o
    GZŽhø?  ã                   @   sØ  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l
mZ d dlmZ d dlmZmZmZ d dlmZmZmZmZ d dlmZ d d	lmZ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%m&Z&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 „ Z0d!d"„ Z1d#d$„ Z2d%d&„ Z3d'd(„ Z4d)d*„ Z5d+d,„ Z6d-d.„ Z7d/d0„ Z8d1d2„ Z9d3d4„ Z:d5d6„ Z;d7d8„ Z<d9d:„ Z=d;d<„ Z>d=d>„ Z?d?d@„ Z@dAdB„ ZAdCdD„ ZBdEdF„ ZCdGdH„ ZDdIdJ„ ZEdKdL„ ZFdMS )Né    )ÚsymbolsÚSymbolÚTupleÚooÚDummy)ÚIndexException)Úraises)Úiterable)ÚSum)ÚFunctionÚSubsÚ
Derivative)ÚStrictLessThanÚGreaterThanÚStrictGreaterThanÚLessThan)ÚS)ÚexpÚlog)ÚcosÚsin©ÚKroneckerDelta)ÚOrder)ÚRange)ÚIndexedBaseÚIdxÚIndexedc                     sô   t ddd\‰ } }tˆ ƒtˆ dƒksJ ‚tˆ | ƒtˆ d| d fƒks$J ‚tˆ tƒtˆ dtfƒks2J ‚t ddd‰tt‡fdd	„ƒ ttd
d	„ ƒ tt‡ ‡fdd	„ƒ tt‡ fdd	„ƒ tt‡ ‡fdd	„ƒ tt‡ ‡fdd	„ƒ tt‡ fdd	„ƒ d S )Núi a bT©Úintegeré   r   ÚxFc                      s   t ˆ ƒS ©N©r   © ©r"   r%   úN/var/www/auris/lib/python3.10/site-packages/sympy/tensor/tests/test_indexed.pyÚ<lambda>   ó    z'test_Idx_construction.<locals>.<lambda>c                   S   ó   t dƒS ©Ng      à?r$   r%   r%   r%   r'   r(      r)   c                      s
   t ˆ ˆƒS r#   r$   r%   ©Úir"   r%   r'   r(      ó   
 c                      ó
   t ˆ dƒS r+   r$   r%   ©r-   r%   r'   r(      r.   c                      s   t ˆ ˆdfƒS )Né   r$   r%   r,   r%   r'   r(      ó    c                      s   t ˆ dˆfƒS )Né   r$   r%   r,   r%   r'   r(       r2   c                      r/   )N)r3   g      @r$   r%   r0   r%   r'   r(   !   r.   )r   r   r   r   Ú	TypeError)ÚaÚbr%   r,   r'   Útest_Idx_construction   s    r7   c                  C   s^   t ddd\} }}t| ƒjsJ ‚t| ƒjdksJ ‚t| d ƒjdks$J ‚tdƒjdks-J ‚d S )Nr   Tr   r-   r3   zi + 2Zfoo)r   r   Ú
is_integerÚname©r-   r5   r6   r%   r%   r'   Útest_Idx_properties$   s
