  Correlation functions for matrix ensembles with orthogonal and
unitarysymplectic rotation symmetry are more complicated to calculate than in
the unitary case. The supersymmetry method and the orthogonal polynomials are
two techniques to tackle this task. Recently, we presented a new method to
average ratios of characteristic polynomials over matrix ensembles invariant
under the unitary group. Here, we extend this approach to ensembles with
orthogonal and unitary-symplectic rotation symmetry. We show that Pfaffian
structures can be derived for a wide class of orthogonal and unitary-symplectic
rotation invariant ensembles in a unifying way. This includes also those for
which this structure was not known previously, as the real Ginibre ensemble and
the Gaussian real chiral ensemble with two independent matrices as well.
