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St. Petersburg Mathematical Journal

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Extension of the Newton-Puiseux algorithm to the case of a nonzero characteristic ground field. I

Author: A. L. Chistov
Translated by: the author
Original publication: Algebra i Analiz, tom 28 (2016), nomer 6.
Journal: St. Petersburg Math. J. 28 (2017), 825-853
MSC (2010): Primary 16W60
Published electronically: October 2, 2017
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Abstract: The Newton-Puiseux algorithm for constructing roots of polynomials in the field of fractional power series is generalized to the case of a ground field of nonzero characteristic.

References [Enhancements On Off] (What's this?)

  • 1. A. L. Chistov, Polynomial complexity of the Newton-Puiseux algorithm, Mathematical foundations of computer science, 1986 (Bratislava, 1986) Lecture Notes in Comput. Sci., vol. 233, Springer, Berlin, 1986, pp. 247–255. MR 874601,
  • 2. A. L. Chistov, Effective construction of a nonsingular in codimension one algebraic variety over a zero-characteristic ground field, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 387 (2011), no. Teoriya Predstavleniĭ, Dinamicheskie Sistemy, Kombinatornye Metody. XIX, 167–188, 192 (English, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 179 (2011), no. 6, 729–740. MR 2822513,
  • 3. -, An algorithm of polynomial complexity for factoring polynomials, and determination of the components of a variety in a subexponential time, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 137 (1984), 1124-188; English transl., J. Soviet Math. 34 (1986), no. 4, 1838-1882. MR 0762101 (86g:11077a)

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Additional Information

A. L. Chistov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia

Keywords: Newton broken lines, nonzero characteristic of the ground field, generalization of the Newton--Puiseux expansions.
Received by editor(s): August 19, 2016
Published electronically: October 2, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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