John Cremona on Fri, 01 Feb 2008 22:15:19 +0100

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The documentation for idealappr(K,P) implies that in the case that P a
prime ideal in the number  field K, the element returned will be a
uniformizer for P and integral.

Will it always be a generator for P when P is principal (as it might
then be), or might the function return some other uniformizer?

If the latter, would it be relatively expensive to call
bnfisprincipal() to ensure that we have a generator when it exists?

John Cremona