  The necessary and sufficient conditions for a spacetime with an invariant
frame to admit a group of isometries of dimension $r$ are given in terms of the
connection tensor $H$ associated with this frame. In Petrov-Bel types I, II and
III, and in other spacetimes where an invariant frame algebraically defined by
the curvature tensor exists, the connection tensor $H$ is given in terms of the
Weyl and Ricci tensors without an explicit determination of the frame. Thus, an
IDEAL (intrinsic, deductive, explicit and algorithmic) characterization of
these spacetimes follows. Some examples show that this algorithm can be easily
implemented on the xAct Mathematica suite of packages.
