On Jan 23, 2008 4:06 AM, Martin Albrecht <[EMAIL PROTECTED]> wrote: > > > > By contrast F.multiplicative_gen() does make sense for all finite > > > fields so should be provided, though not necessarily computed until > > > requested for the reasons given by Martin. (It seems that with the > > > current implementation of non-prime fiinite fields this comes for > > > free, but that might change.) > > > > Only for the Givaro ones, i.e., up to 2^16. For general fields it is not > > for free, unfortunately (I think). > > I think it is 'free' for all extension fields because we either represent the > field elements as powers of the generators or as polynomials in the > generator.
In the latter case, i.e., "as polynomials in the generator", there is no guarantee that the generator is a generator for the multiplicative group in general. Here is an example that might clarify things, in case I'm misunderstanding: sage: k.<x> = GF(3)[] sage: F.<a> = GF(9, modulus = x^2 + 1) sage: a.multiplicative_order() 4 William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
