Mathmatica

Mathematica

Belongs here simply because of the levels of math that this system can do.

English: Publicity photo of en:Stephen Wolfram. (Photo credit: Wikipedia)

Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois.


Features of Mathematica include:

• Elementary mathematical function library
• Special mathematical function library
• Matrix and data manipulation tools including support for sparse arrays
• Support for complex number, arbitrary precision, interval arithmetic and symbolic computation
• 2D and 3D data and function visualization and animation tools
• Solvers for systems of equations, Diophantine equations, ODE’s, PDE’s, DAE’s,DDE’s and recurrence relations
• Numeric and symbolic tools for discrete and continuous calculus
• Multivariate statistics libraries including fitting, hypothesis testing, and probability and expectation calculations on over 100 distributions.
• 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 and morphological image processing including image recognition
• Tools for visualizing and analyzing graphs
• Tools for combinatorics problems
• Tools for text mining including regular expressions and semantic analysis
• Data mining tools such as cluster analysis, sequence alignment and pattern matching
• Number theory function library
• Tools for financial calculations including bonds, annuities, derivatives, options etc.
• Group theory functions
• Libraries for wavelets analysis on sounds, images and data
• Control systems libraries
• Continuous and discrete integral transforms
• Import and export filters for data, images, video, sound, CAD, GIS, document and biomedical formats
• Database collection for mathematical, scientific, and socio-economic information and access to Wolfram Alpha data and computations
• Technical word processing including formula editing and automated report generating
• Tools for connecting to DLL’s. SQL, Java, .NET, C++, FORTRAN,CUDA, OpenCL and http based systems
• Tools for parallel programming
• Using both “free-form linguistic input” (a natural language user interface)  and Mathematica language in notebook when connected to the Internet

Interface

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

The front end, designed by Theodore Gray, provides a GUI, which allows the creation and editing of Notebook documents containing program code with pretty printing, 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. Most standard word processing capabilities are supported, but there is only one level of “undo.”

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 sideshow 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 front end includes development tools such as a debugger, input completion and automatic syntax coloring.

The standard front end is used by default, but alternative front ends are available. They include 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. Mathematica also 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) and sparse matrices (version 5, 2003), 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. This release included CPU specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.

In 2002, grid Mathematica 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.

Support for CUDA, OpenCL, and GPU hardware was added in 2010. Also, version 8 can generate C code, which is automatically compiled by a system C compiler, such as Intel C++ Compiler or compiler of Visual Studio 2010.

Development

There are several ways to deploy 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.
  
• A free-of-charge version, Wolfram CDF Player, is provided for running Mathematica programs that have been saved in the Computable Document Format (CDF). It can also view standard Mathematica files, but not run them. It includes plugins for common web browsers.
• 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.
• Mathematica code can be converted to C code or to an automatically generated DLL.

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.

Wolfram Research freely distributes a developer kit for linking applications written in the C programming language to the Mathematica kernel through MathLink.

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.

Other languages that connect to Mathematica include Haskell, AppleScript, Racket, Visual Basic, Python and Clojure.

Links are available to many specialized mathematical software packages including OpenOffice.org Calc, Microsoft Excel, MATLAB, R, Sage, SINGULAR, Wolfram System Modeler and Origin.

Mathematical equations can be exchanged with other computational or typesetting software via MathML.

Mathematica can capture real-time data via a link to LabView, from financial data feeds and directly from hardware devices via GPIB (IEEE 488), USB and serial interfaces. It automatically detects and reads from HID devices.

Alternative interfaces are available such as JMath, based on GNU readline and MASH which runs self-contained Mathematica programs (with arguments) from the UNIX command line.

Computable  data

A stream plot of live weather data

Mathematica includes collections of curated data provided for use in computations. Mathematica is also integrated with Wolfram Alpha, an online service which provides additional data, some of which is kept updated in real time. Some of the data sets include astronomical, chemical, geopolitical, language, biomedical and weather data, in addition to mathematical data (such as knots and polyhedra).

Licensing

Mathematica is proprietary software restricted by both copyright law and trade secret.

A regular single-user license for Mathematica used in a commercial environment costs $2495 although new customers can purchase the “Starter Edition” for $995. They include four additional kernels for parallel computations and one year of service that 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. Student licenses cost $140. A general “home use” license (“Mathematica Home Edition”) is also available to the public and is priced at $295. 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 8 is supported on various versions of Linux, Apple’s Mac OS X, and NT-based Microsoft Windows. All platforms are supported with 64-bit implementations. Earlier versions of Mathematica up to 6.0.3 supported other operating systems, including Solaris, AIX, Convex, HP-UX, IRIX, MS-DOS, NeXTSTEP, OS/2, Ultrix and Windows Me.