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 1 to 20 of 1195.
Sorted by year (citations)

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  1. Alberich-Carramiñana, Maria; Montaner, Josep Àlvarez; Blanco, Guillem: Effective computation of base points of ideals in two-dimensional local rings (2019-2019)
  2. Cant, Alexander; Eick, Bettina: Polynomials describing the multiplication in finitely generated torsion-free nilpotent groups (2019-2019)
  3. Aoki, Hiroki; Takemori, Sho: The structure of mixed weight Hilbert modular forms (2019)
  4. Bertolini, Marina; Notari, Roberto; Turrini, Cristina: The Bordiga surface as critical locus for 3-view reconstructions (2019)
  5. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  6. Bravo, José Luis; Fernández, Manuel; Ojeda, Ignacio; Sánchez, Fernando: Uniqueness of limit cycles for quadratic vector fields (2019)
  7. Ceria, Michela: Bar code for monomial ideals (2019)
  8. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  9. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  10. Dimca, Alexandru; Sticlaru, Gabriel: Computing the monodromy and pole order filtration on Milnor fiber cohomology of plane curves (2019)
  11. Forsgård, Jens; Matusevich, Laura Felicia; Mehlhop, Nathan; De Wolff, Timo: Lopsided approximation of amoebas (2019)
  12. García-Martínez, Xabier; Van der Linden, Tim: A characterisation of Lie algebras via algebraic exponentiation (2019)
  13. Gazor, Majid; Kazemi, Mahsa: Normal form analysis of (\mathbbZ_2)-equivariant singularities (2019)
  14. Gimenez, Philippe; Srinivasan, Hema: The structure of the minimal free resolution of semigroup rings obtained by gluing (2019)
  15. Greuel, Gert-Martin; Pham, Thuy Huong: Finite determinacy of matrices and ideals (2019)
  16. Guan, Jiancheng; Li, Weiqing; Ouyang, Baiyu: On minor prime factorizations for multivariate polynomial matrices (2019)
  17. Hauer, Michael; Jüttler, Bert; Schicho, Josef: Projective and affine symmetries and equivalences of rational and polynomial surfaces (2019)
  18. Ishitsuka, Yasuhiro; Ito, Tetsushi; Ohshita, Tatsuya: On algorithms to obtain linear determinantal representations of smooth plane curves of higher degree (2019)
  19. Kovács, Z.; Recio, T.; Sólyom-Gecse, C.: Rewriting input expressions in complex algebraic geometry provers (2019)
  20. Kruff, Niclas; Lax, Christian; Liebscher, Volkmar; Walcher, Sebastian: The Rosenzweig-MacArthur system via reduction of an individual based model (2019)

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