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*To*: Guy.Steele@CMU-10A, lisp-forum@MIT-MC*Subject*: Re: Multiple-valued SQRT*From*: CSVAX.fateman at Berkeley*Date*: Wed ,9 Dec 81 16:57:25 EDT

Since, in general, numeric functions which return real values do not give a completely correct answer because of numerical approximations, one could argue for interval answers. Complex answers could be in circular regions. For multiple-valued functions, sets of them... In the case of square-root, returning 2 values is not really so useful, since if we agree to return one value (say in the right half-plane), the other one is easy to compute. I suspect that at the point of use of any elementary function routine, there is however a single meaningful response. The provision of multiple-values, sets, intervals, etc.... would be overkill. Prof. Kahan here would argue however, that in the case of some functions, a "reserved object" (not-a-number) makes sense. A rather elegant proposal for computing with such things is described in the IEEE floating point arithmetic standard. As for ways of representing infinite sets, I think SETL might have something on this, and Macsyma allows a kludge like (assume(n,integer), 2*n*%i*%pi). Computing with these things is naturally a royal pain unless they are anticipated.

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