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


Ondrej

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