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eZejeedd ZdS )z+The anti-commutator: ``{A,B} = A*B + B*A``.    )Expr)KindDispatcher)Mul)Integer)S)
prettyForm)Dagger)_OperatorKindOperatorKindAntiCommutatorc                   @   sp   e Zd ZdZdZedddZedd Zdd	 Z	e
d
d Zdd Zdd Zdd Zdd Zdd Zdd ZdS )r   a  The standard anticommutator, in an unevaluated state.

    Explanation
    ===========

    Evaluating an anticommutator is defined [1]_ as: ``{A, B} = A*B + B*A``.
    This class returns the anticommutator in an unevaluated form.  To evaluate
    the anticommutator, use the ``.doit()`` method.

    Canonical ordering of an anticommutator is ``{A, B}`` for ``A < B``. The
    arguments of the anticommutator are put into canonical order using
    ``__cmp__``. If ``B < A``, then ``{A, B}`` is returned as ``{B, A}``.

    Parameters
    ==========

    A : Expr
        The first argument of the anticommutator {A,B}.
    B : Expr
        The second argument of the anticommutator {A,B}.

    Examples
    ========

    >>> from sympy import symbols
    >>> from sympy.physics.quantum import AntiCommutator
    >>> from sympy.physics.quantum import Operator, Dagger
    >>> x, y = symbols('x,y')
    >>> A = Operator('A')
    >>> B = Operator('B')

    Create an anticommutator and use ``doit()`` to multiply them out.

    >>> ac = AntiCommutator(A,B); ac
    {A,B}
    >>> ac.doit()
    A*B + B*A

    The commutator orders it arguments in canonical order:

    >>> ac = AntiCommutator(B,A); ac
    {A,B}

    Commutative constants are factored out:

    >>> AntiCommutator(3*x*A,x*y*B)
    3*x**2*y*{A,B}

    Adjoint operations applied to the anticommutator are properly applied to
    the arguments:

    >>> Dagger(AntiCommutator(A,B))
    {Dagger(A),Dagger(B)}

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Commutator
    FZAntiCommutator_kind_dispatcherT)Zcommutativec                 C   s   dd | j D }| j| S )Nc                 s   s   | ]}|j V  qd S N)kind).0a r   R/var/www/auris/lib/python3.9/site-packages/sympy/physics/quantum/anticommutator.py	<genexpr>X       z&AntiCommutator.kind.<locals>.<genexpr>)args_kind_dispatcher)selfZ	arg_kindsr   r   r   r   V   s    zAntiCommutator.kindc                 C   s*   |  ||}|d ur|S t| ||}|S r   )evalr   __new__)clsABrobjr   r   r   r   [   s
    zAntiCommutator.__new__c                 C   s   |r|st jS ||kr&td|d  S |js2|jrBtd| | S | \}}| \}}|| }|rtt| | t|t|S ||dkr| ||S d S )N      )r   ZZeror   is_commutativeZargs_cncr   Z
_from_argscompare)r   r   bcaZncacbZncbZc_partr   r   r   r   b   s     zAntiCommutator.evalc                 K   s   ddl m} | jd }| jd }t||rt||rz|j|fi |}W n@ ty   z|j|fi |}W n ty   d}Y n0 Y n0 |dur|jf i |S || ||  jf i |S )z Evaluate anticommutator r   )Operatorr   N)Zsympy.physics.quantum.operatorr%   r   
isinstanceZ_eval_anticommutatorNotImplementedErrordoit)r   hintsr%   r   r   Zcommr   r   r   r(   w   s    

zAntiCommutator.doitc                 C   s   t t| jd t| jd S )Nr   r   )r   r   r   )r   r   r   r   _eval_adjoint   s    zAntiCommutator._eval_adjointc                 G   s*   d| j j|| jd || jd f S )Nz	%s(%s,%s)r   r   )	__class____name___printr   r   printerr   r   r   r   
_sympyrepr   s    
zAntiCommutator._sympyreprc                 G   s$   d| | jd | | jd f S )Nz{%s,%s}r   r   )r-   r   r.   r   r   r   	_sympystr   s    zAntiCommutator._sympystrc                 G   sb   |j | jd g|R  }t|td }t||j | jd g|R   }t|jddd }|S )Nr   ,r   {})leftright)r-   r   r   r6   parens)r   r/   r   Zpformr   r   r   _pretty   s
    "zAntiCommutator._prettyc                    s   dt  fdd| jD  S )Nz\left\{%s,%s\right\}c                    s   g | ]}j |g R  qS r   )r-   )r   argr   r/   r   r   
<listcomp>   s   z)AntiCommutator._latex.<locals>.<listcomp>)tupler   r.   r   r:   r   _latex   s    zAntiCommutator._latexN)r,   
__module____qualname____doc__r    r   r   propertyr   r   classmethodr   r(   r*   r0   r1   r8   r=   r   r   r   r   r      s   ;

c                 C   s   t S )z8Find the kind of an anticommutator of two OperatorKinds.)r
   )e1e2r   r   r   find_op_kind   s    rE   N)r@   Zsympy.core.exprr   Zsympy.core.kindr   Zsympy.core.mulr   Zsympy.core.numbersr   Zsympy.core.singletonr   Z sympy.printing.pretty.stringpictr   Zsympy.physics.quantum.daggerr   Zsympy.physics.quantum.kindr	   r
   __all__r   r   registerrE   r   r   r   r   <module>   s   	 