On the computation of elementary divisors of integer matrices

Abstract

We describe a "semi-modular" algorithm which computes for a given integer matrix A of known rank and a given prime p the multiplicities of p in the factorizations of the elementary divisors of A. Here "semi-modular" means that we apply operations to the integer matrix A but the operations are driven by considering only reductions of row vectors modulo p. © 2002 Academic Press.