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Mathematica
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Mathematica is a computational software program used widely in scientific, engineering, and mathematical fields and other areas of technical computing. It was originally conceived by Stephen Wolfram and developed by a team of mathematicians and programmers that he assembled and led. It is developed by Wolfram Research of Champaign, Illinois.
features of Mathematica include:
ematica is split into two parts, the "kernel" and the "front end".
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Mathematica is a computational software program used widely in scientific, engineering, and mathematical fields and other areas of technical computing. It was originally conceived by Stephen Wolfram and developed by a team of mathematicians and programmers that he assembled and led. It is developed by Wolfram Research of Champaign, Illinois.
Features
Some features of Mathematica include:
- Libraries of elementary and special mathematical functions
- 2D and 3D data and function visualization tools
- Matrix and data manipulation tools including support for sparse arrays
- Solvers for systems of 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
- A programming language supporting procedural, functional and object oriented constructs
- A toolkit for adding user interfaces to calculations and applications
- Tools for image processing
- Tools for visualizing and analysing graphs
- Data mining tools such as cluster analysis, sequence alignment and pattern matching
- Libraries of number theory functions
- Continuous and discrete integral transforms
- Import and export filters for data, images, video, sound, CAD, GIS, document and biomedical formats
- A collection of databases of mathematical, scientific, and socio-economic information (see below)
- Support for complex number, arbitrary precision and symbolic computation for all functions
- Notebook interface for review and re-use of previous inputs and outputs including graphics and text annotations
- Technical word processing including formula editing
Front ends
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 provides a GUI interface which allows the creation and editing of Notebook documents which 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 slide show environment for presentations. Starting with version 3.0 of the software, 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:
- The Wolfram Workbench is an Eclipse based IDE, introduced in 2006, that provides project based code development tools for Mathematica, including revision management, debugging, profiling, and testing.
- Microsoft Excel can be used as a front end to Mathematica.
- GUIKit allows the construction of custom interfaces to Mathematica using the Java Swing libraries.
- Mathematica includes a command line front end.
- JMath is a third party front end based on GNU readline that runs on UNIX-like operating systems.
- MASH makes it possible to run self contained Mathematica programs (with arguments) from the UNIX command line.
High-performance computing
In recent years the capabilities for high-performance computing have been extended with the introduction of packed arrays (version 4, 1999) , sparse matrices (version 5, 2003), and by adopting the free GNU Multi-Precision Library to evaluate high-precision arithmetic.
Version 5.2 (2005) added automatic multi-threading when computations are performed on modern multi-core computers. This release included CPU specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.
In 2002 gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems 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.
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.
- 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. The current version of webMathematica (2.3) does not support Mathematica 6.
Connections with other applications
Communication with other applications occurs through a protocol called . It allows communication between the Mathematica kernel and front-end, and also provides a general interface between the kernel and other applications. Wolfram Research freely distributes a developer kit for linking applications written in the C programming language to the Mathematica kernel through MathLink. Two other components of Mathematica, whose underlying protocol is MathLink, allow developers to establish communication between the kernel and a .NET or Java program: .NET/Link. and J/Link.
Using .NET/Link, 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, but with Java programs instead of .NET programs.
Communication with SQL databases is achieved through built-in support for JDBC.
Mathematica can also install web services from a WSDL description.
Mathematical equations can be exchanged with other computational or typesetting software as MathML.
Computable data
Mathematica includes large 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. 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 protected by both trade secret and copyright law.
A regular single-user license for Mathematica costs around US$2300-2500, and includes four additional kernels for parallel computations and one year of service which includes updates, technical support, a home use license, a webMathematica Amateur license, a Wolfram Workbench license and three Mathematica Player Pro licenses. Discounts are available for government, charity, educational, pre-college, school, student, home use and retiree use and depend on geographical region. Educational site licenses allow use by students at home. A license manager similar to Flexlm is available to provide sharing of licenses within a group.
Platform availability
Mathematica 7 is supported on various versions of Microsoft Windows, Apple's Mac OS X, Linux and Sun's Solaris platforms. All platforms are supported with 64-bit implementations. Earlier versions of Mathematica supported other operating systems, including MS-DOS, NeXTSTEP, HP-UX, IRIX, Ultrix, OS/2, Convex and AIX.
The Mathematica Home Edition, available only in the US and Canada, is a 32-bit application on Microsoft Windows. The Home Edition also runs on Mac OS X (Intel) and Linux, but not Solaris. Whether there is a 32-bit limitation on Mac OS X and Linux for the Home Edition is not clear from the FAQ.
Version history
Mathematica built on the ideas in Cole and Wolfram's earlier Symbolic Manipulation Program (SMP).
Wolfram Research has released the following versions of Mathematica:
See also
External links
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- discussion group
- entry containing a wide variety of useful links and tutorials
- , a wiki for users of Mathematica
- , examples of art using Mathematica
- by Theodore W. Gray and Jerry Glynn, excerpted from The Beginner's Guide to Mathematica V4, published by Cambridge University Press.
- "" by Enrique Zeleny, Wolfram Demonstrations Project.
- documenting the growth of code base and number of functions over time.
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