Modelling Algebraic Structures in a Symbolic Computation Environment

Algebraic structures are a concept from mathematics to bring sets and their operations together. This process is well-known in computer science, too, say in the specification of abstract datatypes [4] or in module systems of some programming languages. Most languages used for symbolic computation and computer algebra are untyped, which means that algebraic structure can't be modelled adequately. Recently typed languages gained more attention in the computer algebra community in form of suitable type system. After giving two different definitions for algebraic structures, we show with a couple of examples how algebras and functions which create algebras are modelled in the symbolic computation system AlgBench which has been extended by a type system for computer algebra. Keywords: Algebraic Structures, Computer Algebra, Type Constructors, Type Systems. 1 Introduction Computer algebra systems deal with the symbolic manipulation of mathematical expressions. They can be seen therefore ..