o
    *ήc                     @   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$ Z_d%d& Z`d'd( Zad)d* Zbd+d, Zcd-d. Zdd/d0 Zed1d2 Zfd3d4 Zgd5d6 Zhd7d8 Zid9d: Zjd;d< Zkd=d> Zld?d@ ZmdAdB ZndCdD ZodEdF ZpdGdH ZqdIdJ ZrdKdL ZsdMdN ZtdOdP ZudQdR ZvdSdT ZwdUdV ZxdWdX ZydYdZ Zzd[d\ Z{d]d^ Z|d_d` Z}dadb Z~dcdd Zdedf ZdgS )h    )dedent)isliceproduct)Basic)Integerordered)Dummysymbols	factorial)Matrix)RGS_enum
RGS_unrankPermutation)2
_partition_set_partitionsbinary_partitions	braceletscapturecartescommon_prefixcommon_suffixconnected_components
dict_mergefilter_symbolsflattengenerate_bellgenerate_derangementsgenerate_involutionsgenerate_oriented_forestgrouphas_dupsibiniproductkbinsminlexmultisetmultiset_combinationsmultiset_partitionsmultiset_permutations	necklacesnumbered_symbols
partitionspermutations	postfixesprefixesreshaperotate_leftrotate_rightrunssiftstrongly_connected_componentssubsetstaketopological_sort	unflattenuniq
variationsordered_partitions	rotationsis_palindromiciterableNotIterablemultiset_derangements)factoring_visitormultiset_partitions_taocp)S)raiseswarns_deprecated_sympyzw,x,y,zc                  C   s   ddl m} m} t  t|ttgttgksJ W d    n1 s$w   Y  t  tttg| dttgks;J W d    d S 1 sFw   Y  d S )Nr   default_sort_keyr   key)sympy.utilities.iterablesrI   r   rG   listyxsortedrH    rQ   K/tmp/pip-target-vg8gfxp4/lib/python/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sJ t drJ t dr$J t dds+J t dd	r2J t dd	d
s:J t dd	dsBJ t ddsIJ t dd	rPJ t dd	dsXJ d S )N rO   xxxyxxyxyzxxxyzzyx         xxyzyx   )r?   rQ   rQ   rQ   rR   test_is_palindromic(   s   r`   c                     s"  t dddgks
J t ttffttgksJ ddgdgg t  dd ks(J t  ddg dks4J t  d	dg d
ks@J t  ddg d
ksLJ tt fdd G dd dt} t | tttg| tttgksoJ t | tttg| dtttgksJ t h dth dksJ d S )N)rZ   rZ   rZ   r\   rZ   r[   r   r   r   levels)rb   rd   re   r[   )rc   r\   rZ   r[   r   r      c                      s   t  ddS )Nr\   rf   )r   rQ   lsrQ   rR   <lambda>C       ztest_flatten.<locals>.<lambda>c                   @      e Zd ZdS )ztest_flatten.<locals>.MyOpN__name__
__module____qualname__rQ   rQ   rQ   rR   MyOpE       rr   cls>   rZ   r[      )r   rO   rF   
ValueErrorr   rN   zrM   )rr   rQ   ri   rR   test_flatten8   s   $$ ry   c                  C   s  t t dgks
J t tg g ksJ t tg dg dks"J ttddgg dg dks3J ttddgddgddgg d	ksGJ tttjd
u sRJ tttjtjd
u s_J dttjv shJ dttjtjv ssJ dttjtjtjv sJ ttttjtjtjd} | D ]\}}}t|t	sJ t|t	sJ t|t	sJ qtt
tddgd  D ]}|ttjtjtjv sJ qd S )NrQ   rZ   r[   rh   ra   r[   rh   rZ   r[   rh      r_   rZ   rh   )rZ   r   )rZ   r_   r[   rh   r[   r   )r[   r_   r   r   r   r   r   r   rZ   )r   rZ   r   r   rZ   rZ   )rZ   r   r   )rZ   r   rZ   )rZ   rZ   r   rZ   rZ   rZ   Tr}   )r   r_   i  rc   rh   )rM   r$   rP   r@   rE   Integerssetr   
isinstancer   r   range)triplesn1n2n3trQ   rQ   rR   test_iproductN   s$   "(r   c                   C   s@  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s)J t ddgddggks6J t ddgdddgksCJ t g dg dgksPJ t g ddddgks]J t g ddgd	gdggksmJ t g dddg d
