#! /usr/bin/env python3
#
def tetrahedron_jaskowiec_rule_test ( ):

#*****************************************************************************80
#
## tetrahedron_jaskowiec_rule_test() tests tetrahedron_jaskowiec_rule().
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    11 July 2023
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'tetrahedron_jaskowiec_rule_test():' )
  print ( '  Python version: ' + platform.python_version ( ) )
  print ( '  tetrahedron_jaskowiec_rule() returns Jaskowiec quadrature' )
  print ( '  rules for a tetrahedron.' )

  p = 5
  tetrahedron_jaskowiec_rule_test01 ( p )

  p = 5
  tetrahedron_jaskowiec_rule_test02 ( p )

  p_lo = 0
  p_hi = 20
  tetrahedron_jaskowiec_rule_test03 ( p_lo, p_hi )

  tetrahedron_jaskowiec_rule_test04 ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'tetrahedron_jaskowiec_rule_test():' )
  print ( '  Normal end of execution.' )
  return

def tetrahedron_jaskowiec_rule_test01 ( p ):

#*****************************************************************************80
#
## tetrahedron_jaskowiec_rule_test01() computes a quadrature rule of given order.
#
#  Licensing:
#
#    This code is distributed under the GNU GPL license.
#
#  Modified:
#
#    26 May 2023
#
#  Author:
#
#    John Burkardt.
#
  import numpy as np

  print ( '' )
  print ( 'tetrahedron_jaskowiec_rule_test01():' )
  print ( '  Quadrature rule for the tetrahedron,' )
  print ( '  given in barycentric coordinates.' )
  print ( '  Precision p =', p )
#
#  Retrieve the rule.
#
  n, a, b, c, d, w = tetrahedron_jaskowiec_rule ( p )
#
#  Print the rule.
#
  print ( '' )
  print ( '     I      W          A           B           C           D' )
  print ( '' )
  for i in range ( 0, n ):
    print ( '  %4d  %10.6f  %10.6f  %10.6f  %10.6f  %10.6f' \
      % ( i, w[i], a[i], b[i], c[i], d[i] ) )
#
#  Verify that weight sum to 1.
#
  w_sum = np.sum ( w )

  print ( '' )
  print ( '  Weight Sum    ', w_sum )

  return

def tetrahedron_jaskowiec_rule_test02 ( p ):

#*****************************************************************************80
#
## tetrahedron_jaskowiec_rule_test02() tests a tetrahedron quadrature rule.
#
#  Licensing:
#
#    This code is distributed under the GNU GPL license.
#
#  Modified:
#
#    23 May 2023
#
#  Author:
#
#    John Burkardt.
#
  import numpy as np

  print ( '' )
  print ( 'tetrahedron_jaskowiec_rule_test02():' )
  print ( '  Test the precision of a quadrature rule for the unit tetrahedron.' )

  dim_num = 3
#
#  Retrieve the rule.
#
  n, a, b, c, d, w = tetrahedron_jaskowiec_rule ( p )
#
#  Pack the x, y, z vectors as rows of an array.
#
  xyz = np.transpose ( np.array ( [ a, b, c ] ) )

  print ( '' )
  print ( '  Stated precision of rule    = ', p )
  print ( '  Number of quadrature points = ', n )
  print ( '' )
  print ( '  Degree  Maximum error' )
  print ( '' )

  for degree in range ( 0, p + 3 ):

    expon = np.zeros ( dim_num, dtype = int )
    more = False
    h = 0
    t = 0
    max_error = 0.0

    while ( True ):

      expon, more, h, t = comp_next ( degree, dim_num, expon, more, h, t )

      v = monomial_value ( expon, xyz )

      quad = tetrahedron_unit_volume ( ) * np.dot ( w, v )

      exact = tetrahedron_unit_monomial_integral ( expon )

      quad_error = np.abs ( quad - exact )

      max_error = max ( max_error, quad_error )

      if ( not more ):
        break

    print ( '  %2d  %24.16f' % ( degree, max_error ) )

  return

def tetrahedron_jaskowiec_rule_test03 ( p_lo, p_hi ):

#*****************************************************************************80
#
## tetrahedron_jaskowiec_rule_test03() tests absolute and relative precision.
#
#  Licensing:
#
#    This code is distributed under the GNU GPL license.
#
#  Modified:
#
#    11 July 2023
#
#  Author:
#
#    John Burkardt.
#
#  Input:
#
#    integer p_lo, p_hi: the lowest and highest rules to check.
#   
  import numpy as np

  print ( '' )
  print ( 'tetrahedron_jaskowiec_rule_test02():' )
  print ( '  Test the precision of quadrature rules for the unit tetrahedron.' )
  print ( '  Check rules of precision p =', p_lo, 'through', p_hi )
  print ( '  for error in approximating integrals of monomials.' )

  dim_num = 3

  print ( '' )
  print ( '              maximum                   maximum' )
  print ( '   p          absolute                  relative' )
  print ( '              error                     error' )
  print ( '' )

  for p in range ( p_lo, p_hi + 1 ):

    n, a, b, c, d, w = tetrahedron_jaskowiec_rule ( p )
#
#  Pack the x, y, z vectors as rows of an array.
#
    xyz = np.transpose ( np.array ( [ a, b, c ] ) )

    max_abs = 0.0
    max_rel = 0.0

    for degree in range ( 0, p + 1 ):

      expon = np.zeros ( dim_num, dtype = int )
      more = False
      h = 0
      t = 0

      while ( True ):

        expon, more, h, t = comp_next ( degree, dim_num, expon, more, h, t )

        v = monomial_value ( expon, xyz )

        quad = tetrahedron_unit_volume ( ) * np.dot ( w, v )

        exact = tetrahedron_unit_monomial_integral ( expon )

        quad_error = np.abs ( quad - exact )

        max_abs = max ( max_abs, quad_error )
        max_rel = max ( max_rel, quad_error / abs ( exact ) )

        if ( not more ):
          break

    print ( '  %2d  %24.16g  %24.16g' % ( p, max_abs, max_rel ) )

  return

def tetrahedron_jaskowiec_rule_test04 ( ):

#*****************************************************************************80
#
## tetrahedron_jaskowiec_rule_test04() integrates 1/sqrt(r).
#
#  Licensing:
#
#    This code is distributed under the GNU GPL license.
#
#  Modified:
#
#    11 July 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.
#
  import numpy as np

  print ( '' )
  print ( 'tetrahedron_jaskowiec_rule_test04():' )
  print ( '  Integrate 1/sqrt(r) over the reference tetrahedron.' )

  exact = 163.0 / 679.0
  print ( '  Exact integral value is', exact )

  tetra = np.array ( [ \
    [ 0.0, 0.0, 0.0 ], \
    [ 1.0, 0.0, 0.0 ], \
    [ 0.0, 1.0, 0.0 ], \
    [ 0.0, 0.0, 1.0 ] ] )
  volume = tetrahedron_volume ( tetra )
  print ( '  Volume of tetrahedron is', volume )

  print ( '' )
  print ( '   P    N     Q     |Q-Exact]' )
  print ( '' )

  for p in range ( 0, 21 ):

    n, a, b, c, d, w = tetrahedron_jaskowiec_rule ( p )
    r = np.sqrt ( a**2 + b**2 + c**2 )
    f = 1.0 / np.sqrt ( r )
    q = volume * np.dot ( w, f )
    e = np.abs ( q - exact )
    print ( '  %2d  %3d  %20.16g  %20.16g' % ( p, n, q, e ) )

  return

def comp_next ( n, k, a, more, h, t ):

#*****************************************************************************80
#
## comp_next() computes the compositions of the integer N into K parts.
#
#  Discussion:
#
#    A composition of the integer N into K parts is an ordered sequence
#    of K nonnegative integers which sum to N.  The compositions (1,2,1)
#    and (1,1,2) are considered to be distinct.
#
#    The routine computes one composition on each call until there are no more.
#    For instance, one composition of 6 into 3 parts is
#    3+2+1, another would be 6+0+0.
#
#    On the first call to this routine, set MORE = FALSE.  The routine
#    will compute the first element in the sequence of compositions, and
#    return it, as well as setting MORE = TRUE.  If more compositions
#    are desired, call again, and again.  Each time, the routine will
#    return with a new composition.
#
#    However, when the LAST composition in the sequence is computed 
#    and returned, the routine will reset MORE to FALSE, signaling that
#    the end of the sequence has been reached.
#
#    This routine originally used a SAVE statement to maintain the
#    variables H and T.  I have decided that it is safer
#    to pass these variables as arguments, even though the user should
#    never alter them.  This allows this routine to safely shuffle
#    between several ongoing calculations.
#
#    There are 28 compositions of 6 into three parts.  This routine will
#    produce those compositions in the following order:
#
#     I         A
#     -     ---------
#     1     6   0   0
#     2     5   1   0
#     3     4   2   0
#     4     3   3   0
#     5     2   4   0
#     6     1   5   0
#     7     0   6   0
#     8     5   0   1
#     9     4   1   1
#    10     3   2   1
#    11     2   3   1
#    12     1   4   1
#    13     0   5   1
#    14     4   0   2
#    15     3   1   2
#    16     2   2   2
#    17     1   3   2
#    18     0   4   2
#    19     3   0   3
#    20     2   1   3
#    21     1   2   3
#    22     0   3   3
#    23     2   0   4
#    24     1   1   4
#    25     0   2   4
#    26     1   0   5
#    27     0   1   5
#    28     0   0   6
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    20 May 2015
#
#  Author:
#
#    John Burkardt.
#
#  Reference:
#
#    Albert Nijenhuis, Herbert Wilf,
#    Combinatorial Algorithms for Computers and Calculators,
#    Second Edition,
#    Academic Press, 1978,
#    ISBN: 0-12-519260-6,
#    LC: QA164.N54.
#
#  Input:
#
#    integer N, the integer whose compositions are desired.
#
#    integer K, the number of parts in the composition.
#
#    integer A(K), the previous composition.  On the first call,
#    with MORE = FALSE, set A = [].  Thereafter, A should be the 
#    value of A output from the previous call.
#
#    bool MORE.  The input value of MORE on the first
#    call should be FALSE, which tells the program to initialize.
#    On subsequent calls, MORE should be TRUE, or simply the
#    output value of MORE from the previous call.
#
#    integer H, T, two internal parameters needed for the
#    computation.  The user may need to initialize these before the
#    very first call, but these initial values are not important.
#    The user should not alter these parameters once the computation
#    begins.
#
#  Output:
#
#    integer A(K), the next composition.
#
#    bool MORE, will be TRUE unless the composition 
#    that is being returned is the final one in the sequence.
#
#    integer H, T, the updated values of the two internal 
#    variables.
#
  if ( k == 0 ):
    a = []
    more = False
    t = n
    h = 0
    return a, more, h, t

  if ( not more ):

    t = n
    h = 0
    a[0] = n
    for i in range ( 1, k ):
      a[i] = 0

  else:
      
    if ( 1 < t ):
      h = 0

    t = a[h]
    a[h] = 0
    a[0] = t - 1
    a[h+1] = a[h+1] + 1
    h = h + 1

  more = ( a[k-1] != n )

  return a, more, h, t

def monomial_value ( e, x ):

#*****************************************************************************80
#
## monomial_value() evaluates a monomial.
#
#  Discussion:
#
#    This routine evaluates a monomial of the form
#
#      product ( 1 <= i <= m ) x(i)^e(i)
#
#    The combination 0.0^0, if encountered, is treated as 1.0.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    15 May 2023
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer E(D): the exponents.
#
#    real X(N,D): the point coordinates.
#
#  Output:
#
#    real V(N): the monomial values.
#
  import numpy as np

  n, d = x.shape

  v = np.ones ( n )

  for j in range ( 0, d ):
    if ( 0 != e[j] ):
      v[0:n] = v[0:n] * x[0:n,j] ** e[j]

  return v

def rule_order ( p ):

#*****************************************************************************80
#
## rule_order() returns the order of a quadrature rule of given precision.
#
#  Discussion:
#
#    The "order" of a quadrature rule is the number of points involved.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    01 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.
#
#  Input:
#
#    integer p: the precision, 0 <= p <= 20.
#
#  Output:
#
#    integer order: the order of the rule.
#
  import numpy as np

  if ( p < 0 ):
    raise Exception ( 'rule_order(): Input p < 0.' )

  if ( 20 < p ):
    raise Exception ( 'rule_order(): Input 20 < p.' )

  order_vec = np.array ( [ \
      1,\
      1,   4,   8,  14,  14, \
     24,  35,  46,  59,  81, \
    110, 168, 172, 204, 264, \
    304, 364, 436, 487, 552 ] )

  order = order_vec[p]

  return order

def rule00 ( ):

#*****************************************************************************80
#
## rule00() returns the rule of precision 0.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.25000000000000000000 ] )

  b = np.array ( [ \
      0.25000000000000000000 ] )

  c = np.array ( [ \
      0.25000000000000000000 ] )

  d = np.array ( [ \
      0.25000000000000000000 ] )

  w = np.array ( [ \
      1.00000000000000000000 ] )

  return a, b, c, d, w

def rule01 ( ):

