Konstantin, Unfortunately the answer to both your questions is "no" at present. The only extensions of finite fields which Sage can currently handle is where the smaller field is a prime field. We all want this to improve, but no-one has done it. That's your question (1). For (2), I am pretty sure that answer is also "no" but others may correct me.
For your problem, after setting V = F.vector_space() and finding its subspaces, you want to be able to test, for such a subspace W, that a*W=W where a is a multiplicative generator of the subfield. You can set a = F.multiplicative_generator()^5, I think, and then use a.matrix () and only keep the W which are stable under that. I hope this helps, John Cremona On Aug 31, 9:28 am, zieglerk <[email protected]> wrote: > Dear list, > > Starting from a finite field, say > > F = GF (16). > > I want to consider a subfield, say > > E = GF(4) > > and have a list of all sub-vectorspaces of F, which are e.g. 1- > dimensional E-vectorspaces. The functions > > FF = F.vector_space() > S = FF.subspaces(4) > > seem to be a possible start. What seems left to do now, is to test > the elements of S for the property of being E-vectorspaces. That's > the place where I'm stuck -- since E seems not be realized as a > subfield of F. Since, I'm a little unsure, if my approach is even a > good one, let me ask some questions > > 1. Is there a canonical way, to build a tower of finite fields, i.e. GF > (p)<E<F ? > 2. Is there a way to tell the vector_space()-function of a field, to > choose a base-field different from the underlying prime field? > > Thanks in advance and kind regards, > Konstantin --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
