REDUCE: a user-oriented interactive system for algebraic simplification

Many of the day-to-day problems which confront applied mathematicians involve extensive algebraic or nonnumerical calculation. Such problems may range from the evaluation of analytical solutions to complicated differential or integral equations on the one hand, to the calculation of coefficients in a power series expansion or the computation of the derivative of a complicated function on the other. The difference between these two classes of problems is obvious; in the former case, no straightforward algorithm exists which will guarantee a solution, and indeed, an analytic form for the solution may not even exist. On the other hand, algorithms do exist for the solution of problems such as series expansion and differentiation, and therefore a correct answer may always be found provided that the researcher possesses sufficient time, perseverance, and accuracy to carry the more complicated problems through free of error. Many examples of this type of problem may be found in physics and engineering. Calculations of general relativistic effects in planetary motion, structural design calculations, and many of the calculations associated with elementary particle physics experiments at high energy accelerators, to name a few, may demand many man-months or even years of work before a useful and error free answer can be found, even though the operations involved are quite straightforward.