ó
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    Partial derivative for tensor expressions.

    Examples
    ========

    >>> from sympy.tensor.tensor import TensorIndexType, tensorhead
    >>> from sympy.tensor.toperators import PartialDerivative
    >>> from sympy import symbols
    >>> L = TensorIndexType("L")
    >>> A = tensorhead("A", [L], [[1]])
    >>> i, j = symbols("i j")

    >>> expr = PartialDerivative(A(i), A(j))
    >>> expr
    PartialDerivative(A(i), A(j))

    The ``PartialDerivative`` object behaves like a tensorial expression:

    >>> expr.get_indices()
    [i, j]

    Indices can be contracted:

    >>> PartialDerivative(A(i), A(-i))
    PartialDerivative(A(L_0), A(-L_0))
    c         G   s‡   t  | t ƒ r( | j | } | j } n  t j | g t | ƒ d t ƒ\ } } } } t j	 |  | Œ } | | _
 | | _ | | _ | S(   Nt   replace_indices(   t
   isinstanceR   t	   variablest   exprR   t   _tensMul_contract_indicest   listt   TrueR    t   __new__t   _indicest   _freet   _dum(   t   clsR   R   t   argst   indicest   freet   dumt   obj(    (    s6   lib/python2.7/site-packages/sympy/tensor/toperators.pyR
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 } | | | ƒ } | j ƒ  } | d } d g g  t	 t
 | ƒ ƒ D] }	 t d  ƒ ^ q¼ } x: t |
 ƒ D], \ }	 } |	 | d <| t | ƒ c | :<qâ W| | k rX| j | ƒ } | | d | d f ƒ } | j | ƒ q8 | j | ƒ q8 W| | f S(   Ni   (   t   derive_by_arrayt   tensorcontractioni    (   t   arrayR   R   R   t   _extract_dataR   t   zipt   as_coeff_Mult
   as_mutablet   ranget   lent   slicet   Nonet	   enumeratet   tuplet   indext   popt   append(   R   t   replacement_dictR   R   R   R   t   variablet   var_indicest	   var_arrayt   it   coeff_arrayt   varindext   coeff_indext   coefft   pos(    (    s6   lib/python2.7/site-packages/sympy/tensor/toperators.pyR   H   s$    +
2
(
   t   __name__t
   __module__t   __doc__R
   R   R   t   propertyR   R   R   (    (    (    s6   lib/python2.7/site-packages/sympy/tensor/toperators.pyR      s   				N(   t   sympy.tensor.tensorR    R   R   (    (    (    s6   lib/python2.7/site-packages/sympy/tensor/toperators.pyt   <module>   s   