@classmethod
def _reals_index(cls, reals, index):
    """Map initial real root index to an index in a factor where the root belongs."""
    i = 0
    for j, (_, factor, k) in enumerate(reals):
        if index < i + k:
            poly, index = factor, 0
            for _, factor, _ in reals[:j]:
                if factor == poly:
                    index += 1
            return poly, index
        else:
            i += k
