a
    {þdç¬  ã                   @   s`  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
mZmZmZmZmZ d dlmZ d dlmZmZ d dlmZmZmZ d d	lmZmZ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( d dl)m*Z*m+Z+m,Z, d dl-m.Z.m/Z/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z? d dl@mAZAmBZBmCZCmDZD d dlEmFZFmGZGmHZHmIZImJZJmKZK d dlLmMZMmNZNmOZO d dlPmQZQ d dlRmSZSmTZT d dlUmVZVmWZW d dlXmYZYmZZZ d dl[m\Z\ d dl]m^Z^ d dl_m`Z` d dlUmaZa d dlbmcZc d dldmeZemfZf d dlgmhZhmiZimjZjmkZk edddd Zld!d" Zmd#d$ Znd%d& Zod'd( Zpd)d* Zqd+d, Zrd-d. Zsd/d0 Ztd1d2 Zud3d4 Zvd5d6 Zwd7d8 Zxd9d: Zyd;d< Zzd=d> Z{d?d@ Z|dAdB Z}dCdD Z~dEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZeedSdT ZdUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zeedudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zeedd Z dd Z¡dd Z¢dd Z£dd Z€dd Z¥dd ZŠdd Z§dd Zšdd Z©dd Zªdd Z«dd  Z¬d¡d¢ Z­d£d€ Z®d¥dŠ Z¯d§dš Z°d©dª Z±d«d¬ Z²d­d® Z³d¯d° ZŽd±d² Zµd³dŽ Z¶dµd¶ Z·d·dž Zžd¹dº Z¹d»dŒ ZºdœdŸ Z»d¿dÀ ZŒdÁdÂ ZœdÃdÄ ZŸdÅdÆ Z¿dÇdÈ ZÀdÉdÊ ZÁdËdÌ ZÂdÍdÎ ZÃdÏdÐ ZÄdÑdÒ ZÅdÓdÔ ZÆdÕdÖ ZÇd×dØ ZÈdÙdÚ ZÉdÛdÜ ZÊdÝdÞ ZËdßdà ZÌdádâ ZÍdãdä ZÎdådæ ZÏdçdè ZÐdédê ZÑdëdì ZÒdídî ZÓdïdð ZÔdñdò ZÕdódô ZÖdõdö Z×eed÷dø ZØdùdú ZÙdûdü ZÚdýdþ ZÛdÿd  ZÜdd ZÝdd ZÞdd Zßdd Zàd	d
 Zádd Zâdd Zãdd Zädd Zådd Zædd Zçdd Zèdd Zédd Zêdd Zëdd  Zìd!d" Zíd#d$ Zîd%d& Zïd'd( Zðd)d* Zñd+d, Zòd-d. Zód/d0 Zôd1d2 Zõd3d4 Zöd5d6 Z÷d7d8 Zød9d: Zùd;d< Zúd=d> Zûd?d@ ZüdAdB ZýdCdD ZþdEdF ZÿdGdH Z dIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX ZdYdZ Z	d[d\ Z
d]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh ZdiS (j  é    )Úproduct)ÚSum)ÚFunctionÚdiff)Ú
EulerGamma)ÚEÚIÚRationalÚooÚpiÚzoo)ÚS)ÚSymbolÚsymbols)ÚbinomialÚ	factorialÚsubfactorial)ÚAbsÚreÚsign)ÚLambertWÚexpÚlog)ÚacoshÚacothÚacschÚasechÚatanhÚsinhÚtanh)ÚceilingÚfloorÚfrac)ÚcbrtÚ	real_rootÚsqrt)Ú	Piecewise)ÚacosÚacotÚacscÚasecÚasinÚatanÚcosÚcotÚcscÚsecÚsinÚtan)ÚbesseliÚbesselyÚbesseljÚbesselk)ÚEiÚerfÚerfcÚerfiÚfresnelcÚfresnels)ÚdigammaÚgammaÚ
uppergamma)Úmeijerg)ÚIntegralÚ	integrate)ÚLimitÚlimit)Ú
logcombineÚsimplify)Úhyperexpand)ÚAccumBounds)ÚMul)Ú
heuristics)ÚOrder)ÚXFAILÚraises)ÚxÚyÚzÚkÚnT©ÚintegerÚpositivec                   C   s  t ttttu sJ t ttt t u s,J t t ttt u sDJ t td tt tu s^J t td  ttt u szJ t ttt tddddksJ t dt ttdks²J t tttttu sÊJ t tt ttt u sæJ t ttt tttu sJ t dt tt  ttdks(J t tdt  tttu sFJ t ttd  ttt u sfJ t dt dtd  tddksJ t dt t tdttd t tdksºJ t dt t tdddttd t tdddksðJ t dt t t tdddtdt t t tdddks.J t tt tt tdt tt ksZJ t t	tt t tdtt	tt ksJ t t
dt d ttdksªJ t tjtt tju sÆJ t tdt ttjtju sèJ t dtd  tdddtu s
J t dtd  tdddt u s.J t ddt d  tdddt u sVJ t ddt d  tdddtu s|J t dtt ttddt u s J t dtt ttddtu sÂJ t dt	t ttd ddt u sêJ t dt	t ttd ddtu sJ t dttd  tdt tdd ddtu sDJ t dttd  tdt tdd ddt u szJ t dttd  tttdd ddt u s¬J t dttd  tttdd ddtu sÜJ t ttttttjtjks J t ttttttjtjks$J t ttttttjtjksHJ t ttttttjtjkslJ t ttt tdd	ddksJ t td tdd	ddks¬J t dtd  tdd	dtu sÎJ t dt tdd	dtu sìJ t ddt  tdtu s
J t ddt  tdddt u s.J t td
 tdddtu sLJ t td tdddt u slJ t dtt tdddt t ksJ t td tddddks²J t tttddddksÐJ t tt  tdddt ddt   ksþJ t dt	t t tdtt	td t tdks4J t dtt tdddtksVJ t dtt tdddt kszJ t dtt tdddtksJ t dtt tdddt ksÀJ t tdt dtt  tdddtksîJ t tdt dt  tdddtksJ d S )Né   r   ú+©Údiré   ú-é   é   ú+-éþÿÿÿéýÿÿÿéÿÿÿÿ)rD   rN   r
   r   r   r%   rC   rO   r   r-   r>   r   ÚNaNrK   r1   r   r2   r	   r.   rH   ÚNegativeInfinityÚInfinityr0   r/   r   r   r+   r   © re   re   úg/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/series/tests/test_limits.pyÚtest_basic1%   sr     $ &.6>,."""$(&$"(&4620$$$$""$ (.6"$"$.rg   c                   C   s  t tt tddddksJ t ttd t tddks<J t ddt  ttdksXJ t tdt  ttdksvJ t ttt  tttu sJ t tttd   tttu s¶J t tttt  tttu sØJ t ddt  tt  ttdksþJ d S )Nr   rW   rX   rZ   ra   rV   é   ©rD   rN   r   r
   re   re   re   rf   Útest_basic2l   s     ""rj   c                   C   s>   t dt tdddtu sJ t dt tdddt u s:J d S )NrZ   r   rW   rX   r[   ©rD   rN   r
   re   re   re   rf   Útest_basic3w   s    rl   c                   C   sÐ   t dt tt  tddks J t dt tt  tddt ksDJ t dtd  ttd   tddtd  kstJ t ttd tt ttdksJ tdtd d  tdtfdt td d	 ksÌJ d S )
NrV   r   rZ   é   r`   r_   i   r\   é	   )rD   rN   rO   r%   r
   rB   r   re   re   re   rf   Útest_basic4|   s
     $0$ro   c                  C   s0  t ddd\} }}t| | t| t|  }| | t¡dksBJ ||  | t¡dksZJ t ddd\}}|d |d |d  t|d  |d d d  d|d d |d    d| t||  |d d d	 t|d |d    |d d d    }t||tt|d
  |d d d  ks,J d S )Nza b cT©rU   r   ztau xrV   rZ   r_   ç      à?r\   )r   r   rD   r
   r,   r   )ÚaÚbÚcÚAÚtaurN   Úexprre   re   rf   Útest_log   s"    8ÿÿ(ÿÿÿrx   c                   C   s6   t ttd dd td  tddtddks2J d S )Né   r\   rV   r_   rW   rZ   é   )rD   r$   rN   r	   re   re   re   rf   Útest_piecewise   s    r{   c               
   C   s   dt t tdt d tt dddt d d    dt d dkfddt  tt dddt d d    df } ttd d tdkftd d df}ttd d	 td
k ftd d	 tdkft ttd df}t| tddksðJ t|tddksJ t|td
