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 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.

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

Singular is developed under the direction of Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, and Hans Schönemann who head  Singular's core development team within the Department of Mathematics of the University of Kaiserslautern.

 

  1. Funding
  1. Jenks Prize
  1. History