Mathematica

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Building on two decades of world-class algorithm and software development, Mathematica 7 represents a dramatic breakthrough that immensely broadens Mathematica's scope and applicability—and redefines the very way we think about computation. Made possible by Mathematica's unique symbolic architecture, Mathematica 7 introduces a sweeping unification of language and interface concepts that makes possible a new level of automation in algorithmic computation, interactive manipulation and dynamic presentation—as well as a whole new way of interacting with the world of data.

Dynamic Interactivity

Mathematica 7 brings a revolution in the concept of interactive computing—for the first time allowing dynamic interfaces to be created instantly as a routine part of everyday work. Based on a series of inventions at Wolfram Research, Mathematica 7 builds on Mathematica's powerful core symbolic architecture to allow sophisticated interactive interfaces to be created from single lines of input—as easily as getting answers to simple calculations.

 

Manipulate function for creating full-function dynamic interfaces for arbitrary objects. Uniform support for manipulating 2D and 3D graphics, math, tables, text, etc. < buttons, checkboxes, menus, sliders, 2D and 1D active of creation> Full integration of controls with graphics objects. Real-time computation based on parameter values defined by interactive controls. Full integration of all interfaces into scrollable Mathematica < interface human other gamepads for support> Fully scalable underlying symbolic dynamic Mathematica language system. Threaded support for dynamic dependency tracking and updating.

Introducing over 1000 new computational functions & interface enhancements

Continuing a 20-year history of unified design & language compatibility

Mathematica 6 radically extends every aspect of Mathematica's functionality

Mathematica from Wolfram Research

Mathematica seamlessly integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications. It is this range of capabilities--many world-leading in their own right--that makes Mathematica uniquely capable as a "one-stop shop" for you or your organization's technical work.

Mathematica has a Wide Range of Uses

• Handling complex symbolic calculations that often involve hundreds of thousands or millions of terms
• Loading, analyzing, and visualizing data
• Solving equations, differential equations, and minimization problems numerically or symbolically
• Doing numerical modeling and simulations, ranging from simple control systems to galaxy collisions, financial derivatives, complex biological systems, chemical reactions, environmental impact studies, and magnetic fields in particle accelerators
• Facilitating rapid application development (RAD) for engineering companies and financial institutions
• Producing professional-quality, interactive technical reports or papers for electronic or print distribution n
• Illustrating mathematical or scientific concepts for students from K-12 to postgraduate levels
• Typesetting technical information--for example, for U.S. patents
• Giving technical presentations and seminars

Key Elements

Notebook Document System

Mathematica notebooks provide a complete technical document system with typeset math, sound, graphics, and animations.

Whether you are creating a report, an academic paper, courseware, or an electronic book or just want to keep a record of your work, Mathematica notebooks are the ideal medium for all of your technical projects. They are the main interface to all Mathematica computations and let you combine all of your calculations, code, results, and graphics into one interactive technical document.

Notebooks are platform independent and combine interactive typeset mathematical expressions, formatted text, hyperlinks, graphics, animations, sound, and fully customizable buttons and palettes. Mathematica's user interface includes such word-processing capabilities as spell checking (with a large technical vocabulary) and automatic hyphenation.

Mathematica’s integrated notebooks allow you to keep your analysis, graphics, report, and presentation together in one unified document.

You can send notebooks by email or put them on a website or an FTP site without affecting their quality, use them to create high-quality printouts or sophisticated on-screen presentations, or translate them to other document formats such as HTML, TeX, and MathML, part of the new XML standard.

Complex Analysis

Mathematica comes with a wide range of high-level statistics and data analysis functions as well as powerful import, export, and connectivity functionality, making even complex analysis of large data sets quick and easy. Mathematica's record-breaking speed for numerical linear algebra also makes processing large data sets faster than ever.

Mathematicamatica includes import and export filters for over 70 popular file formats, including XML. Mathematica can also connect to databases with JDBC or .NET mechanisms through J/Link and .NET/Link. Mathematica's connection tools also allow you to easily build and access online data feeds, other data acquisition software such as LabView, and web services.

