a
    kºhþœ  ã                   @   sL	  d dl mZ d dlmZ d dlmZmZ d dlmZm	Z	 d dl
mZ d dlmZ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 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-m.Z. d dl/m0Z0m1Z1m2Z2 d dl3m4Z4m5Z5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZE d dlFmGZGmHZHmIZImJZJ d dlKmLZLmMZMmNZNmOZOmPZPmQZQ d dlRmSZSmTZTmUZU d dlVmWZW d dlXmYZYmZZZ d dl[m\Z\m]Z] d dl^m_Z_m`Z` d dlambZb d dlcmdZd d dlemfZf d dl[mgZg d dlhmiZi d dljmkZkmlZl d dlmmnZnmoZo d d lpmqZqmrZrmsZsmtZt ed!d"d"d#Zud$d% Zvd&d' Zwd(d) Zxd*d+ Zyd,d- Zzd.d/ Z{d0d1 Z|d2d3 Z}d4d5 Z~d6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZekdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zekdvdw Zdxdy Z dzd{ Z¡d|d} Z¢d~d Z£dd Z€dd Z¥dd ZŠdd Z§ekdd Zšdd Z©dd Zªdd Z«dd Z¬dd Z­dd Z®dd Z¯dd Z°dd Z±dd Z²dd Z³d d¡ ZŽd¢d£ Zµd€d¥ Z¶dŠd§ Z·dšd© Zždªd« Z¹d¬d­ Zºd®d¯ Z»d°d± ZŒd²d³ ZœdŽdµ ZŸd¶d· Z¿džd¹ ZÀdºd» ZÁdŒdœ ZÂdŸd¿ ZÃdÀdÁ ZÄdÂdÃ ZÅdÄdÅ ZÆdÆdÇ ZÇdÈdÉ ZÈdÊdË ZÉdÌdÍ ZÊdÎdÏ ZËdÐdÑ ZÌdÒdÓ ZÍdÔdÕ ZÎdÖd× ZÏdØdÙ ZÐdÚdÛ ZÑdÜdÝ ZÒdÞdß ZÓdàdá ZÔdâdã ZÕdädå ZÖdædç Z×dèdé ZØdêdë ZÙdìdí ZÚdîdï ZÛdðdñ ZÜdòdó ZÝdôdõ ZÞdöd÷ Zßdødù Zàdúdû Zádüdý Zâdþdÿ Zãd d Zädd Zådd Zædd Zçdd	 Zèd
d Zédd Zêdd Zëdd Zìdd Zídd Zîdd Zïdd Zðdd Zñdd Zòdd Zód d! Zôd"d# Zõd$d% Zöd&d' Z÷d(d) Zød*d+ Zùd,d- Zúd.d/ Zûd0d1 Züd2d3 Zýd4d5 Zþd6d7 Zÿd8d9 Z d:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK Z	dLdM Z
dNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Z dzd{ Z!d|d} Z"d~d Z#dd Z$dd Z%dS (  é    )Úproduct)ÚSum)ÚFunctionÚdiff)Ú
EulerGammaÚGoldenRatio)ÚMod)ÚEÚIÚRationalÚooÚpiÚzoo)ÚS)ÚSymbolÚsymbols)Ú	fibonacci)ÚbinomialÚ	factorialÚsubfactorial)ÚAbsÚreÚsign)ÚLambertWÚexpÚlog)ÚatanhÚasinhÚacoshÚacothÚacschÚasechÚtanhÚsinh)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
elliptic_eÚ
elliptic_k)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)rH   rT   r   r   r   r)   rG   rU   r   r1   rB   r   ÚNaNrO   r5   r   r6   r   r2   rL   ÚNegativeInfinityÚInfinityr4   r3   r   r
   r/   r#   © rk   rk   úL/var/www/auris/lib/python3.9/site-packages/sympy/series/tests/test_limits.pyÚtest_basic1)   sr     $ &.6>,."""$(&$"(&4620$$$$""$ (.6"$"$.rm   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   r]   r^   r`   rg   r\   é   ©rH   rT   r   r   rk   rk   rk   rl   Útest_basic2p   s     ""rp   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 )Nr`   r   r]   r^   ra   ©rH   rT   r   rk   rk   rk   rl   Útest_basic3{   s    rr   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 )
Nr\   r   r`   é   rf   re   i   rb   é	   )rH   rT   rU   r)   r   rF   r   rk   rk   rk   rl   Útest_basic4   s
     $0$ru   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©r[   r   ztau xr\   r`   re   ç      à?rb   )r   r   rH   r   r0   r   )ÚaÚbÚcÚAÚtaurT   Úexprrk   rk   rl   Útest_log   s"    8ÿÿ(ÿÿÿr~   c                   C   s6   t ttd dd td  tddtddks2J d S )Né   rb   r\   re   r]   r`   é   )rH   r(   rT   r   rk   rk   rk   rl   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 )Nr\   é   r`   r   Trw   g      À?rt   rc   rg   rb   )r)   rT   r*   r   rH   )Zfunc1Zfunc2Zfunc3rk   rk   rl   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   rj   rh   )ÚclsÚargrk   rk   rl   Úevalš   s    
ztest_basic5.<locals>.my.evalN)Ú__name__Ú
__module__Ú__qualname__Úclassmethodr   rk   rk   rk   rl   Úmy§   s   r   )r   rH   rT   r   rG   )r   rk   rk   rl   Útest_basic5Š   s    r   c                   C   s0   t tt tt  tdtt dt  ks,J d S ©Nr\   )rH   rT   rU   rV   rk   rk   rk   rl   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   r`   rd   r^   )rG   r5   rT   ÚdoitÚargsr   rk   rk   rk   rl   Ú
test_Limit³   s     r   c                   C   s$  t tttdddksJ t tttdddks4J t tttdddksNJ t tttdddkshJ t tttdddksJ t tttdddksJ t tttdddks¶J t tttdddksÐJ t tttdddksêJ t tttdddksJ t tttd	dd	ks"J t tttd	dd
ks>J t ttdt  d tddtddkslJ t ttd tt ttttj tdd ks€J t tttttdksÂJ t ttttt dksâJ t t	ttttdks J t t	tttt dks J d S )Nre   r]   ra   rf   rg   r   r`   r\   éø   é÷   rb   rw   )
