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 1260 articles , 4 standard articles )

Showing results 1 to 20 of 1260.
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  1. Barajas, Paul; Duarte, Daniel: On the module of differentials of order (n) of hypersurfaces (2020)
  2. Len, Yoav; Markwig, Hannah: Lifting tropical bitangents (2020)
  3. Shibuta, Takafumi; Tajima, Shinichi: An algorithm for computing the Hilbert-Samuel multiplicities and reductions of zero-dimensional ideals of Cohen-Macaulay local rings (2020)
  4. Abreu, S.; Dormans, J.; Febres Cordero, F.; Ita, H.; Page, B.; Sotnikov, V.: Analytic form of the planar two-loop five-parton scattering amplitudes in QCD (2019)
  5. Al-Ayyoub, Ibrahim; Jaradat, Imad; Al-Zoubi, Khaldoun: On the normality of a class of monomial ideals via the Newton polyhedron (2019)
  6. Alberich-Carramiñana, Maria; Montaner, Josep Àlvarez; Blanco, Guillem: Effective computation of base points of ideals in two-dimensional local rings (2019)
  7. Algaba, Antonio; García, Cristóbal; Giné, Jaume: Nondegenerate and nilpotent centers for a cubic system of differential equations (2019)
  8. Aoki, Hiroki; Takemori, Sho: The structure of mixed weight Hilbert modular forms (2019)
  9. Assunção de Brito Lira, Fausto; Domitrz, Wojciech; Wik Atique, Roberta: Symplectic singularity of curves with semigroups (4, 5, 6, 7), (4, 5, 6) and (4, 5, 7) (2019)
  10. Balnojan, Sven; Hertling, Claus: Real Seifert forms and polarizing forms of Steenbrink mixed Hodge structures (2019)
  11. Bertolini, Marina; Notari, Roberto; Turrini, Cristina: The Bordiga surface as critical locus for 3-view reconstructions (2019)
  12. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  13. Bravo, José Luis; Fernández, Manuel; Ojeda, Ignacio; Sánchez, Fernando: Uniqueness of limit cycles for quadratic vector fields (2019)
  14. Calviño-Louzao, E.; García-Martínez, Xabier; García-Río, Eduardo; Gutiérrez-Rodríguez, Ixcheldzohara; Vázquez-Lorenzo, R.: Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds (2019)
  15. Cant, Alexander; Eick, Bettina: Polynomials describing the multiplication in finitely generated torsion-free nilpotent groups (2019)
  16. Ceria, Michela: Bar code for monomial ideals (2019)
  17. Chan, Andrew J.; Maclagan, Diane: Gröbner bases over fields with valuations (2019)
  18. Cid-Ruiz, Yairon: Bounding the degrees of a minimal (\mu)-basis for a rational surface parametrization (2019)
  19. Cueto, Maria Angelica; Markwig, Hannah: Tropical geometry of genus two curves (2019)
  20. Dimca, Alexandru; Sticlaru, Gabriel: Computing the monodromy and pole order filtration on Milnor fiber cohomology of plane curves (2019)

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