Using Computer Algebra to Choose and Apply Numerical Routines

In applied mathematics, electronic and chemical engineering, the modelling process can produce a number of mathematical problems which require numerical solutions for which symbolic methods are either not possible or not obvious. With the plethora of numerical library routines for the solution of these problems often the numerical analyst has to answer the question Which routine to choose? and How do I use it? Some analysis needs to be carried out before the appropriate routine can be identiied i.e. How stii is this ODE? and Is this function continuous? It may well be the case that more than one routine is applicable to the problem. So the question may become Which is likely to be the best? Such a choice may be critical for both accuracy and eeciency. An expert system is thus required to make this choice based on the result of its own analysis of the problem, call the routine and act on the outcome. This may be to put the answer in a relevant form or react to an apparent failure of the chosen routine and thus choose and call an alternative. It should also have suucient explanation mechanisms to inform on the choice of routine and the reasons for that choice. Much of this work can be achieved using computer algebra and symbolic algebra packages. This paper describes an expert system currently in prototype in terms of both its object-based structure and its computational agents. Some of these agents are described in detail, paying particular attention to the practical aspects of their algorithms and the use of computer algebra. The axi. om2 y Symbolic Algebra System is used as a user interface as well as the link to the NAG Foundation Library for the numerical routines and the inference mechanisms for the expert system.