rH   r%   rT   r   r   rL   r   ÚHalfr0   r$   rk   rk   rk   rl   Ú
test_floor¹   s$    .8 r   c                   C   s  t ttttdddksJ t ttttdddks<J t ttttdddksZJ t ttttdddksxJ t tdtt tdddksJ t tdtt tdddksŒJ t tdtt tdddksÞJ t tdtt tdddksJ d S )Nr   r]   ra   rg   rc   r   )rH   r%   r5   rT   r1   rk   rk   rk   rl   Ú&test_floor_requires_robust_assumptionsÒ   s    """r   c                   C   sš  t tttdddksJ t tttdddks4J t tttdddksNJ t tttdddkshJ t tttdddksJ t tttdddksJ t tttdddks¶J t tttdddksÐJ t tttdddksêJ t tttdddksJ t tttd	dd
ks"J t tttd	dd	ks>J t ttdt  d tddtddkslJ t ttd tt ttttj tdd ks€J d S )Nre   r]   rg   ra   r   r`   r\   rb   r   éù   rw   )rH   r$   rT   r   r   rL   r   r   rk   rk   rk   rl   Útest_ceilingÝ   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   r]   r`   ra   rc   r   )rH   r$   r5   rT   r1   rk   rk   rk   rl   Ú(test_ceiling_requires_robust_assumptionsð   s    """r   c                   C   s°  t tttttddksJ t ttdt  tttddksDJ t ttdt  tt tdtkslJ t ttt tttdtksJ t ttttdddks¬J t ttttdddksÊJ t ttttdddksèJ t ttd tdddksJ ttdd  t td	t d tdddks:J t td	t d tdddks^J t ttt	j
 tddt	dd ksJ t tdt tdtddks¬J d S )
Nr   r`   r]   ra   rd   r\   c                   S   s   t tttddS ©Nr   rd   )rH   r&   rT   rk   rk   rk   rl   Ú<lambda>  ó    ztest_frac.<locals>.<lambda>re   )rH   r&   rT   r   rL   r5   r1   rQ   Ú
ValueErrorr   r   rk   rk   rk   rl   Ú	test_fracû   s    &(" $$*r   c                   C   s   t tttt tdddks"J t tttt tdddksDJ t ttt t tdddkshJ t ttt t tdddksJ d S )Nr   r]   ra   re   )rH   r%   r5   rT   r6   rk   rk   rk   rl   Útest_issue_14355  s    ""$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 )NrT   T©Úrealr`   r   r\   )r   rH   r0   r5   r)   r   r   ©rT   rk   rk   rl   Ú	test_atan  s    $r€   c                  C   s  t tttddksJ t ttttddks4J t ttttddksPJ t tttd tdtdkstJ t ttt ttt  dt  tdttksšJ t ttttd  tt	dksÌJ t tttttd  tttd td d   d  tt	dksJ t tttd d d tddt	ksBJ t ttttdt	ks`J t tttttdt	ksJ t
ddd} t tt| d t|  | t	dksžJ t | td|  t ttd|     d | ddksòJ t t| t|  | td	d
ksJ d S )Nr   r`   r\   rb   r]   rV   Trv   ra   rg   )rH   ÚabsrT   r5   r1   r   rU   r   r   r   r   r   ©rV   rk   rk   rl   Útest_set_signs  s    $4$J,"*:r§   c                  C   st   t ddd} ttd|  t|  | ddtddks8J ttdtt| ttd|    | dtdkspJ d S )	NrT   Tr¡   r`   r   r]   rg   r\   )r   rN   r5   r0   rL   rH   r   r)   r£   rk   rk   rl   Útest_heuristic8  s    ,rš   c                  C   sN   t ddd} d|  t|  t  }t|ttdks6J | tt¡dksJJ d S )NrV   Trv   rg   r   )r   r   rT   rH   r   )rV   Úfrk   rk   rl   Útest_issue_3871>  s    rª   c                  C   s   t d} t ddd}td||   |  | tt|ks8J td|d|    |  | tt|d ksdJ td|d|  d   |  | tt|d ksJ t|d |d  | |ttdksŒJ tddd|  |  |tdtj ksæJ tdd|  | d| |  |tttd	ksJ d S )
NrX   rT   Tr¡   r`   r\   re   r   z1/3)r   rH   r   r   r   ÚExp1©rX   rT   rk   rk   rl   Útest_exponentialE  s    $,0(*r­   c                  C   s8   t d} tdt| t|    |  | tttks4J d S )NrX   r`   )r   rH   rT   r5   r   r   )rX   rk   rk   rl   Útest_exponential2P  s    r®   c                  C   s.   t dt t} t| tt}| ¡ tu s*J d S r   ©rE   rT   rG   r   r   ©r©   Úlrk   rk   rl   Ú	test_doitU  s    r²   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 )
Nr`   re   r\   rg   rb   rf   F)Úevaluater   )rH   r5   rW   r   rL   r1   rM   rJ   r   rX   Úrewriter   r   rT   )ÚloÚhiÚt1Út2Úerk   rk   rl   Útest_series_AccumBounds[  s    *.. 84:,rº   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 ©Nr`   r   )rH   r9   rT   r   r
   r8   r7   r:   rk   rk   rk   rl   Ú!test_bessel_functions_at_infinityr  s"    "& "  "$ "rŒ   c                  C   s2   t dt t} t| tt}|jdd|ks.J d S )Nr\   F©Údeepr¯   r°   rk   rk   rl   Ú
