subroutine monomial_value ( m, n, e, x, v )

!*****************************************************************************80
!
!! monomial_value() evaluates a monomial.
!
!  Discussion:
!
!    This routine evaluates a monomial of the form
!
!      product ( 1 <= i <= m ) x(i)^e(i)
!
!    where the exponents are nonnegative integers.  Note that
!    if the combination 0^0 is encountered, it should be treated
!    as 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    20 April 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer M, the spatial dimension.
!
!    Input, integer N, the number of points at which the
!    monomial is to be evaluated.
!
!    Input, integer E(M), the exponents.
!
!    Input, real ( kind = rk ) X(M,N), the point coordinates.
!
!    Output, real ( kind = rk ) V(N), the value of the monomial.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer m
  integer n

  integer e(m)
  integer i
  real ( kind = rk ) v(n)
  real ( kind = rk ) x(m,n)

  v(1:n) = 1.0D+00

  do i = 1, m
    if ( 0 /= e(i) ) then
      v(1:n) = v(1:n) * x(i,1:n) ** e(i)
    end if
  end do

  return
end
function triangle01_area ( )

!*****************************************************************************80
!
!! triangle01_area() computes the area of the unit triangle in 2D.
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    12 January 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Output, real ( kind = rk ) TRIANGLE01_AREA, the area.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  real ( kind = rk ) triangle01_area

  triangle01_area = 0.5D+00

  return
end
subroutine triangle01_monomial_integral ( e, integral )

!*****************************************************************************80
!
!! triangle01_monomial_integral(): monomial integrals in the unit triangle in 2D.
!
!  Discussion:
!
!    The monomial is F(X,Y) = X^E(1) * Y^E(2).
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    12 January 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer E(2), the exponents of X and Y in the 
!    monomial.  Each exponent must be nonnegative.
!
!    Output, real ( kind = rk ) INTEGRAL, the integral.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer, parameter :: m = 2

  integer e(m)
  integer i
  real ( kind = rk ) integral
  integer j
  integer k

  if ( any ( e(1:m) < 0 ) ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'TRIANGLE01_MONOMIAL_INTEGRAL - Fatal error!'
    write ( *, '(a)' ) '  All exponents must be nonnegative.'
    stop 1
  end if

  k = 0
  integral = 1.0D+00

  do i = 1, m

    do j = 1, e(i)
      k = k + 1
      integral = integral * real ( j, kind = rk ) / real ( k, kind = rk )
    end do

  end do

  do i = 1, m
    k = k + 1
    integral = integral / real ( k, kind = rk )
  end do

  return
end
subroutine triangle01_sample ( n, x )

!*****************************************************************************80
!
!! triangle01_sample() samples points uniformly from the unit triangle in 2D.
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    12 January 2014
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Reuven Rubinstein,
!    Monte Carlo Optimization, Simulation, and Sensitivity 
!    of Queueing Networks,
!    Krieger, 1992,
!    ISBN: 0894647644,
!    LC: QA298.R79.
!
!  Parameters:
!
!    Input, integer N, the number of points.
!
!    Output, real ( kind = rk ) X(2,N), the points.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer, parameter :: m = 2
  integer n

  real ( kind = rk ) e(m+1)
  real ( kind = rk ) e_sum
  integer j
  real ( kind = rk ) x(m,n)

  do j = 1, n

    call random_number ( harvest = e(1:m+1) )

    e(1:m+1) = - log ( e(1:m+1) )

    e_sum = sum ( e(1:m+1) )

    x(1:m,j) = e(1:m) / e_sum

  end do

  return
end