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

%*****************************************************************************80
%
%% rule13() returns the rule of precision 13.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    02 April 2023
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Jan Jaskowiec, Natarajan Sukumar,
%    High order symmetric cubature rules for tetrahedra and pyramids,
%    International Journal of Numerical Methods in Engineering,
%    Volume 122, Number 1, pages 148-171, 24 August 2020.
%
%  Output:
%
%    a(n), b(n), c(n), d(n): the barycentric coordinates of quadrature points.
%
%    w(n): the quadrature weights.
%
  a = [ ...
      0.02023816786180974298, ...
      0.93928549641457081965, ...
      0.02023816786180974298, ...
      0.02023816786180974298, ...
      0.28901473524352633282, ...
      0.13295579426942091827, ...
      0.28901473524352633282, ...
      0.28901473524352633282, ...
      0.09402870008212707575, ...
      0.71791389975361874498, ...
      0.09402870008212707575, ...
      0.09402870008212707575, ...
      0.19764985444372551449, ...
      0.40705043666882340103, ...
      0.19764985444372551449, ...
      0.19764985444372551449, ...
      0.45953810323981636454, ...
      0.04046189676018363546, ...
      0.45953810323981636454, ...
      0.04046189676018363546, ...
      0.45953810323981636454, ...
      0.04046189676018363546, ...
      0.00000019514803064427, ...
      0.49999980485196937607, ...
      0.00000019514803064427, ...
      0.49999980485196937607, ...
      0.00000019514803064427, ...
      0.49999980485196937607, ...
      0.61189713020429348234, ...
      0.06752926495280242580, ...
      0.06752926495280242580, ...
      0.25304433989010172157, ...
      0.25304433989010172157, ...
      0.25304433989010172157, ...
      0.06752926495280242580, ...
      0.61189713020429348234, ...
      0.06752926495280242580, ...
      0.06752926495280242580, ...
      0.61189713020429348234, ...
      0.06752926495280242580, ...
      0.48683083387981590517, ...
      0.13601051451320292363, ...
      0.13601051451320292363, ...
      0.24114813709377821982, ...
      0.24114813709377821982, ...
      0.24114813709377821982, ...
      0.13601051451320292363, ...
      0.48683083387981590517, ...
      0.13601051451320292363, ...
      0.13601051451320292363, ...
      0.48683083387981590517, ...
      0.13601051451320292363, ...
      0.42737860803490002048, ...
      0.27807834595637015429, ...
      0.27807834595637015429, ...
      0.01646470005235971951, ...
      0.01646470005235971951, ...
      0.01646470005235971951, ...
      0.27807834595637015429, ...
      0.42737860803490002048, ...
      0.27807834595637015429, ...
      0.27807834595637015429, ...
      0.42737860803490002048, ...
      0.27807834595637015429, ...
      0.56675286809679847888, ...
      0.19675501971928607836, ...
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      0.03973709246462935052, ...
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      0.19675501971928607836, ...
      0.56675286809679847888, ...
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      0.56675286809679847888, ...
      0.19675501971928607836, ...
      0.06201970724197542612, ...
      0.38624986292034968471, ...
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      0.16548056691732521140, ...
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      0.38624986292034968471, ...
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      0.10866078208331987620, ...
      0.02353551905465277316, ...
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      0.84426817980737456359, ...
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      0.02353551905465277316, ...
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      0.02353551905465277316, ...
      0.54469649770191619353, ...
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      0.33621089307477192154, ...
      0.00350005986987981903, ...
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      0.11559254935343205029, ...
      0.11559254935343205029, ...
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      0.33621089307477192154, ...
      0.00350005986987981903, ...
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      0.00350005986987981903, ...
      0.33621089307477192154, ...
      0.33621089307477192154, ...
      0.00350005986987981903, ...
      0.54469649770191619353, ...
      0.54469649770191619353, ...
      0.00350005986987981903, ...
      0.33621089307477192154, ...
      0.02886160494075550378, ...
      0.02886160494075550378, ...
      0.68598163012351520695, ...
      0.01057343468672890079, ...
      0.68598163012351520695, ...
      0.01057343468672890079, ...
      0.27458333024900039021, ...
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      0.27458333024900039021, ...
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      0.68598163012351520695, ...
      0.01057343468672890079, ...
      0.02886160494075550378, ...
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      0.01057343468672890079, ...
      0.68598163012351520695, ...
      0.68598163012351520695, ...
      0.01057343468672890079, ...
      0.02886160494075550378, ...
      0.02886160494075550378, ...
      0.01057343468672890079, ...
      0.68598163012351520695, ...
      0.15458664682738043616, ...
      0.15458664682738043616, ...
      0.73567724678185975051, ...
      0.09870239282167234118, ...
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      0.73567724678185975051, ...
      0.09870239282167234118, ...
      0.15458664682738043616, ...
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      0.09870239282167234118, ...
      0.73567724678185975051, ...
      0.73567724678185975051, ...
      0.09870239282167234118, ...
      0.15458664682738043616, ...
      0.15458664682738043616, ...
      0.09870239282167234118, ...
      0.73567724678185975051 ];

  b = [ ...
      0.02023816786180974298, ...
      0.02023816786180974298, ...
      0.93928549641457081965, ...
      0.02023816786180974298, ...
      0.28901473524352633282, ...
      0.28901473524352633282, ...
      0.13295579426942091827, ...
      0.28901473524352633282, ...
      0.09402870008212707575, ...
      0.09402870008212707575, ...
      0.71791389975361874498, ...
      0.09402870008212707575, ...
      0.19764985444372551449, ...
      0.19764985444372551449, ...
      0.40705043666882340103, ...
      0.19764985444372551449, ...
      0.04046189676018363546, ...
      0.45953810323981636454, ...
      0.45953810323981636454, ...
      0.04046189676018363546, ...
      0.04046189676018363546, ...
      0.45953810323981636454, ...
      0.49999980485196937607, ...
      0.00000019514803064427, ...
      0.00000019514803064427, ...
      0.49999980485196937607, ...
      0.49999980485196937607, ...
      0.00000019514803064427, ...
      0.06752926495280242580, ...
      0.61189713020429348234, ...
      0.06752926495280242580, ...
      0.06752926495280242580, ...
      0.61189713020429348234, ...
      0.06752926495280242580, ...
      0.25304433989010172157, ...
      0.25304433989010172157, ...
      0.25304433989010172157, ...
      0.06752926495280242580, ...
      0.06752926495280242580, ...
      0.61189713020429348234, ...
      0.13601051451320292363, ...
      0.48683083387981590517, ...
      0.13601051451320292363, ...
      0.13601051451320292363, ...
      0.48683083387981590517, ...
      0.13601051451320292363, ...
      0.24114813709377821982, ...
      0.24114813709377821982, ...
      0.24114813709377821982, ...
      0.13601051451320292363, ...
      0.13601051451320292363, ...
      0.48683083387981590517, ...
      0.27807834595637015429, ...
      0.42737860803490002048, ...
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      0.27807834595637015429, ...
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      0.27807834595637015429, ...
      0.01646470005235971951, ...
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      0.27807834595637015429, ...
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      0.42737860803490002048, ...
      0.19675501971928607836, ...
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      0.56675286809679847888, ...
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      0.03973709246462935052, ...
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      0.19675501971928607836, ...
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      0.56675286809679847888, ...
      0.38624986292034968471, ...
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      0.15458664682738043616 ];

  c = [ ...
      0.02023816786180974298, ...
      0.02023816786180974298, ...
      0.02023816786180974298, ...
      0.93928549641457081965, ...
      0.28901473524352633282, ...
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end
