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 1277 articles , 4 standard articles )

Showing results 1 to 20 of 1277.
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  1. Algaba, A.; García, C.; Reyes, M.: Quasi-homogeneous linearization of degenerate vector fields (2020)
  2. Amata, Luca; Crupi, Marilena: Hilbert functions of graded modules over an exterior algebra: an algorithmic approach (2020)
  3. Balnojan, Sven; Hertling, Claus: Conjectures on spectral numbers for upper triangular matrices and for singularities (2020)
  4. Barajas, Paul; Duarte, Daniel: On the module of differentials of order (n) of hypersurfaces (2020)
  5. Bauer, Thomas; Malara, Grzegorz; Szemberg, Tomasz; Szpond, Justyna: Quartic unexpected curves and surfaces (2020)
  6. Böhm, Janko; Marais, Magdaleen S.; Steenpaß, Andreas: The classification of real singularities using \textscsingularpart III: unimodal singularities of corank 2 (2020)
  7. Boutin, Mireille; Kemper, Gregor: A drone can hear the shape of a room (2020)
  8. Doran, Charles F.; Harder, Andrew; Novoseltsev, Andrey Y.; Thompson, Alan: Calabi-Yau threefolds fibred by high rank lattice polarized K3 surfaces (2020)
  9. Elias, Juan; Homs, Roser; Mourrain, Bernard: Computing minimal Gorenstein covers (2020)
  10. Fan, Xiang: Permutation polynomials of degree 8 over finite fields of odd characteristic (2020)
  11. Guo, Feng; Phạm, Ti’ên-Son: On types of degenerate critical points of real polynomial functions (2020)
  12. Hashemi, Amir; Seiler, Werner M.: Dimension and depth dependent upper bounds in polynomial ideal theory (2020)
  13. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations of domains (2020)
  14. Len, Yoav; Markwig, Hannah: Lifting tropical bitangents (2020)
  15. Shibuta, Takafumi; Tajima, Shinichi: An algorithm for computing the Hilbert-Samuel multiplicities and reductions of zero-dimensional ideals of Cohen-Macaulay local rings (2020)
  16. Staglianò, Giovanni: Special cubic birational transformations of projective spaces (2020)
  17. 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)
  18. Al-Ayyoub, Ibrahim; Jaradat, Imad; Al-Zoubi, Khaldoun: On the normality of a class of monomial ideals via the Newton polyhedron (2019)
  19. Alberich-Carramiñana, Maria; Montaner, Josep Àlvarez; Blanco, Guillem: Effective computation of base points of ideals in two-dimensional local rings (2019)
  20. Algaba, Antonio; García, Cristóbal; Giné, Jaume: Nondegenerate and nilpotent centers for a cubic system of differential equations (2019)

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