FreeMat is a free numerical interpreted matrix-oriented computing environment and programming language for rapid engineering and scientific prototyping and data processing similar to MATLAB from Mathworks and GNU Octave. In addition to supporting many MATLAB functions and some IDL functionality, it features codeless interface to external C, C++, and Fortran code, further Freemat provides visualization, image manipulation, and plotting as well as parallel programming (parallel distributed algorithm development via MPI), and some extended volume and 3D visualization capabilities. Some features;

• Support for 8,16, 32, and 64 bit integer types (signed and unsigned), 32 and 64 bit floating point types, and 64 and 128 bit complex types;
• Support for solving linear systems of equations via the divide operators;
• Arbitrary-size FFT support;
• 3D Plotting and visualization via OpenGL;
• Full support for dynamic structure arrays;
• Sparse Matrix native support;
• Signal processing functions;
• Numerical methods;
• Optimization and Curve Fitting;
• Object Oriented Programming;
• ...and many others!

FreeMat is available under the GNU GPL license. For more information (...and download) click here.

           

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language. Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. It is easily extensible and customizable via user-defined functions written in Octave's own language, or using dynamically loaded modules written in C++, C, Fortran, or other languages. There is, also, a central storage place for script and function files used with GNU Octave; it's Octave-Forge, a collection of packages for GNU Octave. The Octave-forge packages contains the source for all the functions and are designed to work with the Octave package system. In general the packages are designed to work with the latest development version of Octave, but it should be possible to use most packages with earlier versions. Octave normally is run in a terminal so there are some front-end;

• QtOctave;
• OctaveDE;
• Octaviz;
• Mirai Math.

REDUCE is a system for doing algebra by computer (CAS - Computer Algebra System), which also supports numerical approximation and interfaces to Gnuplot to provide graphics. REDUCE is implemented in standard Lisp expressed in an intuitive imperative-style notation called RLISP but this is completley hidden from the casual user. The latter is used as a basis for REDUCE's user-level language. The development of the REDUCE computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world have contributed to its development. REDUCE has a long and distinguished place in the history of computer algebra systems. Other systems that address some of the same issues but sometimes with rather different emphasis are Axiom, Maxima and so on. REDUCE is distributed for various architecture and/or operating system like GNU/Linux (Debian i686 and x86_64, Fedora Core i686 and x86_64, OpenSUSE i686 and x86_64, Scientific Linux i686, Ubuntu i686 and x86_64....), NetBSD i386, FreeBSD x86_64, PowerPC MAC Darwin and Solaris i386, and is complemented by numerous packages serving specialized mathematical purposes, which have to be loaded explicitly, e.g.;

For a list, but quite incomplete, click here. Its capabilities include:

• Expansion and ordering of polynomials and rational functions;
• Calculations with symbolic matrices;
• Arbitrary precision integer and real arithmetic;
• Analytic differentiation and integration;
• Factorization of polynomials;
• Facilities for the solution of a variety of algebraic equations;
• Facilities for the output of expressions in a variety of formats;
• Facilities for generating optimized numerical programs from symbolic input;
• Dirac matrix calculations of interest to high energy physicists.

Various REDUCE examples here.