numpy.polynomial.polynomial.polyroots

polynomial.polynomial.polyroots(c)

Compute the roots of a polynomial.

Return the roots (a.k.a. “zeros”) of the polynomial

Parameters

c1-D array_like

1-D array of polynomial coefficients.

Returns

outndarray

Array of the roots of the polynomial. If all the roots are real, then out is also real, otherwise it is complex.

See also

numpy.polynomial.chebyshev.chebroots

numpy.polynomial.legendre.legroots

numpy.polynomial.laguerre.lagroots

numpy.polynomial.hermite.hermroots

numpy.polynomial.hermite_e.hermeroots

Notes

The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the power series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton’s method.

Examples

>>> import numpy.polynomial.polynomial as poly
>>> poly.polyroots(poly.polyfromroots((-1,0,1)))
array([-1.,  0.,  1.])
>>> poly.polyroots(poly.polyfromroots((-1,0,1))).dtype
dtype('float64')
>>> j = complex(0,1)
>>> poly.polyroots(poly.polyfromroots((-j,0,j)))
array([  0.00000000e+00+0.j,   0.00000000e+00+1.j,   2.77555756e-17-1.j]) # may vary

numpy.polynomial.polynomial.polyfromroots numpy.polynomial.polynomial.polyvalfromroots