Mathematical software

Software used in mathematical applications

Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.[1]

## Evolution of mathematical software

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Numerical analysis and symbolic computation 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 which exist before the invention of electronic computer, helped to mathematical software developing. On the other hand, by the growth of computing power (such as seeing on Moore's law), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics) needing conversely the progress of the mathematical science or applied mathematics.
The progress of mathematical information presentation such as TeX or MathML[2] 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[3] 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

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This section is an excerpt from Solver.[edit]

A solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.

## Software calculator

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Main article: 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

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Main article: List of computer algebra systems

Many mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human readable notation.

## Cryptography

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* Comparison of cryptography libraries

## Statistics

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See also: List of statistical software, Data mining and machine learning software, Data analysis software, and Comparison of statistical packages

## Theorem provers and proof assistants

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Main articles: List of theorem provers and List of proof assistants

## Optimization software

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Main article: List of optimization software

## Geometry

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Main articles: List of interactive geometry software and List of information graphics software

## Numerical analysis

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See also: List of numerical-analysis software, List of numerical analysis programming languages, Comparison of numerical-analysis software, and List of optimization software

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. A different approach is taken by the Numerical Recipes library, where emphasis is placed on clear understanding of algorithms.

Many computer algebra systems (listed above) can also be used for numerical computations.

## Music mathematics software

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Main article: List of music software

See also: Music and mathematics

Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.

* Musimat (by Gareth Loy)[4]

## Physics

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See also: Physics software, Open-source physics software, List of cosmological computation software, List of software for Monte Carlo molecular modeling, and Computational physics

## Plotting and charting

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See also: Plotting software, Free plotting software, List of information graphics software, List of charting software, Comparison of JavaScript charting libraries, and Diagramming software

## Websites

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A growing number of mathematical software is available in web browsers, without the need to download or install any code.[5]

* Desmos
* GeoGebra
* Jupyter Notebook
* Kaggle
* KaTeX

* OpenPlaG
* Overleaf
* SageMath \- CoCalc
* Symbolab
* WolframAlpha

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## Biomathematics

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See also: Computational Biology and Biophysics

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

## Mathematical chemistry

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* List of quantum chemistry and solid-state physics software
* Comparison of software for molecular mechanics modeling

## Mathematical modeling and simulations

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See also: List of computer simulation software

## Programming libraries

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See also: List of numerical libraries, Comparison of linear algebra libraries, and List of automated theorem provers

Low-level mathematical libraries intended for use within other programming languages:

* GNU Multiple Precision Arithmetic Library (GMP), for high-performance arbitrary-precision arithmetic.
* Class Library for Numbers, a high-level C++ library for arbitrary-precision arithmetic.
* AMD Core Math Library, a software development library released by AMD
* Boost, for C++

## List of mathematical software

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See also: Comparison of software calculators, List of open-source software for mathematics, and List of charting software

* Desmos
* GeoGebra
* GNU Octave
* gnuplot
* KCalc
* Maple (software)
* Mathematica
* Mathcad
* Maxima (software)
* Microsoft Mathematics

* MuPAD
* MATLAB
* R (programming language)
* SageMath
* SciPy
* Matlab Simulink
* SymPy
* TeX
* TI-Nspire
* Wolfram Alpha

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## Mathematical notation software

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See also: Mathematical notation, Typesetting, and Comparison of TeX editors

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

* MathType
* Notepad++
* Overleaf
* Scientific WorkPlace
* TeX
* Texmaker
* TeXnicCenter
* TeXShop
* TeXstudio
* TeXworks
* Verbosus
* Vim
* Visual Studio Code \- LaTeX Workshop
* WinEdt
* WinFIG
* WinShell

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## Mathematical art software

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Main article: List of mathematical art software

* Apophysis
* Electric Sheep
* 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
* gnuplot
* Inkscape spirograph
* Wolfram Mathematica
* Houdini
* MATLAB
* TouchDesigner
* Unity (with math plugins)[6][7][8][9][10]
* LaTeX (PGF/TikZ, PGFPlots)
* Manim
* D3.js