dksJ d S )NrV   é   rZ   r   Trq   g      À?rn   r]   ra   r\   )r%   rN   r&   r   rD   )Zfunc1Zfunc2Zfunc3re   re   rf   Útest_piecewise2   s    @ÿ.ÿ&<r}   c                  C   s8   G dd dt } t| tttt| tttks4J d S )Nc                   @   s   e Zd Zedd ZdS )ztest_basic5.<locals>.myc                 S   s   |t ju rt jS d S ©N)r   rd   rb   )ÚclsÚargre   re   rf   Úeval€   s    
ztest_basic5.<locals>.my.evalN)Ú__name__Ú
__module__Ú__qualname__Úclassmethodr   re   re   re   rf   Úmy£   s   r   )r   rD   rN   r
   rC   )r   re   re   rf   Útest_basic5¢   s    r   c                   C   s0   t tt tt  tdtt dt  ks,J d S ©NrV   )rD   rN   rO   rP   re   re   re   rf   Útest_issue_3885«   s    r   c                   C   sf   t ttt tddksJ t ttt td ¡ dks<J t ttdddjttdtdfksbJ d S )Nr   rZ   r^   rX   )rC   r1   rN   ÚdoitÚargsr   re   re   re   rf   Ú
test_Limit¯   s     r   c                   C   s$  t tttdddksJ t tttdddks4J t tttdddksNJ t tttdddkshJ t tttdddksJ t tttdddksJ t tttdddks¶J t tttdddksÐJ t tttdddksêJ t tttdddksJ t tttd	dd	ks"J t tttd	dd
ks>J t ttdt  d tddtddkslJ t ttd tt ttttj tdd ks€J t tttttdksÂJ t ttttt dksâJ t t	ttttdks J t t	tttt dks J d S )Nr_   rW   r[   r`   ra   r   rZ   rV   éø   é÷   r\   rq   )
rD   r!   rN   r	   r
   rH   r   ÚHalfr,   r    re   re   re   rf   Ú
test_floorµ   s$    .8 r   c                   C   s  t ttttdddksJ t ttttdddks<J t ttttdddksZJ t ttttdddksxJ t tdtt tdddksJ t tdtt tdddksŒJ t tdtt tdddksÞJ t tdtt tdddksJ d S )Nr   rW   r[   ra   r]   r|   )rD   r!   r1   rN   r-   re   re   re   rf   Ú&test_floor_requires_robust_assumptionsÎ   s    """r   c                   C   sš  t tttdddksJ t tttdddks4J t tttdddksNJ t tttdddkshJ t tttdddksJ t tttdddksJ t tttdddks¶J t tttdddksÐJ t tttdddksêJ t tttdddksJ t tttd	dd
ks"J t tttd	dd	ks>J t ttdt  d tddtddkslJ t ttd tt ttttj tdd ks€J d S )Nr_   rW   ra   r[   r   rZ   rV   r\   r   éù   rq   )rD   r    rN   r	   r
   rH   r   r   re   re   re   rf   Útest_ceilingÙ   s    .r   c                   C   s  t ttttdddksJ t ttttdddks<J t ttttdddksZJ t ttttdddksxJ t tdtt tdddksJ t tdtt tdddksŒJ t tdtt tdddksÞJ t tdtt tdddksJ d S )Nr   rW   rZ   r[   r]   ry   )rD   r    r1   rN   r-   re   re   re   rf   Ú(test_ceiling_requires_robust_assumptionsì   s    """r   c                   C   sš  t tttttddksJ t ttdt  tttddksDJ t ttdt  tt tdtkslJ t ttt tttdtksJ t ttttdddks¬J t ttttdddksÊJ t ttttdddksèJ t ttd tdddksJ ttdd  t td	t d tdddks:J t td	t d tdddks^J t ttt	j
 tddd
ksJ t tdt tdtddks€J d S )Nr   rZ   rW   r[   r^   rV   c                   S   s   t tttddS ©Nr   r^   )rD   r"   rN   re   re   re   rf   Ú<lambda>   ó    ztest_frac.<locals>.<lambda>r_   rq   )rD   r"   rN   r
   rH   r1   r-   rM   Ú
ValueErrorr   r   re   re   re   rf   Ú	test_frac÷   s    &(" $$"r   c                   C   s   t tttt tdddks"J t tttt tdddksDJ t ttt t tdddkshJ t ttt t tdddksJ d S )Nr   rW   r[   r_   )rD   r!   r1   rN   r2   re   re   re   rf   Útest_issue_14355  s    ""$r   c                  C   sd   t ddd} tt| td|   | ddks0J tt| t| d  t|  | ttd ks`J d S )NrN   T©ÚrealrZ   r   rV   )r   rD   r,   r1   r%   r
   r   ©rN   re   re   rf   Ú	test_atan  s    $r   c                  C   s  t tttddksJ t ttttddks4J t ttttddksPJ t tttd tdtdkstJ t ttt ttt  dt  tdttksšJ t ttttd  tt	dksÌJ t tttttd  tttd td d   d  tt	dksJ t tttd d d tddt	ksBJ t ttttdt	ks`J t tttttdt	ksJ t
ddd} t tt| d t|  | t	dksžJ t | td|  t ttd|     d | ddksòJ t t| t|  | td	d
ksJ d S )Nr   rZ   rV   r\   rW   rP   Trp   r[   ra   )rD   ÚabsrN   r1   r-   r   rO   r   r   r
   r   r   ©rP   re   re   rf   Útest_set_signs  s    $4$J,"*:r¡   c                  C   st   t ddd} ttd|  t|  | ddtddks8J ttdtt| ttd|    | dtdkspJ d S )	NrN   Tr   rZ   r   rW   ra   rV   )r   rJ   r1   r,   rH   rD   r   r%   r   re   re   rf   Útest_heuristic4  s    ,r¢   c                  C   sN   t ddd} d|  t|  t  }t|ttdks6J | tt¡dksJJ d S )NrP   Trp   ra   r   )r   r   rN   rD   r
   )rP   Úfre   re   rf   Útest_issue_3871:  s    r€   c                  C   s   t d} t ddd}td||   |  | tt|ks8J td|d|    |  | tt|d ksdJ td|d|  d   |  | tt|d ksJ t|d |d  | |ttdksŒJ tddd|  |  |tdtj ksæJ tdd|  | d| |  |tttd	ksJ d S )
NrR   rN   Tr   rZ   rV   r_   ry   z1/3)r   rD   r
   r   r   ÚExp1©rR   rN   re   re   rf   Útest_exponentialA  s    $,0(*r§   c                  C   s8   t d} tdt| t|    |  | tttks4J d S )NrR   rZ   )r   rD   rN   r1   r
   r   )rR   re   re   rf   Útest_exponential2L  s    rš   c                  C   s.   t dt t} t| tt}| ¡ tu s*J d S r   ©rA   rN   rC   r
   r   ©r£   Úlre   re   rf   Ú	test_doitQ  s    r¬   c                  C   sÒ  t ttttd  tttddks*J t ttttd  d tttddksXJ t tttttt  tttddksJ dtd d } dtd d }tt| |ddtd  dd}t tttt	 
t¡t	d	tf ¡  
t¡tt|ksþJ ttdtdd  tdd d ddtd  }t tttt	 
t¡t	d	tf ¡  
t¡tt|kslJ t ttd d t tttd	tksJ dt  ttd t  }t |tttd	tksÎJ d S )
NrZ   r_   rV   ra   r\   r`   F)Úevaluater   )rD   r1   rQ   r
