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
  1. Acknowledgements