Mathematical software is

software Software consists of computer programs that instruct the Execution (computing), execution of a computer. Software also includes design documents and specifications. The history of software is closely tied to the development of digital comput ...

used to

model A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided in ...

, analyze or calculate numeric, symbolic or geometric data.

Evolution of mathematical software

Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

and

symbolic computation In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions ...

had been in most important place of the subject, but other kind of them is also growing now. A useful mathematical knowledge of such as

algorism Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system ...

which exist before the

invention An invention is a unique or novelty (patent), novel machine, device, Method_(patent), method, composition, idea, or process. An invention may be an improvement upon a machine, product, or process for increasing efficiency or lowering cost. It m ...

electronic computer A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as ''programs'', wh ...

, helped to mathematical software developing. On the other hand, by the growth of

computing power In computing, computer performance is the amount of useful work accomplished by a computer system. Outside of specific contexts, computer performance is estimated in terms of accuracy, efficiency and speed of executing computer program instruction ...

(such as seeing on

Moore's law Moore's law is the observation that the Transistor count, number of transistors in an integrated circuit (IC) doubles about every two years. Moore's law is an observation and Forecasting, projection of a historical trend. Rather than a law of ...

), the new treatment (for example, a new kind of technique such as

data assimilation Data assimilation refers to a large group of methods that update information from numerical computer models with information from observations. Data assimilation is used to update model states, model trajectories over time, model parameters, and ...

which combined numerical analysis and

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

) needing conversely the progress of the

mathematical science The Mathematical Sciences are a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper. Statist ...

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

.
The progress of mathematical information presentation such as

TeX Tex, TeX, TEX, may refer to: People and fictional characters * Tex (nickname), a list of people and fictional characters with the nickname * Tex Earnhardt (1930–2020), U.S. businessman * Joe Tex (1933–1982), stage name of American soul singer ...

MathML Mathematical Markup Language (MathML) is a pair of mathematical markup languages, an application of XML for describing mathematical notations and capturing both its structure and content. Its aim is to natively integrate mathematical formulae ...

will demand to evolution form ''formula manipulation language'' to true ''mathematics manipulation language'' (notwithstanding the problem that whether mathematical theory is inconsistent or not). And popularization of general purpose mathematical software, special purpose mathematical software so called ''one purpose software'' which used special subject will alive with adapting for environment progress at normalization of platform. So the diversity of mathematical software will be kept.

Solvers

Software calculator

A software calculator allows the user to perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output is a text label.

Computer algebra systems

Many mathematical suites are

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

s that use

symbolic mathematics In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions ...

. They are designed to solve classical algebra equations and problems in human readable notation.

Cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

Comparison of cryptography libraries The tables below compare cryptography libraries that deal with cryptography algorithms and have ''application programming interface'' (API) function calls to each of the supported features. Cryptography libraries FIPS 140 This table denote ...

Statistics

Theorem provers and proof assistants

Optimization software

Geometry

Numerical analysis

The

Netlib Netlib is a repository of software for scientific computing maintained by AT&T, Bell Laboratories, the University of Tennessee and Oak Ridge National Laboratory. Netlib comprises many separate programs and libraries. Most of the code is written in ...

repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL,

NMath NMath is a numerical package for the Microsoft .NET Framework. It is developed by CenterSpace Software. Version 1.0 was released in March, 2003 as NMath Core. The current version is called NMath 7.1, released in December, 2019. NMath is built o ...

and NAG libraries; a free alternative is the

GNU Scientific Library The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics and science. The GSL is written in C (programming language), C; wrappers are available for other programming languages. The GSL is part of ...

. A different approach is taken by the

Numerical Recipes ''Numerical Recipes'' is the generic title of a series of books on algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a cla ...

library, where emphasis is placed on clear understanding of algorithms. Many

s (listed above) can also be used for numerical computations.

Music mathematics software

''Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.'' * Musimat (by

Gareth Loy Gareth Loy is an American author, composer, musician and mathematician. He is the author of the two volume series about the intersection of music and mathematics titled ''Musimathics''. The series received generally favourable ratings. He was an ...

)

Physics

Plotting and charting

Websites

A growing number of mathematical software is available in web browsers, without the need to download or install any code. *

Desmos Desmos is an advanced graphing calculator implemented as a web application and a mobile application written in TypeScript and JavaScript. History Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, and ...

GeoGebra GeoGebra (a portmanteau of ''geometry'' and ''algebra'') is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is a ...

Jupyter Notebook Project Jupyter (pronounced "Jupiter") is a project to develop open-source software, open standards, and services for interactive computing across multiple programming languages. It was spun off from IPython in 2014 by Fernando Pérez and Bria ...

