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Approximating the Number of Zeroes of a GF[2] Polynomial

✍ Scribed by M. Karpinski; M. Luby

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
325 KB
Volume
14
Category
Article
ISSN
0196-6774

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✦ Synopsis

We develop a probabilistic polynomial time algorithm which on input a polynomial (g\left(x_{1}, \ldots, x_{n}\right)) over (G F[2], \epsilon) and (\delta), outputs an approximation to the number of zeroes of (g) with relative error at most (\epsilon) with probability at least (1-\delta). (\quad) xi 1993 Academic Press, Inc.

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The classical EnestΓΆm-Kekeya Theorem states that a polynomial \(p(z)=\) \(\sum_{i=0}^{n} a_{i} z^{\prime}\) satisfying \(0<a_{0} \leq a_{1} \leq \cdots \leq a_{n}\) has all its zeros in \(|z| \leq 1\). We extend this result to a larger class of polynomials by dropping the conditions that the coeffic