Problem #5

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Abstract
I wish to express a few informal doubts about the effectiveness of a problem which I have previously proposed [1] here as a benchmark exercise for symbolic computing systems. In brief, that problem concerned the generation of functions Y 2n to provide successive approximations to the solutions[EQUATION]of the equation[EQUATION]where[EQUATION]I suggested the use of a recurrence in Y 2n obtained by direct substitution of (1) and (3) into (2). This recurrence contained rational-number coefficients, and one term was quadrilinear in the Y functions. However, Yngve Sundblad (KTH, Stockholm) has demonstrated to me that execution times in this computation can be reduced greatly (in SYMBAL on a CDC 6600) merely if the recurrence is rewritten to remove the numerical denominators, while there is at least one method of finding a recurrence for Y 2n , known to the Uppsala group which has made the most extensive studies [2] of (2), that contains only bilinear terms. No doubt that method must require much less time (and space!) to compute. Thus we should agree on a common algorithm before we can compare benchmark runs directly.

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