  Let $k$ be either a number a field or a function field over $\mathbb{Q}$ with
finitely many variables. We present a practical algorithm to compute the
geometric Picard lattice of a K3 surface over $k$ of degree $2$, i.e., a double
cover of the projective plane over $k$ ramified above a smooth sextic curve.
The algorithm might not terminate, but if it terminates then it returns a
proven correct answer.
