Mathematica is the world's most powerful technical computing
system. Used by over a million people in science, industry, and
academia, Mathematica combines fast, high-precision numeric and
symbolic computation with easy-to-use data visualization and
programming capabilities. Mathematica creates publication-quality
documents with its customizable, cross-platform file format.
From simple calculator operations to large-scale programming and
interactive document preparation, Mathematica is the tool of choice at
the frontiers of scientific research, in engineering analysis and modeling,
in technical education from high school to graduate school, and
wherever quantitative methods are used.
Features
Mathematica as a
Calculator
You can use Mathematica just like a calculator: you type in questions, and
Mathematica prints back the answers. These first examples show ordinary
keyboard input. You can also enter fully formatted input in
Mathematica.
Power Computing with Mathematica
Because it combines the push-button interface of a calculator with legendary
computational capabilities, Mathematica gets the beginner going quickly,
while still giving the advanced user unmatched calculating
power.
Mathematica keeps track of the precision of its numerical results
automatically throughout each calculation and adjusts its internal algorithms as
needed to provide the precision you require.
Accessing Algorithms in Mathematica
Whenever you use Mathematica, you are accessing the world's largest
collection of computational algorithms. And all of Mathematica's numerical
algorithms are set up to work to whatever accuracy or precision
you specify.
Mathematical Knowledge in Mathematica
Mathematica incorporates the knowledge from the world's mathematical
handbooks -- and uses its own revolutionary algorithms to go
much further.
Building Up Computations
Being able to work with formulas lets you easily integrate all the parts of a
computation. Mathematica's functions are carefully designed so that output from one can
easily be used as input to others.
Handling Data
Mathematica lets you import data in any format, then manipulate it using
powerful and flexible functions. Mathematica can work with data
of any kind -- not just numbers.
Visualization with Mathematica
Mathematica makes it easy to create stunning visual images.
Mathematica includes primitives from which you can build up 2D and 3D
graphics of any complexity. Mathematica has made possible many new kinds of scientific, technical, and
artistic images.
Mathematica Notebooks
Every Mathematica notebook is a complete interactive document which
combines text, tables, graphics, calculations, and other elements.
Mathematica notebooks can be built up using explicit commands as well as
interactively.
Palettes and Buttons
Palettes and buttons provide a simple but fully customizable point-and-click
interface to Mathematica. Mathematica comes with a collection of ready-to-use standard palettes.
Palettes work like extensions to your keyboard. It is easy to create your own custom palettes.
You can make custom palettes to execute any function or manipulate any
expression.
Mathematical Notation
Mathematica notebooks fully support standard mathematical
notation -- for both output and input. Mathematica combines the compactness of mathematical notation with the
precision of a computer language. Mathematica's StandardForm is precise and unambiguous.
TraditionalForm requires heuristics for interpretation.
Mathematica and Your Computing Environment
Mathematica runs compatibly across all major computer systems and lets
you exchange data in many standard formats.
The standard Mathematica system consists of two parts:
- The kernel -- which actually does computations
- The front end -- which handles user interaction and
notebooks
From within one notebook you can run several Mathematica kernels--on
local or remote computers.
The Unifying Idea of Mathematica
Mathematica is built on the powerful unifying idea that everything can be
represented as a symbolic expression.
All symbolic expressions are built up from combinations of the basic form:
Head[arg1, arg2, ... ].
The uniformity of symbolic expressions makes it easy to add to Mathematica
any construct you want.
All operations in Mathematica are ultimately transformations of symbolic
expressions. Mathematica has a uniquely powerful pattern matcher for
applying transformation rules.
Mathematica as Programming Language
Mathematica is an unprecedentedly flexible and intuitive programming
language. It includes advanced programming methods from modern computer
science -- as well as adding a host of new ideas of its own.
Mathematica incorporates a range of programming paradigms -- so you can
write every program in its most natural way.
Writing Programs in Mathematica
Mathematica's high-level programming constructs let you build sophisticated
programs more quickly than ever before. Mathematica is a uniquely scalable
language -- suitable for programs of any
size. Writing Programs in Mathematica Mathematica has a compiler for optimizing
programs that work with lists and numbers.
Building Systems with Mathematica
Mathematica has everything you need to create complete systems for
technical and non-technical applications. Any system you build in Mathematica will run unchanged across all computer
platforms.
Mathematica as a Software Component
Mathematica has a modular architecture that makes it easy to use as a highly
powerful software component. You can use MathLink to access the Mathematica kernel from many kinds
of programs. MathLink can also be used to access other programs from within the
Mathematica kernel.
Features added in 4.1
Mathematica 4.1 extends the technologies and advances pioneered by
Wolfram Research, Inc. in Mathematica 4. Enhanced solvers, functions,
and an improved pattern matcher and compiler allow scientists and
researchers to solve more-complex problems more quickly. MathML and
HTML integration helps academics and technical professionals share
their work over the internet, while J/Link allows the design of innovative
applications, combining the strengths of Mathematica and Java.
- Greatly enhanced symbolic differential equation solvers
- Enhanced Mathematica pattern matcher and compiler, increasing
speed and minimizing memory consumption
- New standard package for integration over inequality-defined
regions and piecewise functions
- Dramatic speed improvements in statistics functions
- Conversion between linear systems of equations and matrices
- Java integration with J/Link 1.1
- Improved MathML integration on the web
- Support for saving in IBM techexplorer format
- New and faster import and export filters for Excel files, tabular
data, compressed BMP, DXF, and STL
- Support for real-time manipulation of 3D graphics on Linux and
Unix platforms
- Sound support under X
- Routines for plotting graphics defined by inequalities
- Support for LinuxPPC and AlphaLinux
- Discrete trigonometric package
- Enhanced look and feel for the X front end
What's new in 4.2
New J/Link Version and Pre-installed Java Runtime Environment
For Mathematica users, J/Link makes the whole universe of existing and future
Java classes an automatic extension to the Mathematica environment. For example,
users can use standard Java classes to provide new interfaces to Mathematica or can
create GUI elements using AWT or Swing classes.
For Java programmers, J/Link turns Mathematica into a scripting shell that
allows them to experiment with, build, and test Java classes one line at a time.
It also makes Java a powerful language for writing programs that use the
computational services of Mathematica.
Mathematica 4.2 includes the newest release of J/Link preinstalled, the toolkit
that integrates Mathematica, thereby avoiding the installation step for all platforms.
XML Support
Mathematica has always been the leading environment for technical document processing as well as
for handling and processing structured documents and data.
Mathematica 4.2 greatly improves the already strong foundation that includes full support
for import, export, and manipulation of XML documents; DTDs and style sheets for saving
Mathematica notebooks and expressions as XML documents; and support for XHTML and MathML
2.0. Mathematica 4.2 also includes a new bundled AuthorTools package, new fonts, support
for all languages that are written left to right, and a slide show environment for presentations.