Everything you wanted to know about abstract algebra, but were afraid to buy
SAGE is an open-source program for doing mathematics and is the ideal companion to Abstract Algebra: Theory and Applications. Sage is designed to be a free, open-source alternative to Magma, Maple, Mathematica and Matlab. It includes many mature and powerful open-source tools for mathematics, such as GAP for group theory. With a strength in number theory, SAGE also has excellent support for rings and fields.
There is a tutorial designed to help instructors and students use Sage in an introductory course in group theory. While it could be used profitably in any standard course, it has been written to specifically accompany Judson's Abstract Algebra: Theory and Applications. It is licensed with a Creative Commons BY-SA 3.0 US license. A similar tutorial for rings and fields might be constructed during the Spring 2010 semester.
[PDF] [Sage Worksheet] [LaTeX Source]
The quickest way to view the tutorial in Sage is to first get a free account on Sage's public server at the registration page by simply providing a username and password (it is that simple, no other nosy questions). Then login to the server and click a link in the upper-left that says "Upload." Copy the URL here:
and paste it into the part of the upload form that accepts a link (URL). Then read along, using the "evaluate" link below each cell to have Sage execute it.