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On solving relative norm equations in algebraic number fields

1997; American Mathematical Society; Volume: 66; Issue: 217 Linguagem: Inglês

10.1090/s0025-5718-97-00761-8

1088-6842

Claus Fieker, A. Jurk, Michael Pohst,

Polynomial and algebraic computation

Let $\mathbb {Q}\subseteq \mathcal {E}\subseteq \mathcal {F}$ be algebraic number fields and $M\subset \mathcal {F}$ a free $o\varepsilon$-module. We prove a theorem which enables us to determine whether a given relative norm equation of the form $|N_{\mathcal {F}/\mathcal {E}}(\eta )| = |\theta |$ has any solutions $\eta \in M$ at all and, if so, to compute a complete set of nonassociate solutions. Finally we formulate an algorithm using this theorem, consider its algebraic complexity and give some examples.