a
    <b                     @   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@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZH d dlImJZJmKZK d dlLmMZM d dlNmOZOmPZP ed\ZQZRZSZTdd ZUdd ZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\dd  Z]d!d" Z^d#d$ Z_d%d& Z`d'd( Zad)d* Zbd+d, Zcd-d. Zdd/d0 Zed1d2 Zfd3d4 Zgd5d6 Zhd7d8 Zid9d: Zjd;d< Zkd=d> Zld?d@ ZmdAdB ZndCdD ZodEdF ZpdGdH ZqdIdJ ZrdKdL ZsdMdN ZtdOdP ZudQdR ZvdSdT ZwdUdV ZxdWdX ZydYdZ Zzd[d\ Z{d]d^ Z|d_d` Z}dadb Z~dcdd Zdedf ZdgS )h    )dedent)isliceproduct)Basic)Integerordered)Dummysymbols	factorial)Matrix)RGS_enum
RGS_unrankPermutation)2
_partition_set_partitionsbinary_partitions	braceletscapturecartescommon_prefixcommon_suffixconnected_components
dict_mergefilter_symbolsflattengenerate_bellgenerate_derangementsgenerate_involutionsgenerate_oriented_forestgrouphas_dupsibiniproductkbinsminlexmultisetmultiset_combinationsmultiset_partitionsmultiset_permutations	necklacesnumbered_symbols
partitionspermutations	postfixesprefixesreshaperotate_leftrotate_rightrunssiftstrongly_connected_componentssubsetstaketopological_sort	unflattenuniq
variationsordered_partitions	rotationsis_palindromiciterableNotIterablemultiset_derangements)factoring_visitormultiset_partitions_taocp)S)raiseswarns_deprecated_sympyzw,x,y,zc                  C   s   ddl m} m} t , t|ttgttgks4J W d    n1 sH0    Y  t , tttg| dttgksvJ W d    n1 s0    Y  d S )Nr   default_sort_keyr   key)sympy.utilities.iterablesrI   r   rG   listyxsortedrH    rQ   t/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/utilities/tests/test_iterables.pytest_deprecated_iterables    s
    :rS   c                   C   s   t dsJ t dsJ t ds$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 rO   xxZxyxZxyZxyzxZxxyzzyx         Zxxyzyx   )r?   rQ   rQ   rQ   rR   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)rV   rV   rV   rX   rV   rW   r   r   r   Zlevels)r]   r_   r`   rW   )r^   rX   rV   rW   r   r      c                      s   t  ddS )NrX   ra   )r   rQ   ZlsrQ   rR   <lambda>C       ztest_flatten.<locals>.<lambda>c                   @   s   e Zd ZdS )ztest_flatten.<locals>.MyOpN__name__
__module____qualname__rQ   rQ   rQ   rR   MyOpE   s   rj   cls>   rV   rW      )r   rO   rF   
ValueErrorr   rN   zrM   )rj   rQ   rc   rR   test_flatten8   s    $&rp   c                  C   s  t t dgksJ t tg g ks(J t tg dg dksDJ ttddgg dg dksfJ ttddgddgddgg d	ksJ tttjd
u sJ tttjtjd
u sJ dttjv sJ dttjtjv sJ dttjtjtjv sJ ttttjtjtjd} | D ]<\}}}t|t	s<J t|t	sLJ t|t	s"J q"tt
tddgd  D ]"}|ttjtjtjv sxJ qxd S )NrQ   rV   rW   rb   r\   rW   rb   rV   rW   rb      rZ   rV   rb   )rV   rv   )rV   rZ   rW   rb   rW   rv   )rW   rZ   r   r   r   r   r   r   rV   )r   rV   r   r   rV   rV   )rV   r   r   )rV   r   rV   )rV   rV   r   rV   rV   rV   Trt   )rv   rZ   i  r^   rb   )rM   r$   rP   r@   rE   ZIntegerssetr   
