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
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