The Multivariate Schwartz-Zippel Lemma

@article{Dogan2022TheMS,
  title={The Multivariate Schwartz-Zippel Lemma},
  author={M. Levent Dogan and Alperen Ali Erg{\"u}r and Jake D. Mundo and Elias P. Tsigaridas},
  journal={SIAM J. Discret. Math.},
  year={2022},
  volume={36},
  pages={888-910}
}
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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