isinstancer   r   range)ZtriplesZn1Zn2Zn3trQ   rQ   rR   test_iproductN   s"    "(r   c                   C   sD  t g g ksJ t g ddg ks$J t dgdggks:J t dgdddgksRJ t ddgddggkslJ t ddgdddgksJ t g dg dgksJ t g ddddgksJ t g ddgd	gdggksJ t g dddg d
ksJ t g dddgg ddgddggks"J t g dddg dks@J d S )NF)multiplerV   rV   rV   r_   r   rx   rV   rW   rV   rW   )r   rW   rV   r   )rV   rV   rW   rW   rW   rV   rb   rb   rW   rW   rW   rb   )r_   ry   r   rb   rW   )r!   rQ   rQ   rQ   rR   
test_groupd   s     ,r   c                  C   s  t tg dddgksJ t tg ddg dks:J t tg ddg dksXJ t tg dddgkstJ t td	} t t| dd
ddgksJ t t| dd
dg dksJ t t| dd
dg dksJ t t| dd
dg dksJ tt t| d	d
ddksJ t t| d d dddg ks:J t t| d d dd
dg dksbJ t tddgd
dg dksJ t tddgddg dksJ t tg ddg dksJ t tg ddd
dg dksJ d S )Nrq   r   rQ   rV   rr   rW   )r_   rx   ry   rb   rv   TZ
repetitionr   r\   rs   rt   )
r`   r   rV   r   rW   r   rb   r   r_   rx   rW   rW   ry   rb   rb   )r|   r}   )r   r   rW   )r   r   rb   r~   r   rV   rW   r   rV   rb   )r   rW   rW   r   rW   rb   )r   rb   rb   r   rV   rV   rW   rV   rV   rb   rV   rW   rW   rq   )rV   rb   rb   r   )rW   rW   rb   )rW   rb   rb   )rb   rb   rb   #   F)r|   r}   r~   r   )rQ   r\   rs   r   r_   r   )rQ   r\   rs   r_   )r   r_   rx   r   ry   r   )rM   r7   r   lenlrQ   rQ   rR   test_subsetsy   s0    
 $(


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 )Nrv   r   Fr   rQ   rV   r   rW   )r   r   r   rV   r   r_   rx   rW   r   r   ry   rb   r   rb   rV   r   rb   )r   r   r   rW   rV   r   r   rb   rV   )r   rb   rW   rV   r   rW   )rV   r   rb   rV   rW   r   rq   )rV   rb   r   )rV   rb   rW   rW   r   rV   )rW   r   rb   rW   rV   r   )rW   rV   rb   )rW   rb   r   )rW   rb   rV   )rb   r   rV   )rb   r   rW   )rb   rV   r   )rb   rV   rW   )rb   rW   r   rb   rW   rV   T)r`   r   r   r   r   r   r_   rx   r   r   r   ry   r   r   r   r   @      r{   )rM   r   r<   r   r   rQ   rQ   rR   test_variations   s     $r   c                   C   s   t tddgg dg dks"J t t dgks6J t tddgksLJ t tdddd	gksfJ t tt tdd
dgksJ d S )NrV   rW   ru   rw   rQ   a)r   )repeat)r   r   r   r\   )rM   r   r   rQ   rQ   rQ   rR   test_cartes   s    r   c                  C   s2   t  } t| td}t|dttdks.J d S )Nzx0 x2 x3rb   zx1 x4 x5)r,   r   r
   r8   rM   )sfilteredrQ   rQ   rR   test_filter_symbols   s    r   c                  C   sD   t td} tt| tsJ tt ddtdgdtdks@J d S )Nrk   CrV   ZC1)startexcludeZC2)r,   r	   r   nextr
   )r   rQ   rQ   rR   test_numbered_symbols   s
    
r   c                   C   s   t ttddd ddgg ddks,J t ttgdd tgtgd	ksPJ t tjgd
d ddgikspJ t g ddd ddddgddgfksJ t g ddd dddgg dfksJ ttdd  d S )NrZ   c                 S   s   | d S NrW   rQ   _rQ   rQ   rR   rd      re   ztest_sift.<locals>.<lambda>rV   rb   )r   rW   rv   r   c                 S   s
   |  tS NZhasrO   r   rQ   rQ   rR   rd      re   )FTc                 S   s
