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

  import sympy

  print ( '' )
  print ( 'sympy_derivative():' )
  print ( '  sympy version: ' + sympy.__version__ )
  print ( '  Demonstrate the symbolic computation of derivatives.' )
  print ( '' )

  humps_derivative_test ( )
  xt_derivative_test ( )
  sinc_derivative_test ( )
  sincn_derivative_test ( )

  return

def humps_derivative_test ( ):

  from sympy import diff
  from sympy import symbols

  print ( '' )
  print ( 'humps_derivative_test()' )

  x = symbols ( 'x' )

  humps = 100 / ( ( 10 * x - 3 )**2 + 1 ) \
        + 100 / ( ( 10 * x - 9 )**2 + 4 ) \
        - 6

  dhumpsdx = diff ( humps, x )
  print ( '  d humps /dx = ', dhumpsdx )

  d2humpsdx2 = diff ( humps, x, 2 )
  print ( '  d2 humps /dx2 = ', d2humpsdx2 )

  return

def xt_derivative_test ( ):

  from sympy import diff
  from sympy import exp
  from sympy import symbols

  print ( '' )
  print ( 'xt_derivative_test():' )
  print ( '  z = x * e^(x*t)' )
  x = symbols ( 'x' )
  t = symbols ( 't' )
  z = x * exp ( x * t )
  dzdx = diff ( z, x )
  print ( '  dzdx = ', dzdx )
  dzdt = diff ( z, t )
  print ( '  dzdt = ', dzdt )
  dz2dt2 = diff ( z, t, 2 )
  print ( '  d2zdt2 = ', dz2dt2 )
  dz2dtdx = diff ( z, t, x )
  print ( '  d2zdtdx = ', dz2dtdx )

  return

def sinc_derivative_test ( ):

  from sympy import diff
  from sympy import sin
  from sympy import symbols

  print ( '' )
  print ( 'sinc_derivative_test():' )
  print ( '  sinc(x) = sin(x)/x' )

  x = symbols ( 'x' )

  sinc = sin ( x ) / x

  dsincdx = diff ( sinc, x )
  print ( '  d sinc /dx = ', dsincdx )

  d2sincdx2 = diff ( sinc, x, 2 )
  print ( '  d2 sinc /dx2 = ', d2sincdx2 )

  return

def sincn_derivative_test ( ):

  from sympy import diff
  from sympy import limit
  from sympy import pi
  from sympy import sin
  from sympy import symbols

  print ( '' )
  print ( 'sincn_derivative_test():' )
  print ( '  sincn(x) = sin(pi*x)/pi/x' )

  x = symbols ( 'x' )

  sincn = sin ( pi * x ) / pi / x

  result = limit ( sincn, x, 0 )
  print ( '  limit ( sincn(x), x->0 ', result )

  dsincndx = diff ( sincn, x )
  print ( '  d sincn /dx = ', dsincndx )
  result = limit ( dsincndx, x, 0 )
  print ( '  limit ( dsincndx(x), x->0 ', result )

  d2sincndx2 = diff ( sincn, x, 2 )
  print ( '  d2 sincn /dx2 = ', d2sincndx2 )

  result = limit ( d2sincndx2, x, 0 )
  print ( '  limit ( d2 sincn /dx2, x->0 ', result )

  return

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