a
    {dY                     @   s  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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mZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJ d dlKmLZLmMZM d dlNmOZO d dlPmQZQmRZR ed\ZSZTZUZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\dd Z]dd Z^dd  Z_d!d" Z`d#d$ Zad%d& Zbd'd( Zcd)d* Zdd+d, Zed-d. Zfd/d0 Zgd1d2 Zhd3d4 Zid5d6 Zjd7d8 Zkd9d: Zld;d< Zmd=d> Znd?d@ ZodAdB ZpdCdD ZqdEdF ZrdGdH ZsdIdJ ZtdKdL ZudMdN ZvdOdP ZwdQdR ZxdSdT ZydUdV ZzdWdX Z{dYdZ Z|d[d\ Z}d]d^ Z~d_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj ZdkS )l    )dedent)isliceproduct)Basic)Integerordered)Dummysymbols	factorial)Matrix)RGS_enum
RGS_unrankPermutation)4
_partition_set_partitionsbinary_partitions	braceletscapturecartescommon_prefixcommon_suffixconnected_components
dict_mergefilter_symbolsflattengenerate_bellgenerate_derangementsgenerate_involutionsgenerate_oriented_forestgrouphas_dupsibiniproductkbinsminlexmultisetmultiset_combinationsmultiset_partitionsmultiset_permutations	necklacesnumbered_symbols
partitionspermutations	postfixesprefixesreshaperotate_leftrotate_rightrunssiftstrongly_connected_componentssubsetstaketopological_sort	unflattenuniq
variationsordered_partitions	rotationsis_palindromiciterableNotIterablemultiset_derangementssequence_partitionssequence_partitions_empty)factoring_visitormultiset_partitions_taocp)S)raiseswarns_deprecated_sympyzw,x,y,zc                  C   s   ddl m} m} t , t|ttgttgks4J W d    n1 sH0    Y  t , tttg| dttgksvJ W d    n1 s0    Y  d S )Nr   default_sort_keyr   key)sympy.utilities.iterablesrK   r   rI   listyxsortedrJ    rS   m/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/utilities/tests/test_iterables.pytest_deprecated_iterables!   s
    :rU   c                   C   s   t dsJ t dsJ t ds$J t ds0J t dr<J t drHJ t ddsVJ t dd	rdJ t dd	d
stJ t dd	dsJ t ddsJ t dd	rJ t dd	dsJ d S )N rQ   xxZxyxZxyZxyzxZxxyzzyx         Zxxyzyx   )r?   rS   rS   rS   rT   test_is_palindromic)   s    r]   c                     s&  t dddgksJ t ttffttgks.J ddgdgg t  dd ksPJ t  ddg dkshJ t  d	dg d
ksJ t  ddg d
ksJ tt fdd G dd dt} t | tttg| tttgksJ t | tttg| dtttgksJ t h dth dks"J d S )N)rX   rX   rX   rZ   rX   rY   r   r   r   levels)r_   ra   rb   rY   )r`   rZ   rX   rY   r   r      c                      s   t  ddS )NrZ   rc   )r   rS   ZlsrS   rT   <lambda>D       ztest_flatten.<locals>.<lambda>c                   @   s   e Zd ZdS )ztest_flatten.<locals>.MyOpN__name__
__module____qualname__rS   rS   rS   rT   MyOpF   s   rm   cls>   rX   rY      )r   rQ   rH   
ValueErrorr   rP   zrO   )rm   rS   rf   rT   test_flatten9   s    $&rs   c                  C   s  t t dgksJ t tg g ks(J t tg dg dksDJ ttddgg dg dksfJ ttddgddgddgg d	ksJ tttjd
u sJ tttjtjd
u sJ dttjv sJ dttjtjv sJ dttjtjtjv sJ ttttjtjtjd} | D ]<\}}}t|t	s<J t|t	sLJ t|t	s"J q"tt
tddgd  D ]"}|ttjtjtjv sxJ qxd S )NrS   rX   rY   re   r^   rY   re   rX   rY   re      r\   rX   re   )rX   ry   )rX   r\   rY   re   rY   ry   )rY   r\   r   r   r   r   r   r   rX   )r   rX   r   r   rX   rX   )rX   r   r   )rX   r   rX   )rX   rX   r   rX   rX   rX   Trw   )ry   r\   i  r`   re   )rO   r$   rR   r@   rG   ZIntegerssetr   
isinstancer   r   range)ZtriplesZn1Zn2Zn3trS   rS   rT   test_iproductO   s"    "(r   c                   C   sD  t g g ksJ t g ddg ks$J t dgdggks:J t dgdddgksRJ t ddgddggkslJ t ddgdddgksJ t g dg dgksJ t g ddddgksJ t g ddgd	gdggksJ t g dddg d
ksJ t g dddgg ddgddggks"J t g dddg dks@J d S )NF)multiplerX   rX   rX   ra   r   r{   rX   rY   rX   rY   )r   rY   rX   r   )rX   rX   rY   rY   rY   rX   re   re   rY   rY   rY   re   )ra   r|   r   re   rY   )r!   rS   rS   rS   rT   
