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Singular manufacturer description
Singular is a computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory. It is free and open-source under the GNU General Public Licence.
Singular 4-0-1 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.
Its advanced algorithms, contained in currently more than 90 libraries, address topics such as absolute factorization, algebraic D-modules, classification of singularities, deformation theory, Gauss-Manin systems, Hamburger-Noether (Puiseux) development, invariant theory, (non-) commutative homological algebra, normalization, primary decomposition, resolution of singularities, and sheaf cohomology.