#*****************************************************************************80
#
## rule01() returns the rule of precision 1.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.25000000000000000000 ] )

  b = np.array ( [ \
      0.25000000000000000000 ] )

  c = np.array ( [ \
      0.25000000000000000000 ] )

  d = np.array ( [ \
      0.25000000000000000000 ] )

  w = np.array ( [ \
      1.00000000000000000000 ] )

  return a, b, c, d, w

def rule02 ( ):

#*****************************************************************************80
#
## rule02() returns the rule of precision 2.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.13819660112501050420, \
      0.58541019662496840414, \
      0.13819660112501050420, \
      0.13819660112501050420 ] )

  b = np.array ( [ \
      0.13819660112501050420, \
      0.13819660112501050420, \
      0.58541019662496840414, \
      0.13819660112501050420 ] )

  c = np.array ( [ \
      0.13819660112501050420, \
      0.13819660112501050420, \
      0.13819660112501050420, \
      0.58541019662496840414 ] )

  d = np.array ( [ \
      0.58541019662496840414, \
      0.13819660112501050420, \
      0.13819660112501050420, \
      0.13819660112501050420 ] )

  w = np.array ( [ \
      0.25000000000000000000, \
      0.25000000000000000000, \
      0.25000000000000000000, \
      0.25000000000000000000 ] )

  return a, b, c, d, w

def rule03 ( ):

#*****************************************************************************80
#
## rule03() returns the rule of precision 3.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.32868114666534897772, \
      0.01395656000395302174, \
      0.32868114666534897772, \
      0.32868114666534897772, \
      0.11192072750929155101, \
      0.66423781747212540250, \
      0.11192072750929155101, \
      0.11192072750929155101 ] )

  b = np.array ( [ \
      0.32868114666534897772, \
      0.32868114666534897772, \
      0.01395656000395302174, \
      0.32868114666534897772, \
      0.11192072750929155101, \
      0.11192072750929155101, \
      0.66423781747212540250, \
      0.11192072750929155101 ] )

  c = np.array ( [ \
      0.32868114666534897772, \
      0.32868114666534897772, \
      0.32868114666534897772, \
      0.01395656000395302174, \
      0.11192072750929155101, \
      0.11192072750929155101, \
      0.11192072750929155101, \
      0.66423781747212540250 ] )

  d = np.array ( [ \
      0.01395656000395302174, \
      0.32868114666534897772, \
      0.32868114666534897772, \
      0.32868114666534897772, \
      0.66423781747212540250, \
      0.11192072750929155101, \
      0.11192072750929155101, \
      0.11192072750929155101 ] )

  w = np.array ( [ \
      0.12749131155750642597, \
      0.12749131155750642597, \
      0.12749131155750642597, \
      0.12749131155750642597, \
      0.12250868844249357403, \
      0.12250868844249357403, \
      0.12250868844249357403, \
      0.12250868844249357403 ] )

  return a, b, c, d, w

def rule04 ( ):

#*****************************************************************************80
#
## rule04() returns the rule of precision 4.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.30958216531795190729, \
      0.07125350404614427813, \
      0.30958216531795190729, \
      0.30958216531795190729, \
      0.08344277230397757761, \
      0.74967168308806730881, \
      0.08344277230397757761, \
      0.08344277230397757761, \
      0.07722095407005866163, \
      0.42277904592994131061, \
      0.07722095407005866163, \
      0.42277904592994131061, \
      0.07722095407005866163, \
      0.42277904592994131061 ] )

  b = np.array ( [ \
      0.30958216531795190729, \
      0.30958216531795190729, \
      0.07125350404614427813, \
      0.30958216531795190729, \
      0.08344277230397757761, \
      0.08344277230397757761, \
      0.74967168308806730881, \
      0.08344277230397757761, \
      0.42277904592994131061, \
      0.07722095407005866163, \
      0.07722095407005866163, \
      0.42277904592994131061, \
      0.42277904592994131061, \
      0.07722095407005866163 ] )

  c = np.array ( [ \
      0.30958216531795190729, \
      0.30958216531795190729, \
      0.30958216531795190729, \
      0.07125350404614427813, \
      0.08344277230397757761, \
      0.08344277230397757761, \
      0.08344277230397757761, \
      0.74967168308806730881, \
      0.42277904592994131061, \
      0.42277904592994131061, \
      0.42277904592994131061, \
      0.07722095407005866163, \
      0.07722095407005866163, \
      0.07722095407005866163 ] )

  d = np.array ( [ \
      0.07125350404614427813, \
      0.30958216531795190729, \
      0.30958216531795190729, \
      0.30958216531795190729, \
      0.74967168308806730881, \
      0.08344277230397757761, \
      0.08344277230397757761, \
      0.08344277230397757761, \
      0.07722095407005866163, \
      0.07722095407005866163, \
      0.42277904592994131061, \
      0.07722095407005866163, \
      0.42277904592994131061, \
      0.42277904592994131061 ] )

  w = np.array ( [ \
      0.06540916363445217763, \
      0.06540916363445217763, \
      0.06540916363445217763, \
      0.06540916363445217763, \
      0.05935526423100475485, \
      0.05935526423100475485, \
      0.05935526423100475485, \
      0.05935526423100475485, \
      0.08349038142302871168, \
      0.08349038142302871168, \
      0.08349038142302871168, \
      0.08349038142302871168, \
      0.08349038142302871168, \
      0.08349038142302871168 ] )

  return a, b, c, d, w

def rule05 ( ):

#*****************************************************************************80
#
## rule05() returns the rule of precision 5.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.31088591926330061410, \
      0.06734224221009817157, \
      0.31088591926330061410, \
      0.31088591926330061410, \
      0.09273525031089122073, \
      0.72179424906732636558, \
      0.09273525031089122073, \
      0.09273525031089122073, \
      0.04550370412564964939, \
      0.45449629587435036449, \
      0.04550370412564964939, \
      0.45449629587435036449, \
      0.04550370412564964939, \
      0.45449629587435036449 ] )

  b = np.array ( [ \
      0.31088591926330061410, \
      0.31088591926330061410, \
      0.06734224221009817157, \
      0.31088591926330061410, \
      0.09273525031089122073, \
      0.09273525031089122073, \
      0.72179424906732636558, \
      0.09273525031089122073, \
      0.45449629587435036449, \
      0.04550370412564964939, \
      0.04550370412564964939, \
      0.45449629587435036449, \
      0.45449629587435036449, \
      0.04550370412564964939 ] )

  c = np.array ( [ \
      0.31088591926330061410, \
      0.31088591926330061410, \
      0.31088591926330061410, \
      0.06734224221009817157, \
      0.09273525031089122073, \
      0.09273525031089122073, \
      0.09273525031089122073, \
      0.72179424906732636558, \
      0.45449629587435036449, \
      0.45449629587435036449, \
      0.45449629587435036449, \
      0.04550370412564964939, \
      0.04550370412564964939, \
      0.04550370412564964939 ] )

  d = np.array ( [ \
      0.06734224221009817157, \
      0.31088591926330061410, \
      0.31088591926330061410, \
      0.31088591926330061410, \
      0.72179424906732636558, \
      0.09273525031089122073, \
      0.09273525031089122073, \
      0.09273525031089122073, \
      0.04550370412564964939, \
      0.04550370412564964939, \
      0.45449629587435036449, \
      0.04550370412564964939, \
      0.45449629587435036449, \
      0.45449629587435036449 ] )

  w = np.array ( [ \
      0.11268792571801584945, \
      0.11268792571801584945, \
      0.11268792571801584945, \
      0.11268792571801584945, \
      0.07349304311636195575, \
      0.07349304311636195575, \
      0.07349304311636195575, \
      0.07349304311636195575, \
      0.04254602077708146551, \
      0.04254602077708146551, \
      0.04254602077708146551, \
      0.04254602077708146551, \
      0.04254602077708146551, \
      0.04254602077708146551 ] )

  return a, b, c, d, w

def rule06 ( ):

#*****************************************************************************80
#
## rule06() returns the rule of precision 6.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.04067395853461135136, \
      0.87797812439616595981, \
      0.04067395853461135136, \
      0.04067395853461135136, \
      0.32233789014227548497, \
      0.03298632957317346875, \
      0.32233789014227548497, \
      0.32233789014227548497, \
      0.21460287125915203377, \
      0.35619138622254392645, \
      0.21460287125915203377, \
      0.21460287125915203377, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.26967233145831581709, \
      0.26967233145831581709, \
      0.26967233145831581709, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550 ] )

  b = np.array ( [ \
      0.04067395853461135136, \
      0.04067395853461135136, \
      0.87797812439616595981, \
      0.04067395853461135136, \
      0.32233789014227548497, \
      0.32233789014227548497, \
      0.03298632957317346875, \
      0.32233789014227548497, \
      0.21460287125915203377, \
      0.21460287125915203377, \
      0.35619138622254392645, \
      0.21460287125915203377, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.26967233145831581709, \
      0.26967233145831581709, \
      0.26967233145831581709, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743 ] )

  c = np.array ( [ \
      0.04067395853461135136, \
      0.04067395853461135136, \
      0.04067395853461135136, \
      0.87797812439616595981, \
      0.32233789014227548497, \
      0.32233789014227548497, \
      0.32233789014227548497, \
      0.03298632957317346875, \
      0.21460287125915203377, \
      0.21460287125915203377, \
      0.21460287125915203377, \
      0.35619138622254392645, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.26967233145831581709, \
      0.26967233145831581709, \
      0.26967233145831581709 ] )

  d = np.array ( [ \
      0.87797812439616595981, \
      0.04067395853461135136, \
      0.04067395853461135136, \
      0.04067395853461135136, \
      0.03298632957317346875, \
      0.32233789014227548497, \
      0.32233789014227548497, \
      0.32233789014227548497, \
      0.35619138622254392645, \
      0.21460287125915203377, \
      0.21460287125915203377, \
      0.21460287125915203377, \
      0.26967233145831581709, \
      0.26967233145831581709, \
      0.26967233145831581709, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550, \
      0.60300566479164918743, \
      0.06366100187501752550, \
      0.06366100187501752550 ] )

  w = np.array ( [ \
      0.01007721105532064301, \
      0.01007721105532064301, \
      0.01007721105532064301, \
      0.01007721105532064301, \
      0.05535718154365472377, \
      0.05535718154365472377, \
      0.05535718154365472377, \
      0.05535718154365472377, \
      0.03992275025816749423, \
      0.03992275025816749423, \
      0.03992275025816749423, \
      0.03992275025816749423, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647, \
      0.04821428571428571647 ] )

  return a, b, c, d, w

def rule07 ( ):

#*****************************************************************************80
#
## rule07() returns the rule of precision 7.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.25000000000000000000, \
      0.31570114977820279423, \
      0.05289655066539160344, \
      0.31570114977820279423, \
      0.31570114977820279423, \
      0.05048982259839637082, \
      0.44951017740160364999, \
      0.05048982259839637082, \
      0.44951017740160364999, \
      0.05048982259839637082, \
      0.44951017740160364999, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.04716070036099788421, \
      0.04716070036099788421, \
      0.04716070036099788421, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220 ] )

  b = np.array ( [ \
      0.25000000000000000000, \
      0.31570114977820279423, \
      0.31570114977820279423, \
      0.05289655066539160344, \
      0.31570114977820279423, \
      0.44951017740160364999, \
      0.05048982259839637082, \
      0.05048982259839637082, \
      0.44951017740160364999, \
      0.44951017740160364999, \
      0.05048982259839637082, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.04716070036099788421, \
      0.04716070036099788421, \
      0.04716070036099788421, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303 ] )

  c = np.array ( [ \
      0.25000000000000000000, \
      0.31570114977820279423, \
      0.31570114977820279423, \
      0.31570114977820279423, \
      0.05289655066539160344, \
      0.44951017740160364999, \
      0.44951017740160364999, \
      0.44951017740160364999, \
      0.05048982259839637082, \
      0.05048982259839637082, \
      0.05048982259839637082, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.04716070036099788421, \
      0.04716070036099788421, \
      0.04716070036099788421 ] )

  d = np.array ( [ \
      0.25000000000000000000, \
      0.05289655066539160344, \
      0.31570114977820279423, \
      0.31570114977820279423, \
      0.31570114977820279423, \
      0.05048982259839637082, \
      0.05048982259839637082, \
      0.44951017740160364999, \
      0.05048982259839637082, \
      0.44951017740160364999, \
      0.44951017740160364999, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.14663881381848495322, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.81083024109854850980, \
      0.02126547254148324767, \
      0.02126547254148324767, \
      0.04716070036099788421, \
      0.04716070036099788421, \
      0.04716070036099788421, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220, \
      0.57517163758700007303, \
      0.18883383102600104220, \
      0.18883383102600104220 ] )

  w = np.array ( [ \
      0.09548528946413084584, \
      0.04232958120996702794, \
      0.04232958120996702794, \
      0.04232958120996702794, \
      0.04232958120996702794, \
      0.03189692783285758004, \
      0.03189692783285758004, \
      0.03189692783285758004, \
      0.03189692783285758004, \
      0.03189692783285758004, \
      0.03189692783285758004, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.00811077082990334201, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976, \
      0.03720713072833461976 ] )

  return a, b, c, d, w

def rule08 ( ):

