Besides being faster and more compact than version 3.0, Mathematica 4.0 has a great range of useful new features. It’s the best program I’ve seen in ten years of reviewing technical software.
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Anyone who has used Mathematica 3.0 may find it hard to believe, but Wolfram Research actually found a few important improvements to make in version 4.0. With its beefed-up numeric operations and print and Web output, Mathematica 4.0 reaches beyond its roots as a symbolic-computation program – it’s now an all-purpose tool kit for any task relating to technical information. Mathematica’s number-crunching abilities – particularly with respect to large arrays of numbers – have improved steadily over the years, but in version 4.0, they’re revolutionized. A standard Power Mac G3, running the new version outperforms older SGI RISC workstations, when processing huge data arrays, and when running signal-processing applications. Specifically, the rewritten matrix operations store large and sparse arrays more efficiently, the code for the Fourier-transform routines has been optimized, and the program now reads HDF files at impressive speeds. The MathWorks’ MATLAB, is no longer being developed for the Mac. But, in tests using a ten-item matrix-math test suite, Mathematica 4.0 – on a 266MHz Power Mac G3 – beat MATLAB 5.2 – on a 300MHz Pentium II system – by an average factor of 4.3. And, because Mathematica’s automatic translators can convert MATLAB M-files to Mathematica notebooks, developers of custom matrix-processing applications should be able to make the switch easily. Symbolic advances In the realm of advanced development aids, Wolfram has further refined Mathematica’s rules for simplifying symbolic expressions, and has added to the special-function list some math functions that previously defied useful computer definition. For science and maths development, Mathematica no longer has any direct competitors on the Mac – or, for that matter, on PCs and Unix systems. Mathematica 3.0 simplified the task of producing journal-quality printed output. It introduced features for using standard textbook-style notation, rather than the computer-code output style used by most other maths programs – including earlier versions of Mathematica. In version 4.0, the word-processing features are so solid that you could easily make Mathematica your primary technical word processor. Not only are its editing features and style sheets more useful for technical work than those in Microsoft Word, but printing as TeX and the newer LaTeX 2e files is also faultless. Equally impressive are Mathematica 4.0’s Web facilities. Notebooks, saved as HTML, generate files of HTML source code and folders of GIFs for artwork; notebooks can also contain hyperlinks to other notebooks or to URLs. The program displays any kind of maths notation beautifully on the Web, and version 4.0 can work with Web-sound and -graphics files.