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 1083 articles , 4 standard articles )

Showing results 1 to 20 of 1083.
Sorted by year (citations)

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  1. Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi: Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic $D$-modules (2018-2018)
  2. Wang, Haohao; Goldman, Ron: Syzygies for translational surfaces (2018-2018)
  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. Álvarez, Víctor; Armario, José Andrés; Falcón, Raúl M.; Frau, María Dolores; Gudiel, Félix: Gröbner bases and cocyclic Hadamard matrices (2018)
  6. Blanco, R.; Encinas, S.: A procedure for computing the log canonical threshold of a binomial ideal (2018)
  7. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
  8. Braun, Andreas P.; Lukas, Andre; Sun, Chuang: Discrete symmetries of Calabi-Yau hypersurfaces in toric four-folds (2018)
  9. Coutinho, S. C.: Bounding the degree of solutions of differential equations (2018)
  10. Dimca, Alexandru; Sticlaru, Gabriel: On the Milnor monodromy of the exceptional reflection arrangement of type $G_31$ (2018)
  11. Dória, André; Simis, Aron: The Newton complementary dual revisited (2018)
  12. Dumnicki, M.; Harrer, D.; Szpond, J.: On absolute linear Harbourne constants (2018)
  13. Frühbis-Krüger, Anne: On discriminants, tjurina modifications and the geometry of determinantal singularities (2018)
  14. Hashemi, Amir; Schweinfurter, Michael; Seiler, Werner M.: Deterministic genericity for polynomial ideals (2018)
  15. Hauer, Michael; Jüttler, Bert: Projective and affine symmetries and equivalences of rational curves in arbitrary dimension (2018)
  16. Hernandes, M. E.; Miranda, A. J.; Peñafort-Sanchis, G.: An algorithm to compute a presentation of pushforward modules (2018)
  17. Hill, David C.; Shafer, Douglas S.: Asymptotics and stability of the delayed Duffing equation (2018)
  18. Jiang, Yunfeng; Zhang, Yang: Algebraic geometry and Bethe ansatz. I: The quotient ring for BAE (2018)
  19. Kemper, Gregor; Trung, Ngo Viet; Nguyen, Thi van Anh: Toward a theory of monomial preorders (2018)
  20. Khalid, Asma; Pfister, Gerhard; Popescu, Dorin: A uniform general Neron desingularization in dimension one (2018)

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