#*****************************************************************************80
#
## rule08() returns the rule of precision 8.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.18681275827072096885, \
      0.43956172518783709346, \
      0.18681275827072096885, \
      0.18681275827072096885, \
      0.11446240676123049795, \
      0.65661277971630849226, \
      0.11446240676123049795, \
      0.11446240676123049795, \
      0.31380659227240159659, \
      0.05858022318279514085, \
      0.31380659227240159659, \
      0.31380659227240159659, \
      0.04457737944884624520, \
      0.86626786165346125745, \
      0.04457737944884624520, \
      0.04457737944884624520, \
      0.43451650945615760691, \
      0.06548349054384239309, \
      0.43451650945615760691, \
      0.06548349054384239309, \
      0.43451650945615760691, \
      0.06548349054384239309, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.24282751426755175284, \
      0.24282751426755175284, \
      0.24282751426755175284, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377 ] )

  b = np.array ( [ \
      0.18681275827072096885, \
      0.18681275827072096885, \
      0.43956172518783709346, \
      0.18681275827072096885, \
      0.11446240676123049795, \
      0.11446240676123049795, \
      0.65661277971630849226, \
      0.11446240676123049795, \
      0.31380659227240159659, \
      0.31380659227240159659, \
      0.05858022318279514085, \
      0.31380659227240159659, \
      0.04457737944884624520, \
      0.04457737944884624520, \
      0.86626786165346125745, \
      0.04457737944884624520, \
      0.06548349054384239309, \
      0.43451650945615760691, \
      0.43451650945615760691, \
      0.06548349054384239309, \
      0.06548349054384239309, \
      0.43451650945615760691, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.24282751426755175284, \
      0.24282751426755175284, \
      0.24282751426755175284, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432 ] )

  c = np.array ( [ \
      0.18681275827072096885, \
      0.18681275827072096885, \
      0.18681275827072096885, \
      0.43956172518783709346, \
      0.11446240676123049795, \
      0.11446240676123049795, \
      0.11446240676123049795, \
      0.65661277971630849226, \
      0.31380659227240159659, \
      0.31380659227240159659, \
      0.31380659227240159659, \
      0.05858022318279514085, \
      0.04457737944884624520, \
      0.04457737944884624520, \
      0.04457737944884624520, \
      0.86626786165346125745, \
      0.06548349054384239309, \
      0.06548349054384239309, \
      0.06548349054384239309, \
      0.43451650945615760691, \
      0.43451650945615760691, \
      0.43451650945615760691, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.24282751426755175284, \
      0.24282751426755175284, \
      0.24282751426755175284 ] )

  d = np.array ( [ \
      0.43956172518783709346, \
      0.18681275827072096885, \
      0.18681275827072096885, \
      0.18681275827072096885, \
      0.65661277971630849226, \
      0.11446240676123049795, \
      0.11446240676123049795, \
      0.11446240676123049795, \
      0.05858022318279514085, \
      0.31380659227240159659, \
      0.31380659227240159659, \
      0.31380659227240159659, \
      0.86626786165346125745, \
      0.04457737944884624520, \
      0.04457737944884624520, \
      0.04457737944884624520, \
      0.43451650945615760691, \
      0.43451650945615760691, \
      0.06548349054384239309, \
      0.43451650945615760691, \
      0.06548349054384239309, \
      0.06548349054384239309, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.58714032992535780675, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.00507332075042159041, \
      0.20389317466211026586, \
      0.20389317466211026586, \
      0.24282751426755175284, \
      0.24282751426755175284, \
      0.24282751426755175284, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377, \
      0.71467692639330493432, \
      0.02124777966957167377, \
      0.02124777966957167377 ] )

  w = np.array ( [ \
      0.04781298803430665545, \
      0.04781298803430665545, \
      0.04781298803430665545, \
      0.04781298803430665545, \
      0.02972785408679422259, \
      0.02972785408679422259, \
      0.02972785408679422259, \
      0.02972785408679422259, \
      0.04352732421897526766, \
      0.04352732421897526766, \
      0.04352732421897526766, \
      0.04352732421897526766, \
      0.00863273602081497497, \
      0.00863273602081497497, \
      0.00863273602081497497, \
      0.00863273602081497497, \
      0.03689054126986636428, \
      0.03689054126986636428, \
      0.03689054126986636428, \
      0.03689054126986636428, \
      0.03689054126986636428, \
      0.03689054126986636428, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.01449702671085950460, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752, \
      0.00715740186724360752 ] )

  return a, b, c, d, w

def rule09 ( ):

#*****************************************************************************80
#
## rule09() returns the rule of precision 9.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.25000000000000000000, \
      0.16790660523674277860, \
      0.49628018428977160870, \
      0.16790660523674277860, \
      0.16790660523674277860, \
      0.09143627051407625383, \
      0.72569118845777125237, \
      0.09143627051407625383, \
      0.09143627051407625383, \
      0.32185566481765326419, \
      0.03443300554704020050, \
      0.32185566481765326419, \
      0.32185566481765326419, \
      0.04183769590036560265, \
      0.87448691229890318510, \
      0.04183769590036560265, \
      0.04183769590036560265, \
      0.39327056142515365300, \
      0.10672943857484636088, \
      0.39327056142515365300, \
      0.10672943857484636088, \
      0.39327056142515365300, \
      0.10672943857484636088, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.03401339023811966039, \
      0.03401339023811966039, \
      0.03401339023811966039, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451 ] )

  b = np.array ( [ \
      0.25000000000000000000, \
      0.16790660523674277860, \
      0.16790660523674277860, \
      0.49628018428977160870, \
      0.16790660523674277860, \
      0.09143627051407625383, \
      0.09143627051407625383, \
      0.72569118845777125237, \
      0.09143627051407625383, \
      0.32185566481765326419, \
      0.32185566481765326419, \
      0.03443300554704020050, \
      0.32185566481765326419, \
      0.04183769590036560265, \
      0.04183769590036560265, \
      0.87448691229890318510, \
      0.04183769590036560265, \
      0.10672943857484636088, \
      0.39327056142515365300, \
      0.39327056142515365300, \
      0.10672943857484636088, \
      0.10672943857484636088, \
      0.39327056142515365300, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.03401339023811966039, \
      0.03401339023811966039, \
      0.03401339023811966039, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365 ] )

  c = np.array ( [ \
      0.25000000000000000000, \
      0.16790660523674277860, \
      0.16790660523674277860, \
      0.16790660523674277860, \
      0.49628018428977160870, \
      0.09143627051407625383, \
      0.09143627051407625383, \
      0.09143627051407625383, \
      0.72569118845777125237, \
      0.32185566481765326419, \
      0.32185566481765326419, \
      0.32185566481765326419, \
      0.03443300554704020050, \
      0.04183769590036560265, \
      0.04183769590036560265, \
      0.04183769590036560265, \
      0.87448691229890318510, \
      0.10672943857484636088, \
      0.10672943857484636088, \
      0.10672943857484636088, \
      0.39327056142515365300, \
      0.39327056142515365300, \
      0.39327056142515365300, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.03401339023811966039, \
      0.03401339023811966039, \
      0.03401339023811966039 ] )

  d = np.array ( [ \
      0.25000000000000000000, \
      0.49628018428977160870, \
      0.16790660523674277860, \
      0.16790660523674277860, \
      0.16790660523674277860, \
      0.72569118845777125237, \
      0.09143627051407625383, \
      0.09143627051407625383, \
      0.09143627051407625383, \
      0.03443300554704020050, \
      0.32185566481765326419, \
      0.32185566481765326419, \
      0.32185566481765326419, \
      0.87448691229890318510, \
      0.04183769590036560265, \
      0.04183769590036560265, \
      0.04183769590036560265, \
      0.39327056142515365300, \
      0.39327056142515365300, \
      0.10672943857484636088, \
      0.39327056142515365300, \
      0.10672943857484636088, \
      0.10672943857484636088, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.21369256965239782908, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.71839309398142436880, \
      0.03395716818308888718, \
      0.03395716818308888718, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.00000000341375680369, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.07868363447668792754, \
      0.46065818105477762678, \
      0.46065818105477762678, \
      0.03401339023811966039, \
      0.03401339023811966039, \
      0.03401339023811966039, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451, \
      0.59721072276184994365, \
      0.18438794350001519451, \
      0.18438794350001519451 ] )

  w = np.array ( [ \
      0.05686662425355172579, \
      0.02569427668952317667, \
      0.02569427668952317667, \
      0.02569427668952317667, \
      0.02569427668952317667, \
      0.00229892335302837002, \
      0.00229892335302837002, \
      0.00229892335302837002, \
      0.00229892335302837002, \
      0.03045603866759100803, \
      0.03045603866759100803, \
      0.03045603866759100803, \
      0.03045603866759100803, \
      0.00712372234023888121, \
      0.00712372234023888121, \
      0.00712372234023888121, \
      0.00712372234023888121, \
      0.03684365548094388487, \
      0.03684365548094388487, \
      0.03684365548094388487, \
      0.03684365548094388487, \
      0.03684365548094388487, \
      0.03684365548094388487, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.01032205678220984683, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.00763488715398085490, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046, \
      0.02035802261874757046 ] )

  return a, b, c, d, w

def rule10 ( ):

#*****************************************************************************80
#
## rule10() returns the rule of precision 10.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    01 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.
#
  import numpy as np

  a = np.array ( [ \
      0.25000000000000000000, \
      0.07255175741743780105, \
      0.78234472774768659686, \
      0.07255175741743780105, \
      0.07255175741743780105, \
      0.30789594786692286998, \
      0.07631215639923132066, \
      0.30789594786692286998, \
      0.30789594786692286998, \
      0.47628086039277905961, \
      0.02371913960722092998, \
      0.47628086039277905961, \
      0.02371913960722092998, \
      0.47628086039277905961, \
      0.02371913960722092998, \
      0.09657977306910725535, \
      0.40342022693089274465, \
      0.09657977306910725535, \
      0.40342022693089274465, \
      0.09657977306910725535, \
      0.40342022693089274465, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.89554895506269893701, \
      0.89554895506269893701, \
      0.89554895506269893701, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768 ] )

  b = np.array ( [ \
      0.25000000000000000000, \
      0.07255175741743780105, \
      0.07255175741743780105, \
      0.78234472774768659686, \
      0.07255175741743780105, \
      0.30789594786692286998, \
      0.30789594786692286998, \
      0.07631215639923132066, \
      0.30789594786692286998, \
      0.02371913960722092998, \
      0.47628086039277905961, \
      0.47628086039277905961, \
      0.02371913960722092998, \
      0.02371913960722092998, \
      0.47628086039277905961, \
      0.40342022693089274465, \
      0.09657977306910725535, \
      0.09657977306910725535, \
      0.40342022693089274465, \
      0.40342022693089274465, \
      0.09657977306910725535, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.89554895506269893701, \
      0.89554895506269893701, \
      0.89554895506269893701, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845 ] )

  c = np.array ( [ \
      0.25000000000000000000, \
      0.07255175741743780105, \
      0.07255175741743780105, \
      0.07255175741743780105, \
      0.78234472774768659686, \
      0.30789594786692286998, \
      0.30789594786692286998, \
      0.30789594786692286998, \
      0.07631215639923132066, \
      0.02371913960722092998, \
      0.02371913960722092998, \
      0.02371913960722092998, \
      0.47628086039277905961, \
      0.47628086039277905961, \
      0.47628086039277905961, \
      0.40342022693089274465, \
      0.40342022693089274465, \
      0.40342022693089274465, \
      0.09657977306910725535, \
      0.09657977306910725535, \
      0.09657977306910725535, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.89554895506269893701, \
      0.89554895506269893701, \
      0.89554895506269893701 ] )

  d = np.array ( [ \
      0.25000000000000000000, \
      0.78234472774768659686, \
      0.07255175741743780105, \
      0.07255175741743780105, \
      0.07255175741743780105, \
      0.07631215639923132066, \
      0.30789594786692286998, \
      0.30789594786692286998, \
      0.30789594786692286998, \
      0.47628086039277905961, \
      0.47628086039277905961, \
      0.02371913960722092998, \
      0.47628086039277905961, \
      0.02371913960722092998, \
      0.02371913960722092998, \
      0.09657977306910725535, \
      0.09657977306910725535, \
      0.40342022693089274465, \
      0.09657977306910725535, \
      0.40342022693089274465, \
      0.40342022693089274465, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.52266860528615399772, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.07385418101848620354, \
      0.20173860684767988549, \
      0.20173860684767988549, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.00281574262923683970, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.68750485588303955620, \
      0.15483970074386180227, \
      0.15483970074386180227, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.00065798250734006806, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.17414371649393212138, \
      0.41259915049936390918, \
      0.41259915049936390918, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.65646103832166713410, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.26575750656271990291, \
      0.03889072755780650925, \
      0.03889072755780650925, \
      0.89554895506269893701, \
      0.89554895506269893701, \
      0.89554895506269893701, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768, \
      0.09324134903525840845, \
      0.00560484795102133768, \
      0.00560484795102133768 ] )

  w = np.array ( [ \
      0.05165089225609746648, \
      0.01346797267166026206, \
      0.01346797267166026206, \
      0.01346797267166026206, \
      0.01346797267166026206, \
      0.02646691924968953488, \
      0.02646691924968953488, \
      0.02646691924968953488, \
      0.02646691924968953488, \
      0.00510704782814352509, \
      0.00510704782814352509, \
      0.00510704782814352509, \
      0.00510704782814352509, \
      0.00510704782814352509, \
      0.00510704782814352509, \
      0.02364999615824559670, \
      0.02364999615824559670, \
      0.02364999615824559670, \
      0.02364999615824559670, \
      0.02364999615824559670, \
      0.02364999615824559670, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.02531736665096821770, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00541626340744792625, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.00815365901205422627, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.01112597175961277732, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560, \
      0.00132567884826423560 ] )

  return a, b, c, d, w

def rule11 ( ):

