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Reference.org
Polynomial identity testing
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<p>In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate <a href="/facts/Polynomials/Lzak8VVx">polynomials</a> are identical. More formally, a PIT algorithm is given an <a href="/facts/Arithmetic_circuit/JH8WVCEW">arithmetic circuit</a> that computes a polynomial <i>p</i> in a <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a>, and decides whether <i>p</i> is the zero polynomial. Determining the <a href="/facts/Computational_complexity_theory/etHuVF3U">computational complexity</a> required for polynomial identity testing, in particular <a href="/facts/Randomized_algorithm/Fngl1zgk">finding deterministic algorithms</a> for PIT, is one of the most important open problems in algebraic computing complexity. </p>