Order of roots obtained from function roots

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Shan Chu
Shan Chu 2018-6-14
评论： Shan Chu 2018-6-14
Dear all,
I have a funny problem. I have a third-degree polynomial f(s1) which depends on a variable 'm'. When I vary 'm', at some points, the ROOTS function returns me a different order of roots. For example,
when m=217:
s1 =
2.241355481895662 - 1.756029299682315i
1.921143944919372 + 1.773701622048629i
0.215633777118811 - 0.917762110838706i
when m=218;
s1 =
1.918712404828970 + 1.767930620926665i
2.241124388076128 - 1.749637415502876i
0.222483229595857 - 0.896179899600968i
So, do you know how to solve that problem? Thanks Best

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John D'Errico
John D'Errico 2018-6-14
Roots does not assure any specific order of the returned roots, nor should it rationally do so.
Feel free to sort them in any order you desire. However, you need to recognize there is no natural ordering of a set of complex numbers. Should they be sorted in terms of increasing real part? Imaginary part? Magnitude? Angle in the complex plane?

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