#*****************************************************************************80
#
## rule11() returns the rule of precision 11.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.29931309239934250632, \
      0.10206072280197252267, \
      0.29931309239934250632, \
      0.29931309239934250632, \
      0.03263284396518179725, \
      0.90210146810445457355, \
      0.03263284396518179725, \
      0.03263284396518179725, \
      0.32579558451531082097, \
      0.17420441548468917903, \
      0.32579558451531082097, \
      0.17420441548468917903, \
      0.32579558451531082097, \
      0.17420441548468917903, \
      0.09878462414162506033, \
      0.40121537585837491191, \
      0.09878462414162506033, \
      0.40121537585837491191, \
      0.09878462414162506033, \
      0.40121537585837491191, \
      0.00570190512270035092, \
      0.49429809487729964301, \
      0.00570190512270035092, \
      0.49429809487729964301, \
      0.00570190512270035092, \
      0.49429809487729964301, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.11242856050676119928, \
      0.53514200093145947168 ] )

  b = np.array ( [ \
      0.29931309239934250632, \
      0.29931309239934250632, \
      0.10206072280197252267, \
      0.29931309239934250632, \
      0.03263284396518179725, \
      0.03263284396518179725, \
      0.90210146810445457355, \
      0.03263284396518179725, \
      0.17420441548468917903, \
      0.32579558451531082097, \
      0.32579558451531082097, \
      0.17420441548468917903, \
      0.17420441548468917903, \
      0.32579558451531082097, \
      0.40121537585837491191, \
      0.09878462414162506033, \
      0.09878462414162506033, \
      0.40121537585837491191, \
      0.40121537585837491191, \
      0.09878462414162506033, \
      0.49429809487729964301, \
      0.00570190512270035092, \
      0.00570190512270035092, \
      0.49429809487729964301, \
      0.49429809487729964301, \
      0.00570190512270035092, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.01097757236596030687, \
      0.01097757236596030687 ] )

  c = np.array ( [ \
      0.29931309239934250632, \
      0.29931309239934250632, \
      0.29931309239934250632, \
      0.10206072280197252267, \
      0.03263284396518179725, \
      0.03263284396518179725, \
      0.03263284396518179725, \
      0.90210146810445457355, \
      0.17420441548468917903, \
      0.17420441548468917903, \
      0.17420441548468917903, \
      0.32579558451531082097, \
      0.32579558451531082097, \
      0.32579558451531082097, \
      0.40121537585837491191, \
      0.40121537585837491191, \
      0.40121537585837491191, \
      0.09878462414162506033, \
      0.09878462414162506033, \
      0.09878462414162506033, \
      0.49429809487729964301, \
      0.49429809487729964301, \
      0.49429809487729964301, \
      0.00570190512270035092, \
      0.00570190512270035092, \
      0.00570190512270035092, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492 ] )

  d = np.array ( [ \
      0.10206072280197252267, \
      0.29931309239934250632, \
      0.29931309239934250632, \
      0.29931309239934250632, \
      0.90210146810445457355, \
      0.03263284396518179725, \
      0.03263284396518179725, \
      0.03263284396518179725, \
      0.32579558451531082097, \
      0.32579558451531082097, \
      0.17420441548468917903, \
      0.32579558451531082097, \
      0.17420441548468917903, \
      0.17420441548468917903, \
      0.09878462414162506033, \
      0.09878462414162506033, \
      0.40121537585837491191, \
      0.09878462414162506033, \
      0.40121537585837491191, \
      0.40121537585837491191, \
      0.00570190512270035092, \
      0.00570190512270035092, \
      0.49429809487729964301, \
      0.00570190512270035092, \
      0.49429809487729964301, \
      0.49429809487729964301, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.02642834370417183887, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.72733034634638349392, \
      0.12312065497472235442, \
      0.12312065497472235442, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.80376418553955530921, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.17022807348926419224, \
      0.01300387048559023713, \
      0.01300387048559023713, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.29586938786703270710, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.61825980978911576624, \
      0.04293540117192574251, \
      0.04293540117192574251, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.09125181905014285999, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.53990011685570160616, \
      0.18442403204707777387, \
      0.18442403204707777387, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.02622586544947517681, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.45543531962195954454, \
      0.25916940746428263065, \
      0.25916940746428263065, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.34145186619581896492, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.01097757236596030687, \
      0.01097757236596030687, \
      0.53514200093145947168, \
      0.11242856050676119928, \
      0.53514200093145947168, \
      0.11242856050676119928 ] )

  w = np.array ( [ \
      0.01468934358613074864, \
      0.01468934358613074864, \
      0.01468934358613074864, \
      0.01468934358613074864, \
      0.00338086953062168103, \
      0.00338086953062168103, \
      0.00338086953062168103, \
      0.00338086953062168103, \
      0.01676676867722562761, \
      0.01676676867722562761, \
      0.01676676867722562761, \
      0.01676676867722562761, \
      0.01676676867722562761, \
      0.01676676867722562761, \
      0.01932364034775850906, \
      0.01932364034775850906, \
      0.01932364034775850906, \
      0.01932364034775850906, \
      0.01932364034775850906, \
      0.01932364034775850906, \
      0.00165325361037579671, \
      0.00165325361037579671, \
      0.00165325361037579671, \
      0.00165325361037579671, \
      0.00165325361037579671, \
      0.00165325361037579671, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00979997124703287439, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00203627849130482569, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.00820761375291671758, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01510498736666349325, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.01274239266610638702, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931, \
      0.00527342705968912931 ] )

  return a, b, c, d, w

def rule12 ( ):

#*****************************************************************************80
#
## rule12() returns the rule of precision 12.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.21356799445330179599, \
      0.35929601664009458428, \
      0.21356799445330179599, \
      0.21356799445330179599, \
      0.08080469951147342678, \
      0.75758590146557969192, \
      0.08080469951147342678, \
      0.08080469951147342678, \
      0.14608946852754853274, \
      0.56173159441735442954, \
      0.14608946852754853274, \
      0.14608946852754853274, \
      0.06406537703779889570, \
      0.43593462296220109042, \
      0.06406537703779889570, \
      0.43593462296220109042, \
      0.06406537703779889570, \
      0.43593462296220109042, \
      0.12761830492460168873, \
      0.37238169507539831127, \
      0.12761830492460168873, \
      0.37238169507539831127, \
      0.12761830492460168873, \
      0.37238169507539831127, \
      0.69403517727214536492, \
      0.01481472606744864938, \
      0.01481472606744864938, \
      0.27633537059295731897, \
      0.27633537059295731897, \
      0.27633537059295731897, \
      0.01481472606744864938, \
      0.69403517727214536492, \
      0.01481472606744864938, \
      0.01481472606744864938, \
      0.69403517727214536492, \
      0.01481472606744864938, \
      0.00057879438757249416, \
      0.04406791967562979917, \
      0.04406791967562979917, \
      0.91128536626116796171, \
      0.91128536626116796171, \
      0.91128536626116796171, \
      0.04406791967562979917, \
      0.00057879438757249416, \
      0.04406791967562979917, \
      0.04406791967562979917, \
      0.00057879438757249416, \
      0.04406791967562979917, \
      0.79278383647296557513, \
      0.02900481455515819401, \
      0.02900481455515819401, \
      0.14920653441671805073, \
      0.14920653441671805073, \
      0.14920653441671805073, \
      0.02900481455515819401, \
      0.79278383647296557513, \
      0.02900481455515819401, \
      0.02900481455515819401, \
      0.79278383647296557513, \
      0.02900481455515819401, \
      0.72173183541857577339, \
      0.13841257880150359405, \
      0.13841257880150359405, \
      0.00144300697841704437, \
      0.00144300697841704437, \
      0.00144300697841704437, \
      0.13841257880150359405, \
      0.72173183541857577339, \
      0.13841257880150359405, \
      0.13841257880150359405, \
      0.72173183541857577339, \
      0.13841257880150359405, \
      0.20026851566617670519, \
      0.20026851566617670519, \
      0.01155183527100142084, \
      0.34222404749372364874, \
      0.01155183527100142084, \
      0.34222404749372364874, \
      0.44595560156909819227, \
      0.44595560156909819227, \
      0.44595560156909819227, \
      0.44595560156909819227, \
      0.44595560156909819227, \
      0.44595560156909819227, \
      0.01155183527100142084, \
      0.34222404749372364874, \
      0.20026851566617670519, \
      0.20026851566617670519, \
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      0.42293328666445362263, \
      0.42293328666445362263, \
      0.42293328666445362263, \
      0.25459204502515403457, \
      0.25459204502515403457, \
      0.07295863195082626096, \
      0.24951603635956606797, \
      0.07295863195082626096, \
      0.24951603635956606797, \
      0.25459204502515403457, \
      0.25459204502515403457, \
      0.07295863195082626096, \
      0.24951603635956606797, \
      0.07295863195082626096, \
      0.24951603635956606797, \
      0.25459204502515403457, \
      0.25459204502515403457, \
      0.07295863195082626096, \
      0.24951603635956606797, \
      0.07295863195082626096, \
      0.24951603635956606797, \
      0.55384977168586801977, \
      0.55384977168586801977, \
      0.55384977168586801977, \
      0.55384977168586801977, \
      0.55384977168586801977, \
      0.55384977168586801977, \
      0.39373386599840531908, \
      0.39373386599840531908, \
      0.05001810761518710180, \
      0.00239825470053956630, \
      0.05001810761518710180, \
      0.00239825470053956630, \
      0.39373386599840531908, \
      0.39373386599840531908, \
      0.05001810761518710180, \
      0.00239825470053956630, \
      0.05001810761518710180, \
      0.00239825470053956630, \
      0.39373386599840531908, \
      0.39373386599840531908, \
      0.05001810761518710180, \
      0.00239825470053956630, \
      0.05001810761518710180, \
      0.00239825470053956630, \
      0.59854862905440209264, \
      0.59854862905440209264, \
      0.59854862905440209264, \
      0.59854862905440209264, \
      0.59854862905440209264, \
      0.59854862905440209264, \
      0.03608735666657864050, \
      0.03608735666657864050, \
      0.25183678242711160511, \
      0.11352723185190768951, \
      0.25183678242711160511, \
      0.11352723185190768951, \
      0.03608735666657864050, \
      0.03608735666657864050, \
      0.25183678242711160511, \
      0.11352723185190768951, \
      0.25183678242711160511, \
      0.11352723185190768951, \
      0.03608735666657864050, \
      0.03608735666657864050, \
      0.25183678242711160511, \
      0.11352723185190768951, \
      0.25183678242711160511, \
      0.11352723185190768951 ] )

  w = np.array ( [ \
      0.01761491553503256521, \
      0.01761491553503256521, \
      0.01761491553503256521, \
      0.01761491553503256521, \
      0.00835123593343274628, \
      0.00835123593343274628, \
      0.00835123593343274628, \
      0.00835123593343274628, \
      0.01777571920669439309, \
      0.01777571920669439309, \
      0.01777571920669439309, \
      0.01777571920669439309, \
      0.01016802439757214481, \
      0.01016802439757214481, \
      0.01016802439757214481, \
      0.01016802439757214481, \
      0.01016802439757214481, \
      0.01016802439757214481, \
      0.01574040002395383359, \
      0.01574040002395383359, \
      0.01574040002395383359, \
      0.01574040002395383359, \
      0.01574040002395383359, \
      0.01574040002395383359, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00151128114586428740, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00087265698874856076, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00371288266145752832, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00235831425572737572, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00449084703627170012, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00754961604889951930, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00185051458906769213, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946, \
      0.00978070358195409946 ] )

  return a, b, c, d, w

def rule13 ( ):

