There are certainly few people who have a deep familiarity with both Axiom
and Maxima. Two come to mind, and I doubt they read this newsgroup.
It has seemed unusually difficult to put a "user friendly" front-end on
Axiom,
which would seem to be the solution to the two-worlds issue that Harald
notes. If such a front-end could be constructed, then all the
sloppiness of the
"2nd generation" CAS could be formalized into the language used by Axiom.
I'm not sure that the claims that have appeared from time to time, that
the Axiom system has a better implementation of integration, matters.
Even if it has a more complete version of the Risch "algorithm", that
may not add to its usefulness, and the additional hacking and heuristics
of other systems may be more important to programmers.
From a research perspective in automation of formal mathematics,
Axiom certainly occupies a "higher ground". Experiments building
upon hierarchical mathematical-category systems by others
at Berkeley, Cornell, and within some of the other systems around
(e.g. Reduce and Maple, and directly in Lisp) have not especially
swayed the practical implementations, it seems.
With the extensive documentation and free availabililty of Axiom
and Fricas, it seems that people could try to make a comprehensive
comparison of the base systems. On the other hand, it could be
that the base systems are not so important to most people and
the presence of significant libraries and examples mask their shortcomings.
I suspect that is a major reason for the popularity of Matlab, and
the introduction of (say) object-oriented this and that has not
mattered much. But perhaps others with more experience in
the Matlab world could comment. Frankly I hardly ever use it
personally. It may also explain why Maple and Mathematica
people are so keen to push application packages, thereby
overcoming issues with the base system.
RJF
On 2/27/2013 10:01 AM, harald at lefant.net wrote:
> 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
>
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