SAGE

SAGE stands for 'Software for Algebra and Geometry Exploration' and it's a new concept that was bound to happen in the web sooner or later. Rather than being a new general purpose math tool, it brings together many existing open source math tools under one interface and makes them web accessible.

SAGE is free and open software that supports research and teaching in a wide range of topics including algebra, geometry, number theory, cryptography, etc. SAGE includes the about 9 Softwares allowing symbolic or numerical computations covering topics like Group theory, Commutative algebra, Number theory etc.

Here is Homepage of SAGE. You can directly go to a good tutorial here and the web-based interface here. Currently, SAGE runs on Mac OS X, Linux and Windows.