Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.
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 MathML 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 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.
Educational mathematics software
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.
Solvers
Equation solvers
Optimization software
SMT solvers CVC Yices Z3 Theorem Prover
Theorem-provers
Cryptography
Statistics
Statistical software
Theorem provers and proof assistants
Proof assistants
Theorem provers
Geometry
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.
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
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
Java
.NET
Perl
Open-source Perl Data Language
Python
Open-source CuPy Dask Manim Matplotlib NetworkX NumPy PyMC SciPy SymPy Theano
List of mathematical software
Mathematical notation software
Spreadsheet software
Mathematical art software
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