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 1029 articles , 4 standard articles )

Showing results 1 to 20 of 1029.
Sorted by year (citations)

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  1. Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
  2. Frühbis-Krüger, Anne: On discriminants, tjurina modifications and the geometry of determinantal singularities (2018)
  3. Hashemi, Amir; Schweinfurter, Michael; Seiler, Werner M.: Deterministic genericity for polynomial ideals (2018)
  4. Hernandes, M.E.; Miranda, A.J.; Peñafort-Sanchis, G.: An algorithm to compute a presentation of pushforward modules (2018)
  5. Levandovskyy, Viktor; Heinle, Albert: A factorization algorithm for $G$-algebras and its applications (2018)
  6. Neumann, Eike; Pauly, Arno: A topological view on algebraic computation models (2018)
  7. Artal Bartolo, Enrique; Gorrochategui, Leire; Luengo, Ignacio; Melle-Hernández, Alejandro: On some conjectures about free and nearly free divisors (2017)
  8. Bakuradze, Malkhaz; Gachechiladze, Natia: Some 2-groups from the view of Hilbert-Poincaré polynomials of $K(2)^\ast(BG)$ (2017)
  9. Bell, Jason P.; Heinle, Albert; Levandovskyy, Viktor: On noncommutative finite factorization domains (2017)
  10. Bertone, Cristina; Cioffi, Francesca; Roggero, Margherita: Double-generic initial ideal and Hilbert scheme (2017)
  11. Binyamin, Muhammad Ahsan; Mahmood, Hasan; Kanwal, Shamsa: On the classification of simple maps from the plane to the plane (2017)
  12. Binyamin, Muhammad Ahsan; Rabia; Mahmood, Hasan; Khan, Junaid Alam; Mehmood, Khawar: Characterization of uni-modal parametric plane curve singularities (2017)
  13. Birkmeyer, Anna Lena; Gathmann, Andreas; Schmitz, Kirsten: The realizability of curves in a tropical plane (2017)
  14. Bivià-Ausina, Carles: Log canonical threshold and diagonal ideals (2017)
  15. Bivià-Ausina, Carles; Huarcaya, Jorge A.C.: The special closure of polynomial maps and global non-degeneracy (2017)
  16. Böhm, Janko; Bringmann, Kathrin; Buchholz, Arne; Markwig, Hannah: Tropical mirror symmetry for elliptic curves (2017)
  17. Böhm, Janko; Marais, Magdaleen S.; Pfister, Gerhard: A classification algorithm for complex singularities of corank and modality up to two (2017)
  18. Bruns, Winfried; Conca, Aldo: Linear resolutions of powers and products (2017)
  19. Bruns, Winfried; Conca, Aldo: Products of Borel fixed ideals of maximal minors (2017)
  20. Ceria, Michela; Mora, Teo: Buchberger-Weispfenning theory for effective associative rings (2017)

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