Sigh,
> -----Original Message-----
> From: Rogers, Raymond [mailto:raymond-rogers at idexx.com]
> Sent: Thursday, May 04, 2006 3:55 PM
> To: maxima at math.utexas.edu
> Subject: RE: [Maxima] Re: Interval Arithmetic project
> isolation of part calculations; but consider (my case)
> int((x+a)/(x+b)),x=[c,d]) , you can't determine the answer by straight
> forward interval analysis since the maximum could be at an
> intermediate
> value of v (say x=-b), and "interval analysis" is really
> endpoint analysis.
>
As usual I coughed up the wrong example, that one is forbidden.
But still
int((x+a)/(x+b)),x=[c,d])
Still has the problem that the solution is not unique as a,b vary.
If a is very large, and b is small (and x>-b) the answer is something like
[( xmax+a)/(xmax+b),(xmin+a)/(xmin+b)]
Whereas is a is small and b is large:
[( xmin+a)/(xmin+b),(xmax+a)/(xmax+b)]
This can be untangled but endpoint analysis will not do in more complicated
cases.
OTOH: there are a lot cases where it does work.
Ray