test_doit2  s    r¿   c                   C   s.   t ttt ttd  tt dks*J d S r»   ro   rk   rk   rk   rl   Útest_issue_2929  s    rÀ   c                   C   s   t dtt td  ttjddttj  ks4J t tttd d tdtdtd ksdJ t tttd d tddtd ksJ d S )Nr`   r\   r   r   )rH   r1   rT   r   r   r5   r¥   rk   rk   rk   rl   Útest_issue_3792  s    40rÁ   c                   C   sš   t dtd  tdtddks"J t dtt  tdtjdt  ksHJ t tttd d  tdtdd kstJ t tttd t  tdtddt  ks€J d S )Nr`   rb   r\   rc   é   r   )rH   rT   r   r   r   ÚOner   rk   rk   rk   rl   Útest_issue_4090  s    "&,rÄ   c                   C   s@   t tttdddtu sJ t ttttd dddks<J d S )Nr   r]   r^   r\   )rH   r2   rT   r   r   rk   rk   rk   rl   Útest_issue_4547€  s    rÅ   c                   C   s   t td tttd   kr$tu s*n J t td tddksBJ t td tddksZJ t td ttdksrJ t td tdtjksJ d S )Nrw   é   r   r   g      à¿)rH   rT   r   r   r   rk   rk   rk   rl   Útest_issue_5164©  s
    *rÇ   c                  C   s,   ddt   dt   } t| t dtks(J d S )Nç      ð?r   )rT   rH   r	   )Úfuncrk   rk   rl   Útest_issue_5383±  s    rÊ   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 )Nr`   r\   r   rb   ih  )rT   r   r   r   r   rH   r   ©r}   rk   rk   rl   Útest_issue_14793¶  s    *
ÿÿÿrÌ   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 )	Nrg   r`   r\   rb   ra   r]   r   r^   )Úlistr   rT   r   r   r   r   r
   ÚlenÚ	enumerateÚziprH   ÚAssertionErrorÚprint)
ÚtestsÚresultsÚir   ÚresrU   Úsr¹   ÚdÚeqrk   rk   rl   Útest_issue_5183Œ  s$    ý((ýrÚ   c                  C   sº   t ttt ttdksJ t tttttd ks8J t tttttu sPJ t ttt ttdkslJ t ttttj	t
tksJ tddd} t | td|   | ddks¶J d S )Nr   r\   ÚrTr¡   r`   )rH   r5   rT   r   r0   r   rB   r1   r   r   r)   r   ©rÛ   rk   rk   rl   Útest_issue_5184Ô  s    rÝ   c                   C   s*   t dt dt  tj tddks&J d S r»   )rH   rU   r   r«   rk   rk   rk   rl   Útest_issue_5229ß  s    rÞ   c            	      C   sê   t tttgt d dtd tttdd gddg} ddt tddt tddtt ddtt ddtt f}t| t|ksJ tt	| |D ]V\}\}}|\}}}|t
}zt|t
||d|ksÆJ W q tyâ   d sÞJ Y q0 qd S )Nr\   r   rb   ra   r]   r^   )rÍ   r   r2   r6   r   r   r   rÎ   rÏ   rÐ   rT   rH   rÑ   rÒ   )	rÓ   rÔ   rÕ   r   rÖ   r©   r±   rØ   rÙ   rk   rk   rl   Útest_issue_4546ã  s    
 þÿ
rß   c                   C   sX   t dttd  dt  tddks(J t ddt  ddt   t tddksTJ d S )Nr`   rb   r   rc   )rH   rT   r   rk   rk   rk   rl   Útest_issue_3934ø  s    (rà   c                   C   s   t td dtd   ttdks$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 )NrÆ   r`   éd   i]  éè  ©rH   rT   r   r   rk   rk   rk   rl   Útest_issue_5955ý  s    $$$rä   c                   C   s0   t tdtt ttt tddks,J d S r»   )rH   r   r5   rT   r2   rk   rk   rk   rl   Útest_newissue  s    rå   c                   C   sŒ   t tt ttttt ttks$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 r»   )rH   rT   r   rG   r5   rk   rk   rk   rl   Útest_extended_real_line  s    $<$ræ   c                  C   sJ   t ddd} t| t td| ks&J tt| d d  | ttu sFJ d S )NrT   Trv   r`   r\   r   )r   rO   r   rH   r£   rk   rk   rl   Útest_order_oo  s    rç   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttt ttS r   ©rH   r   rT   rU   r   rk   rk   rk   rl   r     r   z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ttS r   rè   rk   rk   rk   rl   r     r   ©rQ   ÚNotImplementedErrorrk   rk   rk   rl   Útest_issue_5436  s    rë   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttdddS )Nr   r^   ©rG   rT   rk   rk   rk   rl   r     r   z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   Ú0r^   rì   rk   rk   rk   rl   r     r   )rQ   Ú	TypeErrorr   rk   rk   rk   rl   Útest_Limit_dir  s    rï   c                   C   s²   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 t ttdd dttdd   ttdksJ t td dtd   ttdks®J d S )Nr`   râ   éM   rb   gfffffFY@©rH   rT   r   r   rk   rk   rk   rl   Útest_polynomial   s    ,.0rò   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 ©Nr`   )rH   rU   rT   rV   r   rk   rk   rk   rl   Útest_rational'  s    Drô   c                   C   s<   t ttt tdt t  tdtttt  ks8J d S ©Nr\   r   )rH   r   rT   rV   rU   r   r   rk   rk   rk   rl   Útest_issue_5740,  s    rö   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 )NrX   TrY   r`   r\   )r   rT   rH   Úcancel)rX   rÛ   rk   rk   rl   Útest_issue_63660  s    0rø   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   r\   r`   )r   rT   rH   r   r)   r   r	   rB   ©r©   rk   rk   rl   Útest_factorial6  s