   r;   c                  C   sD  t ddd\} }}t| ƒjd u sJ ‚t| ƒjd u sJ ‚t| |ƒjdks%J ‚t| |ƒj|d ks1J ‚t| dƒjdks;J ‚t| dƒjdksEJ ‚t| tƒjdksOJ ‚t| tƒjtu sYJ ‚t| ||fƒj|kseJ ‚t| ||fƒj|ksqJ ‚t| dƒjdks{J ‚t| dƒjdks…J ‚t| t tfƒjt u s“J ‚t| t tfƒjtu s J ‚d S )	Nr   Tr   r   r!   r1   é   ©r!   r1   ©r   r   ÚlowerÚupperr   r:   r%   r%   r'   Útest_Idx_bounds,   s   rA   c                  C   sF  t ddd\} }}}t|ƒjd u sJ ‚t|ƒjd u sJ ‚t||ƒjdks&J ‚t||ƒj|d ks2J ‚t|dƒjdks<J ‚t|dƒjdksFJ ‚t|tƒjdksPJ ‚t|tƒjtu sZJ ‚t|||fƒj|ksfJ ‚t|||fƒj|ksrJ ‚t|dƒjdks|J ‚t|dƒjdks†J ‚t|t tfƒjt u s”J ‚t|t tfƒjtu s¡J ‚d S )	Nzi a b xTr   r   r!   r1   r<   r=   r>   )r-   r5   r6   r"   r%   r%   r'   Útest_Idx_fixed_bounds>   s   rB   c                  C   sâ  t ddƒ} t ddƒ}t ddƒ}t ddƒ}| d	ksJ ‚| d	k s J ‚| d	kr&J ‚| d	kr,J ‚d	| ks2J ‚d	| ks8J ‚d	| kr>J ‚d	| k rDJ ‚t| d	ƒsKJ ‚t| d	ƒsRJ ‚t| d	ƒrYJ ‚t| d	ƒr`J ‚| d
ksfJ ‚t| d
k tƒsoJ ‚t| d
ktƒsxJ ‚| d
kr~J ‚t| dktƒs‡J ‚| dk rJ ‚| dks“J ‚t| dktƒsœJ ‚| dkr¢J ‚| dk r¨J ‚| dks®J ‚| dks´J ‚ddlm} t| |k tƒsÃJ ‚t| |ktƒsÌJ ‚t| |ktƒsÕJ ‚t| |ktƒsÞJ ‚| |k säJ ‚| |ksêJ ‚| |krðJ ‚| |kröJ ‚| |ksüJ ‚t| |k tƒsJ ‚t| |ktƒsJ ‚| |krJ ‚t| |k tƒs!J ‚t| |ktƒs+J ‚t| |ktƒs5J ‚t| |ktƒs?J ‚t dƒ}t dƒ}t||k tƒsQJ ‚t||ktƒs[J ‚t||ktƒseJ ‚t||ktƒsoJ ‚d S )NÚi14©r!   r<   Úi79)é   é	   Úi46)r<   é   Úi35)é   r1   r1   r<   r!   r   r&   ÚiNone1ÚiNone2)r   r   r   r   r   Ú
isinstanceZ	sympy.abcr"   )rC   rE   rH   rJ   r"   rL   rM   r%   r%   r'   Útest_Idx_inequalitiesP   sf   



rO   c                  C   sN   t ddƒ} tdƒ| ksJ ‚tdƒ| ksJ ‚tdƒ| krJ ‚tdƒ| k r%J ‚d S )NrC   rD   r1   )r   r   )rC   r%   r%   r'   Ú#test_Idx_inequalities_current_fails“   s
   
rP   c                  C   sr   t ddd\} }}t| ƒ}|j|jŽ |ksJ ‚t| |ƒ}|j|jŽ |ks&J ‚t| ||fƒ}|j|jŽ |ks7J ‚d S )Nr   Tr   )r   r   ÚfuncÚargs)r-   r5   r6   Úiir%   r%   r'   Útest_Idx_func_argsœ   s   
rT   c                  C   sº   t ddd\} }}t| |ƒ ||¡t| |ƒksJ ‚t| |ƒ | |¡t||ƒks)J ‚t| ƒ | d¡tdƒks7J ‚t| |ƒ |d¡t| dƒksGJ ‚t| ||fƒ | d¡td||fƒks[J ‚d S )Nr   Tr   r3   )r   r   Úsubsr:   r%   r%   r'   Útest_Idx_subs¦   s      ,rV   c                  C   s¦   t ddd\} }t dƒ}t|| |ƒ}t|ƒ}||| |f ks J ‚||| |f ks*J ‚||| |g ks4J ‚||t| |ƒ ks?J ‚tdd„ |d jdd … D ƒƒsQJ ‚d S )	Núi jTr   r5   c                 s   s    | ]}|j V  qd S r#   )Z
