Mathematica

Mathematica
For other uses, see Mathematica (disambiguation).
Mathematica
MathematicaSpikeyVersion8.png
Mathematica logistic bifurcation.png
Mathematica 8.0.0 Linux frontend
Developer(s) Wolfram Research
Initial release June 23, 1988[1]
Stable release 8.0.4  (October 24, 2011) [+/−]
Preview release [+/−]
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 www.wolfram.com/products/mathematica

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.[2][3]

The name of the program "Mathematica" was suggested to Stephen Wolfram by the inventor Steve Jobs[4] although Stephen Wolfram had thought about it earlier.

Contents

Features

Dini's surface plotted with adjustable parameters

Features of Mathematica include:[5]

  • 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, ODEs, PDEs, DAEs, DDEs 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[6] and morphological image processing including image recognition
  • Tools for visualizing and analysing graphs
  • Tools for combinatoric 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 wavelet 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,[7] document and biomedical formats
  • Database collection for mathematical, scientific, and socio-economic information and access to WolframAlpha data and computations
  • Technical word processing including formula editing and automated report generating
  • Tools for connecting to DLLs. SQL, Java, .NET, C++, FORTRAN, CUDA, OpenCL and http based systems
  • Tools for parallel programing
  • Using both "free-form linguistic input" (a natural language user interface) [8] 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 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. 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 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 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.[9] Mathematica also includes a command line front end.[10]

High-performance computing

In recent years, the capabilities for high-performance computing have been extended with the introduction of packed arrays (version 4, 1999)[11] and sparse matrices (version 5, 2003),[12] 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.[13] This release included CPU specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.[14]

In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems [15] 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 and OpenCL 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

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.[16]
  • A free-of-charge version, Wolfram CDF Player, is provided for running Mathematica programs that have been saved in the Computable Document Format (CDF).[17] 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.[18]

Using .NET/Link.,[19] 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.,[20] but with Java programs instead of .NET programs.

Communication with SQL databases is achieved through built-in support for JDBC.[21] Mathematica can also install web services from a WSDL description.[22][23]

Other languages that connect to Mathematica include Haskell,[24] AppleScript,[25] Racket,[26] Visual Basic,[27] Python[28][29] and Clojure.[30]

Links are available to many specialized mathematical software packages including OpenOffice.org Calc,[31] Microsoft Excel,[32] MATLAB,[33][34] R,[35][36] Sage,[37][38] SINGULAR,[39] MathModelica and Origin.[40]

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

Mathematica can capture real-time data via a link to LabView,[41] from financial feeds[42] and directly from hardware devices via GPIB (IEEE 488),[43] USB[44] and serial interfaces.[45] It automatically detects and reads from HID devices.

Alternative interfaces are available such as JMath,[46] based on GNU readline and MASH[47] 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 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.[48] 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
  • Wolfram|Alpha data: trillions of data points from WolframAlpha

Licensing

Mathematica is proprietary software restricted by both trade secret and copyright law.[49]

A regular single-user license for Mathematica used in a commercial environment costs $2495. 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,[50] a Wolfram Workbench license and three Mathematica Player Pro licenses. Discounts are available for government, charity, educational, pre-college, school, student, home use[51] 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.[52] 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.[53]

Version history

Mathematica built on the ideas in Cole and Wolfram's earlier Symbolic Manipulation Program (SMP).[54][55]

Wolfram Research has released the following versions of Mathematica[56]:

