  For a morphism $f:\P^N \to \P^N$, the points whose forward orbit by $f$ is
finite are called preperiodic points for $f$. This article presents an
algorithm to effectively determine all the rational preperiodic points for $f$
defined over a given number field $K$. This algorithm is implemented in the
open-source software Sage for $\Q$. Additionally, the notion of a dynatomic
zero-cycle is generalized to preperiodic points. Along with examining their
basic properties, these generalized dynatomic cycles are shown to be effective.