ks{J t g dddgg ddgddggksJ t g dddg dksJ d S )NF)multiplerZ   rZ   rZ   rd   r   r   rZ   r[   rZ   r[   )r   r[   rZ   r   )rZ   rZ   r[   r[   r[   rZ   rh   rh   r[   r[   r[   rh   )rd   r   r   rh   r[   )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s,J t tg dddgks:J t td	} t t| dd
ddgksNJ t t| dd
dg dks]J t t| dd
dg dkslJ t t| dd
dg dks{J tt t| d	d
ddksJ t t| d d dddg ksJ t t| d d dd
dg dksJ 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 )Nrz   r   rQ   rZ   r{   r[   )rd   r   r   rh   r   T
repetitionr   ra   r|   r}   )
re   r   rZ   r   r[   r   rh   r   rd   r   r[   r[   r   rh   rh   )r   r   )r   r   r[   )r   r   rh   r   r   rZ   r[   r   rZ   rh   )r   r[   r[   r   r[   rh   )r   rh   rh   r   rZ   rZ   r[   rZ   rZ   rh   rZ   r[   r[   rz   )rZ   rh   rh   r   )r[   r[   rh   )r[   rh   rh   )rh   rh   rh   #   F)r   r   r   r   )rQ   ra   r|   r   rd   r   )rQ   ra   r|   rd   )r   rd   r   r   r   r   )rM   r7   r   lenlrQ   rQ   rR   test_subsetsy   s0   
"&r   c                  C   sb  t td} t t| ddddgksJ t t| dddg dks#J t t| dddg d	ks2J t t| d
ddg dksAJ t t| ddddgksOJ t t| dddg dks^J t t| dddg dksmJ tt t| d
dddks|J tt t| ddddksJ t t| d d d
ddg ksJ t t| d d d
ddg dksJ d S )Nr   r   Fr   rQ   rZ   r   r[   )r   r   r   rZ   r   rd   r   r[   r   r   r   rh   r   rh   rZ   r   rh   )r   r   r   r[   rZ   r   r   rh   rZ   )r   rh   r[   rZ   r   r[   )rZ   r   rh   rZ   r[   r   rz   )rZ   rh   r   )rZ   rh   r[   r[   r   rZ   )r[   r   rh   r[   rZ   r   )r[   rZ   rh   )r[   rh   r   )r[   rh   rZ   )rh   r   rZ   )rh   r   r[   )rh   rZ   r   )rh   rZ   r[   )rh   r[   r   rh   r[   rZ   T)re   r   r   r   r   r   rd   r   r   r   r   r   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sJ t tddgks&J t tdddd	gks3J t tt tdd
dgksCJ d S )NrZ   r[   r~   r   rQ   a)r   )repeat)r   r   r   ra   )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 x3rh   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 )Nrt   CrZ   C1)startexclude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s(J t tjgd
d ddgiks8J t g ddd ddddgddgfksMJ t g ddd dddgg dfksaJ ttdd  d S )Nr_   c                 S      | d S Nr[   rQ   _rQ   rQ   rR   rk          ztest_sift.<locals>.<lambda>rZ   rh   )r   r[   r   r   c                 S   
   |  tS NhasrO   r   rQ   rQ   rR   rk         
 )FTc                 S   r   r   r   r   rQ   rQ   rR   rk      r   Fr   rZ   r[   rh   c                 S   r   r   rQ   rO   rQ   rQ   rR   rk      r   Tbinaryr   r[   c                 S   s   | d dkS )Nrh   rZ   rQ   r   rQ   rQ   rR   rk      rl   r   c                   S   s   t g ddd ddS )Nr   c                 S   r   )Nrh   rQ   r   rQ   rQ   rR   rk      r   z-test_sift.<locals>.<lambda>.<locals>.<lambda>Tr   )r5   rQ   rQ   rQ   rR   rk      s   )	r5   rM   r   rO   rN   rE   OnerF   rw   rQ   rQ   rQ   rR   	test_sift   s   ,$ 


r   c                  C   sX   t  } t| dttdksJ t| dttdksJ tg ddg dks*J d S )Nr_   zx0:5zx5:10rZ   r[   rh   r   r_   )r,   r8   rM   r
