Plural: a computer algebra system for noncommutative polynomial algebras

ABSTRACT

Singular is a computer algebra system 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 Gr"obner 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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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

Additional Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.8 Metrics
          Subjects: Performance measures

  H. Information Systems
  H.4 INFORMATION SYSTEMS APPLICATIONS
      H.4.m Miscellaneous

General Terms:
Algorithms, Design, Performance

Keywords:
groebner bases, noncommutative algebras