   rH   r-   rI   rF   r   rR   Úrewriter   r   rN   )ÚloÚhiÚt1Út2Úere   re   rf   Útest_series_AccumBoundsW  s    *.. 84:,rŽ   c                   C   s  t tdtttdksJ t tdttt dks6J t tdtttt tt ksXJ t tdttt t t t ks~J t tdtttdksJ t tdttt dksŽJ t tdtttt t ksÔJ t tdttt t t ksöJ t tdttttksJ t tdttt t ks2J t tdtttt dksRJ t tdttt t dkstJ t tdtttdksJ t tdttt t t ksŽJ t tdtttt dksÔJ t tdttt t dksöJ t tdtttdksJ d S ©NrZ   r   )rD   r5   rN   r
   r   r4   r3   r6   re   re   re   rf   Ú!test_bessel_functions_at_infinityn  s"    "& "  "$ "r¶   c                  C   s2   t dt t} t| tt}|jdd|ks.J d S )NrV   F©Údeepr©   rª   re   re   rf   Ú
test_doit2  s    r¹   c                   C   s.   t ttt ttd  tt dks*J d S rµ   ri   re   re   re   rf   Útest_issue_2929  s    rº   c                   C   s   t dtt td  ttjddttj  ks4J t tttd d tdtdtd ksdJ t tttd d tddtd ksJ d S )NrZ   rV   r|   r   )rD   r-   rN   r   r   r1   r   re   re   re   rf   Útest_issue_3792  s    40r»   c                   C   sš   t dtd  tdtddks"J t dtt  tdtjdt  ksHJ t tttd d  tdtdd kstJ t tttd t  tdtddt  ks€J d S )NrZ   r\   rV   r]   é   r|   )rD   rN   r	   r   r   ÚOner   re   re   re   rf   Útest_issue_4090  s    "&,rŸ   c                   C   s@   t tttdddtu sJ t ttttd dddks<J d S )Nr   rW   rX   rV   )rD   r.   rN   r
   r   re   re   re   rf   Útest_issue_4547   s    r¿   c                   C   s   t td tttd   kr$tu s*n J t td tdtdd ksJJ t td tddksbJ t td ttdkszJ t td tdtdd ksJ d S )Nrq   é   r   g      à¿r|   )rD   rN   r
   r   re   re   re   rf   Útest_issue_5164¥  s
    * rÁ   c                  C   s,   ddt   dt   } t| t dtks(J d S )Nç      ð?r   )rN   rD   r   )Úfuncre   re   rf   Útest_issue_5383­  s    rÄ   c                  C   sp   t tdd  tt  t  tdt d  ttt  tddt    t d  } t| t ttdd kslJ d S )NrZ   rV   rz   r\   ih  )rN   r   r   r   r   rD   r
   ©rw   re   re   rf   Útest_issue_14793²  s    *
ÿÿÿrÆ   c            
       C   s.  t ttt gddgddtjtddgddg} ttt tt t tt dtdd  tddddddddtttt tt t tt dtdd  ddddddddf }t| t|ksžJ t	t
| |D ]b\}\}}|\}}}}|||  }	zt|	td|d|ksJ W qÆ ty&   d s"J Y qÆ0 qÆd S )	Nra   rZ   rV   r\   r[   rW   r   rX   )Úlistr   rN   r   r   r	   r
   r   ÚlenÚ	enumerateÚziprD   ÚAssertionErrorÚprint)
ÚtestsÚresultsÚir   ÚresrO   Úsr³   ÚdÚeqre   re   rf   Útest_issue_5183ž  s$    ý((ýrÔ   c                  C   sº   t ttt ttdksJ t tttttd ks8J t tttttu sPJ t ttt ttdkslJ t ttttj	t
tksJ tddd} t | td|   | ddks¶J d S )Nr   rV   ÚrTr   rZ   )rD   r1   rN   r
   r,   r   r>   r-   r   r   r%   r   ©rÕ   re   re   rf   Útest_issue_5184Ð  s    r×   c                   C   s*   t dt dt  tj tddks&J d S rµ   )rD   rO   r   r¥   re   re   re   rf   Útest_issue_5229Û  s    rØ   c            	      C   sê   t tttgt d dtd tttdd gddg} ddt tddt tddtt ddtt ddtt f}t| t|ksJ tt	| |D ]V\}\}}|\}}}|t
}zt|t
||d|ksÆJ W q tyâ   d sÞJ Y q0 qd S )NrV   r   r\   r[   rW   rX   )rÇ   r   r.   r2   r   r	   r
   rÈ   rÉ   rÊ   rN   rD   rË   rÌ   )	rÍ   rÎ   rÏ   r   rÐ   r£   r«   rÒ   rÓ   re   re   rf   Útest_issue_4546ß  s    
 þÿ
rÙ   c                   C   sX   t dttd  dt  tddks(J t ddt  ddt   t tddksTJ d S )NrZ   r\   r   r]   )rD   rN   r   re   re   re   rf   Útest_issue_3934ô  s    (rÚ   c                   C   sX   t ttdd dttdd   ttdks0J t td dtd   ttdksTJ d S )NéM   r\   rZ   gfffffFY@)rD   rN   r	   r
   re   re   re   rf   Útest_calculate_seriesù  s    0rÜ   c                   C   s   t td dtd   ttdks$J t td dtd   ttdksHJ t td dtd   ttdkslJ t td td d tt   ttdksJ d S )NrÀ   rZ   éd   i]  éè  ©rD   rN   r
   r   re   re   re   rf   Útest_issue_5955  s    $$$rà   c                   C   s0   t tdtt ttt tddks,J d S rµ   )rD   r   r1   rN   r.   re   re   re   rf   Útest_newissue  s    rá   c                   C   sŒ   t tt ttttt ttks$J t dttt  t tdtdttt  t tdks`J t tt ttttt ttksJ t tt dt  ttttt dt  ttksžJ d S rµ   )rD   rN   r
   rC   r1   re   re   re   rf   Útest_extended_real_line  s    $<$râ   c                  C   sJ   t ddd} t| t td| ks&J tt| d d  | ttu sFJ d S )NrN   Trp   rZ   rV   r|   )r   rK   r
   rD   r   re   re   rf   Útest_order_oo  s    rã   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttt ttS r~   ©rD   r   rN   rO   r
   re   re   re   rf   r     r   z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ttS r~   rä   re   re   re   rf   r      r   ©rM   ÚNotImplementedErrorre   re   re   rf   Útest_issue_5436  s    rç   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttdddS )Nr   rX   ©rC   rN   re   re   re   rf   r   $  r   z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   Ú0rX   rè   re   re   re   rf   r   %  r   )rM   Ú	TypeErrorr   re   re   re   rf   Útest_Limit_dir#  s    rë   c                   C   s^   t td d td d d  ttdks,J t td d td d d  tt dksZJ d S )NrZ   rÞ   rk   re   re   re   rf   Útest_polynomial(  s    ,rì   c                   C   s   t dt dtt  ttt  t  t  tttd tt  ksDJ t dt dtt  ttt  t  t  tt td tt  ksJ d S ©NrZ   )rD   rO   rN   rP   r
