REDUCE Meets CAMAL

It is generally accepted that special purpose algebraic systems are more efficient than general purpose ones, but as machines get faster this does not matter. An experiment has been performed to see if using the ideas of the special purpose algebra system CAMAL(F) it is possible to make the general purpose system REDUCE perform calculations in celestial mechanics as efficiently as CAMAL did twenty years ago. To this end a prototype Fourier module is created for REDUCE, and it is tested on some small and medium-sized problems taken from the CAMAL test suite. The largest calculation is the determination of the Lunar Disturbing Function to the sixth order. An assessment is made as to the progress, or lack of it, which computer algebra has made, and how efficiently we are using modern hardware.