numpy.polynomial.polynomial.polyfromroots(roots)
[source]
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: |
|
---|---|
Returns: |
|
See also
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 .
>>> from numpy.polynomial import 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])
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https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.polynomial.polynomial.polyfromroots.html