def METHOD_NAME(self, list):
    """
    recovers the coefficients over a binary tree.
    """
    coeff = {}
    list2 = [self.group.init(ZR, i) for i in list]
    for i in list2:
        result = 1
        for j in list2:
            if not (i == j):
                # lagrange basis poly
                result *= (0 - j) / (i - j)
                #                print("coeff '%d' => '%s'" % (i, result))
        coeff[int(i)] = result
    return coeff