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 1408 articles , 4 standard articles )

Showing results 1 to 20 of 1408.
Sorted by year (citations)

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  1. Algaba, Antonio; García, Cristóbal; Reyes, Manuel: Analytical integrability of perturbations of quadratic systems (2021)
  2. Chen, Justin; Vemulapalli, Sameera; Zhang, Leon: Computing unit groups of curves (2021)
  3. Denham, Graham; Schulze, Mathias; Walther, Uli: Matroid connectivity and singularities of configuration hypersurfaces (2021)
  4. Ðinh, Sĩ Tiệp; Jelonek, Zbigniew: Thom isotopy theorem for nonproper maps and computation of sets of stratified generalized critical values (2021)
  5. Dinu, Rodica; Herzog, Jürgen; Qureshi, Ayesha Asloob: Restricted classes of Veronese type ideals and algebras (2021)
  6. Dufresne, Emilie; Harrington, Heather A.; Hauenstein, Jonathan D.; Kevrekidis, Panayotis G.; Tripoli, Paolo: On some configurations of oppositely charged trapped vortices in the plane (2021)
  7. Eder, Christian; Hofmann, Tommy: Efficient Gröbner bases computation over principal ideal rings (2021)
  8. Eder, Christian; Pfister, Gerhard; Popescu, Adrian: Standard bases over Euclidean domains (2021)
  9. Gasanova, Oleksandra: Powers of monomial ideals and the Ratliff-Rush operation (2021)
  10. Harbourne, Brian; Migliore, Juan; Tutaj-Gasińska, Halszka: New constructions of unexpected hypersurfaces in (\mathbbP^n) (2021)
  11. Heule, Marijn J. H.; Kauers, Manuel; Seidl, Martina: New ways to multiply (3 \times3)-matrices (2021)
  12. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations enjoying enough commutativity (2021)
  13. Jaramillo, Delio; Vaz Pinto, Maria; Villarreal, Rafael H.: Evaluation codes and their basic parameters (2021)
  14. Kapur, Deepak; Lu, Dong; Monagan, Michael; Sun, Yao; Wang, Dingkang: Algorithms for computing greatest common divisors of parametric multivariate polynomials (2021)
  15. Kloosterman, Remke; Rams, Sławomir: Quintic threefolds with triple points (2021)
  16. Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath: Moh’s example of algebroid space curves (2021)
  17. Nieto-Baños, Isidro; Del Angel-Rodriguez, Pedro Luis: Variation of mixed Hodge structures associated to an equisingular one-dimensional family of Calabi-Yau threefolds (2021)
  18. Pfister, Gerhard; Steenpaß, Andreas: On the primary decomposition of some determinantal hyperedge ideal (2021)
  19. Planas-Vilanova, Francesc: Noetherian rings of low global dimension and syzygetic prime ideals (2021)
  20. Portakal, Irem: On rigidity of toric varieties arising from bipartite graphs (2021)

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