    0rú   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 )	Nrc   rb   r   r\   é#   rs   é   r`   )rT   r   rU   r   r   rH   r   ©r¹   rk   rk   rl   Útest_issue_6560@  s    4ÿÿÿ
ÿrþ   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 )NrX   rÛ   Trv   rz   ÚpÚm©Únegativer\   r`   c                      s   t  tS r   )rH   r   rk   ©r}   rX   rk   rl   r   O  r   z!test_issue_5172.<locals>.<lambda>)r   ÚsubsrQ   rê   rH   r   rJ   )rÛ   rz   rÿ   r   rk   r  rl   Útest_issue_5172E  s$    *.ÿÿ
ÿ"ÿr  c                  C   s,   t d} tttt|   ttdks(J d S )Nrx   r`   )r   rH   r)   rT   r   ©rx   rk   rk   rl   Útest_issue_7088U  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 )Nr\   r   ra   re   r`   rg   rb   )rH   r/   r
   rT   r   r+   r0   r   r   r,   r   r   r.   r-   r   r)   r'   rk   rk   rk   rl   Útest_branch_cutsZ  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 )Nrx   r`   r\   r   )r   rV   r)   r5   r1   rH   r   r   )rx   r¹   rk   rk   rl   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 rõ   )rH   r   r;   rT   r   rk   rk   rk   rl   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 )Nrx   r   )r   rH   rT   r   r   r  rk   rk   rl   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dxr`   r   r\   )r   rH   r)   r   rT   )r  rk   rk   rl   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 )Nrk   )r`   )r   r   rd   )rD   rT   rK   rH   r   )ÚGÚgrk   rk   rl   Útest_issue_6052¢  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 )Nr`   rs   r   r\   g       @)r)   rT   r7   rH   r   ZevalfrË   rk   rk   rl   Útest_issue_7224©  s    $r  c                  C   s   t d} t| ttdt| ttdddks0J tt| td  td | td   tdtt| td  td | td   tdddksJ d S )Nr©   r   r]   r^   r\   r   )r   rH   rT   rG   rù   rk   rk   rl   Útest_issue_7391_8166¯  s    (r  c                   C   s&   t ttddd  ttdks"J d S )Nr`   g    eÍÍAr   )rH   rX   r   r   rk   rk   rk   rl   Útest_issue_8208¶  s    r  c                   C   s<   t ttdd d ttd tdd  tddks8J d S )Nr`   r   r\   rb   rÆ   r   )rH   rT   r   r)   rk   rk   rk   rl   Útest_issue_8229º  s    r  c                  C   s4   t ddd\} }ttd||   |tdks0J d S )Nzd tTrv   r`   rg   )r   rH   r<   r   )rØ   Útrk   rk   rl   Útest_issue_8433Ÿ  s    r  c                  C   sH   t dddd} t ddd}t||  t|  t|  | tdksDJ d S )NrW   T)rZ   ZnonnegativeÚlamdarv   r   )r   rH   r   r   r   )rW   r  rk   rk   rl   Útest_issue_8481Ã  s    r  c                   C   sJ   t tttd tttksJ t tttd dt   ttdksFJ d S )Nr\   rb   r   )rH   r   rX   r   rk   rk   rk   rl   Útest_issue_8462É  s    r  c                  C   s@   t dddd} t d}t||  |t ttd|   ks<J d S )NrX   TrY   rT   rg   )r   rH   r   r   r¬   rk   rk   rl   Útest_issue_8634Î  s    r  c                  C   s  t ddd} t ddd}t| t | td   | tdks<J t| t | td   | ttks`J t| t | td   | ttksJ t| t | t| d	   | ttks¬J t ddd} t| t | td	   | ttksÜJ t| t | td
   | tt ksJ d S )NrT   Tr¡   rW   rv   r   rc   g      @r`   r\   )r   rH   rX   r   )rT   rW   rk   rk   rl   Útest_issue_8635_18176Ô  s    $$$($r  c                   C   s   t tttttu sJ d S r   )rH   r   rT   r   rk   rk   rk   rl   Útest_issue_8730à  s    r  c                      s`   t dddt ddd ttt  d    tdksHJ tt fdd	 d S )