Once you have read your data files into Mathematica, you can apply sophisticated analysis or visualization techniques or use Mathematica's computational power to build complex models. Mathematica comes with fast tools for data manipulation, descriptive statistics of uni- and multivariate data, generalized linear and nonlinear fitting, multidimensional interpolation, convolution, correlation, regression, ANOVA, hypothesis testing, and visualization and statistical plotting tools.

Volumes of Knowledge

Put the world's largest collection of mathematical knowledge at your fingertips.

Mathematica takes the most extensive collection of computation and visualization tools you'll find anywhere and puts them right on your desktop. Mathematica contains and surpasses the knowledge of thousands of mathematical tables, hundreds of reference books, and dozens of software systems. Yet Mathematica is faster to use, more accurate, and better integrated than any of them. All of the components you need to pursue a solution are built into Mathematica, from the basic functions like Sin, Log, and Eigenvalues to powerful superfunctions such as Solve, Integrate, and Simplify.

Plotting Functions and Visualization
Mathematica provides many flexible plotting options for visualizing your results: Plot, Plot3D, ContourPlot, DensityPlot, ArrayPlot, ParametricPlot, MoviePlot, MoviePlot3D, LogPlot, LogLogPlot, PolarPlot, ImplicitPlot, ListPlot, ScatterPlot3D, and many other variations. Yet these plotting routines represent only a subset of Mathematica's extensive graphics and visualization capabilities.

Automatic Numeric-Precision Control
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.

Typesetting

Fully typeset input and output are interactive.

In addition to working with pure-text input and output, Mathematica works with typeset expressions. Both text and mathematical expressions can be formatted in any typeface, size, or style. Mathematical expressions are also "live," and you can use them as input or can make instant modifications. This feature allows you to work with mathematical expressions that are familiar from textbooks and to input formulas and parse results far more quickly than you can in any other program.

Symbolic and Numeric Computations

Perform symbolic as well as numeric computations.

Every function in Mathematica is implemented as completely as possible, handling the widest range of numeric and symbolic inputs. Mathematica knows how to evaluate functions to any precision anywhere in the complex plane. Along with supporting numerical inputs, Mathematica supports the world's largest collection of symbolic transformation rules, allowing sophisticated manipulation and reduction of formulas.

Pass the function Sin an exact input such as , and the result comes back exactly as . Pass it the numerical approximation 0.261799, and it returns the numerical result 0.258819. Try a complex value, and you get a complex result. Since all of these cases are handled simply by calling the function Sin, you won't need to memorize a different function name for each kind of argument.

Graphics

Choose from over 50 styles of graphics, or create your own.

Mathematica provides over 50 built-in graphics types for visualizing your results, including a variety of 2D and 3D plots, contour and density graphics, and a full complement of specialized business and statistical plots. Mathematica also lets you generate animations and sounds with simple commands.

However, these plotting routines represent only a subset of Mathematica's extensive graphics and visualization capabilities. Mathematica also comes with a graphics language that lets you customize graphics to your exact specifications or even create your own graphic types from a large set of built-in primitives.

Application Development

Develop applications with Mathematica.

In many cases you want not only to publish your results but also to make your Mathematica applications available to others--coworkers in your organization, customers, or colleagues around the world.

Mathematica's combination of computational sophistication and programmability makes it ideal for prototyping and developing complete applications. Because it provides a high-level environment, you can concentrate on what's unique to your work instead of spend time coding generic, low-level functionality. Once your application is finished, Mathematica offers numerous ways to rapidly deploy it in the way that is most efficient for your purpose.

Mathematica Notebooks and Packages
The most direct way of allowing others to use your Mathematica programs is to send your notebooks or packages to them. All Mathematica documents and programs are fully platform independent, so you do not have to worry about portability issues or incompatibilities. You can even add a point-and-click user interface, using either Mathematica buttons and palettes or Java, so that end users never have to work with the command line.

