[devilsdounut]

I like Mathematica... while their magic functions don't exactly work for much outside of their demo's, it gives good fodder for open source projects to eventually borrow from. IPython would not be where it is right now with its killer notebook interface and interactive plots if it were not for them borrowing some key ideas from Mathematica.

[lutusp]

> while their magic functions don't exactly work for much outside of their demo's ...

I write and solve a lot of differential equations, and of the choices available to me, Mathematica solves more and is easier to use -- compared to the alternatives Sage and IPython. But it's way expensive compared to Sage and IPython, the latter two of which are free.

> IPython would not be where it is right now with its killer notebook interface and interactive plots if it were not for them borrowing some key ideas from Mathematica.

Don't forget Sage. Sage was modeled after Mathematica (but open-source and collaborative), IPython was modeled after Sage (but much more lightweight).

Sage is huge and getting larger, lots of specialized code for various esoteric mathematical fields, IPython has a smaller footprint and is in some ways easier to use.

[rz2k]

I believe that Sage was modeled after Magma, which isn't important, but I highly recommend this long blog post by William Stein[1] talking about his motivations, the problem of basing academic work on closed source software, and in the case of Magma, the potential politics of even being able to get the software.

[1] http://sagemath.blogspot.com/2009/12/mathematical-software-a...

[lutusp]

I agree, I've read that piece, it's very worthwhile, especially with regard to the issue of being able to publish the mathematical methods built into common math environments.

Oh -- my Sage tutorial: http://arachnoid.com/sage