Hello Ondrej, For such questions of Sage usage, it is better to discuss on ask.sagemath.org or sage-support.
You can also deal with all algebraic numbers at once with QQbar sage: sqrt3 = QQbar(sqrt(3)) sage: sqrt5 = QQbar(sqrt(5)) But then polynomials over QQbar are much slower. Vincent 2015-01-19 19:24 UTC+01:00, Ondřej Čertík <ondrej.cer...@gmail.com>: > On Mon, Jan 19, 2015 at 11:19 AM, Ondřej Čertík <ondrej.cer...@gmail.com> > wrote: >> Hi Vincent, >> >> On Sun, Jan 18, 2015 at 10:06 AM, Vincent Delecroix >> <20100.delecr...@gmail.com> wrote: >>> Hi, >>> >>> 2015-01-18 18:03 UTC+01:00, Ondřej Čertík <ondrej.cer...@gmail.com>: >>>> Can you invent an example, that can't be converted to polynomials? >>>> Perhaps (a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)^25? >>> >>> Still doable. You need to involve log, exp, cos or similar >>> transcendental functions. >> >> Can you show me how to do that? I tried: >> >> sage: K.<sqrt3> = QuadraticField(3) >> sage: K.<sqrt5> = QuadraticField(5) >> sage: R.<a1,a2,a3,a4,a5> = K[] >> sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^25 >> >> But I got: >> >> TypeError: unsupported operand parent(s) for '*': 'Number Field in >> sqrt3 with defining polynomial x^2 - 3' and 'Multivariate Polynomial >> Ring in a1, a2 >> , a3, a4, a5 over Number Field in sqrt5 with defining polynomial x^2 - 5' >> >> Full stacktrace here: >> >> https://gist.github.com/certik/a7f2434820f8dbf890b9 > > > I think I figured it out: > > sage: K.<sqrt3> = QuadraticField(3) > sage: L.<sqrt5> = K.extension(x^2-5) > sage: R.<a1,a2,a3,a4,a5> = L[] > sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^18 > CPU times: user 2.43 s, sys: 3.94 ms, total: 2.44 s > Wall time: 2.44 s > > (I did smaller exponent so that it finishes.) > > Ondrej > > -- > 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.