NrX   T©rZ   rz   rv   r`   r   c                      s$   t tt     tS r   )rH   r   r   rk   ©rz   rX   rk   rl   r   é  r   z!test_issue_9252.<locals>.<lambda>)r   rH   r   r   rQ   rê   rk   rk   r  rl   Útest_issue_9252ä  s    0r  c                   C   s"   t ttd tdddksJ d S )Nrü   r   ra   )rH   r5   rT   rk   rk   rk   rl   Útest_issue_9558ì  s    r   c                   C   s2   t dt ttdt td   tttks.J d S )NrÆ   r\   )rH   rW   r   r   r   rk   rk   rk   rl   Útest_issue_10801ð  s    r!  c                  C   s8   t ddd\} }tt| | t|  | d|ks4J d S )Nzs xTr¡   r   )r   rH   r<   )r×   rT   rk   rk   rl   Útest_issue_10976õ  s    r"  c                   C   s<   t ttttd t tdt t   ttdks8J d S ©Nr`   r\   )rH   r   rX   r   r)   r   r   rk   rk   rk   rl   Útest_issue_9041ú  s    r$  c                  C   s   t d\} }}t| | |j|hks&J t| | |dj|hks@J t| | | | |j|hks`J t| d  | | d |j||hksJ d S )Nzx, y, ara   r\   )r   rG   Zfree_symbols)rT   rU   rx   rk   rk   rl   Útest_issue_9205þ  s
     r%  c                   C   sT   t dttd td  ttdks&J t dttdd  td  ttdksPJ d S )Né   rb   r`   )rH   r   rX   r   rk   rk   rk   rl   Útest_issue_9471  s    &r'  c                   C   s(   t ttd tt tttks$J d S ró   )rH   r   rX   r   r   rk   rk   rk   rl   Útest_issue_10382  s    r(  c                   C   s$   t ttdt ttdks J d S r#  )rH   r=   r   rT   r   rk   rk   rk   rl   Útest_issue_11496  s    r)  c                   C   s<   t ttt t tt  t tdtttd   ks8J d S ©Nr   r`   )rJ   rH   rT   rU   rX   rk   rk   rk   rl   Útest_issue_11879  s    r+  c                  C   sF   t d} td|  | tdks J tdd|   | ttddksBJ d S )NrW   rÈ   r`   g333333Ó?rb   é
   )r   rH   r   r   )rW   rk   rk   rl   Útest_limit_with_Float  s    r-  c                   C   sD   t dt dt d   td d  td  tttddks@J d S ©Nrb   r`   r\   rñ   rk   rk   rk   rl   Útest_issue_10610  s    r/  c                   C   s  t tttt tddtdks&J t tttt tddtddt t  ksXJ ttdd  t tttt tttksJ t ttt	t tddtdks¬J t ttt	t tddt ksÐJ ttdd  t ttt	t tttksþJ d S )Nr   r]   r\   ra   c                   S   s   t tttt tddS r   )rH   r   rT   r!   rk   rk   rk   rl   r   $  r   z"test_issue_10868.<locals>.<lambda>c                   S   s   t tttt tddS r   )rH   r   rT   r    rk   rk   rk   rl   r   (  r   )
rH   r   rT   r!   r
   r   rQ   r   r   r    rk   rk   rk   rl   Útest_issue_10868!  s    &2 &$r0  c                   C   s$   t ttt t ttdks J d S ró   )rH   rX   r1   r   rk   rk   rk   rl   Útest_issue_6599,  s    r1  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 )Nrb   r\   r,  ro   rk   rk   rk   rl   Útest_issue_125550  s    6r2  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)r[   r¢   r\   r`   rœ   )r   r)   r  ZfactorrH   )rÛ   rV   rT   rx   ry   Ús0ÚKZF0r×   ÚTÚfxrk   rk   rl   Útest_issue_127695  s$    :"ÿ:ÿ:þ:ý*üüür7  c                   C   sz   t tdddt d   dt t  dt d dt dtj    dt d dt dtj    tttd	d
ksvJ d S )Né   rc   éûÿÿÿr`   i@¶  r\   r   iúÿÿÿé   é$   )rH   r)   rT   r   r   r   r   rk   rk   rk   rl   Útest_issue_13332A  s    Bÿÿÿr<  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   )rH   rT   r5   r1   r   Úexpandrk   rk   rk   rl   Útest_issue_12564F  s    .,$$&r>  c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t tttt ¡ S r   )rG   r   rT   r   r   rk   rk   rk   rl   r   P  r   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  tt ¡ S )Nr\   r`   )rG   rT   r   r   rk   rk   rk   rl   r   Q  r   ré   rk   rk   rk   rl   Útest_issue_14456O  s    r?  c                   C   sB   t dtdt t td   tdt dt d  t u s>J d S )Nrb   r   é   r\   )rH   r4   r   rT   r   rk   rk   rk   rl   Útest_issue_14411T  s    rA  c                   C   s8   t ttd d d td d  d  ttdks4J d S r#  rq   rk   rk   rk   rl   Útest_issue_13382X  s    rB  c                   C   s<   t tdtttd  d ttt    ttdks8J d S )Nrg   r`   ©rH   rT   r   r   rk   rk   rk   rl   Útest_issue_13403\  s    rD  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.  rC  rk   rk   rk   rl   Útest_issue_13416`  s    rE  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 )Nr\   r`   r   rb   r@  rs   r   )rH   rX   rT   r   rk   rk   rk   rl   Útest_issue_13462d  s    rF  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 )Nrx   rg   )r   rH   r<   rT   r   r)   r  rk   rk   rl   Útest_issue_13750h  s    rG  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
