Expand, factor... as a way to solve, simplify?

Jay Belanger wrote:
> 
> Daniel Lemire <lemire@ondelette.com> writes:
> 
> >Daniel:
> > If the only support the computer is providing me is a set of
> > functions to modify expression manually (do this, do that), then it
> > is of no use. (Mind you, that's not what Maxima does, but that's
> > what you seem to be arguing it should do.)
> 
> "You" who?
> 
> > For simple problems, I will do it faster with pen and paper.
> 
> Pencil and paper is good.
> 

Computer algebra systems can do rote calculations quite accurately,
even if they would require large amounts of paper, pencil, and time,
if done the traditional way. If all you have are toy problems,
and especially if your input/output overhead like slow typing 
is considerable, then pencil and paper may be best.

But the real problem is that you expect computers to know
what is in your mind, and/or to follow instructions that are
vague or non-existent, as pointed out by Jay.

> Anyhow, from the subject and the following excerpt (I didn't find the
> parent article)
> 
> > > I'm not saying that you should use expand, factor, etc. at random;
> > > it may be necessary to examine the problem carefully before you
> > > attack it with computer algebra - to map out where you're going.
> 
> it looks like you want Maxima to do some simplification.
> The problem is that "simplify" is very vague, and which of two
> expressions is simpler depends very much on what needs to be done with
> it.  So if you want Maxima to simplify an expression, Maxima needs to
> know what you mean by "simplify".  So there are a lot of choices
> (expand, factor, etc.).
> If you are talking about using Maxima to solve an equation, then I
> agree that Maxima should decide what simplification is necessary and
> do the solving.  Do you have an example of something you want Maxima
> to solve that it won't?
> 
> > The truth, it seems, is that Maxima cannot solve
> >
> > exp(a * x) = C * exp(b * x)

In fact, most computer algebra systems solve a*x+b=0 for x=-b/a
when a more correct answer is  x=-b/a if a is not zero.

RJF