Geodesic
An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic. II
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 261-290 
A. L. Chistov. An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic. II. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 261-290. http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a14/
@article{ZNSL_2023_528_a14,
     author = {A. L. Chistov},
     title = {An algorithm for factoring polynomials in the ring of multivariable formal power series in zero{\textendash}characteristic. {II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {261--290},
     year = {2023},
     volume = {528},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a14/}
}
TY  - JOUR
AU  - A. L. Chistov
TI  - An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic. II
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 261
EP  - 290
VL  - 528
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a14/
LA  - ru
ID  - ZNSL_2023_528_a14
ER  - 
%0 Journal Article
%A A. L. Chistov
%T An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic. II
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 261-290
%V 528
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a14/
%G ru
%F ZNSL_2023_528_a14

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We suggest algorithms for factoring polynomials in the rings of multivariables formal power series over the ground field of zero–characteristic and over an algebraic closure of this ground field. Also we construct algorithms for factoring monic polynomials in one variable over these formal power series rings. We give explicit estimates for the complexity of suggested algorithms. These results are important for local investigation of algebraic varieties from the algorithmic point of view.

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

[2] N. Burbaki, Kommutativnaya algebra, Mir, M., 1971

[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

[4] A. L. Chistov, “Effective Construction of a Nonsingular in Codimension One Algebraic Variety over a Zero-Characteristic Ground Field”, Zap. nauchn. semin. POMI, 387, 2011, 167–188

[5] A. L. Chistov, “An overview of effective normalization of a nonsingular in codimension one projective algebraic variety”, Zap. nauchn. semin. POMI, 373, 2009, 295–317

[6] A. L. Chistov, “Effektivnaya normalizatsiya neosobogo v korazmernosti odin algebraicheskogo nogoobraziya”, Dokl. Akad. nauk, 427:5 (2009), 605–608

[7] A. L. Chistov, “Polynomial complexity of the Newton–Puiseux algorithm”, International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, 233, Springer, 1986, 247–255

[8] A. L. Chistov, “Algoritm dlya faktorizatsii mnogochlenov v koltse formalnykh stepennykh ryadov ot mnogikh peremennykh v nulevoi kharakteristike”, Zap. nauchn. semin. POMI, 517, 2022, 268–290

[9] A. L. Chistov, “Otsenka stepeni sistemy uravnenii, zadayuschei mnogoobrazie privodimykh mnogochlenov”, Algebra i analiz, 24:3 (2012), 1999–222

[10] A. L. Chistov, “Ob otsenke koeffitsientov neprivodimykh mnozhitelei mnogochlenov nad polem formalnykh stepennykh ryadov v nenulevoi kharakteristike”, Dokl. Akad. Nauk, 489:3 (2019), 12–14

[11] A. L. Chistov, “Effektivnaya otsenka kornei iz polya drobno-stepennykh ryadov zadannogo mnogochlena v nenulevoi kharakteristike”, Zap. nauchn. semin. POMI, 498, 2020, 64–74

[12] A. L. Chistov, A correction of my result on the estimation of roots from a field of fractional–power series of a polynomial in nonzero characteristic, Preprint of SPbMO, 2023

[13] W.-L. Chow, “On the theorem of Bertini for local domains”, Proc. National Academy of Sciences, 44:6 (1958), 580–584

[14] H. Flenner, “Die Sätze von Bertini für lokale Ringe”, Math. Ann., 229 (1977), 97–111

[15] M. Nagata, Local rings, Interscience Publishers, New York–London, 1962

[16] A. Seidenberg, “Constructions in algebra”, Trans. Amer. Math. Soc., 197 (1974), 273–313

[17] O. Zarisskii, P. Samyuel, Kommutativnaya algebra, v. I–II, Izd. inostrannoi literatury, M., 1963