Singular is a computer algebra system (CAS) developed for efficient computations with polynomials. We describe Plural as an extension of Singular to noncommutative polynomial rings (G-/GR-algebras): to which structures does it apply, the prerequisites to monomial orderings, left- and two-sided Gröbner bases. The usual criteria to avoid “useless pairs” are revisited for their applicability in the case of G-/GR-algebras. Benchmark tests are used to evaluate the concepts compare them with other systems.

References in zbMATH (referenced in 45 articles , 2 standard articles )

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  1. Kredel, Heinz: Common divisors of solvable polynomials in JAS (2016)
  2. Kredel, Heinz: Parametric solvable polynomial rings and applications (2015)
  3. Seiler, Werner M.; Zerz, Eva: Algebraic theory of linear systems: a survey (2015)
  4. Cimprič, Jakob; Helton, J.William; Klep, Igor; McCullough, Scott; Nelson, Christopher: On real one-sided ideals in a free algebra (2014)
  5. Damiano, Alberto; Sabadini, Irene; Souček, Vladimir: Different approaches to the complex of three Dirac operators (2014)
  6. Robertz, Daniel: Formal algorithmic elimination for PDEs (2014)
  7. Dang Tuan Hiep: Computation in multivariate quaternionic polynomial ring (2013)
  8. Quadrat, Alban: Grade filtration of linear functional systems. (2013)
  9. Studzinski, Grischa: Implementation and applications of fundamental algorithms relying on Gröbner bases in free associative algebras. (2013)
  10. Bringmann, Kathrin; Raum, Martin; Richter, Olav K.: Kohnen’s limit process for real-analytic Siegel modular forms (2012)
  11. Levandovskyy, Viktor; Schindelar, Kristina: Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases (2012)
  12. Levandovskyy, V.; Martín-Morales, J.: Algorithms for checking rational roots of $b$-functions and their applications (2012)
  13. Levandovskyy, Viktor; Koutschan, Christoph; Motsak, Oleksandr: On two-generated non-commutative algebras subject to the affine relation. (2011)
  14. Levandovskyy, Viktor; Schindelar, Kristina: Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases (2011)
  15. Levandovskyy, Viktor; Zerz, Eva; Schindelar, Kristina: Exact linear modeling using Ore algebras (2011)
  16. Abłamowicz, Rafał: Computation of non-commutative Gröbner bases in Grassmann and Clifford algebras (2010)
  17. Anderson, Lara B.; Braun, Volker; Karp, Robert L.; Ovrut, Burt A.: Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories (2010)
  18. Andres, Daniel; Brickenstein, Michael; Levandovskyy, Viktor; Martín-Morales, Jorge; Schönemann, Hans: Constructive $D$-module theory with Singular (2010)
  19. Benkart, Georgia; Pereira, Mariana; Witherspoon, Sarah: Yetter-Drinfeld modules under cocycle twists. (2010)
  20. Brickenstein, Michael: Slimgb: Gröbner bases with slim polynomials (2010)

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