Abstract
Comparing the speed of computation in algebra systems is a perennial occupation of system designers, algorithm implementors, and, more recently, marketing personnel. At least some people have observed that for many problems, the choice of a system makes much less difference than the approach used to represent the problem. The mapping from mathematics to a data representation and the choice of algorithms can make significant, and separate, contributions to efficiency. Systems which have the flexibility to provide several data structures and algorithms can provide an advantage in this respect. Macsyma [1] is probably the system with the largest selection, currently. On the other hand, Macsyma has not taken advantage of recent advances such as the extensive use of hash-coding incorporated in the University of Waterloo's Maple [2] system. For the one somewhat artificial benchmark we discuss in this paper, it appears that the Maple system does considerably better than any representation in Macsyma by precisely this mechanism.
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