test_groupe   s     ,r   c                  C   s  t tg dddgksJ t tg ddg dks:J t tg ddg dksXJ t tg dddgkstJ t td	} t t| dd
ddgksJ t t| dd
dg dksJ t t| dd
dg dksJ t t| dd
dg dksJ tt t| d	d
ddksJ t t| d d dddg ks:J t t| d d dd
dg dksbJ t tddgd
dg dksJ t tddgddg dksJ t tg ddg dksJ t tg ddd
dg dksJ d S )Nrt   r   rS   rX   ru   rY   )ra   r{   r|   re   ry   TZ
repetitionr   r^   rv   rw   )
rb   r   rX   r   rY   r   re   r   ra   r{   rY   rY   r|   re   re   )r   r   )r   r   rY   )r   r   re   r   r   rX   rY   r   rX   re   )r   rY   rY   r   rY   re   )r   re   re   r   rX   rX   rY   rX   rX   re   rX   rY   rY   rt   )rX   re   re   r   )rY   rY   re   )rY   re   re   )re   re   re   #   F)r   r   r   r   )rS   r^   rv   r   ra   r   )rS   r^   rv   ra   )r   ra   r{   r   r|   r   )rO   r7   r   lenlrS   rS   rT   test_subsetsz   s0    
 $(


r   c                  C   sh  t td} t t| ddddgks(J t t| dddg dksFJ t t| dddg d	ksdJ t t| d
ddg dksJ t t| ddddgksJ t t| dddg dksJ t t| dddg dksJ tt t| d
dddksJ tt t| ddddksJ t t| d d d
ddg ks<J t t| d d d
ddg dksdJ d S )Nry   r   Fr   rS   rX   r   rY   )r   r   r   rX   r   ra   r{   rY   r   r   r|   re   r   re   rX   r   re   )r   r   r   rY   rX   r   r   re   rX   )r   re   rY   rX   r   rY   )rX   r   re   rX   rY   r   rt   )rX   re   r   )rX   re   rY   rY   r   rX   )rY   r   re   rY   rX   r   )rY   rX   re   )rY   re   r   )rY   re   rX   )re   r   rX   )re   r   rY   )re   rX   r   )re   rX   rY   )re   rY   r   re   rY   rX   T)rb   r   r   r   r   r   ra   r{   r   r   r   r|   r   r   r   r   @      r~   )rO   r   r<   r   r   rS   rS   rT   test_variations   s     $r   c                   C   s   t tddgg dg dks"J t t dgks6J t tddgksLJ t tdddd	gksfJ t tt tdd
dgksJ d S )NrX   rY   rx   rz   rS   a)r   )repeat)r   r   r   r^   )rO   r   r   rS   rS   rS   rT   test_cartes   s    r   c                  C   s2   t  } t| td}t|dttdks.J d S )Nzx0 x2 x3re   zx1 x4 x5)r,   r   r
   r8   rO   )sfilteredrS   rS   rT   test_filter_symbols   s    r   c                  C   sD   t td} tt| tsJ tt ddtdgdtdks@J d S )Nrn   CrX   ZC1)startexcludeZC2)r,   r	   r   nextr
   )r   rS   rS   rT   test_numbered_symbols   s
    
r   c                   C   s   t ttddd ddgg ddks,J t ttgdd tgtgd	ksPJ t tjgd
d ddgikspJ t g ddd ddddgddgfksJ t g ddd dddgg dfksJ ttdd  d S )Nr\   c                 S   s   | d S NrY   rS   _rS   rS   rT   rg      rh   ztest_sift.<locals>.<lambda>rX   re   )r   rY   ry   r   c                 S   s
   |  tS NZhasrQ   r   rS   rS   rT   rg      rh   )FTc                 S   s
   |  tS r   r   r   rS   rS   rT   rg      rh   Fr   rX   rY   re   c                 S   s   | d S r   rS   rQ   rS   rS   rT   rg      rh   Tbinaryr   rY   c                 S   s   | d dkS )Nre   rX   rS   r   rS   rS   rT   rg      rh   r   c                   S   s   t g ddd ddS )Nr   c                 S   s   | d S )Nre   rS   r   rS   rS   rT   rg      rh   z-test_sift.<locals>.<lambda>.<locals>.<lambda>Tr   )r5   rS   rS   rS   rT   rg      s    )	r5   rO   r   rQ   rP   rG   ZOnerH   rq   rS   rS   rS   rT   	test_sift   s    ,$ 


r   c                  C   sX   t  } t| dttdks J t| dttdks:J tg ddg dksTJ d S )Nr\   zx0:5zx5:10rX   rY   re   ry   r\   )r,   r8   rO   r
