  We use the implicitization procedure to generate polynomial equality
constraints on the set of distributions induced by local interventions on
variables governed by a causal Bayesian network with hidden variables. We show
how we may reduce the complexity of the implicitization problem and make the
problem tractable in certain causal Bayesian networks. We also show some
preliminary results on the algebraic structure of polynomial constraints. The
results have applications in distinguishing between causal models and in
testing causal models with combined observational and experimental data.