  • Mathematica 1.0 (June 23, 1988)[57][58][59][60]
  • Mathematica 1.1 (1989)[61]
  • Mathematica 1.2 (August 1, 1989)[62][63]
  • Mathematica 2.0 (January 15, 1991)[64][65]
  • Mathematica 2.1 (June 15, 1992)[66][18]
  • Mathematica 2.2 (June 1, 1993)[67][68]
  • Mathematica 3.0 (September 3, 1996)[69]
  • Mathematica 4.0 (May 19, 1999)[70][71]
  • Mathematica 4.1 (November 2, 2000)[72]
  • Mathematica 4.2 (November 1, 2002)[73]
  • Mathematica 5.0 (June 12, 2003)[74][75]
  • Mathematica 5.1 (October 25, 2004)[76][77]
  • Mathematica 5.2 (June 20, 2005)[78][79]
  • Mathematica 6.0 (May 1, 2007)[80][81]
  • Mathematica 6.0.1 (July 5, 2007)[82]
  • Mathematica 6.0.2 (2008)[83]
  • Mathematica 6.0.3 (2008)[84]
  • Mathematica 7.0 (November 18, 2008)[85]
  • Mathematica 7.0.1 (March 5, 2009)[86]
  • Mathematica 8.0 (November 15, 2010)
  • Mathematica 8.0.1 (March 7, 2011)
  • Mathematica 8.0.4 (October 24, 2011)

