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 1441 articles , 4 standard articles )

Showing results 1 to 20 of 1441.
Sorted by year (citations)

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  1. Abbott, John; Bigatti, Anna Maria; Robbiano, Lorenzo: Ideals modulo a prime (2021)
  2. Algaba, Antonio; García, Cristóbal; Reyes, Manuel: Analytical integrability of perturbations of quadratic systems (2021)
  3. Altmann, Klaus; Witt, Frederik: Toric co-Higgs sheaves (2021)
  4. Aziz, Waleed; Amen, Azad; Pantazi, Chara: Integrability and linearizability of a family of three-dimensional quadratic systems (2021)
  5. 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)
  6. Berthomieu, Christian Eder, Mohab Safey El Din: msolve: A Library for Solving Polynomial Systems (2021) arXiv
  7. Besier, Marco; Festi, Dino: Rationalizability of square roots (2021)
  8. Böhm, Janko; Decker, Wolfram; Frühbis-Krüger, Anne; Pfreundt, Franz-Josef; Rahn, Mirko; Ristau, Lukas: Towards massively parallel computations in algebraic geometry (2021)
  9. Braun, Lukas: Completing the classification of representations of (SL_n) with complete intersection invariant ring (2021)
  10. Cao, Jin; Movasati, Hossein; Yau, Shing-Tung: Gauss-Manin connection in disguise: genus two curves (2021)
  11. Cardoso Gonçalves, Maria Inez; Gonçalves, Daniel; Martín Barquero, Dolores; Martín González, Cándido; Siles Molina, Mercedes: Squares and associative representations of two-dimensional evolution algebras (2021)
  12. Chen, Justin; Vemulapalli, Sameera; Zhang, Leon: Computing unit groups of curves (2021)
  13. Dall’Agata, G.; Inverso, G.; Partipilo, D.: Old and new vacua of 5D maximal supergravity (2021)
  14. Denham, Graham; Schulze, Mathias; Walther, Uli: Matroid connectivity and singularities of configuration hypersurfaces (2021)
  15. Ðinh, Sĩ Tiệp; Jelonek, Zbigniew: Thom isotopy theorem for nonproper maps and computation of sets of stratified generalized critical values (2021)
  16. Dinu, Rodica; Herzog, Jürgen; Qureshi, Ayesha Asloob: Restricted classes of Veronese type ideals and algebras (2021)
  17. Dufresne, Emilie; Harrington, Heather A.; Hauenstein, Jonathan D.; Kevrekidis, Panayotis G.; Tripoli, Paolo: On some configurations of oppositely charged trapped vortices in the plane (2021)
  18. Dumnicki, Marcin; Harbourne, Brian; Roé, Joaquim; Szemberg, Tomasz; Tutaj-Gasińska, Halszka: Unexpected surfaces singular on lines in (\mathbbP^3) (2021)
  19. Eder, Christian; Hofmann, Tommy: Efficient Gröbner bases computation over principal ideal rings (2021)
  20. Eder, Christian; Pfister, Gerhard; Popescu, Adrian: Standard bases over Euclidean domains (2021)

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