Interactive Web and Intranet Sites
With very little effort almost any Mathematica program can be turned into an MSP, an interactive web application running on a webMathematica server. In many cases, the process requires only a few steps--for example, saving the notebook as HTML, extracting the code, and then adding a few simple Mathlet tags. The resulting web application can be used from any web browser and through an interface; no Mathematica knowledge is required. You can also easily create more-advanced user interfaces using any number of standard web-development tools and languages such as JavaScript, JSP, or PHP.

Mathematica as a Software Component
With Mathematica's J/Link and MathLink API, you can also deploy your Mathematica application as part of a Java, .NET, or C/C++ program right out of the box. Additional products from Wolfram Research and independent developers provide prebuilt links to Visual Basic, scripting languages, and Microsoft Excel, which enable the products to interface with Mathematica and a variety of application packages.

Programmable Palettes

Programmable palettes let you have instant access to sophisticated functionality.

Mathematica comes with a collection of ready-to-use palettes that give you instant access to many of the built-in functions with one click. Because Mathematica is so flexible, you can also easily create your own palettes in seconds.

Put the functions and symbols you use most often on a single palette, or make notebooks interactive by including custom buttons in them. You can even add the palettes you use most often to a menu for quick access or can send them via email to your colleagues.

Since you can run any Mathematica function or program from a button, you can build complete interfaces to your Mathematica packages or courseware--making Mathematica an even more productive environment in which to work.

Special-Purpose Interfaces

Create special-purpose interfaces using Java, .NET, or C/C++.

Mathematica allows you to create complete document-centric and graphical user interfaces. You can build buttons and palettes, input forms and dialogs, and even fully interactive documents using nothing but built-in Mathematica functions. Moreover, your programs can generate any of these interface elements on the fly.

Automatically generate reports with completely cross-referenced hyperlinks. Create a survey that adapts itself to the answers given by the user. Make self-modifying palettes. The possibilities are endless, and the programs and interfaces created are platform independent.

There are many additional ways to generate custom user and programmatic interfaces for Mathematica. For example, Mathematica now comes with J/Link and a Java Runtime Environment preinstalled, allowing you to use AWT or Swing components to create a Java-based graphical user interface to Mathematica that will run seamlessly on all platforms for which Mathematica and Java are available.

The Windows version of Mathematica also includes .NET/Link for full integration with the Microsoft .NET Framework. With .NET/Link, Mathematica users can load any .NET object into Mathematica and extend it. .NET/Link also provides an easy way to call any DLL or COM object from within Mathematica.

Programming Language

Program in the uniquely productive Mathematica language.

Whether you call them simulations, models, or algorithms, representing your concepts in Mathematica is easy. There's hardly a distinction between interactive and programmed calculations in Mathematica. You can build intricate calculations piece by piece. Specify a definition for an expression. Look up a formula and add it as a Mathematica transformation rule. Add more rules for other cases or for related formulas. The intuitive nature of Mathematica lets you build surprisingly sophisticated calculations easily and incrementally.

Mathematica includes a modern, wide-ranging, and highly versatile language that doesn't force you into a single style of programming. Just as a spoken language gives you many ways to express each idea, Mathematica provides many different programming paradigms.

Your code reflects your style of specifying the problem, which can make the command much shorter and easier to read. This unique flexibility makes switching to Mathematica from other programming languages easy--and cost effective. Even those who haven't programmed before can write powerful programs without extensive training.

Concentrate on your ideas.

Mathematica takes care of the programming infrastructure. There is no need to predeclare variable types or dimensions of lists and arrays, to direct memory management, or to compile your programs.

Common procedures such as sorting, searching, handling files, and manipulating data are built in and remove peripheral code from your routines. This feature helps to make typical Mathematica programs only 5 to 10 percent the size of those created in traditional languages or numerical systems and greatly shrinks development time.

Choose your programming style.

Mathematica handles problems of any scale and complexity equally well; it's more than a simple scripting language. One key feature is dynamic arrays of arbitrary size and dimension; optional compilation is another. By providing multiple paradigms and the world's most powerful pattern-matching engine, Mathematica lets you choose the most effective programming style for your problem. You don't have to work around the limitations of a restrictive language.

