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 1150 articles , 4 standard articles )

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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. Bertolini, Marina; Notari, Roberto; Turrini, Cristina: The Bordiga surface as critical locus for 3-view reconstructions (2019)
  4. Bravo, José Luis; Fernández, Manuel; Ojeda, Ignacio; Sánchez, Fernando: Uniqueness of limit cycles for quadratic vector fields (2019)
  5. Ceria, Michela: Bar code for monomial ideals (2019)
  6. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  7. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  8. Dimca, Alexandru; Sticlaru, Gabriel: Computing the monodromy and pole order filtration on Milnor fiber cohomology of plane curves (2019)
  9. Forsgård, Jens; Matusevich, Laura Felicia; Mehlhop, Nathan; De Wolff, Timo: Lopsided approximation of amoebas (2019)
  10. García-Martínez, Xabier; Van der Linden, Tim: A characterisation of Lie algebras via algebraic exponentiation (2019)
  11. Gimenez, Philippe; Srinivasan, Hema: The structure of the minimal free resolution of semigroup rings obtained by gluing (2019)
  12. Algaba, Antonio; García, Cristóbal; Giné, Jaume: Nondegenerate centers and limit cycles of cubic Kolmogorov systems (2018)
  13. Allman, Elizabeth S.; Degnan, James H.; Rhodes, John A.: Split probabilities and species tree inference under the multispecies coalescent model (2018)
  14. Alonso, M. E.; Castro-Jiménez, F. J.; Hauser, Herwig: Encoding algebraic power series (2018)
  15. Álvarez, Víctor; Armario, José Andrés; Falcón, Raúl M.; Frau, María Dolores; Gudiel, Félix: Gröbner bases and cocyclic Hadamard matrices (2018)
  16. Artal Bartolo, E.; Cassou-Noguès, P.; Luengo, I.; Melle-Hernández, A.: On the $b$-exponents of generic isolated plane curve singularities (2018)
  17. Aslam, Saima; Binyamin, Muhammad Ahsan; Pfister, Gerhard: Recognition of unimodal map germs from the plane to the plane by invariants (2018)
  18. Baskoroputro, Herolistra; Ene, Viviana; Ion, Cristian: Koszul binomial edge ideals of pairs of graphs (2018)
  19. Blanco, R.; Encinas, S.: A procedure for computing the log canonical threshold of a binomial ideal (2018)
  20. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)

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