  Computer algebra programs are presented for application in general
relativity, in electrodynamics, and in gauge theories of gravity. The
mathematical formalism used is the calculus of exterior differential forms, the
computer algebra system applied Hearn's Reduce with Schruefer's exterior form
package Excalc. As a non-trivial example we discuss a metric of Plebanski &
Demianski (of Petrov type D) together with an electromagnetic potential and a
triplet of post-Riemannian one-forms. This whole geometrical construct
represents an exact solution of a metric-affine gauge theory of gravity. We
describe a sample session and verify by computer that this exact solution
fulfills the appropriate field equations.-- Computer programs are described for
the irreducible decomposition of (non-Riemannian) curvature, torsion, and
nonmetricity.
