  A procedure for the construction and the classification of multilattices in
arbitrary dimension is proposed. The algorithm allows to determine explicitly
the location of the points of a multilattice given its space group, and to
determine whether two multilattices are arithmetically equivalent. The
algorithm is based on ideas from integer matrix theory, in particular the
reduction to the Smith normal form. Among the applications of this procedure is
a software package that allows the classification of complex crystalline
structures and the determination of their space groups. Also, it can be used to
determine the symmetry of regular systems of points in high dimension, with
applications to the study of quasicrystals and sets of points with
noncrystallographic symmetry in low dimension, such as viral capsid structures.