   )XrQ   rQ   rR   	test_take   s   r   c                   C   s   t i dtttidtttiksJ t dtttii dtttiks"J t dtidtttidtdtttiks7J t dtttidtidtdtttiksLJ t ttddtttidtdtttiksbJ t dtttittddtdtttiksxJ d S )NrZ   r[   rd   )r   rO   rN   rx   rQ   rQ   rQ   rR   test_dict_merge   s   ""**,0r   c                   C   s   t tg g ks
J t tdgdggksJ t tddgdgddggks(J t tg ddgddgg dg dg dgksBJ d S )NrZ   r[   r   rz   rZ   r[   rh   r   )rM   r0   rQ   rQ   rQ   rR   test_prefixes      "r   c                   C   s   t tg g ks
J t tdgdggksJ t tddgdgddggks(J t tg ddgddgg dg dg dgksBJ d S )NrZ   r[   r   r_   r   r~   )r[   rh   r   r_   )rM   r/   rQ   rQ   rQ   rR   test_postfixes   r   r   c                      s`   g dg d t  fg dksJ t  fdd dg dks$J tt fdd d S )	N)r[   rh   r_         	   
   rv   )	)r   rv   r   r   )r_   rv   )rh   r   )rh   r   )rv   r[   )rv   r   )rv   r   )r   r   )rh   r_   r   r   rv   r[   r   r   c                 S   s   |  S r   rQ   )vrQ   rQ   rR   rk         z'test_topological_sort.<locals>.<lambda>rJ   )r   r_   rv   rh   r   r   r   r[   c                      s   t  dg fS )N)r   r   )r9   rQ   EVrQ   rR   rk         )r9   rF   rw   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sJ g d} g d}t | |fg dgks1J g d} g d}t | |fdgddgdggksJJ g d} g d	}t | |fddgddggksbJ d S )
Nrz   rZ   r[   rh   rd   r   r   r   r   r   rd   r   r   rh   r   r   )rd   r   r   )r   rh   )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sJ g d} g d}t | |fg dgks1J g d} g d}t | |fg dgksFJ g d} dd	g}t | |fddgdd
ggks^J d S )Nrz   rZ   r[   rh   r   r   r   rd   r   r   )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sJ g } t| d}|g ks'J |d | g ks2J t | d}|g ks=J |d | g ksHJ d S )Nr   rZ   r[   rh   r   r[   )r[   rh   r   r   rZ   rZ   )r   r   rZ   r[   rh   )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sJ tt t| ddks'J tt t| dd	ks4J 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sbJ 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sJ 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s"J t tdgd ddgddgggks7J t tdgd g dgdgddggdgdgdgggksVJ g d}t t|t tt|kskJ t t|dg kswJ t t|dg dggksJ t t|dg dg ksJ t t|dg dg dggksJ t tddg ksJ 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s#J g d}t dd tdD |ks7J dgd dgd!dgdd"gg d#g d$g d%g}t d&d tddgD |ks_J d S )'Nr   r_   r   rZ   r[   rh   r   r      )rZ   rZ   rZ   r[   r[   )rZ   rZ   rZ   r[   r   )rZ   rZ   r[   r[   r   r   r   rz   )rZ   r[   r   rZ   rh   r   r[   rh   r   r   r   r   abbaaa)$)mpsyy)mpsyrN   )mpsyy)r   rN   rN   )mpyyr   )mpysy)r  r   rN   )mpsyy)r  r  rN   )r  r   r  )r  r   rN   rN   )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   )m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       | ]}d  |V  qdS rT   Njoin).0partrQ   rQ   rR   	<genexpr>z      z5test_multiset_partitions.<locals>.<genexpr>.<genexpr>N)tupler  r  rQ   rQ   rR   r  z  s    z+test_multiset_partitions.<locals>.<genexpr>sympy   r      r]   )r   r[   rh   )r]   r[   r[   )r[   r[   r[   rh   c                 s   s    | ]
}t |d dgV  qdS )r[   rh   N)rC   r  rQ   rQ   rR   r  ~  s    )rM   r)   r   rP   rD   )r   r   ans
