Mathematica

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For other uses, see Mathematica (disambiguation).
"Mathematica (programming language)" and "Mathematica programming language" redirect here. For the programming language used by Mathematica, see Wolfram (programming language).
Mathematica
MathematicaSpikeyVersion9.png
Mathematica logistic bifurcation.png
Mathematica 8.0.0 GNU/Linux frontend
Developer(s) Wolfram Research
Initial release June 23, 1988 (1988-06-23)[1]
Stable release 10 (July 9, 2014 (2014-07-09)) [±]
Preview release Non [±]
Written in Wolfram Language,[2] C/C++, Java and Mathematica[3]
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/mathematica/

Mathematica is a computational software program used in many scientific, engineering, mathematical and computing fields, based on symbolic mathematics. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois.[4][5] The Wolfram Language is the programming language used in Mathematica.[6]

Features[edit]

Dini's surface plotted with adjustable parameters

Features of Mathematica include:[7]

  • Automatic translation of English sentences into Mathematica code[8]
  • 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, function and geo visualization and animation tools
  • Solvers for systems of equations, diophantine equations, ODEs, PDEs, DAEs, DDEs, SDEs 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 140 distributions.
  • Support for censored data, temporal data, time-series and unit based data
  • Calculations and simulations on random processes and queues
  • Machine learning tools for data, images and sounds
  • Computational geometry in 2D and 3D
  • Finite element analysis including 2D and 3D adaptive mesh generation
  • 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 2D and 3D image processing[9] and morphological image processing including image recognition
  • Tools for visualizing and analysing directed and undirected 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 and symbolic tensor functions
  • Libraries for signal processing including wavelet analysis on sounds, images and data
  • Linear and non-linear Control systems libraries
  • Continuous and discrete integral transforms
  • Import and export filters for data, images, video, sound, CAD, GIS,[10] 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 DLL, 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) [11] and Mathematica language in notebook when connected to the Internet

Interface[edit]

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. It includes a spell-checker but does not spell check automatically as you type.

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.

Among the alternative front ends is 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.[12] The Mathematica Kernel also includes a command line front end.[13] Other interfaces include JMath,[14] based on GNU readline and MASH[15] which runs self-contained Mathematica programs (with arguments) from the UNIX command line.

High-performance computing[edit]

In recent years, the capabilities for high-performance computing have been extended with the introduction of packed arrays (version 4, 1999)[16] and sparse matrices (version 5, 2003),[17] 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.[18] This release included CPU specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed.[19]

In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems [20] 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, since version 8 it can generate C code, which is automatically compiled by a system C compiler, such as the Intel C++ Compiler or Visual Studio 2010.

Deployment[edit]

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.[21]
  • A free-of-charge version, Wolfram CDF Player, is provided for running Mathematica programs that have been saved in the Computable Document Format (CDF).[22] It can also view standard Mathematica files, but not run them. It includes plugins for common web browsers on Windows and Macintosh.
  • 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.
  • Mathematica code can be run on a Wolfram cloud service as a web-app or as an API

Connections with other applications[edit]

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. Wolfram Research freely distributes a developer kit for linking applications written in the C programming language to the Mathematica kernel through MathLink.[23] Using J/Link.,[24] a Java program can ask Mathematica to perform computations; likewise, a Mathematica program can load Java classes, manipulate Java objects and perform method calls. Similar functionality is achieved with .NET /Link,[25] but with .NET programs instead of Java programs. Other languages that connect to Mathematica include Haskell,[26] AppleScript,[27] Racket,[28] Visual Basic,[29] Python[30][31] and Clojure.[32]

Links are available to many specialized mathematical software packages including OpenOffice.org Calc,[33] Microsoft Excel,[34] MATLAB,[35][36][37] R,[38] Sage,[39][40] SINGULAR,[41] Wolfram SystemModeler and Origin.[42] Mathematical equations can be exchanged with other computational or typesetting software via MathML.

Communication with SQL databases is achieved through built-in support for JDBC.[43] Mathematica can also install web services from a WSDL description.[44][45]

Mathematica can capture real-time data via a link to LabVIEW,[46] from financial data feeds[47] and directly from hardware devices via GPIB (IEEE 488),[48] USB[49] and serial interfaces.[50] It automatically detects and reads from HID devices.

Computable data[edit]

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).[51]

Design[edit]

Wolfram Research provides documents[52] listing the algorithms used to implement the functions in Mathematica.

