A modular greatest common divisor algorithm for gaussian polynomials

In this paper the Brown-Collins modular greatest common divisor algorithm for polynomials in Z[x1,...,xv], where Z denotes the ring of rational integers, is generalized to apply to polynomials in G[x1,...,xv], where G denotes the ring of Gaussian integers, i.e., complex numbers of the form a + ib where a, b are in Z Under certain simplifying assumptions, a function is found that dominates the maximum computing time of the new god algorithm.