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s(J dd t|dD g ks6J t td	gd
dggd
d	gd
dgggksLJ tt tdddksYJ tt tddd	ksfJ t tdd	dgdgdggkswJ ttdd  d S )N)iiiiimiipiisimpimsippipsissmppr   mssppspsssssc                 S      g | ]}d  |qS rT   r  r  irQ   rQ   rR   
<listcomp>      z.test_multiset_combinations.<locals>.<listcomp>mississippirh   c                 S   r1  r2  r  r3  rQ   rQ   rR   r5    r6  c                 S   r1  r2  r  r3  rQ   rQ   rR   r5    r6     rZ   r[   r   r   abcr   cc                   S   s   t tddddS )Nrh   r\   r   r[   )rM   r(   rQ   rQ   rQ   rR   rk     s    z,test_multiset_combinations.<locals>.<lambda>)rM   r(   r'   r   rF   rw   )r   MrQ   rQ   rR   test_multiset_combinations  s$   ,"r<  c                     sr  g d} dd t dD | ksJ dd t tdD | ks J tt g ddddggks0J tt g d	ddd
gddgd
dgd
dgddgdd
ggksOJ ttt ddd
ks\J ttt dddksiJ g i dfD ]}tt |g gks{J qntt |dg gksJ tt |d
g ksJ tt |dg ksJ dd  t fddtdksJ ttdd  d S )N)abbyabybaybbbabybaybbbaybbyabyabbybayabbybabybbac                 S   r1  r2  r  r3  rQ   rQ   rR   r5    r6  z.test_multiset_permutations.<locals>.<listcomp>r@  c                 S   r1  r2  r  r3  rQ   rQ   rR   r5    r6  r   r[   r   r   rZ   r   rh   rT   r\   c                  S   s8   t ddD ]} t|  tg d| D ]}t| qqd S )NrZ   r   )r   r   rZ   r   rZ   )r   printr*   )r4  r  rQ   rQ   rR   test  s   
z(test_multiset_permutations.<locals>.testc                           S r   rQ   rQ   rJ  rQ   rR   rk     r   z,test_multiset_permutations.<locals>.<lambda>a          1
        [0]
        [1]
        2
        [0, 0]
        [0, 1]
        [1, 0]
        [1, 1]
        3
        [0, 0, 0]
        [0, 0, 1]
        [0, 1, 0]
        [0, 1, 1]
        [1, 0, 0]
        [1, 0, 1]
        [1, 1, 0]
        4
        [0, 0, 0, 1]
        [0, 0, 1, 0]
        [0, 0, 1, 1]
        [0, 1, 0, 0]
        [0, 1, 0, 1]
        [0, 1, 1, 0]
        [1, 0, 0, 0]
        [1, 0, 0, 1]
        [1, 0, 1, 0]
        [1, 1, 0, 0]
        5
        [0, 0, 0, 1, 1]
        [0, 0, 1, 0, 1]
        [0, 0, 1, 1, 0]
        [0, 1, 0, 0, 1]
        [0, 1, 0, 1, 0]
        [0, 1, 1, 0, 0]
        [1, 0, 0, 0, 1]
        [1, 0, 0, 1, 0]
        [1, 0, 1, 0, 0]
        [1, 1, 0, 0, 0]
        6
c                   S   s   t tdddS )Nrh   r\   r   )rM   r*   rQ   rQ   rQ   rR   rk     r   )r*   r'   rM   r   r   r   rF   rw   )r   nulrQ   rL  rR   test_multiset_permutations  s"    $
(rN  c               	   C   s  i gdi fgg} t dD ]_}ttd|d| | ksJ ttdd|d| | ks+J ttddd|d| | ks;J ttddd |d| | ksKJ ttdd d|d| | ks[J ttddd|d| | kskJ qdd tdddD dd	iddd
ddd
ddigksJ 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sJ 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sJ  J dd ttd	ddD d	diddd
gksJ dd tdd	dD dddddiddd
