function aberth_test01 ( )

%*****************************************************************************80
%
%% aberth_test01() considers degree 4 polynomial with a complex pair of roots.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    12 January 2026
%
%  Author:
%
%    John Burkardt
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'aberth_test01():\n' );
  fprintf ( 1, '  Try aberth() on a degree four polynomial with a pair of complex roots.\n' );

  c = [ -56.0, -75.0, -26.0, 0.0, 1.0 ];

  poly_print ( c, '  Polynomial to be analyzed:' );

  roots = aberth ( c );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Computed roots:\n' );
  disp ( roots );

  exact = [ ...
    0.5 * (   5.0 + sqrt ( 57.0 ) ), ...
    0.5 * (   5.0 - sqrt ( 57.0 ) ), ...
    0.5 * ( - 5.0 + sqrt ( -3.0 ) ), ...
    0.5 * ( - 5.0 - sqrt ( -3.0 ) ) ];
  fprintf ( 1, '  Exact roots:\n' );
  disp ( exact );

  return
end