is_Integer)Ú.0r5   r%   r%   r'   Ú	<genexpr>¹   s   € z)test_IndexedBase_sugar.<locals>.<genexpr>)r!   r   r!   )r   r   r   r   ÚallrR   )r-   Újr5   ÚA1ÚA2r%   r%   r'   Útest_IndexedBase_sugar°   s   (r^   c                  C   sl   t ddd} t dƒ\}}t|ƒ}t|ƒ}||  ||   ||¡ks"J ‚ddi}|d |d  ||¡ks4J ‚d S )Nr-   Tr   úa br!   r3   ©r   r   rU   )r-   r5   r6   ÚAÚBÚCr%   r%   r'   Útest_IndexedBase_subs¼   s    rd   c                     sF  t ddd\‰‰} }td| | fd}td| |fd‰ˆjt| |ƒks$J ‚|ˆˆf ˆˆˆf ks2J ‚|ˆˆf ˆˆˆf  || ¡ksDJ ‚ˆjˆjŽ ˆksNJ ‚ˆˆˆf jˆˆˆf jŽ ˆˆˆf ksdJ ‚tt‡‡fdd„ƒ tt‡‡‡fdd„ƒ td	| d‰ ˆ jt| ƒksˆJ ‚ˆ ˆ  ˆˆ¡ˆ ˆ ks–J ‚tt‡ ‡‡fd
d„ƒ d S )Nzi j m nTr   r5   ©Úshapec                      s   ˆ ˆ S r#   r%   r%   )r6   r-   r%   r'   r(   Ï   r)   z(test_IndexedBase_shape.<locals>.<lambda>c                      s   ˆ ˆˆˆf S r#   r%   r%   )r6   r-   r[   r%   r'   r(   Ð   r2   ÚFc                      s   ˆ ˆˆf S r#   r%   r%   )rg   r-   r[   r%   r'   r(   Ô   ó    )	r   r   rf   r   rU   rQ   rR   r   r   )ÚmÚnr5   r%   )rg   r6   r-   r[   r'   Útest_IndexedBase_shapeÆ   s   $,rk   c                  C   sÂ   t ddd} t dƒ}t|dd}|||  fD ]*}|jsJ ‚|js"J ‚|jr'J ‚|js,J ‚|js1J ‚|js6J ‚tt	|ƒƒ|ks@J ‚q|t|ƒksIJ ‚|t|dddksTJ ‚||  t
|| ƒks_J ‚d S )Nr-   Tr   r5   )Úpositive)rl   Úreal)r   r   Úis_realZ
is_complexZis_imaginaryZis_nonnegativeZ
is_nonzeroZis_commutativer   r   r   )r-   r5   ra   Úcr%   r%   r'   Útest_IndexedBase_assumptions×   s   





rp   c                  C   s\   t ddd} t| ƒ}tddd}|jsJ ‚|jsJ ‚|jjs J ‚|jjs&J ‚||ks,J ‚d S )NÚITr   )r   r   r8   Úlabel)rq   Z	I_inheritZ
I_explicitr%   r%   r'   Ú(test_IndexedBase_assumptions_inheritanceé   s   

rs   c                  C   sV   G dd„ dt ƒ} | dƒ}t|ƒ| ksJ ‚t|ƒ}t|ƒ| ks J ‚t|jƒ| ks)J ‚dS )z`Regression test issue #17652.

