I have a polynomial $R\in\mathbb{Z}[x]$. I then define $R' = \frac{d}{dx}R$, and look at the splitting field of $R'$, $K$, an algebraic number field. Now, I want to find a prime ideal $\mathfrak{p}$ of $L$ of absolute degree 1 such that $R\mod\mathfrak{p}$ is irreducible.
To do this, I've set up:
p0, n = 5, 7
L = PolynomialRing(ZZ,'x')
R = L(x^n-p0^(n-1)x+p0)
Rprime = L(n*x^(n-1)-p0^(n-1))
K = NumberField(Rprime, 'z')
for P in K.primes_of_degree_one_iter():
<stuff>
I'm now trying ti find the right thing to do for <stuff>. Namely, how can I reduce the polynomial R with respect to the ideal P?
