docs: def vietes(coefficients):
      r'''
      Given the coefficients of a polynomial of a single variable,
      compute an elementary symmetric polynomial of the roots of the
      input polynomial by Viete's Formula:
  
      .. math::
          \sum_{1\le i_1<i_2<...<i_k \le n} x_{i_1}x_{i_2}...x_{i_k} = (-1)^k\frac{a_{n-k}}{a_n}
  
      Parameters
      ----------
      coefficients: list of float
          A list of coefficients of the input polynomial of arbitrary length (degree) `n`
  
      Returns
      -------
      list of float:
          A list containing the expression of the roots of the input polynomial of length `n`
  
      See Also
      --------
      https://en.wikipedia.org/wiki/Vieta%27s_formulas
  
      '''
      elementary_symmetric_polynomial = []
      tail = float(coefficients[-1])
      size = len(coefficients)
  
      for i in range(size):
          sign = 1 if (i % 2) == 0 else -1
          el = sign * coefficients[size - i - 1] / tail
          elementary_symmetric_polynomial.append(el)
      return elementary_symmetric_polynomial