Maxima - Maxima is a fairly complete computer algebra system written in Lisp with an emphasis on symbolic computation.

Cadabra - Cadabra is the name of a universal computer algebra system designed for those users looking for the solution to problems encountered in the filed theory.

Wolfram Mathematica - Mathematica has characterized the cutting edge in specialized processing—and gave the chief calculation environment to a large number of pioneers, instructors, understudies, and others around the globe.

MATLAB - A high-level language and interactive environment for numerical computation, visualization, and programming

Macaulay2 - Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, whose creation has been funded by the National Science Foundation since 1992.

Sage Math - Sage is a free open-source mathematics software system licensed under the GPL.