#! /usr/bin/env python
#
def pythag_triple_next ( i, j ):

#*****************************************************************************80
#
## PYTHAG_TRIPLE_NEXT computes the next Pythagorean triple.
#
#  Example:
#
#     I       J       A       B       C    A^2+B^2 = C^2
#
#     2       1       3       4       5      25
#     3       2       5      12      13     169
#     4       1      15       8      17     289
#     4       3       7      24      25     625
#     5       2      21      20      29     841
#     5       4       9      40      41    1681
#     6       1      35      12      37    1369
#     6       3      27      36      45    2025
#     6       5      11      60      61    3721
#     7       2      45      28      53    2809
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 May 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer I, J, the generators.
#    On first call, set I = J = 0.  On repeated calls, set I and J
#    to the output values of I and J from the previous call.
#
#    Output, integer A, B, C, the next Pythagorean triple.
#    A, B, and C are positive integers which have no common factors,
#    and A**2 + B**2 = C**2.
#
#    Output, integer I, J, the updated values of the generators,
#    which should be used as the input values of I and J if the routine
#    is to be called again.
#

#
#  I starts at 2, and when it increases, increases by 1 and resets J;
#
#  When I is reset, J starts out at 2 if I is odd, or 1 if I is even;
#  Then I is held fixed and J increases by 2, as long as it remains less than I.
#
  if ( i == 0 and j == 0 ):
    i = 2
    j = 1
  elif ( j + 2 < i ):
    j = j + 2
  else:
    i = i + 1
    j = ( i % 2 ) + 1

  a = i ** 2 - j ** 2
  b = 2 * i * j
  c = i ** 2 + j ** 2

  return a, b, c, i, j

def pythag_triple_next_test ( ):

#*****************************************************************************80
#
## PYTHAG_TRIPLE_NEXT_TEST tests PYTHAG_TRIPLE_NEXT
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 May 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'PYTHAG_TRIPLE_NEXT_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  PYTHAG_TRIPLE_NEXT computes the "next"' )
  print ( '    Pythagorean triple.' )
  print ( '' )
  print ( '   I   J   A   B   C  A^2+B^2   C^2' )
  print ( '' )

  i = 0
  j = 0

  for k in range ( 0, 21 ):
    a, b, c, i, j = pythag_triple_next ( i, j )
    d = a ** 2 + b ** 2
    e = c ** 2
    print ( '%4d  %4d  %4d  %4d  %4d  %8d  %8d' % ( i, j, a, b, c, d, e ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'PYTHAG_TRIPLE_NEXT_TEST:' )
  print ( '  Normal end of execution.' )
  return

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