Degree 9, real and imaginary parts of the coefficients are integers.
The polynomial has four simple complex roots with small imaginary
parts ( )
in two close sets (21 common digits):
The remaining roots are well separated.
The condition number of the above roots is .
Therefore at least 41 digits of working precision are needed
to separate the roots with a floating point computation.
More difficult situations can be obtained with larger values of the
parameter c. For
we have roots with 70
common digits and nonzero imaginary part of modulus less than
.
For we have roots with about 247 common digits and nonzero
imaginary part
of modulus less than
.