   re   re   re   rf   Útest_rational-  s    Drî   c                   C   s<   t ttt tdt t  tdtttt  ks8J d S ©NrV   r   )rD   r   rN   rP   rO   r
   r   re   re   re   rf   Útest_issue_57402  s    rð   c                  C   s^   t dddd} | d t| d   t| d  d  ttd   }t|td ¡ | d ksZJ d S )NrR   TrS   rZ   rV   )r   rN   rD   Úcancel)rR   rÕ   re   re   rf   Útest_issue_63666  s    0rò   c                  C   s   t t} t| tttu sJ tt|  ttdks4J t| tdt t tt t   ttdksdJ t| tt tt ksJ d S )Nr   rV   rZ   )r   rN   rD   r
   r%   r   r   r>   ©r£   re   re   rf   Útest_factorial<  s
    0rô   c                  C   sž   dt d  d t tdd  tdt d  d tj  dt d  d  dt d  d  tdd dtd    } t| ttdt d  d dt d  d  dt  d  tdd ksŽJ d S )	Nr]   r\   r|   rV   é#   rm   é   rZ   )rN   r	   rO   r   r   rD   r
   ©r³   re   re   rf   Útest_issue_6560F  s    4ÿÿÿ
ÿrø   c                     s&  t dt ddd} t d}t ddd}t ddd}d	 |  d
  | |  d
    | | d
 |  d	  | |  d
    |    |      ||d
 ¡ tt fdd t  ||¡td
ksàJ t  ||¡t ¡ d	|d
  |  d
 | d
 |d
   ks"J d S )NrR   rÕ   Trp   rt   ÚpÚm)ÚnegativerV   rZ   c                      s   t  tS r~   )rD   r
   re   ©rw   rR   re   rf   r   U  r   z!test_issue_5172.<locals>.<lambda>)r   ÚsubsrM   ræ   rD   r
   rF   )rÕ   rt   rù   rú   re   rü   rf   Útest_issue_5172K  s$    *.ÿÿ
ÿ"ÿrþ   c                  C   s,   t d} tttt|   ttdks(J d S )Nrr   rZ   )r   rD   r%   rN   r
   ©rr   re   re   rf   Útest_issue_7088[  s    r   c                   C   s  t ttt d tdttd ks(J t ttt d tddtdksNJ t ttt d tdtd kstJ t ttt d tddt td ks J t ttt d tdtd ksÆJ t ttt d tddtdksìJ t ttt d tdtdksJ t ttt d tdddt td ksBJ t ttdt  tdttd kslJ t ttdt  tddt ttd  ksJ t ttdt  tdtttd  ksÌJ t ttdt  tddt td ksúJ t tdt tdtd ksJ t tdt tddt d ksBJ t tttttd ks`J t tttt t d ksJ t t	tt
dd t  tdtttt
dd   ksÀJ t t	tt
dd t  tddt tt
dd  ksþJ t t	tt
dd t  tdttt
dd  ks8J t t	tt
dd t  tddt ttt
dd   kszJ t t	ttdtd ksJ t t	ttddt d ksºJ t ttt t
dd  tdtt
dd ksðJ t ttt t
dd  tddtt
dd  ks*J t ttt t
dd  tddt tt
d d  ksjJ t ttt t
dd  tddtt
d d ks€J t ttt t
dd  tdtt
dd ksÚJ t ttt t
dd  tddttt
dd  ksJ t ttt t
dd  tdt tt
dd  ksRJ t ttt t
dd  tddtt
dd  ksJ t ttt d tdtt ks²J t ttt d tddt t ksÜJ t tt t d tdt t ksJ t tt t d tddtt ks0J t ttt d tdtksRJ t ttt d tddt ksxJ t tt t d tdt ksJ t tt t d tddtksÄJ t ttt d tddt
dd  ksòJ t ttt d tdddt
dd   ks$J t tt t d tddt
dd   ksVJ t tt t d tdddt
dd  ksJ d S )NrV   r   r[   r_   rZ   ra   r\   )rD   r+   r   rN   r   r'   r,   r   r
   r(   r   r   r*   r)   r   r%   r#   re   re   re   rf   Útest_branch_cuts`  sT    (&&,&&&0*2.."&">>:B"6:@:6<<:&***"&&&.22r  c                  C   sj   t d} tdtdt t| d   tdt t| d    }t|tddt| d tj  ksfJ d S )Nrr   rZ   rV   r   )r   rP   r%   r1   r-   rD   r   r   )rr   r³   re   re   rf   Útest_issue_6364  s    8r  c                   C   s6   t tdtt  td  tdtdt ks2J d S rï   )rD   r   r7   rN   r   re   re   re   rf   Útest_issue_6682  s    r  c                  C   s   t d} t| t tdtt|  ks(J t|  t tdt t|  ksLJ t|  t ttt t|  kspJ t| t tttt|  ksJ d S )Nrr   r   )r   rD   rN   r
   r   rÿ   re   re   rf   Útest_issue_4099  s
     $$r  c                  C   s\   t d} ttdtt|   tdtt  |  | dttdtttd   ksXJ d S )NÚdxrZ   r   rV   )r   rD   r%   r   rN   )r  re   re   rf   Útest_issue_4503¢  s    .ÿr  c                  C   sJ   t ddddt } t| }t|tdddks0J t|ttt ksFJ d S )Nre   )rZ   )r   r   r^   )r@   rN   rG   rD   r
   )ÚGÚgre   re   rf   Útest_issue_6052š  s    r	  c                  C   sj   t ttdt dt  } ttt| tt |  tddks>J ttt| tt |  td ¡ dksfJ d S )NrZ   rm   r   rV   g       @)r%   rN   r3   rD   r   ZevalfrÅ   re   re   rf   Útest_issue_7224¯  s    $r
  c                   C   s&   t ttddd  ttdks"J d S )NrZ   g    eÍÍAr   )rD   rR   r	   r
   re   re   re   rf   Útest_issue_8208µ  s    r  c                   C   s<   t ttdd d ttd tdd  tddks8J d S )NrZ   r|   rV   r\   rÀ   r   )rD   rN   r	   r%   re   re   re   rf   Útest_issue_8229¹  s    r  c                  C   s4   t ddd\} }ttd||   |tdks0J d S )Nzd tTrp   rZ   ra   )r   rD   r8   r
   )rÒ   Útre   re   rf   Útest_issue_8433œ  s    r  c                  C   sH   t dddd} t ddd}t||  t|  t|  | tdksDJ d S )NrQ   T)rT   ZnonnegativeÚlamdarp   r   )r   rD   r   r   r
   )rQ   r  re   re   rf   Útest_issue_8481Â  s    r  c                   C   sJ   t tttd tttksJ t tttd dt   ttdksFJ d S )NrV   r\   r   )rD   r   rR   r
   re   re   re   rf   Útest_issue_8462È  s    r  c                  C   s@   t dddd} t d}t||  |t ttd|   ks<J d S )NrR   TrS   rN   ra   )r   rD   r
   r   rŠ   re   re   rf   Útest_issue_8634Í  s    r  c                  C   s  t ddd} t ddd}t| t | td   | tdks<J t| t | td   | ttks`J t| t | td   | ttksJ t| t | t| d	   | ttks¬J t ddd} t| t | td	   | ttksÜJ t| t | td
   | tt ksJ d S )NrN   Tr   rQ   rp   r   r]   g      @rZ   rV   )r   rD   rR   r
   )rN   rQ   re   re   rf   Útest_issue_8635_18176Ó  s    $$$($r  c                   C   s   t tttttu sJ d S r~   )rD   r   rN   r
