[Octave-bug-tracker] [bug #53897] poly of conjugate complex pairs should return a real polynomial

[Marco Caliari]

URL:
  <http://savannah.gnu.org/bugs/?53897>

                 Summary: poly of conjugate complex pairs should return a real
polynomial
                 Project: GNU Octave
            Submitted by: caliari
            Submitted on: Mon 14 May 2018 09:11:56 AM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: GNU/Linux

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Details:

If you try the following


n = 3;
fr = 436;
x = 1i * 2 * pi * fr * [-n:-1 1:n];
N = poly (x);


you see that N has spurious imaginary parts (quite large, in absolute value).
This should not happen, since the roots x are complex conjugate pairs. We
should first detect this fact (I thought to imag (sum (sort (x))) == 0, it is
probably possible to do without computations, but only with sorting and
comparison). Then, either we use the formula

+verbatim
(y-x(1))*(y-conj(x(1)) = y^2-2*real(x(1))*y+abs(x(1))^2


for each complex conjugate pair or we simply remove the spurious imaginary
parts after the computation of the coefficients.




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