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 ...

of electronic computer, 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 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 or

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. 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

Statistics

Theorem provers and proof assistants

Optimization software

Geometry

Numerical analysis

The Netlib 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 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 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)

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 * GeoGebra * Jupyter Notebook *

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 * SageMath - CoCalc * Symbolab * WolframAlpha

Biomathematics

* List of bioinformatics software * Biostatistics software * List of systems biology modeling software * List of systems biology visualization software

Mathematical chemistry

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

List of mathematical software

* Desmos * GeoGebra *

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 * KCalc * Maple (software) *

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) * 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 ...

* SageMath * SciPy * Matlab Simulink * SymPy *

* TI-Nspire *

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 * Authorea * Apache OpenOffice Math * AsciiMath * Calligra Words - Formula editor * CoCalc * GeoGebra * GNOME LaTeX * GNU TeXmacs * Gummi * KaTeX * Kile *

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 *

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++ * Overleaf * Scientific WorkPlace *

* Texmaker * TeXnicCenter * TeXShop * TeXstudio * TeXworks * 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 * GeoGebra * Desmos * Grapher * Winplot * Processing * Grasshopper 3D * 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. ...

* gnuplot * 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 *

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

( PGF/TikZ, PGFPlots) * Manim * D3.js

References

External links

Calcular
Database on mathematical software {{Authority control