In the esoteric realm, Wolfram Research’s Mathematica and Waterloo Maple Software’s Maple V contend for supremacy in symbolic math. (Symbolic math, roughly, means that this software can give answers as equations and relations rather than just numbers.)
Release 3.0 of Maple V contains nearly everything a working scientist could reasonably want. First, the company recently bought Expressionist (an equation-typesetting program) and Theorist (the friendliest symbolic-math program) from California-based Prescience. The acquisition of Expressionist resulted in on-screen real-math-notation equations as a replacement for the Courier-font kludge that characterized earlier versions (the equations are exportable to LaTex). Maple’s output now compares favorably with the output from specialized graphing and math-typesetting programs. EPS and color PostScript support, both long overdue, have been added since our last review of Maple V. A minor problem is that this new output takes longer to produce than that of earlier versions of Maple V, but it’s generally worth the wait.
Also added are user-demanded features. Numeric functions can handle complex-value inputs and outputs, and minimax capabilities can be defined to work over finite ranges rather than the whole x-axis. More than a hundred new functions have been added to Maple V’s libraries, and the handling of ordinary differential equations has been improved both algorithmically and in terms of solution representation. The statistics package now includes chi-square, t, and other distributions that were missing from earlier releases. Because of Maple’s design, which uses a small kernel and libraries loaded only as needed, you can run Maple V on a 4MB PowerBook and use Microsoft Word at the same time — while the full version of Mathematica seems cramped running in 8MB of RAM.
The problem with Maple V, however, is that it hasn’t garnered the level of external support that Mathematica has. Maple has libraries of functions contributed by users, but they are not comparable in scope to Wolfram Research’s MathSource. The designers of Maple have licensed symbolic-computation capabilities into the numeric-math programs MathCAD and MatLab, but that still leaves Maple users typing in their own functions for a large assortment of common problems.
If you want access to a wider world of tutorials and preprogrammed solutions (and a bigger user group), Mathematica has a serious advantage over Maple. But if you prefer to do your own programming and function creation, you will benefit from Maple’s efficient use of your Mac’s resources, and version 3.0 hits most of the points on your symbolic-math wish list.
Seiter, Charles. (October 1994). Maple V 3.0. Macworld. (pg. 73).
Waterloo Maple Software
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Maple_V_Release_3.sit
Emulating this? It could probably run under: 
Basilisk II
