A modular algorithm to compute the generalized Hermite normal form for Z[x]-lattices

In this paper, a modular algorithm is given to compute the generalized Hermite normal form of matrices over Z[x], or equivalently, the reduced Gröbner basis of Z[x]-modules in Z[x]n. The main advantage of the algorithm is that the special structure of the Gröbner basis of ideals in Z[x] is taken into consideration. The algorithm is deterministic and seems to be the most efficient available algorithm for inputs with relatively low degrees.