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 970 articles , 4 standard articles )

Showing results 1 to 20 of 970.
Sorted by year (citations)

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  1. Artal Bartolo, Enrique; Gorrochategui, Leire; Luengo, Ignacio; Melle-Hernández, Alejandro: On some conjectures about free and nearly free divisors (2017)
  2. Bakuradze, Malkhaz; Gachechiladze, Natia: Some 2-groups from the view of Hilbert-Poincaré polynomials of $K(2)^\ast(BG)$ (2017)
  3. Bell, Jason P.; Heinle, Albert; Levandovskyy, Viktor: On noncommutative finite factorization domains (2017)
  4. Bertone, Cristina; Cioffi, Francesca; Roggero, Margherita: Double-generic initial ideal and Hilbert scheme (2017)
  5. Binyamin, Muhammad Ahsan; Rabia; Mahmood, Hasan; Khan, Junaid Alam; Mehmood, Khawar: Characterization of uni-modal parametric plane curve singularities (2017)
  6. Birkmeyer, Anna Lena; Gathmann, Andreas; Schmitz, Kirsten: The realizability of curves in a tropical plane (2017)
  7. Bivià-Ausina, Carles: Log canonical threshold and diagonal ideals (2017)
  8. Böhm, Janko; Marais, Magdaleen S.; Pfister, Gerhard: A classification algorithm for complex singularities of corank and modality up to two (2017)
  9. Bruns, Winfried; Conca, Aldo: Products of Borel fixed ideals of maximal minors (2017)
  10. Bruns, Winfried; Conca, Aldo: Linear resolutions of powers and products (2017)
  11. Cherednik, Ivan; Danilenko, Ivan: DAHA approach to iterated torus links (2017)
  12. Cifuentes, Diego; Parrilo, Pablo A.: Chordal networks of polynomial ideals (2017)
  13. Claus Fieker, William Hart, Tommy Hofmann, Fredrik Johansson: Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language (2017) arXiv
  14. David Kahle, Christopher O’Neill, Jeff Sommars: A computer algebra system for R: Macaulay2 and the m2r package (2017) arXiv
  15. Decker, Wolfram (ed.); Pfister, Gerhard (ed.); Schulze, Mathias (ed.): Singularities and computer algebra. Festschrift for Gert-Martin Greuel on the occasion of his 70th birthday. Based on the conference, Lambrecht (Pfalz), Germany, June 2015 (2017)
  16. Deeba Afzal, Sidra Mubarak, Gerhard Pfister, Asad Yaqub: Unimodular ICIS, a Classifier (2017) arXiv
  17. Dimca, Alexandru: Hyperplane arrangements. An introduction (2017)
  18. Donten-Bury, Maria; Keicher, Simon: Computing resolutions of quotient singularities (2017)
  19. Donten-Bury, Maria; Wiśniewski, Jarosław A.: On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32 (2017)
  20. Elias, J.; Rossi, M.E.: The structure of the inverse system of Gorenstein $k$-algebras (2017)

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