We review the enveloping algebra of the 10-dimensional chiral sigma matrice
s. To facilitate the computation of the product of several chiral sigma mat
rices we have developed a symbolic program. Using this program one can redu
ce the multiplication of the sigma matrices down to linear combinations of
irreducible elements. We are able to quickly derive several identities that
are not restricted to traces. A copy of the program written in the Mathema
tica language is provided for the community. (C) 2001 Elsevier Science B.V.
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