Hi!
> What I want is a reasonable comparison of the two systems in terms of
> capabilities, efficiency, ease of use, etc. I do not want to start a flame
> war nor I am not looking for "X simply is better." I need facts to
> determine if Axiom is worth the learning curve.
I did something like that a few years back when the university of
vienna was discussing which CAS to promote. Probably other people
on this list can refine these points:
Maxima is what is called a CAS of the 2nd generation. (As are
Mma, Maple and most other popular CAS). OTOH in the same terminology
Axiom is a CAS of the 3rd generation. The main difference being
the introduction of mathematical types for expressions: In Maxima
there is just one (core) simplifier that produces roughly one
canonical form of expressions but can be adjusted by a zillion flags.
In Axiom there are many types of expressions, each one having its
own canonical form and thus (in some sense) its own simplifier.
(Probably employing polymorphism and similar "modern" concepts
of computer science.)
>From the point of view of somebody implementing a CAS, Axiom is
great. Actually several former developers of Maxima joined Axiom
after it was released as free software.
But this hierarchical system of mathematical types also adds a lot
of complexity and requires lots of knowledge (probably being a
few years into studying math) to actually fully understand.
We wanted something that we could recommend to students in their
first year, so Axiom finally wasn't really an option. Also people
coming from an engineering context probably will like Maxima
better. If you are in an environment where everbody else uses
Mma, then Maxima is the obvious free alternative.
If your interest is mainly research on symbolic computation then
Axiom likely provides you lots of useful infrastructure, that
Maxima will never have by design.
<sarcasm>
In my experience the question somewhat boils down to: You want to
develop a CAS or you actually want to use it?
</sarcasm>
As you note the communities of both systems are so completely split,
that they don't even compare with each other. There is some tragedy
in this as both probably could learn a lot from each other.
HTH,
Harald