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Algorithm of polynomial complexity for factoring polynomials and finding the components of varieties in subexponential time

Abstract

An algorithm of polynomial complexity is described for factoring polynomials in several variables into irreducible factors over a field F which is finitely generated over the prime subfield H. An algorithm is also constructed for finding the components of the protective variety of common roots of homogeneous polynomials

(let c−1 denote its dimension) with working time polynomial in

. where

, the number L is the size of the representation of the polynomials

and

.

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 137, pp. 124–188, 1984.

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Chistov, A.L. Algorithm of polynomial complexity for factoring polynomials and finding the components of varieties in subexponential time. J Math Sci 34, 1838–1882 (1986). https://doi.org/10.1007/BF01095643

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Keywords

  • Polynomial Complexity
  • Subexponential Time