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.

• 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.

Further functionality is obtained by combining Singular with third-party software linked to SINGULAR. This includes tools for convex geometry, tropical geometry, and visualization.

1. Funding

1. Jenks Prize

1. History

1. Acknowledgements