Re: Re-submission of motion 5: multiple-format arithmetic.

[Dominique Lohez <dominique.lohez@xxxxxxx>]

Ralph Baker Kearfott a écrit :
> Arnold Neumaier wrote:
> > Nate Hayes schrieb:
> > > John Pryce wrote:
> .
> .
> .
> > > > I believe nothing in this motion and rationale hinders the
> > > > implementation of various forms of non-standard intervals -- Kahan,
> > > > modal, etc. -- as discussed at the end of Vienna/1.2.
> > >
> > > I've mentioned before this is simply not true. If traps or flags are 
> > > only
> > > way to obtain NaI result from an interval operation such as 
> > > 1/[-2,3], this
> > > is hinderance to efficient modal interval implementations.
> >
> > This is another eason why modal intervals should not be part of
> > the standard. It makes the latter unnecessarily complicated,
> > only to introduce an error-prone technique that can be safely handled
> > only by a tiny minority of users.
> >
> > Not deciding this issue (modal or not) very soon will constitute a
> > major quarrel in each issue to be decided.
>
> Does someone wish to formulate and formally put forward a
> simple motion to decide whether or not the standard should
> explicitly contain specifications for modal arithmetic?
>
> Baker
My opinion is that a decision in favor or against the inclusion of a 
explicit mention of modal intervals should be delayed
 until the following points are elucidated

            1) The motion 3 states that
                                    - the intended number set is R and 
not R*
                                     - the intervals are the connected  
closed subset of R
                    However no method was given to handle  calculation 
with infinite bound intervals.
                     IMHO searching for such methods would provide a  
natural way to introduce modal intervals simply as a feature of the the 
mathematical required background.
                     This could obviate the otherwise meaningful 
argument of  Arnold Neumaier.
                      I intended to propose a position in two weeks. 
                      However , owing to the evolution of the the 
discussion , I feel the need to send this summary of my position.


          2)From a mathematical point going from uncountable sets of 
numbers and  intervals to finite such sets is a dramatic change.
              This change should be   carefully studied before detailed 
considerations of    some specific  computer representations.
              Further arguments in favor of  modal intervals might  
arise from this study.

Dominique LOHEZ

--
Dr Dominique LOHEZ
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