This page has some links to programs useful for manipulating mathematical structures
GAP: Groups, Algorithms and Programming
LatDraw: A lattice drawing Java applet
by Ralph Freese
MACE: a program that searches for small models
by William McCune
Maude: A term-rewriting system
Minion: A constraint satisfier
Minisat: A boolean satisfaction solver
Nauty: a program for computing automorphism groups of graphs and digraphs
by Brendan McKay
Prover9: An Automated Deduction System
by William McCune
Sage Mathematical Software
The Sage Group, lead by William Stein
UACalc: The universal algebra calculator
by Ralph Freese and Emil Kiss