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 1241 to 1260 of 1305.
Sorted by year (citations)

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  1. Bondil, Romain; Lê Dũng Tráng: Resolution of surface singularities by normalized blow-ups. (Multiplicity, polar multiplicity, and minimal singularities) (2002)
  2. Campillo, A.; Farrán, J. I.: Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes (2002)
  3. Faugère, Jean-Charles: A new efficient algorithm for computing Gröbner bases without reduction to zero ((F_5)). (2002)
  4. Freiermuth, Hans Georg; Burban, Igor: Geometrical properties of sections of Buchsbaum-Rim sheaves (2002)
  5. Freitag, Eberhard: A graded algebra related to cubic surfaces. (2002)
  6. Greuel, Gert-Martin; Pfister, Gerhard: Computer algebra and finite groups. (2002)
  7. Greuel, Gert-Martin; Pfister, Gerhard: A Singular introduction to commutative algebra. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann (2002)
  8. Kemper, Gregor: The calculation of radical ideals in positive characteristic (2002)
  9. Laza, Radu; Pfister, Gerhard; Popescu, Dorin: Maximal Cohen-Macaulay modules over the cone of an elliptic curve (2002)
  10. Lecerf, G.: Quadratic Newton iteration for systems with multiplicity (2002)
  11. Martin, Bernd: Algorithmic computation of flattenings and of modular deformations (2002)
  12. Park, Hyungju: Effective computation of singularities of parametric affine curves (2002)
  13. Schulze, Mathias: The differential structure of the Brieskorn lattice (2002)
  14. Wang, Mingsheng; Kwong, C. P.: Computing GCLF using syzygy algorithm (2002)
  15. Bayer, Thomas: Computing stratifications of quotients of finite groups and an application to shape memory alloys (2001)
  16. Bermejo, Isabel; Gimenez, Philippe: Computing the Castelnuovo-Mumford regularity of some subschemes of (\mathbbP_K^n) using quotients of monomial ideals (2001)
  17. Decker, W.; Schreyer, F.-O.: Computational algebraic geometry today (2001)
  18. Frühbis-Krüger, Anne: Computing moduli spaces for space curve singularities (2001)
  19. Gatermann, Karin: Counting stable solutions of sparse polynomial systems in chemistry (2001)
  20. Gerdt, Vladimir P.; Blinkov, Yuri A.; Yanovich, Denis A.: Construction of Janet bases. II: Polynomial bases (2001)

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