With such a variety of programming approaches, it's easy to see why Mathematica has become the language of choice for technical professionals around the world. Add it all together: Mathematica makes you many times more productive.

Interactive Help Browser

All documentation is available through the interactive Help Browser.

The Mathematica Help Browser includes the complete documentation for all functions in Mathematica and the entire text of The Mathematica Book as fully indexed Mathematica notebooks with advanced search capabilities and comprehensive hyperlinks.

The Help Browser also contains thousands of interactive examples that demonstrate the use of Mathematica functions, its general capabilities, and the best way to take advantage of them.

Unlike any other software, Mathematica enables users to modify and evaluate expressions directly within the Help Browser. The online material for the majority of built-in functions includes several examples to be evaluated or altered, providing a particularly helpful aid for those who learn best by example. User modifications of material within the Help Browser are not permanent, however. If you accidentally delete an example or section of help text, you need only to exit and reenter that page to restore the original information.

However, the material presented in the Help Browser is not fixed permanently to include only what is provided with the Mathematica installation. Help Browser information is stored as a Mathematica notebook. Thus, you can create help notebooks that become fully integrated with other Help Browser information, including the insertion of new entries into the Help Browser's master index.

Revision History

Mathematica 7 includes over 500 new functions and 12 additional application areas.

Mathematica 7 introduces a new generation of digital image processing and analysis, with broad and deep built-in support for both programmatic and interactive modern industrial-strength image processing—all fully integrated with Mathematica's powerful mathematical and algorithmic capabilities. Mathematica's unique symbolic architecture and notebook paradigm allows images in visual form to be included and manipulated directly both interactively and in programs—making possible a new form of streamlined image processing workflow.

Mathematica 7 adds the capability for instant parallel computing. On any multicore computer system, Mathematica 7 is automatically set up to be able to run multiple parts of a computation concurrently—and for the first time makes parallel computing easy enough that it can be used in seconds as a routine part of everyday work. The symbolic character of the Mathematica language allows unprecedentedly straightforward support of many existing and new parallel programming paradigms and data-sharing models—and Mathematica's parallel infrastructure is set up to allow seamless scaling to networks, clusters, grids and clouds.

Mathematica 7 introduces a new generation of information visualization—made possible by Mathematica's unique symbolic architecture, as well as its programmability, graphics and dynamic interface. With an unprecedentedly convenient symbolic mechanism for specifying labeling, legending, styling and dynamic behavior, Mathematica 7 automates the process of creating a fully extensible range of compelling information visualizations for data of all kinds.

Mathematica 7 introduces state-of-the-art visualization of vector fields generated from both functions and data. Building on Mathematica's powerful capabilities in differential equations, geometry and symbolic analysis, Mathematica 7 brings a new level of automation and computational aesthetics to vector visualization. With applications in fluid mechanics, meteorology, electromagnetism, dynamical systems and other areas, Mathematica 7 for the first time allows textbook-quality images of vector fields to be generated immediately as a routine part of computational work.

Mathematica 7 introduces highly general systemwide support for splines—covering Bézier curves, B-spline curves and surfaces and NURBS curves and surfaces, all with any degree, and in any number of dimensions. In addition to complete integration with 2D and 3D graphics, as well as with interpolation, Mathematica 7 for the first time provides full exact symbolic handling of splines, making it possible to take advantage of spline methods in many new mathematical settings.

Mathematica 7 continues to add richness and functionality to Mathematica's symbolic graphics system—with new capabilities and even more refined control over detailed graphics appearance. Notable additions include 3D tubes, rounded rectangle corners, 3D arrows, line cap and join controls and shaded lines and points

• High-Impact Adaptive Visualization
• Automated Computational Aesthetics
• Fully Automated Graph Layout
• Real-Time 3D Graphics
• Automated Table Layout
• Dynamic Interactivity

Mathematics & Algorithms

Industrial-Strength Boolean Computation Apply high-performance Boolean analysis, optimization, and verification to systems with thousands of variables--all integrated into the Mathematica workflow...

Computable Data

Data Manipulation

Core Language