# Mathematica

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File:WolframSpikeyVersion7.png | |
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Developer(s) | Wolfram Research |

Initial release | June 23, 1988^{[1]} |

Written in | Mathematica, C |

Platform | Cross-platform (list) |

Available in | English, Chinese and Japanese. |

Type | Computer algebra, numerical computations, Information visualization, statistics, user interface creation |

License | Proprietary |

Website | Mathematica homepage |

**Mathematica** is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing. It was originally conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois.^{[2]}^{[3]}

## Contents |

## Features

Features of Mathematica include^{[4]}:

- Elementary mathematical function library
- Special mathematical function library
- 2D and 3D data and function visualization and animation tools
- Matrix and data manipulation tools including support for sparse arrays
- Solvers for systems of equations, diophantine equations ODEs, PDEs, DAEs, DDEs and recurrence relations
- Numeric and symbolic tools for discrete and continuous calculus
- Multivariate statistics libraries
- Constrained and unconstrained local and global optimization
- Programming language supporting procedural, functional and object oriented constructs
- Toolkit for adding user interfaces to calculations and applications
- Tools for image processing
^{[5]} - Tools for visualizing and analysing graphs
- Tools for combinatoric problems
- Data mining tools such as cluster analysis, sequence alignment and pattern matching
- Number theory function library
- Continuous and discrete integral transforms
- Import and export filters for data, images, video, sound, CAD, GIS
^{[6]}, document and biomedical formats - Database collection for mathematical, scientific, and socio-economic information
- Support for complex number, arbitrary precision, interval arithmetic and symbolic computation
- Notebook interface for review and re-use of previous inputs and outputs including graphics and text annotations
- Technical word processing including formula editing and automated report generating
- Tools for connecting to SQL, Java, .NET, C++, FORTRAN and http based systems
- Tools for parallel programing

## Interface

Mathematica is split into two parts, the "kernel" and the "front end". The kernel interprets expressions (Mathematica code) and returns result expressions.

The Mathematica Front End, designed by Theodore Gray, provides a GUI, which allows the creation and editing of Notebook documents that can contain program code with prettyprinting, formatted text together with results including typeset mathematics, graphics, GUI components, tables, and sounds. All contents and formatting can be generated algorithmically or interactively edited, and most standard word processing capabilities are supported but only one level of "undo" is supported.

Documents can be structured using a hierarchy of cells, which allow for outlining and sectioning of a document and support automatic numbering index creation. Documents can be presented in a slideshow environment for presentations. Notebooks and their contents are represented as Mathematica expressions that can be created, modified or analysed by Mathematica programs. This allows conversion to other formats such as TeX or XML.

The Mathematica Front End includes development tools such as a debugger, input completion and automatic syntax coloring.

The kernel and the front end communicate via the MathLink protocol. It is possible to use the kernel on one computer and the front end on another.

The standard Mathematica front-end is used by default, but alternative front-ends are available, including the Wolfram Workbench, an Eclipse based IDE, introduced in 2006. It provides project-based code development tools for Mathematica, including revision management, debugging, profiling, and testing.^{[7]}
Mathematica includes a command line front end.

## High-performance computing

In recent years, the capabilities for high-performance computing have been extended with the introduction of packed arrays (version 4, 1999) ^{[8]}, sparse matrices (version 5, 2003)^{[9]}, and by adopting the GNU Multi-Precision Library to evaluate high-precision arithmetic.

Version 5.2 (2005) added automatic multi-threading when computations are performed on multi-core computers.^{[10]} This release included CPU specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.^{[11]}

In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems ^{[12]} and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such as Windows HPC Server 2008, Microsoft Compute Cluster Server and Sun Grid.

Planned support for CUDA hardware was announced in 2008 but is still only provided by a third party add-on.

## Development

Several solutions are available for deploying applications written in Mathematica:

- Mathematica Player Pro is a runtime version of Mathematica that will run any Mathematica application but does not allow editing or creation of the code.
^{[13]} - Mathematica Player is a free interactive player is provided for running Mathematica programs that have been digitally signed for non-commercial use via a Wolfram Research web service, or published on the Wolfram Demonstrations Project website. It can also view unsigned Mathematica files, but not run them.
- webMathematica allows a web browser to act as a front end to a remote Mathematica server. It is designed to allow a user written application to be remotely accessed via a browser on any platform. It may not be used to give full access to Mathematica.

## Connections with other applications

Communication with other applications occurs through a protocol called MathLink. It allows communication between the Mathematica kernel and front-end, and also provides a general interface between the kernel and other applications.

Although Mathematica has a large array of functionality, a number of interfaces to other software have been developed, for use where other programs have functionality that Mathematica does not provide, to enhance those applications, or to access legacy code.

### Languages

- Wolfram Research freely distributes a developer kit for linking applications written in the C programming language to the Mathematica kernel through
*MathLink*.^{[14]} - Using
*.NET/Link*.^{[15]}, a .NET program can ask Mathematica to perform computations; likewise, a Mathematica program can load .NET classes, manipulate .NET objects and perform method calls. This makes it possible to build .NET graphical user interfaces from within Mathematica. - Similar functionality is achieved with
*J/Link*.^{[16]}, but with Java programs instead of .NET programs. - GUIKit allows the construction of custom interfaces to Mathematica using the Java Swing libraries.
- Communication with SQL databases is achieved through built-in support for JDBC.
^{[17]} - Mathematica can also install web services from a WSDL description.
^{[18]}^{[19]} - Other languages that connect to Mathematica include Haskell
^{[20]},AppleScript^{[21]}and PLT Scheme.^{[22]}

### Spreadsheets

- The OpenOffice.org office suite supports bi-directional access to Mathematica via a commercial add-on
^{[23]}. - Microsoft Excel can call Mathematica via a commercial add-on
^{[24]}

### Specialized Mathematical software

- MATLAB can be called from Mathematica, using freeware software written by Wolfram Research
^{[25]}. - R can be called from within Mathematica using a commercial interface
^{[26]}^{[27]}. - Sage, can be called from within Mathematica
^{[28]}^{[29]}. - SINGULAR can be called from within Mathematica.
^{[30]} - MathModelica, integrates with Mathematica
- Mathematica can be called from Origin
^{[31]} - Mathematical equations can be exchanged with other computational or typesetting software as MathML.

