Some nifty additions make an upgrade worthwhile

While not a major upgrade for this established mathematical software, there are enough new features in Mathematica 5.1 to make the change worthwhile. With the launch of version 5.0, this package gained algorithmic efficiencies that lead to noticeable speed increments for larger and more complex computations. With this latest upgrade, the user will find significant additions to many areas of numerical and symbolic computation, as well as data handling and visualization, database access, graphical user interface (GUI) tools, and core system upgrades. The new version works on Windows, Macintosh, Unix and Linux.

It seems as if installation gets easier and faster with each upgrade, and this is no exception. The disk comes with a small ‘Getting Started’ manual that introduces some

of the general features but, basically, it is up to the user to fully explore those areas of interest. By clicking on the Welcome palette, a list of the new features can be accessed and a 10-minute tutorial taken to assist the novice in general usage.

Moving large spreadsheets into this version got easier but is still not quite where the non-programmer would like it. EXCEL files may be imported as .txt but not .xls. However, once in, the software will rapidly manipulate the rows and columns and quickly perform the most demanding calculations. Indeed, many users will be limited by the amount of memory in their computers, and not by any shortcomings in the software. Now let’s take a closer look at several features that caught my eye, and a few that I will actively use.

As many analysts quickly realize, importing data into a platform and wrestling it into shape sometimes takes more time than the actual analysis. Mathematica has added built-in Universal Database Connectivity to lighten the load. According to the developers, this “provides an industrial-strength, ready-made solution for integrating Mathematica with any standard SQL database.” This feature, called DatabaseLink, works with all major databases, including Oracle and Microsoft Access, and includes point-and-click tools for connections and querying. The graphical interface supplied goes far to make connectivity an easy task.

For the mathematical user of piecewise functions (functions with different definitions in different regions) the software now has system-wide support. Over 100 enhancements have been included for solving and automatically handling these functions, whether entered implicitly or explicitly. As these are frequently encountered in engineering problems, the addition is not trivial. I found this to be very helpful in many routine calculus problems applied to areas in biology and chemistry where piecewise is the norm.

Although not engaging in nearly as many theoretical studies as I would have liked, the new ArrayPlot was a fun way to visualize cellular automata systems generated to mimic certain biological processes. On the more applied side, the visualization of matrix data is sometimes very useful in spotting patterns in large data sets. Also, as a heavy user of multivariate statistics, I often find use for classification tools in work with biological microarrays (nucleic acid chips that are used to demonstrate genetic changes). The addition of optimized Cluster Analysis capabilities is welcome in this regard. The clustering of high-dimensional data is now quickly accomplished through a variety of different methods, which may be selected manually or automatically, and used with built-in or user-defined distance functions. Output includes both standard dot-cluster diagrams as well as dendograms, to visually display relationships. (Note to developers: the help browser badly needs optimization; it could not find the ‘Find Cluster’ function under that name. I had to query ‘Cluster Analysis/Statistics to find it!) Although some programming is needed to import/format the data, set the cluster graphics, and output the results for the nice diagrams, the effort is minimal and the code easily recycled.

The last nifty addition that I commend to your attention is the EquationTrekker, an interactive tool for differential equations. This graphical tool is useful for exploring solutions of ODEs (ordinary differential equations). It is a quick and efficient way to examine dynamical systems properties in a variety of settings. Many chemical and engineering examples are easily envisioned, and use in the life sciences may spur further experimentation in such areas as ecology, genetics and cellular physiology. By clicking on this feature in the help section, an interactive GUI is activated that allows the user to specify initial conditions for an ODE and then visualize the 2-D phase plots of the solutions. With this interface, conditions, parameters and ranges may be varied on-the-fly, and changes in the solution are immediately displayed.

Mathematica has always been a fast, powerful calculating engine, and now the mechanics have gotten even easier. With the recent release of version 5.2, this feature set is available for 64-bit procesing as well.

Availability

• Standard version: $1,880
• Upgrade from 5.0: $375

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John Wass is a statistician with GPRD Pharmacogenetics, Abbott Laboratories. He may be reached at sceditor@scimag.com.