Geodesic
An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 268-290 
A. L. Chistov. An algorithm for factoring polynomials in the ring of multivariable formal power series in zero–characteristic. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 268-290. http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a14/
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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.

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