Geodesic
Extension of the Newton--Puiseux algorithm to the case of a~nonzero characteristic ground field.~I
Algebra i analiz, Tome 28 (2016) no. 6, pp. 147-188.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Newton broken lines, nonzero characteristic of the ground field, generalization of the Newton-Puiseux expansions. 
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A. L. Chistov. Extension of the Newton--Puiseux algorithm to the case of a~nonzero characteristic ground field.~I. Algebra i analiz, Tome 28 (2016) no. 6, pp. 147-188. http://geodesic.mathdoc.fr/item/AA_2016_28_6_a6/

[1] Chistov A. L., “Polynomial complexity of the Newton–Puiseux algorithm”, Lecture Notes in Comput. Sci., 233, Springer, Berlin, 1986, 247–255 | DOI | MR

[2] Chistov A. L., “Effective construction of an algebraic variety nonsingular in codimension one over a ground field of zero characteristic”, Zap. nauch. semin. POMI, 387, 2011, 167–188 | MR

[3] Chistov A. L., “Algoritm polinomialnoi slozhnosti dlya razlozheniya mnogochlenov na neprivodimye mnozhiteli i nakhozhdenie komponent mnogoobraziya v subeksponentsialnoe vremya”, Zap. nauch. semin. LOMI, 137, 1984, 124–188 | MR | Zbl