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...It features its own programming language, and many users have contributed useful packages in various areas over the decades. It 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.
Website: https://maxima.sourceforge.io
Additional add-on packages for Maxima can be found at: https://github.com/maxima-project-on-github/maxima-packages
A Portable General-Purpose Computer Algebra System
...Other systems that address some of the same issues but sometimes with rather different emphasis are Axiom, Derive, Macsyma (Maxima), Maple, Mathematica and MuPAD.
REDUCE primarily runs on either Portable Standard Lisp (PSL) or Codemist Standard Lisp (CSL), both of which are included in the SourceForge distribution. By modern standards, REDUCE is a surprisingly small and compact application, which runs well on all major operating systems.
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.
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/
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MatLisp is a package for Common Lisp for handling matrices with real-valued or complex-valued elements. BLAS is used for elementary matrix operations and LAPACK is used for linear algebra routines.
An implementation of the Joint Generation Algorithm of Fredman and Khachiyan for the computation of a dual pair of monotone boolean formulas in DNF (hypergraph transversals, extreme rays of polyhedral cones...). User-replaceable oracle.
A system for computer algebra and symbolic mathematics
OpenAxiom is an open source Computer Algebra System. It offers an interactive environment, an expressive programming language, a compiler, a large set of mathematical libraries of interest to researchers and practitioners of computational sciences.
NLISP is an extension to Common Lisp that provides an interactive numerical computation environment, similar to packages like Matlab and IDL. NLISP has array syntax, scientific plotting and a numerical library. It currently runs under CMUCL & SBCL Lisp.
The interactive mathematical programming system GYWOPT is released as free software. It has been developed since early 2000 for experiments with the Integral Basis Method for integer programming by U.-U. Haus, M. Köppe and R. Weismantel.
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FrAid(FRactal AID) is an interface to Java, allowing it to proc. math. data(functions/equations). A compl. standalone system utilizing the FrAid prog. lang. is available(no need to be Java programmer to use it!). Use instead of Matlab. High res. graphics
mupacs is a lisp mode for editing MuPAD code (automatic indentation, fontification, ...), as well as running MuPAD in a subshell, with support for debugger and online documentation
Kandid generates images using genetic algorithms. In a simulated evolution surprising images can be found calculated with Lisp expressions, Textures, Iterated Function Systems, Linear Cellular Automata, Voroni diagrams, Lindenmayer Systems and POVray
Computational modelling is a interdisciplinary field spanning many techniques and programming languages. AgenTools is a project dedicated to establishing increased modularity in scientific computing packages and a portal linking to other existing project
kin is a set of libraries and tools supporting meta-programming for engineering and technical computing applications. This JVM version of kin has been superseded by the stand-alone version being developed at http://purl.org/net/kin.
Charlemagne is a versatile genetic programming application which includes a command-line client and an interactive console mode. It features built in input-output mapping support, and is user-extensible for complex fitness evaluation in Python and Lisp
MAED is a simple but powerfull math program with educational character.
It has a Lisp like programming language, a nice GUI. It can work in client-server mode.
A main goal is to make a program which can solve math problems using both numerical and symb
MATHOOL is an online and offline javascript application powered by REDUCE computer algebra system, JSXGraph and other open source javascript programs devoted to scientific calculations and graphic visualization.