Kaggle Kaggle is a data science competition platform and online community for data science, data scientists and machine learning practitioners under Google LLC. Kaggle enables users to find and publish datasets, explore and build models in a web-based d ...

* KaTeX * OpenPlaG *

Overleaf Overleaf is software for running a collaborative cloud-based LaTeX editor used for writing, editing and publishing scientific documents. More precisely, the term "Overleaf" may refer to the free-licensed software itself, to the main website runn ...

SageMath SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentia ...

CoCalc CoCalc (formerly called SageMathCloud) is a web-based cloud computing (SaaS) and course management platform for computational mathematics. It supports editing of Sage worksheets, LaTeX documents and Jupyter notebooks. CoCalc runs an Ubuntu Linu ...

* Symbolab *

WolframAlpha WolframAlpha ( ) is an answer engine developed by Wolfram Research. It is offered as an online service that answers factual queries by computing answers from externally sourced data. History Launch preparations for WolframAlpha began on Ma ...

Biomathematics Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development ...

List of bioinformatics software {{short description, none The list of bioinformatics software tools can be split up according to the license used: * List of proprietary bioinformatics software * List of open-source bioinformatics software Alternatively, here is a categorization a ...

* Biostatistics software * List of systems biology modeling software *

List of systems biology visualization software Online software Applications References {{Reflist Systems A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environme ...

Mathematical chemistry Mathematical chemistry is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. Mathematical chemistry has also sometimes been called ...

* List of quantum chemistry and solid-state physics software *

Comparison of software for molecular mechanics modeling This is a list of computer programs that are predominantly used for molecular mechanics calculations. See also *Car–Parrinello molecular dynamics *Comparison of force-field implementations *Comparison of nucleic acid simulation software * ...

Mathematical modeling and simulations

Programming libraries

Low-level mathematical libraries intended for use within other

programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...

s: *

GNU Multiple Precision Arithmetic Library GNU Multiple Precision Arithmetic Library (GMP) is a free software, free library for arbitrary-precision arithmetic, operating on Sign (mathematics), signed integers, Rational data type, rational numbers, and Floating-point arithmetic, floating-p ...

(GMP), for high-performance

arbitrary-precision arithmetic In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are po ...

. * Class Library for Numbers, a high-level C++ library for

. *

AMD Core Math Library AMD Core Math Library (ACML) is an end-of-life software development library released by AMD, replaced by many open source libraries, including AMD libm 4.0. This library provides mathematical routines optimized for AMD processors. The successor to ...

, a software development library released by AMD * Boost, for C++

List of mathematical software

GNU Octave GNU Octave is a scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly ...

gnuplot gnuplot is a command-line and GUI program that can generate two- and three-dimensional plots of functions, data, and data fits. The program runs on all major computers and operating systems (Linux, Unix, Microsoft Windows, macOS, FreeDOS, a ...

* KCalc *

Maple (software) Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and other ...

Mathematica Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ...

* Mathcad *

Maxima (software) Maxima () is a software package for performing computer algebra calculations in mathematics and the physical sciences. It is written in Common Lisp and runs on all POSIX platforms such as macOS, Unix, BSD, and Linux, as well as under Microsoft Wi ...

* Microsoft Mathematics * MuPAD *

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...

R (programming language) R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is ...

SciPy SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, fast Fourier ...

* Matlab Simulink *

SymPy SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live or SymPy Gamma. SymPy is simple ...

TI-Nspire The TI-Nspire is a graphing calculator line made by Texas Instruments, with the first version released on 25 September 2007. The calculators feature a non-QWERTY keyboard and a different key-by-key layout than Texas Instruments's previous ...

Wolfram Alpha WolframAlpha ( ) is an answer engine developed by Wolfram Research. It is offered as an online service that answers factual queries by computing answers from externally sourced data. History Launch preparations for WolframAlpha began on Ma ...

Mathematical notation software

AUCTeX AUCTeX is an extensible package for writing and formatting TeX files in Emacs and XEmacs. Package AUCTeX provides syntax highlighting, smart indentation and formatting, previews of mathematics and other elements directly in the editing buffer, s ...

* Authorea * Apache OpenOffice Math * AsciiMath * Calligra Words - Formula editor *

* GNOME LaTeX *

GNU TeXmacs GNU TeXmacs is a scientific word processor and typesetting component of the GNU Project. It originated as a variant of GNU Emacs with TeX functionalities, though it shares no code with those programs, while using TeX fonts. It is written and maint ...

Gummi Gummies, fruitgums, gummi candies, gummy candies, or jelly sweets are a broad category of gelatin-based chewable sweets. Popular types include gummy bears, Sour Patch Kids, Jelly Babies and gummy worms. Various brands such as Bassett's, Hari ...

