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   a?  The standard commutator, in an unevaluated state.

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

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

    Canonical ordering of a commutator is ``[A, B]`` for ``A < B``. The
    arguments of the commutator are put into canonical order using ``__cmp__``.
    If ``B < A``, then ``[B, A]`` is returned as ``-[A, B]``.

    Parameters
    ==========

    A : Expr
        The first argument of the commutator [A,B].
    B : Expr
        The second argument of the commutator [A,B].

    Examples
    ========

    >>> from sympy.physics.quantum import Commutator, Dagger, Operator
    >>> from sympy.abc import x, y
    >>> A = Operator('A')
    >>> B = Operator('B')
    >>> C = Operator('C')

    Create a commutator and use ``.doit()`` to evaluate it:

    >>> comm = Commutator(A, B)
    >>> comm
    [A,B]
    >>> comm.doit()
    A*B - B*A

    The commutator orders it arguments in canonical order:

    >>> comm = Commutator(B, A); comm
    -[A,B]

    Commutative constants are factored out:

    >>> Commutator(3*x*A, x*y*B)
    3*x**2*y*[A,B]

    Using ``.expand(commutator=True)``, the standard commutator expansion rules
    can be applied:

    >>> Commutator(A+B, C).expand(commutator=True)
    [A,C] + [B,C]
    >>> Commutator(A, B+C).expand(commutator=True)
    [A,B] + [A,C]
    >>> Commutator(A*B, C).expand(commutator=True)
    [A,C]*B + A*[B,C]
    >>> Commutator(A, B*C).expand(commutator=True)
    [A,B]*C + B*[A,C]

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

    >>> Dagger(Commutator(A, B))
    -[Dagger(A),Dagger(B)]

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Commutator
    Fc                 C   s*   |  ||}|d k	r|S t| ||}|S )N)evalr   __new__)clsABrobj r   a/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/physics/quantum/commutator.pyr   a   s
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   expandrange)	selfr   r   signr   r    commresultir   r   r   _expand_pow}   s    
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   _eval_expand_commutatorappendr   r   r(   )r#   hintsr   r   Zsargstermr%   r   r   cZcomm1Zcomm2firstsecondr   r   r   r+      sb    
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z"Commutator._eval_expand_commutatorc                 K   s   | j d }| j d }t|trt|trz|j|f|}W nD tk
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
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   r   r)   )r#   r   r   r   _eval_adjoint   s    zCommutator._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   
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     zCommutator._prettyc                    s   dt  fdd| jD  S )Nz\left[%s,%s\right]c                    s   g | ]}j |f  qS r   )r7   ).0argr)   r9   r   r   
<listcomp>   s    z%Commutator._latex.<locals>.<listcomp>)tupler)   r8   r   rE   r   _latex   s    zCommutator._latexN)r6   
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      s   G
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   r   r   r   r   <module>   s   	