p = 3
m = 2
F = GF(p)
Rx.<x> = PolynomialRing(F)
f = x^3 - x
C = superelliptic(f, m)
print(auxilliary_derivative((C.x^3 - C.x).teichmuller()))
print('Result should be: [2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5])')
print(2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn())
print(C.y.teichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()) #F(d[y]) = y^2*dy