Sage

Sage is an open source project founded by a math graduate/professor which they say is designed to be a "viable free open source alternative to Magma, Maple, Mathematica and Matlab". After using it for a while, I have to say it even goes beyond that. The project website is [1]

This is what it is in a nutshell: they took about 100 different open-source libraries related to math, science, and computing, then made it so they all worked together, and put a common python interface in which ties it all together. Then what they did was create a notebook interface, which is used in a web browser, based on ajax. The web interface allows one to create an account on the server and upload and save worksheets there. (those who have used mathematica will know what a notebook is. It's like a hybrid between a document and code) There's even a free server where anyone can sign up, browse examples, and start running code within minutes: [2]

If you're running windows you download a big file and you have to load that into virtual box. Then you use your web browser to access the server on local host. You can also use the command line in the virtual machine if you want. If you're running linux, you just download and install locally. You can use a local web browser, or anyone on the network can use it.

Here's a blogger's review from a few years ago: [3]