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 1362 articles , 4 standard articles )

Showing results 1 to 20 of 1362.
Sorted by year (citations)

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  1. Eder, Christian; Pfister, Gerhard; Popescu, Adrian: Standard bases over Euclidean domains (2021)
  2. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations enjoying enough commutativity (2021)
  3. Kapur, Deepak; Lu, Dong; Monagan, Michael; Sun, Yao; Wang, Dingkang: Algorithms for computing greatest common divisors of parametric multivariate polynomials (2021)
  4. Kloosterman, Remke; Rams, Sławomir: Quintic threefolds with triple points (2021)
  5. Planas-Vilanova, Francesc: Noetherian rings of low global dimension and syzygetic prime ideals (2021)
  6. Abbott, John; Bigatti, Anna Maria; Palezzato, Elisa; Robbiano, Lorenzo: Computing and using minimal polynomials (2020)
  7. Al-Ayyoub, Ibrahim; Jaradat, Malik; Al-Zoubi, Khaldoun: A note on the ascending chain condition of ideals (2020)
  8. Algaba, A.; García, C.; Reyes, M.: Quasi-homogeneous linearization of degenerate vector fields (2020)
  9. Amata, Luca; Crupi, Marilena: Hilbert functions of graded modules over an exterior algebra: an algorithmic approach (2020)
  10. Aoki, Satoshi: Introduction to computational algebraic statistics (2020)
  11. Bahloul, Rouchdi: Gröbner bases in (D)-modules: application to Bernstein-Sato polynomials (2020)
  12. Bajnok, Zoltan; Jacobsen, Jesper Lykke; Jiang, Yunfeng; Nepomechie, Rafael I.; Zhang, Yang: Cylinder partition function of the 6-vertex model from algebraic geometry (2020)
  13. Balnojan, Sven; Hertling, Claus: Conjectures on spectral numbers for upper triangular matrices and for singularities (2020)
  14. Barajas, Paul; Duarte, Daniel: On the module of differentials of order (n) of hypersurfaces (2020)
  15. Bauer, Thomas; Malara, Grzegorz; Szemberg, Tomasz; Szpond, Justyna: Quartic unexpected curves and surfaces (2020)
  16. Bendle, Dominik; Böhm, Janko; Decker, Wolfram; Georgoudis, Alessandro; Pfreundt, Franz-Josef; Rahn, Mirko; Wasser, Pascal; Zhang, Yang: Integration-by-parts reductions of Feynman integrals using singular and GPI-space (2020)
  17. Binyamin, Muhammad Ahsan; Aslam, Saima; Mehmood, Khawar; Mahmood, Hasan; Ishaq, Muhammad: Recognition of contact map germs from the plane to the plane by invariants (2020)
  18. Bivià-Ausina, Carles; Ruas, Maria Aparecida Soares: Mixed Bruce-Roberts numbers (2020)
  19. Böhm, Janko; Keicher, Simon; Ren, Yue: Computing GIT-fans with symmetry and the Mori chamber decomposition of (\overlineM_0,6) (2020)
  20. Böhm, Janko; Marais, Magdaleen S.; Steenpaß, Andreas: The classification of real singularities using \textscSingular. III: Unimodal singularities of corank 2 (2020)

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