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 1057 articles , 4 standard articles )

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  1. Allman, Elizabeth S.; Degnan, James H.; Rhodes, John A.: Split probabilities and species tree inference under the multispecies coalescent model (2018)
  2. Blanco, R.; Encinas, S.: A procedure for computing the log canonical threshold of a binomial ideal (2018)
  3. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
  4. Dória, André; Simis, Aron: The Newton complementary dual revisited (2018)
  5. Frühbis-Krüger, Anne: On discriminants, tjurina modifications and the geometry of determinantal singularities (2018)
  6. Hashemi, Amir; Schweinfurter, Michael; Seiler, Werner M.: Deterministic genericity for polynomial ideals (2018)
  7. Hauer, Michael; Jüttler, Bert: Projective and affine symmetries and equivalences of rational curves in arbitrary dimension (2018)
  8. Hernandes, M.E.; Miranda, A.J.; Peñafort-Sanchis, G.: An algorithm to compute a presentation of pushforward modules (2018)
  9. Levandovskyy, Viktor; Heinle, Albert: A factorization algorithm for $G$-algebras and its applications (2018)
  10. Neumann, Eike; Pauly, Arno: A topological view on algebraic computation models (2018)
  11. Torrente, Maria-Laura; Varbaro, Matteo: Computing the Betti table of a monomial ideal: a reduction algorithm (2018)
  12. Yoshida, Hiroshi: A model for analyzing phenomena in multicellular organisms with multivariable polynomials: polynomial life (2018)
  13. Artal Bartolo, Enrique; Gorrochategui, Leire; Luengo, Ignacio; Melle-Hernández, Alejandro: On some conjectures about free and nearly free divisors (2017)
  14. Bakuradze, Malkhaz; Gachechiladze, Natia: Some 2-groups from the view of Hilbert-Poincaré polynomials of $K(2)^\ast(BG)$ (2017)
  15. Bell, Jason P.; Heinle, Albert; Levandovskyy, Viktor: On noncommutative finite factorization domains (2017)
  16. Bermejo, Isabel; García-Llorente, Eva; García-Marco, Ignacio; Morales, Marcel: Noether resolutions in dimension 2 (2017)
  17. Bertone, Cristina; Cioffi, Francesca; Roggero, Margherita: Double-generic initial ideal and Hilbert scheme (2017)
  18. Binyamin, Muhammad Ahsan; Mahmood, Hasan; Kanwal, Shamsa: On the classification of simple maps from the plane to the plane (2017)
  19. Binyamin, Muhammad Ahsan; Rabia; Mahmood, Hasan; Khan, Junaid Alam; Mehmood, Khawar: Characterization of uni-modal parametric plane curve singularities (2017)
  20. Birkmeyer, Anna Lena; Gathmann, Andreas; Schmitz, Kirsten: The realizability of curves in a tropical plane (2017)

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