Re: MidRad -- and Two Different Application Domains (TDAD).

[John Pryce <j.d.pryce@xxxxxxxxxxxx>]

P1788

On 17 Sep 2009, at 11:59, Arnold Neumaier wrote:
> Michel Hack wrote:
> > It should be noted that the discussions about different ways to deal
> > with domain violations (ignore or flag/NaI), and hence the entire
> > topic of decorated intervals, are applicable only to the second  
> > domain....
> > A large part of past discussions may have suffered from arguments  
> > that
> > had only ONE of the two domains in mind, triggering disagreement from
> > those who had the OTHER domain in mind!
>
> This is why I recommend not to consider standardizing midrad  
> operations,
> but only their conversion to and from infsup intervals.
>
> We save a lot of work, and do not incur a penalty for it -- midrad  
> use does not become any harder than it is now.

I entirely agree. Paul Zimmermann: your reply to me today suggests  
there is a symmetry between (finite precision) infsup and midrad. But  
it seems to me this is emphatically _not_ the case, either in their  
theoretical properties or in the applications to which they are most  
suited.

Standardising midrad has difficulties not present with infsup (non- 
uniqueness of finite precision interval hull, lack of representation  
for semi-infinite intervals); partly as a result, midrad has less  
wide application than infsup. So if P1788 worked on midrad, it would  
get less bang for the buck. Let's stick to the limited midrad aspect  
that Arnold suggests.

John