singular

Computer algebra system for polynomials

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