isinstancerH   r5   rT   r   r   rG   r1   r	   rk   rk   rk   rl   Útest_issue_14276n  s    """rI  c                   C   s0   t dtttt  dt  ttdks,J d S ró   )rH   r   rT   r   rk   rk   rk   rl   Útest_issue_14514u  s    rJ  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   )rH   r5   rT   r1   r6   r3   r   rL   r   ri   rj   r2   rÃ   rk   rk   rk   rl   Útest_issues_14525y  s    >>..04rK  c                   C   s4   t tttttd   td  ttdks0J d S ©Nr\   r`   r   )rH   r)   rT   r1   r   rk   rk   rk   rl   Útest_issue_14574  s    rM  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 )Nrb   rc   r\   rg   r   re   )rH   r@   rT   r   r   r   r   r?   rk   rk   rk   rl   Útest_issue_10102  s    "" rN  c                   C   s   t tdd  d S )Nc                   S   s    t ttt ttt  ttS r   )rH   r   r
   rT   r5   r   r   rk   rk   rk   rl   r     r   z"test_issue_14377.<locals>.<lambda>ré   rk   rk   rk   rl   Útest_issue_14377  s    rO  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 )Nr\   re   rb   r`   )rT   rA   rH   r   r   rý   rk   rk   rl   Útest_issue_15146  s    8*ÿÿÿrP  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 )Nr\   re   r`   rÂ   r,  rc   rb   )rT   rH   r   r   r   r   rý   rk   rk   rl   Útest_issue_15202  s    :FrQ  c                   C   s0   t td td d  td  ttdks,J d S )NiÐ  r`   iÏ  i0øÿÿrq   rk   rk   rk   rl   Útest_issue_15282¢  s    rR  c                   C   s2   t t tttd  t ttdddks.J d S )Nr`   ra   r^   r   )rH   rT   r   r   r   rk   rk   rk   rl   Útest_issue_15984Š  s    rS  c                   C   s&   t ttdtt ttdks"J d S ró   )rH   rC   rT   rB   r   rk   rk   rk   rl   Útest_issue_13571ª  s    rT  c                   C   s*   t ttttdtttjks&J d S ró   )rH   r+   r>   rT   r   rÃ   rk   rk   rk   rl   Útest_issue_13575®  s    rU  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   rd   r^   r`   r\   )rG   r5   rT   r   r   r   rk   rk   rk   rl   Útest_issue_17325²  s    $ $rV  c                   C   s   t t td¡dksJ d S ©Nr   )r   rT   rH   rk   rk   rk   rl   Útest_issue_10978¹  s    rX  c                   C   s    t ttd tttu sJ d S r   )rH   r%   rX   r   rk   rk   rk   rl   Útest_issue_14313_commentœ  s    rY  c                  C   s2   ddt   t   t ¡} t| t ddddks.J d S ©Nr`   r]   r^   )rT   r   rH   )rØ   rk   rk   rl   Útest_issue_15323Á  s    r[  c                   C   s,   t ttt  tt tddks(J d S ró   )rH   r   r   rT   rk   rk   rk   rl   Útest_issue_12571Æ  s    r\  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.  rã   rk   rk   rk   rl   Útest_issue_14590Ê  s    r]  c                  C   sR   t d\} }tt| t|  t|  t|    tt|t|  |   |  ksNJ d S )Núa b)r   rH   rT   rU   ©rx   ry   rk   rk   rl   Útest_issue_14393Î  s    r`  c                   C   s@   t ttd dtd   ttdt   tttdks<J d S )Nr`   rg   )rH   r   rX   r   r   rk   rk   rk   rl   Útest_issue_14556Ó  s    ra  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 )Nr`   r\   rb   r   ©rH   r   rT   r   rk   rk   rk   rl   Útest_issue_14811×  s    rc  c                   C   s    t tttdtdksJ d S )Ni Ê;)rH   r   rT   rk   rk   rk   rl   Útest_issue_16222Û  s    rd  c                   C   sD   t ttd  td t  ttd   t ttttdks@J d S ró   rã   rk   rk   rk   rl   Útest_issue_16714ß  s    re  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 )NrV   Trv   r`   )r[   rZ   )r   rH   r   rX   r   rB   rŠ   rk   rk   rl   Útest_issue_16722ã  s    4rf  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 )Nr`   r\   r   rb   )rH   rX   r   r   rk   rk   rk   rl   Útest_issue_17431ê  s"    $ÿÿÿÿÿ0ÿÿrg  c                   C   s2   t ttt tttt  tdtks.J d S ró   )rH   r;   r   rT   r   rk   rk   rk   rl   Útest_issue_17671ò  s    rh  c                  C   sf   t ddd\} }}}t| d | t| d d |d  ||  |  |t| d|  d  ksbJ d S )Nza b c xTrv   r`   