   )XrS   rS   rT   	test_take   s    r   c                   C   s   t i dtttidtttiks"J t dtttii dtttiksDJ t dtidtttidtdtttiksnJ t dtttidtidtdtttiksJ t ttddtttidtdtttiksJ t dtttittddtdtttiksJ d S )NrX   rY   ra   )r   rQ   rP   rr   rS   rS   rS   rT   test_dict_merge   s    ""**,r   c                   C   s   t tg g ksJ t tdgdggks.J t tddgdgddggksPJ t tg ddgddgg dg dg dgksJ d S )NrX   rY   r   rt   rX   rY   re   ry   )rO   r0   rS   rS   rS   rT   test_prefixes   s    "r   c                   C   s   t tg g ksJ t tdgdggks.J t tddgdgddggksPJ t tg ddgddgg dg dg dgksJ d S )NrX   rY   r   r\   ry   rx   )rY   re   ry   r\   )rO   r/   rS   rS   rS   rT   test_postfixes   s    "r   c                      s`   g dg d t  fg dks(J t  fdd dg dksHJ tt fdd d S )	N)rY   re   r\         	   
   rp   )	)r   rp   r   r   )r\   rp   )re   r   )re   r   )rp   rY   )rp   r   )rp   r   )r   r   )re   r\   r   r   rp   rY   r   r   c                 S   s   |  S r   rS   )vrS   rS   rT   rg   	  rh   z'test_topological_sort.<locals>.<lambda>rL   )r   r\   rp   re   r   r   r   rY   c                      s   t  dg fS )N)r   r   )r9   rS   EVrS   rT   rg     rh   )r9   rH   rq   rS   rS   r   rT   test_topological_sort  s    r   c                  C   s   t g g fg ksJ t g dg fdgdgdggks8J g d} g d}t | |fg dgksbJ g d} g d}t | |fdgddgdggksJ g d} g d	}t | |fddgddggksJ d S )
Nrt   rX   rY   re   ra   r{   r   r|   r   r   ra   r|   r   re   ry   ry   )ra   r   r   )ry   re   )r6   r   r   rS   rS   rT   "test_strongly_connected_components  s    $"r   c                  C   s   t g g fg ksJ t g dg fdgdgdggks8J g d} g d}t | |fg dgksbJ g d} g d}t | |fg dgksJ g d} dd	g}t | |fddgdd
ggksJ d S )Nrt   rX   rY   re   r   r   r   ra   r   ry   )r   r   rS   rS   rT   test_connected_components   s    $r   c                  C   s   g d} t | dg dksJ t| dg dks4J g } t| d}|g ksNJ |d | g ksdJ t | d}|g kszJ |d | g ksJ d S )Nr   rX   rY   re   ry   rY   )rY   re   ry   r   rX   rX   )ry   r   rX   rY   re   )r2   r3   append)ABrS   rS   rT   test_rotate1  s    



r   c               
   C   s  g d} t t| ddgdgdgdgdgggks4J tt t| ddksNJ tt t| dd	kshJ t tg d
dg ddggg dddggg ddggg dddggddgg dggksJ t tg ddg ddggddgddggg ddggddgddgggksJ t tg ddg ddggg ddggddgddggg ddggddgddggddgddggdgg dggksJ t tg ddddgdggdgddgggksJ t tdg dgddgdggddgdggdgddggdgdgdgggksJ t tddddgdggddgdggdgddgggksJJ t tdgd ddgddgggkstJ t tdgd g dgdgddggdgdgdgggksJ g d}t t|t tt|ksJ t t|dg ksJ t t|dg dggksJ t t|dg dg ks2J t t|dg dg dggksXJ t tddg kspJ t tddddgggksJ t tddgggksJ t tddg ksJ t tdddggdgdgggksJ t tddddgggksJ t tdddggks(J t tddgdddgggksLJ g d}dd tdD |kspJ dgd dgd!dgdd"gg d#g d$g d%g}d&d tddgD |ksJ d S )'Nr   r\   r   rX   rY   re   ry   r      )rX   rX   rX   rY   rY   )rX   rX   rX   rY   r   )rX   rX   rY   rY   r   r   r   rt   )rX   rY   ry   rX   re   ry   rY   re   ry   r   r   r   abbaaa)$)Zmpsyy)ZmpsyrP   )mpsyy)r   rP   rP   )Zmpyyr   )mpysy)r   r   rP   )mpsyy)r   r   rP   )r   r   r   )r   r   rP   rP   )Zmsyyp)msypy)r   r   rP   )mspyy)r   r   rP   )r   r   r   )r   r   rP   rP   )myyps)r   r   r   )mypsy)r   r   rP   )r   r   r   )r   r   r   )r   r   r   rP   )mZpsyy)r   r   rP   )r   r   r   )r   r   rP   rP   )r   r   r   )r   r   r   )r   r   r   rP   )r   r   r   )r   r   r   rP   )r   r   r   r   )r   r   r   rP   rP   c                 S   s   g | ]}t d d |D qS )c                 s   s   | ]}d  |V  qdS rV   Njoin).0partrS   rS   rT   	<genexpr>{  rh   z6test_multiset_partitions.<locals>.<listcomp>.<genexpr>)tupler   r   rS   rS   rT   
<listcomp>{  s   z,test_multiset_partitions.<locals>.<listcomp>Zsympy   r      r[   )ry   rY   re   )r[   rY   rY   )rY   rY   rY   re   c                 S   s   g | ]}t |d dgqS r|   )rE   r   rS   rS   rT   r     s   )rO   r)   r   rR   rF   )r   r   ansZ