ddig  kr'dd tdD ks*J  J t ddD ]&}d}t|D ]\}}|t||ksEJ |d7 }q7|t|ksTJ q/d S )Nr   r[   )sizerZ   r]   c                 S      g | ]}|qS rQ   rQ   r  rQ   rQ   rR   r5        z#test_partitions.<locals>.<listcomp>)krh   rd   r   c                 S   rP  rQ   rQ   r  rQ   rQ   rR   r5    rQ  rz   r   c                 S   rP  rQ   rQ   r  rQ   rQ   rR   r5    rQ  r   )rR  r  r   r   r   c                 S   s2   g | ]}t d d |D rt| dkr|qS )c                 s       | ]}|d kV  qdS )r   NrQ   r  rR  rQ   rQ   rR   r        -test_partitions.<locals>.<listcomp>.<genexpr>rh   )allsumvaluesr3  rQ   rQ   rR   r5    s    c                 S   rP  rQ   rQ   r  rQ   rQ   rR   r5    rQ  )r  c                 S   rP  rQ   rQ   r3  rQ   rQ   rR   r5    rQ  c                 S   s"   g | ]}t d d |D r|qS )c                 s   rS  )rh   NrQ   rT  rQ   rQ   rR   r    rU  rV  )rW  r3  rQ   rQ   rR   r5    s
    )r   rM   r-   rE   r   r   r   )r   r4  nr  qrQ   rQ   rR   test_partitions  sN      "
&
 


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s7J tdd t dD dksFJ d S )Nc                 S      g | ]}|d d  qS r   rQ   r3  rQ   rQ   rR   r5        z*test_binary_partitions.<locals>.<listcomp>r   r   r[   )r   rZ   rZ   )r   r   r[   )r   r   rZ   rZ   )r   r[   r[   r[   )r   r[   r[   rZ   rZ   )r   r[   rZ   rZ   rZ   rZ   )r   rZ   rZ   rZ   rZ   rZ   rZ   )r[   r[   r[   r[   r[   )r[   r[   r[   r[   rZ   rZ   )r[   r[   r[   rZ   rZ   rZ   rZ   )r[   r[   rZ   rZ   rZ   rZ   rZ   rZ   )	r[   rZ   rZ   rZ   rZ   rZ   rZ   rZ   rZ   )
rZ   rZ   rZ   rZ   rZ   rZ   rZ   rZ   rZ   rZ   c                 S   r]  r   rQ   r  jrQ   rQ   rR   r5    r^     $   )r   r   rQ   rQ   rQ   rR   test_binary_partitions  s   
"rc  c                  C   s   dd t ddD dd t ddD ksJ ttdg dks"J t ddD ]} tt | }t| }|D ]}|t|jks@J | }q5q'ttd	d
  d S )Nc                 S   s   g | ]
}t tt|qS rQ   )r   r   r   r3  rQ   rQ   rR   r5  	  s    z"test_bell_perm.<locals>.<listcomp>rZ   r   c                 S   s   g | ]}t |qS rQ   r   r3  rQ   rQ   rR   r5  	  s    rh   )r   r   r   r   r   r   r_   c                   S   s   t tdS )Nr   )rM   r   rQ   rQ   rQ   rR   rk     rl   z test_bell_perm.<locals>.<lambda>)	r   rM   r   r   r  
array_formnext_trotterjohnsonrF   rw   )rZ  r  r   birQ   rQ   rR   test_bell_perm  s   
rg  c                  C   sX   g d} t | D ]!\}}tt|d }t||ksJ tdd |D dks)J qd S )N)rZ   r[   r   r      L   rZ   c                 S   s   h | ]}t |d  qS r|   )r   r_  rQ   rQ   rR   	<setcomp>  r^  z#test_involutions.<locals>.<setcomp>)	enumeraterM   r   r   )lengthsrZ  Nr4  rQ   rQ   rR   test_involutions  s   rn  c                  C   s  t ttttddksJ ddd tdD dks J ttg dg d	g d
g dg dg dg dg dg dg dg	ksGJ ttg dg dg dgksYJ ttdtdgksfJ t} t| dg ksrJ dd | dD dgksJ dd | dD ddgksJ dd | dD d gksJ d!d | d"D g d#ksJ d$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	  rT   c                 s   r  r  r  r3  rQ   rQ   rR   r  #  r  z$test_derangements.<locals>.<genexpr>abcdebadecbaecdbcaedbcdeabceadbdaecbdeacbdecabeacdbedacbedcacabedcadebcaebdcdaebcdbeacdeabcdebaceabdcebadcedabcedbadabecdaebcdaecbdcaebdcbeadceabdcebadeabcdeacbdebacdebcaeabcdeadbceadcbecabdecbadecdabecdbaedabcedacbedbacedbcar   )rZ   r   rh   r[   )rZ   r[   rh   r   )rZ   rh   r   r[   )r[   r   rh   rZ   )r[   rh   r   rZ   )r[   rh   rZ   r   )rh   r   rZ   r[   )rh   r[   r   rZ   )rh   r[   rZ   r   )r   rZ   r[   r[   )r[   r[   r   rZ   )r[   r[   rZ   r   bar   abbc                 S   r1  r2  r  r3  rQ   rQ   rR   r5  1  r6  z%test_derangements.