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## See also

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* Computational mathematics
* Computer-Based Math and computer-based mathematics education
* Comparison of formula editors
* Gödel's incompleteness theorems
* List of information graphics software
* Manim \- open-source Python mathematical animation and visualisation software
* Mathlete
* Mathethon
* Plot (graphics)
* Time complexity

## References

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1. ^ See, e.g., the editorial charter of the ACM Transactions on Mathematical Software or the problem taxonomy of the National Institute of Standards and Technology Guide to Available Mathematical Software (both retrieved 2015-02-15).
2. ^ Both MathML and TeX may be only simple a kind of computer language which enable also to present the mathematical formula. However they also may be the mathematical software if the term of software interpreted as whole technology on how to use computer, at most wide sense.
3. ^ Included your written script code on the general purpose mathematical software.
4. ^ Musimathics website, freeware download
5. ^ Internet Accessible Mathematical Computation, Institute for Computational Mathematics, Kent State University, retrieved 2015-02-15.
6. ^ https://assetstore.unity.com/packages/tools/utilities/ultimate-math-library-228481
7. ^ https://assetstore.unity.com/packages/tools/gui/math-equation-writer-199520
8. ^ https://assetstore.unity.com/packages/tools/game-toolkits/mathplus-library-72197
9. ^ https://www.evilwizardstudios.com/smithy/
10. ^ https://assetstore.unity.com/packages/3d/environments/neurofractals-pack-124436

## External links

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* Calcular Database on mathematical software

* v
* t
* e

Industrial and applied mathematics

Computational|

* Algorithms
* design
* analysis
* Automata theory
* Automated theorem proving
* Coding theory
* Computational geometry
* Constraint satisfaction
* Constraint programming
* Computational logic
* Cryptography
* Information theory
* Statistics

| Mathematical
software|

* Arbitrary-precision arithmetic
* Finite element analysis
* Tensor software
* Interactive geometry software
* Optimization software
* Statistical software
* Numerical-analysis software
* Numerical libraries
* Solvers

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Discrete|

* Computer algebra
* Computational number theory
* Combinatorics
* Graph theory
* Discrete geometry

Analysis|

* Approximation theory
* Clifford analysis
* Clifford algebra
* Differential equations
* Ordinary differential equations
* Partial differential equations
* Stochastic differential equations
* Differential geometry
* Differential forms
* Gauge theory
* Geometric analysis
* Dynamical systems
* Chaos theory
* Control theory
* Functional analysis
* Operator algebra
* Operator theory
* Harmonic analysis
* Fourier analysis
* Multilinear algebra
* Exterior
* Geometric
* Tensor
* Vector
* Multivariable calculus
* Exterior
* Geometric
* Tensor
* Vector
* Numerical analysis
* Numerical linear algebra
* Numerical methods for ordinary differential equations
* Numerical methods for partial differential equations
* Validated numerics
* Variational calculus

Probability theory|

* Distributions (random variables)
* Stochastic processes / analysis
* Path integral
* Stochastic variational calculus

Mathematical
physics|

* Analytical mechanics
* Lagrangian
* Hamiltonian
* Field theory
* Classical
* Conformal
* Effective
* Gauge
* Quantum
* Statistical
* Topological
* Perturbation theory
* in quantum mechanics
* Potential theory
* String theory
* Bosonic
* Topological
* Supersymmetry
* Supersymmetric quantum mechanics
* Supersymmetric theory of stochastic dynamics

| Algebraic
structures|

* Algebra of physical space
* Feynman integral
* Poisson algebra
* Quantum group
* Renormalization group
* Representation theory
* Spacetime algebra
* Superalgebra
* Supersymmetry algebra

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Decision sciences|

* Game theory
* Operations research
* Optimization
* Social choice theory
* Statistics
* Mathematical economics
* Mathematical finance

Other applications|

* Biology
* Chemistry
* Psychology
* Sociology
* "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"

Related|

* Mathematics

Organizations|

* Society for Industrial and Applied Mathematics
* Japan Society for Industrial and Applied Mathematics
* Société de Mathématiques Appliquées et Industrielles
* International Council for Industrial and Applied Mathematics
* European Community on Computational Methods in Applied Sciences

* Category
* Mathematics portal / outline / topics list

Authority control databases: National |

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