def knot_removal_alpha_j(u, degree, knotvector, num, idx):
    """ Computes :math:`\\alpha_{j}` coefficient for knot removal algorithm.

    Please refer to Eq. 5.29 of The NURBS Book by Piegl & Tiller, 2nd Edition, p.184 for details.

    :param u: knot
    :type u: float
    :param degree: degree
    :type degree: int
    :param knotvector: knot vector
    :type knotvector: tuple
    :param num: knot removal index
    :type num: int
    :param idx: iterator index
    :type idx: int
    :return: coefficient value
    :rtype: float
    """
    return (u - knotvector[idx - num]) / (knotvector[idx + degree + 1] - knotvector[idx - num])