#*****************************************************************************80
#
## rule13() returns the rule of precision 13.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      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, \
      0.19675501971928607836, \
      0.03973709246462935052, \
      0.03973709246462935052, \
      0.03973709246462935052, \
      0.19675501971928607836, \
      0.56675286809679847888, \
      0.19675501971928607836, \
      0.19675501971928607836, \
      0.56675286809679847888, \
      0.19675501971928607836, \
      0.06201970724197542612, \
      0.38624986292034968471, \
      0.38624986292034968471, \
      0.16548056691732521140, \
      0.16548056691732521140, \
      0.16548056691732521140, \
      0.38624986292034968471, \
      0.06201970724197542612, \
      0.38624986292034968471, \
      0.38624986292034968471, \
      0.06201970724197542612, \
      0.38624986292034968471, \
      0.10866078208331987620, \
      0.02353551905465277316, \
      0.02353551905465277316, \
      0.84426817980737456359, \
      0.84426817980737456359, \
      0.84426817980737456359, \
      0.02353551905465277316, \
      0.10866078208331987620, \
      0.02353551905465277316, \
      0.02353551905465277316, \
      0.10866078208331987620, \
      0.02353551905465277316, \
      0.54469649770191619353, \
      0.54469649770191619353, \
      0.33621089307477192154, \
      0.00350005986987981903, \
      0.33621089307477192154, \
      0.00350005986987981903, \
      0.11559254935343205029, \
      0.11559254935343205029, \
      0.11559254935343205029, \
      0.11559254935343205029, \
      0.11559254935343205029, \
      0.11559254935343205029, \
      0.33621089307477192154, \
      0.00350005986987981903, \
      0.54469649770191619353, \
      0.54469649770191619353, \
      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, \
      0.27458333024900039021, \
      0.27458333024900039021, \
      0.27458333024900039021, \
      0.27458333024900039021, \
      0.27458333024900039021, \
      0.68598163012351520695, \
      0.01057343468672890079, \
      0.02886160494075550378, \
      0.02886160494075550378, \
      0.01057343468672890079, \
      0.68598163012351520695, \
      0.68598163012351520695, \
      0.01057343468672890079, \
      0.02886160494075550378, \
      0.02886160494075550378, \
      0.01057343468672890079, \
      0.68598163012351520695, \
      0.15458664682738043616, \
      0.15458664682738043616, \
      0.73567724678185975051, \
      0.09870239282167234118, \
      0.73567724678185975051, \
      0.09870239282167234118, \
      0.01103371356908743224, \
      0.01103371356908743224, \
      0.01103371356908743224, \
      0.01103371356908743224, \
      0.01103371356908743224, \
      0.01103371356908743224, \
      0.73567724678185975051, \
      0.09870239282167234118, \
      0.15458664682738043616, \
      0.15458664682738043616, \
      0.09870239282167234118, \
      0.73567724678185975051, \
      0.73567724678185975051, \
      0.09870239282167234118, \
      0.15458664682738043616, \
      0.15458664682738043616, \
      0.09870239282167234118, \
      0.73567724678185975051 ] )

  b = np.array ( [ \
      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, \
      0.27807834595637015429, \
      0.27807834595637015429, \
      0.42737860803490002048, \
      0.27807834595637015429, \
      0.01646470005235971951, \
      0.01646470005235971951, \
      0.01646470005235971951, \
      0.27807834595637015429, \
      0.27807834595637015429, \
      0.42737860803490002048, \
      0.19675501971928607836, \
      0.56675286809679847888, \
      0.19675501971928607836, \
      0.19675501971928607836, \
      0.56675286809679847888, \
      0.19675501971928607836, \
      0.03973709246462935052, \
      0.03973709246462935052, \
      0.03973709246462935052, \
      0.19675501971928607836, \
      0.19675501971928607836, \
      0.56675286809679847888, \
      0.38624986292034968471, \
      0.06201970724197542612, \
      0.38624986292034968471, \
      0.38624986292034968471, \
      0.06201970724197542612, \
      0.38624986292034968471, \
      0.16548056691732521140, \
      0.16548056691732521140, \
      0.16548056691732521140, \
      0.38624986292034968471, \
      0.38624986292034968471, \
      0.06201970724197542612, \
      0.02353551905465277316, \
      0.10866078208331987620, \
      0.02353551905465277316, \
      0.02353551905465277316, \
      0.10866078208331987620, \
      0.02353551905465277316, \
      0.84426817980737456359, \
      0.84426817980737456359, \
      0.84426817980737456359, \
      0.02353551905465277316, \
      0.02353551905465277316, \
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      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00322185277500176316, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00146420674110399047, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816, \
      0.00226835492745013816 ] )

  return a, b, c, d, w

def rule14 ( ):

#*****************************************************************************80
#
## rule14() returns the rule of precision 14.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.32981515178461928706, \
      0.01055454464614207291, \
      0.32981515178461928706, \
      0.32981515178461928706, \
      0.05753828268975920424, \
      0.82738515193072237341, \
      0.05753828268975920424, \
      0.05753828268975920424, \
      0.00585616861378350419, \
      0.98243149415864949869, \
      0.00585616861378350419, \
      0.00585616861378350419, \
      0.16055547584795665239, \
      0.51833357245613009834, \
      0.16055547584795665239, \
      0.16055547584795665239, \
      0.09873964607404908667, \
      0.70378106177785271225, \
      0.09873964607404908667, \
      0.09873964607404908667, \
      0.20805319615972650560, \
      0.37584041152082048320, \
      0.20805319615972650560, \
      0.20805319615972650560, \
      0.00975202881222352394, \
      0.49024797118777646565, \
      0.00975202881222352394, \
      0.49024797118777646565, \
      0.00975202881222352394, \
      0.49024797118777646565, \
      0.39706059988446740228, \
      0.10293940011553258385, \
      0.39706059988446740228, \
      0.10293940011553258385, \
      0.39706059988446740228, \
      0.10293940011553258385, \
      0.46208653653878484224, \
      0.03791346346121513694, \
      0.46208653653878484224, \
      0.03791346346121513694, \
      0.46208653653878484224, \
      0.03791346346121513694, \
      0.18142642381613963143, \
      0.31857357618386039633, \
      0.18142642381613963143, \
      0.31857357618386039633, \
      0.18142642381613963143, \
      0.31857357618386039633, \
      0.41893877883766694747, \
      0.24990921886349984349, \
      0.24990921886349984349, \
      0.08124278343533337943, \
      0.08124278343533337943, \
      0.08124278343533337943, \
      0.24990921886349984349, \
      0.41893877883766694747, \
      0.24990921886349984349, \
      0.24990921886349984349, \
      0.41893877883766694747, \
      0.24990921886349984349, \
      0.56287668024978376735, \
      0.21326337806187573021, \
      0.21326337806187573021, \
      0.01059656362646482081, \
      0.01059656362646482081, \
      0.01059656362646482081, \
      0.21326337806187573021, \
      0.56287668024978376735, \
      0.21326337806187573021, \
      0.21326337806187573021, \
      0.56287668024978376735, \
      0.21326337806187573021, \
      0.89546897271401615370, \
      0.04918128494015905350, \
      0.04918128494015905350, \
      0.00616845740566568986, \
      0.00616845740566568986, \
      0.00616845740566568986, \
      0.04918128494015905350, \
      0.89546897271401615370, \
      0.04918128494015905350, \
      0.04918128494015905350, \
      0.89546897271401615370, \
      0.04918128494015905350, \
      0.02066357892967346510, \
      0.39286261797006011287, \
      0.39286261797006011287, \
      0.19361118513020625365, \
      0.19361118513020625365, \
      0.19361118513020625365, \
      0.39286261797006011287, \
      0.02066357892967346510, \
      0.39286261797006011287, \
      0.39286261797006011287, \
      0.02066357892967346510, \
      0.39286261797006011287, \
      0.12690220240749577885, \
      0.01261760553257071024, \
      0.01261760553257071024, \
      0.84786258652736279373, \
      0.84786258652736279373, \
      0.84786258652736279373, \
      0.01261760553257071024, \
      0.12690220240749577885, \
      0.01261760553257071024, \
      0.01261760553257071024, \
      0.12690220240749577885, \
      0.01261760553257071024, \
      0.06214000311762152978, \
      0.06214000311762152978, \
      0.12161878434869899390, \
      0.57674061745509475063, \
      0.12161878434869899390, \
      0.57674061745509475063, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.12161878434869899390, \
      0.57674061745509475063, \
      0.06214000311762152978, \
      0.06214000311762152978, \
      0.57674061745509475063, \
      0.12161878434869899390, \
      0.12161878434869899390, \
      0.57674061745509475063, \
      0.06214000311762152978, \
      0.06214000311762152978, \
      0.57674061745509475063, \
      0.12161878434869899390, \
      0.55179413211842465170, \
      0.55179413211842465170, \
      0.34890229604702455157, \
      0.01552211922320787148, \
      0.34890229604702455157, \
      0.01552211922320787148, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.34890229604702455157, \
      0.01552211922320787148, \
      0.55179413211842465170, \
      0.55179413211842465170, \
      0.01552211922320787148, \
      0.34890229604702455157, \
      0.34890229604702455157, \
      0.01552211922320787148, \
      0.55179413211842465170, \
      0.55179413211842465170, \
      0.01552211922320787148, \
      0.34890229604702455157, \
      0.01784164064765456428, \
      0.01784164064765456428, \
      0.68223832016828933611, \
      0.01547929731317247183, \
      0.68223832016828933611, \
      0.01547929731317247183, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.68223832016828933611, \
      0.01547929731317247183, \
      0.01784164064765456428, \
      0.01784164064765456428, \
      0.01547929731317247183, \
      0.68223832016828933611, \
      0.68223832016828933611, \
      0.01547929731317247183, \
      0.01784164064765456428, \
      0.01784164064765456428, \
      0.01547929731317247183, \
      0.68223832016828933611, \
      0.16953955070016224482, \
      0.16953955070016224482, \
      0.73399829865858101652, \
      0.01777660277014278187, \
      0.73399829865858101652, \
      0.01777660277014278187, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.73399829865858101652, \
      0.01777660277014278187, \
      0.16953955070016224482, \
      0.16953955070016224482, \
      0.01777660277014278187, \
      0.73399829865858101652, \
      0.73399829865858101652, \
      0.01777660277014278187, \
      0.16953955070016224482, \
      0.16953955070016224482, \
      0.01777660277014278187, \
      0.73399829865858101652 ] )