   |  tS r   r   r   rQ   rQ   rR   rd      re   Fr   rV   rW   rb   c                 S   s   | d S r   rQ   rO   rQ   rQ   rR   rd      re   Tbinaryr   rW   c                 S   s   | d dkS )Nrb   rV   rQ   r   rQ   rQ   rR   rd      re   r   c                   S   s   t g ddd ddS )Nr   c                 S   s   | d S )Nrb   rQ   r   rQ   rQ   rR   rd      re   z-test_sift.<locals>.<lambda>.<locals>.<lambda>Tr   )r5   rQ   rQ   rQ   rR   rd      s    )	r5   rM   r   rO   rN   rE   ZOnerF   rn   rQ   rQ   rQ   rR   	test_sift   s    ,$ 


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 )NrZ   zx0:5zx5:10rV   rW   rb   rv   rZ   )r,   r8   rM   r
   )XrQ   rQ   rR   	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 )NrV   rW   r_   )r   rO   rN   ro   rQ   rQ   rQ   rR   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 )NrV   rW   r   rq   rV   rW   rb   rv   )rM   r0   rQ   rQ   rQ   rR   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 )NrV   rW   r   rZ   rv   ru   )rW   rb   rv   rZ   )rM   r/   rQ   rQ   rQ   rR   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)rW   rb   rZ         	   
   rm   )	)r   rm   r   r   )rZ   rm   )rb   r   )rb   r   )rm   rW   )rm   r   )rm   r   )r   r   )rb   rZ   r   r   rm   rW   r   r   c                 S   s   |  S r   rQ   )vrQ   rQ   rR   rd     re   z'test_topological_sort.<locals>.<lambda>rJ   )r   rZ   rm   rb   r   r   r   rW   c                      s   t  dg fS )N)r   r   )r9   rQ   EVrQ   rR   rd     re   )r9   rF   rn   rQ   rQ   r   rR   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 )
Nrq   rV   rW   rb   r_   rx   r   ry   r   r   r_   ry   r   rb   rv   rv   )r_   r   r   )rv   rb   )r6   r   r   rQ   rQ   rR   "test_strongly_connected_components  s    $"r   c                  C   s   t g g fg ksJ t g dg fdgdgdggks8J g d} g d}t | |fg dgksbJ g d} g d}t | |fg dgksJ g d} dd	g}t | |fddgdd
ggksJ d S )Nrq   rV   rW   rb   r   r   r   r_   r   rv   )r   r   rQ   rQ   rR   test_connected_components  s    $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   rV   rW   rb   rv   rW   )rW   rb   rv   r   rV   rV   )rv   r   rV   rW   rb   )r2   r3   append)ABrQ   rQ   rR   test_rotate0  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}t dd tdD |kstJ dgd dgd!dgdd"gg d#g d$g d%g}t d&d tddgD |ksJ d S )'Nr   rZ   r   rV   rW   rb   rv   r      )rV   rV   rV   rW   rW   )rV   rV   rV   rW   r   )rV   rV   rW   rW   r   r   r   rq   )rV   rW   rv   rV   rb   rv   rW   rb   rv   r   r   r   abbaaa)$)Zmpsyy)ZmpsyrN   )mpsyy)r   rN   rN   )Zmpyyr   )mpysy)r   r   rN   )mpsyy)r   r   rN   )r   r   r   )r   r   rN   rN   )Zmsyyp)msypy)r   r   rN   )mspyy)r   r   rN   )r   r   r   )r   r   rN   rN   )myyps)r   r   r   )mypsy)r   r   rN   )r   r   r   )r   r   r   )r   r   r   rN   )mZpsyy)r   r   rN   )r   r   r   )r   r   rN   rN   )r   r   r   )r   r   r   )r   r   r   rN   )r   r   r   )r   r   r   rN   )r   r   r   r   )r   r   r   rN   rN   c                 s   s    | ]}t d d |D V  qdS )c                 s   s   | ]}d  |V  qdS rT   Njoin).0partrQ   rQ   rR   	<genexpr>z  re   z5test_multiset_partitions.<locals>.<genexpr>.<genexpr>N)tupler   r   rQ   rQ   rR   r   z  s   z+test_multiset_partitions.<locals>.<genexpr>Zsympy   r      rY   )rv   rW   rb   )rY   rW   rW   )rW   rW   rW   rb   c                 s   s   | ]}t |d dgV  qdS )rW   rb   N)rC   r   rQ   rQ   rR   r   ~  s   )rM   r)   r   rP   rD   )r   r   ansZ
