Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.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).
Evolution of mathematical software
Mathematical knowledge of techniques such as algorisms which existed before the invention of the electronic computer, helped to develop mathematical software. On the other hand, due to the growth of computing power (such as Moore's law), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics) needed the progress of the mathematical science or applied mathematics. The progress of mathematical information presentation such as TeX or MathMLBoth 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. will demand to evolution form formula manipulation language to true mathematics manipulation language (not withstanding the problem that whether mathematical theory is inconsistent or not). And popularisation of general purpose mathematical software, special purpose mathematical softwareIncluded your written script code on the general purpose mathematical software. so called one purpose software which use special subjects will adapt for environmental progress at the normalisation of the platform, keeping the diversity of mathematical software.
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) 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)Musimathics website, freeware download 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.Internet Accessible Mathematical Computation , Institute for Computational Mathematics, Kent State University, retrieved 2015-02-15.
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
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
Proprietary IMSL Numerical Libraries NAG Numerical Library
Java
Open-source Colt Efficient Java Matrix Library JAMA Matrix Toolkit Java ojAlgo Parallel Colt
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
Artificial intelligence for mathematics AlphaDev – algorithm discovery AlphaEvolve – mathematical and algorithm discovery AlphaGeometry – geometry problem solving AlphaTensor – matrix multiplication discovery FunSearch – mathematical discovery Ramanujan machine – conjecture discovery
See also Computational mathematics Comparison of formula editors Gödel's incompleteness theorems List of information graphics software List of MATLAB software and tools List of open-source software for mathematics Mathlete MathOverflow Plot (graphics) Time complexity
References
External links swMATH Database on mathematical software