function [ x, y, z, w ] = rule17 ( )

%*****************************************************************************80
%
%% rule17() returns the rule of precision 17.
%
%  Discussion:
%
%    The data is given for the following triangle:
%
%     (0,1) 
%       |   \ 
%       |    \ 
%       |     \ 
%       |      \ 
%     (0,0)----(1,0)
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    23 April 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Freddie Witherden, Peter Vincent,
%    On the identification of symmetric quadrature rules for finite element methods,
%    Computers and Mathematics with Applications,
%    Volume 69, pages 1232-1241, 2015.
%
%  Output:
%
%    real x(n), y(n), z(n): the barycentric coordinates of quadrature points.
%
%    real w(n): the quadrature weights.
%
  x = [ ...
      0.4171034443615992, ...
      0.1657931112768016, ...
      0.4171034443615992, ...
      0.0147554916607540, ...
      0.9704890166784921, ...
      0.0147554916607540, ...
      0.4655978716188903, ...
      0.0688042567622194, ...
      0.4655978716188903, ...
      0.1803581162663706, ...
      0.6392837674672588, ...
      0.1803581162663706, ...
      0.0666540634795969, ...
      0.8666918730408062, ...
      0.0666540634795969, ...
      0.2857065024365866, ...
      0.4285869951268267, ...
      0.2857065024365866, ...
      0.0160176423621193, ...
      0.8247900701650881, ...
      0.1591922874727927, ...
      0.8247900701650881, ...
      0.1591922874727927, ...
      0.0160176423621193, ...
      0.3062815917461865, ...
      0.6263690303864522, ...
      0.0673493778673612, ...
      0.6263690303864522, ...
      0.0673493778673612, ...
      0.3062815917461865, ...
      0.0132296727600869, ...
      0.5712948679446841, ...
      0.4154754592952291, ...
      0.5712948679446841, ...
      0.4154754592952291, ...
      0.0132296727600869, ...
      0.0780423405682824, ...
      0.7532351459364581, ...
      0.1687225134952595, ...
      0.7532351459364581, ...
      0.1687225134952595, ...
      0.0780423405682824, ...
      0.0131358708340027, ...
      0.7150722591106424, ...
      0.2717918700553549, ...
      0.7150722591106424, ...
      0.2717918700553549, ...
      0.0131358708340027, ...
      0.0115751759031806, ...
      0.9159193532978169, ...
      0.0725054707990024, ...
      0.9159193532978169, ...
      0.0725054707990024, ...
      0.0115751759031806, ...
      0.1575054779268699, ...
      0.5432755795961598, ...
      0.2992189424769703, ...
      0.5432755795961598, ...
      0.2992189424769703, ...
      0.1575054779268699 ];

  y = [ ...
      0.1657931112768016, ...
      0.4171034443615992, ...
      0.4171034443615992, ...
      0.9704890166784921, ...
      0.0147554916607540, ...
      0.0147554916607540, ...
      0.0688042567622194, ...
      0.4655978716188903, ...
      0.4655978716188903, ...
      0.6392837674672588, ...
      0.1803581162663706, ...
      0.1803581162663706, ...
      0.8666918730408062, ...
      0.0666540634795969, ...
      0.0666540634795969, ...
      0.4285869951268267, ...
      0.2857065024365866, ...
      0.2857065024365866, ...
      0.8247900701650881, ...
      0.0160176423621193, ...
      0.8247900701650881, ...
      0.1591922874727927, ...
      0.0160176423621193, ...
      0.1591922874727927, ...
      0.6263690303864522, ...
      0.3062815917461865, ...
      0.6263690303864522, ...
      0.0673493778673612, ...
      0.3062815917461865, ...
      0.0673493778673612, ...
      0.5712948679446841, ...
      0.0132296727600869, ...
      0.5712948679446841, ...
      0.4154754592952291, ...
      0.0132296727600869, ...
      0.4154754592952291, ...
      0.7532351459364581, ...
      0.0780423405682824, ...
      0.7532351459364581, ...
      0.1687225134952595, ...
      0.0780423405682824, ...
      0.1687225134952595, ...
      0.7150722591106424, ...
      0.0131358708340027, ...
      0.7150722591106424, ...
      0.2717918700553549, ...
      0.0131358708340027, ...
      0.2717918700553549, ...
      0.9159193532978169, ...
      0.0115751759031806, ...
      0.9159193532978169, ...
      0.0725054707990024, ...
      0.0115751759031806, ...
      0.0725054707990024, ...
      0.5432755795961598, ...
      0.1575054779268699, ...
      0.5432755795961598, ...
      0.2992189424769703, ...
      0.1575054779268699, ...
      0.2992189424769703 ];

