Before revision:  Moreover , we develop a symbolic algorithm to detect \lambda-reducibility. Our work is motivated by and has applications in combinatorial geometry. Along the way we also present a multivariate generalization of Combinatorial Nullstellensatz, which might be of independent interest .
After revision:  Moreover , we develop a symbolic algorithm that identifies certain \lambda-reducible polynomials. More precisely, our symbolic algorithm detects polynomials that include a cartesian product of hypersurfaces in their zero set. It is likely that using Chow forms the algorithm can be generalized to handle arbitrary \lambda-reducible polynomials, which we leave as an open problem .