Geodesic
Efficient estimation of roots from the field of fractional power series of a given polynomial in nonzero characteristic
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 55-63
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 efficient estimates of the roots of a polynomial in the field of fractional power series in the case of arbitrary characteristic. 
@article{ZNSL_2020_498_a4,
     author = {A. L. Chistov},
     title = {Efficient estimation of roots from the field of fractional power series of a given polynomial in nonzero characteristic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {55--63},
     year = {2020},
     volume = {498},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a4/}
}
TY  - JOUR
AU  - A. L. Chistov
TI  - Efficient estimation of roots from the field of fractional power series of a given polynomial in nonzero characteristic
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 55
EP  - 63
VL  - 498
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a4/
LA  - ru
ID  - ZNSL_2020_498_a4
ER  - 
%0 Journal Article
%A A. L. Chistov
%T Efficient estimation of roots from the field of fractional power series of a given polynomial in nonzero characteristic
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 55-63
%V 498
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a4/
%G ru
%F ZNSL_2020_498_a4
A. L. Chistov. Efficient estimation of roots from the field of fractional power series of a given polynomial in nonzero characteristic. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 55-63. http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a4/

[1] A. L. Chistov, “Rasshirenie algoritma Nyutona–Pyuize na sluchai nenulevoi kharakteristiki osnovnogo polya. I”, Algebra i analiz, 28:6 (2016), 147–188

[2] A. L. Chistov, “Polynomial complexity of the Newton–Puiseux algorithm”, International Symposium on Mathematical Foundations of Computer Science 1986, Lect. Notes Comput. Sci., 233, eds. J. Gruska, B. Rovan, J. Wiedermann, Springer, Berlin, 1986, 247–255 | DOI | MR

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

[4] Z. I. Borevich, I. R. Shafarevich, Teoriya chisel, Nauka, M., 1964