Product Reviews

In celebration of Wolfram Research's 20th birthday, Mathematica 6 is billed as 'the most important advance in the 20-year history of Mathematica', with hyperbolic terms such as 'revolution' and 'reinvented' peppering its exhaustive list of functions and features.

Although Mathematica's core language and notebook structure lend themselves to development and evaluation in stepwise fashion, in recognition of the increasingly complex programs that are being developed, version 6 introduces a simple debugger. Some of the strongest claims surround another addition termed a 'symbolic dynamic interface', and heralded as defining 'a major new paradigm for computing'.

If you define x = 2 and then evaluate x^2, you'll get the result of x squared - that is, 4. Further down your notebook, set x = 4, and the previous output of x squared remains 4 in true static style. Now declare x as dynamic using Dynamic[x], and the value returned will reflect the current value of x. Change x from 4 to 2, and the earlier evaluation of Dynamic[x] is immediately recomputed as 2. Unlike a conventional programming language, though, you need to invoke the Dynamic[] wrapper wherever you want output to be updated: enter x^2 and you will get the same static result as ever - you have to evaluate Dynamic[x^2] if you want dynamic output.

There are obvious and valuable applications of dynamics that allow you to adjust the value of variables using controls such as sliders and pop-up menus, but this paradigm is already popular if not universal in most conventional programming languages. It starts coming into its own with dynamic interactive models, which are certainly very easy to implement in Mathematica 6, but perhaps not quite as revolutionary as is claimed.

Version 6 has a long list of new and improved import and export file formats, including US Geological Survey 1û and 7.5' DEM files, QuickTime 7 movie import, and more than a dozen others. You can now directly access online data sources from a range of different

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fields (graphs, physics, chemistry, demography, economics and others) - for example, WordData["dish"] returns a list of uses and senses of the word 'dish'. This is but one practical illustration of generally enhanced Internet access in the spirit of webMathematica.

Mathematica 6 is also set to expand its appeal. Sound, including Midi, gains full support, which could entice those wishing to make music algorithmically. Computational scientists, who may not have rated Mathematica highly in their list of teaching aids, should find the new Turing Machine function a useful addition, with its excellent graphical support, although they'll still have to hand-code tools such as Universal Register Machines.

Among these hundreds of new and improved functions, some aren't yet as fully baked as they should be. For instance, PDF documents can be imported, but anything more complex than a single page with uncompressed images can readily upset Mathematica, and the dream of being able to import whole notebooks from PDF still seems some way off.

Upgrading from version 5 wasn't as seamless as it could have been, as version 6 defaults to using prior preference settings. In particular, it uses the old location for its kernel computation engine, which, of course, was that for 5.x and not 6.0. This may leave you (and Mathematica) floundering around at first, but can be rectified quickly by correcting the path in Kernel Configuration Options in the Evaluation menu. Because of a bug recently introduced to Apple's Intel 64-bit Mac OS X kernel that limits the number of files opened, Wolfram has disabled the 64-bit version of Mathematica, but still ships this with the Universal Binary application so users can enable 64-bit processing if they prefer.

Mathematica's pricing model is generous to students and committing to professionals, but sadly locks out many who could benefit from its rich and stimulating environment. The same is true for other heavyweight maths products. It's perhaps time for someone to break ranks and put such tools within the reach of all those who are numerate.

For some specialist tasks, you may still prefer to use different applications, such as Matlab for matrices or R for statistics. But for all-round symbolic and numeric maths, with galactic support for almost any theoretical or applied discipline, it's difficult to match Mathematica. Version 6 does have abundant and impressive new features; how useful they will prove will depend on how their potential will be realised over the next couple of years. For existing users, this upgrade is completely compelling.