Short overview of PLURAL
SINGULAR :: PLURAL is a kernel extension of SINGULAR , which is designed for considerably fast computations within the class of non-commutative polynomial algebras.

The system allows us to handle many problems, coming from representation theory (including Lie and quantum algebras), algebraic geometry, theoretical physics and differential equations.

  • Major tools: a generalization of Buchberger's algorithm for computing Gröbner bases and of Schreyer's algorithm for computing syzygies and free resolutions.

  • Main computational objects: ideals/modules over non-commutative G-algebras over various ground fields.

  • Many algorithms implemented in kernel (written in C/C++).

  • Intuitive, C-like programming language

  • Some algorithms implemented as PLURAL libraries.

  • Development started in 2000. PLURAL will be freely available for most hard- and software platforms (Unix, Windows, Macintosh) soon.

KL, 06/03 http://www.singular.uni-kl.de