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