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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.

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.

wxMaxima is a document based interface for the computer algebra system Maxima. wxMaxima uses wxWidgets and runs natively on Windows, X11 and Mac OS X. wxMaxima provides menus and dialogs for many common maxima commands, autocompletion, inline plots and simple animations. wxMaxima is distributed under the GPL license.

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. »

Microsoft Mathematics is a desktop graphing calculator that can help you visualize and see mathematical concepts as you’ve never seen them before. Microsoft Mathematics includes ink handwriting support to recognize hand-written problems.

FreeMat is an environment for rapid engineering and scientific processing. It is similar to commercial systems such as MATLAB from Mathworks and IDL from Research Systems, but is Open Source.

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. »