Schwartz Zippel Lemma
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High Quality Content by WIKIPEDIA articles! The 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 the 0-polynomial or identically equal to 0. The input to the problem is an n-variable polynomial over a field F. It can occur in the following forms: Algebraic form for example, is (x_1 + 3x_2 - x_3)(3x_1 + x_4 - 1) cdots (x_7 - x_2) equiv 0. To solve this, we can multiply it out and check that all the coefficients are 0. However, this takes exponential time. In general, a polyno...
High Quality Content by WIKIPEDIA articles! The 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 the 0-polynomial or identically equal to 0. The input to the problem is an n-variable polynomial over a field F. It can occur in the following forms: Algebraic form for example, is (x_1 + 3x_2 - x_3)(3x_1 + x_4 - 1) cdots (x_7 - x_2) equiv 0. To solve this, we can multiply it out and check that all the coefficients are 0. However, this takes exponential time. In general, a polynomial can be algebraically represented by an arithmetic formula or circuit. Currently, there is no known sub-exponential time algorithm that can solve this problem deterministically. However, there are randomized polynomial algorithms for testing polynomial identities. The first of these algorithms was discovered independently by Jack Schwartz and Richard Zippel.
