On 19 January 2015 at 23:03, mmarco <mma...@unizar.es> wrote: > It is much faster to work with absolute fields instead of towers of > extensions: > > sage: K.<sqrt3>=QuadraticField(3) > sage: F.<sqrt5>=K.extension(x^2-5) > sage: R.<a1,a2,a3,a4,a5> = F[] > sage: %time _=(a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 > CPU times: user 27.4 s, sys: 12 ms, total: 27.4 s > Wall time: 27.5 s > sage: FF.<a>=F.absolute_field() > sage: fsqrt3=FF(F(sqrt3)) > sage: fsqrt5=FF(sqrt5) > sage: RR.<a1,a2,a3,a4,a5> = FF[] > sage: %time _=(a1+a2+a3+fsqrt5*a4+fsqrt3*a5)^25 > CPU times: user 1.26 s, sys: 3 ms, total: 1.27 s > Wall time: 1.27 s > > > I guess that pari internally follows the second approach.
No I don't think so. In gp: ? Mod(x,x^2-3) + Mod(y,y^2-5) %2 = Mod(x + Mod(y, y^2 - 5), x^2 - 3) This can be read as a polynomial in x subject to the side condition that x^2=3, where one of the coefficients is y subject to y^2=5. Before I tried the above I did this: ? Mod(x,x^2-3) + Mod(x,x^2-5) %1 = 0 which is a warning to anyone trying to interface between Sage and Pari/GP! John > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
