Plural

Singular is a computer algebra system (CAS) developed for efficient computations with polynomials. Plural is a (kernel) extension of Singular to noncommutative polynomial rings having PBW bases and their quotients (called G-/GR-algebras, also known as solvable polynomial algebras and PBW-algebras). All fields available in Singular and all the global monomial orderings are supported for computing left, right and two-sided Gröbner bases. There are many advanced functions, available both in the kernel and via the third-party libraries in the Singular language.


References in zbMATH (referenced in 83 articles , 2 standard articles )

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  1. Eder, Christian; Pfister, Gerhard; Popescu, Adrian: Standard bases over Euclidean domains (2021)
  2. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations enjoying enough commutativity (2021)
  3. Cluzeau, Thomas; Koutschan, Christoph; Quadrat, Alban; Tõnso, Maris: Effective algebraic analysis approach to linear systems over Ore algebras (2020)
  4. Decker, Wolfram; Eder, Christian; Levandovskyy, Viktor; Tiwari, Sharwan K.: Modular techniques for noncommutative Gröbner bases (2020)
  5. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations of domains (2020)
  6. Levandovskyy, Viktor; Metzlaff, Tobias; Zeid, Karim Abou: Computation of free non-commutative Gröbner bases over (\mathbbZ) with \textscSingular:Letterplace (2020)
  7. Levandovskyy, Viktor; Schönemann, Hans; Zeid, Karim Abou: \textscLetterplace-- a subsystem of \textscSingularfor computations with free algebras via letterplace embedding (2020)
  8. Lezama, Oswaldo; Venegas, Helbert: Center of skew \textitPBWextensions (2020)
  9. Quadrat, Alban (ed.); Zerz, Eva (ed.): Algebraic and symbolic computation methods in dynamical systems. Based on articles written for the invited sessions of the 5th symposium on system structure and control, IFAC, Grenoble, France, February 4--6, 2013 and of the 21st international symposium on mathematical theory of networks and systems (MTNS 2014), Groningen, the Netherlands, July 7--11, 2014 (2020)
  10. Schilli, Christian; Zerz, Eva; Levandovskyy, Viktor: Controlled and conditioned invariance for polynomial and rational feedback systems (2020)
  11. Ceria, Michela; Mora, Teo; Roggero, Margherita: A general framework for Noetherian well ordered polynomial reductions (2019)
  12. Fajardo, William: A computational Maple library for skew PBW extensions (2019)
  13. Khan, Muhammad Abdul Basit; Alam Khan, Junaid; Binyamin, Muhammad Ahsan: SAGBI bases in (G)-algebras (2019)
  14. Mialebama Bouesso, Andre S. E.; Mobouale Wamba, G.: Relations of the algebra of polynomial integrodifferential operators (2019)
  15. Hoffmann, Johannes; Levandovskyy, Viktor: Constructive arithmetics in Ore localizations with enough commutativity (2018)
  16. Hossein Poor, Jamal; Raab, Clemens G.; Regensburger, Georg: Algorithmic operator algebras via normal forms in tensor rings (2018)
  17. Huang, Hau-Wen: An algebra behind the Clebsch-Gordan coefficients of (U_q(\mathfraksl_2)) (2018)
  18. Levandovskyy, Viktor; Heinle, Albert: A factorization algorithm for (G)-algebras and its applications (2018)
  19. Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi: Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic (D)-modules (2018)
  20. Pumplün, Susanne: How to obtain lattices from ((f,\sigma,\delta))-codes via a generalization of construction A (2018)

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