   re   re   re   rf   Útest_issue_8730ß  s    r  c                      s`   t dddt ddd ttt  d    tdksHJ tt fdd	 d S )
NrR   T)rT   rt   rp   rZ   r   c                      s$   t tt     tS r~   )rD   r   r
   re   ©rt   rR   re   rf   r   è  r   z!test_issue_9252.<locals>.<lambda>)r   rD   r   r
   rM   ræ   re   re   r  rf   Útest_issue_9252ã  s    0r  c                   C   s"   t ttd tdddksJ d S )Nrö   r   r[   )rD   r1   rN   re   re   re   rf   Útest_issue_9558ë  s    r  c                   C   s2   t dt ttdt td   tttks.J d S )NrÀ   rV   )rD   rQ   r   r
   r   re   re   re   rf   Útest_issue_10801ï  s    r  c                  C   s8   t ddd\} }tt| | t|  | d|ks4J d S )Nzs xTr   r   )r   rD   r8   )rÑ   rN   re   re   rf   Útest_issue_10976ô  s    r  c                   C   s<   t ttttd t tdt t   ttdks8J d S ©NrZ   rV   )rD   r   rR   r   r%   r   r
   re   re   re   rf   Útest_issue_9041ù  s    r  c                  C   s   t d\} }}t| | |j|hks&J t| | |dj|hks@J t| | | | |j|hks`J t| d  | | d |j||hksJ d S )Nzx, y, ar[   rV   )r   rC   Zfree_symbols)rN   rO   rr   re   re   rf   Útest_issue_9205ý  s
     r  c                   C   sT   t dttd td  ttdks&J t dttdd  td  ttdksPJ d S )Né   r\   rZ   )rD   r   rR   r
   re   re   re   rf   Útest_issue_9471  s    &r  c                   C   s$   t ttdt ttdks J d S r  )rD   r9   r   rN   r
   re   re   re   rf   Útest_issue_11496
  s    r  c                   C   s<   t ttt t tt  t tdtttd   ks8J d S )Nr   rZ   )rF   rD   rN   rO   rR   re   re   re   rf   Útest_issue_11879  s    r   c                  C   sF   t d} td|  | tdks J tdd|   | ttddksBJ d S )NrQ   rÂ   rZ   g333333Ó?r\   é
   )r   rD   r
   r	   )rQ   re   re   rf   Útest_limit_with_Float  s    r"  c                   C   sD   t dt dt d   td d  td  tttddks@J d S ©Nr\   rZ   rV   )rD   rN   r
   r	   re   re   re   rf   Útest_issue_10610  s    r$  c                   C   s  t tttt tddtdks&J t tttt tddtddt t  ksXJ ttdd  t tttt tttksJ t ttt	t tddtdks¬J t ttt	t tddt ksÐJ ttdd  t ttt	t tttksþJ d S )Nr   rW   rV   r[   c                   S   s   t tttt tddS r   )rD   r   rN   r   re   re   re   rf   r     r   z"test_issue_10868.<locals>.<lambda>c                   S   s   t tttt tddS r   )rD   r   rN   r   re   re   re   rf   r   #  r   )
rD   r   rN   r   r   r   rM   r   r
   r   re   re   re   rf   Útest_issue_10868  s    &2 &$r%  c                   C   s$   t ttt t ttdks J d S rí   )rD   rR   r-   r
   re   re   re   rf   Útest_issue_6599'  s    r&  c                   C   sn   t dt dtd   td tt  tt dks6J t dt dtd   td tt  tttu sjJ d S )Nr\   rV   r!  ri   re   re   re   rf   Útest_issue_12555+  s    6r'  c                  C   sÔ  t ddd\} }}t dddd\}}}}}}}	|| ||  |  | t|d |d|   |d  |d  |d|  |d  |d  |d   |d|  |d|   |d  |d  |d d|  d   d|d|   ||d   | |  | |d d|  d   d||d   |d|   | |  | |d d|  d   d||d   ||d   |d  |d   |d |d d|  d    ||  | |  d  }
|
 ||¡jddt|
||jddksÐJ d S )	Nzr z xTr   za b s0 K F0 s T)rU   r   rV   rZ   r·   )r   r%   rý   ZfactorrD   )rÕ   rP   rN   rr   rs   Ús0ÚKZF0rÑ   ÚTÚfxre   re   rf   Útest_issue_127690  s$    :"ÿ:ÿ:þ:ý*üüür,  c                   C   sz   t tdddt d   dt t  dt d dt dtj    dt d dt dtj    tttd	d
ksvJ d S )Né   r]   éûÿÿÿrZ   i@¶  rV   ry   iúÿÿÿé   é$   )rD   r%   rN   r   r   r
   r	   re   re   re   rf   Útest_issue_13332<  s    Bÿÿÿr1  c                   C   sò   t td ttt  tt tt tu s.J t td ttt  tt tttu sZJ t ttt d  ¡ tttu s~J t ttt d  ¡ tttu s¢J t ttt d  ¡ tt tu sÈJ t ttt d  ¡ tt tu sîJ d S r   )rD   rN   r1   r-   r
   Úexpandre   re   re   rf   Útest_issue_12564A  s    .,$$&r3  c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t tttt ¡ S r~   )rC   r   rN   r   r   re   re   re   rf   r   K  r   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  tt ¡ S )NrV   rZ   )rC   rN   r   r   re   re   re   rf   r   L  r   rå   re   re   re   rf   Útest_issue_14456J  s    r4  c                   C   sB   t dtdt t td   tdt dt d  t u s>J d S )Nr\   r|   é   rV   )rD   r0   r   rN   r
   re   re   re   rf   Útest_issue_14411O  s    r6  c                   C   s8   t ttd d d td d  d  ttdks4J d S r  rk   re   re   re   rf   Útest_issue_13382S  s    r7  c                   C   s<   t tdtttd  d ttt    ttdks8J d S )Nra   rZ   ©rD   rN   r   r
   re   re   re   rf   Útest_issue_13403W  s    r9  c                   C   sb   t td  ttd  td td d  ttd d   td ttd   ttdks^J d S r#  r8  re   re   re   rf   Útest_issue_13416[  s    r:  c                   C   sx   t td dt dddt   t  d  t td  d td  t   tttd d td d  td  kstJ d S )NrV   rZ   r|   r\   r5  rm   rz   )rD   rR   rN   r
   re   re   re   rf   Útest_issue_13462_  s    r;  c                  C   sH   t d} tt| t ttdks$J ttttt ttdksDJ d S )Nrr   ra   )r   rD   r8   rN   r
   r%   rÿ   re   re   rf   Útest_issue_13750c  s    r<  c                   C   s   t ttttt ttts"J t ttttt tttsDJ t ttttttttsfJ tddtd tt   td t  tttksJ d S r  )	Ú