factoringsrQ   rQ   rR   test_multiset_partitions@  sz    ,&
&&(
,$*"

 & ( $

r   c                  C   s   g d} dd t tddD | ks(J td}dd t t|dD | ksPJ dd t|dD g kslJ t td	gd
dggd
d	gd
dgggksJ tt tdddksJ tt tddd	ksJ t tdd	dgdgdggksJ ttdd  d S )N)ZiiiZiimZiipZiisimpZimsZippipsZissZmppr   ZmssZppsZpssZsssc                 S   s   g | ]}d  |qS rT   r   r   irQ   rQ   rR   
<listcomp>  re   z.test_multiset_combinations.<locals>.<listcomp>Zmississippirb   c                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r    re   c                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r    re      rV   rW   r   r   abcr   cc                   S   s   t tddddS )Nrb   rX   r   rW   )rM   r(   rQ   rQ   rQ   rR   rd     re   z,test_multiset_combinations.<locals>.<lambda>)rM   r(   r'   r   rF   rn   )r   MrQ   rQ   rR   test_multiset_combinations  s$    ,"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  rQ   rQ   rR   r    re   z.test_multiset_permutations.<locals>.<listcomp>r  c                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r    re   r|   rW   r   r   rV   r   rb   rT   rX   c                  S   s8   t ddD ](} t|  tg d| D ]}t| q$q
d S )NrV   r   )r   r   rV   r   rV   )r   printr*   )r  r   rQ   rQ   rR   test  s    z(test_multiset_permutations.<locals>.testc                      s     S r   rQ   rQ   r  rQ   rR   rd     re   z,test_multiset_permutations.<locals>.<lambda>a          1
        [0]
        [1]
        2
        [0, 0]
        [0, 1]
        [1, 0]
        [1, 1]
        3
        [0, 0, 0]
        [0, 0, 1]
        [0, 1, 0]
        [0, 1, 1]
        [1, 0, 0]
        [1, 0, 1]
        [1, 1, 0]
        4
        [0, 0, 0, 1]
        [0, 0, 1, 0]
        [0, 0, 1, 1]
        [0, 1, 0, 0]
        [0, 1, 0, 1]
        [0, 1, 1, 0]
        [1, 0, 0, 0]
        [1, 0, 0, 1]
        [1, 0, 1, 0]
        [1, 1, 0, 0]
        5
        [0, 0, 0, 1, 1]
        [0, 0, 1, 0, 1]
        [0, 0, 1, 1, 0]
        [0, 1, 0, 0, 1]
        [0, 1, 0, 1, 0]
        [0, 1, 1, 0, 0]
        [1, 0, 0, 0, 1]
        [1, 0, 0, 1, 0]
        [1, 0, 1, 0, 0]
        [1, 1, 0, 0, 0]
        6
c                   S   s   t tdddS )Nrb   rX   r   )rM   r*   rQ   rQ   rQ   rR   rd     re   )r*   r'   rM   r   r   r   rF   rn   )r   nulrQ   r  rR   test_multiset_permutations  s"     $
(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dd tdddD dd	iddd
ddd
ddigksJ dd td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shJ dd td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 dd ttd	ddD d	diddd
