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*To*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Subject*: Re: implementation categories, exact rationals*From*: "John.Cowan" <jcowan@xxxxxxxxxxxxxxxxx>*Date*: Fri, 14 Oct 2005 16:16:15 -0400*Cc*: srfi-77@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-77@xxxxxxxxxxxxxxxxx*In-reply-to*: <20051014193848.EEB2D1B77BD@xxxxxxxxxxxxxxxxxxxxx>*References*: <20051014181146.599D01B77BB@xxxxxxxxxxxxxxxxxxxxx> <20051014192646.GB152@NYCMJCOWA2> <20051014193848.EEB2D1B77BD@xxxxxxxxxxxxxxxxxxxxx>*User-agent*: Mutt/1.4.2.1i

Aubrey Jaffer scripsit: > | > A case could be made if (expt -26. 1/3) returned -2.9624960684073702; > | > but I know of no Scheme implementation that does so. > | > | Why would that be desirable? > > Because it is the cube root of -26. A better example is: > (expt -27 1/3) ==> -3 -3 is *a* cube root of 27, but not the *principal* cube root. Consider the third part of Quux's Tripartite Acceptance Test: 1) the value of T is T (or in Scheme, of #t is #t) 2) the value of (/ (factorial 1000) (factorial 999)) is 1000 (given the usual iterative definition of factorial) 3) the value of (atanh -2) is a complex number (if it is the right complex number, approximately -0.54930615+1.5707964i, so much the better) -- Andrew Watt on Microsoft: John Cowan Never in the field of human computing jcowan@xxxxxxxxxxxxxxxxx has so much been paid by so many http://www.ccil.org/~cowan to so few! (pace Winston Churchill) http://www.reutershealth.com

**References**:**implementation categories, exact rationals***From:*Aubrey Jaffer

**Re: implementation categories, exact rationals***From:*John.Cowan

**Re: implementation categories, exact rationals***From:*Aubrey Jaffer

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