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 66 articles , 2 standard articles )

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  1. Fajardo, William: A computational Maple library for skew PBW extensions (2019)
  2. Hossein Poor, Jamal; Raab, Clemens G.; Regensburger, Georg: Algorithmic operator algebras via normal forms in tensor rings (2018)
  3. Huang, Hau-Wen: An algebra behind the Clebsch-Gordan coefficients of (U_q(\mathfraksl_2)) (2018)
  4. Levandovskyy, Viktor; Heinle, Albert: A factorization algorithm for (G)-algebras and its applications (2018)
  5. Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi: Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic (D)-modules (2018)
  6. Pumplün, Susanne: How to obtain lattices from ((f,\sigma,\delta))-codes via a generalization of construction A (2018)
  7. Bell, Jason P.; Heinle, Albert; Levandovskyy, Viktor: On noncommutative finite factorization domains (2017)
  8. Ceria, Michela; Mora, Teo: Buchberger-Zacharias theory of multivariate Ore extensions (2017)
  9. Heinle, Albert; Levandovskyy, Viktor: Factorization of ( \mathbbZ)-homogeneous polynomials in the first (q)-Weyl algebra (2017)
  10. Johannes Hoffmann, Viktor Levandovskyy: Constructive Arithmetics in Ore Localizations of Domains (2017) arXiv
  11. La Scala, Roberto: Computing minimal free resolutions of right modules over noncommutative algebras (2017)
  12. Reyes, Armando; Suárez, Héctor: (\sigma)-PBW extensions of skew Armendariz rings (2017)
  13. Walther, Uli: The Jacobian module, the Milnor fiber, and the (D)-module generated by (f^s) (2017)
  14. Chrapary, Hagen; Ren, Yue: The software portal swMATH: a state of the art report and next steps (2016)
  15. Heinle, Albert; Levandovskyy, Viktor: A factorization algorithm for (G)-algebras and applications (2016)
  16. Kredel, Heinz: Common divisors of solvable polynomials in JAS (2016)
  17. Kredel, Heinz: Parametric solvable polynomial rings and applications (2015)
  18. Robertz, Daniel: Recent progress in an algebraic analysis approach to linear systems (2015)
  19. Seiler, Werner M.; Zerz, Eva: Algebraic theory of linear systems: a survey (2015)
  20. Zhao, Xiangui; Zhang, Yang: A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings. (2015)

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