Rings and Computer algebra software, part of OpenXM.
http://www.math.sci.kobe-u.ac.jp/KAN/
Fundamental domains for Shimura curves, written in GAP. Documented with description of algorithms used and program structure, input and output. Results for quaternion algebras with discriminant up to 100.
http://www.geocities.com/assafwool/Quat/Quat.html
Open computer algebra system for symbolic and numerical computations. Library routines for linear algebra, integration, polynomials, and graphics. Can generate and be called from C or Fortran code. Free download by FTP for personal research purposes: requires registration.
http://www.mupad.de/
Mordell-Weil rank of elliptic curves over the rationals, by John Cremona.
http://www.maths.nott.ac.uk/personal/jec/ftp/progs/
Magma implementation of Silverman's algorithm to compute the canonical height on an elliptic curve over a number field or function field, by Martine Girard.
http://www.institut.math.jussieu.fr/~girard/magma/anglais.html
Mathscribe is free dynamic graphing and modeling software for use in algebra classes. Lesson plans for linears and quadratics are included.
http://www.mathscribe.com/
Online computation of reduced ideal bases.
http://grobner.nuigalway.ie/
A special-purpose system for computations in Commutative Algebra.
http://cocoa.dima.unige.it/