Mathematical software

{{Short description|Software used in mathematical applications}} '''Mathematical software''' is software used to model, analyze or calculate numeric, symbolic or geometric data.<ref>See, e.g., the [http://toms.acm.org/Charter.html editorial charter] of the ''ACM Transactions on Mathematical Software'' or the [http://gams.nist.gov/cgi-bin/serve.cgi problem taxonomy] of the National Institute of Standards and Technology Guide to Available Mathematical Software (both retrieved 2015-02-15).</ref>

==Evolution of mathematical software== {{cleanup rewrite|section=yes|date=May 2021}} 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<ref>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.</ref> 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<ref>Included your written script code on the general purpose mathematical software.</ref> 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|Software calculator}} {{See also|List of software calculators}} 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.

{{div col|colwidth=18em}} * DeskCalc * Desmos * Mac OS calculator * Calculator (Nintendo Switch) * Grapher * GeoGebra * GNOME Calculator * GraphCalc * KCalc * Qalculate! * Windows Calculator * WRPN Calculator * xcalc {{div col end}}

== Educational mathematics software == {{See also|Computer-based mathematics education|Computer-Based Math}} {{div col|colwidth=18em}} * 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 {{div col end}}

=== Mathematical education video games === * DragonBox * Tux, of Math Command

==Computer algebra systems== {{main|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. {{div col|colwidth=18em}} * 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 {{div col end}}

==Solvers== {{Excerpt|Solver}}

=== Equation solvers === {{div col|colwidth=18em}} * Maxima * Mathematica * Maple * SageMath * SymPy {{div col end}}

=== Optimization software === {{See also|List of optimization software}} {{div col|colwidth=18em}} * 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 {{div col end}}

=== SMT solvers === * CVC * Yices * Z3 Theorem Prover

=== Theorem-provers === {{div col|colwidth=18em}} * ACL2 * Coq (now Rocq) * HOL Light * HOL4 * Isabelle * Lean * Metamath * Mizar * NuPRL * Twelf {{div col end}}

==Cryptography== {{See also|Comparison of cryptography libraries}} {{div col|colwidth=18em}} * Botan * Bouncy Castle * BSAFE * cryptlib * Crypto++ * GnuTLS * JCA / JCE * Libgcrypt * libsodium * Mbed TLS * NaCl * Nettle * NSS * OpenSSL * wolfCrypt {{div col end}}

==Statistics== {{See also|List of statistical software|List of data science software|Category:Data analysis software|l3=Data analysis software|Comparison of statistical packages}} === Statistical software === {{div col|colwidth=18em}} * 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 {{div col end}}

==Theorem provers and proof assistants== {{main|List of proof assistants|List of theorem provers}} ===Proof assistants=== {{div col|colwidth=18em}} * 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 {{div col end}}

=== Theorem provers === {{div col|colwidth=18em}} * Alt-Ergo * Automath * CARINE * CVC * E * IsaPlanner * LCF * Mizar * NuPRL * Paradox * Prover9 * PVS * ResearchCyc * SPARK (programming language) * Twelf * Wolfram Mathematica * Z3 Theorem Prover {{div col end}}

==Geometry== {{main|List of interactive geometry software|List of information graphics software}} {{div col|colwidth=18em}} * Archimedes Geo3D * Cabri Geometry * CaRMetal * Cinderella * Dr. Geo * GeoGebra * Geometry Expert * GEUP * Kig * KSEG * The Geometer's Sketchpad * TracenPoche * WIRIS {{div col end}}

==Numerical analysis== {{See also|List of numerical-analysis software|List of programming languages by type#Numerical analysis|l2=List of numerical analysis programming languages|Comparison of numerical-analysis software|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|List of music software}} {{see also|Music and mathematics}} ''Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.'' * jMusic * Musimat (by Gareth Loy)<ref>[http://www.musimat.com/ Musimathics website, freeware download]</ref> * OpenMusic * Opusmodus * Rubato Composer * SuperCollider * UPIC

==Physics== {{See also|List of computational physics software|List of free and open-source software packages#Physics|l2=Open-source physics software|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== {{See also|Category:Plotting software|l1=Plotting software|Category:Free plotting software|l2=Free plotting software|List of information graphics software|List of charting software|Comparison of JavaScript charting libraries|Category:Diagramming software|l6=Diagramming software}}

==Websites== A growing number of mathematical software is available in web browsers, without the need to download or install any code.<ref>[http://icm.mcs.kent.edu/research/iamc.html Internet Accessible Mathematical Computation] {{Webarchive|url=https://web.archive.org/web/20170628180519/http://icm.mcs.kent.edu/research/iamc.html |date=2017-06-28 }}, Institute for Computational Mathematics, Kent State University, retrieved 2015-02-15.</ref> {{col-begin|width=65%}} {{col-2}} * Desmos * GeoGebra * Google Colaboratory * Jupyter Notebook * Kaggle * KaTeX {{col-2}} * OpenPlaG * Overleaf * SageMath – CoCalc * Symbolab * WolframAlpha {{col-end}}

