p = 3
m = 2
F = GF(p^2, 'a')
a = F.gens()[0]
Rxx.<x> = PolynomialRing(F)
#f = (x^3 - x)^3 + x^3 - x
f = x^3 + a*x + 1
f1 = f(x = x^p - x)
C = superelliptic(f, m)
C1 = superelliptic(f1, m, prec = 500)
#B = C.crystalline_cohomology_basis(prec = 100, info = 1)
#B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1)

def crystalline_matrix(C, prec = 50):
    B = C.crystalline_cohomology_basis(prec = prec)
    g = C.genus()
    p = C.characteristic
    Zp2 = Integers(p^2)
    M = matrix(Zp2, 2*g, 2*g)
    for i, b in enumerate(B):
        M[i, :] = vector(autom(b).coordinates(basis = B))
    return M

#b0 = de_rham_witt_lift(C.de_rham_basis()[0], prec = 100)
#b1 = de_rham_witt_lift(C1.de_rham_basis()[2], prec = 300)
#print(b0.regular_form())
#print(b1.regular_form())
for b in C1.de_rham_basis():
    print(mult_by_p(b.omega0).regular_form())

#for b in B:
#    print(b.regular_form())
    
#for b in B1:
#    print(b.regular_form())

#M = crystalline_matrix(C, prec = 150)
#print(M)
#print(M^3)