    IndexedBase.label should not upcast subclasses of Symbol
    c                   @   s   e Zd ZdS )z"test_issue_17652.<locals>.SubClassN)Ú__name__Ú
__module__Ú__qualname__r%   r%   r%   r'   ÚSubClassú   s    rw   ÚXN)r   Útyper   rr   )rw   r"   Úbaser%   r%   r'   Útest_issue_17652õ   s   r{   c                      sŽ   t ddd\‰‰tdˆˆƒ‰ ˆ ttdƒˆˆƒksJ ‚ˆ ttdƒˆˆƒks&J ‚tt‡ ‡‡fdd„ƒ ttdd„ ƒ ˆ jˆ ˆ jj	ˆˆhksEJ ‚d S )NrW   Tr   ra   c                      s   t ˆ ˆˆƒS r#   ©r   r%   ©ra   r-   r[   r%   r'   r(   	  rh   z*test_Indexed_constructor.<locals>.<lambda>c                   S   r*   ©Nra   r|   r%   r%   r%   r'   r(   
  r)   )
r   r   r   r   r   r4   r   Zfree_symbolsrz   rr   r%   r%   r}   r'   Útest_Indexed_constructor  s   r   c                  C   s<   t ddd\} }t dƒ}t|| |ƒ}||j|jŽ ksJ ‚d S )NrW   Tr   r5   )r   r   rQ   rR   )r-   r[   r5   ra   r%   r%   r'   Útest_Indexed_func_args  s   r€   c                  C   sz   t ddd\} }}t dƒ\}}t|ƒ}t|ƒ}|| |f || |f  ||¡ks)J ‚|| |f || |f  ||¡ks;J ‚d S )Nzi j kTr   r_   r`   )r-   r[   Úkr5   r6   ra   rb   r%   r%   r'   Útest_Indexed_subs  s   $(r‚   c                     s  t ddd\‰‰tdˆˆƒ‰ ˆ jdksJ ‚ˆ jdksJ ‚ˆ jˆˆfks%J ‚ˆ jtdƒks.J ‚ˆ jd d gks7J ‚tt	‡ fdd„ƒ t d	dd\} ‰tdt
ˆˆƒt
ˆ| ƒƒjtd
ˆd ƒtd
| d ƒgkseJ ‚tdt
ˆˆƒt
ˆ| ƒƒjtˆ| ƒksyJ ‚tt	‡‡‡fdd„ƒ d S )NrW   Tr   ra   zA[i, j]r3   c                      s   ˆ j S r#   re   r%   )ra   r%   r'   r(   &  s    z)test_Indexed_properties.<locals>.<lambda>ún mr   r!   c                      s   t dtˆ ˆƒtˆƒƒjS r~   )r   r   rf   r%   )r-   r[   ri   r%   r'   r(   ,  s    )r   r   r9   ÚrankÚindicesrz   r   Úrangesr   r   r   r   rf   )rj   r%   )ra   r-   r[   ri   r'   Útest_Indexed_properties  s$   ÿÿÿ(r‡   c                  C   s  t ddd\} }t ddd\}}t ddd\}}td||fd}|jt||ƒks*J ‚t|t| |ƒt||ƒƒjtd|d	 ƒtd|d	 ƒgksGJ ‚t|t| |ƒt||ƒƒjt||ƒks[J ‚t|t| |ƒt|ƒƒjtd|d	 ƒd
gksrJ ‚t|t| |ƒt|ƒƒjt||ƒks…J ‚d S )NrW   Tr   zo prƒ   r5   re   r   r!   )NN)r   r   rf   r   r   r   r†   )r-   r[   ÚoÚprj   ri   r5   r%   r%   r'   Útest_Indexed_shape_precedence/  s"   ÿÿ(ÿÿ*rŠ   c                  C   sH   t ddd\} }td| | | ƒ}|jdksJ ‚|j| | | fks"J ‚d S )NrW   Tr   ra   r3   )r   r   r„   r…   ©r-   r[   ra   r%   r%   r'   Útest_complex_indices=  s   rŒ   c                  C   s0   t ddd\} }td| | | ƒ}t|ƒrJ ‚d S )NrW   Tr   ra   )r   r   r	   r‹   r%   r%   r'   Útest_not_interableD  s   r   c                  C   s|   t ddd} | }td|d ƒ}td|fd}d||d   ||   || ¡}|| ||d    || ¡}||ks<J ‚d S )NÚNTr   r-   r!   Úyre   )r   r   r   Zcoeff)rŽ   Zlen_yr-   r   r5   r6   r%   r%   r'   Útest_Indexed_coeffJ  s   "r   c                  C   sÞ  ddl m}  tdtd\}}}}tdƒ}tdddd\}}|js"J ‚td	td\}}	|| || }
