The Schwartz-Zippel Lemma

Sunpill Kim and Yong Kiam Tan 📧

April 27, 2023

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

This short entry formalizes a version of the Schwartz-Zippel lemma for probabilistic (multivariate) polynomial identity testing. The entry includes a textbook example using the lemma to test for perfect matchings in a bipartite graph. The lemma is attributed to several independent authors, including Schwartz, Zippel, and DeMillo and Lipton; a historical perspective is given by Lipton.

License

BSD License

Topics

Session Schwartz_Zippel

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Cite

× 
@article{Schwartz_Zippel-AFP,
  author  = {Sunpill Kim and Yong Kiam Tan},
  title   = {The Schwartz-Zippel Lemma},
  journal = {Archive of Formal Proofs},
  month   = {April},
  year    = {2023},
  note    = {\url{https://isa-afp.org/entries/Schwartz_Zippel.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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