Problem Solving Environments and Symbolic Computing

Abstract

What role should be played by symbolic mathematical computation facilities in scientific and engineering “problem solving environments”? Drawing upon standard facilities such as numerical and graphical libraries, symbolic computation should be useful for: The creation and manipulation of mathematical models; The production of custom optimized numerical software; The solution of delicate classes of mathematical problems that require handling beyond that available in traditional machine-supported floating-point computation. Symbolic representation and manipulation can potentially play a central organizing role in PSEs since their more general object representation allows a program to deal with a wider range of computational issues. In particular Numerical, graphical, and other processing can be viewed as special cases of symbolic manipulation with interactive symbolic computing providing both an organizing backbone and the communication “glue” among otherwise dissimilar components. This is an extended abstract. A full-length version can be found at www.cs.berkeley.edu/~fateman/papers/pse-kluwer.pdf.