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 1261 to 1280 of 1305.
Sorted by year (citations)

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  1. Greuel, Gert-Martin: Applications of computer algebra to algebraic geometry, singularity theory and symbolic-numerical solving (2001)
  2. Greuel, G.-M.; Lossen, C.; Schulze, M.: Three algorithms in algebraic geometry, coding theory and singularity theory (2001)
  3. Lin, Zhiping; Ying, Jiang Qian; Xu, Li: Factorizations for (n)D polynomial matrices (2001)
  4. Orecchia, F.: Implicitization of a general union of parametric varieties (2001)
  5. Schulze, Mathias: Algorithms for the Gauss-Manin connection (2001)
  6. Selesnick, Ivan W.: Smooth wavelet tight frames with zero moments (2001)
  7. Siqveland, Arvid: The method of computing formal moduli (2001)
  8. Zerz, Eva: Extension modules in behavioral linear systems theory (2001)
  9. Albano, G.; Cioffi, F.; Orecchia, F.; Ramella, I.: Minimally generating ideals of rational parametric curves in polynomial time (2000)
  10. Bermejo, Isabel; Gimenez, Philippe: On Castelnuovo-Mumford regularity of projective curves (2000)
  11. Đoković, Dragomir Ž.: The irreducible six-dimensional complex representations of (\Aut(F_2)) that are nontrivial on (F_2) (2000)
  12. Gatermann, Karin: Computer algebra methods for equivariant dynamical systems (2000)
  13. Greuel, Gert-Martin: Computer algebra and algebraic geometry -- achievements and perspectives (2000)
  14. Greuel, Gert-Martin; Lossen, Christoph; Shustin, Eugenii: Castelnuovo function, zero-dimensional schemes and singular plane curves. (2000)
  15. Guerrieri, Anna; Swanson, Irena: Jacobian ideals of trilinear forms: An application of 1-genericity (2000)
  16. Sottile, Frank: Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro (2000)
  17. Decker, Wolfram; de Jong, Theo; Greuel, Gert-Martin; Pfister, Gerhard: The normalization: A new algorithm, implementation and comparisons (1999)
  18. Decker, Wolfram; Greuel, Gert-Martin; Pfister, Gerhard: Primary decomposition: Algorithms and comparisons (1999)
  19. Martin, Bernd: Computing versal deformations with SINGULAR (1999)
  20. Matzat, B. Heinrich (ed.); Greuel, Gert-Martin (ed.); Hiss, Gerhard (ed.): Algorithmic algebra and number theory. Selected papers from a conference, Heidelberg, Germany, October 1997 (1999)

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