Characteristic polynomials of isometries of even unimodular lattices

E. Bayer-Fluckiger gave a necessary and sufficient condition for a polynomial to be realized as the characteristic polynomial of a semisimple isometry of an even unimodular lattice, by describing the local-global obstruction, and the present author extended that result. This article describes a systematic way to compute the obstruction. As an application, we give a necessary and sufficient condition for a Salem number of degree $10$ or $18$ to be realized as the dynamical degree of an automorphism of a non-projective K3 surface, in terms of its minimal polynomial.