r\   )r   rH   r)   r   )rx   ry   rz   rT   rk   rk   rl   Útest_issue_17751ö  s    ri  c                   C   s@   t tttt tdt t  tttdtt ks<J d S r#  )rH   r   rX   r)   r   r   r   rk   rk   rk   rl   Útest_issue_17792û  s    rj  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   ra   rg   r]   r`   )rH   r   r5   rT   rk   rk   rk   rl   Útest_issue_18118ÿ  s    rk  c                   C   s.   t tttttt tdddks*J d S )Nr   r]   r`   )rH   r5   r)   rT   rk   rk   rk   rl   Útest_issue_18306  s    rl  c                   C   s<   t ttdt t ttttd   ttdks8J d S )Nrb   rá   )rH   r   r   rT   r   rk   rk   rk   rl   Útest_issue_18378  s    rm  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 )Nr`   r\   rb   )rH   r   rT   r   r   rk   rk   rk   rl   Útest_issue_18399  s    ,rn  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 )Nr\   ra   r^   )rH   r6   rT   r)   r   r   rG   rk   rk   rk   rl   Útest_issue_18442  s    ro  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   r`   ra   )rH   r¥   r   rT   rk   rk   rk   rl   Útest_issue_18452  s     rp  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 )Nr`   ra   r^   r\   r,  r   )rH   r5   rT   r   rG   r1   r6   rL   rk   rk   rk   rl   Útest_issue_18473  s    888$$B,,,..rq  c                   C   s@   t dtdt  tdt d  dt  tttdks<J d S ©Nr\   rb   r`   )rH   r   rT   r   rk   rk   rk   rl   Útest_issue_18482*  s    rs  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 )Nr`   r   r\   r]   r^   ra   )rH   r5   rT   r)   r1   rk   rk   rk   rl   Útest_issue_18508.  s    ,0rt  c                   C   s   t tdd  d S )Nc                   S   s   t tdt t ttS r   )rH   r   rX   rT   r   rk   rk   rk   rl   r   5  r   z"test_issue_18521.<locals>.<lambda>ré   rk   rk   rk   rl   Útest_issue_185214  s    ru  c                  C   sT   t ddd\} }tt| | |t|ks,J ttt| | |tt|ksPJ d S )Nr^  Trv   )r   rH   r   r   r_  rk   rk   rl   Útest_issue_189698  s    rv  c                   C   s,   t tttdt   tttdks(J d S ró   )rH   rX   r   r   r   rk   rk   rk   rl   Útest_issue_18992>  s    rw  c                  C   s<   t d} tt| t| d t| d   | ddks8J d S )NrT   r`   r\   r   rg   )r   rH   rB   r£   rk   rk   rl   Útest_issue_19067B  s    rx  c                   C   s*   t tdt dt    ttdks&J d S rr  rq   rk   rk   rk   rl   Útest_issue_19586G  s    ry  c                  C   s0   t d} t ddd}t| | | ddks,J d S )NrX   rÿ   T)Zzeror   )r   rH   )rX   rÿ   rk   rk   rl   Útest_issue_13715K  s    rz  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.  )rH   rX   r5   r   rk   rk   rk   rl   Útest_issue_15055Q  s    r{  c                  C   s   t ddd\} }t d\}}}t|| | t| td| | | | |d     | |  ||  |d|||  | ks~J d S )Nzm viTrv   zB ti dre   r\   r   )r   rH   r)   )r   ÚviÚBZtirØ   rk   rk   rl   Útest_issue_16708U  s    r~  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 )Nr`   rb   r\   re   )rH   r7   rT   r   r)   r   rk   rk   rk   rl   Útest_issue_19154[  s    @r  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betaTrv   Úhr   Úomegar  r`   rb   r\   rw   r   r   )r   r   r   r   rH   r   rJ   )r  r  r   Úwr  r¹   Úqrÿ   r×   ÚZr	   rk   rk   rl   Útest_issue_19453`  s    (Lÿ"r  c                   C   s&   t td d t ttdks"J d S )Nr`   r   r   rb  rk   rk   rk   rl   Útest_issue_19739s  s    r  c                   C   s2   t dt  tdtd  d  ttdks.J d S )Nr\   r   r`   )rH   rT   r)   r   rk   rk   rk   rl   Útest_issue_19766w  s    r  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 )
