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 1195 articles , 4 standard articles )

Showing results 1141 to 1160 of 1195.
Sorted by year (citations)

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  1. Martin, Bernd: Algorithmic computation of flattenings and of modular deformations (2002)
  2. Park, Hyungju: Effective computation of singularities of parametric affine curves (2002)
  3. Schulze, Mathias: The differential structure of the Brieskorn lattice (2002)
  4. Wang, Mingsheng; Kwong, C. P.: Computing GCLF using syzygy algorithm (2002)
  5. Bayer, Thomas: Computing stratifications of quotients of finite groups and an application to shape memory alloys (2001)
  6. Bermejo, Isabel; Gimenez, Philippe: Computing the Castelnuovo-Mumford regularity of some subschemes of (\mathbbP_K^n) using quotients of monomial ideals (2001)
  7. Decker, W.; Schreyer, F.-O.: Computational algebraic geometry today (2001)
  8. Frühbis-Krüger, Anne: Computing moduli spaces for space curve singularities (2001)
  9. Gatermann, Karin: Counting stable solutions of sparse polynomial systems in chemistry (2001)
  10. Gerdt, Vladimir P.; Blinkov, Yuri A.; Yanovich, Denis A.: Construction of Janet bases. II: Polynomial bases (2001)
  11. Greuel, Gert-Martin: Applications of computer algebra to algebraic geometry, singularity theory and symbolic-numerical solving (2001)
  12. Greuel, G.-M.; Lossen, C.; Schulze, M.: Three algorithms in algebraic geometry, coding theory and singularity theory (2001)
  13. Lin, Zhiping; Ying, Jiang Qian; Xu, Li: Factorizations for (n)D polynomial matrices (2001)
  14. Orecchia, F.: Implicitization of a general union of parametric varieties (2001)
  15. Schulze, Mathias: Algorithms for the Gauss-Manin connection (2001)
  16. Selesnick, Ivan W.: Smooth wavelet tight frames with zero moments (2001)
  17. Siqveland, Arvid: The method of computing formal moduli (2001)
  18. Zerz, Eva: Extension modules in behavioral linear systems theory (2001)
  19. Albano, G.; Cioffi, F.; Orecchia, F.; Ramella, I.: Minimally generating ideals of rational parametric curves in polynomial time (2000)
  20. Bermejo, Isabel; Gimenez, Philippe: On Castelnuovo-Mumford regularity of projective curves (2000)

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