#! /usr/bin/env python
#
def mono_between_enum ( m, n1, n2 ):

#*****************************************************************************80
#
## MONO_BETWEEN_ENUM enumerates monomials in M dimensions of degrees in a range.
#
#  Discussion:
#
#    For M = 3, we have the following table:
#
#     N2 0  1  2  3  4  5  6   7   8
#   N1 +----------------------------
#    0 | 1  4 10 20 35 56 84 120 165
#    1 | 0  3  9 19 34 55 83 119 164
#    2 | 0  0  6 16 31 52 80 116 161
#    3 | 0  0  0 10 25 46 74 110 155
#    4 | 0  0  0  0 15 36 64 100 145
#    5 | 0  0  0  0  0 21 49  85 130
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 October 2014
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer M, the spatial dimension.
#
#    Input, integer N1, N2, the minimum and maximum degrees.
#    0 <= N1 <= N2.
#
#    Output, integer VALUE, the number of monomials in M variables,
#    of total degree between N1 and N2 inclusive.
#
  from i4_choose import i4_choose

  n1 = max ( n1, 0 )

  if ( n2 < n1 ):
    value = 0
    return value
 
  if ( n1 == 0 ):
    value = i4_choose ( n2 + m, n2 )
  elif ( n1 == n2 ):
    value = i4_choose ( n2 + m - 1, n2 )
  else:
    n0 = n1 - 1
    value = i4_choose ( n2 + m, n2 ) - i4_choose ( n0 + m, n0 )

  return value

def mono_between_enum_test ( ):

#*****************************************************************************80
#
## MONO_BETWEEN_ENUM_TEST tests MONO_BETWEEN_ENUM.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 October 2014
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'MONO_BETWEEN_ENUM_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  MONO_BETWEEN_ENUM can enumerate the number of monomials' )
  print ( '  in M variables, of total degree between N1 and N2.' )

  m = 3
  print ( '' )
  print ( '  Using spatial dimension M = %d' % ( m ) )
  print ( '' )
  print ( '   N2:', end = '' )
  for n2 in range ( 0, 9 ):
    print ( '  %4d' % ( n2 ), end = '' )
  print ( '' )
  print ( '  N1 +---------------------------------------------------------------' )
  for n1 in range ( 0, 9 ):
    print ( '  %2d |' % ( n1 ), end = '' )
    for n2 in range ( 0, 9 ):
      v = mono_between_enum ( m, n1, n2 )
      print ( '  %4d' % ( v ), end = '' )
    print ( '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'MONO_BETWEEN_ENUM_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  mono_between_enum_test ( )
  timestamp ( )