gks J dd tdd	dD dddddiddd
ddig  krTdd tdD ksZn J t ddD ]L}d}t|D ]&\}}|t||ksJ |d7 }qt|t|ksdJ qdd S )Nr   rW   )sizerV   rY   c                 S   s   g | ]}|qS rQ   rQ   r   rQ   rQ   rR   r    re   z#test_partitions.<locals>.<listcomp>)krb   r_   rv   c                 S   s   g | ]}|qS rQ   rQ   r   rQ   rQ   rR   r    re   rq   rx   c                 S   s   g | ]}|qS rQ   rQ   r   rQ   rQ   rR   r    re   r   )r  r   r   rz   ry   c                 S   s2   g | ]*}t d d |D rt| dkr|qS )c                 s   s   | ]}|d kV  qdS )rv   NrQ   r   r  rQ   rQ   rR   r     re   -test_partitions.<locals>.<listcomp>.<genexpr>rb   )allsumvaluesr  rQ   rQ   rR   r    s   c                 S   s   g | ]}|qS rQ   rQ   r   rQ   rQ   rR   r    re   )r   c                 S   s   g | ]}|qS rQ   rQ   r  rQ   rQ   rR   r    re   c                 S   s"   g | ]}t d d |D r|qS )c                 s   s   | ]}|d kV  qdS )rb   NrQ   r  rQ   rQ   rR   r     re   r  )r  r  rQ   rQ   rR   r    s   )r   rM   r-   rE   r   r   r   )r   r  nr   qrQ   rQ   rR   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   rQ   r  rQ   rQ   rR   r    re   z*test_binary_partitions.<locals>.<listcomp>r   r   rW   )r   rV   rV   )rv   rv   rW   )rv   rv   rV   rV   )rv   rW   rW   rW   )rv   rW   rW   rV   rV   )rv   rW   rV   rV   rV   rV   )rv   rV   rV   rV   rV   rV   rV   )rW   rW   rW   rW   rW   )rW   rW   rW   rW   rV   rV   )rW   rW   rW   rV   rV   rV   rV   )rW   rW   rV   rV   rV   rV   rV   rV   )	rW   rV   rV   rV   rV   rV   rV   rV   rV   )
rV   rV   rV   rV   rV   rV   rV   rV   rV   rV   c                 S   s   g | ]}|d d  qS r   rQ   r   jrQ   rQ   rR   r    re      $   )r   r   rQ   rQ   rQ   rR   test_binary_partitions  s    
r  c                  C   s   dd t ddD dd t ddD ks,J ttdg dksDJ t ddD ]<} tt | }t| }|D ]}|t|jksJ | }qjqNttd	d
  d S )Nc                 S   s   g | ]}t tt|qS rQ   )r   r   r   r  rQ   rQ   rR   r  	  re   z"test_bell_perm.<locals>.<listcomp>rV   r   c                 S   s   g | ]}t |qS rQ   r   r  rQ   rQ   rR   r  	  s   rb   )r   r   r   r   r   r   rZ   c                   S   s   t tdS )Nr   )rM   r   rQ   rQ   rQ   rR   rd     re   z test_bell_perm.<locals>.<lambda>)	r   rM   r   r   r   Z
array_formZnext_trotterjohnsonrF   rn   )r  r   r   ZbirQ   rQ   rR   test_bell_perm  s    r   c                  C   sX   g d} t | D ]B\}}tt|d }t||ks8J tdd |D dksJ qd S )N)rV   rW   rv   r      L   rV   c                 S   s   h | ]}t |d  qS rs   )r   r  rQ   rQ   rR   	<setcomp>  re   z#test_involutions.<locals>.<setcomp>)	enumeraterM   r   r   )lengthsr  Nr  rQ   rQ   rR   test_involutions  s
    r'  c                  C   s  t ttttddks J ddd tdD dks@J ttg dg d	g d
