Mathematical software

Short description: Software used in mathematical applications

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

## Contents

* 1 Evolution of mathematical software
* 2 Software calculator
* 3 Educational mathematics software
* 3.1 Mathematical education video games
* 4 Computer algebra systems
* 5 Solvers
* 5.1 Equation solvers
* 5.2 Optimization software
* 5.3 SMT solvers
* 5.4 Theorem-provers
* 6 Cryptography
* 7 Statistics
* 7.1 Statistical software
* 8 Theorem provers and proof assistants
* 8.1 Proof assistants
* 8.2 Theorem provers
* 9 Geometry
* 10 Numerical analysis
* 11 Music mathematics software
* 12 Physics
* 13 Plotting and charting
* 14 Websites
* 15 Biomathematics
* 16 Mathematical chemistry
* 17 Mathematical modeling and simulations
* 18 Mathematical and numerical libraries
* 18.1 C
* 18.1.1 Open-source
* 18.1.2 Proprietary
* 18.2 C++
* 18.2.1 Open-source
* 18.3 Fortran
* 18.3.1 Open-source
* 18.3.2 Proprietary
* 18.4 Java
* 18.4.1 Open-source
* 18.4.2 Proprietary
* 18.5 .NET
* 18.5.1 Open-source
* 18.5.2 Proprietary
* 18.6 Perl
* 18.6.1 Open-source
* 18.7 Python
* 18.7.1 Open-source
* 19 List of mathematical software
* 20 Mathematical notation software
* 21 Spreadsheet software
* 22 Mathematical art software
* 23 See also
* 24 References
* 25 External links

## Evolution of mathematical software

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.

## Software calculator

Main article: Engineering: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.

* DeskCalc
* Desmos
* Mac OS calculator
* Calculator (Nintendo Switch)
* Grapher
* GeoGebra
* GNOME Calculator
* GraphCalc
* KCalc
* Qalculate!
* Windows Calculator
* WRPN Calculator
* xcalc

## Educational mathematics software

See also: Computer-based mathematics education and Computer-Based Math

* Accelerated Math
* Algebrator
* Cantor
* DataScene
* Desmos
* DrGeo
* GeoGebra
* Mathletics
* Maths Pathway
* Mathspace
* Microsoft Math Solver
* StatCrunch
* Statistics Online Computational Resource
* Symbolab
* TK Solver
* WolframAlpha
* Zearn

### Mathematical education video games

* DragonBox
* Tux, of Math Command

## Computer algebra systems

Main article: Software: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.

* Axiom
* Cadabra
* FriCAS
* GAP
* GNU Octave
* Magma
* Magnus
* Maple
* Mathcad
* Mathematica
* Mathomatic
* Maxima
* PARI/GP
* REDUCE
* SageMath
* Scilab
* SMath Studio
* Symbolic Math Toolbox (MATLAB)
* SymPy
* Wolfram Alpha
* Xcas / Giac
* Yacas

## Solvers

This section is an excerpt from Solver[ edit ]

### Equation solvers

* Maxima
* Mathematica
* Maple
* SageMath
* SymPy

### Optimization software

See also: Software:List of optimization software

* ADMB
* ALGLIB
* AIMMS
* AMPL
* ANTIGONE
* APMonitor
* ASCEND
* BARON
* CasADi
* COIN-OR
* Concorde TSP Solver
* Couenne
* CPLEX
* CUTEr
* Dlib
* FICO Xpress
* Galahad library
* GEKKO
* GLPK
* Gurobi Optimizer
* HiGHS
* IPOPT
* Lp solve
* MIDACO
* MiniZinc
* MINOS
* MINUIT
* MOSEK
* NEOS Server
* OpenMDAO
* OR-Tools
* Pyomo
* SCIP
* SciPy
* SNOPT
* TOMLAB
* WORHP

### SMT solvers

* CVC
* Yices
* Z3 Theorem Prover

### Theorem-provers

* ACL2
* Coq (now Rocq)
* HOL Light
* HOL4
* Isabelle
* Lean
* Metamath
* Mizar
* NuPRL
* Twelf

