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 926 articles , 4 standard articles )

Showing results 1 to 20 of 926.
Sorted by year (citations)

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  1. Bell, Jason P.; Heinle, Albert; Levandovskyy, Viktor: On noncommutative finite factorization domains (2017)
  2. Bertone, Cristina; Cioffi, Francesca; Roggero, Margherita: Double-generic initial ideal and Hilbert scheme (2017)
  3. Binyamin, Muhammad Ahsan; Rabia; Mahmood, Hasan; Khan, Junaid Alam; Mehmood, Khawar: Characterization of uni-modal parametric plane curve singularities (2017)
  4. Birkmeyer, Anna Lena; Gathmann, Andreas; Schmitz, Kirsten: The realizability of curves in a tropical plane (2017)
  5. Bivià-Ausina, Carles: Log canonical threshold and diagonal ideals (2017)
  6. Cherednik, Ivan; Danilenko, Ivan: DAHA approach to iterated torus links (2017)
  7. Donten-Bury, Maria; Keicher, Simon: Computing resolutions of quotient singularities (2017)
  8. Giné, Jaume: Center conditions for generalized polynomial Kukles systems (2017)
  9. Greuel, Gert-Martin; Pham, Thuy Huong: Mather-Yau theorem in positive characteristic (2017)
  10. Janko Boehm, Wolfram Decker, Simon Keicher, Yue Ren: Current Challenges in Developing Open Source Computer Algebra Systems (2017) arXiv
  11. Krone, Robert; Leykin, Anton: Eliminating dual spaces (2017)
  12. Lampa-Baczyńska, Magdalena; Szpond, Justyna: From Pappus theorem to parameter spaces of some extremal line point configurations and applications (2017)
  13. La Scala, Roberto: Monomial right ideals and the Hilbert series of noncommutative modules (2017)
  14. Markwig, Thomas; Ren, Yue; Wienand, Oliver: Standard bases in mixed power series and polynomial rings over rings (2017)
  15. Matsumoto, Ryutaroh; Ruano, Diego; Geil, Olav: List decoding algorithm based on voting in Gröbner bases for general one-point AG codes (2017)
  16. Stout, Andrew R.: On the auto Igusa-zeta function of an algebraic curve (2017)
  17. Walther, Uli: The Jacobian module, the Milnor fiber, and the $D$-module generated by $f^s$ (2017)
  18. Alberich-Carramiñana, Maria; Dachs-Cadefau, Ferran; Àlvarez Montaner, Josep: Multiplier ideals in two-dimensional local rings with rational singularities (2016)
  19. Bainbridge, Matt; Habegger, Philipp; Möller, Martin: Teichmüller curves in genus three and just likely intersections in $\mathbfG_m^n\times\mathbfG_a^n$ (2016)
  20. Birkmeyer, Anna Lena: The realizability of tropical hypersurfaces in matroid fans (2016)

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