  We construct an algorithm for solving the following problem: given a number
field $K$, a positive integer $N$, and a positive real number $B$, determine
all points in $\mathbb P^N(K)$ having relative height at most $B$. A
theoretical analysis of the efficiency of the algorithm is provided, as well as
sample computations showing how the algorithm performs in practice. Two
variants of the method are described, and examples are given to compare their
running times. In the case $N=1$ we compare our method to an earlier algorithm
for enumerating elements of bounded height in number fields.

Number Theory