A matrix calculator program, written in C. Calculations can be performed on matrices with complex rational coefficients using exact arithmetic routines, as well as on matrices with elements mod p.
http://www.numbertheory.org/cmat/krm_cmat.html
A MuPAD package for counting and randomly generating combinatorial structures. Download.
http://dept-info.labri.fr/~dutour/ANCIENNE/CS/
Designed to ease the difficulties many students experience during the transition from arithmetic into the world of algebra using visualization. Covers linear and quadratic equations.
http://www.mathematicssoftware.com/mathematics-software-html/algebra-1-software.php
HECKE can be used to compute basis of q-expansions and Hecke operators on fairly general spaces of modular forms.
http://modular.fas.harvard.edu/Tables/software.html
Directory of links on Symbolic Algebraic Computation: Frequently Asked Questions, Live Demos, software for download, events, bibliography, research groups, and researcher directory.
http://www.SymbolicNet.org/
Algorithms coded in Maple for computing with algebraic curves. The main algorithm computes an integral basis of an algebraic function field using Puiseux expansions.
http://www.math.fsu.edu/~hoeij/compalg/IntBasis/
An interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions. Linux RPM distribution.
http://swissnet.ai.mit.edu/~jaffer/JACAL.html
Tiny Elliptic Curve Calculator, by Masanari Kida. Requires KASH 2.2.
http://matha.e-one.uec.ac.jp/~kida/TECC.html