function [ x, y, z, w ] = rule13 ( )

%*****************************************************************************80
%
%% rule13() returns the rule of precision 13.
%
%  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 = [ ...
      0.3333333333333334, ...
      0.4890769464525394, ...
      0.0218461070949213, ...
      0.4890769464525394, ...
      0.2213722862918329, ...
      0.5572554274163342, ...
      0.2213722862918329, ...
      0.4269414142598004, ...
      0.1461171714803992, ...
      0.4269414142598004, ...
      0.0215096811088432, ...
      0.9569806377823136, ...
      0.0215096811088432, ...
      0.0878954830321973, ...
      0.7485071158999522, ...
      0.1635974010678505, ...
      0.7485071158999522, ...
      0.1635974010678505, ...
      0.0878954830321973, ...
      0.1109220428034634, ...
      0.8647077702954428, ...
      0.0243701869010938, ...
      0.8647077702954428, ...
      0.0243701869010938, ...
      0.1109220428034634, ...
      0.3084417608921178, ...
      0.6235459955536755, ...
      0.0680122435542067, ...
      0.6235459955536755, ...
      0.0680122435542067, ...
      0.3084417608921178, ...
      0.0051263891023824, ...
      0.7223577931241880, ...
      0.2725158177734297, ...
      0.7223577931241880, ...
      0.2725158177734297, ...
      0.0051263891023824 ];

  y = [ ...
      0.3333333333333334, ...
      0.0218461070949213, ...
      0.4890769464525394, ...
      0.4890769464525394, ...
      0.5572554274163342, ...
      0.2213722862918329, ...
      0.2213722862918329, ...
      0.1461171714803992, ...
      0.4269414142598004, ...
      0.4269414142598004, ...
      0.9569806377823136, ...
      0.0215096811088432, ...
      0.0215096811088432, ...
      0.7485071158999522, ...
      0.0878954830321973, ...
      0.7485071158999522, ...
      0.1635974010678505, ...
      0.0878954830321973, ...
      0.1635974010678505, ...
      0.8647077702954428, ...
      0.1109220428034634, ...
      0.8647077702954428, ...
      0.0243701869010938, ...
      0.1109220428034634, ...
      0.0243701869010938, ...
      0.6235459955536755, ...
      0.3084417608921178, ...
      0.6235459955536755, ...
      0.0680122435542067, ...
      0.3084417608921178, ...
      0.0680122435542067, ...
      0.7223577931241880, ...
      0.0051263891023824, ...
      0.7223577931241880, ...
      0.2725158177734297, ...
      0.0051263891023824, ...
      0.2725158177734297 ];

  z = [ ...
      0.3333333333333333, ...
      0.4890769464525394, ...
      0.4890769464525394, ...
      0.0218461070949214, ...
      0.2213722862918329, ...
      0.2213722862918329, ...
      0.5572554274163342, ...
      0.4269414142598003, ...
      0.4269414142598003, ...
      0.1461171714803991, ...
      0.0215096811088433, ...
      0.0215096811088433, ...
      0.9569806377823138, ...
      0.1635974010678505, ...
      0.1635974010678505, ...
      0.0878954830321973, ...
      0.0878954830321973, ...
      0.7485071158999522, ...
      0.7485071158999522, ...
      0.0243701869010938, ...
      0.0243701869010938, ...
      0.1109220428034634, ...
      0.1109220428034634, ...
      0.8647077702954428, ...
      0.8647077702954428, ...
      0.0680122435542068, ...
      0.0680122435542067, ...
      0.3084417608921178, ...
      0.3084417608921178, ...
      0.6235459955536755, ...
      0.6235459955536756, ...
      0.2725158177734296, ...
      0.2725158177734296, ...
      0.0051263891023823, ...
      0.0051263891023823, ...
      0.7223577931241879, ...
      0.7223577931241879 ];

  w = [ ...
      0.0339800182934158, ...
      0.0119972009644474, ...
      0.0119972009644474, ...
      0.0119972009644474, ...
      0.0291392425596000, ...
      0.0291392425596000, ...
      0.0291392425596000, ...
      0.0278009837652267, ...
      0.0278009837652267, ...
      0.0278009837652267, ...
      0.0030261685517696, ...
      0.0030261685517696, ...
      0.0030261685517696, ...
      0.0120895199057969, ...
      0.0120895199057969, ...
      0.0120895199057969, ...
      0.0120895199057969, ...
      0.0120895199057969, ...
      0.0120895199057969, ...
      0.0074827005525828, ...
      0.0074827005525828, ...
      0.0074827005525828, ...
      0.0074827005525828, ...
      0.0074827005525828, ...
      0.0074827005525828, ...
      0.0173206380704242, ...
      0.0173206380704242, ...
      0.0173206380704242, ...
      0.0173206380704242, ...
      0.0173206380704242, ...
      0.0173206380704242, ...
      0.0047953405017716, ...
      0.0047953405017716, ...
      0.0047953405017716, ...
      0.0047953405017716, ...
      0.0047953405017716, ...
      0.0047953405017716 ];
%
%  The weights should sum to 1, not 1/2!
%
  w = w * 2.0;

  return
end