}|
}| |¡| ||ƒksAJ ‚| |
¡| ||ƒksMJ ‚td
ƒ|
 }| |¡td
ƒ| ||ƒ kscJ ‚| |
¡td
ƒ| ||ƒ kssJ ‚| |¡tju s}J ‚t	||t
 t
fƒ |¡t	d
| ||ƒ |t
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ksÇJ ‚t	| |
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|t
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fƒ ¡ ksâJ ‚t	||t
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¡ ¡ t
u sôJ ‚|| | td
ƒ }| |
¡|||  | ||ƒ ksJ ‚| |¡|| td
ƒ ks!J ‚| |d
¡tju s-J ‚t	||t
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¡t	|| ||ƒ ||  |t
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fƒ |
¡ ¡ |||  ks†J ‚t	||t
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¡t	|| ||ƒ ||  |t
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fƒks§J ‚t	| |
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fƒ |
¡ ¡ |||  ksßJ ‚|t|| ƒ }| |
¡d
| t|| ƒ | | ||ƒ ks J ‚| |¡d
| t|| ƒ | ksJ ‚||	||f  ||  }| |
¡||	||f  | ||ƒ ks5J ‚| |¡||	||f  ksEJ ‚| |	||f ¡|||  ksWJ ‚| |	||f ¡|| ||ƒ | ||ƒ ||  kssJ ‚| |	||f ¡|| ||ƒ ||  ksŠJ ‚t	||t
 t
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| ksmJ ‚d S )Nr   r   zi j k l©Úclsr5   zm, nT)r    Zfinitezh Lr3   r!   )Ú(sympy.functions.special.tensor_functionsr   r   r   rn   r   Údiffr   ZZeror
   r   Zdoitr   r   )r   r-   r[   r   Úlr5   ri   rj   ÚhÚLÚhiZhjÚexprr%   r%   r'   Útest_differentiationT  s\   
  88$6$& BB.BB.2(* $8.T@"F2F:rš   c                  C   sp   t dƒ} tddd}t| | ƒ | | ¡| | | | d d  | | d d  t| | d | | ƒ ks6J ‚d S )	Nra   r-   Tr   rK   rI   r1   éx   )r   r   r   Zseriesr   )ra   r-   r%   r%   r'   Útest_indexed_series  s   \rœ   c                  C   s²   t dƒ} tdƒ\}}}| |  ¡ rJ ‚| |  |¡sJ ‚| dd|  |f  ¡ r*J ‚| dd|  |f  |¡r9J ‚| dd|  |f  |¡sHJ ‚| dd|  |f  |¡rWJ ‚d S )Nra   úi,j,kr!   r3   )r   r   Úis_constant)ra   r-   r[   r   r%   r%   r'   Útest_indexed_is_constant–  s   "rŸ   c                  C   s–   t dƒ} t tdƒƒtdddƒksJ ‚| d  tdƒtdƒ¡dks"J ‚| d  | tdƒ¡dks0J ‚| d  | tdƒ¡dks>J ‚ttdƒdƒdksIJ ‚d S )NÚdr1   r   r!   r3   )r   Úranger   rU   r   r   )r    r%   r%   r'   Útest_issue_12533¡  s    r¢   c                      s.   t dƒ‰tddˆfƒ‰ tt‡ ‡fdd„ƒ d S )Nrj   r-   r   c                      s   ˆ   ˆd¡S )Ng      ø?)rU   r%   ©r-   rj   r%   r'   r(   ­  rh   z"test_issue_12780.<locals>.<lambda>)r   r   r   r4   r%   r%   r£   r'   Útest_issue_12780ª  s   r¤   c                      sj   t dƒ‰ tdˆ ƒjdksJ ‚tdˆ ƒjdksJ ‚tdˆ ƒjˆ d ks$J ‚t ddd‰ tt‡ fdd„ƒ d S )	Nri   r-   r   r!   F)rm   c                      s