==Biomathematics== {{See also|Computational Biology|Biophysics}} * 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|List of computer simulation software}} * Conway's Game of Life

==Mathematical and numerical libraries== {{see also|List of numerical libraries|Comparison of linear algebra libraries|List of automated theorem provers|onvex optimization#Software|l4=Convex optimization software}} === C === {{col-begin}} {{col-break}} ==== 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 <div style="height:1em;"></div> {{col-break}}

==== Proprietary ==== * Intel Math Kernel Library {{col-end}}

=== C++ === {{See also|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 === {{col-begin}} {{col-break}} ==== Open-source ==== * ARPACK * Automatically Tuned Linear Algebra Software * BLAS * BLIS * EISPACK * LAPACK * Librsb * LINPACK * Lis * MINPACK * PETSc * QUADPACK * SLATEC * SOFA <div style="height:1em;"></div> {{col-break}}

==== Proprietary ==== * IMSL Numerical Libraries * NAG Numerical Library {{col-end}}

=== Java === {{col-begin}} {{col-break}} ==== Open-source ==== * Colt * Efficient Java Matrix Library * JAMA * Matrix Toolkit Java * ojAlgo * Parallel Colt <div style="height:1em;"></div> {{col-break}}

==== Proprietary ==== * OptimJ * SuanShu numerical library {{col-end}}

=== .NET === {{col-begin}} {{col-break}} ==== Open-source ==== * Accord.NET * Math.NET Numerics * Meta.Numerics {{col-break}}

==== Proprietary ==== * ALGLIB * NMath {{col-end}}

=== Perl === ==== Open-source ==== * Perl Data Language

=== Python === ==== Open-source ==== * CuPy * Dask * Manim * Matplotlib * NetworkX * NumPy * PyMC * SciPy * SymPy * Theano

== List of mathematical software == {{See also|Comparison of software calculators|List of open-source software for mathematics|List of charting software}} {{col-begin|width=70%}} {{col-2}} * Axiom * Calcpad * Desmos * GeoGebra * GNU Octave * gnuplot * KCalc * Maple (software) * Mathematica * Mathcad * Maxima (software) {{col-2}} * Microsoft Mathematics * MuPAD * MATLAB * R (programming language) * SageMath * SciPy * Matlab Simulink * SymPy * TeX * TI-Nspire * Wolfram Alpha {{col-end}}

== Mathematical notation software == {{See also|Mathematical notation|Typesetting|Comparison of TeX editors}} {{col-begin|width=70%}} {{col-2}} * 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 {{col-2}} * MathType * Notepad++ * Overleaf * Scientific WorkPlace * TeX * Texmaker * TeXnicCenter * TeXShop * TeXstudio * TeXworks * Verbosus * Vim * Visual Studio Code – * WinEdt * WinFIG * WinShell {{col-end}}

== Spreadsheet software == {{See also|List of spreadsheet software}} {{div col|colwidth=18em}} * 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 {{div col end}}

==Mathematical art software== {{Main|List of mathematical art software}} {{col-begin|width=70%}} {{col-2}} * Apophysis * Electric Sheep * Fractint * Fyre * Mandelbulb * MilkDrop * openPlaG * Ultra Fractal * XaoS * R / R Mandelbrot sets * Sterling * Bryce * Picogen * Terragen * GeoGebra * Desmos {{col-2}} * Grapher * Winplot * Processing * Grasshopper 3D * P5.js * matplotlib * gnuplot * Inkscape spirograph * Wolfram Mathematica * Houdini * MATLAB * TouchDesigner * Unity (with math plugins)<ref>{{cite web | title=Ultimate Math Library | Utilities Tools | Unity Asset Store | url=https://assetstore.unity.com/packages/tools/utilities/ultimate-math-library-228481 }}</ref><ref>{{Cite web | title=Math Equation Writer {{!}} GUI Tools {{!}} Unity Asset Store | url=https://assetstore.unity.com/packages/tools/gui/math-equation-writer-199520 | access-date=2025-08-06 | website=assetstore.unity.com}}</ref><ref>{{cite web | title=MathPlus Library | Game Toolkits | Unity Asset Store | url=https://assetstore.unity.com/packages/tools/game-toolkits/mathplus-library-72197 }}</ref><ref>{{cite web | title=Smithy Procedural Generation Framework | url=https://www.evilwizardstudios.com/smithy/ }}</ref><ref>{{Cite web | title=NeuroFractals Pack {{!}} 3D Environments {{!}} Unity Asset Store | url=https://assetstore.unity.com/packages/3d/environments/neurofractals-pack-124436 | access-date=2025-08-06 | website=assetstore.unity.com}}</ref> * LaTeX (PGF/TikZ, PGFPlots) * Manim * D3.js {{col-end}}

==References== {{reflist}}

==External links== * [https://zbmath.org/software/ swMATH] Database on mathematical software

Category:Mathematical software