Wolfram Mathematica


Wolfram Mathematica is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others. The system is used in many technical, scientific, engineering, mathematical, and computing fields. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica.

The Notebook interface

Wolfram Mathematica is split into two parts, the kernel and the front end. The kernel interprets expressions and returns result expressions, which can then be displayed by the front end.
The front end, designed by Theodore Gray in 1988, provides a graphical user interface, which allows the creation and editing of Notebook documents containing program code with Syntax highlighting, formatted text together with results including typeset mathematics, graphics, GUI components, tables, and sounds. All content and formatting can be generated algorithmically or edited interactively. Standard word processing capabilities are supported, including real-time multi-lingual spell-checking.
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 analyzed by Mathematica programs or converted to other formats.
Presenter tools support the creation of slide-show style presentations that support interactive elements and code execution during the presentation.
Among the alternative front ends is the Wolfram Workbench, an Eclipse based integrated development environment, introduced in 2006. It provides project-based code development tools for Mathematica, including revision management, debugging, profiling, and testing.
There is a plugin for IntelliJ IDEA based IDEs to work with Wolfram Language code which in addition to syntax highlighting can analyse and auto-complete local variables and defined functions.
The Mathematica Kernel also includes a command line front end. Other interfaces include JMath, based on GNU readline and WolframScript which runs self-contained Mathematica programs from the UNIX command line.

High-performance computing

Capabilities for high-performance computing were extended with the introduction of packed arrays in version 4
and sparse matrices,
and by adopting the GNU Multi-Precision Library to evaluate high-precision arithmetic.
Version 5.2 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, 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.
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 GCC or Microsoft Visual Studio.
In 2019 support was added for compiling Wolfram Language code to LLVM.

Features

Features of Wolfram Mathematica include:

Deployment

There are several ways to deploy applications written in Wolfram Mathematica:
Communication with other applications occurs through a protocol called Wolfram Symbolic Transfer Protocol. It allows communication between the Wolfram 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 programming language C to the Mathematica kernel through WSTP. Using J/Link., 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, but with.NET programs instead of Java programs. Other languages that connect to Mathematica include Haskell, AppleScript, Racket, Visual Basic, Python, and Clojure.
Mathematica supports the generation and execution of Modelica models for Systems modeling and connects with Wolfram System Modeler.
Links are available to many third party software packages including OpenOffice.org Calc, Microsoft Excel, MATLAB, R, SageMath, Singular, Wolfram SystemModeler, and Origin. It also links to the Unity game engine and the OpenAI Gym. Mathematical equations can be exchanged with other computational or typesetting software via MathML.
Mathematica includes interfaces to SQL databases, MongoDB, and it can access RDF graph databases via SPARQL. It can read and write to Multichain and Bitcoin Blockchains. Mathematica can also install web services from a Web Services Description Language description. It can access HDFS data via Hadoop..
Mathematica can call a variety of cloud services to retrieve or send data including ArXiv, Bing, ChemSpider, CrossRef, Dropbox, Facebook, Federal Reserve, Fitbit, Flickr, Google, Instagram, LinkedIn, MailChimp, Microsoft Translator, Mixpanel, OpenLibrary, OpenPHACTS, PubChem, PubMed, Reddit, RunKeeper, SeatGeek, SurveyMonkey, Twilio, Twitter, Wikipedia, and Yelp.
Mathematica can capture real-time data via a link to LabVIEW, from financial data feeds, and directly from hardware devices via GPIB, USB, and serial interfaces. It automatically detects and reads from devices following the HID USB protocol. It can read directly from a range of Vernier sensors that are Go!Link-compatible.
Mathematica can read and write to public blockchains.
It supports import and export of over 220 data, image, video, sound, computer-aided design, geographic information systems, document, and biomedical formats

Computable data

Wolfram Mathematica includes collections of curated data provided for use in computations. Mathematica is also integrated with Wolfram Alpha, an online computational knowledge answer engine 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.

Reception

BYTE in 1989 listed Mathematica as among the "Distinction" winners of the BYTE Awards, stating that it "is another breakthrough Macintosh application... it could enable you to absorb the algebra and calculus that seemed impossible to comprehend from a textbook".

Version history

Wolfram Mathematica built on the ideas in Cole and Wolfram's earlier Symbolic Manipulation Program. The name of the program "Mathematica" was suggested to Stephen Wolfram by Apple cofounder Steve Jobs although Wolfram had thought about it earlier and rejected it.
Wolfram Research has released the following versions of Mathematica: