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    3Ih                     @   s   d Z ddlmZ ddlmZ ddlmZ ddlmZ ddl	m
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 ddlmZ ddlmZ dd	lmZ dd
lmZmZ dgZG dd deZejeedd ZdS )z"The commutator: [A,B] = A*B - B*A.    )Add)Expr)KindDispatcher)Mul)Pow)S)
prettyForm)Dagger)_OperatorKindOperatorKind
Commutatorc                   @   s   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d Zdd ZdS )r   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
    FCommutator_kind_dispatcherT)commutativec                 C   s   dd | j D }| j| S )Nc                 s   s    | ]}|j V  qd S N)kind).0a r   `/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/sympy/physics/quantum/commutator.py	<genexpr>f   s    z"Commutator.kind.<locals>.<genexpr>)args_kind_dispatcher)self	arg_kindsr   r   r   r   d   s   
zCommutator.kindc                 C   s*   |  ||}|d ur|S t| ||}|S r   )evalr   __new__)clsABrobjr   r   r   r   i   s
   zCommutator.__new__c                 C   s   |r|st jS ||krt jS |js|jrt jS | \}}| \}}|| }|r9tt| | t|t|S ||dkrHt j| || S d S )N   )r   Zerois_commutativeargs_cncr   
_from_argscompareNegativeOne)r   r   bcancacbncbc_partr   r   r   r   p   s    zCommutator.evalc           	      C   s   |j }|jr| rt|dkr| S |j}|jr |jd }| }t||jdd}||d  | }td|D ]}|||d |  | ||  7 }q6||  S )Nr!   T)
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"zCommutator._expand_powc                 K   s  | j d }| j d }t|tr.g }|j D ]}t||}t|tr$| }|| qt| S t|trRg }|j D ]}t||}t|trH| }|| q8t| S t|tr|j d }t|j dd   }|}	t||	}
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isinstancer   r   _eval_expand_commutatorappendr   r   r<   )r   hintsr   r   sargstermr9   r   r(   ccomm1comm2firstsecondr   r   r   r>      sb   
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z"Commutator._eval_expand_commutatorc                 K   s   ddl m} | jd }| jd }t||rTt||rTz|j|fi |}W n" tyG   zd|j|fi | }W n tyD   d}Y nw Y nw |durT|jdi |S || ||  jdi |S )z Evaluate commutator r   )Operatorr!   r.   Nr   )sympy.physics.quantum.operatorrH   r   r=   _eval_commutatorNotImplementedErrordoit)r   r@   rH   r   r   r9   r   r   r   rL      s"   

zCommutator.doitc                 C   s   t t| jd t| jd S )Nr!   r   )r   r	   r   )r   r   r   r   _eval_adjoint   s   zCommutator._eval_adjointc                 G   s*   d| j j|| jd || jd f S )Nz	%s(%s,%s)r   r!   )	__class____name___printr   r   printerr   r   r   r   
_sympyrepr   s   
zCommutator._sympyreprc                 G   s$   d| | jd | | jd f S )Nz[%s,%s]r   r!   )rP   r   rQ   r   r   r   	_sympystr   s   zCommutator._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)rP   r   r   rY   parens)r   rR   r   pformr   r   r   _pretty   s
   "zCommutator._prettyc                    s   dt  fdd| jD  S )Nz\left[%s,%s\right]c                    s   g | ]}j |g R  qS r   )rP   )r   argr   rR   r   r   
<listcomp>   s    z%Commutator._latex.<locals>.<listcomp>)tupler   rQ   r   r^   r   _latex   s   
zCommutator._latexN)rO   
__module____qualname____doc__r#   r   r   propertyr   r   classmethodr   r<   r>   rL   rM   rS   rT   r\   ra   r   r   r   r   r      s"    G

<c                 C   s   t S )z8Find the kind of an anticommutator of two OperatorKinds.)r   )e1e2r   r   r   find_op_kind   s   ri   N)rd   sympy.core.addr   sympy.core.exprr   sympy.core.kindr   sympy.core.mulr   sympy.core.powerr   sympy.core.singletonr    sympy.printing.pretty.stringpictr   sympy.physics.quantum.daggerr	   sympy.physics.quantum.kindr
   r   __all__r   r   registerri   r   r   r   r   <module>   s     	 f