REDUCE Computer Algebra System
Science, Math, Algebra, Software - REDUCE Computer Algebra System. Bibliography, documentation, available packages, online demonstrations and ordering information for versions from 3.
http://www.reduce-algebra.com/
Algebra Helper - Welcome!
Science, Math, Algebra, Software - Algebra Helper. Helps students with equations and inequalities, simplifying expression, graphing and complex numbers.
https://www.algebra-answer.com/
Maxima, a Computer Algebra System
Maxima is a fairly complete computer algebra system written in lisp with an emphasis on symbolic computation. It is based on DOE-MACSYMA and licensed under the GPL. Its abilities include symbolic integration, 3D plotting, and an ODE solver.
https://maxima.sourceforge.net/
Matrix Expression Templates (MET)
Science, Math, Algebra, Software - Matrix Expression Templates (MET). C++ matrix class library which promotes the notational convenience of linear algebraic codes.
https://met.sourceforge.net/
Felix
Science, Math, Algebra, Software - Felix. Computer algebra system for computation in commutative and non-commutative rings and modules.
http://felix.hgb-leipzig.de/
GiNaC is Not a CAS
Science, Math, Algebra, Software - GiNaC. An open framework for symbolic computation within the C++ programming language.
https://www.ginac.de/
CoCoA System
Science, Math, Algebra, Software - CoCoA. A special-purpose system for computations in Commutative Algebra.
https://cocoa.dima.unige.it/
Mathscribe
Science, Math, Algebra, Software - Mathscribe. Mathscribe is free dynamic graphing and modeling software for use in algebra classes.
https://mathscribe.com/
Aldor
Science, Math, Algebra, Software - Aldor. Originally an extension to Axiom, now a separate product.
http://www.aldor.org/