Spot checking polynomial identities

This article discusses the Schwartz-Zippel lemma, a fundamental result in computer science and algebra used to verify polynomial identities by evaluating them at random points. It explains how the lemma bounds the probability of a non-zero polynomial evaluating to zero, making it a powerful tool for efficient identity testing. Applications include algebraic circuits, zero-knowledge proofs, and cryptographic systems where large finite fields (e.g., integers mod 2^255-19) enable high-confidence verification with few evaluations. The post also covers the lemma's formulation over integral domains and its practical implications for probabilistic algorithms.