Machine Design

Math software solves equations, and more

Mathematica is programmable, high-end math software with a steep learning curve.

— David Gehrig


The interface combines CalcCenter 3's math, graphing, and word-processing capabilities into one "notebook" document.

Selecting Import a File pulls up the Controller associated with the ImportData function.

The Mathematica Help Browser contains extensive documentation including examples, tutorials, and explanations of functions.

For those of us with more modest calculation requirements (and pocketbooks), Mathematica Calc-Center 3, based on the same engine, provides a midrange system that is easier to use while providing plenty of calculation power. As such, the software combines mathematical capabilities beyond spreadsheets, a considerable suite of data-analysis and statistical routines, 2D and 3D graphing, and a word processor that records computations.

If you're in a hurry, Version 3 provides a brief slide-show tour on its first startup that contains just enough information for you to dive in and start poking around. This may be sufficient for users good at learning by trial and error, but I strongly recommend first going through the examples in the brief "Getting Started" guide, which comes both in hardcopy and as part of an extensive Help Browser system. Other helpful features include a redesigned interface that combines the program's math, graphing, and word-processing capabilities into one "notebook" document. This contains spread-sheetlike cells, each potentially containing a math input or output, text, graphics, or a combination of these. You can express math input using a broad subset of Mathematica's language. And if you've ever wondered about the equations in an Excel spreadsheet, which hides this information behind each cell, you will appreciate how a notebook lays out everything in the open.

The interface eases the burden for new and occasional users by providing helpful menu items and function Controllers, which guide users in plain English through calculations. Many Controllers have a "Show example" button that provides sample parameters.

Most calculations take four easy steps: (1) Pick a function, (2) click in the function's controller to bring up a calculator (controller dialog) that helps set up a problem, (3) apply inputs, and (4) get results printed in the notebook. This process gives correct answers, maybe a spiffy graph or two, and provides self-documenting records of user steps.

For example, when I import a matrix of numbers from a data file, I use the menu item Lists & Matrices > Data Import/Export > Import a File. Selecting the latter item pulls up the controller dialog associated with the ImportData function. In the document window I type "z=" and then click the "Import a known format" button. (Import formats include CSV, FITS, and USGS STDS, and Hartwell-Boeing sparse matrix.) This brings up a wizard in the notebook, which prompts users for the parameters to the ImportData command. Like all the wizards in CalcCenter, this one sticks around in case users want to try other input values. When finished with the wizard, I click its "Convert to text input" button, which transforms the wizard into an equivalent CalcCenter command and parameters.

Version 3 also provides the best of numeric and symbolic-algebra systems. These differ in that a numeric system, for example, adds 1 /3 to 1 /7 and delivers the approximate 0.866667. An algebraic system, on the other hand, delivers the exact 10 /21. And when you add x + x without first specifying its value, a symbolic algebra system responds with 2x, but a numeric one returns an error message such as #VALUE!#. Including both systems, however, lets CalcCenter perform calculations in a flash that took me three semesters of calculus and differential equations to learn (and, in too many cases, forget). The software solves systems of equations along with ordinary and partial-differential equations and analyzes data using a set of statistical functions more comprehensive than are available in Excel.

Also a programming language in Version 3 lets users define functions and build up numerical solutions. It is possible to use Excel to create complex, intricate solutions. But seeing one reminds me of an elaborate scale model of the Eiffel Tower made from toothpicks and Elmer's Glue. It may or may not be a work of genius, but it's clearly a work of tenacity. Calc-Center makes the job much easier.

Also helpful are the Error messages that point to more in-depth information in the Help Browser. As with any software, CalcCenter's responses are sometimes inscrutable so the developer has put a lot of effort into smoothing the path between error messages and resolving the problem.

Lastly, a recent application gives an idea of the software's speed. I had created a CSV (comma separated values) formatted file containing a 1,000 X 1,000 matrix of random integers between 1 and 1,000,000. Importing the CSV data into the software on a 866-MHz Powerbook took about a minute, which struck me as surprisingly long. But once the data was ready to crunch, the software calculated the inverse of the million-element matrix in less than 10 sec.

Mathematica CalcCenter 3 comes from Wolfram Research Inc., 100 Trade Center Dr., Champaign, IL 61820, (217) 398-0700. It is available for Windows and Mac OS X. A professional license is $595. Scalable site licensing is also available.

David Gehrig, 304 W. Elm #5, Urbana, IL 61801, (217) 333-0378, is a training coordinator for a large national computing laboratory, and has trained technical users on systems ranging from single desktop workstations to grids with hundreds of compute nodes.

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