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Re: Comparisons and decorations, part 2

Dan Zuras Intervals wrote:

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.


	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?


Then not even addition is simple anymore:
   Empty+[0,inf]=[Inf,NaN]

I still believe that the representation of Empty by [NaN,NaN]
is by far the least cumbersome.


Arnold Neumaier