Sage is a free mathematics software system. It is built out of nearly 100 open-source packages and features a unified Python interface. There is a nice video introduction to Sage by William Stein.
Sage 5.0 is available
You can try it online: http://demo.sagenb.org/ and http://demo2.sagenb.org/ and exchange your source codes with others: http://interact.sagemath.org/