A modular algorithm to compute the generalized Hermite normal form for Z[x]-lattices. (July 2017) - Jing, Rui-Juan; Yuan, Chun-Ming
Abstract: 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.