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.

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  1. Ceria, Michela; Mora, Teo; Roggero, Margherita: A general framework for Noetherian well ordered polynomial reductions (2019)
  2. Fajardo, William: A computational Maple library for skew PBW extensions (2019)
  3. Khan, Muhammad Abdul Basit; Alam Khan, Junaid; Binyamin, Muhammad Ahsan: SAGBI bases in (G)-algebras (2019)
  4. Mialebama Bouesso, Andre S. E.; Mobouale Wamba, G.: Relations of the algebra of polynomial integrodifferential operators (2019)
  5. Hossein Poor, Jamal; Raab, Clemens G.; Regensburger, Georg: Algorithmic operator algebras via normal forms in tensor rings (2018)
  6. Huang, Hau-Wen: An algebra behind the Clebsch-Gordan coefficients of (U_q(\mathfraksl_2)) (2018)
  7. Levandovskyy, Viktor; Heinle, Albert: A factorization algorithm for (G)-algebras and its applications (2018)
  8. Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi: Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic (D)-modules (2018)
  9. Pumplün, Susanne: How to obtain lattices from ((f,\sigma,\delta))-codes via a generalization of construction A (2018)
  10. Bell, Jason P.; Heinle, Albert; Levandovskyy, Viktor: On noncommutative finite factorization domains (2017)
  11. Ceria, Michela; Mora, Teo: Buchberger-Zacharias theory of multivariate Ore extensions (2017)
  12. Heinle, Albert; Levandovskyy, Viktor: Factorization of ( \mathbbZ)-homogeneous polynomials in the first (q)-Weyl algebra (2017)
  13. Johannes Hoffmann, Viktor Levandovskyy: Constructive Arithmetics in Ore Localizations of Domains (2017) arXiv
  14. La Scala, Roberto: Computing minimal free resolutions of right modules over noncommutative algebras (2017)
  15. Reyes, Armando; Suárez, Héctor: (\sigma)-PBW extensions of skew Armendariz rings (2017)
  16. Walther, Uli: The Jacobian module, the Milnor fiber, and the (D)-module generated by (f^s) (2017)
  17. Chrapary, Hagen; Ren, Yue: The software portal swMATH: a state of the art report and next steps (2016)
  18. Heinle, Albert; Levandovskyy, Viktor: A factorization algorithm for (G)-algebras and applications (2016)
  19. Kredel, Heinz: Common divisors of solvable polynomials in JAS (2016)
  20. Kredel, Heinz: Parametric solvable polynomial rings and applications (2015)

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