def group_action_matrices(C_AS):
    F = C_AS.base_ring
    n = C_AS.height
    holo = C_AS.holomorphic_differentials_basis()
    holo_forms = [omega.form for omega in holo]
    denom = LCM([denominator(omega) for omega in holo_forms])
    variable_names = 'x, y'
    for j in range(n):
        variable_names += ', z' + str(j)
    Rxyz = PolynomialRing(F, n+2, variable_names)
    x, y = Rxyz.gens()[:2]
    z = Rxyz.gens()[2:]
    holo_forms = [Rxyz(omega*denom) for omega in holo_forms]
    A = [[] for i in range(n)]
    for omega in holo:
        for i in range(n):
            ei = n*[0]
            ei[i] = 1
            omega1 = omega.group_action(ei)
            omega1 = denom * omega1
            v1 = omega1.coordinates(holo_forms)
            A[i] += [v1]
    for i in range(n):
        A[i] = matrix(F, A[i])
        A[i] = A[i].transpose()
    return A

def group_action_matrices_log(C_AS):
    F = C_AS.base_ring
    n = C_AS.height
    holo = C_AS.at_most_poles_forms(1)
    holo_forms = [omega.form for omega in holo]
    denom = LCM([denominator(omega) for omega in holo_forms])
    variable_names = 'x, y'
    for j in range(n):
        variable_names += ', z' + str(j)
    Rxyz = PolynomialRing(F, n+2, variable_names)
    x, y = Rxyz.gens()[:2]
    z = Rxyz.gens()[2:]
    holo_forms = [Rxyz(omega*denom) for omega in holo_forms]
    A = [[] for i in range(n)]
    for omega in holo:
        for i in range(n):
            ei = n*[0]
            ei[i] = 1
            omega1 = omega.group_action(ei)
            omega1 = denom * omega1
            v1 = omega1.coordinates(holo_forms)
            A[i] += [v1]
    for i in range(n):
        A[i] = matrix(F, A[i])
        A[i] = A[i].transpose()
    return A