function [ a, b, c, w ] = rule13 ( )

%*****************************************************************************80
%
%% rule13() returns the rule of precision 13.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    09 June 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Hong Xiao, Zydrunas Gimbutas,
%    A numerical algorithm for the construction of efficient
%    quadrature rules in two and higher dimensions, 
%    Computers and Mathematics with Applications,
%    Volume 59, 2010, pages 663-676.
%
%  Output:
%
%    real a(n), b(n), c(n): the barycentric coordinates of quadrature points.
%
%    real w(n): the quadrature weights.
%
  a = [ ...
          0.4961358947410461, ...
          0.4961358947410460, ...
          0.0077282105179078, ...
          0.4696086896534919, ...
          0.4696086896534918, ...
          0.0607826206930162, ...
          0.2311102849490822, ...
          0.5377794301018355, ...
          0.2311102849490823, ...
          0.2920786885766364, ...
          0.6889333070396045, ...
          0.0189880043837591, ...
          0.6889333070396045, ...
          0.2920786885766364, ...
          0.0189880043837589, ...
          0.3333333333333333, ...
          0.2667452533103511, ...
          0.6355187156236324, ...
          0.0977360310660165, ...
          0.6355187156236323, ...
          0.2667452533103513, ...
          0.0977360310660164, ...
          0.4144775702790545, ...
          0.4144775702790545, ...
          0.1710448594418908, ...
          0.1135599125721331, ...
          0.7728801748557336, ...
          0.1135599125721334, ...
          0.1267997757838373, ...
          0.8512338800096334, ...
          0.0219663442065294, ...
          0.8512338800096334, ...
          0.1267997757838374, ...
          0.0219663442065290, ...
          0.0248959314912162, ...
          0.9502081370175671, ...
          0.0248959314912167 ];

  b = [ ...
          0.0077282105179079, ...
          0.4961358947410461, ...
          0.4961358947410462, ...
          0.0607826206930162, ...
          0.4696086896534920, ...
          0.4696086896534921, ...
          0.2311102849490824, ...
          0.2311102849490823, ...
          0.5377794301018356, ...
          0.0189880043837590, ...
          0.2920786885766364, ...
          0.6889333070396048, ...
          0.0189880043837590, ...
          0.6889333070396046, ...
          0.2920786885766367, ...
          0.3333333333333334, ...
          0.0977360310660166, ...
          0.2667452533103512, ...
          0.6355187156236326, ...
          0.0977360310660166, ...
          0.6355187156236323, ...
          0.2667452533103514, ...
          0.1710448594418909, ...
          0.4144775702790546, ...
          0.4144775702790547, ...
          0.1135599125721333, ...
          0.1135599125721331, ...
          0.7728801748557337, ...
          0.0219663442065293, ...
          0.1267997757838373, ...
          0.8512338800096335, ...
          0.0219663442065293, ...
          0.8512338800096335, ...
          0.1267997757838377, ...
          0.0248959314912165, ...
          0.0248959314912162, ...
          0.9502081370175673 ];

  c = [ ...
          0.4961358947410460, ...
          0.0077282105179078, ...
          0.4961358947410459, ...
          0.4696086896534919, ...
          0.0607826206930161, ...
          0.4696086896534917, ...
          0.5377794301018354, ...
          0.2311102849490823, ...
          0.2311102849490821, ...
          0.6889333070396045, ...
          0.0189880043837590, ...
          0.2920786885766361, ...
          0.2920786885766364, ...
          0.0189880043837589, ...
          0.6889333070396044, ...
          0.3333333333333333, ...
          0.6355187156236323, ...
          0.0977360310660164, ...
          0.2667452533103509, ...
          0.2667452533103511, ...
          0.0977360310660164, ...
          0.6355187156236322, ...
          0.4144775702790546, ...
          0.1710448594418909, ...
          0.4144775702790545, ...
          0.7728801748557337, ...
          0.1135599125721334, ...
          0.1135599125721329, ...
          0.8512338800096335, ...
          0.0219663442065293, ...
          0.1267997757838371, ...
          0.1267997757838373, ...
          0.0219663442065291, ...
          0.8512338800096333, ...
          0.9502081370175672, ...
          0.0248959314912166, ...
          0.0248959314912159 ];

  w = [ ...
          0.0099414763610726, ...
          0.0099414763610726, ...
          0.0099414763610726, ...
          0.0327812416037230, ...
          0.0327812416037230, ...
          0.0327812416037230, ...
          0.0460624095927782, ...
          0.0460624095927782, ...
          0.0460624095927782, ...
          0.0181254986462009, ...
          0.0181254986462009, ...
          0.0181254986462009, ...
          0.0181254986462009, ...
          0.0181254986462009, ...
          0.0181254986462009, ...
          0.0516226466642908, ...
          0.0372119604572615, ...
          0.0372119604572615, ...
          0.0372119604572615, ...
          0.0372119604572615, ...
          0.0372119604572615, ...
          0.0372119604572615, ...
          0.0469470955421552, ...
          0.0469470955421552, ...
          0.0469470955421552, ...
          0.0309030979757598, ...
          0.0309030979757598, ...
          0.0309030979757598, ...
          0.0153930726837822, ...
          0.0153930726837822, ...
          0.0153930726837822, ...
          0.0153930726837822, ...
          0.0153930726837822, ...
          0.0153930726837822, ...
          0.0080293997952584, ...
          0.0080293997952584, ...
          0.0080293997952584 ];

  return
end
