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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.

Restrictions:
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.