#! /usr/bin/env python
#
def rat_normalize ( a, b ):

#*****************************************************************************80
#
## RAT_NORMALIZE normalizes a rational number.
#
#  Discussion:
#
#    If A = B = 0, return.
#
#    If A = 0 (and B nonzero) set B => 1 and return.
#
#    If A nonzero, and B = 0, then A => 1 and return.
#
#    If A = B, then set A => 1, B => 1 and return.
#
#    If B < 0, then A => -A, B => -B.
#
#    If 1 < C = GCD(|A|,|B|), A => A/C, B => B/C.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    03 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer A, B, the rational number.
#
#    Output, integer A, B, the normalized rational number.
#

#
#  Cases where one or both is 0.
#
  from i4_gcd import i4_gcd

  if ( a == 0 and b == 0 ):
    return a, b
  elif ( a == 0 and b != 0 ):
    b = 1
    return a, b
  elif ( a != 0 and b == 0 ):
    a = 1
    return a, b

  if ( a == b ):
    a = 1
    b = 1
    return a, b

  if ( b < 0 ):
    a = -a
    b = -b

  c = i4_gcd ( abs ( a ), abs ( b ) )

  if ( 1 < c ):
    a = a // c
    b = b // c

  return a, b

def rat_normalize_test ( ):

#*****************************************************************************80
#
## RAT_NORMALIZE_TEST tests RAT_NORMALIZE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    03 June 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  print ( '' )
  print ( 'RAT_NORMALIZE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  RAT_NORMALIZE normalizes a rational.' )

  rat_num = 7
  rat_top = np.array ( [ 3, 1,    20,  8, -10,   9, -11 ] )
  rat_bot = np.array ( [ 4, 1000,  1,  4,   7, -15, -11 ] )

  print ( '' )
  print ( '           A           B             A             B' )
  print ( '                                 normalized     normalized' )
  print ( '' )

  for i in range ( 0, rat_num ):
    a1 = rat_top[i]
    b1 = rat_bot[i]
    a2, b2 = rat_normalize ( a1, b1 )
    print ( '  %10d  %10d    %10d  %10d' % ( a1, b1, a2, b2 ) )

  return
#
#  Terminate.
#
  print ( '' )
  print ( 'RAT_NORMALIZE_TEST' )
  print ( '  Normal end of execution.' )
  return

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