### Data acquisition

### Alternative Interfaces

- JMath is a third-party front end based on GNU readline that runs on UNIX-like operating systems.
^{[36]} - MASH runs self contained Mathematica programs (with arguments) from the UNIX command line.
^{[37]}

## Computable data

Mathematica includes collections of curated data in a consistent framework for immediate computation. Data can be accessed programmatically to inform or test models and is updated automatically from a data server at Wolfram Research^{[38]}. Some data such as share prices and weather are delivered in real-time. Data sets currently include:

- Astronomical data: 99 properties of 155,000 astronomical bodies
- Chemical data: 111 properties of 34,000 chemical compounds, 86 properties of 118 chemical elements and 35 properties of 1000 subatomic particles
- Geopolitical data: 225 properties of 237 countries and 14 properties of 160,000 cities around the world
- Financial data: 71 historical and real-time properties of 186,000 shares and financial instruments
- Mathematical data: 89 properties of 187 polyhedra, 258 properties of 3000 graphs, 63 properties of 6 knots, 37 properties of 21 lattice structures, 32 properties of 52 geodesic schemes
- Language data: 37 properties of 149,000 English words. 26 additional language dictionaries
- Biomedical data: 41 properties of all 40,000 human genes, 30 properties of 27,000 proteins
- Weather data: live and historical measurements of 43 properties of 17,000 weather stations around the world

## Licensing

Mathematica is proprietary software restricted by both trade secret and copyright law.^{[39]}

A regular single-user license for Mathematica used in a commercial environment costs between $2495 and $3120. It includes four additional kernels for parallel computations and one year of service that includes updates, technical support, a home use license, a webMathematica Amateur license^{[40]}, a Wolfram Workbench license and three Mathematica Player Pro licenses. Discounts are available for government, charity, educational, pre-college, school, student, home use^{[41]} and retiree use and depend on geographical region. Student licenses cost $140. Educational site licenses allow use by students at home. A license manager similar to FLEXnet is available to provide sharing of licenses within a group.

## Platform availability

Mathematica 7 is supported on various versions of Linux, Apple's Mac OS X, NT-based Microsoft Windows, and Sun's Solaris platforms. All platforms are supported with 64-bit implementations.^{[42]} Earlier versions of Mathematica up to 6.0.3 supported other operating systems, including AIX, Convex, HP-UX, IRIX, MS-DOS, NeXTSTEP, OS/2, Ultrix and Windows Me^{[43]}.

The Mathematica Home Edition is a 32-bit application on Microsoft Windows, Linux and Mac OS X (Intel).

## Support

Support via email is available to registered users by emailing support@wolfram.com.

There is no official public support forum for professional users, although there is an official support forum for students.^{[44]} Posts are reviewed by a Wolfram Research moderator before they appear on the student forum.

MathGroup is a moderated email list and internet newsgroup * comp.soft-sys.math.mathematica. It has more than 100,000 posts ^{[45]} and is the dominant public forum although it is not controlled by Wolfram Research. The moderator is Steve Christensen. Wolfram Research staff regularly answer questions on Mathgroup. The posts are archived by Wolfram Research.

There are several other unofficial support forums, which are unmoderated, so posts appear without delay. These include the newsgroup sci.math.symbolic and http://www.mathematica-users.org, but none have the popularity of the dominant Mathgroup.

## Books

There are a large number of books written about Mathematica. While some are general introductions, other cover specific areas such as graphics, numerics, symbolic computation, programming etc.

The 408 page book *Mathematica programming: An advanced Introduction* written by Leonid Shifrin, released under the Creative Commons License may be read online or downloaded as a PDF file for no charge.

## Version history

Mathematica built on the ideas in Cole and Wolfram's earlier Symbolic Manipulation Program (SMP).^{[46]}^{[47]}

Wolfram Research has released the following versions of Mathematica^{[48]}:

- Mathematica 1.0 (1988)
^{[49]} - Mathematica 1.1 (1989)
^{[50]} - Mathematica 1.2 (1989)
^{[51]} - Mathematica 2.0 (1991)
^{[52]} - Mathematica 2.1 (1992)
^{[14]} - Mathematica 2.2 (1993)
^{[53]} - Mathematica 3.0 (1996)
^{[54]} - Mathematica 4.0 (1999)
^{[55]} - Mathematica 4.1 (2000)
- Mathematica 4.2 (2002)
^{[16]} - Mathematica 5.0 (2003)
^{[56]} - Mathematica 5.1 (2004)
^{[57]} - Mathematica 5.2 (2005)
^{[58]} - Mathematica 6.0 (2007)
^{[59]} - Mathematica 6.0.1 (2007)
- Mathematica 6.0.2 (2008)
- Mathematica 6.0.3 (2008)
- Mathematica 7.0 (2008)
^{[60]} - Mathematica 7.0.1 (2009)