Intersection at infinity. Let
and compute a prime
factorization of the polynomial
,
Each factor that appeared also in the prime factorization
(4) of
corresponds to a closed point
in the intersection
of with the plane curve defined by . For the corresponding
closed places we compute
where
is the primitive
parametrization obtained from the sHNE of
(cf. Step 4 of the algorithm in Section
2.4.1).
Finally, if
and
then we compute for the
corresponding closed places the multiplicities