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 1121 articles , 4 standard articles )

Showing results 1 to 20 of 1121.
Sorted by year (citations)

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  1. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  2. Forsgård, Jens; Matusevich, Laura Felicia; Mehlhop, Nathan; De Wolff, Timo: Lopsided approximation of amoebas (2019)
  3. Algaba, Antonio; García, Cristóbal; Giné, Jaume: Nondegenerate centers and limit cycles of cubic Kolmogorov systems (2018)
  4. Allman, Elizabeth S.; Degnan, James H.; Rhodes, John A.: Split probabilities and species tree inference under the multispecies coalescent model (2018)
  5. Alonso, M. E.; Castro-Jiménez, F. J.; Hauser, Herwig: Encoding algebraic power series (2018)
  6. Álvarez, Víctor; Armario, José Andrés; Falcón, Raúl M.; Frau, María Dolores; Gudiel, Félix: Gröbner bases and cocyclic Hadamard matrices (2018)
  7. Baskoroputro, Herolistra; Ene, Viviana; Ion, Cristian: Koszul binomial edge ideals of pairs of graphs (2018)
  8. Blanco, R.; Encinas, S.: A procedure for computing the log canonical threshold of a binomial ideal (2018)
  9. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
  10. Böhm, Janko; Georgoudis, Alessandro; Larsen, Kasper J.; Schönemann, Hans; Zhang, Yang: Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections (2018)
  11. Braun, Andreas P.; Lukas, Andre; Sun, Chuang: Discrete symmetries of Calabi-Yau hypersurfaces in toric four-folds (2018)
  12. Brown, Gavin; Wemyss, Michael: Gopakumar-Vafa invariants do not determine flops (2018)
  13. Coutinho, S. C.: Bounding the degree of solutions of differential equations (2018)
  14. Dimca, Alexandru; Sticlaru, Gabriel: On the Milnor monodromy of the exceptional reflection arrangement of type $G_31$ (2018)
  15. Dória, André; Simis, Aron: The Newton complementary dual revisited (2018)
  16. Dumnicki, M.; Harrer, D.; Szpond, J.: On absolute linear Harbourne constants (2018)
  17. Frühbis-Krüger, Anne: On discriminants, tjurina modifications and the geometry of determinantal singularities (2018)
  18. García, Isaac A.; Maza, Susanna; Shafer, Douglas S.: Cyclicity of polynomial nondegenerate centers on center manifolds (2018)
  19. Greuel, Gert-Martin; Pham, Thuy Huong: On finite determinacy for matrices of power series (2018)
  20. Hashemi, Amir; Dehghani Darmian, Mahdi; Barkhordar, Marzieh: Universal Gröbner basis for parametric polynomial ideals (2018)

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