Free Open Source Mathematics Software

Maxima is a computer algebra system comparable to commercial systems like Mathematica and Maple. It emphasizes symbolic mathematical computation: algebra, trigonometry, calculus, and much more. For example, Maxima solves x^2-r*x-s^2-r*s=0 giving the symbolic results [x=r+s, x=-s]. Maxima can calculate with exact integers and fractions, native floating-point and high-precision big floats. Maxima has user-friendly front-ends, an on-line manual, plotting commands, and numerical libraries. Users can write programs in its native programming language, and many have contributed useful packages in a variety of areas over the decades. Maxima is GPL-licensed and largely written in Common Lisp. Executables can be downloaded for Windows, Mac, Linux, and Android; source code is also available. An active community maintains and extends the system. Maxima is widely used. Additional add-on packages for Maxima can be found at: https://github.com/maxima-project-on-github/maxima-packages

A famous scientific plotting package, features include 2D and 3D plotting, a huge number of output formats, interactive input or script-driven options, and a large set of scripted examples.

gretl is a cross-platform software package for econometric analysis, written in the C programming language.

Open tool platform for the cost effective rigorous development of dependable complex software systems services. This platform is based on the event-B formal method and provides natural support for refinement and mathematical proof.

SciDAVis is a user-friendly data analysis and visualization program primarily aimed at high-quality plotting of scientific data. It strives to combine an intuitive, easy-to-use graphical user interface with powerful features such as Python scriptability.

JAGS is Just Another Gibbs Sampler. It is a program for the statistical analysis of Bayesian hierarchical models by Markov Chain Monte Carlo.

* Fast C++ library for linear algebra (matrix maths) and scientific computing * Easy to use functions and syntax, deliberately similar to Matlab / Octave * Uses template meta-programming techniques to increase efficiency * Provides user-friendly wrappers for OpenBLAS, Intel MKL, LAPACK, ATLAS, ARPACK and SuperLU libraries * Useful for machine learning, pattern recognition, signal processing, bioinformatics, statistics, finance, etc. * Downloads: http://arma.sourceforge.net/download.html * Documentation: http://arma.sourceforge.net/docs.html * Bug reports: http://arma.sourceforge.net/faq.html * Git repo: https://gitlab.com/conradsnicta/armadillo-code

Mixed Integer Linear Programming (MILP) solver lp_solve solves pure linear, (mixed) integer/binary, semi-cont and special ordered sets (SOS) models.lp_solve is written in ANSI C and can be compiled on many different platforms like Linux and WINDOWS

A Tiny Mathematical Speed Parser ATMSP is a portable C++ parser for mathematical expressions like "sin(x)+y^2" e.g. These may contain arbitrary numbers of functions, variables and constants. Major design goal was minimalistic size and maximum speed. Tiny 320 code-lines offer a parser plus bytecode-generator, 26 mathematical functions and 17 supported base-types including complex and arbitrary MPFR-multiprecision. Both parser and bytecode may run in threads. The usage of ATMSP is most simple - just include a single header in your own code and go. Reasonably experienced coders may implement other base-types like bool, SSE2, rationals or bigint's with a few changes. Have fun, Heinz van Saanen

A cross-platform application for exploring Conway's Game of Life and many other types of cellular automata. Features include bounded and unbounded universes, fast generating algorithms, Lua/Python scripting, and a state-of-the-art pattern collection.

CLISP is a portable ANSI Common Lisp implementation and development environment by Bruno Haible. Interpreter, compiler, debugger, CLOS, MOP, FFI, Unicode, sockets, CLX. UI in English, German, French, Spanish, Dutch, Russian, and Danish.

The General Mission Analysis Tool (GMAT) is an open-source tool for space mission design and navigation. GMAT is developed by a team of NASA, private industry, and public and private contributors. The GMAT development team is pleased to announce the release of GMAT version R2020a. New features in this release include a new 3D graphics engine based on OpenFrames, the first production-quality C++ release of the Collocation Stand-Alone Library and Toolkit (CSALT), a new optimal control subsystem that supports finite-thrust optimization, a new (beta) API developed to provide users low-level access to GMAT functionality and to support interoperability between NASA's GMAT, Copernicus, and MONTE software applications, a new continuous thrust mission design and navigation feature, and a new (alpha) Extended Kalman Filter Smoother with process noise. For a complete list of new features, compatibility changes, and bug fixes, see the R2020a Release Notes in the Users Guide.

This is the main repository for the SciPy library, one of the core packages that make up the SciPy stack. SciPy is an open source software used in the fields of mathematics, science, and engineering, with modules for statistics, optimization, integration, linear algebra, signal and image processing, and many more. The SciPy library contains many of the user-friendly and efficient numerical routines, including those for numerical integration, interpolation, and optimization. SciPy is built to work with NumPy, a software that provides convenient and fast N-dimensional array manipulation. Both SciPy and NumPy run on all popular operating systems, are fast and easy to install, and are powerful yet easy to use. They’re currently depended upon by numerous leading scientists and engineers all over the world. Try them for yourself!

