Intelligent result checking before asking positive/negative/zero...?

--- Richard Fateman  wrote:

> edA-qa mort-ora-y wrote:
> 
> > Is there anyway to tell Maxima to try all possibilities and give
> > all answers rather than asking questions such as "is x positive
> > negative or zero?"?
>
> There is no simple way to do this.
> You can try to anticipate all such questions and use "assume" to
> try all combinations, in turn.

In general wouldn't this be a bad idea?  What about something where
there might be a "solvable" problem given a positive x, and an
"unsolvable" (at least to Maxima) problem in the negative case -
wouldn't there be a danger of Maxima "churning" for a while and not
providing the result it can provide?  Presumably it would have to try
each case in turn, and there might be some problems where the best
thing to do is avoid the "bad" cases in order to save time.  (I'm
reminded of an integral I needed a solution for for a homework problem
in grad school once - people were trying to solve the bugger in Maple,
and it was taking lots and lots of steps.  I stuck it in Maxima, it
asked me one assume question, and immediately provided exactly the
desired answer :-).

I agree it's annoying when you answer the question both ways and the
answer is the same.  Somebody correct me if I'm wrong, but isn't that
inevitable simply because, in general, Maxima can't "know" that will
happen until it tries it?

> I agree that it would be nice, but this requires some level of
> introspection that is generally difficult to put into a program 
> like Maxima. Some specific examples could probably be handled by 
> (say) better integration programs.

I'm definitely not up on this - is there some kind of heuristic that
could be applied to allow Maxima to say "well, this looks like it is
solvable for all cases of x, so I'll try all of them?"  What about
(say) real vs. complex, or the even more complicated questions one can
ask in higher level math?  (I don't even know - is Maxima able to make
decisions to ask questions based on real vs. complex assumptions?)

CY 



		
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