  b = np.array ( [ \
      0.32981515178461928706, \
      0.32981515178461928706, \
      0.01055454464614207291, \
      0.32981515178461928706, \
      0.05753828268975920424, \
      0.05753828268975920424, \
      0.82738515193072237341, \
      0.05753828268975920424, \
      0.00585616861378350419, \
      0.00585616861378350419, \
      0.98243149415864949869, \
      0.00585616861378350419, \
      0.16055547584795665239, \
      0.16055547584795665239, \
      0.51833357245613009834, \
      0.16055547584795665239, \
      0.09873964607404908667, \
      0.09873964607404908667, \
      0.70378106177785271225, \
      0.09873964607404908667, \
      0.20805319615972650560, \
      0.20805319615972650560, \
      0.37584041152082048320, \
      0.20805319615972650560, \
      0.49024797118777646565, \
      0.00975202881222352394, \
      0.00975202881222352394, \
      0.49024797118777646565, \
      0.49024797118777646565, \
      0.00975202881222352394, \
      0.10293940011553258385, \
      0.39706059988446740228, \
      0.39706059988446740228, \
      0.10293940011553258385, \
      0.10293940011553258385, \
      0.39706059988446740228, \
      0.03791346346121513694, \
      0.46208653653878484224, \
      0.46208653653878484224, \
      0.03791346346121513694, \
      0.03791346346121513694, \
      0.46208653653878484224, \
      0.31857357618386039633, \
      0.18142642381613963143, \
      0.18142642381613963143, \
      0.31857357618386039633, \
      0.31857357618386039633, \
      0.18142642381613963143, \
      0.24990921886349984349, \
      0.41893877883766694747, \
      0.24990921886349984349, \
      0.24990921886349984349, \
      0.41893877883766694747, \
      0.24990921886349984349, \
      0.08124278343533337943, \
      0.08124278343533337943, \
      0.08124278343533337943, \
      0.24990921886349984349, \
      0.24990921886349984349, \
      0.41893877883766694747, \
      0.21326337806187573021, \
      0.56287668024978376735, \
      0.21326337806187573021, \
      0.21326337806187573021, \
      0.56287668024978376735, \
      0.21326337806187573021, \
      0.01059656362646482081, \
      0.01059656362646482081, \
      0.01059656362646482081, \
      0.21326337806187573021, \
      0.21326337806187573021, \
      0.56287668024978376735, \
      0.04918128494015905350, \
      0.89546897271401615370, \
      0.04918128494015905350, \
      0.04918128494015905350, \
      0.89546897271401615370, \
      0.04918128494015905350, \
      0.00616845740566568986, \
      0.00616845740566568986, \
      0.00616845740566568986, \
      0.04918128494015905350, \
      0.04918128494015905350, \
      0.89546897271401615370, \
      0.39286261797006011287, \
      0.02066357892967346510, \
      0.39286261797006011287, \
      0.39286261797006011287, \
      0.02066357892967346510, \
      0.39286261797006011287, \
      0.19361118513020625365, \
      0.19361118513020625365, \
      0.19361118513020625365, \
      0.39286261797006011287, \
      0.39286261797006011287, \
      0.02066357892967346510, \
      0.01261760553257071024, \
      0.12690220240749577885, \
      0.01261760553257071024, \
      0.01261760553257071024, \
      0.12690220240749577885, \
      0.01261760553257071024, \
      0.84786258652736279373, \
      0.84786258652736279373, \
      0.84786258652736279373, \
      0.01261760553257071024, \
      0.01261760553257071024, \
      0.12690220240749577885, \
      0.12161878434869899390, \
      0.57674061745509475063, \
      0.06214000311762152978, \
      0.06214000311762152978, \
      0.57674061745509475063, \
      0.12161878434869899390, \
      0.12161878434869899390, \
      0.57674061745509475063, \
      0.06214000311762152978, \
      0.06214000311762152978, \
      0.57674061745509475063, \
      0.12161878434869899390, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.23950059507858473262, \
      0.57674061745509475063, \
      0.12161878434869899390, \
      0.57674061745509475063, \
      0.12161878434869899390, \
      0.06214000311762152978, \
      0.06214000311762152978, \
      0.34890229604702455157, \
      0.01552211922320787148, \
      0.55179413211842465170, \
      0.55179413211842465170, \
      0.01552211922320787148, \
      0.34890229604702455157, \
      0.34890229604702455157, \
      0.01552211922320787148, \
      0.55179413211842465170, \
      0.55179413211842465170, \
      0.01552211922320787148, \
      0.34890229604702455157, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.08378145261134291311, \
      0.01552211922320787148, \
      0.34890229604702455157, \
      0.01552211922320787148, \
      0.34890229604702455157, \
      0.55179413211842465170, \
      0.55179413211842465170, \
      0.68223832016828933611, \
      0.01547929731317247183, \
      0.01784164064765456428, \
      0.01784164064765456428, \
      0.01547929731317247183, \
      0.68223832016828933611, \
      0.68223832016828933611, \
      0.01547929731317247183, \
      0.01784164064765456428, \
      0.01784164064765456428, \
      0.01547929731317247183, \
      0.68223832016828933611, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.28444074187088363992, \
      0.01547929731317247183, \
      0.68223832016828933611, \
      0.01547929731317247183, \
      0.68223832016828933611, \
      0.01784164064765456428, \
      0.01784164064765456428, \
      0.73399829865858101652, \
      0.01777660277014278187, \
      0.16953955070016224482, \
      0.16953955070016224482, \
      0.01777660277014278187, \
      0.73399829865858101652, \
      0.73399829865858101652, \
      0.01777660277014278187, \
      0.16953955070016224482, \
      0.16953955070016224482, \
      0.01777660277014278187, \
      0.73399829865858101652, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.07868554787111389781, \
      0.01777660277014278187, \
      0.73399829865858101652, \
      0.01777660277014278187, \
      0.73399829865858101652, \
      0.16953955070016224482, \
      0.16953955070016224482 ] )

  c = np.array ( [ \
      0.32981515178461928706, \
      0.32981515178461928706, \
      0.32981515178461928706, \
      0.01055454464614207291, \
      0.05753828268975920424, \
      0.05753828268975920424, \
      0.05753828268975920424, \
      0.82738515193072237341, \
      0.00585616861378350419, \
      0.00585616861378350419, \
      0.00585616861378350419, \
      0.98243149415864949869, \
      0.16055547584795665239, \
      0.16055547584795665239, \
      0.16055547584795665239, \
      0.51833357245613009834, \
      0.09873964607404908667, \
      0.09873964607404908667, \
      0.09873964607404908667, \
      0.70378106177785271225, \
      0.20805319615972650560, \
      0.20805319615972650560, \
      0.20805319615972650560, \
      0.37584041152082048320, \
      0.49024797118777646565, \
      0.49024797118777646565, \
      0.49024797118777646565, \
      0.00975202881222352394, \
      0.00975202881222352394, \
      0.00975202881222352394, \
      0.10293940011553258385, \
      0.10293940011553258385, \
      0.10293940011553258385, \
      0.39706059988446740228, \
      0.39706059988446740228, \
      0.39706059988446740228, \
      0.03791346346121513694, \
      0.03791346346121513694, \
      0.03791346346121513694, \
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      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00097575276415068943, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178, \
      0.00375793629976672178 ] )

  return a, b, c, d, w

def rule15 ( ):

#*****************************************************************************80
#
## rule15() returns the rule of precision 15.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.01692642158547220249, \
      0.94922073524358341334, \
      0.01692642158547220249, \
      0.01692642158547220249, \
      0.28367792545957221106, \
      0.14896622362128333905, \
      0.28367792545957221106, \
      0.28367792545957221106, \
      0.18219841399758585077, \
      0.45340475800724244770, \
      0.18219841399758585077, \
      0.18219841399758585077, \
      0.48549199484781541125, \
      0.01450800515218459395, \
      0.48549199484781541125, \
      0.01450800515218459395, \
      0.48549199484781541125, \
      0.01450800515218459395, \
      0.35725585623414363168, \
      0.14274414376585639608, \
      0.35725585623414363168, \
      0.14274414376585639608, \
      0.35725585623414363168, \
      0.14274414376585639608, \
      0.77663574937330037695, \
      0.07321727256195353917, \
      0.07321727256195353917, \
      0.07692970550279260022, \
      0.07692970550279260022, \
      0.07692970550279260022, \
      0.07321727256195353917, \
      0.77663574937330037695, \
      0.07321727256195353917, \
      0.07321727256195353917, \
      0.77663574937330037695, \
      0.07321727256195353917, \
      0.22256065549243442270, \
      0.01056558410489698979, \
      0.01056558410489698979, \
      0.75630817629777158384, \
      0.75630817629777158384, \
      0.75630817629777158384, \
      0.01056558410489698979, \
      0.22256065549243442270, \
      0.01056558410489698979, \
      0.01056558410489698979, \
      0.22256065549243442270, \
      0.01056558410489698979, \
      0.05575022240565973008, \
      0.26379726266881464714, \
      0.26379726266881464714, \
      0.41665525225671096177, \
      0.41665525225671096177, \
      0.41665525225671096177, \
      0.26379726266881464714, \
      0.05575022240565973008, \
      0.26379726266881464714, \
      0.26379726266881464714, \
      0.05575022240565973008, \
      0.26379726266881464714, \
      0.11129092670553288047, \
      0.43549027029938169875, \
      0.43549027029938169875, \
      0.01772853269570365958, \
      0.01772853269570365958, \
      0.01772853269570365958, \
      0.43549027029938169875, \
      0.11129092670553288047, \
      0.43549027029938169875, \
      0.43549027029938169875, \
      0.11129092670553288047, \
      0.43549027029938169875, \
      0.54488653229756034424, \
      0.05347259364185193153, \
      0.05347259364185193153, \
      0.34816828041873582045, \
      0.34816828041873582045, \
      0.34816828041873582045, \
      0.05347259364185193153, \
      0.54488653229756034424, \
      0.05347259364185193153, \
      0.05347259364185193153, \
      0.54488653229756034424, \
      0.05347259364185193153, \
      0.76947037794054062854, \
      0.11053089395801002359, \
      0.11053089395801002359, \
      0.00946783414343936938, \
      0.00946783414343936938, \
      0.00946783414343936938, \
      0.11053089395801002359, \
      0.76947037794054062854, \
      0.11053089395801002359, \
      0.11053089395801002359, \
      0.76947037794054062854, \
      0.11053089395801002359, \
      0.60309364407709864508, \
      0.60309364407709864508, \
      0.04104670514991076019, \
      0.35353072635750920627, \
      0.04104670514991076019, \
      0.35353072635750920627, \
      0.00232892441548140190, \
      0.00232892441548140190, \
      0.00232892441548140190, \
      0.00232892441548140190, \
      0.00232892441548140190, \
      0.00232892441548140190, \
      0.04104670514991076019, \
      0.35353072635750920627, \
      0.60309364407709864508, \
      0.60309364407709864508, \
      0.35353072635750920627, \
      0.04104670514991076019, \
      0.04104670514991076019, \
      0.35353072635750920627, \
      0.60309364407709864508, \
      0.60309364407709864508, \
      0.35353072635750920627, \
      0.04104670514991076019, \
      0.02939319332917082403, \
      0.02939319332917082403, \
      0.09201667327695257914, \
      0.01132552826969512351, \
      0.09201667327695257914, \
      0.01132552826969512351, \
      0.86726460512418146465, \
      0.86726460512418146465, \
      0.86726460512418146465, \
      0.86726460512418146465, \
      0.86726460512418146465, \
      0.86726460512418146465, \
      0.09201667327695257914, \
      0.01132552826969512351, \
      0.02939319332917082403, \
      0.02939319332917082403, \
      0.01132552826969512351, \
      0.09201667327695257914, \
      0.09201667327695257914, \
      0.01132552826969512351, \
      0.02939319332917082403, \
      0.02939319332917082403, \
      0.01132552826969512351, \
      0.09201667327695257914, \
      0.70778148731559709095, \
      0.70778148731559709095, \
      0.06822627868000051554, \
      0.20198579644578576464, \
      0.06822627868000051554, \
      0.20198579644578576464, \
      0.02200643755861661846, \
      0.02200643755861661846, \
      0.02200643755861661846, \
      0.02200643755861661846, \
      0.02200643755861661846, \
      0.02200643755861661846, \
      0.06822627868000051554, \
      0.20198579644578576464, \
      0.70778148731559709095, \
      0.70778148731559709095, \
      0.20198579644578576464, \
      0.06822627868000051554, \
      0.06822627868000051554, \
      0.20198579644578576464, \
      0.70778148731559709095, \
      0.70778148731559709095, \
      0.20198579644578576464, \
      0.06822627868000051554, \
      0.12958095976745337419, \
      0.12958095976745337419, \
      0.18900155563861761876, \
      0.61334215480592257919, \
      0.18900155563861761876, \
      0.61334215480592257919, \
      0.06807532978800637236, \
      0.06807532978800637236, \
      0.06807532978800637236, \
      0.06807532978800637236, \
      0.06807532978800637236, \
      0.06807532978800637236, \
      0.18900155563861761876, \
      0.61334215480592257919, \
      0.12958095976745337419, \
      0.12958095976745337419, \
      0.61334215480592257919, \
      0.18900155563861761876, \
      0.18900155563861761876, \
      0.61334215480592257919, \
      0.12958095976745337419, \
      0.12958095976745337419, \
      0.61334215480592257919, \
      0.18900155563861761876, \
      0.46953330036626755861, \
      0.46953330036626755861, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.07251484323369149221, \
      0.07251484323369149221, \
      0.07251484323369149221, \
      0.07251484323369149221, \
      0.07251484323369149221, \
      0.07251484323369149221, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.46953330036626755861, \
      0.46953330036626755861, \
      0.15247189000943978110, \
      0.30547996639060115420, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.46953330036626755861, \
      0.46953330036626755861, \
      0.15247189000943978110, \
      0.30547996639060115420, \
      0.57783462614827529880, \
      0.57783462614827529880, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.57783462614827529880, \
      0.57783462614827529880, \
      0.26012308345640794416, \
      0.15091455008251053460, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.57783462614827529880, \
      0.57783462614827529880, \
      0.26012308345640794416, \
      0.15091455008251053460, \
      0.01082194753682293349, \
      0.01082194753682293349, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.01082194753682293349, \
      0.01082194753682293349, \
      0.23472603374410913601, \
      0.33684506585476453600, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.01082194753682293349, \
      0.01082194753682293349, \
      0.23472603374410913601, \
      0.33684506585476453600 ] )

