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 1504 articles , 4 standard articles )

Showing results 1 to 20 of 1504.
Sorted by year (citations)

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  1. Arcet, Barbara; Giné, Jaume; Romanovski, Valery G.: Linearizability of planar polynomial Hamiltonian systems (2022)
  2. Bilski, Marcin; Scheiblechner, Peter: Effective approximation of the solutions of algebraic equations (2022)
  3. Binyamin, Muhammad Ahsan; Mehmood, Khawar; Pfister, Gerhard: Simple singularities of reducible curves in characteristic (p > 0) (2022)
  4. Böhm, Janko; Decker, Wolfram; Laplagne, Santiago; Pfister, Gerhard: Computing integral bases via localization and Hensel lifting (2022)
  5. Byszewski, Jakub; Cornelissen, Gunther; Tijsma, Djurre: Automata and finite order elements in the Nottingham group (2022)
  6. Caboara, Massimo; Mascia, Carla: A partial characterization of Hilbert quasi-polynomials in the non-standard case (2022)
  7. Coutinho, S. C.: On the classification of foliations of degree three with one singularity (2022)
  8. Dias, Luis Renato G.; Ribeiro, Nilva Rodrigues: Lipschitz normally embedded set and tangent cones at infinity (2022)
  9. Ferreiro-Subrido, M.; García-Río, E.; Vázquez-Lorenzo, R.: Ricci solitons on four-dimensional Lorentzian Lie groups (2022)
  10. Gimenez, Philippe; Srinivasan, Hema: On gluing semigroups in (\mathbbN^n) and the consequences (2022)
  11. Gryszka, Beata: Approximate roots of quasi-ordinary polynomials (2022)
  12. Hashemi, Amir; Parnian, Hossein; Seiler, Werner M.: Computation of Macaulay constants and degree bounds for Gröbner bases (2022)
  13. Jafari, Raheleh; Yaghmaei, Marjan: Type and conductor of simplicial affine semigroups (2022)
  14. Kudo, Momonari: Computing representation matrices for the action of Frobenius on cohomology groups (2022)
  15. Kummini, Manoj; Mondal, Mandira: On Hilbert ideals for a class of (p)-groups in characteristic (p) (2022)
  16. La Scala, Roberto; Tiwari, Sharwan K.: Stream/block ciphers, difference equations and algebraic attacks (2022)
  17. Liang, Yihui: Degree bounds for Gröbner bases of modules (2022)
  18. Panizzut, Marta; Vigeland, Magnus Dehli: Tropical lines on cubic surfaces (2022)
  19. Planas-Vilanova, Francesc: Regular local rings of dimension four and Gorenstein syzygetic prime ideals (2022)
  20. Reinke, Bernhard: Diverging orbits for the Ehrlich-Aberth and the Weierstrass root finders (2022)

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