Re: Comparisons and decorations, part 2
> Date: Sun, 26 Sep 2010 12:34:34 +0200
> From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> CC: John Pryce <j.d.pryce@xxxxxxxxxxxx>, stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: Comparisons and decorations
>
> Dan Zuras Intervals wrote:
> >> Subject: Re: Comparisons and decorations
> >> From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
> >> Date: Sat, 25 Sep 2010 16:48:40 +0100
> >> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> >>
> >> Nate
> >>
> >> On 24 Sep 2010, at 11:48, Arnold Neumaier wrote:
> >>> Nate Hayes wrote:
> >>>> special cases for
> >>>> A \interior B
> >>>> such as when A and B are both Entire or A=[1,Infnity]
> >>>> and B=[0,Infinity]. In these cases, the interior operator
> >>>> would need to return a different result than when A and B
> >>>> are compact intervals, such as A=[1,100] and B=[0,200].
> >>> ??? There is a uniform formula in 754:
> >>>
> >>> [al,au] interior [bl,bu] iff ~(bl-al>=0) and ~(au-bu>=0).
> >> Looking at 754-2008 §5.3.1, I think
> >> (nextDown(al) >= bl) and (nextUp(au) <= bu)
> >> also works, since nextDown(-oo) = -oo and nextUp(+oo) = +oo.
> >>
> > interior([al,au],[bl,bu]) ==
> > ((bl < al) || (bl == -infinity)) &&
> > ((au < bu) || (bu == +infinity))
> >
>
> None of the three formulas works correctly in some cases where
> A or B or both are Empty, represented as a pair of NaN's,
> (Note that Empty is interior to every interval.)
>
> So some additional patching seems unavoidable anyway.
>
>
> Arnold Neumaier
>
Hmm.
I guess it depends on what we store in the interval
part when we are trying to represent empty.
Would [+oo,-oo] do the trick?
Dan