g dg dg dg dg dg dg dg	ksJ ttg dg dg dgksJ ttdtdgksJ t} t| dg ksJ dd | dD dgksJ dd | dD ddgks"J dd | dD d gks@J d!d | d"D g d#ks`J d$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 )-NrY   i	  rT   c                 s   s   | ]}d  |V  qdS r   r   r  rQ   rQ   rR   r   #  re   z$test_derangements.<locals>.<genexpr>abcdeZbadecbaecdbcaedbcdeabceadbdaecbdeacbdecabeacdbedacbedcacabedcadebcaebdcdaebcdbeacdeabcdebaceabdcebadcedabcedbadabecdaebcdaecbdcaebdcbeadceabdcebadeabcdeacbdebacdebcaeabcdeadbceadcbecabdecbadecdabecdbaedabcedacbedbacedbcar   )rV   r   rb   rW   )rV   rW   rb   r   )rV   rb   r   rW   )rW   r   rb   rV   )rW   rb   r   rV   )rW   rb   rV   r   )rb   r   rV   rW   )rb   rW   r   rV   )rb   rW   rV   r   )r   rV   rW   rW   )rW   rW   r   rV   )rW   rW   rV   r   bar   Zabbc                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r  1  re   z%test_derangements.<locals>.<listcomp>c                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r  2  re   r  ZbcaZcabc                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r  3  re   ZaabbZbbaac                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r  4  re   Zaabbcccc)ZccccaabbZccccababZccccabbaZccccbaabZccccbabaZccccbbaac                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r  7  re   Zaabbccc)ZcccabbaZcccababZcccaabbZccacbbaZccacbabZccacabbZcbccbaaZcbccabaZcbccaabZbcccbaaZbcccabaZbcccaabc                 S   s   g | ]}d  |qS r  r   r  rQ   rQ   rR   r  ;  re   Zbooks)ZkbsooZksbooZsbkooZskbooZoksboZoskboZokbsoZobksoZoskobZoksobZosbokZobsokrb   rW   rV   )r   rM   r   r   r   rB   )DrQ   rQ   rR   test_derangements!  s.     

    $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   rM   r+   )r  r  frQ   rQ   rR   countC  s    ztest_necklaces.<locals>.countrV   r   rW   r   rb   )rV   rW   rW   rb   )rW   rb   rb   rY   )rb   rv   rv   r   )rv   rY   rY      )rZ   r   r   '   )rY         \   )r            )r   r   r   )r-  r   r  rQ   rQ   rR   test_necklacesB  s     r6  c                  C   s   dd t d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sdJ dd t ddD } t| tg d	g d
g dg dg dg dgksJ d S )Nc                 S   s   g | ]}|qS rQ   rQ   r  rQ   rQ   rR   r  T  re   z"test_bracelets.<locals>.<listcomp>rW   rv   r   rV   rb   c                 S   s   g | ]}|qS rQ   rQ   r  rQ   rQ   rR   r  a  re   )r   r   r   r   )r   r   r   rV   )r   r   rV   rV   )r   rV   r   rV   )r   rV   rV   rV   )rV   rV   rV   rV   )r   r   )ZbcrQ   rQ   rR   test_braceletsS  s,    r7  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 )NrZ   r   )r   rV   rW   rb   rb   )r   rV   rW   rb   rW   )r   rV   rW   rb   rV   )r   rV   rW   rb   r   )r   rV   rW   rW   rW   )r   rV   rW   rW   rV   )r   rV   rW   rW   r   )r   rV   rW   rV   rW   )r   rV   rW   rV   rV   )r   rV   rW   rV   r   )r   rV   rW   r   rV   )r   rV   rW   r   r   )r   rV   rV   rV   rV   )r   rV   rV   rV   r   )r   rV   rV   r   rV   )r   rV   rV   r   r   )r   rV   r   rV   r   )r   rV   r   r   r   )r   r   r   r   r   r   i2  )rM   r    r   rQ   rQ   rQ   rR   test_generate_oriented_forestl  s    
