SINGULAR – Computer Algebra System for Polynomial Computations

SINGULAR is a Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, singularity theory, and polynomial system solving.

SINGULAR’s main computational objects are ideals and modules over a large variety of baserings. The baserings are polynomial rings or localizations thereof over a field (e.g., finite fields, the rationals, floats, algebraic extensions, transcendental extensions) or over a limited set of rings, or over quotient rings with respect to an ideal.

SINGULAR features one of the fastest and most general implementations of various algorithms for computing Groebner resp. standard bases. The implementation includes Buchberger’s algorithm (if the ordering is a wellordering) and Mora’s algorithm (if the ordering is a tangent cone ordering) as special cases. Furthermore, it provides polynomial factorization, resultant, characteristic set and gcd computations, syzygy and free-resolution computations, and many more related functionalities.

Features include:

  • Main computational objects: ideals/modules over very general polynomial rings over various ground fields.
  • Large variety of algorithms implemented in kernel (written in C/C++).
  • Many more algorithms implemented as SINGULAR libraries. 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.
  • Intuitive, C-like programming language.
  • Extensive documentation: Manual (info, ps, and html), Publications.
  • Emacs user interface.
  • Large set of libraries.
  • Dynamically extend the functionality by loading functions written in C/C++ or some other higher programming language.
  • Cross-platform support – runs under Linux, Mac OS X, and Windows.

Website: www.singular.uni-kl.de
Support: Manual, GitHub Code Repository
Developer: Department of Mathematics of the University of Kaiserslautern
License: GNU GPL v2

SINGULAR is written in C++. Learn C++ with our recommended free books and free tutorials.

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