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

  from sympy import Matrix
  from sympy import pprint
  from sympy import symbols

  print ( '' )
  print ( 'jacobian_example():' )
  print ( '  Compute the jacobian matrix for f(x,y,z).' )
  print ( '' )

  x = symbols ( 'x' )
  y = symbols ( 'y' )
  z = symbols ( 'z' )
#
#  f(x,y,z) is a vector of two rows and one column.
#
  f = Matrix ( [
    [ x - y**3 + 5 * y**2 -  2 * y - 13 + 3 * ( z - 1 ) ],
    [ x + y**3 +     y**2 - 14 * y - 29 -31 * ( z - 1 ) ] ] )
#
#  The Jacobian J is a matrix of two rows and three columns.
#
  J = f.jacobian ( [ x, y, z ] )

  pprint ( J )

  return

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