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Journal of Mathematical Sciences

, Volume 134, Issue 6, pp 2511–2548 | Cite as

Computation of the Galois group of a polynomial with rational coefficients. I

  • N. V. Durov
Article

Abstract

A new method, which enables us to compute rather efficiently the Galois group of a polynomial over ℚ or ℤ, is presented. Reductions of this polynomial with respect to 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 probabilistic 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. This is the first part of the paper. The second part (the tables included) will be published in a subsequent issue. Bibliography: 9 titles.

Keywords

Probabilistic Method Symmetric Group Rational Coefficient Galois Group Prime Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • N. V. Durov
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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