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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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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DOI: https://doi.org/10.1007/BF01095643