Maths

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.

Return to Geometry | Return to Computer Algebra Systems


Popular series
Free and Open Source SoftwareThe largest compilation of the best free and open source software in the universe. Each article is supplied with a legendary ratings chart helping you to make informed decisions.
ReviewsHundreds of in-depth reviews offering our unbiased and expert opinion on software. We offer helpful and impartial information.
Alternatives to Proprietary SoftwareReplace proprietary software with open source alternatives: Google, Microsoft, Apple, Adobe, IBM, Autodesk, Oracle, Atlassian, Corel, Cisco, Intuit, and SAS.
GamesAwesome Free Linux Games Tools showcases a series of tools that making gaming on Linux a more pleasurable experience. This is a new series.
Artificial intelligence iconMachine Learning explores practical applications of machine learning and deep learning from a Linux perspective. We've written reviews of more than 40 self-hosted apps. All are free and open source.
Guide to LinuxNew to Linux? Read our Linux for Starters series. We start right at the basics and teach you everything you need to know to get started with Linux.
Alternatives to popular CLI tools showcases essential tools that are modern replacements for core Linux utilities.
System ToolsEssential Linux system tools focuses on small, indispensable utilities, useful for system administrators as well as regular users.
ProductivityLinux utilities to maximise your productivity. Small, indispensable tools, useful for anyone running a Linux machine.
AudioSurveys popular streaming services from a Linux perspective: Amazon Music Unlimited, Myuzi, Spotify, Deezer, Tidal.
Saving Money with LinuxSaving Money with Linux looks at how you can reduce your energy bills running Linux.
Home ComputersHome computers became commonplace in the 1980s. Emulate home computers including the Commodore 64, Amiga, Atari ST, ZX81, Amstrad CPC, and ZX Spectrum.
Now and ThenNow and Then examines how promising open source software fared over the years. It can be a bumpy ride.
Linux at HomeLinux at Home looks at a range of home activities where Linux can play its part, making the most of our time at home, keeping active and engaged.
Linux CandyLinux Candy reveals the lighter side of Linux. Have some fun and escape from the daily drudgery.
DockerGetting Started with Docker helps you master Docker, a set of platform as a service products that delivers software in packages called containers.
Android AppsBest Free Android Apps. We showcase free Android apps that are definitely worth downloading. There's a strict eligibility criteria for inclusion in this series.
Programming BooksThese best free books accelerate your learning of every programming language. Learn a new language today!
Programming TutorialsThese free tutorials offer the perfect tonic to our free programming books series.
Linux Around The WorldLinux Around The World showcases usergroups that are relevant to Linux enthusiasts. Great ways to meet up with fellow enthusiasts.
Stars and StripesStars and Stripes is an occasional series looking at the impact of Linux in the USA.
Subscribe
Notify of
guest

This site uses Akismet to reduce spam. Learn how your comment data is processed.

0 Comments
Inline Feedbacks
View all comments