  In recent years there has been a great interest in topological photonics and
protected edge states. Here, we present a first principles method to compute
topological invariants of three-dimensional gapless phases. Our approach allows
to calculate the topological charges of Weyl points through the efficient
numerical computation of gap Chern numbers, which relies solely on the photonic
Green's function of the system. We particularize the framework to the Weyl
points that are found to emerge in a magnetized plasma due to the breaking of
time reversal symmetry. We discuss the relevance of modelling nonlocality when
considering the topological properties of continuous media such as the
magnetized plasma. We find that for some of the considered material models the
charge of the Weyl point can be expressed in terms of a difference of the gap
Chern numbers of two-dimensional material subcomponents. Our theory may be
extended to other three-dimensional topological phases, or to Floquet systems.
