aluates 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`: >>> import numpy as np >>> 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)]``): >>> p[1] 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]) Nc