factoringsrS   rS   rT   test_multiset_partitionsA  sz    ,&
&&(
,$*"

 & ( $

r  c                  C   s   g d} dd t tddD | ks(J td}dd t t|dD | ksPJ dd t|dD g kslJ t td	gd
dggd
d	gd
dgggksJ tt tdddksJ tt tddd	ksJ t tdd	dgdgdggksJ ttdd  d S )N)ZiiiZiimZiipZiisimpZimsZippipsZissZmppr   ZmssZppsZpssZsssc                 S   s   g | ]}d  |qS rV   r   r   irS   rS   rT   r     rh   z.test_multiset_combinations.<locals>.<listcomp>Zmississippire   c                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r     rh   c                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r     rh      rX   rY   r   r   abcr   cc                   S   s   t tddddS )Nre   rZ   r   rY   )rO   r(   rS   rS   rS   rT   rg     rh   z,test_multiset_combinations.<locals>.<lambda>)rO   r(   r'   r   rH   rq   )r  MrS   rS   rT   test_multiset_combinations  s$    ,"r  c                     sz  g d} dd t dD | ks"J dd t tdD | ks@J tt g ddddggks`J tt g d	ddd
gddgd
dgd
dgddgdd
ggksJ ttt ddd
ksJ ttt dddksJ g i dfD ]}tt |g gksJ qtt |dg gksJ tt |d
g ks*J tt |dg ksBJ dd  t fddtdkshJ ttdd  d S )N)ZabbyZabybZaybbbabyZbaybZbbayZbbyaZbyabZbybaZyabbZybabZybbac                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r     rh   z.test_multiset_permutations.<locals>.<listcomp>r  c                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r     rh   r   rY   r   r   rX   r   re   rV   rZ   c                  S   s8   t ddD ](} t|  tg d| D ]}t| q$q
d S )NrX   r   )r   r   rX   r   rX   )r   printr*   )r  r   rS   rS   rT   test  s    z(test_multiset_permutations.<locals>.testc                      s     S r   rS   rS   r  rS   rT   rg     rh   z,test_multiset_permutations.<locals>.<lambda>a          1
        [0]
        [1]
        2
        [0, 0]
        [0, 1]
        [1, 0]
        [1, 1]
        3
        [0, 0, 0]
        [0, 0, 1]
        [0, 1, 0]
        [0, 1, 1]
        [1, 0, 0]
        [1, 0, 1]
        [1, 1, 0]
        4
        [0, 0, 0, 1]
        [0, 0, 1, 0]
        [0, 0, 1, 1]
        [0, 1, 0, 0]
        [0, 1, 0, 1]
        [0, 1, 1, 0]
        [1, 0, 0, 0]
        [1, 0, 0, 1]
        [1, 0, 1, 0]
        [1, 1, 0, 0]
        5
        [0, 0, 0, 1, 1]
        [0, 0, 1, 0, 1]
        [0, 0, 1, 1, 0]
        [0, 1, 0, 0, 1]
        [0, 1, 0, 1, 0]
        [0, 1, 1, 0, 0]
        [1, 0, 0, 0, 1]
        [1, 0, 0, 1, 0]
        [1, 0, 1, 0, 0]
        [1, 1, 0, 0, 0]
        6
c                   S   s   t tdddS )Nre   rZ   r   )rO   r*   rS   rS   rS   rT   rg     rh   )r*   r'   rO   r   r   r   rH   rq   )r  nulrS   r  rT   test_multiset_permutations  s"     $
(r  c               	   C   s  i gdi fgg} t dD ]}ttd|d| | ks8J ttdd|d| | ksVJ ttddd|d| | ksvJ ttddd |d| | ksJ ttdd d|d| | ksJ ttddd|d| | ksJ qttdddddidddd	ddddigksJ ttdddddidddd
dddddidddd	ddddigks\J ttdd	ddd	diddddddddddg  krdd tdd	ddD ksn J tttdddddidddgksJ ttd	dddddddiddddd	ig  kr6dd td	D ks<n J t ddD ]L}d}t|D ]&\}}|t||ksrJ |d7 }qV|t|ksFJ qFd S )Nr   rY   )sizerX   r[   )kre   ra   ry   rt   r{   r   )r  r   r   r}   r|   c                 S   s2   g | ]*}t d d |D rt| dkr|qS )c                 s   s   | ]}|d kV  qdS )ry   NrS   r   r  rS   rS   rT   r     rh   -test_partitions.<locals>.<listcomp>.<genexpr>re   )allsumvaluesr  rS   rS   rT   r     s   z#test_partitions.<locals>.<listcomp>)r   c                 S   s"   g | ]}t d d |D r|qS )c                 s   s   | ]}|d kV  qdS )re   NrS   r  rS   rS   rT   r     rh   r  )r  r  rS   rS   rT   r     s   )r   rO   r-   rG   r   r   r   )r  r  nr   qrS   rS   rT   test_partitions  sL       "& 
