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Computing subfields in algebraic number fields

Part of: Field theory and polynomials

Published online by Cambridge University Press:  09 April 2009

John D. Dixon
John D. Dixon
Affiliation:
Department of Mathematics and Statistics Carleton UniversityOttawa K1S 5B6, Canada
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Abstract

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Let K:= Q(α) be an algebraic number field which is given by specifying the minimal polynomial f(X) for α 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(α)) and g(X) is the minimal polynomial for w(α). 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.

MSC classification

Secondary: 12-04: Explicit machine computation and programs (not the theory of computation or programming)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 3 , December 1990 , pp. 434 - 448
Copyright
Copyright © Australian Mathematical Society 1990

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