General purpose with object-oriented language. The commercial version is discontinued. Open axiom is now developed under the BSD-liked lincence. Its compilor is ALDOR.
Object-Oriented language. a CAS without AXIOM.
General purpose.
Soft Warehouse(http://www.derive.com/)Group theory.
GAP(http://www-gap.dcs.st-and.ac.uk/gap)Commutative algebra. Very unique system.
General purpose.
GPLed DOE-Macsyma based on the common lisp environment.
http://www.ma.utexas.edu/users/wfs/maxima.html
http://www.bekkoame.ne.jp/~ponpoko/Math/maxima/maxima_toc.html
General purpose, former called "Theorist".
General purpose.
General purpose.
General purpose.
General purpose.
Number theory with large analytical functions.
PARI/GP WebPage: (http://www.ufr-mi.u-bordeaux.fr/A2X/Logiciels.html/)
pariGUIde
http://www.skalatan.de/pariguide/General purpose.
General purpose. Very fast to calculate the groebner basis.
Commutative algebra.
Albegraic geometry, Commutative algebra.
GNU MATLAB Clone.
MATLAB Clone.
http://freemat.sourceforge.net/MATLAB like, not clone. Euler Math Toolbox includes Maxima.
http://eumat.sourceforge.net/MATLAB like, not clone.
http://rlab.sourceforge.net/The most excellent and powerfull system of the Matlab-like systems.
Tensor Language for large systems.
C-like interactive language. Fast calculation and plotting features.
Statistics.
GNU-S based S version 3.
http://www.r-project.orgInteractive geometry for educations. Written in JAVA.
Interactive geometry for educations alike Cinderella. Needs QT2 or QT3 library.
Visualize curves and surfaces in 3D space. Almost same to Maple's graphics functions.
http://www.math.umbc.edu/~rouben/dynagraphViewer for OOGL-objects with many features.
To draw beatiful images of algebraic curves and surfaces. C-like (primitive) language and GUI.
http://enriques.mathematik.uni-mainz.de/surf/surf.shtml
An interactive Sketchpad for Euclid Geometry, ressembles to Cinderella. Excellent!
Compute invariants for Hyperbolic manifolds.
Compute invariants for Hyperbolic manifolds. Enhanced SnapPea.
http://www.ms.unimelb.edu.au/~snap/3D modeler written in JAVA. Teddy makes the closed curve to 3D object, of which projection is the closed curve what you drawed. You can bend it and attach bodies and drawing on it. To color it, you can use Chameleon, which works only on Windows.
Powerful FEM solver, charge free!!!