Compiled by Xah Lee, 1997,...,2008.
This page is a listing of math software for programers. I've used half of them. For those i haven't used, i know that they have high quality.
Mathematica from http://www.wolfram.com/. Mathematica.
GNU Octave, a MatLab-like program. Primarily intended for numerical computations. http://www.octave.org/. GNU Octave.
Maxima is a computer algebra system written in Common Lisp, originated from DOE Macsyma. http://maxima.sourceforge.net/. Maxima (software).
3D-XplorMath-J. Math visualization software. Written in Java. Come with source code. http://3d-xplormath.org/j/index_en.html.
GlSurf, by C Raffalli. A Implicit Surface plotter using OpenGL. http://www.lama.univ-savoie.fr/~raffalli/glsurf
jReality. A 3D Viewer engine in Java. By Charles Gunn, Tim Hoffmann, Markus Schmies, Steffen Weissmann et al. http://www3.math.tu-berlin.de/jreality/ (2006-07,)
GeomView is developed by the The Geometry Center. Freeware. Available for Unix platforms. http://www.geomview.org/.
MathGL3D, from Wolfram Research, for use with Mathematica. See http://www.wolfram.com/products/applications/mathgl3d/.
JavaView is a 3D visualization tool. You give it a 3D data file, and it displays the 3D object on screen, and allows you to rotate or zoom. The data file can be Mathematica Graphics Format or the Obj format. See JavaView Tutorial. JavaView home page.
LiveGraphics3D, is a Java applet by Martin Kraus. Free. You give it a 3D data file, and it displays the 3D object on screen, and allows you to rotate or zoom. The data file should be a Mathematica Graphics Format. For a tutorial, see LiveGraphics3D tutorial. LiveGraphics3D home page.
gnuplot. A command-line plotting software. You write a text file descripting your data or plot command, and it generate a image file showing the plot. See Wikipedia: Gnuplot. Gnuplot home page: http://www.gnuplot.info/.
POV-Ray. POV-Ray is a 3d-modeling and rendering software. You write a scene description file, then it generate a image file as output. Great for 3D math illustration. See: POV-Ray tutorial, Illustrating Geometry with POV-Ray. POV-Ray.
MathEclipse is a computer algebra system written in Java, modeled after Mathematica. http://www.matheclipse.org/
jtem is a large math library contaning many advanced special functions and numerical methods. Author is Markus Schmies et al. http://www-sfb288.math.tu-berlin.de/~jtem/index.html (2006-07,)
Computational Geometry Algorithms Library. http://www.cgal.org/. Library in C++. See Wikipedia CGAL.
2Geom. 2D geometry lib. http://2geom.org/