r8  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   rW   rV   rZ   c                   S   s   t ttddS )Nr   rb   r:   rM   r   rQ   rQ   rQ   rR   rd   z  re   z test_unflatten.<locals>.<lambda>c                   S   s   t ttddS )Nr   r^   r9  rQ   rQ   rQ   rR   rd   {  re   )rM   r   r:   zipr   rF   rn   )rrQ   rQ   rR   test_unflattenv  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 )NrV   rb   r   rv   rq   )rV   rW   rZ   rW   )rV   rb   rZ   )r   rW   rb   )r   r   rb   )r   rM   r   r   rQ   rQ   rQ   rR   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   rJ   )r  r   r>  r   )r&   r   rQ   rQ   rQ   rR   test_minlex  s    r?  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   rW   rV   c                 S   s   t | S r   )r   r   rQ   rQ   rR   rd     re   ztest_ordered.<locals>.<lambda>c                 S   s   t | S r   )r  r   rQ   rQ   rR   rd     re   r@  warnc                      s   t t dddS )NFTrA  )rM   r   rQ   keysseqrQ   rR   rd     s    )rM   r   rO   rN   hashrF   rn   rQ   rQ   rC  rR   test_ordered  s    *rG  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 )NrV   r   rW   r   )rW   rV   rV   r   lt)r4   operatorrI  rH  rQ   rQ   rR   	test_runs  s     rK  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 )NrV   r   rv   r   )rZ   rY   r   r   )rv   r   rW   rb   rZ   rY   r   r   rs   r_   )rZ   rY   r   r   r   )rV   rt   rV   r   r   )r   )r   r   r   rm   c                   S   s   t ddgdgS )Nr   rV   rX   r1   rQ   rQ   rQ   rR   rd     re   ztest_reshape.<locals>.<lambda>c                   S   s   t ddgdgS )Nr   rV   rb   rL  rQ   rQ   rQ   rR   rd     re   )rM   r   r1   r   rF   rn   )rE  rQ   rQ   rR   test_reshape  s<    



rM  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   rQ   r   rQ   rQ   rR   r     re   ztest_uniq.<locals>.<genexpr>rv   rV   rx   rW   r_   c                 s   s   | ]}|d  V  qdS )rW   NrQ   )r   rO   rQ   rQ   rR   r     re   rZ   r   r   Zababcr  c                 s   s   | ]
}|V  qd S r   rQ   r  rQ   rQ   rR   r     re   rb   c                      s    fddt  D S )Nc                    s   g | ]}  |qS rQ   remover  r,  rQ   rR   r    re   /test_uniq.<locals>.<lambda>.<locals>.<listcomp>r;   rQ   rP  rQ   rR   rd     re   ztest_uniq.<locals>.<lambda>c                      s    fddt  D S )Nc                    s   g | ]}  |qS rQ   rN  r  rP  rQ   rR   r    re   rQ  rR  rQ   rP  rQ   rR   rd     re   )rM   r;   r-   r   r.   rF   RuntimeErrorrQ   rQ   rP  rR   	test_uniq  s"    $&,  
&
rT  c                      s   t ttdddddksJ t ttdddddks<J t ttdddddksZJ t ttddd	dd
ksxJ t ttddd ddksJ dd  t fddtdksJ dd tfddtdksJ d S )NZ1123rW   rV   r   r   rm   r  r   r   rZ   rb   c                  S   s:   dD ]0} t d|  tg dd| dD ]}t d| q$qd S )NNr   rV   r   rm   	ordered =r}   rW   r      )r  r%   Z
orderedvalr   rQ   rQ   rR   test1  s    
