PROGRAM SUMMARY
Title of program:
SigmaVector10D.m
Catalogue identifier:
ADNT
Ref. in CPC:
136(2001)173
Distribution format: gzip file
Number of lines in distributed program, including test data, etc:
569
Keywords:
Supersymmetry, Sigma matrices, 10 dimensions, Mathematica,
General purpose, Algebras.
Programming language used: Mathematica
Computer:
DEC Alpha 133 MHz .
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.
Method of solution:
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.
Restrictions:
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.
Typical 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.