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 1305 articles , 4 standard articles )

Showing results 21 to 40 of 1305.
Sorted by year (citations)

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  1. García-García, J. I.; Ojeda, I.; Rosales, J. C.; Vigneron-Tenorio, A.: On pseudo-Frobenius elements of submonoids of (\mathbbN^d) (2020)
  2. Greuel, Gert-Martin; Pham, Thuy Huong: Algorithms for group actions in arbitrary characteristic and a problem in singularity theory (2020)
  3. Gromada, Daniel; Weber, Moritz: Intertwiner spaces of quantum group subrepresentations (2020)
  4. Guo, Feng; Phạm, Ti’ên-Son: On types of degenerate critical points of real polynomial functions (2020)
  5. Hashemi, Amir; Seiler, Werner M.: Dimension and depth dependent upper bounds in polynomial ideal theory (2020)
  6. Herzog, Jürgen; Jafari, Raheleh; Nasrollah Nejad, Abbas: On the Gauss algebra of toric algebras (2020)
  7. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations of domains (2020)
  8. Iohara, Kenji (ed.); Malbos, Philippe (ed.); Saito, Masa-Hiko (ed.); Takayama, Nobuki (ed.): Two algebraic byways from differential equations: Gröbner bases and quivers (2020)
  9. Ishitsuka, Yasuhiro; Ito, Tetsushi; Ohshita, Tatsuya: Explicit calculation of the mod 4 Galois representation associated with the Fermat quartic (2020)
  10. Kruff, Niclas: Invariant ideals of local analytic and formal vector fields (2020)
  11. Kruff, Niclas; Schilli, Christian; Walcher, Sebastian; Zerz, Eva: Attracting and natural invariant varieties for polynomial vector fields and control systems (2020)
  12. Kruff, Niclas; Walcher, Sebastian: Coordinate-independent criteria for Hopf bifurcations (2020)
  13. Len, Yoav; Markwig, Hannah: Lifting tropical bitangents (2020)
  14. Lenz, Matthias: On powers of Plücker coordinates and representability of arithmetic matroids (2020)
  15. Messerschmidt, Miek: On compact packings of the plane with circles of three radii (2020)
  16. Nasrollah Nejad, Abbas; Shahidi, Zahra: The Valabrega-Valla module of the Jacobian ideal of points in a projective plane (2020)
  17. Shibuta, Takafumi; Tajima, Shinichi: An algorithm for computing the Hilbert-Samuel multiplicities and reductions of zero-dimensional ideals of Cohen-Macaulay local rings (2020)
  18. Silva, O. N.: Equimultiplicity of families of map germs from (\mathbbC^2) to (\mathbbC^3) (2020)
  19. Staglianò, Giovanni: Special cubic birational transformations of projective spaces (2020)
  20. Zhou, Zhengxin; Romanovski, Valery G.; Yu, Jiang: Centers and limit cycles of a generalized cubic Riccati system (2020)

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