  Using an interplay between superspace and component superconformal tensor
calculus techniques, recently, the off-shell construction of the supersymmetric
extension of the three independent curvature-squared invariants for minimal (N
= 1) gauged supergravity in five dimensions (5D) was completed. A key
ingredient in obtaining these results is the implementation of computer algebra
algorithms. In this report, we describe how to use cadabra to systematically
study component reduction from superspace with computer algebra in the case of
5D, N = 1 supergravity.
