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1 results

  • Computing subfields in algebraic number fields

  • Part of
  • John D. Dixon
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 49 / Issue 3 / December 1990
    Published online by Cambridge University Press:
    09 April 2009, pp. 434-448
    Print publication:
    December 1990
    • Article
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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.