   t dˆ ƒS )Nr-   r$   r%   ©ri   r%   r'   r(   ¶  r.   z"test_issue_18604.<locals>.<lambda>)r   r   r9   r?   r@   r   r4   r%   r%   r¥   r'   Útest_issue_18604°  s   r¦   c                  C   sÌ  t dƒ} tdƒ\}}}tdƒ\}}}tdƒ}t| | | | | | ƒ | | ¡dks+J ‚t| | | | |ƒ | | ¡dks>J ‚t| | | | |ƒ | | ¡dksQJ ‚t| | | | |ƒ |¡dksbJ ‚t| | | | |ƒ |¡dkssJ ‚t| | | | | | ƒ | | ¡t||ƒks‹J ‚t||| | ƒ | | ¡t||ƒksŸJ ‚t|| | ƒ| | |ƒ | | ¡dks´J ‚t|| | ƒ| | | | ƒ | | ¡t|| | ƒ| | ƒt||ƒ ksÙJ ‚t||| | d ƒ | | ¡dt||ƒ | |  ksõJ ‚t| | | | | | d ƒ | | ¡dt||ƒ | |  ksJ ‚t| | | || | ƒ | | ¡d| |  ks0J ‚t| | | || | ƒ | | ¡d| |  t||ƒ ksOJ ‚t| | | || | ƒ | | ¡| | | | t||ƒ  kspJ ‚t| | | || | ƒ | | ¡| | | | t||ƒ  ks‘J ‚t| | | || | ƒ | | ¡d| |  t||ƒ ks°J ‚t| | | || | ƒ | | ¡t||ƒ| |  t||ƒ| |   ksÖJ ‚t| | | | | |ƒ | | ¡dksìJ ‚t| | | | | |ƒ | | ¡dksJ ‚t| | | | | |ƒ | | ¡|ksJ ‚t| | | | | |ƒ | | ¡|t||ƒ ks3J ‚t| | | | | |ƒ | | ¡dksIJ ‚t| | | | | |ƒ | | ¡|t||ƒ ksdJ ‚d S )Nra   r   zx,y,zÚfr!   r   r3   )r   r   r   r   r”   r   r   )ra   r-   r[   r   r"   r   Úzr§   r%   r%   r'   Útest_Subs_with_Indexed¸  s6   *&&""0(*J8B4>BB>L,,,6,:r©   c               
   C   sž  t dtd\} }t dƒ}t dƒ\}}}t dƒ\}}}}	}
}tdƒ}|| | ||  d | ƒ}t dtd}| | | ¡ | | ||  t||ƒ d tt||ƒ|ƒ|f| | ||  d | fƒ | ¡sgJ ‚| | | ¡ | | ¡ dt||ƒ t||ƒ tt||ƒ|ƒ|f| | ||  d | fƒ | d	| | ||  d  t||ƒ t||ƒ tt||ƒ||ƒ|f| | ||  d | fƒ |d   ¡sÍJ ‚d S )
Nzx,yr‘   Úsigmar   zm0:6r§   r3   Zxi_1r<   )	r   r   r   r   r”   Zdummy_eqr   r   r   )r"   r   rª   r-   r[   r   Zm0Úm1Úm2Zm3Zm4Zm5r§   r™   Z_xi_1r%   r%   r'   Ú(test_complicated_derivative_with_IndexedÙ  sV   ÿýÿûÿÿýÿû*ýÿûúÿr­   c                  C   sl   t ddd} t ddd}t dƒ}| d |d  |d | d  ks"J ‚| d |d  |d | d  ks4J ‚d S )NÚtF)ZcommutativeÚuÚvr   )r   )r®   r¯   r°   r%   r%   r'   Útest_IndexedBase_commutativeú  s
   $(r±   N)GZ
sympy.corer   r   r   r   r   Zsympy.tensor.indexedr   Zsympy.testing.pytestr   Zsympy.utilities.iterablesr	   Zsympy.concrete.summationsr
   Zsympy.core.functionr   r   r   Zsympy.core.relationalr   r   r   r   Zsympy.core.singletonr   Z&sympy.functions.elementary.exponentialr   r   Z(sympy.functions.elementary.trigonometricr   r   r“   r   Zsympy.series.orderr   Zsympy.sets.fancysetsr   r   r   r   r7   r;   rA   rB   rO   rP   rT   rV   r^   rd   rk   rp   rs   r{   r   r€   r‚   r‡   rŠ   rŒ   r   r   rš   rœ   rŸ   r¢   r¤   r¦   r©   r­   r±   r%   r%   r%   r'   Ú<module>   sZ    C	



	
<	!!