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A large number of calculations in high-energy elementary particle physics involve the manipulation of complicated algebraic expressions containing both tensor and noncommutative matrix quantities. Many of these calculations take several months to complete, although the operations involved follow straightforward rules. In this paper program is described, which has been developed in LISP far solving such problems. The manner in which these problems are encountered is outlined, and their representation in the computer discussed. At present, about six months of human work takes less than Fifteen minutes on an IBM 7090. Limitations of the present system and future plans are also outlined. [ABSTRACT FROM AUTHOR]