p = 3
m = 2
F = GF(p)
Rx.<x> = PolynomialRing(F)
f = x^3 - x
C = superelliptic(f, m)
#C1 = patch(C)
#print(C1.crystalline_cohomology_basis())
#g1 = C1.polynomial
#g_AS = g1(x^p - x)
#C2 = superelliptic(g_AS, 2)
#print(convert_super_into_AS(C2))
#converted = (C2.x)^4 - (C2.x)^2
#print(convert_super_fct_into_AS(converted))
#b = C.crystalline_cohomology_basis()
#print(autom(b[0]).coordinates(basis = b))
#eta1 = (dy + dV(2xy) + V(x^5 \, dy), V(y/x))
#eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
#eta2 =  (  x \, dy + 3 x^3 \, dy + dV((2x^4 + 2x^2 + 2) y) + V( (x^4 + x^2 + 1) dy), -[y/x])
#eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teichmuller())
#omega8_lift0, compare = de_rham_witt_lift(C.de_rham_basis()[1])
#omega8_lift = -(C.x^(-3)).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*C.x.teichmuller().diffn()
#eta2 = de_rham_witt_lift(C.de_rham_basis()[1])
#b = autom(eta2)
#print(autom(C.crystalline_cohomology_basis()[1]).coordinates())