<locals>.<listcomp>c                 S   r1  r2  r  r3  rQ   rQ   rR   r5  2  r6  r9  bcacabc                 S   r1  r2  r  r3  rQ   rQ   rR   r5  3  r6  aabbbbaac                 S   r1  r2  r  r3  rQ   rQ   rR   r5  4  r6  aabbcccc)ccccaabbccccababccccabbaccccbaabccccbabaccccbbaac                 S   r1  r2  r  r3  rQ   rQ   rR   r5  7  r6  aabbccc)cccabbacccababcccaabbccacbbaccacbabccacabbcbccbaacbccabacbccaabbcccbaabcccababcccaabc                 S   r1  r2  r  r3  rQ   rQ   rR   r5  ;  r6  books)kbsooksboosbkooskboooksbooskbookbsoobksooskoboksobosbokobsokrh   r[   rZ   )r   rM   r   r   r  rB   )DrQ   rQ   rR   test_derangements!  s.    

$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sBJ d S )Nc                 S   s   t tt| ||S r   )r   rM   r+   )rZ  rR  frQ   rQ   rR   countC     ztest_necklaces.<locals>.countrZ   r   r[   r   rh   )rZ   r[   r[   rh   )r[   rh   rh   r]   )rh   r   r   r   )r   r]   r]      )r_   r   r   '   )r]         \   )r            )r   r   r   )r  r  r4  rQ   rQ   rR   test_necklacesB  s    r  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s2J dd t ddD } t| tg d	g d
g dg dg dg dgksXJ d S )Nc                 S   rP  rQ   rQ   r3  rQ   rQ   rR   r5  T  rQ  z"test_bracelets.<locals>.<listcomp>r[   r   r   rZ   rh   c                 S   rP  rQ   rQ   r3  rQ   rQ   rR   r5  a  rQ  )r   r   r   r   )r   r   r   rZ   )r   r   rZ   rZ   )r   rZ   r   rZ   )r   rZ   rZ   rZ   )rZ   rZ   rZ   rZ   )r   r   )bcrQ   rQ   rR   test_braceletsS  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sFJ tt tddksRJ d S )Nr_   r   )r   rZ   r[   rh   rh   )r   rZ   r[   rh   r[   )r   rZ   r[   rh   rZ   )r   rZ   r[   rh   r   )r   rZ   r[   r[   r[   )r   rZ   r[   r[   rZ   )r   rZ   r[   r[   r   )r   rZ   r[   rZ   r[   )r   rZ   r[   rZ   rZ   )r   rZ   r[   rZ   r   )r   rZ   r[   r   rZ   )r   rZ   r[   r   r   )r   rZ   rZ   rZ   rZ   )r   rZ   rZ   rZ   r   )r   rZ   rZ   r   rZ   )r   rZ   rZ   r   r   )r   rZ   r   rZ   r   )r   rZ   r   r   r   )r   r   r   r   r   r   i2  )rM   r    r   rQ   rQ   rQ   rR   test_generate_oriented_forestl  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s4J ttdd  ttdd  d S )Nr   r[   rZ   r_   c                   S      t ttddS )Nr   rh   r:   rM   r   rQ   rQ   rQ   rR   rk   z  r   z test_unflatten.<locals>.<lambda>c                   S   r  )Nr   rc   r  rQ   rQ   rQ   rR   rk   {  r   )rM   r   r:   zipr  rF   rw   )rrQ   rQ   rR   test_unflattenv  s
   ..r  c                   C   sF  t g dgg ks
J t ttdg dksJ t ttdttdg dks+J t g dg dddgks:J t g dg ddgksHJ tg dgg ksRJ tttdg dks`J tttdttdg dkssJ tttdttdg ksJ tg dg d	ddgksJ tg dg d
dgksJ d S )NrZ   rh   r   r   rz   )rZ   r[   r_   r[   )rZ   rh   r_   )r   r[   rh   )r   r   rh   )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sJ t ddddks$J t ddks,J t d	td
