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P1788, Dan On 14 Oct 2009, at 22:06, Dan Zuras Intervals wrote:
I started out intending to just answer John's questions & make a few comments. I ended up writing a rather long argument for a particular form of an interval xx^yy. ... John Pryce had written(***) Or, horrors, do you actually want to use the definition -exp (y*log(|x|) for ALL x<0 and all y??
I had forgotten that both values -exp(y*log(|x|) and +exp(y*log(|x|) are taken at points sprinkled densely in the relevant (x,y) region, as Dan pointed out.
So, I agree 100% with Dan's analysis, and description of a possible all-singing-all-dancing power function. But on reflection I don't think the "negative x to a rational power" aspect is of benefit to any interval application I can envisage. I think the Vienna proposal 3.12 has it exactly right with its two functions
The binary operation pow, where a pow b is defined for nonnegative a and real b, provided that b is positive when a is zero must be complemented by a binary operation intpow, where a intpow p is defined for real a and integer p, provided that p is nonnegative when a is zero.
That is what I expect to vote for. John