On 10 July 2017 at 14:56, Nils Bruin <nbr...@sfu.ca> wrote: > On Monday, July 10, 2017 at 3:38:27 PM UTC+2, John Cremona wrote: >> >> Sage does have a function is_norm() for number field elements so the >> underlying algebraic problem should be solvable. > > > It looks like the implementation of this routine requires a galois > extension:
True but in the given context the base field has the p'th roots of unity and the extensions are just Kummer extensions, Galois with cyclic group of order p. > > sage: K.<a>=NumberField(x^3-2) > sage: 7.is_norm(K) > NotImplementedError: is_norm is not implemented unconditionally for norms > from non-Galois number fields > > gp/pari does seem to be able to compute these things via s-unit equations, > though: > > sage: len([i for i in range(100) if gp.bnfisnorm(K,i)[1].norm() == i]) > 68 > > -- > 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 sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- 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 sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
