MAS is an experimental computer algebra system with algebraic specification capabilities for the design and study of algebraic algorithms. Downloads, documentation.
http://www.fmi.uni-passau.de/algebra/projects/mas.php3
A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.
http://fchabaud.free.fr/English/ZEN/
A package of PARI programs (v.2.1.1 or higher) for calculations described in "Periods of Hilbert modular forms and rational points on elliptic curves" by H. Darmon and A. Logan.
http://www.math.mcgill.ca/darmon/programs/logan/logan.html
Program solves variable equations and gives explanations of steps used.
http://www.bacsoftware.co.uk/algebra/
A Java 1.1.1 applet for drawing fundamental domains for congruence subgroups acting on the upper-half plane. By Helena Verrill.
http://hverrill.net/fundomain/
A simple opensource library in C++ for arithmetic between elements and polynomials over finite fields.
http://www.partow.net/projects/galois/
A set of C routines for matrix and vector operations over the reals (matrxf07).
http://www.simtel.net/pub/pd/61050.shtml
Free C software for computing primitive polynomials of degree n modulo p for p^n up to about 2^60.
http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/overview.html