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R.<x, y> = GF(p)[]

Then everything will work nicely.

For instance, define the setup as follows.

p = 631

F = GF(p)
R.<x,y> = F[]

a = 30
b = 34

E = EllipticCurve(F, [a, b])

P = E((36, 60))
Q = E((121, 387))
S = E((0, 36))

n = 5

def g(P, Q):
    (x_P, y_P) = P.xy()
    (x_Q, y_Q) = Q.xy()
    if x_P == x_Q and y_P + y_Q == 0:
        return x - x_P
    if P == Q:
        slope = (3 * x_P^2 + a)/(2 * y_P)
    else:
        slope = (y_P - y_Q)/(x_P - x_Q)
    return (y - y_P - slope * (x - x_P))/(x + x_P + x_Q - slope^2)

def miller(m, P):
    m = bin(m)[3:]
    n = len(m)
    T = P
    f = 1
    for i in range(n):
        f = f^2 * g(T, T)
        T = T + T
        if int(m[i]) == 1:
            f = f * g(T, P)
            T = T + P
    return f

def eval_miller(P, Q):
    f = miller(n, P)
    (x1, y1) = Q.xy()
    return f(x = x1, y = y1)

def weil_pairing(P, Q, S):
    num = eval_miller(P, Q+S)/eval_miller(P,  S)
    den = eval_miller(Q, P-S)/eval_miller(Q, -S)
    return (num/den)

Then the following works as expected:

sage: e = weil_pairing(P, Q, S)
sage: print "e(P, Q) =", e
e(P, Q) = 242
sage: print "e(P, Q)^n =", e^n
e(P, Q)^n = 1
sage: P3 = P * 3
sage: Q4 = Q * 4
sage: e12 = weil_pairing(P3, Q4, S)
sage: print "[3]P =", P3.xy()
[3]P = (617, 5)
sage: print "[4]Q =", Q4.xy()
[4]Q = (121, 244)
sage: print "e([3]P, [4]Q) =", e12
e([3]P, [4]Q) = -119
sage: print "e(P, Q)^12 =", e^12
e(P, Q)^12 = -119

Minimal example for the segmentation fault