Finding the "norm" of a relative polynomial

[Kurt Foster <drsardonicus@earthlink.net>]

Suppose I have K = nfinit(f) where f is monic and irreducible in Z[y]  
(variable of lower priority than x) and R is the ring of algebraic  
integers in K.  Let L = rnfinit(K, T) where T is a monic irreducible  
polynomial in R[x].  Then (according to tha manual users.pdf)

L[11] = rnfequation(K,T,1) = [P, a, k],

where P is a defining polynomial for L/Q, a is a polynomial in Q[x] of  
degree less than poldegree(P) such that

Mod(f(a), P) = 0 [that is, a is a zero of f expressed as a polynomial  
in x with rational coefficients, where x is a zero of P],

and k is an integer such that if T(beta) = f(alpha) = 0, then P(beta +  
k*alpha) = 0.

Now if k = 0, P is the obvious "norm" of T from R[x] to Z[x].  But if  
k != 0, it isn't.  And I don't know how to predict when k != 0.

Now, because of some special algebraic properties of the relative  
polynomial T, (and not connected with the information given by  
rnfinit()), I want that norm polynomial.  Now if K/Q is a Galois  
extension, the "Galois polynomials" for conjugating the zeroes of f in  
Z[y] give explicit expressions for the algebraic conjugates of the  
coefficients of T in R[x], so I have something that's not too  
horrendous that is guaranteed to give me what I want.

But if K/Q is *not* Galois, I'm not sure what to do.  I *could* try  
using numerical approximations of the zeroes of f, multiplying  
approximate conjugates of T, and rounding, but I'd need to know the  
approximations were good enough to give the correct answer.  Or, I  
could use resultants to get a polynomial of degree [L:Q]*[K:Q] whose  
factors included the polynomial I want.  But this seems rather  
cumbersome.  Is there a quicker and slicker method to get the "norm"  
polynomial wen k != 0?