OK, that makes sense now. It boils down to this: given an element of F12=GF(p^12) which happens to lie in F2 = GF(p^2), how to express it in terms of a generator of F2. This is not quite as easy as it should be but this works (assuming that you have defined F12 with generator a and F2 with generator b):
sage: bb = b.minpoly().roots(F12)[0][0] sage: i = F2.hom([bb],F12) sage: j = i.section() Here we have defined an embedding i of F2 into F12 by find a place to map b (called bb) and set j to be an inverse to i. (I think we should be use i.inverse_image() but that gave me a NotImplementedError, which is a pity since I have used sort of construction easily in extensions of number fields). Now if f is your polynomial in F12[x] whose coefficients lie in F2 you can say sage: PolynomialRing(F2,'X')([j(c) for c in f.coeffs()]) to get what you want, I hope! John On 17 April 2014 02:52, Irene <irene.alv...@gmail.com> wrote: > Sorry, I didn't write it correctly. I meant GF(p^12,'a') instead of > GF(p^13,'a'). As 2 divides 12, GF(p^12,'a') is an extension of GF(p^2,'b'). > My question is the same now with the correct data. > > On Thursday, April 17, 2014 11:04:40 AM UTC+2, John Cremona wrote: >> >> On 17 April 2014 01:55, Irene <irene....@gmail.com> wrote: >> > Hello! >> > >> > I want to define a polynomial that I know lies in GF(p^2,'b')[x], >> > p=3700001. >> > The problem is that I have to define it as a product >> > E=(X-a_1)*(X-a_2)*(X-a_3)*(X-a_4)*(X-a_5)*(X-a_6), where every a_j is in >> > GF(p^13,'a')[X]. >> > I tried to do GF(p^2,'b')[x](E), but then Sage just changes the >> > generator >> > 'a' and writes the same expression with the generator 'b'. >> > Any idea about how to do this? >> > Thank you!! >> >> Did you write that correctly? GF(p^13) is not an extension of >> GF(p^2). If a1 is in GF(p^13) then a1.minpoly() will give its min >> poly, in GF(p)[x]. >> >> John Cremona >> >> > >> > -- >> > 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...@googlegroups.com. >> > To post to this group, send email to sage-s...@googlegroups.com. >> > Visit this group at http://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 http://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 http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
