Generate a monic polynomial with given roots.
Return the coefficients of the polynomial
where the r_n are the roots specified in roots. If a zero has multiplicity n, then it must appear in roots n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then roots looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.
If the returned coefficients are c, then
The coefficient of the last term is 1 for monic polynomials in this form.
roots : array_like
out : ndarray
chebfromroots, legfromroots, lagfromroots, hermfromroots, hermefromroots
The coefficients are determined by multiplying together linear factors of the form (x - r_i), i.e.
where n == len(roots) - 1; note that this implies that 1 is always returned for .
>>> import numpy.polynomial as P >>> P.polyfromroots((-1,0,1)) # x(x - 1)(x + 1) = x^3 - x array([ 0., -1., 0., 1.]) >>> j = complex(0,1) >>> P.polyfromroots((-j,j)) # complex returned, though values are real array([ 1.+0.j, 0.+0.j, 1.+0.j])