See also

References

  1. ^ http://blog.wolfram.com/2008/06/23/mathematica-turns-20-today/
  2. ^ Stephen Wolfram: Simple Solutions; The iconoclastic physicist's Mathematica software nails complex puzzles, BusinessWeek, October 3, 2005.
  3. ^ Wolfram Research Contact Info
  4. ^ http://blog.wolframalpha.com/2011/10/06/steve-jobs-a-few-memories/#more-15338
  5. ^ Mathematica documentation
  6. ^ Review: Mathematica 7. Technical computing powerhouse gets more oomph Macworld, Jan 2009
  7. ^ Mathematica 6 Labs Review Cadalyst Feb 1, 2008
  8. ^ The Free-Form Linguistics Revolution in Mathematica
  9. ^ MacWorld review of Wolfram Workbench
  10. ^ Using a Text-Based Interface documentation at wolfram.com
  11. ^ Math software packs new power; new programs automate such tedious processes as solving nonlinear differential equations and converting units by Agnes Shanley, Chemical Engineering, March 1, 2002.
  12. ^ Mathematica 5.1: additional features make software well-suited for operations research professionals by ManMohan S. Sodhi, OR/MS Today, December 1, 2004.
  13. ^ The 21st annual Editors' Choice Awards, Macworld, February 1, 2006.
  14. ^ ClearSpeed Advance(TM) Accelerator Boards Certified by Wolfram Research; Math Coprocessors Enable Mathematica Users to Quadruple Performance.
  15. ^ gridMathematica offers parallel computing solution by Dennis Sellers, MacWorld, November 20, 2002.
  16. ^ Mathematica Player Pro - new Application Delivery System for Mathematica www.gizmag.com
  17. ^ Computable Document Format for Interactive Content
  18. ^ a b New Mathematica: faster, leaner, linkable and QuickTime-compatible: MathLink kit allows ties to other apps. (Wolfram Research Inc. ships Mathematica 2.1, new QuickTime-compatible version of Mathematica software) by Daniel Todd, MacWeek, June 15, 1992.
  19. ^ .NET/Link: .NET/Link is a toolkit that integrates Mathematica and the Microsoft .NET Framework.
  20. ^ Mathematica 4.2 by Charles Seiter, Macworld, November 1, 2002.
  21. ^ Mathematica 5.1 Available , Database Journal, Jan 3, 2005.
  22. ^ Mathematical Web Services: W3C Note 1 August 2003
  23. ^ Introduction to Web Services, Mathematica Web Services Tutorial
  24. ^ Haskell packages
  25. ^ Unisoftware plus
  26. ^ MrMathematica website
  27. ^ Mathematica for ActivX
  28. ^ Pythonika MathLink module for Python
  29. ^ PYML (Python Mathematica interface)
  30. ^ [1]
  31. ^ CalcLink Lauschke Consulting
  32. ^ [2] Mathematica Link for Excel
  33. ^ Mathematica Toolbox for Matlab
  34. ^ Mathsource item #618 for calling MATLAB from Mathematica Roger Germundsson from Wolfram Research
  35. ^ R-Link Calling R from within Mathematica
  36. ^ Using R's functionality with Mathematica Wolfram Technology Conference in 2006
  37. ^ http://facstaff.unca.edu/mcmcclur/Mathematica/Sage/ Calling Sage from Mathematica
  38. ^ http://facstaff.unca.edu/mcmcclur/Mathematica/Sage/UsingSage.nb A Mathematica notebook to call Sage from Mathematica.
  39. ^ [3] Manuel Kauers and Viktor Levandovskyy of the Johannes Kepler University in Austria
  40. ^ * Interface Links Origin And Mathematica Software Electronic Design
  41. ^ Mathematica Link to Labview BetterView Consulting
  42. ^ DDFLink Lauschke Consulting
  43. ^ GITM SourceForge
  44. ^ BTopTools A commercial interface to USB devices
  45. ^ Interfacing Hardware with Mathematica
  46. ^ JMath website
  47. ^ MASH website
  48. ^ http://reference.wolfram.com/mathematica/guide/ScientificAndTechnicalData.html
  49. ^ Wolfram Mathematica License Agreement
  50. ^ webMathematica terms
  51. ^ Mathematica Home Edition Released Macworld, Feb 2009
  52. ^ Supported platforms list
  53. ^ Mathematica 6 Platform Availability
  54. ^ Math, the universe, and Stephen: the author of Mathematica created a whirlwind of scientific controversy this year when, after more than 10 years of research, he published his treatise on the ability of simple structures to create unpredictable complex patterns. (2002 Scientist Of The Year).(Stephen Wolfram) by Tim Studt, R&D, November 1 , 2002.
  55. ^ A Top Scientist's Latest: Math Software by Andrew Pollack, The New York Times, June 24, 19988.
  56. ^ Quick Revision History of Mathematica
  57. ^ http://www.wolfram.com/company/scrapbook/page03.html
  58. ^ http://www.mathematica-journal.com/issue/v9i1/news.html Mathematica Journal, Volume 9, Issue 1
  59. ^ Supercomputer Pictures Solve the Once Insoluble, John Markoff, October 30, 1988.
  60. ^ [4], Nasser M. Abbasi.
  61. ^ Mathematica 1.1. Biotechnology Software. Vogel, W. K. (1989)
  62. ^ Mathematica 1.2 adds new graphics options: upgrade also promises concurrent operations by Elinor Craig, MacWeek, July 25, 1989.
  63. ^ [5], Nasser M. Abbasi.
  64. ^ Mathematica + 283 functions = Mathematica 2.0 by Raines Cohen, MacWeek, January 15, 1991.
  65. ^ [6], Nasser M. Abbasi.
  66. ^ [7], Nasser M. Abbasi.
  67. ^ [8], Nasser M. Abbasi.
  68. ^ New version of Mathematica, Mechanical Engineering, June 1, 1993.
  69. ^ [9], Wolfram news archive, 1996.
  70. ^ [10], Nasser M. Abbasi.
  71. ^ Mathematica 4.0 by Charles Seiters, Macworld, October 1, 1999.
  72. ^ [11], Nasser M. Abbasi.
  73. ^ [12], Nasser M. Abbasi.
  74. ^ [13], Nasser M. Abbasi.
  75. ^ Mathematica 5.0 Adds Up: Exactly 15 years after Mathematica's initial release, Wolfram Research has released Mathematica , PC Magazine, September 3, 2003.
  76. ^ [14], Nasser M. Abbasi.
  77. ^ Mathematica 5.1's Web Services Add Up; Mathematica 5.1 delivers improvements over Version 5.0 that are vastly out of proportion for a .1 upgrade. by Peter Coffee, eWeek, December 6, 2004.
  78. ^ [15], Nasser M. Abbasi.
  79. ^ Mathematica hits 64-bit, MacWorld UK, July 13, 2005.
  80. ^ [16] Today, Mathematica is reinvented - Blog by Stephen Wolfram
  81. ^ Mathematica 6: Felix Grant finds that version 6 of Wolfram Research's symbolic mathematical software really does live up to its expectations. Scientific Computing, 2007.
  82. ^ [17], Wolfram Blog, 2007.
  83. ^ [18], Mathematica Quick Revision History.
  84. ^ [19], Mathematica Quick Revision History.
  85. ^ [20], Mathematica 7.0 Released Today! - Blog by Stephen Wolfram
  86. ^ [21], Announcing Mathematica 7.0.1.

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