On 17 April 2014 08:43, Irene <irene.alv...@gmail.com> wrote: > I think that this is exactly what I need. Nevertheless I cannot use neither > i.section() nor i.inverse_image(). The second one because of the same reason > as you, and the first one when I try it is says "TypeError: 'NoneType' > object is not callable".
You'll have to post your actual code (and say which Sage version) for us to help debug that! John > > > On Thursday, April 17, 2014 12:07:18 PM UTC+2, John Cremona wrote: >> >> 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....@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...@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.