isinstancerD   r1   rN   r   r
   rC   r-   r   re   re   re   rf   Útest_issue_14276i  s    """r>  c                   C   s0   t dtttt  dt  ttdks,J d S rí   )rD   r   rN   r
   re   re   re   rf   Útest_issue_14514p  s    r?  c                   C   s~  t ttd tt tttt  ttttj	tj
ks>J t ttd tt tttt  ttttj	tj
ks|J t ttttd  ttttj	tj
ksªJ t ttttd  ttttj	tjksØJ t ttttd  ttttj	tjksJ t ttd ttd  ttttj	tjks<J t ttd ttd  tt ttttj tj
kszJ d S r   )rD   r1   rN   r-   r2   r/   r
   rH   r   rc   rd   r.   rœ   re   re   re   rf   Útest_issues_14525t  s    >>..04r@  c                   C   s4   t tttttd   td  ttdks0J d S )NrV   rZ   r   )rD   r%   rN   r-   r
   re   re   re   rf   Útest_issue_14574~  s    rA  c                   C   sº   t tttttjksJ t dtt ttdtj ks<J t dtt tttddks^J t tttttjksxJ t tttt tddksJ t dtt tt dks¶J d S )Nr\   r]   rV   ra   r|   r_   )rD   r<   rN   r
   r   r   r	   r;   re   re   re   rf   Útest_issue_10102  s    "" rB  c                   C   s   t tdd  d S )Nc                   S   s    t ttt ttt  ttS r~   )rD   r   r   rN   r1   r   r
   re   re   re   rf   r     r   z"test_issue_14377.<locals>.<lambda>rå   re   re   re   rf   Útest_issue_14377  s    rC  c                  C   s   t d dt d  dt d d  t d  tt d d   dt d d  t d  tt d t  d   t  d  } t| t ttdd ksJ d S )NrV   r_   r\   rZ   )rN   r=   rD   r
   r   r÷   re   re   rf   Útest_issue_15146  s    8*ÿÿÿrD  c                  C   s°   dt  ddt   ddt   t  d    t d  t d  } t| t ttdksRJ tt dd dt  tt   dt   tt d dtt   dt    } t| t tdks¬J d S )NrV   r_   rZ   rŒ   r!  r]   r\   )rN   rD   r
   r   r   r   r÷   re   re   rf   Útest_issue_15202  s    :FrE  c                   C   s0   t td td d  td  ttdks,J d S )NiÐ  rZ   iÏ  i0øÿÿrk   re   re   re   rf   Útest_issue_15282  s    rF  c                   C   s2   t t tttd  t ttdddks.J d S )NrZ   r[   rX   r   )rD   rN   r   r   r
   re   re   re   rf   Útest_issue_15984¡  s    rG  c                   C   s&   t ttdtt ttdks"J d S rí   )rD   r?   rN   r>   r
   re   re   re   rf   Útest_issue_13571¥  s    rH  c                   C   s*   t ttttdtttjks&J d S rí   )rD   r'   r:   rN   r   rœ   re   re   re   rf   Útest_issue_13575©  s    rI  c                   C   s   t ttt tddd ¡ dks$J t td tddd ¡ dksDJ t dtd  tddd ¡ tu shJ t dt tddd ¡ tu sJ d S )Nr   r^   rX   rZ   rV   )rC   r1   rN   r   r
   r   re   re   re   rf   Útest_issue_17325­  s    $ $rJ  c                   C   s   t t td¡dksJ d S )Nr   )r   rN   rD   re   re   re   rf   Útest_issue_10978Ž  s    rK  c                   C   s    t ttd tttu sJ d S r   )rD   r!   rR   r
   re   re   re   rf   Útest_issue_14313_commentž  s    rL  c                  C   s2   ddt   t   t ¡} t| t ddddks.J d S )NrZ   rW   rX   )rN   r   rD   )rÒ   re   re   rf   Útest_issue_15323Œ  s    rM  c                   C   s,   t ttt  tt tddks(J d S rí   )rD   r   r   rN   re   re   re   rf   Útest_issue_12571Â  s    rN  c                   C   sH   t td td t t  td td  td   tttdksDJ d S r#  rß   re   re   re   rf   Útest_issue_14590Æ  s    rO  c                  C   sR   t d\} }tt| t|  t|  t|    tt|t|  |   |  ksNJ d S )Núa b)r   rD   rN   rO   ©rr   rs   re   re   rf   Útest_issue_14393Ê  s    rR  c                   C   s@   t ttd dtd   ttdt   tttdks<J d S )NrZ   ra   )rD   r   rR   r
   r   re   re   re   rf   Útest_issue_14556Ï  s    rS  c                   C   sL   t dtdd td   dt  dtdd td    tttksHJ d S )NrZ   rV   r\   r|   ©rD   r   rN   r
   re   re   re   rf   Útest_issue_14811Ó  s    rU  c                   C   s    t tttdtdksJ d S )Ni Ê;)rD   r   rN   re   re   re   rf   Útest_issue_16222×  s    rV  c                   C   sD   t ttd  td t  ttd   t ttttdks@J d S rí   rß   re   re   re   rf   Útest_issue_16714Û  s    rW  c                  C   s   t ddd} ttt|  tt|    ttdt| d  ks@J t dddd} ttt|  tt|    ttdt| d  ksJ d S )NrP   Trp   rZ   )rU   rT   )r   rD   r   rR   r
   r>   r    re   re   rf   Útest_issue_16722ß  s    4rX  c                   C   sÀ   t td d td d ttd   td  tt td  ttdksLJ t td d tt td td  ttd   ttdksJ t td tt tttd   ttdksŒJ d S )NrZ   rV   r   r\   )rD   rR   r   r
   re   re   re   rf   Útest_issue_17431æ  s"    $ÿÿÿÿÿ0ÿÿrY  c                   C   s2   t ttt tttt  tdtks.J d S rí   )rD   r7   r   rN   r   re   re   re   rf   Útest_issue_17671î  s    rZ  c                  C   sf   t ddd\} }}}t| d | t| d d |d  ||  |  |t| d|  d  ksbJ d S )Nza b c xTrp   rZ   rV   )r   rD   r%   r
   )rr   rs   rt   rN   re   re   rf   Útest_issue_17751ò  s    r[  c                   C   s@   t tttt tdt t  tttdtt ks<J d S r  )rD   r   rR   r%   r   r
   r   re   re   re   rf   Útest_issue_17792÷  s    r\  c                   C   s@   t ttttdddksJ t ttttdddks<J d S )Nr   r[   ra   rW   rZ   )rD   r   r1   rN   re   re   re   rf   Útest_issue_18118û  s    r]  c                   C   s.   t tttttt tdddks*J d S )Nr   rW   rZ   )rD   r1   r%   rN   re   re   re   rf   Útest_issue_18306   s    r^  c                   C   s<   t ttdt t ttttd   ttdks8J d S )Nr\   rÝ   )rD   r   r   rN   r