r  c                   C   s   dd t dD ddgg dg dg dg d	g d
g dg dg dg dg dg dg dg dgksnJ tdd t dD dksJ d S )Nc                 S   s   g | ]}|d d  qS r   rS   r  rS   rS   rT   r      rh   z*test_binary_partitions.<locals>.<listcomp>r   r   rY   )r   rX   rX   )ry   ry   rY   )ry   ry   rX   rX   )ry   rY   rY   rY   )ry   rY   rY   rX   rX   )ry   rY   rX   rX   rX   rX   )ry   rX   rX   rX   rX   rX   rX   )rY   rY   rY   rY   rY   )rY   rY   rY   rY   rX   rX   )rY   rY   rY   rX   rX   rX   rX   )rY   rY   rX   rX   rX   rX   rX   rX   )	rY   rX   rX   rX   rX   rX   rX   rX   rX   )
rX   rX   rX   rX   rX   rX   rX   rX   rX   rX   c                 S   s   g | ]}|d d  qS r   rS   r   jrS   rS   rT   r     rh      $   )r   r   rS   rS   rS   rT   test_binary_partitions  s    
r"  c                  C   s   dd t ddD dd t ddD ks,J ttdg dksDJ t ddD ]<} tt | }t| }|D ]}|t|jksJ | }qjqNttd	d
  d S )Nc                 S   s   g | ]}t tt|qS rS   )r   r   r   r  rS   rS   rT   r   
  rh   z"test_bell_perm.<locals>.<listcomp>rX   r   c                 S   s   g | ]}t |qS rS   r   r  rS   rS   rT   r   
  s   re   )r   r   r   r   r   r   r\   c                   S   s   t tdS )Nr   )rO   r   rS   rS   rS   rT   rg     rh   z test_bell_perm.<locals>.<lambda>)	r   rO   r   r   r   Z
array_formZnext_trotterjohnsonrH   rq   )r  r   r   ZbirS   rS   rT   test_bell_perm	  s    r#  c                  C   sX   g d} t | D ]B\}}tt|d }t||ks8J tdd |D dksJ qd S )N)rX   rY   ry   r      L   rX   c                 S   s   h | ]}t |d  qS rv   )r   r  rS   rS   rT   	<setcomp>  rh   z#test_involutions.<locals>.<setcomp>)	enumeraterO   r   r   )lengthsr  Nr  rS   rS   rT   test_involutions  s
    r*  c                  C   s  t ttttddks J ddd tdD dks@J ttg dg d	g d
g dg dg dg dg dg dg dg	ksJ ttg dg dg dgksJ ttdtdgksJ t} t| dg ksJ dd | dD dgksJ dd | dD ddgks"J dd | dD d gks@J d!d | d"D g d#ks`J d$d | d%D g d&ksJ d'd | d(D g d)ksJ ttd*gd+gd+gd,ggd+gd,gd*gd+ggd+gd*gd,gd+gggksJ d S )-Nr[   i	  rV   c                 s   s   | ]}d  |V  qdS r   r   r  rS   rS   rT   r   $  rh   z$test_derangements.<locals>.<genexpr>abcdeZbadecbaecdbcaedbcdeabceadbdaecbdeacbdecabeacdbedacbedcacabedcadebcaebdcdaebcdbeacdeabcdebaceabdcebadcedabcedbadabecdaebcdaecbdcaebdcbeadceabdcebadeabcdeacbdebacdebcaeabcdeadbceadcbecabdecbadecdabecdbaedabcedacbedbacedbcar   )rX   r   re   rY   )rX   rY   re   r   )rX   re   r   rY   )rY   r   re   rX   )rY   re   r   rX   )rY   re   rX   r   )re   r   rX   rY   )re   rY   r   rX   )re   rY   rX   r   )r   rX   rY   rY   )rY   rY   r   rX   )rY   rY   rX   r   bar   Zabbc                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r   2  rh   z%test_derangements.<locals>.<listcomp>c                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r   3  rh   r
  ZbcaZcabc                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r   4  rh   ZaabbZbbaac                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r   5  rh   Zaabbcccc)ZccccaabbZccccababZccccabbaZccccbaabZccccbabaZccccbbaac                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r   8  rh   Zaabbccc)ZcccabbaZcccababZcccaabbZccacbbaZccacbabZccacabbZcbccbaaZcbccabaZcbccaabZbcccbaaZbcccabaZbcccaabc                 S   s   g | ]}d  |qS r  r   r  rS   rS   rT   r   <  rh   Zbooks)ZkbsooZksbooZsbkooZskbooZoksboZoskboZokbsoZobksoZoskobZoksobZosbokZobsokre   rY   rX   )r   rO   r   r   r   rB   )DrS   rS   rT   test_derangements"  s.     

