Towards a general theory of special functions
Communications of the ACM
Applications of symbol manipulation in theoretical physics
Communications of the ACM
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In this paper we consider some of the applications of automated algebraic manipulation which have been made in celestial mechanics. Particular attention is paid to the use of Poisson series, and a typical problem in perturbation theory is described. The requirements of processors for use in celestial mechanics are considered and compared with those for general manipulation packages. Some future directions for research using these systems are briefly outlined.To illustrate the relative simplicity of the algorithms required in celestial mechanics, a typical integration problem is considered in an appendix.