Related products[edit]

Products from Wolfram Research associated with Mathematica include the following:[53]

  • webMathematica – call Mathematica through a web server
  • gridMathematica – run Mathematica across a parallel grid
  • Mathematica add-ons[54] – computational solutions and tools
  • Mobile apps – mobile Wolfram|Alpha and other computational applications
  • Wolfram|Alpha[55] – a computational knowledge engine or answer engine
  • Wolfram SystemModeler – a platform for engineering and life science modeling and simulation based on the Modelica language
  • Wolfram Finance Platform[56] – real-time data, computations, reporting, and algorithmic trading for financial applications
  • Wolfram Workbench[57] – an IDE built on Eclipse for development of Mathematica and other technologies from Wolfram Research
  • Wolfram Programming Cloud – create and deploy Wolfram Language applications in the cloud
  • Wolfram Cloud[58] – the infrastructure for Mathematica Online, Wolfram Programming Cloud, Wolfram Discovery Platform, and Wolfram Data Science Platform
  • Wolfram Data Framework (WDF)[59] – provides a standardized representation and semantic framework for real-world constructs and data
  • Computable Document Format (CDF) – a document format for dynamically generated interactive content
  • Wolfram Discovery Platform (under development)[60] – research & development workflows using the Wolfram Language and the Computable Document Format (CDF)
  • Wolfram Data Science Platform (under development)[61] – science data analysis and visualization using the Wolfram Language and the Wolfram Data Framework (WDF)

Licensing and platform availability[edit]

Mathematica is proprietary software licensed at a range of prices for commercial, educational, and other uses.[62]

Mathematica 10 is supported on various versions of Microsoft Windows (Vista, 7 and 8), Apple's OS X, Linux and Raspbian.[63] All platforms are supported with 64-bit implementations. [64] Mathematica prior to version 10 for OS X required Java SE 6 which is a deprecated component of Mavericks. 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.[65]

Version history[edit]

Mathematica built on the ideas in Cole and Wolfram's earlier Symbolic Manipulation Program (SMP).[66][67]

Wolfram Research has released the following versions of Mathematica:[68]

  • Mathematica 1.0 (June 23, 1988)[69][70][71][72]
  • Mathematica 1.1 (October 31, 1988)
  • Mathematica 1.2 (August 1, 1989)[73][72]
  • Mathematica 2.0 (January 15, 1991)[74][72]
  • Mathematica 2.1 (June 15, 1992)[72][23]
  • Mathematica 2.2 (June 1, 1993)[72][75]
  • Mathematica 3.0 (September 3, 1996)[76]
  • Mathematica 4.0 (May 19, 1999)[72][77]
  • Mathematica 4.1 (November 2, 2000)[72]
  • Mathematica 4.2 (November 1, 2002)[72]
  • Mathematica 5.0 (June 12, 2003)[72][78]
  • Mathematica 5.1 (October 25, 2004)[72][79]
  • Mathematica 5.2 (June 20, 2005)[72][80]
  • Mathematica 6.0 (May 1, 2007)[81][82]
  • Mathematica 7.0 (November 18, 2008)[83]
  • Mathematica 7.0.1 (March 5, 2009)[84]
  • Mathematica 8.0 (November 15, 2010)
  • Mathematica 8.0.1 (March 7, 2011)
  • Mathematica 8.0.4 (October 24, 2011)
  • Mathematica 9.0 (November 28, 2012)
  • Mathematica 9.0.1 (January 30, 2013)
  • Mathematica 10.0 (July 9, 2014)

Trivia[edit]

The name of the program “Mathematica” was suggested to Stephen Wolfram by Apple co-founder Steve Jobs although Stephen Wolfram had thought about it earlier and rejected it.[85]

See also[edit]

References[edit]

