Computing generator of ideal I^n

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

Hello,

This is probably more a mathematics than PARI question, but I hope the 
question is appropriate anyway.

I have a number field K and an ideal I which has order n in the class 
group. Therefore, I^n is a principal ideal.

I want to compute a generator for I^n and I'm wondering if there is a 
faster way than first computing I^n and then calling bnfisprincipal(). 
Can the information that the ideal is given as n-th power be used to 
speed up this computation?

It suffices to do this for the ideals generating the class group, but 
that's already slow enough for the field that I'm using.

Cheers,
Jeroen.