On the Computation of Elementary Divisors of Integer Matrices

The εi are called the elementary divisors of A and à is called the Smith normal form or elementary divisors form of A. In Section 3 we give an algorithm for computing for a given matrix A, its rank r and a prime p the p-parts of the elementary divisors of A. During the algorithm we perform row operations on the matrix A which are driven by only considering certain reductions of row vectors modulo p. The method does not give transforming matrices L and R as in the proposition. A crucial point for the application of our algorithm is that one needs to know the prime numbers dividing εr (or δr). These are often known from the mathematical context. In