Computation of the Galois group of a~polynomial with rational coefficients.~II
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 90-135
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A new method, which enables us to compute rather efficiently the Galois
group of a polynomial over $\mathbb Q$, respectively, over $\mathbb Z$ is presented.
Reductions of this polynomial with respect different prime modules are
studied, and the information obtained is used for the calculation of the
Galois group of the initial polynomial. This method uses an original
modification of the Chebotarev density theorem and it is in essence a
probability method. The irreducibility of the polynomial under
consideration is not assumed. The appendix to this paper contains tables
which enable one to find the Galois group of polynomials of degree less
than or equal to 10 as a subgroup of the symmetric group.
Here the final part of the paper is published. The first part is contained in the previous issue (see Vol. 319 (2004)).
@article{ZNSL_2005_321_a4,
author = {N. V. Durov},
title = {Computation of the {Galois} group of a~polynomial with rational {coefficients.~II}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {90--135},
publisher = {mathdoc},
volume = {321},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a4/}
}
N. V. Durov. Computation of the Galois group of a~polynomial with rational coefficients.~II. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 90-135. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a4/