Multidimensional greatest common divisor and Lehmer algorithms

A class of multidimensional greatest common divisor algorithms is studied. Their connection with the Jacobi algorithm is established and used to obtain theoretical properties such as the existence of digit frequencies. A technique of D. H. Lehmer's for Euclid's algorithm is generalized for efficient computation of the multidimensional algorithms. For triples of integers, two algorithms of interest are studied empirically.This work was partially supported by NSF grant #DCR75-07070.