  We present a small computer algebra program for use in Maxwell's theory. The
Maxwell equations and the energy-momentum current of the electromagnetic field
are formulated in the language of exterior differential forms. The
corresponding program can be applied (in the presence of a gravitational field)
in curved Riemannian spacetime as well as in flat Minkowski spacetime in
inertial or {\em non-inertial} frames. Our program is written for the computer
algebra system REDUCE with the help of the EXCALC package for exterior
differential forms.\par The two major advantages of this modern approch to
electrodynamics --- the natural formulation, free of both metric and
coordinates, and the straightforward programming of problems --- are
illustrated by examining a number of examples ranging from the Coulomb field of
a static point charge to the Kerr--Newman solution of the Einstein--Maxwell
equations.
