Fast parallel Hermite normal form computation of matrices over F[x]

We present an algorithm for computing the Hermite normal form of a polynomial matrix and an unimodular transformation matrix on a distributed computer network. We provide an algorithm for reducing the off-diagonal entries which is a combination of the standard algorithm and the reduce off-diagonal algorithm given by Chou and Collins. This algorithm is parametrised by an integer variable. We provide a technique for producing small multiplier matrices if the input matrix is not full-rank, and give an upper bound for the degrees of the entries in the multiplier matrix.