dks6J d S )Nr   r   r   r   F)directedabaaab)bbr   r:  r   rJ   )r:  r   r  r   )r&   r   rQ   rQ   rQ   rR   test_minlex  s   r  c                      s   t tttftddttgttgfv sJ t tttftddt tttftddks-J t tttfttgks;J g dg dg ddgdggdd	 d
d	 fg\ t t ddddgdgg dg dg dgksoJ tt fdd	 d S )NF)defaultr   r   r   r[   rZ   c                 S      t | S r   )r   r   rQ   rQ   rR   rk     r   ztest_ordered.<locals>.<lambda>c                 S   r  r   )rX  r   rQ   rQ   rR   rk     r   r  warnc                      s   t t dddS )NFTr  )rM   r   rQ   keysseqrQ   rR   rk     r  )rM   r   rO   rN   hashrF   rw   rQ   rQ   r  rR   test_ordered  s   *r  c                  C   s   t g g ksJ t dgdggksJ t ddgdgdggks!J t g ddgddggks0J t g dddgdggks?J t g ddgdgdggksOJ ddlm}  t g d| ddgdggkseJ d S )NrZ   r   r[   r   )r[   rZ   rZ   r   lt)r4   operatorr  r  rQ   rQ   rR   	test_runs  s    $r  c                  C   s  t tdd} t| dgg dg dgksJ t| dddgks"J t| dddgks-J t| ddgfddd	dgfd
dddgfgksEJ t| ddgfdd	dgfdddgfgks[J t| ddgdfddd	gdfd
ddgdfgkstJ tt| dgddgfdgddgfd
gddgffksJ tt| dgddfdgddfd
gddffksJ 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 )NrZ   r   r   r   )r_   r]   r   r   )r   r   r[   rh   r_   r]   r   r   r|   rd   )r_   r]   r   r   r  )rZ   r}   rZ   r   r   )r   )r   r   r   rv   c                   S      t ddgdgS )Nr   rZ   r\   r1   rQ   rQ   rQ   rR   rk     rQ  ztest_reshape.<locals>.<lambda>c                   S   r  )Nr   rZ   rh   r  rQ   rQ   rQ   rR   rk     rQ  )rM   r   r1   r  rF   rw   )r  rQ   rQ   rR   test_reshape  s<   
r  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s"J t tdd td	D d
dgks5J t tddgks@J t tdt dksLJ t tdgddgdggdgddggksbJ 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sJ 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sJ dg tt fdd dgg tt fdd d S )Nc                 s       | ]}|V  qd S r   rQ   r  rQ   rQ   rR   r        ztest_uniq.<locals>.<genexpr>r   rZ   r   r[   rd   c                 s   s    | ]}|d  V  qdS )r[   NrQ   )r  rO   rQ   rQ   rR   r    rU  r_   r   r   ababcr9  c                 s   r  r   rQ   r3  rQ   rQ   rR   r    r  rh   c                          fddt  D S )Nc                       g | ]}  |qS rQ   remover3  r  rQ   rR   r5    r6  /test_uniq.<locals>.<lambda>.<locals>.<listcomp>r;   rQ   r  rQ   rR   rk     r6  ztest_uniq.<locals>.<lambda>c                      r  )Nc                    r  rQ   r  r3  r  rQ   rR   r5    r6  r  r  rQ   r  rQ   rR   rk     r6  )rM   r;   r-   r   r.   rF   RuntimeErrorrQ   rQ   r  rR   	test_uniq  s"   $&,  &r  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s-J t ttddd	dd
ks<J t ttddd ddksKJ dd  t fddtdks]J dd tfddtdksoJ d S )N1123r[   rZ   r   r  rv   rb  r   r   r_   rh   c                  S   s:   dD ]} t d|  tg dd| dD ]}t d| qqd S )NNr   rZ   r   rv   	ordered =r   r[   r      )rI  r%   
orderedvalr  rQ   rQ   rR   test1  s   
ztest_kbins.<locals>.test1c                      rK  r   rQ   rQ   )r  rQ   rR   rk     r   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 ]} t d|  tttdd| dD ]}t d| qqd S )Nr  r  rh   r[   r   r  )rI  r%   rM   r   r  rQ   rQ   rR   test2  s   