  1. ^ Wolfram, Stephen (23 Jun 2008), Mathematica Turns 20 Today, Wolfram, retrieved 16 May 2012 
  2. ^ Celebrating Mathematica’s First Quarter Century
  3. ^ The Software Engineering of Mathematica—Wolfram Mathematica 9 Documentation. Reference.wolfram.com. Retrieved on 2013-12-09.
  4. ^ Stephen Wolfram: Simple Solutions; The iconoclastic physicist's Mathematica software nails complex puzzles, BusinessWeek, October 3, 2005.
  5. ^ Wolfram Research Contact Info
  6. ^ Slate's article Stephen Wolfram's New Programming Language: He Can Make The World Computable, March 6, 2014. Retrieved on 2014-05-14.
  7. ^ Mathematica documentation
  8. ^ Free-Form Linguistic Input: New in Mathematica 8
  9. ^ Review: Mathematica 7. Technical computing powerhouse gets more oomph Macworld, Jan 2009
  10. ^ Mathematica 6 Labs Review Cadalyst Feb 1, 2008
  11. ^ The Free-Form Linguistics Revolution in Mathematica
  12. ^ MacWorld review of Wolfram Workbench
  13. ^ Using a Text-Based Interface documentation at wolfram.com
  14. ^ JMath website
  15. ^ MASH website
  16. ^ 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.
  17. ^ Mathematica 5.1: additional features make software well-suited for operations research professionals by ManMohan S. Sodhi, OR/MS Today, December 1, 2004.
  18. ^ The 21st annual Editors' Choice Awards, Macworld, February 1, 2006.
  19. ^ ClearSpeed Advance(TM) Accelerator Boards Certified by Wolfram Research; Math Coprocessors Enable Mathematica Users to Quadruple Performance.
  20. ^ gridMathematica offers parallel computing solution by Dennis Sellers, MacWorld, November 20, 2002.
  21. ^ Mathematica Player Pro - new Application Delivery System for Mathematica www.gizmag.com
  22. ^ Computable Document Format for Interactive Content
  23. ^ 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.
  24. ^ Mathematica 4.2 by Charles Seiter, Macworld, November 1, 2002.
  25. ^ .NET/Link: .NET/Link is a toolkit that integrates Mathematica and the Microsoft .NET Framework.
  26. ^ Haskell packages
  27. ^ Unisoftware plus
  28. ^ MrMathematica website
  29. ^ Mathematica for ActivX
  30. ^ Pythonika MathLink module for Python
  31. ^ PYML (Python Mathematica interface)
  32. ^ "Clojuratica - Home". Clojuratica.weebly.com. Retrieved 2013-08-16. 
  33. ^ CalcLink Lauschke Consulting
  34. ^ Mathematica Link for Excel
  35. ^ MATLink
  36. ^ Mathematica Toolbox for Matlab
  37. ^ Mathsource item #618 for calling MATLAB from Mathematica Roger Germundsson from Wolfram Research
  38. ^ RLink Mathematica Documentation
  39. ^ Calling Sage from Mathematica
  40. ^ A Mathematica notebook to call Sage from Mathematica.
  41. ^ Manuel Kauers and Viktor Levandovskyy of the Johannes Kepler University in Austria
  42. ^ * Interface Links Origin And Mathematica Software Electronic Design
  43. ^ Mathematica 5.1 Available , Database Journal, Jan 3, 2005.
  44. ^ Mathematical Web Services: W3C Note 1 August 2003
  45. ^ Introduction to Web Services, Mathematica Web Services Tutorial
  46. ^ Mathematica Link to Labview BetterView Consulting
  47. ^ DDFLink Lauschke Consulting
  48. ^ GITM SourceForge. Note that the GITM project currently (as of 2014-08-03) has no downloadable artefacts and appears to be inactive so GPIB support for Mathematica may not actually exist.
  49. ^ BTopTools A commercial interface to USB devices
  50. ^ Interfacing Hardware with Mathematica
  51. ^ "Scientific and Technical Data", Mathematic Guide, Wolfram Research, retrieved 16 May 2012 
  52. ^ "Wolfram Language & System Documentation Center – Some Notes on Internal Implementation". Wolfram Research. 
  53. ^ "Wolfram Products & Services". Wolfram Research. 
  54. ^ "All Mathematica Applications". Wolfram Research. 
  55. ^ "What is Wolfram|Alpha?". Wolfram Research. 
  56. ^ "Wolfram Finance Platform™". Wolfram Research. 
  57. ^ "WolframWorkbench™2". Wolfram Research. 
  58. ^ "Wolfram Cloud™". Wolfram Research. 
  59. ^ "Wolfram Data Framework™ (WDF)". Wolfram Research. 
  60. ^ "Wolfram Discovery Platform™". Wolfram Research. 
  61. ^ "Wolfram Data Science Platform™". Wolfram Research. 
  62. ^ Wolfram Mathematica License Agreement
  63. ^ Raspberry Pi Includes Mathematica for Free The Verge
  64. ^ Supported platforms list
  65. ^ Mathematica 6 Platform Availability
  66. ^ 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.
  67. ^ A Top Scientist's Latest: Math Software by Andrew Pollack, The New York Times, June 24, 1988.
  68. ^ Quick Revision History of Mathematica
  69. ^ Mathematica: The Scrapbook, Wolfram, retrieved 16 May 2012 
  70. ^ Mathematica Journal, Volume 9, Issue 1
  71. ^ Supercomputer Pictures Solve the Once Insoluble, John Markoff, October 30, 1988.
  72. ^ a b c d e f g h i j k Nasser M. Abbasi. "A little bit of Mathematica history". 
  73. ^ Mathematica 1.2 adds new graphics options: upgrade also promises concurrent operations by Elinor Craig, MacWeek, July 25, 1989.
  74. ^ Mathematica + 283 functions = Mathematica 2.0 by Raines Cohen, MacWeek, January 15, 1991.
  75. ^ New version of Mathematica, Mechanical Engineering, June 1, 1993.
  76. ^ "Wolfram News Archive". Wolfram.com. Retrieved 2013-08-16. 
  77. ^ Mathematica 4.0 by Charles Seiters, Macworld, October 1, 1999.
  78. ^ Mathematica 5.0 Adds Up: Exactly 15 years after Mathematica's initial release, Wolfram Research has released Mathematica , PC Magazine, September 3, 2003.
  79. ^ 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.
  80. ^ Mathematica hits 64-bit, MacWorld UK, July 13, 2005.
  81. ^ Today, Mathematica is reinvented - Blog by Stephen Wolfram
  82. ^ 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.
  83. ^ Mathematica 7.0 Released Today! - Blog by Stephen Wolfram
  84. ^ Announcing Mathematica 7.0.1.
  85. ^ Wolfram, Stephen (6 Oct 2011), STEVE JOBS: A FEW MEMORIES, Wolfram Alpha, retrieved 16 May 2012 

External links[edit]