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.
Parameters :  roots : array_like


Returns :  out : ndarray

See also
chebfromroots, legfromroots, lagfromroots, hermfromroots, hermefromroots
Notes
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 .
Examples
>>> 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])