    $r.  c               
   C   s   dd } g }t ddD ].}||| |dd| |dd| |ddf qt|tg dg d	g d
g dg dg dg dgksJ d S )Nc                 S   s   t tt| ||S r   )r   rO   r+   )r  r  frS   rS   rT   countD  s    ztest_necklaces.<locals>.countrX   r   rY   r   re   )rX   rY   rY   re   )rY   re   re   r[   )re   ry   ry   r   )ry   r[   r[      )r\   r   r   '   )r[         \   )r            )r   r   r   )r0  r   r  rS   rS   rT   test_necklacesC  s     r9  c                  C   s   t tdd} t| tddgddgddgddgddgddgddgddgddgddgg
ks^J t tdd} t| tg dg dg dg d	g d
g dgksJ d S )NrY   ry   r   rX   re   )r   r   r   r   )r   r   r   rX   )r   r   rX   rX   )r   rX   r   rX   )r   rX   rX   rX   )rX   rX   rX   rX   )rO   r   r   )ZbcrS   rS   rT   test_braceletsT  s,    r:  c                   C   s   t tdg dg dg dg dg dg dg dg d	g d
g dg dg dg dg dg dg dg dg dg dg dgksJ tt tddksJ d S )Nr\   r   )r   rX   rY   re   re   )r   rX   rY   re   rY   )r   rX   rY   re   rX   )r   rX   rY   re   r   )r   rX   rY   rY   rY   )r   rX   rY   rY   rX   )r   rX   rY   rY   r   )r   rX   rY   rX   rY   )r   rX   rY   rX   rX   )r   rX   rY   rX   r   )r   rX   rY   r   rX   )r   rX   rY   r   r   )r   rX   rX   rX   rX   )r   rX   rX   rX   r   )r   rX   rX   r   rX   )r   rX   rX   r   r   )r   rX   r   rX   r   )r   rX   r   r   r   )r   r   r   r   r   r   i2  )rO   r    r   rS   rS   rS   rT   test_generate_oriented_forestm  s    
r;  c                  C   s   t td} t| t t| d d d | dd d ks:J t| dt| d d t| dd  gkshJ ttdd  ttdd  d S )Nr   rY   rX   r\   c                   S   s   t ttddS )Nr   re   r:   rO   r   rS   rS   rS   rT   rg   {  rh   z test_unflatten.<locals>.<lambda>c                   S   s   t ttddS )Nr   r`   r<  rS   rS   rS   rT   rg   |  rh   )rO   r   r:   zipr   rH   rq   )rrS   rS   rT   test_unflattenw  s
    ..r?  c                   C   sL  t g dgg ksJ t ttdg dks0J t ttdttdg dksVJ t g dg dddgkstJ t g dg ddgksJ tg dgg ksJ tttdg dksJ tttdttdg dksJ tttdttdg ks
J tg dg d	ddgks*J tg dg d
dgksHJ d S )NrX   re   r   ry   rt   )rX   rY   r\   rY   )rX   re   r\   )r   rY   re   )r   r   re   )r   rO   r   r   rS   rS   rS   rT   test_common_prefix_suffix  s    &&$ r@  c                   C   sp   t g ddksJ t ddks$J t ddks4J t ddddksHJ t ddksXJ t d	td
dkslJ d S )Nr   r   r   r   F)ZdirectedZabaZaab)bbr   r  r   rL   )r  r   rA  r   )r&   r   rS   rS   rS   rT   test_minlex  s    rB  c                      s   t tttftddttgttgfv s*J t tttftddt tttftddksZJ t tttfttgksvJ g dg dg ddgdggdd	 d
d	 fg\ t t ddddgdgg dg dg dgksJ tt fdd	 d S )NF)defaultr   r   r   rY   rX   c                 S   s   t | S r   )r   r   rS   rS   rT   rg     rh   ztest_ordered.<locals>.<lambda>c                 S   s   t | S r   )r  r   rS   rS   rT   rg     rh   rC  warnc                      s   t t dddS )NFTrD  )rO   r   rS   keysseqrS   rT   rg     s    )rO   r   rQ   rP   hashrH   rq   rS   rS   rF  rT   test_ordered  s    *rJ  c                  C   s   t g g ksJ t dgdggks&J t ddgdgdggksBJ t g ddgddggks`J t g dddgdggks~J t g ddgdgdggksJ ddlm}  t g d| ddgdggksJ d S )NrX   r   rY   r   )rY   rX   rX   r   lt)r4   operatorrL  rK  rS   rS   rT   	test_runs  s     rN  c                  C   s  t tdd} t| dgg dg dgks.J t| dddgksDJ t| dddgksZJ t| ddgfddd	dgfd
dddgfgksJ t| ddgfdd	dgfdddgfgksJ t| ddgdfddd	gdfd
ddgdfgksJ tt| dgddgfdgddgfd
gddgffks"J tt| dgddfdgddfd
gddffksVJ tt tddd	gdhdgddg dd
dhdggksJ ttdd  ttdd  d S )NrX   r   ry   r   )r\   r[   r   r   )ry   r   rY   re   r\   r[   r   r   rv   ra   )r\   r[   r   r   r  )rX   rw   rX   r   r   )r   )r   r   r   rp   c                   S   s   t ddgdgS )Nr   rX   rZ   r1   rS   rS   rS   rT   rg     rh   ztest_reshape.<locals>.<lambda>c                   S   s   t ddgdgS )Nr   rX   re   rO  rS   rS   rS   rT   rg     rh   )rO   r   r1   r   rH   rq   )rH  rS   rS   rT   test_reshape  s<    



