p = 3
m = 1
F = GF(p)
Rx.<x> = PolynomialRing(F)
f = x
C_super = superelliptic(f, m)

Rxy.<x, y> = PolynomialRing(F, 2)
f1 = superelliptic_function(C_super, x^7)
f2 = superelliptic_function(C_super, x^4)
AS = as_cover(C_super, [f1, f2], prec=1000)
n = AS.height
d_test = (p^n - 1)
Gi = AS.group
i = 1
while(len(Gi) > 1):
    Gi = AS.ith_ramification_gp(i)
    d_test += len(Gi) - 1
    i+=1
print(d_test == AS.exponent_of_different())