On Tue, Apr 22, 2008 at 10:38 AM, Richard Fateman <fateman at cs.berkeley.edu>
wrote:
> why is it an error to try to find a divergent sum? If a sum is positive
> and
> unbounded, wouldn't it be inf?
> if a sum is positive and unbounded, why not return inf?
>
> I tried Mathematica 6.0, and it gives error messages, but I don't see why
> that is a good idea, if you can actually compute with symbols like inf.
> (which, arguably, we can't :) )
> <http://www.math.utexas.edu/mailman/listinfo/maxima>;
>
The major reason for any subsystem in any software system to signal an error
rather than returning a special value is that other systems cannot handle
the special value or error condition usefully or cleanly. This is the case
with Maxima. As you put it, we *can't* actually compute usefully with
symbols like inf. (I think this is indisputable for the current state of
Maxima, not "arguable"!)
Returning a value of UND, INF, or MINF is fine if there is a human user
there to interpret it. However, returning it in the middle of a computation
is bound to lead to incorrect results given the current simplifier, e.g.
sum(i^2,i,1,inf)-sum(i,i,1,inf),simpsum => 0
-s