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

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

* Grobner resp. standard bases and free resolutions,
* polynomial factorization,
* resultants, characteristic sets, and numerical root finding.