SINGULAR

SINGULAR is a Computer Algebra system (CAS) for polynomial computations in commutative algebra, algebraic geometry, and singularity theory. SINGULAR’s main computational objects are ideals and modules over a large variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields, the rationals, floats, algebraic extensions, transcendental extensions), or localizations thereof, or quotient rings with respect to an ideal. SINGULAR features fast and general implementations for computing Groebner and standard bases, including e.g. Buchberger’s algorithm and Mora’s Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy and free-resolution computations, and many more related functionalities. Based on an easy-to-use interactive shell and a C-like programming language, SINGULAR’s internal functionality is augmented and user-extendible by libraries written in the SINGULAR programming language. A general and efficient implementation of communication links allows SINGULAR to make its functionality available to other programs.

This software is also referenced in ORMS.


References in zbMATH (referenced in 1305 articles , 4 standard articles )

Showing results 1281 to 1300 of 1305.
Sorted by year (citations)

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  1. Siebert, Thomas: Algorithms for the computation of free resolutions (1999)
  2. Abo, Hirotachi; Decker, Wolfram; Sasakura, Nobuo: An elliptic conic bundle in (\mathbbP^4) arising from a stable rank-3 vector bundle (1998)
  3. Bachmann, Olaf; Schönemann, Hans: Monomial representations of Gröbner bases computations (1998)
  4. Decker, Wolfram; de Jong, Theo: Gröbner bases and invariant theory (1998)
  5. Decker, Wolfram; Heydtmann, Agnes Eileen; Schreyer, Frank-Olaf: Generating a Noetherian normalization of the invariant ring of a finite group (1998)
  6. De Jong, Theo: An algorithm for computing the integral closure (1998)
  7. Gatermann, Karin; Lauterbach, Reiner: Automatic classification of normal forms (1998)
  8. Greuel, Gert-Martin; Pfister, Gerhard: Gröbner bases and algebraic geometry (1998)
  9. Greuel, G. M.: Standard bases and applications (1998)
  10. Kemper, Gregor: Computational invariant theory (1998)
  11. La Scala, Roberto; Stillman, Michael: Strategies for computing minimal free resolutions (1998)
  12. Vasconcelos, Wolmer V.: Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman (1998)
  13. Capani, A.; De Dominicis, G.; Niesi, G.; Robbiano, L.: Computing minimal finite free resolutions (1997)
  14. Greuel, G.-M.; Pfister, G.; Schönemann, H.: SINGULAR: A computer algebra system for singularity theory, algebraic geometry and commutative algebra (1997)
  15. Kemper, G.; Malle, G.: The finite irreducible linear groups with polynomial ring of invariants (1997)
  16. Bachmann, Olaf; Schönemann, Hans; Gray, Simon: MPP: A framework for distributed polynomial computations (1996)
  17. Grassmann, H.; Greuel, G.-M.; Martin, B.; Neumann, W.; Pfister, G.; Pohl, W.; Schönemann, H.; Siebert, T.: On an implementation of standard bases and syzygies in SINGULAR (1996)
  18. Greuel, G.-M.; Pfister, G.: Advances and improvements in the theory of standard bases and syzygies (1996)
  19. Michler, Gerhard O. (ed.): Computational methods in Lie theory. Selected papers from the workshop on computational methods in Lie theory, Essen, Germany, August 15-19, 1994 (1996)
  20. Nüßler, Thomas: Structure and construction of instanton bundles on (\mathbbP_ 3) (1996)

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Further publications can be found at: http://www.singular.uni-kl.de/index.php/publications/singular-related-publications.html