On 2/13/07, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> On 13 Feb 2007 07:00:02 -0000, Scott Ballantyne <sdb at ssr.com> wrote:
> > Experimenting with maxima for the first time, I tried to compute the
> > derivative of (%e^x-%e^(-x))/(%e^x+%e^(-x)), which I believe should
> > be: 4/(e^x+e^-x)^2.
> >
> > Maxima gives 1 - (e^x-e^(-x))^2/(e^x+e^(-x))^2
> As previous writers have mentioned, there are *many* correct forms.
True enough. Maxima implements some small subset of the set of
all possible simplification heuristics. Which is fine, but Maxima is
not very strong in this respect. Maxima's weaknesses are that the set
of built-in heuristics is limited and difficult to extend.
> Here are a few, in increasing order of length. Pick your favorite.
>
> sech(x)^2
> 1/cosh(x)^2
> 1-tanh(x)^2
> 2/(cosh(2*x)+1)
> {4/(%e^x+%e^-x)^2
It seems within the realm of possiiblity to use a mix-n-match approach
as shown by the moreforms function to attempt to automatically find
a "good" equivalent expression (for various kinds of "good").
Robert