class superelliptic_drw_cech:
    def __init__(self, omega0, f):
        self.curve = omega0.curve
        self.omega0 = omega0
        self.omega8 = omega0 - f.diffn()
        self.f = f
        
        
    def reduce(self):
        C = self.curve
        fct = self.f
        f_first_comp = fct.t
        f_second_comp = fct.f
        decomp_first_comp = decomposition_g0_g8(f_first_comp)
        decomp_second_comp = decomposition_g0_g8(f_second_comp)
        new = self
        new.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()
        new.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()
        new.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()
        new.omega8 = new.omega0 - new.f.diffn()
        return new
        
    def __repr__(self):
        return("(" + str(self.omega0) + ", "+ str(self.f) + ", " + str(self.omega8) + ")")

    def __add__(self, other):
        C = self.curve
        omega0 = self.omega0
        f = self.f
        omega0_1 = other.omega0
        f_1 = other.f
        return superelliptic_drw_cech(omega0 + omega0_1, f + f_1)
    
    def __sub__(self, other):
        C = self.curve
        omega0 = self.omega0
        f = self.f
        omega0_1 = other.omega0
        f_1 = other.f
        return superelliptic_drw_cech(omega0 - omega0_1, f - f_1)
        
    def __neg__(self):
        C = self.curve
        omega0 = self.omega0
        f = self.f
        return superelliptic_drw_cech(-omega0, -f)
    
    def __rmul__(self, other):
        omega0 = self.omega0
        f = self.f
        return superelliptic_drw_cech(other*omega0, other*f)
    
    def r(self):
        omega0 = self.omega0
        f = self.f
        C = self.curve
        return superelliptic_cech(C, omega0.h1*C.dx, f.t)
    
    def coordinates(self, basis = 0):
        C = self.curve
        g = C.genus()
        coord_mod_p = self.r().coordinates()
        print(coord_mod_p)
        coord_lifted = [lift(a) for a in coord_mod_p]
        if basis == 0:
            basis = C.crystalline_cohomology_basis()
        aux = self
        for i, a in enumerate(basis):
            aux -= coord_lifted[i]*a
        print('aux before reduce', aux)
        #aux = aux.reduce() # Now aux = p*cech class.
        # Now aux should be of the form (V(smth), V(smth), V(smth))
        print('aux V(smth)', aux)
        aux_divided_by_p = superelliptic_cech(C, aux.omega0.omega.cartier(), aux.f.f.pth_root())
        print('aux.omega0.omega.cartier()', aux.omega0.omega.cartier())
        coord_aux_divided_by_p = aux_divided_by_p.coordinates()
        coord_aux_divided_by_p = [ZZ(a) for a in coord_aux_divided_by_p]
        coordinates = [ (coord_lifted[i] + p*coord_aux_divided_by_p[i])%p^2 for i in range(2*g)]
        return coordinates
    
    def is_regular(self):
        print(self.omega0.r().is_regular_on_U0(), self.omega8.r().is_regular_on_Uinfty(), self.omega0.frobenius().is_regular_on_U0(),     self.omega8.frobenius().is_regular_on_Uinfty())
        eq1 = self.omega0.r().is_regular_on_U0() and self.omega8.r().is_regular_on_Uinfty()
        eq2 = self.omega0.frobenius().is_regular_on_U0() and self.omega8.frobenius().is_regular_on_Uinfty()
        return eq1 and eq2