ABSTRACT SPECIFICATION OF STRUCTURES AND METHODS IN SYMBOLIC MATHEMATICAL COMPUTATION

This paper describes a methodology based on the object-oriented programming paradigm, to support the design and implementation of a symbolic computation system. The requirements of the system are related to the specification and treatment of mathematical structures. This treatment is considered from both the numerical and the symbolic points of view. The resulting programming system should be able to support the formal definition of mathematical data structures and methods at their highest level of abstraction, to perform computations on instances created from such definitions, and to handle abstract data structures through the manipulation of their logical properties. Particular consideration is given to the correctness aspects. Some examples of convenient application of the proposed design methodology are presented.