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Singular

Singular is an open source computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.

Singular provides: highly efficient core algorithms, a multitude of advanced algorithms in the above fields, an intuitive, C-like programming language, easy ways to make it user-extendible through libraries, and a comprehensive online manual and help function. Its main computational objects are ideals, modules and matrices over a large number of baserings. These include: polynomial rings over various ground fields and some rings (including the integers), localizations of the above, a general class of non-commutative algebras (including the exterior algebra and the Weyl algebra), quotient rings of the above, tensor products of the above. Singular's core algorithms handle Gröbner resp. standard bases and free resolutions, polynomial factorization, resultants, characteristic sets, and numerical root finding.

GAP

GAP

GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a pro ...

Giac/Xcas

Giac/Xcas

Giac/Xcas is a free computer algebra system for Windows, Mac OS X and Linux/Unix (license GPL3, for commercial dual-license co ...

Scilab

Scilab

Scilab is a scientific software package for numerical computations providing a powerful open computing environment for enginee ...