About: Schwartz–Zippel lemma

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In mathematics, the Schwartz–Zippel lemma (also called the DeMillo-Lipton-Schwartz–Zippel lemma) is a tool commonly used in probabilistic polynomial identity testing, i.e. in the problem of determining whether a given multivariate polynomial is the0-polynomial (or identically equal to 0). It was discovered independently by Jack Schwartz, , and Richard DeMillo and Richard J. Lipton, although DeMillo and Lipton's version was shown a year prior to Schwartz and Zippel's result. The finite field version of this bound was proved by Øystein Ore in 1922.

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rdfs:label	توطئة شفارتز-زيبل (ar) Lemme de Schwartz-Zippel (fr) Schwartz–Zippel lemma (en) Лемма Шварца — Зиппеля (ru)
rdfs:comment	توطئة شفارتز-زيبل أو مبرهنة شفارتز-زيبل هي نتيجة أساسية في علم الاحتمال ولها تأثير على عدة مجالات في الرياضيات وعلم الحاسوب. (ar) En mathématiques, le lemme de Schwartz-Zippel est un résultat important pour évaluer l'égalité entre deux polynômes multivariés. Ce lemme donne naturellement un algorithme probabiliste efficace pour résoudre la question de l'égalité entre polynômes, qui fut historiquement le premier à être prouvé correct. De fait il possède de nombreuses applications en théorie des nombres, en cryptographie, en géométrie, mais également dans les problèmes issues de la théorie des graphes et en théorie de la complexité. (fr) In mathematics, the Schwartz–Zippel lemma (also called the DeMillo-Lipton-Schwartz–Zippel lemma) is a tool commonly used in probabilistic polynomial identity testing, i.e. in the problem of determining whether a given multivariate polynomial is the0-polynomial (or identically equal to 0). It was discovered independently by Jack Schwartz, , and Richard DeMillo and Richard J. Lipton, although DeMillo and Lipton's version was shown a year prior to Schwartz and Zippel's result. The finite field version of this bound was proved by Øystein Ore in 1922. (en) Лемма Шварца — Зиппеля (также лемма Де Милло — Липтона — Шварца — Зиппеля) — результат, широко используемый в , то есть, в задаче проверки некоторого многочлена многих переменных на тождественное равенство нулю. Лемма была независимо открыта , , а также и Ричардом Липтоном, хотя версия Де Милло и Липтона появилась на год раньше результата Шварца и Зиппеля. Версия леммы для конечных полей было доказана Ойстином Оре в 1922 году. (ru)
dcterms:subject	Mathematical theorems in theoretical computer science Lemmas in algebra Theorems about polynomials Computer algebra
Wikipage page ID	2789076 (xsd:integer)
Wikipage revision ID	1087566490 (xsd:integer)
Link from a Wikipage to another Wikipage	Determinant Algorithm Perfect matching Richard DeMillo Degree of a polynomial Cryptography Mathematical induction Mathematical theorems in theoretical computer science Tutte matrix Frobenius endomorphism Graph (discrete mathematics) Dana Moshkovitz Pseudorandom Øystein Ore Pfaffian Polynomial identity testing Field (mathematics) Edmonds matrix Prime number Lemmas in algebra Theorems about polynomials Computer algebra Binary decision diagram Bipartite graph Block matrix Polynomial matrix Manindra Agrawal Boolean function Polynomial If and only if Iff Skew-symmetric matrix Exponential time Multilinear polynomial Richard Lipton Jack Schwartz Arithmetic circuit dbr:Richard_Zippel
Link from a Wikipage to an external page	http://historical.ncstrl.org/tr/ps/cornellcs/TR89-965.ps https://ieeexplore.ieee.org/document/814592 http://delivery.acm.org/10.1145/330000/322225/p701-schwartz.pdf http://www.egr.unlv.edu/~larmore/Research/pattern.ps.gz https://www.springer.com/computer/mathematics/book/978-0-7923-9375-7 http://rjlipton.wordpress.com/2009/11/30/the-curious-history-of-the-schwartz-zippel-lemma
sameAs	Schwartz–Zippel lemma Schwartz–Zippel lemma Schwartz–Zippel lemma Schwartz–Zippel lemma Schwartz–Zippel lemma Schwartz–Zippel lemma
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