ztest_kbins.<locals>.test2c                      rK  r   rQ   rQ   )r  rQ   rR   rk     r   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   )r  r  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 s+J t dgdggdu s7J d S )NFrh   r   TrZ   r[   )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s'J dg df} t dg| R  ddgddgdggksAJ d S )	Nro  )rZ   r   rZ   r[   r   r   er   r:  drh   )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 ]6}d gttd| D ])}tdd |||dD tdd |||dD   krW| ||ksZJ  J q1q%d S )Nr   )nTrZ   r   c                 s       | ]}d V  qdS rZ   NrQ   r  rQ   rQ   rR   r  ?  r  z*test_ordered_partitions.<locals>.<genexpr>c                 s   r  r  rQ   r  rQ   rQ   rR   r  @  r  )%sympy.functions.combinatorial.numbersr  r=   rM   r   rX  )r  r  r4  r`  rQ   rQ   rR   test_ordered_partitions7  s   r  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s%J t ttddd	g dg dg dgks<J d S )
Nr   r   r   rh   r   r   r   r\   )dir)rM   r>   r   rQ   rQ   rQ   rR   test_rotationsD  s    *2r  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s*J tt dd	g d
ks7J tt ddddg dksFJ ttdd  ttdd  d S )Nrh   rZ   r   T)str11011r[   rW  )re   r   r   r   rT   )000110r  c                   S   s   t dS )Ng      ࿩r#   rQ   rQ   rQ   rR   rk   Q  r   ztest_ibin.<locals>.<lambda>c                   S   s
   t ddS )Nr[   rZ   r  rQ   rQ   rQ   rR   rk   R  r   )r#   rM   rF   rw   rQ   rQ   rQ   rR   	test_ibinJ  s   r  c                  C   s   t ddu sJ t ddu sJ t d du sJ G dd dt} t |  du s)J G dd dt}t | du s:J G d	d
 d
}t | du sJJ G dd d}t | du sZJ G dd d}t | du sjJ G dd d|}t | du s{J d S )Nr   FrZ   c                   @   rm   )ztest_iterable.<locals>.Test1Nrn   rQ   rQ   rQ   rR   Test1Z  rs   r  c                   @      e Zd ZdZdS )ztest_iterable.<locals>.Test2TNro   rp   rq   	_iterablerQ   rQ   rQ   rR   Test2_      r  Tc                   @   rm   )ztest_iterable.<locals>.Test3Nrn   rQ   rQ   rQ   rR   Test3d  rs   r  c                   @   r  )ztest_iterable.<locals>.Test4TNr  rQ   rQ   rQ   rR   Test4i  r  r  c                   @   s   e Zd Zdd ZdS )ztest_iterable.<locals>.Test5c                 s   s    dV  d S )NrZ   rQ   )selfrQ   rQ   rR   __iter__o  s   
z%test_iterable.<locals>.Test5.__iter__N)ro   rp   rq   r  rQ   rQ   rQ   rR   Test5n  s    r  c                   @   r  )ztest_iterable.<locals>.Test6FNr  rQ   rQ   rQ   rR   Test6t  r  r  )r@   rA   )r  r  r  r  r  r  rQ   rQ   rR   test_iterableU  s   r  N)textwrapr   	itertoolsr   r   sympy.core.basicr   sympy.core.numbersr   sympy.core.sortingr   sympy.core.symbolr	   r
   (sympy.functions.combinatorial.factorialsr   sympy.matrices.denser   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   sympy.utilities.enumerativerC   rD   sympy.core.singletonrE   sympy.testing.pytestrF   rG   wrO   rN   rx   rS   r`   ry   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r"  r<  rN  r\  rc  rg  rn  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rQ   rQ   rQ   rR   <module>   st    (				BA+
!
	N	