Mathematica Broadens Appeal

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Its been said that anyone who doesnt already know about Mathematica may safely ignore news about its updates, since “nearly anyone whod have a use for it would have heard of it” (in the words of MacAddict reviewer Ian Sammis). Theres a grain of truth in that comment, but still we beg to differ. This springs 4.2 update of Wolf- ram Research Inc.s marquee product will appeal to a much broader audience than the researchers and the rocket-scientist types who have long been the companys core market.

Mathematica 4.2 augments extensive mathematical, symbolic processing and graphical facilities with increased convenience in XML-based data exchange with other enterprise systems. It offers assistance to operations staff with improved optimization tools and can take its results directly to an audience with expanded technical publishing and slide-show capabilities.

Available on Windows, Mac OS (including OS X) and Linux (PC and PPC) at a single-seat price of $1,880, Mathematica is a leading example of supercomputer power for single-user systems. Notably rivaled by Waterloo Maple Inc.s Maple 8 (also released in the spring) and by The MathWorks Inc.s Matlab 6.1 (released last month), Mathematica is the only one supporting the Macintosh at all with a current version and the only one shipping for Mac OS X—no small advantage in the academic and graphical communities that still have important Macintosh contingents.

We found the Mac OS X implementation consistent with the Windows version, and the combination of processor-intensive workload and cross-platform availability makes Mathematica (like Adobe Systems Inc.s Photoshop) useful ammunition in the ever-popular sport of processor wars. After adjusting for clock-speed differences, we found the same operations running 10 to 30 percent more quickly (on a per-cycle basis) on a G4-equipped Titanium PowerBook than on a Pentium III-equipped Windows 2000 laptop.

The Mathematica environment provides an interactive calculator of essentially unlimited precision, with an enormous vocabulary of specialized functions. An interactive session is transcribed in a “notebook” document, arranged in a series of cells or hierarchical groups of cells that can be used to organize and selectively display the progress of a calculation or to package and present the results of a larger study in a platform-neutral format.

Not Just Pretty

Not Just Pretty

Beyond its vast number-crunching powers, Mathematica offers symbolic calculation facilities (for problems such as “Solve x^2—3x + 2 = 0 for all possible values of x”) and sophisticated visualization tools. Mathematicas graphics become more than decorative when the problem is one of visualizing—for example, the fit and motion of a complex mechanism (see screen).

Its remarkably simple to use Mathematica to generate a series of graphics representing successive snapshots of a changing situation, to collapse those into a single notebook cell and to show the result as an animated view with convenient on-screen controls.

We have to give at least a respectful nod to Maple 8, with its substantial redesign of its own user interface—especially its new interactive plot builder, which many will prefer to Mathematicas interface of command-line plus point-and-click palettes.

In enterprise applications, however, Mathematicas approach lends itself at least as well to documenting and reproducing previous analyses, and anyone evaluating this type of product should think about long-range ease of use as well as immediate ease of learning and experimentation. Mathematicas notebook interface takes some learning before it becomes second nature, but its top-to-bottom consistency and its interaction with programmable output facilities offer a return on that invested effort.

The XML Leader

The XML Leader

Both Mathematica and Maple acknowledge the growing importance of XML as a framework for data exchange, with Mathematica currently looking to us like the leader in providing built-in functions for more than simple data import and export. For example, Mathematica includes facilities for exchanging its structured notebook documents, or generically formatted mathematical expressions, with other XML producers and consumers.

By contrast, even the Matlab Web site describes The MathWorks product as providing only “limited” XML support at this time, with only simple parsing and Java Document Object Model manipulations. We should note, though, that all three of these products benefit from large libraries of user-written contributed code, and prospective users should consider such resources when making their decision.

In manufacturing, retail and other operations-intensive domains, Mathematica 4.2 can make its users look good with its more robust abilities to find true optimal solutions without getting trapped in what turns out to be only a local optimum. Fitting a nonlinear function to a set of data points, Mathematica 4.2 was able to optimize the elements of a function to find a much better description of the behavior than was possible with earlier versions. That doesnt always provide a foundation for a more accurate forecast of future behavior, since the better fit may only be describing a particular episode of transient or random effects, but at least it offers the hope of identifying cyclical or trend components that were previously unrecognized.

When Mathematica gets better, as we have said when examining earlier versions, the worlds work gets easier. For example, Version 4.2s improved performance in factoring large integers could make it easier to break some previously robust encryption algorithms. Perhaps thats not an example that makes anyone want to cheer, but it illustrates the increasingly strategic role of advanced mathematical tools and techniques in industry and commerce as well as in the “black” worlds of defense and counterintelligence. Enterprise users who are familiar only with spreadsheets or with traditional statistical packages would do well to consider products such as Mathematica, Maple and Matlab as potential additions to their tool kits.

Technology Editor Peter Coffee can be reached at [email protected].

Executive Summary

: Mathematica 4.2″>

Executive Summary: Mathematica 4.2

Mathematica 4.2 continues the trend of past releases by augmenting its computational, symbolic-math and graphical tools with additional facilities useful to enterprise operations and technical publishing professionals. Its elegant, consistent notebook format and palette-enhanced, command-line interface make the product easy to customize and extend but in some ways harder to learn than competing products such as Waterloos Maple 8 or The MathWorks Matlab.

COST ANALYSIS

Far more expensive than spreadsheets or many packaged statistical software suites, Mathematica and other high-end tool kits must be justified in terms of the staff hours they can save or the breakthroughs they may enable—with consequences that go straight to the bottom line. Few organizations will deploy it to more than a few high-end strategists, making its price per seat a relatively minor issue.

(+) Reduces need to combine Mathematica with other tools for presentation and statistical analysis; makes surprisingly large improvements in core computational functions, while also staying abreast of enterprisewide developments such as growing reliance on XML; offers current version in consistent environments on Windows and Mac OS, unlike competing products.

(-) A law unto itself in notation and user interface design: rigorously consistent and generally well-designed but a bottom-up learning task for new users.

EVALUATION SHORT LIST

• Waterloos Maple 8
• The MathWorks Matlab 6.1
• www.wolfram.com