Hello sage community,
I want to localize a variety's field at a certain point. First I construct the field of fractions $K(V)$ for a coordinate ring $K[V]$
K.<x, y> = GF(11)[]
S = K.quotient(y^2 - x^3 - 4*x).fraction_field()
Now I wish to construct the ideal $\langle x - 2 \rangle$, but unforunately $1/(x - 2) \in S$ so $I = S$.
sage: I = S.ideal(x - 2)
sage: I
Principal ideal (1) of Fraction Field of Quotient of Multivariate Polynomial Ring in x, y over Finite Field of size 11 by the ideal (-x^3 + y^2 - 4*x)
How can I exclude all denominators from the fraction field corresponding to $x = 2, y = 4$?
That is $S$ is all $f/g \in K[V] : g(2, 4) \neq 0$.
Thank you
