Sage is a free, open-source computational mathematics system in the vein of things like Mathematica and Maple. For the past few years, there’s been an online version called the Sage Notebook which worked pretty well, but it was pretty slow and not particularly easy to use.
Now the creator of Sage, William Stein, has started work on The Sagemath Cloud. It’s considerably more ambitious than Sage notebook – as well as the Sage notebook interface, it gives you a sophisticated area where you can write LaTeX files with live preview, work on IPython notebooks, and even bring up a Unix terminal to do the kinds of things you need a Unix terminal for.
As well as 3d rendering, the Sage worksheets can include portions of HTML (or Markdown), with mathematical notation rendered by MathJax, plus all the computation and diagram-drawing you could ever need: computation can be done in Sage, R, Python, Cython, GAP, Macaulay2, or Singular, to name just a few of the supported languages. The only thing that’s really missing at the moment is the ability to share worksheets with the public via a link instead of an individual invitation, but Stein says that’s in the works.
It’s all very impressive, and it’s backed by the University of Washington so it should be around for a good while. If you fancy giving it a go and you haven’t used Sage before, the Sage tutorial is a good place to start.
The Sagemath Cloud.
William Stein’s homepage.
William Stein on Google+.
The Sage mathematical software system.