John, I agree. In fact in my case I know a multiple of the order of the ideal. The ideal is one of norm 2, and I can produce an element of norm 2^k, which is not divisible by 2. But, I can't find the method to test principality, or to extract the generator. I would like something like
I.principal_generator() which would either return None if the ideal wasn't principal (or maybe throw an exception), otherwise it would return a generator. I'm sure that there's some Pari function to do this, but I don't know what it is. Victor On Wednesday, April 3, 2013 4:32:16 AM UTC-4, John Cremona wrote: > > If you knew a multiple of the class number, and could factor it, then > you could use that in place of the actual class number. > > Certainly, if your ideal was principal and easy to prove as such then > computing the class group would be overkill! > > John > > On 3 April 2013 09:09, Jeroen Demeyer <[email protected] <javascript:>> > wrote: > > On 2013-04-02 21:13, Victor Miller wrote: > >> I have a bunch of ideals in number fields whose orders in the class > >> group I want to calculate. If K is the number field and a is the > ideal, > >> I had been doing something like > >> > >> H = K.class_group() > >> print H(a).order() > >> > >> But if K is a big number field this seems wasteful (and takes a long > >> time), since it computes the whole class group. > > As far as I know, there is no way to do this without computing the class > > group. > > > > -- > > You received this message because you are subscribed to the Google > Groups "sage-support" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected] <javascript:>. > > To post to this group, send email to > > [email protected]<javascript:>. > > > Visit this group at http://groups.google.com/group/sage-support?hl=en. > > For more options, visit https://groups.google.com/groups/opt_out. > > > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
