Determining the structure of a crystal by X-ray methods requires repeated computation of the three-dimensional Fourier transform. Over the last few years, algorithms for computing finite Fourier transforms that take advantage of various crystal symmetries have been developed. These algorithms are efficient especially when the sampling space contains a prime number of points in each coordinate direction. In this work, we present a method of combining programs for two relatively prime integers p and q to obtain a program for sampling space containing p · q number of points in each coordinate direction. © 1990.