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

  from sympy import cos
  from sympy import exp
  from sympy import log
  from sympy import pprint
  from sympy import symbols
  from sympy.vector import CoordSys3D
  from sympy.vector import curl
  from sympy.vector import divergence
  import sympy

  print ( '' )
  print ( 'divergence_example():' )
  print ( '  sympy version: ' + sympy.__version__ )
  print ( '  We want the divergence and curl of a vector field.' )
  print ( '  v(x,y,z) = [ f, g, h ].' )
#
#  Name a coordinate system.
#
  C = CoordSys3D ( 'C' )
#
#  Name the components of the coordinate system.
#
  x, y, z = C.x, C.y, C.z
#
#  Define the vector field.
#
  f = x**3 + y**2 + log ( z )
  g = x * y**2 * z
  h = exp ( 2 * z + x )

  v = f * C.i + g * C.j + h * C.k
#
#  Compute the divergence.
#  df/dx + dg/dy + dh/dz
#
  div = divergence ( v )
  print ( '' )
  print ( '  divergence(v)' )
  pprint ( div )
#
#  Compute the curl.
#  dh/dy-dg/dz, df/dz-dh/dx, dg/dx-df/dy
#
  print ( '' )
  print ( '  curl(v)' )
  crl = curl ( v )
  pprint ( crl )

  return

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