function [ a, b, c, w ] = rule40 ( )

%*****************************************************************************80
%
%% rule40() returns the rule of precision 40.
%
%  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 = [ ...
          0.1671778383557105, ...
          0.8312942125952762, ...
          0.0015279490490133, ...
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  b = [ ...
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          0.0060844538754953, ...
          0.0060844538754953, ...
          0.0002785606250486, ...
          0.0002785606250486, ...
          0.0002785606250486, ...
          0.0002785606250486, ...
          0.0002785606250486, ...
          0.0002785606250486 ];

  return
end