   re   re   re   rf   Útest_issue_18378  s    r_  c                   C   sJ   t dtdd t  dt  tttu s,J t t t tttu sFJ d S )NrZ   rV   r\   )rD   r   rN   r
   r   re   re   re   rf   Útest_issue_18399  s    ,r`  c                   C   sH   t ttdtt  ttddtttdtt  ttddksDJ d S )NrV   r[   rX   )rD   r2   rN   r%   r   r
   rC   re   re   re   rf   Útest_issue_18442  s    ra  c                   C   sF   t tttt tddks J t tttt tdddksBJ d S )Nr   rZ   r[   )rD   r   r   rN   re   re   re   rf   Útest_issue_18452  s     rb  c                   C   sD  t ttdt  tttttdt  ttddks8J t ttdt  tttttdt  ttddkspJ t ttdt  tttttdt  ttddksšJ t ttd dt  ttdksÌJ t ttd dt  ttdksðJ t ttd dt  tttttd dt  ttddks2J t ttd dt  tttddks^J t ttd dt  tttdtksJ t ttd dt  tttddks¶J t ttd dt  tt tdtksäJ t ttd dt  tt tdtksJ t ttd dt  tt tdtks@J d S )NrZ   r[   rX   rV   r!  r   )rD   r1   rN   r
   rC   r-   r2   rH   re   re   re   rf   Útest_issue_18473  s    888$$B,,,..rc  c                   C   s@   t dtdt  tdt d  dt  tttdks<J d S ©NrV   r\   rZ   )rD   r   rN   r
   re   re   re   rf   Útest_issue_18482&  s    re  c                   C   s   t tttdtt  tdtdks,J t tttdtt  tdddtdks\J t tttdtt  tdddtd ksJ d S )NrZ   r   rV   rW   rX   r[   )rD   r1   rN   r%   r-   re   re   re   rf   Útest_issue_18508*  s    ,0rf  c                   C   s   t tdd  d S )Nc                   S   s   t tdt t ttS r   )rD   r   rR   rN   r
   re   re   re   rf   r   1  r   z"test_issue_18521.<locals>.<lambda>rå   re   re   re   rf   Útest_issue_185210  s    rg  c                  C   sT   t ddd\} }tt| | |t|ks,J ttt| | |tt|ksPJ d S )NrP  Trp   )r   rD   r   r   rQ  re   re   rf   Útest_issue_189694  s    rh  c                   C   s,   t tttdt   tttdks(J d S rí   )rD   rR   r   r
   r   re   re   re   rf   Útest_issue_18992:  s    ri  c                  C   s<   t d} tt| t| d t| d   | ddks8J d S )NrN   rZ   rV   r   ra   )r   rD   r>   r   re   re   rf   Útest_issue_19067>  s    rj  c                   C   s*   t tdt dt    ttdks&J d S rd  rk   re   re   re   rf   Útest_issue_19586C  s    rk  c                  C   s0   t d} t ddd}t| | | ddks,J d S )NrR   rù   T)Zzeror   )r   rD   )rR   rù   re   re   rf   Útest_issue_13715G  s    rl  c                   C   sT   t td t d tdt  td tdtd     t d  ttdksPJ d S r#  )rD   rR   r1   r
   re   re   re   rf   Útest_issue_15055M  s    rm  c                  C   s   t ddd\} }t d\}}}t|| | t| td| | | | |d     | |  ||  |d|||  | ks~J d S )Nzm viTrp   zB ti dr_   rV   r   )r   rD   r%   )rú   ÚviÚBZtirÒ   re   re   rf   Útest_issue_16708Q  s    rp  c                   C   s   t tddt ttdtd   ttdtd t d ks@J t tddt ttdtd   tt dtd t d ksJ d S )NrZ   r\   rV   r_   )rD   r3   rN   r
   r%   r   re   re   re   rf   Útest_issue_19154W  s    @rq  c                  C   sR  t ddd} t ddd}t ddd}t ddd}t ddd}td}d	|d
  |  | |d| |  |   }|d
 |d
  }|||  |  d }| d| |  |d
| |d
    ||||  |  d  d
| |d	    |d| |  |  |  }	tt|	|  }
t|
d| |  | tdks(J t|
 ¡ d| |  | tdksNJ d S )NÚbetaTrp   Úhrú   Úomegar  rZ   r\   rV   rq   r|   r   )r   r   r   r   rD   r
   rF   )rr  rs  rú   Úwr  r³   Úqrù   rÑ   ÚZr   re   re   rf   Útest_issue_19453\  s    (Lÿ"rx  c                   C   s&   t td d t ttdks"J d S )NrZ   r|   r   rT  re   re   re   rf   Útest_issue_19739o  s    ry  c                   C   s2   t dt  tdtd  d  ttdks.J d S )NrV   r|   rZ   )rD   rN   r%   r
   re   re   re   rf   Útest_issue_19766s  s    rz  c                  C   sÖ   t d} tt| t t tttt| t t ttddks@J t ddd} tt| t t tttt| t t ttddksJ t ddd} tt| t tttddks²J tt| t t ttd	ksÒJ d S )
Nrú   r[   rX   Tr   )Znonzerora   rZ   r   )r   rD   r-   rN   r
   rC   rH   )rú   re   re   rf   Útest_issue_19770w  s    88"r{  c                   C   s  t ttttt ttd tttttt ttd ddksHJ t ttttt ttd ddtttttt ttd ddksJ t ttttt ttd ddtttttt ttd ddksàJ t tttttd tddksJ t dtt   tt tks.J tdtt  tt tksPJ tdtt   tt tkstJ t dtt  tt tksJ d S )NrV   rW   rX   r[   r^   ra   rZ   )rD   r2   rN   r1   r   rC   rH   r
   re   re   re   rf   Útest_issue_7535  s    HLL(&"$r|  c                   C   s2   t td dt  t t tdt d ks.J d S )NrZ   r   rV   )rD   rN   r   re   re   re   rf   Útest_issue_20365  s    r}  c                   C   sH   t dt dt  ddt  ddt    tt tdtd ksDJ d S )NrZ   rV   r   )rD   rN   r+   r   re   re   re   rf   Útest_issue_21031  s    r~  c                   C   s0   t ttt dt d  tdtd ks,J d S )Nr\   rz   r|   )rD   r1   r   rN   re   re   re   rf   Útest_issue_21038  s    r  c                  C   sZ   t ttdt  } t| tdddks*J t| tdddks@J t| tdddksVJ d S )NrZ   r   rW   r[   r^   )r   rN   r1   rD   rÅ   re   re   rf   Útest_issue_20578  s    r  c                  C   s|  t t} | jttdtksJ | jtt dt ks8J t t t } | jttdt t ksbJ | jtt dt tks~J t t t} | jttdt tks€J | jtt dt t ksÂJ | jttdt tksÜJ t t t dt } | jttdt t t ksJ | jtt dt t tks4J | jttdt t t ksVJ | jtt dt t tksxJ d S )N)ZlogxrZ   )r   rN   ZnseriesrO   ró   re   re   rf   Útest_issue_21227¡  s    """r  c                  C   sH   t d tdt d   } |  t d¡dks,J |  ¡  t d¡dksDJ d S rµ   )rN   r-   rD   r2  )r   re   re   rf   Útest_issue_21415º  s    r  c                   C   s(   t ttd tt tttks$J d S rí   )rD   r   rR   r
