docs: def newton(power_sum, elementary_symmetric_polynomial, order):
      r'''
      Given two lists of values, the first list being the `power sum`s of a
      polynomial, and the second being expressions of the roots of the
      polynomial as found by Viete's Formula, use information from the longer list to
      fill out the shorter list using Newton's Identities.
  
      .. note::
          Updates are done **in place**
  
      Parameters
      ----------
      power_sum: list of float
      elementary_symmetric_polynomial: list of float
      order: int
          The number of terms to expand to when updating `elementary_symmetric_polynomial`
  
      See Also
      --------
      https://en.wikipedia.org/wiki/Newton%27s_identities[https://en.wikipedia.org/wiki/Newton%27s_identities]
      '''
      if len(power_sum) > len(elementary_symmetric_polynomial):
          _update_elementary_symmetric_polynomial(power_sum, elementary_symmetric_polynomial, order)
      elif len(power_sum) < len(elementary_symmetric_polynomial):
          _update_power_sum(power_sum, elementary_symmetric_polynomial, order)