Here's Alec Mihailovs' answer to a student trying to decide whether to buy Maple or Mathematica. This is followed by postings by Thomas Roelz and Carl Devore who both have something positive to say about Mathematica.

Subject: Re: Maple or Mathematica
Date:  Fri, 05 Jul 2002 07:50:23 GMT
From:  "Alec Mihailovs" <alec@mihailovs.com>
Newsgroup:  sci.math.symbolic

In brief, Maple represents The Force, and Mathematica is often referred to as The Dark Force.

Maple uses the standard mathematics notation, such as sin(x) or sqrt(x). Mathematica uses square brackets instead and capital letters, Sin[x] and Sqrt[x].

To execute a command in Maple, one clicks Enter. To execute a command in Mathematica, one clicks Shift+Enter.

The Maple newsgroup, comp.soft-sys.math.maple, is unmoderated. The Mathematica newsgroup, comp.soft-sys.math.mathematica is moderated and censored (any posting telling that there are other CAS systems better than Mathematica, is censored, in particular).

Maple has better symbolic and numerical capabilities, see http://lie.uwaterloo.ca/odetools/comparison.html for ODE.

Mathematica has a better marketing department. More people are working there than in their research division. Also, people selling Mathematica are paid better than people developing it.

Both of them, Maple and Mathematica, are very buggy, much more buggy than even Linux and Microsoft together, and much more than one can expect from a modern CAS system.

Both of them have very poor customer support. However, the Maple Users Group and the Maple newsgroup mentioned above, provide excellent help and support from thousands of people using Maple. Comparing the amount of messages in the Maple newsgroup and in the Mathematica newsgroup, one can tell that Mathematica users have much more trouble than Maple users. From my personal experience, Maple is much more user friendly. People having any previous programming experience, won't have any trouble with Maple. Mathematica, for some historical reasons, uses rather odd programming language, different from any others, so previous programming experience is not only not helpful, but will also interfere with Mathematica's programming paradigm.

If you are going to buy a student version, then the most important question is what system is in use in your school. If both systems are used, check which is used in the classes you are going to take. What's the point to have the better system, Maple, if your lecturer is using Mathematica?

Best wishes,
Alec Mihailovs
http://webpages.shepherd.edu/amihailo/


Here's a followup to the above posting by Thomas Roelz:

Subject: Re: Maple or Mathematica
Date: Fri, 05 Jul 2002 14:02:54 +0200
From: Thomas Roelz <tom@suse.de>
Organization: SuSE GmbH, Nuernberg
Newsgroup: sci.math.symbolic

Alec Mihailovs" <alec@mihailovs.com> already provided a good summary of both systems. However I would like to add some notes knowing Maple better than Mathematica. The following comments relate to Mathematica 4.1 and Maple 7.

Programming language
====================
Alec stated that Mathematica has an odd programming language. That may be true in the sense that there is a bit of learning expense in the beginning since it may imply "exotic" paradigms like pattern matching (which can turn out to be a benefit in certain situations).

The structure of the Maple language OTOH is easy to understand if you already have some programming experience (purely procedural).

But...

The Maple language is inconsistent due to the fact that it has evolved for a long time. Different order of parameters in similar functions are ugly. The spelling of command names is not consistent, e.g. with/without intermediate capital letters etc.

Mathematica syntax has been "designed" to be consistent which makes it very elegant and efficient.

==> This may be relevant if you want to get deeper into programming.
 

Graphics
========
The quality of graphics that can be produced with Mathematica are outstanding and slightly superior to Maple but the handling of graphics in the notebooks is very bad. Once a graphic has been displayed you can't do anything with it. If you want to change some of the very many options (viewpoint, lighting, coloring etc.) you have to re-evaluate it again and again. This is _very_ cumbersome if you want to "play around" with it (what you almost always will do).

Maple graphics OTOH are "live" (OpenGL). One click with the mouse and you can spin them around (3D) in full display which is _very_ convenient for exploring purposes. A context menu reachable via the right mouse
button lets you adjust the most important options and any change there is put into practice almost instantly.

==> As you said that graphics are important that may also be relevant.

Nevertheless
============
As Alec already pointed out the environment you will find at school is most important. Aside from the facts mentioned above this should be the key criterion.

And another followup by Carl Devore who is a leading Maple expert:

Subject:  Re: Maple or Mathematica
Date: Wed, 10 Jul 2002 14:24:24 -0400
From:  Carl Devore <devore@math.udel.edu>
Organization: University of Delaware
Newsgroups:  sci.math.symbolic, 100digits@yahoogroups.com

One can "do" functional programming in Maple also, so one's preference for functional programming should not be used to decide between the two.

In a recent international numerical analysis / programming competition (sponsored by SIAM and written by Professor Lloyd Nick Trefethen) in which teams including Professor Robert Israel, me, and 18 other teams received a perfect score, several of the teams have published their solutions.  (See http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/hundred.html).  At least two of the perfect entrants easily obtained all the answers with Mathematica, sometimes with a single command.  (See http://www.stanwagon.com and http://mathworld.wolfram.com/news/2002--5-25_challenge).  By contrast, I had a great struggle getting some of the answers from Maple.  For example, some numerical integrals needed to be broken into several pieces and each piece transformed in a different way, whereas Mathematica seems to figure all that out by itself.  Problems 1, 4, 5, and 9 have remarkably simple solutions in Mathematica that cannot be duplicated in Maple (without major low-level programming).  None of the problems has a remarkably simple solution in Maple (that I am aware of) which cannot be duplicated by Mathematica.

I think that Mathematica is the true winner of SIAM's and Trefethen's  contest, despite the fact that Professor Trefethen is a renown expert with  Matlab.

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