Sage

About
Sage is a free, open-source computer algebra system, with the mission of, "Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab." It has a python-based syntax, and is under very active development, with new versions typically released on a two-week cycle. In the backend, it utilizes existing open source mathematics software such as Maxima and GAP.

Install
Sage uses tweaked versions of its backend programs, and essentially creates a complete, self-contained environment for itself. It is not currently in Portage.

To install Sage as a binary package in Gentoo, you can try using the Debian binary provided at the sage website, which should (at least) work for 32-bit x86 processors.

To compile from source, you can obtain the source distribution from the website, and just run make in the resulting directory.

Compilation can take quite a while, especially if there isn't a pre-existing profile for your processor. This is partly because of extensive tests that are run by the program during the install process to optimize for speed, and partly because Sage compiles a complete environment for itself, including customized versions of large programs like Maxima.

Given the fast release cycles, you'll be glad to know that you don't need to recompile every two weeks. You can update Sage by running

Usage
In the sage directory, type

This will start the Sage command prompt. At this point, you should probably start reading the Sage tutorial.

To access the graphical front-end, you can run  Or from the sage prompt,

The graphical front-end will be more familiar to users of programs like Mathematica or Maple, but uses the same commands and syntax as the command line interface.