o
    à8Vaê  ã                   @   s„   d dl mZmZmZmZ d dlmZ G dd„ deƒZdd„ ZG dd„ deƒZ	d	d
„ Z
d dlmZmZ d dlmZ dd„ Zeed< dS )é    )ÚBasicÚExprÚSÚsympify)ÚNonSquareMatrixErrorc                   @   s>   e Zd ZdZdZdd„ Zedd„ ƒZedd„ ƒZdd
d„Z	dS )ÚDeterminanta  Matrix Determinant

    Represents the determinant of a matrix expression.

    Examples
    ========

    >>> from sympy import MatrixSymbol, Determinant, eye
    >>> A = MatrixSymbol('A', 3, 3)
    >>> Determinant(A)
    Determinant(A)
    >>> Determinant(eye(3)).doit()
    1
    Tc                 C   s8   t |ƒ}|jstdt|ƒ ƒ‚|jstdƒ‚t | |¡S )Nz&Input to Determinant, %s, not a matrixzDet of a non-square matrix)r   Ú	is_MatrixÚ	TypeErrorÚstrZ	is_squarer   r   Ú__new__©ÚclsZmat© r   úH/usr/lib/python3/dist-packages/sympy/matrices/expressions/determinant.pyr      s   zDeterminant.__new__c                 C   ó
   | j d S ©Nr   ©Úargs©Úselfr   r   r   Úarg    ó   
zDeterminant.argc                 C   s
   | j jjS ©N)r   ÚkindZelement_kindr   r   r   r   r   $   r   zDeterminant.kindFc              	   C   ó(   z| j  ¡ W S  ttfy   |  Y S w r   )r   Z_eval_determinantÚAttributeErrorÚNotImplementedError©r   Úexpandr   r   r   Údoit(   ó
   ÿzDeterminant.doitN©F)
Ú__name__Ú
__module__Ú__qualname__Ú__doc__Zis_commutativer   Úpropertyr   r   r   r   r   r   r   r      s    


r   c                 C   ó   t | ƒ ¡ S )zÅ Matrix Determinant

    Examples
    ========

    >>> from sympy import MatrixSymbol, det, eye
    >>> A = MatrixSymbol('A', 3, 3)
    >>> det(A)
    Determinant(A)
    >>> det(eye(3))
    1
    )r   r   ©Zmatexprr   r   r   Údet.   s   r)   c                   @   s.   e Zd ZdZdd„ Zedd„ ƒZd
dd„Zd	S )Ú	Permanenta  Matrix Permanent

    Represents the permanent of a matrix expression.

    Examples
    ========

    >>> from sympy import MatrixSymbol, Permanent, ones
    >>> A = MatrixSymbol('A', 3, 3)
    >>> Permanent(A)
    Permanent(A)
    >>> Permanent(ones(3, 3)).doit()
    6
    c                 C   s*   t |ƒ}|jstdt|ƒ ƒ‚t | |¡S )Nz$Input to Permanent, %s, not a matrix)r   r   r	   r
   r   r   r   r   r   r   r   N   s   zPermanent.__new__c                 C   r   r   r   r   r   r   r   r   U   r   zPermanent.argFc              	   C   r   r   )r   Úperr   r   r   r   r   r   r   Y   r    zPermanent.doitNr!   )r"   r#   r$   r%   r   r&   r   r   r   r   r   r   r*   >   s    
r*   c                 C   r'   )a   Matrix Permanent

    Examples
    ========

    >>> from sympy import MatrixSymbol, Matrix, per, ones
    >>> A = MatrixSymbol('A', 3, 3)
    >>> per(A)
    Permanent(A)
    >>> per(ones(5, 5))
    120
    >>> M = Matrix([1, 2, 5])
    >>> per(M)
    8
    )r*   r   r(   r   r   r   r+   _   s   r+   )ÚaskÚQ)Úhandlers_dictc                 C   sL   t t | j¡|ƒrtjS t t | j¡|ƒrtjS t t | j¡|ƒr$tjS | S )zÜ
    >>> from sympy import MatrixSymbol, Q, assuming, refine, det
    >>> X = MatrixSymbol('X', 2, 2)
    >>> det(X)
    Determinant(X)
    >>> with assuming(Q.orthogonal(X)):
    ...     print(refine(det(X)))
    1
    )	r,   r-   Z
orthogonalr   r   ZOneZsingularZZeroZunit_triangular)ÚexprZassumptionsr   r   r   Úrefine_Determinantv   s   
r0   N)Zsympyr   r   r   r   Zsympy.matrices.commonr   r   r)   r*   r+   Zsympy.assumptions.askr,   r-   Zsympy.assumptions.refiner.   r0   r   r   r   r   Ú<module>   s    )!