Treating undefined values

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Nate Hayes wrote in ''The current proposal'':

> > No. 1/0 is not defined, hence it does not contribute to the range.
> > It is like sqrt([-1,4]) returning [0,2] and not a complex interval.
> >
> > This behavior is highly desirable in the applications
>
> I think sqrt([-1,4])=[NaN,NaN] is more desireable. In our application 
> codes and software, if we are interested only in the natural domain of 
> the function, then we explicitly intersect the interval argument with 
> the desired domain, e.g.:
>
>    sqrt([-1,4]&[0,Inf])=[0,2].

But you'll have to do it _always_.

Otherwise you get NaN even in a harmless case such as
   sqrt(1-x+x^2) for x=[0,2],
where the negative numbers are due to overestimation.


Arnold Neumaier