  b = np.array ( [ \
      0.01692642158547220249, \
      0.01692642158547220249, \
      0.94922073524358341334, \
      0.01692642158547220249, \
      0.28367792545957221106, \
      0.28367792545957221106, \
      0.14896622362128333905, \
      0.28367792545957221106, \
      0.18219841399758585077, \
      0.18219841399758585077, \
      0.45340475800724244770, \
      0.18219841399758585077, \
      0.01450800515218459395, \
      0.48549199484781541125, \
      0.48549199484781541125, \
      0.01450800515218459395, \
      0.01450800515218459395, \
      0.48549199484781541125, \
      0.14274414376585639608, \
      0.35725585623414363168, \
      0.35725585623414363168, \
      0.14274414376585639608, \
      0.14274414376585639608, \
      0.35725585623414363168, \
      0.07321727256195353917, \
      0.77663574937330037695, \
      0.07321727256195353917, \
      0.07321727256195353917, \
      0.77663574937330037695, \
      0.07321727256195353917, \
      0.07692970550279260022, \
      0.07692970550279260022, \
      0.07692970550279260022, \
      0.07321727256195353917, \
      0.07321727256195353917, \
      0.77663574937330037695, \
      0.01056558410489698979, \
      0.22256065549243442270, \
      0.01056558410489698979, \
      0.01056558410489698979, \
      0.22256065549243442270, \
      0.01056558410489698979, \
      0.75630817629777158384, \
      0.75630817629777158384, \
      0.75630817629777158384, \
      0.01056558410489698979, \
      0.01056558410489698979, \
      0.22256065549243442270, \
      0.26379726266881464714, \
      0.05575022240565973008, \
      0.26379726266881464714, \
      0.26379726266881464714, \
      0.05575022240565973008, \
      0.26379726266881464714, \
      0.41665525225671096177, \
      0.41665525225671096177, \
      0.41665525225671096177, \
      0.26379726266881464714, \
      0.26379726266881464714, \
      0.05575022240565973008, \
      0.43549027029938169875, \
      0.11129092670553288047, \
      0.43549027029938169875, \
      0.43549027029938169875, \
      0.11129092670553288047, \
      0.43549027029938169875, \
      0.01772853269570365958, \
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      0.43549027029938169875, \
      0.43549027029938169875, \
      0.11129092670553288047, \
      0.05347259364185193153, \
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      0.54488653229756034424, \
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      0.34816828041873582045, \
      0.34816828041873582045, \
      0.34816828041873582045, \
      0.05347259364185193153, \
      0.05347259364185193153, \
      0.54488653229756034424, \
      0.11053089395801002359, \
      0.76947037794054062854, \
      0.11053089395801002359, \
      0.11053089395801002359, \
      0.76947037794054062854, \
      0.11053089395801002359, \
      0.00946783414343936938, \
      0.00946783414343936938, \
      0.00946783414343936938, \
      0.11053089395801002359, \
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      0.76947037794054062854, \
      0.04104670514991076019, \
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      0.04104670514991076019, \
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      0.46953330036626755861, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.46953330036626755861, \
      0.46953330036626755861, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.46953330036626755861, \
      0.46953330036626755861, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.30547996639060115420, \
      0.15247189000943978110, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.01112774031280626234, \
      0.57783462614827529880, \
      0.57783462614827529880, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.57783462614827529880, \
      0.57783462614827529880, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.57783462614827529880, \
      0.57783462614827529880, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.15091455008251053460, \
      0.26012308345640794416, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.41760695286430338236, \
      0.01082194753682293349, \
      0.01082194753682293349, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.01082194753682293349, \
      0.01082194753682293349, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.01082194753682293349, \
      0.01082194753682293349, \
      0.33684506585476453600, \
      0.23472603374410913601, \
      0.33684506585476453600, \
      0.23472603374410913601 ] )

  w = np.array ( [ \
      0.00051120297714549352, \
      0.00051120297714549352, \
      0.00051120297714549352, \
      0.00051120297714549352, \
      0.01620740592022657661, \
      0.01620740592022657661, \
      0.01620740592022657661, \
      0.01620740592022657661, \
      0.01552578602041313621, \
      0.01552578602041313621, \
      0.01552578602041313621, \
      0.01552578602041313621, \
      0.00121901025997542137, \
      0.00121901025997542137, \
      0.00121901025997542137, \
      0.00121901025997542137, \
      0.00121901025997542137, \
      0.00121901025997542137, \
      0.00847286285312591654, \
      0.00847286285312591654, \
      0.00847286285312591654, \
      0.00847286285312591654, \
      0.00847286285312591654, \
      0.00847286285312591654, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00179753430540573298, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00081980152207600612, \
      0.00768177527247301210, \
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      0.00768177527247301210, \
      0.00768177527247301210, \
      0.00447985038577478067, \
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      0.00561529860838435452, \
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      0.00176970368579728991, \
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      0.00113113832918702211, \
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      0.00084049934075774871, \
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      0.00508442932752266839, \
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      0.00508442932752266839, \
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      0.00508442932752266839, \
      0.00713938372800399564, \
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      0.00713938372800399564, \
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      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00713938372800399564, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
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      0.00337855056822929448, \
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      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00337855056822929448, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239, \
      0.00220168077770146239 ] )

  return a, b, c, d, w

def rule16 ( ):

#*****************************************************************************80
#
## rule16() returns the rule of precision 16.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.32967147384406064736, \
      0.01098557846781809087, \
      0.32967147384406064736, \
      0.32967147384406064736, \
      0.11204210441737877391, \
      0.66387368674786362277, \
      0.11204210441737877391, \
      0.11204210441737877391, \
      0.28044602591109291101, \
      0.15866192226672123922, \
      0.28044602591109291101, \
      0.28044602591109291101, \
      0.03942164444076165508, \
      0.88173506667771506251, \
      0.03942164444076165508, \
      0.03942164444076165508, \
      0.42508258143523242056, \
      0.07491741856476755168, \
      0.42508258143523242056, \
      0.07491741856476755168, \
      0.42508258143523242056, \
      0.07491741856476755168, \
      0.16430689704436540755, \
      0.33569310295563459245, \
      0.16430689704436540755, \
      0.33569310295563459245, \
      0.16430689704436540755, \
      0.33569310295563459245, \
      0.76468706758018034630, \
      0.04904898759556675092, \
      0.04904898759556675092, \
      0.13721495722868609635, \
      0.13721495722868609635, \
      0.13721495722868609635, \
      0.04904898759556675092, \
      0.76468706758018034630, \
      0.04904898759556675092, \
      0.04904898759556675092, \
      0.76468706758018034630, \
      0.04904898759556675092, \
      0.23282680458942511814, \
      0.01412609568309253390, \
      0.01412609568309253390, \
      0.73892100404438987304, \
      0.73892100404438987304, \
      0.73892100404438987304, \
      0.01412609568309253390, \
      0.23282680458942511814, \
      0.01412609568309253390, \
      0.01412609568309253390, \
      0.23282680458942511814, \
      0.01412609568309253390, \
      0.28324176830779468350, \
      0.06239652058154325498, \
      0.06239652058154325498, \
      0.59196519052911877878, \
      0.59196519052911877878, \
      0.59196519052911877878, \
      0.06239652058154325498, \
      0.28324176830779468350, \
      0.06239652058154325498, \
      0.06239652058154325498, \
      0.28324176830779468350, \
      0.06239652058154325498, \
      0.01283187405611824032, \
      0.18909592756965598603, \
      0.18909592756965598603, \
      0.60897627080456984139, \
      0.60897627080456984139, \
      0.60897627080456984139, \
      0.18909592756965598603, \
      0.01283187405611824032, \
      0.18909592756965598603, \
      0.18909592756965598603, \
      0.01283187405611824032, \
      0.18909592756965598603, \
      0.38727096031949032051, \
      0.27501760012954440393, \
      0.27501760012954440393, \
      0.06269383942142089938, \
      0.06269383942142089938, \
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      0.27501760012954440393, \
      0.38727096031949032051, \
      0.27501760012954440393, \
      0.27501760012954440393, \
      0.38727096031949032051, \
      0.27501760012954440393, \
      0.03723805935523542138, \
      0.00594489825256994554, \
      0.00594489825256994554, \
      0.95087214413962473092, \
      0.95087214413962473092, \
      0.95087214413962473092, \
      0.00594489825256994554, \
      0.03723805935523542138, \
      0.00594489825256994554, \
      0.00594489825256994554, \
      0.03723805935523542138, \
      0.00594489825256994554, \
      0.74829410783088590176, \
      0.11830580710999444305, \
      0.11830580710999444305, \
      0.01509427794912522776, \
      0.01509427794912522776, \
      0.01509427794912522776, \
      0.11830580710999444305, \
      0.74829410783088590176, \
      0.11830580710999444305, \
      0.11830580710999444305, \
      0.74829410783088590176, \
      0.11830580710999444305, \
      0.51463578878883953216, \
      0.51463578878883953216, \
      0.08011846127872501722, \
      0.01444363851364341769, \
      0.08011846127872501722, \
      0.01444363851364341769, \
      0.39080211141879206416, \
      0.39080211141879206416, \
      0.39080211141879206416, \
      0.39080211141879206416, \
      0.39080211141879206416, \
      0.39080211141879206416, \
      0.08011846127872501722, \
      0.01444363851364341769, \
      0.51463578878883953216, \
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      0.01444363851364341769, \
      0.08011846127872501722, \
      0.08011846127872501722, \
      0.01444363851364341769, \
      0.51463578878883953216, \
      0.51463578878883953216, \
      0.01444363851364341769, \
      0.08011846127872501722, \
      0.16457394683790985135, \
      0.16457394683790985135, \
      0.31025854986272727309, \
      0.45521657006972920945, \
      0.31025854986272727309, \
      0.45521657006972920945, \
      0.06995093322963369387, \
      0.06995093322963369387, \
      0.06995093322963369387, \
      0.06995093322963369387, \
      0.06995093322963369387, \
      0.06995093322963369387, \
      0.31025854986272727309, \
      0.45521657006972920945, \
      0.16457394683790985135, \
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      0.45521657006972920945, \
      0.31025854986272727309, \
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      0.45521657006972920945, \
      0.16457394683790985135, \
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      0.45521657006972920945, \
      0.31025854986272727309, \
      0.03435867950145695543, \
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      0.10852408019289846997, \
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      0.85571569922057522106, \
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      0.10852408019289846997, \
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      0.00140154108506938347, \
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      0.00392928947333557113 ] )

  return a, b, c, d, w

def rule17 ( ):

#*****************************************************************************80
#
## rule17() returns the rule of precision 17.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.10925941103913998365, \
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      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569, \
      0.00572288840189160569 ] )

  return a, b, c, d, w

def rule18 ( ):

