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Re: The current proposal

Siegfried M. Rump schrieb:
On Mon, 23 Feb 2009 16:22:11 -0100, Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> wrote: 


(1') X = F(isup(A)) returns for all continuous F an inclusion
of lim_{x->A.sup} F(x).

 (2') B = convexHull(iinf(A),isup(A)) always returns B=A

 even though interval(inf) = Empty, so that your original
constructions don't work correctly.



This slipped me, it looks like a good alternative. It may
take some time but users may get used to it. Definitely better
than

   convexHull(number2interval(A.inf),number2interval(A.sup))



 But writing (1') and (2') is much nicer anyway, and also avoids
nasty issues for cases when the bound representation and the
float representation differ,


I don't understand this, I thought bounds are always fl-pt
numbers (including Infinity).


Well, the Vienna Proposal currently allows for different kind of floats,
and one kind of interval bounds.

Also, it was phrased in such a way that should some design choices
change, the rest needs minimal adaptation. Thus suppose we allow midrad
representations of intervals. Then <m=1,r=1e-100> is a valid interval, but there are no floats representing inf and sup exactly. 
(But I strongly recommend against the midrad representation as
datatype with its own artithmetic operations; it would cause
difficult problems in many places.)


Arnold Neumaier