Abstract
We discuss some results and problems related to the Newton–Puiseux algorithm and its generalization for nonzero characteristic obtained by the author earlier. A new method is suggested for obtaining effective estimates of the roots of a polynomial in the field of fractional power series in the case of arbitrary characteristic.
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REFERENCES
A. L. Chistov, St. Petersburg Math. J. 28 (6), 825–853 (2017).
A. L. Chistov, “Polynomial complexity of the Newton–Puiseux algorithm,” in Wiedermann International Symposium on Mathematical Foundations of Computer Science 1986, Ed. J. Gruska and B. Rovan, Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1986), Vol. 233, pp. 247–255.
Z. I. Borevich and I. R. Shafarevich, Number Theory (Nauka, Moscow, 1964; Academic, London, 1966). https://doi.org/10.1007/BFb0016248
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Chistov, A.L. On the Estimation of Coefficients of Irreducible Factors of Polynomials over a Field of Formal Power Series in Nonzero Characteristic. Dokl. Math. 100, 542–544 (2019). https://doi.org/10.1134/S1064562419060097
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DOI: https://doi.org/10.1134/S1064562419060097