If you’ve never heard of Mathematica, skip to the next review with a clear conscience — Mathematica’s dominance in the science and engineermg market is so absolute that nearly anyone who’d have a use for it would have heard of it. Mathematica has long been the premier symbolic package for mathematicians and theoretical physicists. It is famous for its high-quality, three-dimensional graphics, its ability to handle arbitrary-precision arithmetic, its symbolic-processing abilities, and its enormous, dictionary-size hardback manual. With Mathematica 4.0, Wolfram has once again improved the product by adding a few long-sought features (along with a few more pages in the manual).
Two new features will immediately win praise from longtime users. One of the oldest complaints about Mathematica has been its inability to use information about the domains of variables in simplifying algebraic expressions. It used to leave expressions like Sin[(2n+1) Pi] and Sqrt[x^2] unsimplified, because there was no way to tell Mathematica that n was an integer and x was positive. All this has changed with Mathematica 4.0 — the Simplify command now takes a second argument in which one can specify the domains of variables. On the numerical side, Mathematica 4.0 dramatically reduces the space required for large arrays and significantly improves the speed of array operations.
Some aspects of Mathematica are a bit disappointing. Perhaps the biggest shortcoming is the lack of a version for either Linux PPC or Mac OS X Server, which effectively relegates Mac users to client status in many settings. Although Mathematica’s unusual structure — in which the front end and the kernel (the part of Mathematica that actually does the work) are separate programs — is often quite useful, the interface between the kernel and the front end is still fairly sluggish; this makes the package feel much slower than it ought to.
Still, these objections are quibbles. Mathematica 4.0 is an outstanding package unequaled on both the Mac and Wintel platforms. Following the tremendously discouraging withdrawal of the Mac version of MathWorks’ Matlab, it’s good to see that Wolfram is dedicated to supporting the Mac and improving Mathematica.
Sammis, Ian. (December 1999). Mathematica 4.0. MacAddict. (pg. 79).