#*****************************************************************************80
#
## rule18() returns the rule of precision 18.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.20637218186812095189, \
      0.38088345439563714434, \
      0.20637218186812095189, \
      0.20637218186812095189, \
      0.16253879451764061126, \
      0.51238361644707808296, \
      0.16253879451764061126, \
      0.16253879451764061126, \
      0.31162667282556427706, \
      0.06511998152330712719, \
      0.31162667282556427706, \
      0.31162667282556427706, \
      0.33072791608903129301, \
      0.00781625173290610535, \
      0.33072791608903129301, \
      0.33072791608903129301, \
      0.03374408201299505805, \
      0.89876775396101482585, \
      0.03374408201299505805, \
      0.03374408201299505805, \
      0.06568138278425954268, \
      0.80295585164722138583, \
      0.06568138278425954268, \
      0.06568138278425954268, \
      0.01169072420259710532, \
      0.96492782739220872568, \
      0.01169072420259710532, \
      0.01169072420259710532, \
      0.19482708587852060056, \
      0.30517291412147939944, \
      0.19482708587852060056, \
      0.30517291412147939944, \
      0.19482708587852060056, \
      0.30517291412147939944, \
      0.25018283465846002933, \
      0.24981716534153994291, \
      0.25018283465846002933, \
      0.24981716534153994291, \
      0.25018283465846002933, \
      0.24981716534153994291, \
      0.48663347708394377733, \
      0.01336652291605620185, \
      0.48663347708394377733, \
      0.01336652291605620185, \
      0.48663347708394377733, \
      0.01336652291605620185, \
      0.24965765642411447134, \
      0.25034234357588552866, \
      0.24965765642411447134, \
      0.25034234357588552866, \
      0.24965765642411447134, \
      0.25034234357588552866, \
      0.16754822774571606625, \
      0.33245177225428396151, \
      0.16754822774571606625, \
      0.33245177225428396151, \
      0.16754822774571606625, \
      0.33245177225428396151, \
      0.16710640252945341278, \
      0.33289359747054658722, \
      0.16710640252945341278, \
      0.33289359747054658722, \
      0.16710640252945341278, \
      0.33289359747054658722, \
      0.39461100170587065650, \
      0.10538899829412931575, \
      0.39461100170587065650, \
      0.10538899829412931575, \
      0.39461100170587065650, \
      0.10538899829412931575, \
      0.45682278058633507545, \
      0.04317721941366493843, \
      0.45682278058633507545, \
      0.04317721941366493843, \
      0.45682278058633507545, \
      0.04317721941366493843, \
      0.13527540213032007710, \
      0.03310306761504428624, \
      0.03310306761504428624, \
      0.79851846263959136429, \
      0.79851846263959136429, \
      0.79851846263959136429, \
      0.03310306761504428624, \
      0.13527540213032007710, \
      0.03310306761504428624, \
      0.03310306761504428624, \
      0.13527540213032007710, \
      0.03310306761504428624, \
      0.00117187904704725305, \
      0.19461857844676747065, \
      0.19461857844676747065, \
      0.60959096405941781693, \
      0.60959096405941781693, \
      0.60959096405941781693, \
      0.19461857844676747065, \
      0.00117187904704725305, \
      0.19461857844676747065, \
      0.19461857844676747065, \
      0.00117187904704725305, \
      0.19461857844676747065, \
      0.32789600981495031773, \
      0.01321252126131118240, \
      0.01321252126131118240, \
      0.64567894766242728277, \
      0.64567894766242728277, \
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      0.01321252126131118240, \
      0.32789600981495031773, \
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      0.01321252126131118240, \
      0.32789600981495031773, \
      0.01321252126131118240, \
      0.02028399843152169785, \
      0.12293207217705982848, \
      0.12293207217705982848, \
      0.73385185721435863826, \
      0.73385185721435863826, \
      0.73385185721435863826, \
      0.12293207217705982848, \
      0.02028399843152169785, \
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      0.02028399843152169785, \
      0.12293207217705982848, \
      0.34989612196236530295, \
      0.06199506095168379888, \
      0.06199506095168379888, \
      0.52611375613426714093, \
      0.52611375613426714093, \
      0.52611375613426714093, \
      0.06199506095168379888, \
      0.34989612196236530295, \
      0.06199506095168379888, \
      0.06199506095168379888, \
      0.34989612196236530295, \
      0.06199506095168379888, \
      0.16668307969529239099, \
      0.08407187546991698457, \
      0.08407187546991698457, \
      0.66517316936487369539, \
      0.66517316936487369539, \
      0.66517316936487369539, \
      0.08407187546991698457, \
      0.16668307969529239099, \
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      0.08407187546991698457, \
      0.16668307969529239099, \
      0.08407187546991698457, \
      0.18591795912287514825, \
      0.00786704887445389099, \
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      0.79834794312821710793, \
      0.79834794312821710793, \
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      0.00786704887445389099, \
      0.18591795912287514825, \
      0.00786704887445389099, \
      0.00786704887445389099, \
      0.18591795912287514825, \
      0.00786704887445389099, \
      0.24827074115031172452, \
      0.04217582498871236263, \
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      0.66737760887226360573, \
      0.66737760887226360573, \
      0.66737760887226360573, \
      0.04217582498871236263, \
      0.24827074115031172452, \
      0.04217582498871236263, \
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      0.24827074115031172452, \
      0.04217582498871236263, \
      0.06698102226768763712, \
      0.00868349187213884009, \
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      0.91565199398803465147, \
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      0.00868349187213884009, \
      0.06698102226768763712, \
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      0.06698102226768763712, \
      0.00868349187213884009, \
      0.29184170779811624552, \
      0.11111853675762081717, \
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      0.48592121868664212014, \
      0.48592121868664212014, \
      0.48592121868664212014, \
      0.11111853675762081717, \
      0.29184170779811624552, \
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      0.29184170779811624552, \
      0.11111853675762081717, \
      0.06377078964518405335, \
      0.06377078964518405335, \
      0.00368546384560602220, \
      0.71634546470767967996, \
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      0.71634546470767967996, \
      0.21619828180153019548, \
      0.21619828180153019548, \
      0.21619828180153019548, \
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      0.21619828180153019548, \
      0.00368546384560602220, \
      0.71634546470767967996, \
      0.06377078964518405335, \
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      0.71634546470767967996, \
      0.00368546384560602220, \
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      0.71634546470767967996, \
      0.06377078964518405335, \
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      0.71634546470767967996, \
      0.00368546384560602220, \
      0.00402409810322379782, \
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      0.85583991442254980786, \
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      0.85583991442254980786, \
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      0.09147563979493070208, \
      0.85583991442254980786, \
      0.00402409810322379782, \
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      0.85583991442254980786, \
      0.00402409810322379782, \
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      0.85583991442254980786, \
      0.09147563979493070208, \
      0.41687745973852602388, \
      0.41687745973852602388, \
      0.13265637401840363330, \
      0.42232296038012673289, \
      0.13265637401840363330, \
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      0.13265637401840363330, \
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      0.13265637401840363330, \
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      0.42232296038012673289, \
      0.41687745973852602388, \
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      0.42232296038012673289, \
      0.13265637401840363330, \
      0.24643302248016774048, \
      0.24643302248016774048, \
      0.44391986692788093505, \
      0.28045267653575517430, \
      0.44391986692788093505, \
      0.28045267653575517430, \
      0.02919443405619611201, \
      0.02919443405619611201, \
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      0.02919443405619611201, \
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      0.44391986692788093505, \
      0.28045267653575517430, \
      0.24643302248016774048, \
      0.24643302248016774048, \
      0.28045267653575517430, \
      0.44391986692788093505, \
      0.44391986692788093505, \
      0.28045267653575517430, \
      0.24643302248016774048, \
      0.24643302248016774048, \
      0.28045267653575517430, \
      0.44391986692788093505, \
      0.12712074880700960366, \
      0.12712074880700960366, \
      0.23954508858951903405, \
      0.38757671289171524709, \
      0.23954508858951903405, \
      0.38757671289171524709, \
      0.24575744971175611520, \
      0.24575744971175611520, \
      0.24575744971175611520, \
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      0.24575744971175611520, \
      0.24575744971175611520, \
      0.23954508858951903405, \
      0.38757671289171524709, \
      0.12712074880700960366, \
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      0.38757671289171524709, \
      0.23954508858951903405, \
      0.23954508858951903405, \
      0.38757671289171524709, \
      0.12712074880700960366, \
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      0.23954508858951903405, \
      0.21370490618618503964, \
      0.21370490618618503964, \
      0.16571308871687792652, \
      0.55034235855999624754, \
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      0.55034235855999624754, \
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      0.16571308871687792652, \
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      0.17887766860263659696, \
      0.42547639224809885583, \
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      0.17887766860263659696, \
      0.42547639224809885583, \
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      0.00784628836168125426, \
      0.37522676082048844748, \
      0.54587730091263853005, \
      0.12935575346620128978, \
      0.12935575346620128978, \
      0.02510439859007851382, \
      0.59255160790628813583, \
      0.02510439859007851382, \
      0.59255160790628813583, \
      0.25298824003743208833, \
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      0.25298824003743208833, \
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      0.02510439859007851382, \
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      0.59255160790628813583, \
      0.02510439859007851382, \
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      0.12935575346620128978, \
      0.12935575346620128978, \
      0.59255160790628813583, \
      0.02510439859007851382 ] )

  b = np.array ( [ \
      0.20637218186812095189, \
      0.20637218186812095189, \
      0.38088345439563714434, \
      0.20637218186812095189, \
      0.16253879451764061126, \
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      0.51238361644707808296, \
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      0.31162667282556427706, \
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      0.06511998152330712719, \
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      0.33072791608903129301, \
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      0.00781625173290610535, \
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      0.03374408201299505805, \
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      0.89876775396101482585, \
      0.03374408201299505805, \
      0.06568138278425954268, \
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      0.01169072420259710532, \
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      0.96492782739220872568, \
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      0.30517291412147939944, \
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      0.24981716534153994291, \
      0.25018283465846002933, \
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      0.01336652291605620185, \
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      0.24965765642411447134, \
      0.33245177225428396151, \
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      0.00362877511769905915, \
      0.00362877511769905915, \
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      0.00362877511769905915, \
      0.00362877511769905915, \
      0.00362877511769905915, \
      0.00362877511769905915 ] )

  return a, b, c, d, w

def rule19 ( ):

#*****************************************************************************80
#
## rule19() returns the rule of precision 19.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.25000000000000000000, \
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      0.71129959617489657564, \
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      0.00174479123876261502 ] )

  return a, b, c, d, w

def rule20 ( ):

#*****************************************************************************80
#
## rule20() returns the rule of precision 20.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    13 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.
#
  import numpy as np

  a = np.array ( [ \
      0.29677595969341313831, \
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      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00336359299264356619, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545, \
      0.00113881952395300545 ] )

  return a, b, c, d, w
def tetrahedron_jaskowiec_rule ( p ):

#*****************************************************************************80
#
## tetrahedron_jaskowiec_rule() returns a tetrahedron quadrature rule of given precision.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    07 May 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.
#
#  Input:
#
#    integer p: the precision, 0 <= p <= 20.
#
#  Output:
#
#    integer n: the order of the rule.
#
#    real a(n), b(n), c(n), d(n): the barycentric coordinates of quadrature points.
#
#    real w(n): the quadrature weights.
#
  if ( p < 0 ): 
    raise Exception ( 'tetrahedron_jaskowiec_rule(): Input p < 0.' )

  if ( 20 < p ):
    raise Exception ( 'tetrahedron_jaskowiec_rule(): Input 20 < p.' )

  n = rule_order ( p )

  if ( p == 0 ):
    a, b, c, d, w = rule00 ( )
  elif ( p == 1 ):
    a, b, c, d, w = rule01 ( )
  elif ( p == 2 ):
    a, b, c, d, w = rule02 ( )
  elif ( p == 3 ):
    a, b, c, d, w = rule03 ( )
  elif ( p == 4 ):
    a, b, c, d, w = rule04 ( )
  elif ( p == 5 ):
    a, b, c, d, w = rule05 ( )
  elif ( p == 6 ):
    a, b, c, d, w = rule06 ( )
  elif ( p == 7 ):
    a, b, c, d, w = rule07 ( )
  elif ( p == 8 ):
    a, b, c, d, w = rule08 ( )
  elif ( p == 9 ):
    a, b, c, d, w = rule09 ( )
  elif ( p == 10 ):
    a, b, c, d, w = rule10 ( )
  elif ( p == 11 ):
    a, b, c, d, w = rule11 ( )
  elif ( p == 12 ):
    a, b, c, d, w = rule12 ( )
  elif ( p == 13 ):
    a, b, c, d, w = rule13 ( )
  elif ( p == 14 ):
    a, b, c, d, w = rule14 ( )
  elif ( p == 15 ):
    a, b, c, d, w = rule15 ( )
  elif ( p == 16 ):
    a, b, c, d, w = rule16 ( )
  elif ( p == 17 ):
    a, b, c, d, w = rule17 ( )
  elif ( p == 18 ):
    a, b, c, d, w = rule18 ( )
  elif ( p == 19 ):
    a, b, c, d, w = rule19 ( )
  elif ( p == 20 ):
    a, b, c, d, w = rule20 ( )

  return n, a, b, c, d, w

def tetrahedron_unit_monomial_integral ( e ):

#*****************************************************************************80
#
## tetrahedron_unit_monomial_integral(): integrals in the unit tetrahedron.
#
#  Discussion:
#
#    The monomial is F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3).
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    23 May 2023
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    integer E(3), the exponents.  
#    Each exponent must be nonnegative.
#
#  Output:
#
#    real integral, the integral.
#
  m = 3

  for i in range ( 0, m ):
    if ( e[i] < 0 ):
      print ( '' )
      print ( 'tetrahedron_unit_monomial_integral(): Fatal error!' )
      print ( '  All exponents must be nonnegative.' )
      raise Exception ( 'tetrahedron01_monomial_integral(): Fatal error!' )

  k = 0
  integral = 1.0

  for i in range ( 0, m ):

    for j in range ( 1, e[i] + 1 ):
      k = k + 1
      integral = integral * float ( j ) / float ( k )

  for i in range ( 0, m ):
    k = k + 1
    integral = integral / float ( k )

  return integral

def tetrahedron_unit_volume ( ):

#*****************************************************************************80
#
## tetrahedron_unit_volume() computes the volume of a unit tetrahedron.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    23 May 2023
#
#  Author:
#
#    John Burkardt
#
#  Output:
#
#    real volume: the volume of the unit tetrahedron.
#
  volume = 1.0 / 6.0

  return volume

def tetrahedron_volume ( tetra ):

#*****************************************************************************80
#
## tetrahedron_volume() computes the volume of a tetrahedron.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    20 July 2018
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real tetra(4,3): the vertices of the tetrahedron.
#
#  Output:
#
#    real volume: the volume of the tetrahedron.
#
  import numpy as np

  a = np.zeros ( [ 4, 4 ] )
  a[0:4,0:3] = tetra[0:4,0:3]
  a[0:4,3] = 1.0

  volume = np.abs ( np.linalg.det ( a ) ) / 6.0

  return volume

def timestamp ( ):

#*****************************************************************************80
#
## timestamp() prints the date as a timestamp.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    21 August 2019
#
#  Author:
#
#    John Burkardt
#
  import time

  t = time.time ( )
  print ( time.ctime ( t ) )

  return

if ( __name__ == '__main__' ):
  timestamp ( )
  tetrahedron_jaskowiec_rule_test ( )
  timestamp ( )