Examples, test files, plots, documentation.
http://www.math.fsu.edu/~hoeij/compalg/algcurves.html
C code which computes the Hodge number of complete intersection Calabi-Yau manifolds embedded in products of ordinary projective spaces.
http://www.th.physik.uni-bonn.de/th/People/netah/cy/codes/tess.html
Java applet based online Matrix calculation program for analyzing various simultaneous equations.
http://www.mathpad.com/public/htmls/main/left/matrix/MatrixInfo.html
An open framework for symbolic computation within the C++ programming language. The name GiNaC is an iterated and recursive abbreviation for "GiNaC is Not a CAS", where CAS stands for Computer Algebra System. Its design is revolutionary in a sense that contrary to other CAS it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities. It is published under the GNU Public License (GPL).
http://www.ginac.de/
C++ matrix class library which promotes the notational convenience of linear algebraic codes. Free download.
http://met.sourceforge.net/
A Java package for multivariate polynomials over polymorphic rings.
http://ring.perisic.com/
Computer Algebra System for polynomial computations with special emphasis on commutative algebra, algebraic geometry, and singularity theory.
http://www.singular.uni-kl.de/
Helps students with equations and inequalities, simplifying expression, graphing and complex numbers. Includes problem solving exercises.
http://www.algebra-answer.com/