  z = [ ...
      0.4171034443615992, ...
      0.4171034443615992, ...
      0.1657931112768016, ...
      0.0147554916607540, ...
      0.0147554916607540, ...
      0.9704890166784921, ...
      0.4655978716188903, ...
      0.4655978716188903, ...
      0.0688042567622194, ...
      0.1803581162663707, ...
      0.1803581162663706, ...
      0.6392837674672589, ...
      0.0666540634795969, ...
      0.0666540634795969, ...
      0.8666918730408062, ...
      0.2857065024365867, ...
      0.2857065024365866, ...
      0.4285869951268268, ...
      0.1591922874727927, ...
      0.1591922874727926, ...
      0.0160176423621192, ...
      0.0160176423621192, ...
      0.8247900701650881, ...
      0.8247900701650881, ...
      0.0673493778673613, ...
      0.0673493778673613, ...
      0.3062815917461866, ...
      0.3062815917461866, ...
      0.6263690303864523, ...
      0.6263690303864523, ...
      0.4154754592952290, ...
      0.4154754592952290, ...
      0.0132296727600869, ...
      0.0132296727600869, ...
      0.5712948679446841, ...
      0.5712948679446841, ...
      0.1687225134952595, ...
      0.1687225134952595, ...
      0.0780423405682824, ...
      0.0780423405682824, ...
      0.7532351459364581, ...
      0.7532351459364581, ...
      0.2717918700553549, ...
      0.2717918700553549, ...
      0.0131358708340027, ...
      0.0131358708340027, ...
      0.7150722591106424, ...
      0.7150722591106424, ...
      0.0725054707990025, ...
      0.0725054707990024, ...
      0.0115751759031806, ...
      0.0115751759031806, ...
      0.9159193532978169, ...
      0.9159193532978169, ...
      0.2992189424769703, ...
      0.2992189424769703, ...
      0.1575054779268699, ...
      0.1575054779268699, ...
      0.5432755795961597, ...
      0.5432755795961598 ];

  w = [ ...
      0.0136554632640511, ...
      0.0136554632640511, ...
      0.0136554632640511, ...
      0.0013869437888188, ...
      0.0013869437888188, ...
      0.0013869437888188, ...
      0.0125097254752487, ...
      0.0125097254752487, ...
      0.0125097254752487, ...
      0.0131563152940090, ...
      0.0131563152940090, ...
      0.0131563152940090, ...
      0.0062295004011527, ...
      0.0062295004011527, ...
      0.0062295004011527, ...
      0.0188581185763976, ...
      0.0188581185763976, ...
      0.0188581185763976, ...
      0.0039891501029648, ...
      0.0039891501029648, ...
      0.0039891501029648, ...
      0.0039891501029648, ...
      0.0039891501029648, ...
      0.0039891501029648, ...
      0.0112438862733455, ...
      0.0112438862733455, ...
      0.0112438862733455, ...
      0.0112438862733455, ...
      0.0112438862733455, ...
      0.0112438862733455, ...
      0.0051992199779198, ...
      0.0051992199779198, ...
      0.0051992199779198, ...
      0.0051992199779198, ...
      0.0051992199779198, ...
      0.0051992199779198, ...
      0.0102789491602273, ...
      0.0102789491602273, ...
      0.0102789491602273, ...
      0.0102789491602273, ...
      0.0102789491602273, ...
      0.0102789491602273, ...
      0.0043461072505006, ...
      0.0043461072505006, ...
      0.0043461072505006, ...
      0.0043461072505006, ...
      0.0043461072505006, ...
      0.0043461072505006, ...
      0.0022921742008679, ...
      0.0022921742008679, ...
      0.0022921742008679, ...
      0.0022921742008679, ...
      0.0022921742008679, ...
      0.0022921742008679, ...
      0.0130858129676685, ...
      0.0130858129676685, ...
      0.0130858129676685, ...
      0.0130858129676685, ...
      0.0130858129676685, ...
      0.0130858129676685 ];
%
%  The weights should sum to 1, not 1/2!
%
  w = w * 2.0;

  return
end