* KaTeX *

Kile Kile or KILE may refer to: * Darryl Kile, a Major League Baseball player * Kile, a TeX/LaTeX text editor * Kile, Warmian-Masurian Voivodeship, Poland * Kile (surname) * Kile (unit), an Ottoman unit of volume * KWCC-FM, a radio station (89.5 FM ...

LaTeX Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latices are found in nature, but synthetic latices are common as well. In nature, latex is found as a wikt:milky, milky fluid, which is present in 10% of all floweri ...

* LibreOffice Math *

LyX LyX (styled as LYX; pronounced ) is an open-source software, open source, graphical user interface document processor based on the LaTeX typesetting system. Unlike most word processors, which follow the WYSIWYG ("what you see is what you get") ...

MathJax MathJax is a cross-browser JavaScript library that displays mathematical notation in web browsers, using MathML, LaTeX, and ASCIIMathML markup. MathJax is released as open-source software under the Apache License. The MathJax project started in ...

* MathType *

Notepad++ Notepad++ (sometimes npp or NPP) is a text and source code editor for use with Microsoft Windows. It supports tabbed editing, which allows working with multiple open files in one window. The program's name comes from the C postfix increment op ...

* Scientific WorkPlace *

* Texmaker * TeXnicCenter *

TeXShop TeXShop is a free LaTeX and TeX editor and previewer for macOS. It is licensed under the GNU GPL. Details TeXShop was developed by American mathematician Richard Koch. It was modeled on NeXTstep's bundled TeXview.app and developed for the then n ...

* TeXstudio *

TeXworks TeXworks is free and open-source application software, available for Microsoft Windows, Windows, Linux and macOS. It is a Qt (software), Qt-based graphical user interface to the TeX typesetting system and its LaTeX, ConTeXt, and XeTeX extensions. ...

* Verbosus * Vim *

Visual Studio Code Visual Studio Code, commonly referred to as VS Code, is an integrated development environment developed by Microsoft for Windows, Linux, macOS and web browsers. Features include support for debugging, syntax highlighting, intelligent code comp ...

LaTeX Workshop
* WinEdt * WinFIG * WinShell

Mathematical art software

* Apophysis *

Electric Sheep Electric Sheep is a volunteer computing project for animating and evolving fractal flames, which are in turn distributed to the networked computers, which display them as a screensaver. Process The process is transparent to the casual user, ...

* Fractint * Fyre * Mandelbulb * MilkDrop * openPlaG * Ultra Fractal * XaoS * R / R Mandelbrot sets * Sterling * Bryce * Picogen *

Terragen Terragen is a scenery generator program for Microsoft Windows and Mac OS X developed and published by Planetside Software. It can be used to create renderings and animations of landscapes. History Released in stages (tech preview and beta ...

Grapher Grapher is a computer program bundled with macOS since version 10.4 that is able to create 2D and 3D graphs from simple and complex equations. It includes a variety of samples ranging from differential equations to 3D-rendered Toroids and ...

Winplot Winplot is a general-purpose plotting utility for Microsoft Windows that can draw (and animate) curves and surfaces presented in a variety of formats. The final 2012 release of Winplot can run on Windows 95, 98, Me, 2000, XP, Vista, 7. It may als ...

* Processing *

Grasshopper 3D Grasshopper is a visual programming language and environment that runs within the Rhinoceros 3D computer-aided design (CAD) application. The program was created by David Rutten, at Robert McNeel & Associates. Programs are created by dragging comp ...

* P5.js *

matplotlib Matplotlib (portmanteau of MATLAB, plot, and library) is a Plotter, plotting Library (computer science), library for the Python (programming language), Python programming language and its Numerical analysis, numerical mathematics extension NumPy. ...

* Inkscape spirograph *

Wolfram Mathematica Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ...

Houdini Erik Weisz (March 24, 1874 – October 31, 1926), known professionally as Harry Houdini ( ), was a Hungarian-American escapologist, illusionist, and stunt performer noted for his escape acts. Houdini first attracted notice in vaudeville in ...

* TouchDesigner * Unity (with math plugins)https://assetstore.unity.com/packages/3d/environments/neurofractals-pack-124436 *

(

PGF/TikZ PGF/Ti''k''Z is a pair of languages for producing vector graphics (e.g., technical illustrations and drawings) from a geometric/algebraic description, with standard features including the drawing of points, lines, arrows, paths, circles, ellipse ...

, PGFPlots) * Manim *

D3.js D3.js (also known as D3, short for Data-Driven Documents) is a JavaScript library for producing dynamic, interactive data visualizations in web browsers. It makes use of Scalable Vector Graphics (SVG), HTML5, and Cascading Style Sheets (CSS) stan ...

References

External links

Calcular
Database on mathematical software {{Authority control