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 1337 articles , 4 standard articles )

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  1. Abbott, John; Bigatti, Anna Maria; Palezzato, Elisa; Robbiano, Lorenzo: Computing and using minimal polynomials (2020)
  2. Algaba, A.; García, C.; Reyes, M.: Quasi-homogeneous linearization of degenerate vector fields (2020)
  3. Amata, Luca; Crupi, Marilena: Hilbert functions of graded modules over an exterior algebra: an algorithmic approach (2020)
  4. Aoki, Satoshi: Introduction to computational algebraic statistics (2020)
  5. Bahloul, Rouchdi: Gröbner bases in (D)-modules: application to Bernstein-Sato polynomials (2020)
  6. Balnojan, Sven; Hertling, Claus: Conjectures on spectral numbers for upper triangular matrices and for singularities (2020)
  7. Barajas, Paul; Duarte, Daniel: On the module of differentials of order (n) of hypersurfaces (2020)
  8. Bauer, Thomas; Malara, Grzegorz; Szemberg, Tomasz; Szpond, Justyna: Quartic unexpected curves and surfaces (2020)
  9. 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)
  10. Bivià-Ausina, Carles; Ruas, Maria Aparecida Soares: Mixed Bruce-Roberts numbers (2020)
  11. Böhm, Janko; Marais, Magdaleen S.; Steenpaß, Andreas: The classification of real singularities using \textscsingularpart III: unimodal singularities of corank 2 (2020)
  12. Boutin, Mireille; Kemper, Gregor: A drone can hear the shape of a room (2020)
  13. Brown, Gavin; Fatighenti, Enrico: Hodge numbers and deformations of Fano 3-folds (2020)
  14. Cimpoeaş, Mircea: On the restricted partition function via determinants with Bernoulli polynomials (2020)
  15. Clarke, Oliver; Mohammadi, Fatemeh; Rauh, Johannes: Conditional independence ideals with hidden variables (2020)
  16. da Cruz, Leonardo P. C.; Romanovski, Valery G.; Torregrosa, J.: The center and cyclicity problems for quartic linear-like reversible systems (2020)
  17. Decker, Wolfram; Eder, Christian; Levandovskyy, Viktor; Tiwari, Sharwan K.: Modular techniques for noncommutative Gröbner bases (2020)
  18. Di Marca, Michela; Malara, Grzegorz; Oneto, Alessandro: Unexpected curves arising from special line arrangements (2020)
  19. Dimca, Alexandru; Sticlaru, Gabriel: Computing Milnor fiber monodromy for some projective hypersurfaces (2020)
  20. Dimca, Alexandru; Sticlaru, Gabriel: Plane curves with three syzygies, minimal Tjurina curves, and nearly cuspidal curves (2020)

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