OpenGL Mathematics (GLM) is a header only C++ mathematics library for graphics software based on the OpenGL Shading Language (GLSL) specifications. GLM provides classes and functions designed and implemented with the same naming conventions and functionality than GLSL so that anyone who knows GLSL, can use GLM as well in C++. This project isn't limited to GLSL features. An extension system, based on the GLSL extension conventions, provides extended capabilities: matrix transformations, quaternions, data packing, random numbers, noise, etc. This library works perfectly with OpenGL but it also ensures interoperability with other third party libraries and SDK. It is a good candidate for software rendering (raytracing / rasterisation), image processing, physics simulations and any development context that requires a simple and convenient mathematics library. GLM is written in C++98 but can take advantage of C++11 when supported by the compiler.

Asymptote is a powerful descriptive vector graphics language for technical drawing, inspired by MetaPost but with an improved C++-like syntax. Asymptote provides for figures the same high-quality typesetting that LaTeX does for scientific text.

CGAL or the Computational Geometry Algorithms Library is a C++ library that gives you easy access to a myriad of efficient and reliable geometric algorithms. These algorithms are useful in a wide range of applications, including computer aided design, robotics, molecular biology, medical imaging, geographic information systems and more. CGAL features a great range of data structures and algorithms, including Voronoi diagrams, cell complexes and polyhedra, triangulations, arrangements of curves, surface and volume mesh generation, spatial searching, alpha shapes, geometry processing, and many more. The use of these result in beautiful, visually complex and accurate representations.

DWSIM is an open source, CAPE-OPEN compliant chemical process simulator for Windows, Linux and macOS systems. Written in VB.NET and C#, DWSIM features a comprehensive set of unit operations, advanced thermodynamic models, support for reacting systems, petroleum characterization tools and a fully-featured graphical interface.

Elmer is a finite element software for numerical solution of partial differential equations and multiphysical problems. It includes models of structural mechanics, fluid dynamics, heat transfer, electromagnetics etc. Elmer home is www.csc.fi/elmer

MatCont is a Matlab software project for the numerical continuation and bifurcation study of continuous and discrete parameterized dynamical systems. Leaders of the project are Willy Govaerts (Gent,B) and Yuri A. Kuznetsov (Utrecht,NL) and Hil G.E. Meijer (UT, Enschede, NL). Matcont for ODE's and MatcontM for Maps Publish a paper using our software? That's great. Please do us a favour and cite: New features of the software MatCont for bifurcation analysis of dynamical systems. A. Dhooge, and W. Govaerts, Yu.A. Kuznetsov, H.G.E. Meijer and B. Sautois, MCMDS 2008, Vol. 14, No. 2, pp 147-175 In case you're stuck, use the forum, but to get a good answer provide: 1. What command do you give when this appears? Provide the exact steps (not all code, a simple example will suffice). 2. Indicate whether you use the GUI or CL version. Also Matlab-version and Operating System may help. 3. We hope you followed the tutorial(s)?

SOFA is a statistics, analysis, and reporting program with an emphasis on ease of use, learn as you go, and beautiful output.

SymPy is an open source Python library for symbolic mathematics. Its goal is to become a full-featured computer algebra system (CAS) while maintaining the simplicity of its code. Written entirely in Python, SymPy is easy to use, comprehensible and easily extensible. It’s also very lightweight as it solely depends on mpmath, a pure Python library for arbitrary floating point arithmetic. SymPy has participated in every Google Summer of Code since 2007 and because of this has continuously improved. A lot more people have also contributed to it, and used it in their projects. Beyond being an interactive tool, it can be embedded in other apps and extended with custom functions.

wxMaxima is a cross-platform graphical front-end for the computer algebra system Maxima based on wxWidgets. It provides nice display of mathematical output and easy access to Maxima functions through menus and dialogs. This project has moved to github and can be reached at http://wxmaxima-developers.github.io/wxmaxima/

R portable configures R to work with the PortableApps framework, so that R can be ran from a thumb drive or portable hard drive without leaving artifacts on the computer.

ATLAS (Automatically Tuned Linear Algebra Software) provides highly optimized Linear Algebra kernels for arbitrary cache-based architectures. ATLAS provides ANSI C and Fortran77 interfaces for the entire BLAS API, and a small portion of the LAPACK AP

JGraphT is a free Java class library that provides mathematical graph-theory objects and algorithms. JGraphT supports a rich gallery of graphs and is designed to be powerful, extensible, and easy to use.