Jeroen Demeyer on Wed, 07 Aug 2013 17:05:36 +0200

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Computing generator of ideal I^n


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.