Function roots

numpy/lib/_polynomial_impl.py:169–262

Return the roots of a polynomial with coefficients given in p. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`trans

(p)

@array_function_dispatch(_roots_dispatcher)
def roots(p):
    """
    Return the roots of a polynomial with coefficients given in p.

    .. note::
       This forms part of the old polynomial API. Since version 1.4, the
       new polynomial API defined in `numpy.polynomial` is preferred.
       A summary of the differences can be found in the
       :doc:`transition guide </reference/routines.polynomials>`.

    The values in the rank-1 array `p` are coefficients of a polynomial.
    If the length of `p` is n+1 then the polynomial is described by::

      p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]

    Parameters
    ----------
    p : array_like
        Rank-1 array of polynomial coefficients.

    Returns
    -------
    out : ndarray
        An array containing the roots of the polynomial.

    Raises
    ------
    ValueError
        When `p` cannot be converted to a rank-1 array.

    See also
    --------
    poly : Find the coefficients of a polynomial with a given sequence
           of roots.
    polyval : Compute polynomial values.
    polyfit : Least squares polynomial fit.
    poly1d : A one-dimensional polynomial class.

    Notes
    -----
    The algorithm relies on computing the eigenvalues of the
    companion matrix [1]_.

    References
    ----------
    .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*.  Cambridge, UK:
        Cambridge University Press, 1999, pp. 146-7.

    Examples
    --------
    >>> import numpy as np
    >>> coeff = [3.2, 2, 1]
    >>> np.roots(coeff)
    array([-0.3125+0.46351241j, -0.3125-0.46351241j])

    """
    # If input is scalar, this makes it an array
    p = atleast_1d(p)