Freemat!

MATLAB is a numerical computing environment and programming language. Maintained by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it is numeric only, an optional toolbox uses the MuPAD symbolic engine, allowing access to computer algebra capabilities. An additional package, Simulink, adds graphical multidomain simulation and Model-Based Design for dynamic and embedded systems. »

Octave is a computer program for performing numerical computations which is mostly compatible with MATLAB. It is part of the GNU Project. It is free software under the terms of the GNU General Public License.

Mathematica is a computational software program used widely in scientific, engineering, and mathematical fields and other areas of technical computing.

SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation.

Spyder (previously known as Pydee) is a free open-source Python development environment providing MATLAB-like features in a simple and light-weighted software, available for Windows XP/Vista/7, GNU/Linux and Mac OS X.

Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. Scilab is an open source software and includes hundreds of mathematical functions with the possibility to add interactively programs from various languages (C, C++, Fortran…).It has sophisticated data structures (including lists, polynomials, rational functions, linear systems...), an interpreter and a high level programming language.

Maple is a general-purpose commercial computer algebra system. Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbolic computation and visualization. Examples of symbolic computations are given below.Maple incorporates a dynamically typed imperative-style programming language which resembles Pascal. The language permits variables of lexical scope. There are also interfaces to other languages (C, C#, Fortran, Java, MATLAB, and Visual Basic). There is also an interface with Excel.Maple supports MathML 2.0, a W3C format for representing and interpreting mathematical expressions, including their display in Web pages. »

Xcos is a graphical editor to design hybrid dynamical systems models. Models can be designed, loaded, saved, compiled and simulated.

Jasymca is an interactive System for solving math problems. It supports arbitrary precision numbers and symbolic variables. Scalars, vectors, and matrices can be built from all datatypes and used in calculations. From the pseudoinverse of symbolic matrices over trigonometric simplifications to symbolic solutions of integrals and systems of equations, the main functionalities of CAS-programs are provided. Additionaly, high performance numerical routines from LAPACK and a plotmodule are implemented. The user interface can be selected from either an Octave/Matlab/SciLab-like language or a GNU-Maxima style. Three versions of Jasymca are provided which cover almost any computer platform: A Midlet version for portable devices like cellphones or PDAs, a java application for desktop PCs, laptops and workstation, and an applet which can be integrated in webpages. Jasymca is free software covered by the GNU public license. »

Graphical frontend for GNU Octave. Edit formulas in native mathematical notation. Available / tested for Linux x586 / x86_64, WinXP, Vista, and MacOS.

With Euler Math Toolbox, you experience mathematical computations, numerical as well as symbolic, with ease and beauty.The program will display results with nice graphics, which can be exported to files or to web pages, or can be pasted into presentations.Not only can you do quick and reliable numerical computations using real or complex numbers, intervals, vectors or matrices; but with the powerful computer algebra system Maxima you also have symbolic algebra and infinite rational arithmetic at your fingertips. Both systems work together, so that you need learn one syntax only.The friendly interface and the various user assistance let you start quickly and successfully. The documentation, introduction notebooks, and examples give you a thorough understanding of the program, while you can look into the full reference at any time, just be pressing F1 for each command.The program is free of royalties and open source. »

ASCEND is a free open-source software program for solving small to very large mathematical models. ASCEND can solve systems of non-linear equations, linear and nonlinear optimisation problems, and dynamic systems expressed in the form of differential/algebraic equations.