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

  from sympy import limit
  from sympy import log
  from sympy import oo
  from sympy import sin
  from sympy import symbols

  print ( '' )
  print ( 'sympy_limit():' )
  print ( '  Demonstrate the sympy limit() operations.' )
  print ( '' )

  x = symbols ( 'x' )

  humps = 100 / ( ( 10 * x - 3 )**2 + 1 ) \
        + 100 / ( ( 10 * x - 9 )**2 + 4 ) \
        - 6
#
#  Here, we say "humps", not "humps(x)"...
#
  result = limit ( humps, x, -oo )
  print ( '  limit ( humps ) as x -> -oo = ', result )

  result = limit ( sin ( x ) / x, x, 0 )
  print ( '  limit ( sin ( x ) / x ) as x -> 0 = ', result )

  result = limit ( log ( x ) / x, x, oo )
  print ( '  limit ( log ( x ) / x ) as x -> +oo = ', result )

  n = symbols ( 'n' )
  expr = ( 1 + x / n )**n
  result = limit ( expr, n, oo )
  print ( '  limit ( ( 1 + x/n )**n ) as n -> +oo = ', result )

  return

if ( __name__ == "__main__" ):
  sympy_limit ( )