   r   re   re   re   rf   Útest_issue_21530À  s    r  c                  C   sD   t dd d } tt|  td t d  t| t dd ks@J d S )Nr]   rZ   rV   )r%   rD   rN   rÖ   re   re   rf   Útest_issue_21550Ä  s    r  c                  C   sL   t ttd  ttd  d t td} | tdd dtd  ksHJ d S )NrZ   é   l   Ñqjl   SÍ[	)rD   rN   r   r   )Úoutre   re   rf   Útest_issue_21661É  s    (r  c                   C   s6   t ttttt   td¡tdtdd ks2J d S )NrŒ   r   rZ   i Ø	 )rD   r5   rP   rN   rý   r   re   re   re   rf   Útest_issue_21701Î  s    r  c                  C   sD   t ddd} tdtdt|  d    t}| tt¡tjks@J d S )Nrr   Tr   rZ   rV   )r   rB   r   rN   rD   r
   r   r   )rr   r   re   re   rf   Útest_issue_21721Ò  s    r  c                  C   sd   dt dt t t  dt dt t t d   } |  td¡dksHJ t|  td¡dks`J d S )NrZ   r_   r]   r   )r   r   r   rP   rD   r   )Ztermre   re   rf   Útest_issue_21756Ø  s    4r  c                  C   s@   t d} t| d  td  dtd    | dd¡tks<J d S )Nrr   rV   rZ   r[   )r   r%   rN   rD   r   rÿ   re   re   rf   Útest_issue_21785Þ  s    r  c                   C   s&   t dt dt   ttdks"J d S )Nra   rV   r   rk   re   re   re   rf   Útest_issue_22181ã  s    r  c                  C   sÞ  t dtt dttd  d  d } t dt tt dttd  dt d t d   tt dttd  dt d t d  
   d }t| tt t d t d ksžJ t|tt t d t d ksÜJ t| tt dt dt d ksJ t|tt ddksJ ttt tt t  }t|d	d
}t|tt	t|tt	  krntt kstn J tttd t  tttd t   }}t|ttddt t ksÂJ t|ttddksÚJ d S )Nr-  rV   ry   rö   r]   é<   r[   r   T)ÚforcerW   )
r%   r,   r2   rN   r   r   rD   r   rE   r
   )Úe1Úe2rw   Úexpr2re   re   rf   Útest_issue_22220ç  s     (6,ÿÿ$$&2. r  c                  C   sâ   t ddd\} }t|d |  |d | d  || d    |td| d  ksPJ t|d |  |d | d  || d    ¡  |td| d  ksJ t|d |  |||   |d |    |d |    |td| d  ksÞJ d S )Nzk, nTrp   rZ   )r   rD   r
   r2  )rQ   rR   re   re   rf   Útest_issue_22334ý  s    @Dr  c                   C   s0   t tddt  tt tttdks,J d S r  )rD   r   rN   r%   r
   re   re   re   rf   Útest_sympyissue_22986  s    r  c                  C   s>   dt  dt    dt  dt     } t| t t dks:J d S )NrV   ra   )rN   rD   r
   ró   re   re   rf   Útest_issue_23231  s    $r  c                   C   s4   t dt td  tdt  tdtftks0J d S )NrZ   rV   ra   r   )rB   rN   r   r
   re   re   re   rf   Útest_issue_23596  s    r  c                  C   sº   t t td  t d } t t td  tt  d }t| tddt d t ksXJ t| tddt d t ksxJ t|tddt dt ksJ t|tddt d t ks¶J d S )NrV   r\   r   rW   r[   )r%   r   rN   rD   )Úexpr1r  re   re   rf   Útest_issue_23752  s      r  c                  C   s   t ttd tt  t¡} |  tt¡dks2J |  ¡  tt¡dksJJ |  	t
¡ tt¡dksdJ |  	t
¡ ¡  tt¡dksJ d S r   )r   r2   r   r   rN   r   rD   r
   rF   r®   r1   )r+  re   re   rf   Útest_issue_24276  s
    r  N(  Ú	itertoolsr   Zsympy.concrete.summationsr   Zsympy.core.functionr   r   Z
sympy.corer   Zsympy.core.numbersr   r   r	   r
   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z(sympy.functions.combinatorial.factorialsr   r   r   Z$sympy.functions.elementary.complexesr   r   r   Z&sympy.functions.elementary.exponentialr   r   r   Z%sympy.functions.elementary.hyperbolicr   r   r   r   r   r   r   Z#sympy.functions.elementary.integersr    r!   r"   Z(sympy.functions.elementary.miscellaneousr#   r$   r%   Z$sympy.functions.elementary.piecewiser&   Z(sympy.functions.elementary.trigonometricr'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   Zsympy.functions.special.besselr3   r4   r5   r6   Z'sympy.functions.special.error_functionsr7   r8   r9   r:   r;   r<   Z'sympy.functions.special.gamma_functionsr=   r>   r?   Zsympy.functions.special.hyperr@   Zsympy.integrals.integralsrA   rB   Zsympy.series.limitsrC   rD   Zsympy.simplify.simplifyrE   rF   Zsympy.simplify.hyperexpandrG   Z!sympy.calculus.accumulationboundsrH   Zsympy.core.mulrI   rJ   Zsympy.series.orderrK   Zsympy.testing.pytestrL   rM   Z	sympy.abcrN   rO   rP   rQ   rR   rg   rj   rl   ro   rx   r{   r}   r   r   r   r   r   r   r   r   r   r   r¡   r¢   r€   r§   rš   r¬   rŽ   r¶   r¹   rº   r»   rŸ   r¿   rÁ   rÄ   rÆ   rÔ   r×   rØ   rÙ   rÚ   rÜ   rà   rá   râ   rã   rç   rë   rì   rî   rð   rò   rô   rø   rþ   r   r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r"  r$  r%  r&  r'  r,  r1  r3  r4  r6  r7  r9  r:  r;  r<  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rR  rS  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  re  rf  rg  rh  ri  rj  rk  rl  rm  rp  rq  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  re   re   re   rf   Ú<module>   s   $8 G
	



0	
	

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