In 1984, the author suggested an algorithm for solving systems of polynomial equations. Now we modify it and improve the bounds on its complexity as well as the degrees and lengths of coefficients from the ground filed of the elements constructed by this algorithm. Bibliography: 4 titles.
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A. L. Chistov, “Polynomial complexity algorithm for factoring polynomials and constructing components of a variety in subexponential time,” Zap. Nauchn. Semin. LOMI, 137, 124–188 (1984).
A. L. Chistov, “Efficient smooth stratification of an algebraic variety in zero characteristics and its applications,” Zap. Nauchn. Semin. POMI, 266, 254–311 (2000).
A. L. Chistov, “Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic,” Zap. Nauchn. Semin. POMI, 326, 248–278 (2005)
A. L. Chistov, “Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristics zero),” Zap. Nauchn. Semin. POMI, 378, 133–170 (2010).
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 390, 2011, pp. 299–306.
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Chistov, A.L. An improvement of the complexity bound for solving systems of polynomial equations. J Math Sci 181, 921–924 (2012). https://doi.org/10.1007/s10958-012-0724-4
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DOI: https://doi.org/10.1007/s10958-012-0724-4