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 1471 articles , 4 standard articles )

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  1. Bilski, Marcin; Scheiblechner, Peter: Effective approximation of the solutions of algebraic equations (2022)
  2. Böhm, Janko; Decker, Wolfram; Laplagne, Santiago; Pfister, Gerhard: Computing integral bases via localization and Hensel lifting (2022)
  3. Jafari, Raheleh; Yaghmaei, Marjan: Type and conductor of simplicial affine semigroups (2022)
  4. Kudo, Momonari: Computing representation matrices for the action of Frobenius on cohomology groups (2022)
  5. Kummini, Manoj; Mondal, Mandira: On Hilbert ideals for a class of (p)-groups in characteristic (p) (2022)
  6. La Scala, Roberto; Tiwari, Sharwan K.: Stream/block ciphers, difference equations and algebraic attacks (2022)
  7. Abbott, John; Bigatti, Anna Maria; Robbiano, Lorenzo: Ideals modulo a prime (2021)
  8. Algaba, Antonio; García, Cristóbal; Reyes, Manuel: Analytical integrability of perturbations of quadratic systems (2021)
  9. Altmann, Klaus; Witt, Frederik: Toric co-Higgs sheaves (2021)
  10. Aziz, Waleed; Amen, Azad; Pantazi, Chara: Integrability and linearizability of a family of three-dimensional quadratic systems (2021)
  11. Aziz, Waleed; Christopher, Colin; Llibre, Jaume; Pantazi, Chara: Three-dimensional Lotka-Volterra systems with 3:(-1):2-resonance (2021)
  12. Barakat, Mohamed; Behrends, Reimer; Jefferson, Christopher; Kühne, Lukas; Leuner, Martin: On the generation of rank 3 simple matroids with an application to Terao’s freeness conjecture (2021)
  13. Berthomieu, Christian Eder, Mohab Safey El Din: msolve: A Library for Solving Polynomial Systems (2021) arXiv
  14. Besier, Marco; Festi, Dino: Rationalizability of square roots (2021)
  15. Böhm, Janko; Decker, Wolfram; Frühbis-Krüger, Anne; Pfreundt, Franz-Josef; Rahn, Mirko; Ristau, Lukas: Towards massively parallel computations in algebraic geometry (2021)
  16. Bonnafé, Cédric: Some singular curves and surfaces arising from invariants of complex reflection groups (2021)
  17. Braun, Lukas: Completing the classification of representations of (SL_n) with complete intersection invariant ring (2021)
  18. Busé, Laurent; Dimca, Alexandru; Schenck, Hal; Sticlaru, Gabriel: The hessian polynomial and the Jacobian ideal of a reduced hypersurface in (\mathbbP^n) (2021)
  19. Calviño-Louzao, E.; García-Río, E.; Gutiérrez-Rodríguez, I.; Vázquez-Lorenzo, R.: Homogeneous conformal (C)-spaces in dimension four (2021)
  20. Cao, Jin; Movasati, Hossein; Yau, Shing-Tung: Gauss-Manin connection in disguise: genus two curves (2021)

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