`numpy.polynomial.polynomial:polyfromroots`

source: build-install/usr/lib/python3.14/site-packages/numpy/polynomial/polynomial.py :151

Signature

def polyfromroots ( roots )

Summary

Generate a monic polynomial with given roots.

Extended Summary

Return the coefficients of the polynomial

p (x) = (x - r_{0}) * (x - r_{1}) * ... * (x - r_{n}),

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

p (x) = c_{0} + c_{1} * x + ... + x^{n}

The coefficient of the last term is 1 for monic polynomials in this form.

Parameters

roots : array_like: Sequence containing the roots.

Returns

out : ndarray: 1-D array of the polynomial's coefficients If all the roots are real, then out is also real, otherwise it is complex. (see Examples below).

Notes

The coefficients are determined by multiplying together linear factors of the form (x - r_i), i.e.

p (x) = (x - r_{0}) (x - r_{1}) ... (x - r_{n})

where n == len(roots) - 1; note that this implies that 1 is always returned for $a_{n}$ .

Examples

from numpy.polynomial import polynomial as P
P.polyfromroots((-1,0,1))  # x(x - 1)(x + 1) = x^3 - x
j = complex(0,1)

✓

P.polyfromroots((-j,j))  # complex returned, though values are real

✗

Aliases

numpy.polynomial.Polynomial._fromroots
numpy.polynomial.polynomial.polyfromroots