## Cryptography

See also: Comparison of cryptography libraries

* Botan
* Bouncy Castle
* BSAFE
* cryptlib
* Crypto++
* GnuTLS
* JCA / JCE
* Libgcrypt
* libsodium
* Mbed TLS
* NaCl
* Nettle
* NSS
* OpenSSL
* wolfCrypt

## Statistics

See also: Software:List of statistical software, List of data science software, Data analysis software, and Comparison of statistical packages

### Statistical software

* ADaMSoft
* ADMB
* Alt-Ergo
* Alteryx
* Analytica
* Angoss
* ASReml
* BMDP
* BV4.1
* CARINE
* Chronux
* CSPro
* DAP
* Dataplot
* DataGraph
* EViews
* FAME
* Fityk
* GAUSS
* GeoDA
* Genedata
* GenStat
* GLIM
* GNU Octave
* GraphPad InStat
* GraphPad Prism
* gretl
* Igor Pro
* IMSL Numerical Libraries
* jamovi
* JASP
* JMulTi
* JMP
* KNIME
* LabPlot
* LIBSVM
* LIMDEP
* LISREL
* MATLAB
* Mathematica
* MedCalc
* MINUIT
* Minitab
* MLwiN
* Mondrian
* NAG Numerical Library
* NCSS
* Neural Designer
* NLOGIT
* nQuery Sample Size Software
* O-Matrix
* OpenBUGS
* OpenEpi
* OpenMx
* OpenNN
* Orange
* OriginPro
* Pandas
* PASS Sample Size Software
* Perl Data Language
* Ploticus
* Primer-E Primer
* PSPP
* PV-WAVE
* Qlucore
* RapidMiner
* R
* RATS
* ROOT
* Salstat
* S-PLUS
* SAS
* Scilab
* SciPy
* Shogun (toolbox)
* Simfit
* SOCR
* SOFA Statistics
* SPSS
* SPSS Modeler
* Stan
* StatCrunch
* Statgraphics
* Statistica
* StatsDirect
* StatXact
* Stata
* SYSTAT
* TOPCAT
* Torch
* WarpPLS
* Weka
* WinBUGS
* Winpepi
* Wolfram Language
* World Programming System
* X-13ARIMA-SEATS
* XploRe

## Theorem provers and proof assistants

### Proof assistants

* ACL2
* Agda
* Albatross
* ETPS
* F*
* HOL theorem prover
* HOL Light
* HOL4
* Isabelle
* Jape
* Lean
* LEGO
* Matita
* Metamath
* MINLOG
* Mizar
* Nqthm
* NuPRL
* PhoX
* PVS
* Rocq
* Theorem Proving System
* Twelf

### Theorem provers

* Alt-Ergo
* Automath
* CARINE
* CVC
* E
* IsaPlanner
* LCF
* Mizar
* NuPRL
* Paradox
* Prover9
* PVS
* ResearchCyc
* SPARK (programming language)
* Twelf
* Wolfram Mathematica
* Z3 Theorem Prover

## Geometry

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

* Archimedes Geo3D
* Cabri Geometry
* CaRMetal
* Cinderella
* Dr. Geo
* GeoGebra
* Geometry Expert
* GEUP
* Kig
* KSEG
* The Geometer's Sketchpad
* TracenPoche
* WIRIS

## Numerical analysis

See also: Software: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

Main article: Software:List of music software

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

* jMusic
* Musimat (by Gareth Loy)[4]
* OpenMusic
* Opusmodus
* Rubato Composer
* SuperCollider
* UPIC

## Physics

See also: Software:List of computational physics software, Open-source physics software, and Computational physics

* Comparison of electromagnetic simulation software
* List of cosmological computation software
* List of computational fluid dynamics software
* List of software for Monte Carlo molecular modeling

## Plotting and charting

## Websites

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

* Desmos
* GeoGebra
* Google Colaboratory
* Jupyter Notebook
* Kaggle
* KaTeX

* OpenPlaG
* Overleaf
* SageMath – CoCalc
* Symbolab
* WolframAlpha

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## 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

