A one-dimensional polynomial class.
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's coefficients, in decreasing powers, or if the value of the second parameter is True, the polynomial'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'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)
Display the order (the leading zero-coefficients are removed):
>>> p.order 2
Show the coefficient of the k-th power in the polynomial (which is equivalent to ``p.c-(i+1)``):
>>> p1 2
Polynomials can be added, subtracted, multiplied, and divided (returns quotient and remainder):
>>> p * p poly1d( 1, 4, 10, 12, 9)
>>> (p**3 + 4) / p (poly1d( 1., 4., 10., 12., 9.), poly1d(4.))
``asarray(p)`` gives the coefficient array, so polynomials can be used in all functions that accept arrays:
>>> p**2 # square of polynomial poly1d( 1, 4, 10, 12, 9)
>>> np.square(p) # square of individual coefficients array(1, 4, 9)
The variable used in the string representation of `p` can be modified, using the `variable` parameter:
>>> p = np.poly1d(1,2,3, variable='z') >>> print(p) 2 1 z + 2 z + 3
Construct a polynomial from its roots:
>>> np.poly1d(1, 2, True) poly1d( 1., -3., 2.)
This is the same polynomial as obtained by:
>>> np.poly1d(1, -1) * np.poly1d(1, -2) poly1d( 1, -3, 2)