U
    Ç-e`  ã                   @   s   d dl m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Z d dlmZm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ZmZmZmZmZ d dlmZ d dlm Z  dd„ Z!dd„ Z"dd„ Z#dd„ Z$dd„ Z%dd„ Z&dd„ Z'dd„ Z(dd „ Z)d!d"„ Z*d#d$„ Z+d%d&„ Z,d'S )(é    )ÚAdd)Ú	unchanged)ÚMul)Úsymbols)ÚEq)ÚSum)ÚimÚre)Ú	Piecewise)ÚImmutableDenseMatrix)ÚMatrixSymbol)ÚMatAdd)Ú
ZeroMatrixÚGenericZeroMatrixÚIdentityÚGenericIdentityÚ	OneMatrix)ÚMatMul)Úraisesc                      sÌ   t tddƒst‚t tddƒs t‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttd	d„ ƒ td
ƒ‰ t tˆ ˆ ƒsŒt‚td
dd‰ tt‡ fdd„ƒ td
dd‰ tt‡ fdd„ƒ d S )Né   r   c                   S   s
   t ddƒS ©Néÿÿÿÿr   ©r   © r   r   ún/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/matrices/expressions/tests/test_special.pyÚ<lambda>   ó    z+test_zero_matrix_creation.<locals>.<lambda>c                   S   s
   t ddƒS ©Nç       @r   r   r   r   r   r   r      r   c                   S   s
   t ddƒS ©Nù               @r   r   r   r   r   r   r      r   c                   S   s
   t ddƒS ©Nr   r   r   r   r   r   r   r      r   c                   S   s
   t ddƒS ©Nr   r   r   r   r   r   r   r      r   c                   S   s
   t ddƒS ©Nr   r    r   r   r   r   r   r      r   ÚnF©Úintegerc                      s
   t ˆ ˆ ƒS ©Nr   r   ©r$   r   r   r      r   T©Únegativec                      s
   t ˆ ˆ ƒS r'   r   r   r(   r   r   r   !   r   )r   r   ÚAssertionErrorr   Ú
ValueErrorr   r   r   r(   r   Útest_zero_matrix_creation   s    r-   c                     s²   t ƒ ‰ tddd} td| | ƒ}ˆ ˆ ks*t‚ˆ |ks6t‚|ˆ ksBt‚ˆ jsLt‚tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ tƒ ˆ kst‚tˆ |ƒt|ƒks¦t‚tˆ ƒ d S )	Nr$   Tr%   ÚAc                      s   ˆ j S r'   ©Úshaper   ©Úzr   r   r   /   r   z*test_generic_zero_matrix.<locals>.<lambda>c                      s   ˆ j S r'   ©Úrowsr   r1   r   r   r   0   r   c                      s   ˆ j S r'   ©Úcolsr   r1   r   r   r   1   r   )	r   r   r   r+   Zis_ZeroMatrixr   Ú	TypeErrorr   Úhash©r$   r.   r   r1   r   Útest_generic_zero_matrix$   s    
r:   c                      s–   t dƒst‚t dƒst‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ tdƒ‰ t ˆ ƒsVt‚tddd	‰ tt‡ fd
d„ƒ tddd‰ tt‡ fdd„ƒ d S )Nr   r   c                   S   s   t dƒS )Nr   ©r   r   r   r   r   r   <   r   z/test_identity_matrix_creation.<locals>.<lambda>c                   S   s   t dƒS )Nr   r;   r   r   r   r   r   =   r   c                   S   s   t dƒS )Nr    r;   r   r   r   r   r   >   r   r$   Fr%   c                      s   t ˆ ƒS r'   r;   r   r(   r   r   r   C   r   Tr)   c                      s   t ˆ ƒS r'   r;   r   r(   r   r   r   E   r   )r   r+   r   r,   r   r   r   r(   r   Útest_identity_matrix_creation9   s    r<   c                     sÂ   t ƒ ‰ tddd} td| | ƒ}ˆ ˆ ks*t‚ˆ |ks6t‚|ˆ ksBt‚ˆ jsLt‚ˆ d ˆ ks\t‚tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fd	d„ƒ tƒ ˆ ks t‚tˆ |ƒt|ƒks¶t‚tˆ ƒ d S )
Nr$   Tr%   r.   r   c                      s   ˆ j S r'   r/   r   ©ÚIr   r   r   T   r   z'test_generic_identity.<locals>.<lambda>c                      s   ˆ j S r'   r3   r   r=   r   r   r   U   r   c                      s   ˆ j S r'   r5   r   r=   r   r   r   V   r   )	r   r   r   r+   Zis_Identityr   r7   r   r8   r9   r   r=   r   Útest_generic_identityH   s    