rP  c                      s  t tdd tdD ddidddddidddddigksDJ t tdd td	D d
dgksjJ t tddgksJ t tdt dksJ t tdgddgdggdgddggksJ t ttdd dgddfD dgddfddgdfdddgfgksJ t tdddddgdgdgdgdgg	ddddgdgdggksRJ dg tt fdd dgg tt fdd d S )Nc                 s   s   | ]
}|V  qd S r   rS   r   rS   rS   rT   r     rh   ztest_uniq.<locals>.<genexpr>ry   rX   r{   rY   ra   c                 s   s   | ]}|d  V  qdS )rY   NrS   )r   rQ   rS   rS   rT   r     rh   r\   r   r   Zababcr
  c                 s   s   | ]
}|V  qd S r   rS   r  rS   rS   rT   r     rh   re   c                      s    fddt  D S )Nc                    s   g | ]}  |qS rS   remover  r/  rS   rT   r     rh   /test_uniq.<locals>.<lambda>.<locals>.<listcomp>r;   rS   rS  rS   rT   rg     rh   ztest_uniq.<locals>.<lambda>c                      s    fddt  D S )Nc                    s   g | ]}  |qS rS   rQ  r  rS  rS   rT   r     rh   rT  rU  rS   rS  rS   rT   rg     rh   )rO   r;   r-   r   r.   rH   RuntimeErrorrS   rS   rS  rT   	test_uniq  s"    $&,  
&
rW  c                      s   t ttdddddksJ t ttdddddks<J t ttdddddksZJ t ttddd	dd
ksxJ t ttddd ddksJ dd  t fddtdksJ dd tfddtdksJ d S )NZ1123rY   rX   r   r   rp   r!  r   r   r\   re   c                  S   s:   dD ]0} t d|  tg dd| dD ]}t d| q$qd S )NNr   rX   r   rp   	ordered =r   rY   r      )r  r%   Z
orderedvalr   rS   rS   rT   test1  s    
ztest_kbins.<locals>.test1c                      s     S r   rS   rS   )r\  rS   rT   rg     rh   ztest_kbins.<locals>.<lambda>a#          ordered = None
            [[0], [0, 1]]
            [[0, 0], [1]]
        ordered = 0
            [[0, 0], [1]]
            [[0, 1], [0]]
        ordered = 1
            [[0], [0, 1]]
            [[0], [1, 0]]
            [[1], [0, 0]]
        ordered = 10
            [[0, 0], [1]]
            [[1], [0, 0]]
            [[0, 1], [0]]
            [[0], [0, 1]]
        ordered = 11
            [[0], [0, 1]]
            [[0, 0], [1]]
            [[0], [1, 0]]
            [[0, 1], [0]]
            [[1], [0, 0]]
            [[1, 0], [0]]
c                  S   s>   dD ]4} t d|  tttdd| dD ]}t d| q(qd S )NrX  rY  re   rY   r   rZ  )r  r%   rO   r   r[  rS   rS   rT   test2  s    
ztest_kbins.<locals>.test2c                      s     S r   rS   rS   )r]  rS   rT   rg     rh   a[          ordered = None
            [[0], [1, 2]]
            [[0, 1], [2]]
        ordered = 0
            [[0, 1], [2]]
            [[0, 2], [1]]
            [[0], [1, 2]]
        ordered = 1
            [[0], [1, 2]]
            [[0], [2, 1]]
            [[1], [0, 2]]
            [[1], [2, 0]]
            [[2], [0, 1]]
            [[2], [1, 0]]
        ordered = 10
            [[0, 1], [2]]
            [[2], [0, 1]]
            [[0, 2], [1]]
            [[1], [0, 2]]
            [[0], [1, 2]]
            [[1, 2], [0]]
        ordered = 11
            [[0], [1, 2]]
            [[0, 1], [2]]
            [[0], [2, 1]]
            [[0, 2], [1]]
            [[1], [0, 2]]
            [[1, 0], [2]]
            [[1], [2, 0]]
            [[1, 2], [0]]
            [[2], [0, 1]]
            [[2, 0], [1]]
            [[2], [1, 0]]
            [[2, 1], [0]]
)r   rO   r%   r   r   rS   rS   )r\  r]  rT   
test_kbins  s    r^  c                   C   sr   t t du sJ t ttddu s*J t g ddu s>J t dgdggdu sVJ t dgdggdu snJ d S )NFre   r   TrX   rY   )r"   r   rO   r   rS   rS   rS   rT   test_has_dups'  s
    r_  c                  C   s   t dg dddgddgdggks&J t dg ddddgddgdggksNJ dg df} t dg| R  ddgddgdggksJ d S )	Nr+  )rX   r   rX   rY   r   r   er   r  dre   )r   )outputrS   rS   rT   test__partition/  s    