ztest_kbins.<locals>.test1c                      s     S r   rQ   rQ   )rY  rQ   rR   rd     re   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 )NrU  rV  rb   rW   r   rW  )r  r%   rM   r   rX  rQ   rQ   rR   test2  s    
ztest_kbins.<locals>.test2c                      s     S r   rQ   rQ   )rZ  rQ   rR   rd     re   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   rM   r%   r   r   rQ   rQ   )rY  rZ  rR   
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 )NFrb   r   TrV   rW   )r"   r   rM   r   rQ   rQ   rQ   rR   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(  )rV   r   rV   rW   r   r   er   r  drb   )r   )outputrQ   rQ   rR   test__partition.  s    

r`  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   )nTrV   r   c                 s   s   | ]
}d V  qdS rV   NrQ   r   rQ   rQ   rR   r   ?  re   z*test_ordered_partitions.<locals>.<genexpr>c                 s   s   | ]
}d V  qdS rb  rQ   r   rQ   rQ   rR   r   @  re   )Z%sympy.functions.combinatorial.numbersra  r=   rM   r   r  )ra  r,  r  r  rQ   rQ   rR   test_ordered_partitions7  s    rc  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   rb   r   r   r   rX   )dir)rM   r>   r   rQ   rQ   rQ   rR   test_rotationsD  s     *re  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 )Nrb   rV   r~   T)str11Z011rW   r  )r`   r   r   r   rT   )Z00Z0110rg  c                   S   s   t dS )Ng      ࿩r#   rQ   rQ   rQ   rR   rd   Q  re   ztest_ibin.<locals>.<lambda>c                   S   s
   t ddS )NrW   rV   ri  rQ   rQ   rQ   rR   rd   R  re   )r#   rM   rF   rn   rQ   rQ   rQ   rR   	test_ibinJ  s    rj  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   FrV   c                   @   s   e Zd ZdS )ztest_iterable.<locals>.Test1Nrf   rQ   rQ   rQ   rR   Test1Z  s   rk  c                   @   s   e Zd ZdZdS )ztest_iterable.<locals>.Test2TNrg   rh   ri   Z	_iterablerQ   rQ   rQ   rR   Test2_  s   rm  Tc                   @   s   e Zd ZdS )ztest_iterable.<locals>.Test3Nrf   rQ   rQ   rQ   rR   Test3d  s   rn  c                   @   s   e Zd ZdZdS )ztest_iterable.<locals>.Test4TNrl  rQ   rQ   rQ   rR   Test4i  s   ro  c                   @   s   e Zd Zdd ZdS )ztest_iterable.<locals>.Test5c                 s   s
   dV  d S )NrV   rQ   )selfrQ   rQ   rR   __iter__o  s    z%test_iterable.<locals>.Test5.__iter__N)rg   rh   ri   rq  rQ   rQ   rQ   rR   Test5n  s   rr  c                   @   s   e Zd ZdZdS )ztest_iterable.<locals>.Test6FNrl  rQ   rQ   rQ   rR   Test6t  s   rs  )r@   rA   )rk  rm  rn  ro  rr  rs  rQ   rQ   rR   test_iterableU  s    rt  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   rL   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   Zsympy.utilities.enumerativerC   rD   Zsympy.core.singletonrE   Zsympy.testing.pytestrF   rG   wrO   rN   ro   rS   r[   rp   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r
  r  r  r  r   r'  r+  r6  r7  r8  r<  r=  r?  rG  rK  rM  rT  r[  r\  r`  rc  re  rj  rt  rQ   rQ   rQ   rR   <module>   sr   (				BA+
!
	N	