I have a polynomial R∈Z[x]. I then define R′=ddxR, and look at the splitting field of R′, K, an algebraic number field. Now, I want to find a prime ideal 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?