Plural, a Non-commutative Extension of Singular: Past, Present and Future

We describe the non–commutative extension of the computer algebra system Singular, called Plural. In the system, we provide rich functionality for symbolic computation within a wide class of non– commutative algebras. We discuss the computational objects of Plural, the implementation of main algorithms, various aspects of software engineering and numerous applications. Singular:Plural or, shortly, Plural [19] is a subsystem of a computer algebra system Singular [20]. It provides the framework for symbolic computations with one– and two–sided ideals and modules over non–commutative GR–algebras (Def. 2). Most of Gröbner basics (Sect. 2.5) are available in the kernel of the implementation, ranging from the elimination of variables to free resolutions. Additional functions and libraries provide many useful tools and advanced algorithms for non–commutative algebra. The powerful implementation and rich functionality make Plural a very helpful system for supporting the research in many fields on mathematics and its applications.