Re: Comparisons and decorations

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

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