J Austral Math Soc Ser A 49 pp434--448, 1990.

Computing Subfields in Algebraic Number Fields

John D. Dixon

(Received 23 May 1989; revised 26 April 1990)

Abstract

Let K : = Q(a) be an algebraic number field which is given by specifying the minimal polynomial f(X) for a over Q. We describe a procedure for finding the subfields L of K by constructing pairs (w(X), g(X)) of polynomials over Q such that L = Q(w(a)) and g(X) is the minimal polynomial for w(a). The construction uses local information obtained from the Frobenius-Chebotarev theorem about the Galois group Gal(f), and computations over p-adic extensions of Q.

1980 AMS Subject Classification (1985 Revision): 12-04

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Authors

John D. Dixon: Department of Mathematics and Statistics, Carleton University, Ottawa K1S 5B6, Canada.

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Last Modified: Wed Feb 19 10:27:52 2003