rc  c               	   C   s   ddl m}  t}t|ddg gks(J t|ddg gks@J tddD ]j}d gttd| D ]P}tdd |||dD tdd |||dD   kr| ||ksbn J qbqJd S )Nr   )nTrX   r   c                 s   s   | ]
}d V  qdS rX   NrS   r   rS   rS   rT   r   @  rh   z*test_ordered_partitions.<locals>.<genexpr>c                 s   s   | ]
}d V  qdS re  rS   r   rS   rS   rT   r   A  rh   )Z%sympy.functions.combinatorial.numbersrd  r=   rO   r   r  )rd  r/  r  r  rS   rS   rT   test_ordered_partitions8  s    rf  c                   C   s|   t tdddgddggks J t ttdg dg dg dgksJJ t ttddd	g dg dg dgksxJ d S )
Nr   r   r   re   r   r   r   rZ   )dir)rO   r>   r   rS   rS   rS   rT   test_rotationsE  s     *rh  c                   C   s   t dddgksJ t ddg dks*J t ddddks>J t dddddksTJ tt dd	g d
ksnJ tt ddddg dksJ ttdd  ttdd  d S )Nre   rX   r   T)str11Z011rY   r  )rb   r   r   r   rV   )Z00Z0110rj  c                   S   s   t dS )Ng      ࿩r#   rS   rS   rS   rT   rg   R  rh   ztest_ibin.<locals>.<lambda>c                   S   s
   t ddS )NrY   rX   rl  rS   rS   rS   rT   rg   S  rh   )r#   rO   rH   rq   rS   rS   rS   rT   	test_ibinK  s    rm  c                  C   s   t ddu sJ t ddu s J t d du s0J G dd dt} t |  du sRJ G dd dt}t | du stJ G d	d
 d
}t | du sJ G dd d}t | du sJ G dd d}t | du sJ G dd d|}t | du sJ d S )Nr   FrX   c                   @   s   e Zd ZdS )ztest_iterable.<locals>.Test1Nri   rS   rS   rS   rT   Test1[  s   rn  c                   @   s   e Zd ZdZdS )ztest_iterable.<locals>.Test2TNrj   rk   rl   Z	_iterablerS   rS   rS   rT   Test2`  s   rp  Tc                   @   s   e Zd ZdS )ztest_iterable.<locals>.Test3Nri   rS   rS   rS   rT   Test3e  s   rq  c                   @   s   e Zd ZdZdS )ztest_iterable.<locals>.Test4TNro  rS   rS   rS   rT   Test4j  s   rr  c                   @   s   e Zd Zdd ZdS )ztest_iterable.<locals>.Test5c                 s   s
   dV  d S )NrX   rS   )selfrS   rS   rT   __iter__p  s    z%test_iterable.<locals>.Test5.__iter__N)rj   rk   rl   rt  rS   rS   rS   rT   Test5o  s   ru  c                   @   s   e Zd ZdZdS )ztest_iterable.<locals>.Test6FNro  rS   rS   rS   rT   Test6u  s   rv  )r@   rA   )rn  rp  rq  rr  ru  rv  rS   rS   rT   test_iterableV  s    rw  c                   C   sJ  t tdgddgggksJ t tddgdddgggks@J t tddgddgdgggksdJ t tg ddg dggksJ t tg dddgddggddgdgggksJ t tg dddgdgdgggksJ t tg dg ksJ t tg dg ksJ t tddgdg ks*J t tddgdg ksFJ d S )NrX   rY   rt   re   r   )rO   rC   rS   rS   rS   rT   test_sequence_partitions{  s    "$"(rx  c                   C   s  t tg dg ggksJ t tg dg g ggks6J t tg dg g g ggksTJ t tdgddgggksrJ t tdgdg dggdgg ggksJ t tdgdg g dggg dgg gdgg g ggksJ t tddgdddgggksJ t tddgdg ddggdgdggddgg ggks,J t tddgdg g ddggg dgdggg ddgg gdgg dggdgdgg gddgg g ggksJ t tg ddg dggksJ t tg ddg g dgdgddggddgdggg dg ggksJ t tg ddg g g dgg dgddggg ddgdggg g dg gdgg ddggdgdgdggdgddgg gddgg dggddgdgg gg dg g gg
ksJ t tg dg ksJ t tdgdg ksJ t tddgdg ksJ d S )NrX   rY   re   rt   r   )rO   rD   rC   rS   rS   rS   rT   test_sequence_partitions_empty  s<    ( " 
$$$.
	ry  N)textwrapr   	itertoolsr   r   Zsympy.core.basicr   Zsympy.core.numbersr   Zsympy.core.sortingr   Zsympy.core.symbolr	   r
   Z(sympy.functions.combinatorial.factorialsr   Zsympy.matrices.denser   Zsympy.combinatoricsr   r   r   rN   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   Zsympy.utilities.enumerativerE   rF   Zsympy.core.singletonrG   Zsympy.testing.pytestrH   rI   wrQ   rP   rr   rU   r]   rs   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r"  r#  r*  r.  r9  r:  r;  r?  r@  rB  rJ  rN  rP  rW  r^  r_  rc  rf  rh  rm  rw  rx  ry  rS   rS   rS   rT   <module>   sv   (				BA+
!
	N	%