Computer Physics Communications Program Library

Programs in Physics & Physical Chemistry

PROGRAM SUMMARY

Manuscript Title: The Canon package: a fast kernel for tensor manipulators.
Authors: L.R.U. Manssur, R. Portugal
Program title: Canon
Catalogue identifier: ADSP
Journal reference: Comput. Phys. Commun. 157(2004)173
Programming language: Maple.
Computer: Any m/c running Maple versions 6 to 9.
Operating system: Windows, Linux.
RAM: 3M words
Keywords: Tensor calculus, Maple, Computational group theory, Computer algebra.
Classification: 5.
Nature of problem: Manipulation and simplification of tensor expressions (or any expression in terms of indexed objects) in explicit index notation, where the indices obey generic permutation symmetries and there may exist dummy (summed over) indices.
Solution method: Computational Group Theory algorithms have been used, specially algorithms for finding canonical representations of single and double cosets, and algorithms for creating strong generating sets.
Restrictions: Computer memory. With current equipment, expressions with hundreds of indices have been manipulated successfully.
Unusual features: The use of Computational Group Theory algorithms allows the package to manipulate objects with a few hundreds of indices.
Running time: Simplification of expressions with 15 Riemann tensors was done in less than 1 minute on a personal computer.