polyroots(c)
Return the roots (a.k.a. "zeros") of the polynomial
$$p(x) = \sum_i c[i] * x^i.$$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.
1-D array of polynomial coefficients.
Array of the roots of the polynomial. If all the roots are real, then :None:None:`out` is also real, otherwise it is complex.
Compute the roots of a polynomial.
>>> 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)See :
... 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
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.polynomial.hermite_e.hermeroots
numpy.polynomial.chebyshev.chebroots
numpy.polynomial.hermite.hermroots
numpy.polynomial.polynomial.polyvalfromroots
numpy.polynomial.legendre.legroots
numpy.polynomial.laguerre.lagroots
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