I am not familiar with maxima or mathematica, but I often use maple.
I have been always dreaming for a full integration of CAS into Lyx, but
I always thought that it could be really difficult and it requires lot
of effort. However, it could be easy to add some basic functionality.
First of all, maple functionality seems different from the other CAS, at
least it seems that only eval, simplify evalm and factor are supported.
Moreover, it is not possible to write down an expression in math like
\[integrate(x/(1+x^3)+1,x)\]
as shown at the document provided by Liviu, it does not work for maple.
I think that in order to provide a wider support to CAS one way could be
to enter in the math boxes something like ERT, but know it could be
called, EMT, Evil Math Text. Perhaps some tools preferences can
establish the CAS selected by the user and the math menu will be reduced
to something to Use CAS. The idea is try to be as closer as possible to
the CAS system language. As the language of every CAS differ from the
other and the set of commands and expression could be really big I think
that this is the way to go.
However, there are other implications. For instance, in maple you can
type something like the following and it works
L:=sigma*x:
M:=sigma*x:
N:=L+mu*N;
eq1:=diff(N,x);
At lyx level, I think that something have to be done in order to assign
variables which are going to be used after, perhaps by defining the
operator := as EMT, but lyx should pass every equation to maple to get
the correct answer.
That is to show two basic problems. From my point of view what is
lacking is to define a requirement of what users and developers would
like to happen with this feature. Moreover, perhaps the first thing is
try to know who is willing to work in this feature or at least support
by providing testing, requirements, developer expertise etc.
Best regards
Oscar
