In the initial set up of the proof by contradiction, given that `beta in F(alpha)` and `alpha` is transcendental over F, how is `beta` necessarily expressed to proceed with the argument:
A) As a polynomial in `alpha` with coefficients from F, i.e. `p(alpha)` where `p(x) in F[x]`.
B) As a rational function of `alpha` with coefficients from F, i.e. `f(alpha)"/"g(alpha)` where `f(x),g(x) in F[x]` and `g(x) ne 0` ?