r?   c                      sÞ   t ddƒst‚t ddƒst‚tt ddƒtdƒƒs4t‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttd	d„ ƒ ttd
d„ ƒ tdƒ‰ t ˆ ˆ ƒsžt‚tddd‰ tt‡ fdd„ƒ tddd‰ tt‡ fdd„ƒ d S )Nr   r   é   c                   S   s
   t ddƒS r   ©r   r   r   r   r   r   b   r   z*test_one_matrix_creation.<locals>.<lambda>c                   S   s
   t ddƒS r   rA   r   r   r   r   r   c   r   c                   S   s
   t ddƒS r   rA   r   r   r   r   r   d   r   c                   S   s
   t ddƒS r!   rA   r   r   r   r   r   e   r   c                   S   s
   t ddƒS r"   rA   r   r   r   r   r   f   r   c                   S   s
   t ddƒS r#   rA   r   r   r   r   r   g   r   r$   Fr%   c                      s
   t ˆ ˆ ƒS r'   rA   r   r(   r   r   r   l   r   Tr)   c                      s
   t ˆ ˆ ƒS r'   rA   r   r(   r   r   r   n   r   )r   r+   r   r   r   r,   r   r   r   r(   r   Útest_one_matrix_creation^   s    rB   c                  C   s  t ddd\} }td| |ƒ}t| |ƒ}|| |ks6t‚||j t| | ƒksNt‚||j t| | ƒksft‚|| t|jŽ ks|t‚|s„t‚| ¡ t|| ƒksšt‚| ¡ |ksªt‚| ¡ t|| ƒksÀt‚t	|ƒ|ksÐt‚t
|ƒ|ksàt‚t| | ƒd t| ƒksút‚tddƒ ¡ t dd¡kst‚d S )Nún mTr%   r.   r   é   )r   r   r   r+   ÚTr0   Ú	transposeÚ	conjugateÚadjointr	   r   r   Úas_explicitr   Zzeros)r$   Úmr.   ÚZr   r   r   Útest_ZeroMatrixq   s    
rL   c                  C   sb   t ddd} tt| | dd| ƒ}t|jtƒs0t‚| ¡ td|  | ƒksJt‚t| ¡ jtƒs^t‚d S ©Nr$   Tr%   F)Úevaluater   )r   r   r   Ú
isinstancer4   r+   Údoitr   )r$   ZZnnr   r   r   Útest_ZeroMatrix_doit‡   s
    rQ   c                  C   s  t ddd\} }td| |ƒ}t| |ƒ}|j| |fks8t‚t|| tƒsJt‚| ¡ t|| ƒks`t‚| ¡ |kspt‚| 	¡ t|| ƒks†t‚t
|ƒ|ks–t‚t|ƒt| |ƒks¬t‚t| | ƒd t| ƒksÆt‚t| | ƒ}|d dksàt‚tdd	ƒ}| ¡ t dd	¡kst‚d S )
NrC   Tr%   r.   r   )r@   r   r@   r   rD   )r   r   r   r0   r+   rO   r   rF   rG   rH   r	   r   r   r   rI   r   Zones)r$   rJ   r.   ÚUr   r   r   Útest_OneMatrix   s    


rS   c                  C   sb   t ddd} tt| | dd| ƒ}t|jtƒs0t‚| ¡ td|  | ƒksJt‚t| ¡ jtƒs^t‚d S rM   )r   r   r   rO   r4   r+   rP   r   )r$   ZUnnr   r   r   Útest_OneMatrix_doit¥   s
    rT   c                  C   sx   t ddd\} }}td| dƒ}t| |ƒt||ƒ t| |ƒ| ksDt‚|tddƒ |ksZt‚tddƒ|j |jkstt‚d S )Nzn m kTr%   Úwr@   )r   r   r   r+   rE   )r$   rJ   ÚkrU   r   r   r   Útest_OneMatrix_mul­   s
    &rW   c                  C   s4  t ddd\} }td| |ƒ}t dƒ\}}t| ƒ}t|ƒ}|| |ksHt‚|| |ksXt‚| ¡ |ksht‚| ¡ |ksxt‚| ¡ |ksˆt‚| ¡ |ks˜t‚t|ƒ|ks¨t‚t	|ƒt
| | ƒks¾t‚|||f dksÒt‚t|||f |d| d f|d| d fƒ | d¡ ¡ dkst‚tt|||f |d| d fƒ|d| d fƒ | d¡ ¡ dksRt‚t|||f |d| d fƒ}| ¡ dks€t‚t|||f |d| d	 fƒ}| ¡  td|dk|| d	 k@ fd
ƒ¡sÊt‚t|||f |d| d fƒ}| ¡  td|dk|| d k@ fd
ƒ¡st‚tdƒ ¡ t d¡ks0t‚d S )NrC   Tr%   r.   zi jr   r@   rD   r   )r   T)r   r   r   r+   rF   ZinverserG   rH   r	   r   r   r   ÚsubsrP   Zdummy_eqr
   rI   r   Úeye)r$   rJ   r.   ÚiÚjÚInZImÚexprr   r   r   Útest_Identityµ   sB    >Bþÿ
þÿ
r^   c                  C   s^   t ddd} tt| | ddƒ}t|jtƒs.t‚| ¡ td|  ƒksFt‚t| ¡ jtƒsZt‚d S rM   )r   r   r   rO   r4   r+   rP   r   )r$   ZInnr   r   r   Útest_Identity_doitß   s
    r_   N)-Zsympy.core.addr   Zsympy.core.exprr   Zsympy.core.mulr   Zsympy.core.symbolr   Zsympy.core.relationalr   Zsympy.concrete.summationsr   Z$sympy.functions.elementary.complexesr   r	   Z$sympy.functions.elementary.piecewiser
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