Computer Systems for the Representation and Manipulation of Mathematical Knowledge

摘要

There have been many attempts to design systems which use computers for the manipulation of symbolic mathematical data. Existing systems begin to provide a useful level of assistance to engineers, applied mathematicians, scientific programmers, and others who must perform large-scale or in other ways tedious symbolic, algebraic computation, accurately, as part of their work. However, systems which are currently available suffer from the fact that they are generally weakly-structured collections of ad hoc programs, and do not have systematic methods for the representation of knowledge (data and algorithms). In some cases, there are fundamental conflicts in being required to deal with notations and manipulations from different contexts. The current implementation strategy for systems consists of developing an efficient core algebra system, and tools with which to access it conveniently. These tools include user-programming languages, specialized environments, and graphics interfaces. The goal is to enable a user to deal with the computer and its mathematical knowledge in forms of discourse which are natural for analysis and applications. We used as a core system, parts of the MACSYMA algebra system. Although it would have been preferable in some respects to use a smaller modular system, resources were insufficient to build such programs.