class as_cech:
    def __init__(self, C, omega, f):
        self.curve = C
        n = C.height
        F = C.base_ring
        variable_names = 'x, y'
        for i in range(n):
            variable_names += ', z' + str(i)
        Rxyz = PolynomialRing(F, n+2, variable_names)
        x, y = Rxyz.gens()[:2]
        z = Rxyz.gens()[2:]
        RxyzQ = FractionField(Rxyz)
        self.omega0 = omega
        self.f = f

    def __repr__(self):
        return "( " + str(self.omega0)+", " + str(self.f) + " )"

    def __add__(self, other):
        C = self.curve
        omega = self.omega0
        f = self.f
        omega1 = other.omega0
        f1 = other.f
        return as_cech(C, omega + omega1, f+f1)

    def __sub__(self, other):
        C = self.curve
        omega = self.omega0
        f = self.f
        omega1 = other.omega0
        f1 = other.f
        return as_cech(C, omega - omega1, f - f1)
    
    def __rmul__(self, constant):
        C = self.curve
        omega = self.omega0
        f = self.f
        return as_form(C, constant*omega, constant*f)