We show that, except for a special family of polynomials -that we call \lambda -reducible-, a natural  generalization of Schwartz-Zippel-DeMillo-Lipton lemma holds. 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.
We show that, except for a special family of polynomials -that we call \lambda -reducible-, a natural multivariate generalization of Schwartz-Zippel-DeMillo-Lipton lemma holds. 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.
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