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 58 articles , 2 standard articles )

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  1. Hossein Poor, Jamal; Raab, Clemens G.; Regensburger, Georg: Algorithmic operator algebras via normal forms in tensor rings (2018)
  2. Levandovskyy, Viktor; Heinle, Albert: A factorization algorithm for $G$-algebras and its applications (2018)
  3. Bell, Jason P.; Heinle, Albert; Levandovskyy, Viktor: On noncommutative finite factorization domains (2017)
  4. Ceria, Michela; Mora, Teo: Buchberger-Zacharias theory of multivariate Ore extensions (2017)
  5. Johannes Hoffmann, Viktor Levandovskyy: Constructive Arithmetics in Ore Localizations of Domains (2017) arXiv
  6. La Scala, Roberto: Computing minimal free resolutions of right modules over noncommutative algebras (2017)
  7. Walther, Uli: The Jacobian module, the Milnor fiber, and the $D$-module generated by $f^s$ (2017)
  8. Chrapary, Hagen; Ren, Yue: The software portal swMATH: a state of the art report and next steps (2016)
  9. Heinle, Albert; Levandovskyy, Viktor: A factorization algorithm for $G$-algebras and applications (2016)
  10. Kredel, Heinz: Common divisors of solvable polynomials in JAS (2016)
  11. Kredel, Heinz: Parametric solvable polynomial rings and applications (2015)
  12. Robertz, Daniel: Recent progress in an algebraic analysis approach to linear systems (2015)
  13. Seiler, Werner M.; Zerz, Eva: Algebraic theory of linear systems: a survey (2015)
  14. Zhao, Xiangui; Zhang, Yang: A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings. (2015)
  15. Cimprič, Jakob; Helton, J.William; Klep, Igor; McCullough, Scott; Nelson, Christopher: On real one-sided ideals in a free algebra (2014)
  16. Damiano, Alberto; Sabadini, Irene; Souček, Vladimir: Different approaches to the complex of three Dirac operators (2014)
  17. Robertz, Daniel: Formal algorithmic elimination for PDEs (2014)
  18. Dang Tuan Hiep: Computation in multivariate quaternionic polynomial ring (2013)
  19. Quadrat, Alban: Grade filtration of linear functional systems. (2013)
  20. Studzinski, Grischa: Implementation and applications of fundamental algorithms relying on Gröbner bases in free associative algebras. (2013)

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