Singular

Supported by DFG SFB-TRR 195 and Forschungsinitiative Rheinland-Pfalz.

Copyright 1990-2026 Singular group

Computer algebra system

Singular is an open-source computer algebra system for polynomial computations.

Download Singular GitHub Read the manual
PublicationsSearch, view, or submit Singular-related publications. Report bugsSend precise reports for Singular issues and regressions. DiscussionsUse GitHub Discussions for questions and support.

To all Singular users and friends, unfortunately, we have some sad news to share:

Hans Schönemann passed away on December 28th, 2025. Hans was a well-established expert in the computer algebra community whose advice was frequently sought. He was central to the Singular development from the beginning, and a good friend.
His death is a great loss.
--
Gert-Martin Greuel, Gerhard Pfister, and Wolfram Decker

Hans Schönemann

In honor of Hans Schönemann, the conference Advances in Computer Algebra will take place on June 10, 2026, at RPTU in Kaiserslautern. Topics include the role of computational algebraic geometry in theoretical physics, themes close to Hans’s work, including Singular, Zariski’s multiplicity conjecture, syzygy methods for Feynman integrals, SAGBI bases, comprehensive Gröbner systems, and singularities.

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.

Singular is the commutative algebra and algebraic geometry cornerstone of OSCAR. OSCAR is an open-source computer algebra system bringing together leading mathematical software in a common Julia-based environment.

Singular's 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 Janko Boehm, Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, and Hans Schönemann (†), who head Singular's core development team within the Department of Mathematics of RPTU Kaiserslautern-Landau. Hans Schönemann was there from the start of Singular and was Singular's main author of code until he passed away in 2025. Much of what makes up Singular's identity carries his ideas and work.

 

Supported by DFG SFB-TRR 195 and Forschungsinitiative Rheinland-Pfalz, Potentialbereich SymbTools.

DFG SFB-TRR 195 logo SymbTools logo
Funding Jenks Prize History

Original page in the preserved old site: index.html.