants.

Running time:
Depends on the individual problem. Fractions of a second to a few minutes have been observed in tests.