Introduction

Mathematica 4 is the fourth generation Mathematica system and represents great progress both in technical computing and technical communication--the two pillars of Mathematica.

Technical computing: Some of the most noticeable features in numerics are performance and scalability improvements. In particular this is true for very large precision numbers, very large integers, and large arrays of machine numbers. These core improvements lead to improvements across the system. Many more specific enhancements, such as new functions for data and image processing like convolution and correlation, and greatly improved discrete Fourier transform, mean that large-scale data processing in Mathematica is quite feasible. Finally, improvements to the high-level numerics solvers such as NSolve and FindMinimum mean that many more things can now be accomplished without delving into special methods.

In symbolics, the main thrust has been to expand the scope of mathematics that Mathematica has mastered. Being able to simplify under certain assumptions, for instance, often means that resulting formulae are more compact and succinct. Several new special functions, and knowledge about special functions such as equation solving, simplification, or integration, means that the high-level symbolic solvers have reached a new high watermark. Finally, a very fundamental way of breaking down systems of inequalities into cylinders (solve) opens up a whole range of new applications for symbolic computation, whether in geometry, optimization, graphics, or theorem proving.

One of the core improvements to the programming language happens transparently in that many functions (e.g., Table and Map) automatically compile their function arguments when fed packed arrays and execute in the Mathematica virtual machine. Other improvements include extensions to the functional and list-based programming models with new powerful programming primitives.

Technical communication: Being able to effectively import and export graphics, data, and documents in a wide variety of file formats means that it should be even easier to work with other programs and people. There are currently some 25 file formats supported. For instance, the greatly enhanced export to HTML now also supports exporting formulae as MathML (the new standard for mathematics on the web) instead of GIFs (as is currently the standard). One consequence of this is that web documents containing mathematics should both look good and mean something; i.e., you should be able to copy and paste a formula and have Mathematica evaluate it, which actually works right now in Mathematica 4.

The user interface took a giant leap in Version 3 and in this version the changes are less visible but productive. There are many additional helper programs that are designed to make the interface more convenient and productive and are meant to be more or less invisible. Some of these include unmatched bracket highlighting, automatic input replacements of sequences of characters, and intelligent indentation. Others aim at improving document quality, such as spell checking and hyphenation. We have also included experimental support for real-time viewpoint and zoom of 3D graphics (Windows and Macintosh).

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