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SINGULAR : PLURAL is a kernel extension of SINGULAR , which is designed to fill the present gap in considerably fast computations within the certain class of noncommutative 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. The major tools we use are the generalization of Buchberger's algorithm for computing Groebner basis and Schreyer's algorithm for computing syzygies and free resolutions
- Main computational objects: ideals/modules over noncommutative 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; currently is not yet distributed. PLURAL will be freely available for most hard- and software platforms (Unix, Windows, Macintosh).