## Mathematical modeling and simulations

See also: Software:List of computer simulation software

* Conway's Game of Life

## Mathematical and numerical libraries

See also: Software:List of numerical libraries, Comparison of linear algebra libraries, List of automated theorem provers, and Convex optimization software

### C

#### Open-source

* Basic Linear Algebra Subprograms
* Fastest Fourier Transform in the West
* GNU MPFR
* GNU Multi-Precision Library
* GNU Scientific Library
* hypre
* Integer set library
* Libfixmath
* OpenBLAS
* UMFPACK

#### Proprietary

* Intel Math Kernel Library

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### C++

See also: Software:List of C++ multiple precision arithmetic libraries

#### Open-source

* Adept
* Advanced Simulation Library
* Armadillo
* Blitz++
* Boost.uBLAS
* CGAL
* Class Library for Numbers
* deal.II
* Eigen
* GetFEM++
* IML++
* IT++
* LAPACK++
* Matrix Template Library
* MFEM
* Multiple Precision Integers and Rationals
* Number Theory Library
* SU2 code
* Template Numerical Toolkit
* Trilinos

### Fortran

#### Open-source

* ARPACK
* Automatically Tuned Linear Algebra Software
* BLAS
* BLIS
* EISPACK
* LAPACK
* Librsb
* LINPACK
* Lis
* MINPACK
* PETSc
* QUADPACK
* SLATEC
* SOFA

#### Proprietary

* IMSL Numerical Libraries
* NAG Numerical Library

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### Java

#### Open-source

* Colt
* Efficient Java Matrix Library
* JAMA
* Matrix Toolkit Java
* ojAlgo
* Parallel Colt

#### Proprietary

* OptimJ
* SuanShu numerical library

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### .NET

#### Open-source

* Accord.NET
* Math.NET Numerics
* Meta.Numerics

#### Proprietary

* ALGLIB
* NMath

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### Perl

#### Open-source

* Perl Data Language

### Python

#### Open-source

* CuPy
* Dask
* Manim
* Mathics
* Matplotlib
* NetworkX
* NumPy
* PyMC
* SciPy
* SymPy
* Theano

## List of mathematical software

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

* Axiom
* Calcpad
* Desmos
* GeoGebra
* GNU Octave
* gnuplot
* KCalc
* Maple
* Mathematica
* Mathcad
* Maxima

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

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## Mathematical notation software

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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## Spreadsheet software

See also: Software:List of spreadsheet software

* Apache OpenOffice Calc
* Airtable
* Calligra Sheets
* Coda
* GNU Oleo
* Gnumeric
* Google Sheets
* KSpread
* LibreOffice Calc
* Lotus 1-2-3
* Microsoft Excel
* Numbers
* PlanMaker
* Pyspread
* Quattro Pro
* sc
* Smartsheet
* WPS Office
* Zoho Sheet

## Mathematical art software

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

* Computational mathematics
* Comparison of formula editors
* Gödel's incompleteness theorems
* List of information graphics software
* List of MATLAB software and tools
* Mathlete
* MathOverflow
* Plot (graphics)
* Time complexity

## References

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. ↑ "Ultimate Math Library | Utilities Tools | Unity Asset Store". https://assetstore.unity.com/packages/tools/utilities/ultimate-math-library-228481.
7. ↑ "Math Equation Writer | GUI Tools | Unity Asset Store". https://assetstore.unity.com/packages/tools/gui/math-equation-writer-199520.
8. ↑ "MathPlus Library | Game Toolkits | Unity Asset Store". https://assetstore.unity.com/packages/tools/game-toolkits/mathplus-library-72197.
9. ↑ "Smithy Procedural Generation Framework". https://www.evilwizardstudios.com/smithy/.
10. ↑ "NeuroFractals Pack | 3D Environments | Unity Asset Store". https://assetstore.unity.com/packages/3d/environments/neurofractals-pack-124436.

## External links

* swMATH Database on mathematical software

Template:Applied mathematics

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