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Manuscript Title: Irreducible decompositon of products of 10D chiral sigma matrices.
Authors: S.J. Gates Jr, B. Radak, V.G.J. Rodgers
Program title: SigmaVector10D.m
Catalogue identifier: ADNT_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 136(2001)173
Programming language: Mathematica.
Computer: DEC Alpha 133 MHz.
Keywords: Supersymmetry, Sigma matrices, 10 dimensions, Mathematica, General purpose, Algebras.
Classification: 4.2.

Nature of problem:
Products of 10D chiral sigma matrices are calculated and irreducible sums are produced. The program takes advantage of the identity matrices and all possible contractions of the ten-dimensional epsilon tensor with itself to produce results. Several user-implementable rules are included to reduce output and to take the dual of p-forms. The code knows the difference between commuting and non-Abelian elements.

Solution method:
The code is designed to write every product of matrices as a linear combination of the fundamental set of chiral matrices up to multiplication by the epsilon tensor and metric. It continues to reduce every product until no further reduction is possible. The program uses some builtin functions from Mathematica as well as private functions.

The number of sigma matrices products that can be processed depends on the RAM allocated by each machine. It is advised to use the builtin function ExpandAll for every product in order to get the fastest output.

Running time:
The total run time is from less than a second to minutes depending on the requested product. Tested on a DEC Alpha 133 MHz.