Class poly1d

numpy/lib/polynomial.py:1078–1449

A one-dimensional polynomial class. .. 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/rou

@set_module('numpy')
class poly1d:
    """
    A one-dimensional polynomial class.

    .. 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>`.

    A convenience class, used to encapsulate "natural" operations on
    polynomials so that said operations may take on their customary
    form in code (see Examples).

    Parameters
    ----------
    c_or_r : array_like
        The polynomial&#x27;s coefficients, in decreasing powers, or if
        the value of the second parameter is True, the polynomial&#x27;s
        roots (values where the polynomial evaluates to 0).  For example,
        ``poly1d([1, 2, 3])`` returns an object that represents
        :math:`x^2 + 2x + 3`, whereas ``poly1d([1, 2, 3], True)`` returns
        one that represents :math:`(x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6`.
    r : bool, optional
        If True, `c_or_r` specifies the polynomial&#x27;s roots; the default
        is False.
    variable : str, optional
        Changes the variable used when printing `p` from `x` to `variable`
        (see Examples).

    Examples
    --------
    Construct the polynomial :math:`x^2 + 2x + 3`:

    >>> p = np.poly1d([1, 2, 3])
    >>> print(np.poly1d(p))
       2
    1 x + 2 x + 3

    Evaluate the polynomial at :math:`x = 0.5`:

    >>> p(0.5)
    4.25

    Find the roots:

    >>> p.r
    array([-1.+1.41421356j, -1.-1.41421356j])
    >>> p(p.r)
    array([ -4.44089210e-16+0.j,  -4.44089210e-16+0.j]) # may vary

    These numbers in the previous line represent (0, 0) to machine precision

    Show the coefficients:

    >>> p.c
    array([1, 2, 3])