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FreeMat is a free environment for rapid engineering and scientific prototyping and data processing. It is similar to commercial systems such as MATLAB from Mathworks, and IDL from Research Systems, but is Open Source. FreeMat is available under the GPL license.
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. GNU Octave is freely redistributable software under the terms of the GNU General Public License.
Origin is NOT open source, but does offer 1-year licenses to students for $50. It is a spreadsheet-based numerical analysis program, and also has an excellent graphing interface.
R is a free software environment for statistical computing and graphics.
Scilab is an interactive platform for numerical computation providing a powerful computing environment for engineering and scientific applications.
Gnuplot is a portable command-line driven graphing utility for linux, OS/2, MS Windows, OSX, VMS, and many other platforms. Gnuplot supports many types of plots in either 2D and 3D. It can draw using lines, points, boxes, contours, vector fields, surfaces, and various associated text. It also supports various specialized plot types.
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