Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.
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.<br />
The progress of mathematical information presentation such as TeX or MathML 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.
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
- 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
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
Equation solvers
- Maxima
- Mathematica
- Maple
- SageMath
- SymPy
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
- Botan
- Bouncy Castle
- BSAFE
- cryptlib
- Crypto++
- GnuTLS
- JCA / JCE
- Libgcrypt
- libsodium
- Mbed TLS
- NaCl
- Nettle
- NSS
- OpenSSL
- wolfCrypt
Statistics
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
- Archimedes Geo3D
- Cabri Geometry
- CaRMetal
- Cinderella
- Dr. Geo
- GeoGebra
- Geometry Expert
- GEUP
- Kig
- KSEG
- The Geometer's Sketchpad
- TracenPoche
- WIRIS
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. 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
Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.
- jMusic
- Musimat (by Gareth Loy)
- OpenMusic
- Opusmodus
- Rubato Composer
- SuperCollider
- UPIC
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.
- Desmos
- GeoGebra
- Google Colaboratory
- Jupyter Notebook
- Kaggle
- 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
Mathematical modeling and simulations
- Conway's Game of Life
Mathematical and numerical libraries
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
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Proprietary
- Intel Math Kernel Library
C++
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
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Proprietary
- IMSL Numerical Libraries
- NAG Numerical Library
Java
Open-source
- Colt
- Efficient Java Matrix Library
- JAMA
- Matrix Toolkit Java
- ojAlgo
- Parallel Colt
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Proprietary
- OptimJ
- SuanShu numerical library
.NET
Open-source
- Accord.NET
- Math.NET Numerics
- Meta.Numerics
Proprietary
- ALGLIB
- NMath
Perl
Open-source
- Perl Data Language
Python
Open-source
- CuPy
- Dask
- Manim
- Matplotlib
- NetworkX
- NumPy
- PyMC
- SciPy
- SymPy
- Theano
List of mathematical software
- Axiom
- Calcpad
- 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
Mathematical notation software
- 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 –
- WinEdt
- WinFIG
- WinShell
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
- 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)
- LaTeX (PGF/TikZ, PGFPlots)
- Manim
- D3.js
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
External links
- swMATH Database on mathematical software