Post Made Community Wiki by S. Carnahan
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Here are some links.

• Axiom and Maxima are good general purpose computer algebra systems.
• GAP is a system for computational discrete algebra (with particular emphasis on computational group theory).
• PARI/GP is a CAS for fast computations in number theory.
• SAGE is a kind of unified framework for several systems, including GAP, PARI, and Maxima.
• Octave is a system for numerical computations (it is close to Matlab).
• Cadabra is a computer algebra system designed for the solution of the field theory problems.
• CoCoA stands for "Computations in commutative algebra".
• KANT / KASH stands for "Computational Algebraic Number Theory".
• Macaulay 2 is a system for research in commutative algebra and algebraic geometryresearch.
• Snap is a computer program for studying arithmetic invariants of hyperbolic 3-manifolds.
• Symmetrica is an object oriented computer algebra system for representations, combinatorics and applications of symmetric groups.
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Here are some links.

• Axiom and Maxima are good general purpose computer algebra systems.
• GAP is a system for computational discrete algebra (with particular emphasis on computational group theory).
• PARI/GP is a CAS for fast computations in number theory.
• SAGE is a kind of unified framework for several systems, including GAP, PARI, and Maxima.
• Octave is a system for numerical computations (it is close to Matlab).
• Cadabra is a computer algebra system designed for the solution of the field theory problems.
• CoCoA stays stands for "Computations in commutative algebra".
• KANT / KASH stands for "Computational Algebraic Number Theory".
• Macaulay 2 is a system for algebraic geometry research.
• Snap is a computer program for studying arithmetic invariants of hyperbolic 3-manifolds.
• Symmetrica is an object oriented computer algebra system for representations, combinatorics and applications of symmetric groups.
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