Nr   ra   r^   Tr¡   )Znonzerorg   r`   r   )r   rH   r1   rT   r   rG   rL   )r   rk   rk   rl   Útest_issue_19770{  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 )Nr\   r]   r^   ra   rd   rg   r`   )rH   r6   rT   r5   r   rG   rL   r   rk   rk   rk   rl   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 )Nr`   r   r\   )rH   rT   r	   rk   rk   rk   rl   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 )Nr`   r\   r   )rH   rT   r/   r	   rk   rk   rk   rl   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 )Nrb   r   r   )rH   r5   r   rT   rk   rk   rk   rl   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 )Nr`   r   r]   ra   rd   )r¥   rT   r5   rH   rË   rk   rk   rl   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logxr`   )r   rT   ZnseriesrU   rù   rk   rk   rl   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 r»   )rT   r1   rH   r=  )r   rk   rk   rl   Útest_issue_21415Ÿ  s    r  c                   C   s(   t ttd tt tttks$J d S ró   )rH   r#   rX   r   r	   rk   rk   rk   rl   Útest_issue_21530Ä  s    r  c                  C   sD   t dd d } tt|  td t d  t| t dd ks@J d S )Nrc   r`   r\   )r)   rH   rT   rÜ   rk   rk   rl   Útest_issue_21550È  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 )Nr`   é   l   Ñqjl   SÍ[	)rH   rT   r   r   )Úoutrk   rk   rl   Útest_issue_21661Í  s    (r  c                   C   s6   t ttttt   td¡tdtdd ks2J d S )NrÂ   r   r`   i Ø	 )rH   r9   rV   rT   r  r   rk   rk   rk   rl   Útest_issue_21701Ò  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 )Nrx   Tr¡   r`   r\   )r   rF   r   rT   rH   r   r   r   )rx   r
   rk   rk   rl   Útest_issue_21721Ö  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 )Nr`   re   rc   r   )r   r
   r   rV   rH   r   )Ztermrk   rk   rl   Útest_issue_21756Ü  s    4r  c                  C   s@   t d} t| d  td  dtd    | dd¡tks<J d S )Nrx   r\   r`   ra   )r   r)   rT   rH   r
   r  rk   rk   rl   Útest_issue_21785â  s    r  c                   C   s&   t dt dt   ttdks"J d S )Nrg   r\   r   rq   rk   rk   rk   rl   Útest_issue_22181ç  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 )Nr8  r\   r   rü   rc   é<   ra   r   T)Úforcer]   )
r)   r0   r6   rT   r
   r   rH   r   rI   r   )Úe1Úe2r}   Úexpr2rk   rk   rl   Útest_issue_22220ë  s     (6,ÿÿ$$&2. r   c                  C   sâ   t ddd\} }t|d |  |d | d  || d    |td| d  ksPJ t|d |  |d | d  || d    ¡  |td| d  ksJ t|d |  |||   |d |    |d |    |td| d  ksÞJ d S )Nzk, nTrv   r`   )r   rH   r   r=  )rW   rX   rk   rk   rl   Útest_issue_22334  s    @Dr¡  c                   C   s.   t ddt  tdt  tdtjks*J d S rL  )rH   rT   r   r   ZZerork   rk   rk   rl   Útest_issue_22836_limit  s    r¢  c                   C   s0   t tddt  tt tttdks,J d S r#  )rH   r   rT   r)   r   rk   rk   rk   rl   Útest_sympyissue_22986  s    r£  c                  C   s>   dt  dt    dt  dt     } t| t t dks:J d S )Nr\   rg   )rT   rH   r   rù   rk   rk   rl   Útest_issue_23231  s    $r€  c                   C   s4   t dt td  tdt  tdtftks0J d S )Nr`   r\   rg   r   )rF   rT   r   r   rk   rk   rk   rl   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 )Nr\   rb   r   r]   ra   )r)   r
   rT   rH   )Úexpr1r  rk   rk   rl   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   r6   r   r"   rT   r   rH   r   rJ   rŽ   r5   )r6  rk   rk   rl   Útest_issue_24276"  s
    rš  c                     sÆ   t ddd t ddd} t ddd}t ddd	}tt fd
d ttt| t||  ddksbJ ttt| t||  d| ksJ ttt|t|| d|ks¢J ttt|t|| ddksÂJ d S )Nrx   Tr¡   ry   rv   rz   r  rX   r  c                      s   t tt t S r   )rH   r   rT   rk   r  rk   rl   r   .  r   z"test_issue_25230.<locals>.<lambda>r]   r   ra   )r   rQ   rê   rH   r   rT   )ry   rz   rX   rk   r  rl   Útest_issue_25230)  s       r©  c                   C   sÊ   t tttttdt t ks$J t tttttdtt ksFJ t tttttdtd kshJ t t	ttttddksJ t t
ttttdtd ksšJ t tttttddksÆJ d S )Nra   r\   r   )rH   r/   r   rT   r   r
   r+   r0   r   r,   r.   r-   rk   rk   rk   rl   Útest_issue_255825  s    $"""rª  c                   C   sx  t tttt tddtd ks&J t ttdt tddtd ksLJ t ttdt tdddksnJ t tttt tddtd ksJ t ttdt tddt t ksŒJ t ttdt tdddksÞJ t t	ttt tdddksJ t t	tdt tddtt ks*J t t	tdt tddtd ksRJ t t
ttt tddtd kszJ t t
tdt tdddksJ t t
tdt tddtd ksÆJ t tttt tdddksêJ t ttdt tddtd ksJ t ttdt tddtt ks:J t tttt tddtd ksbJ t ttdt tdddksJ t ttdt tddt t ks°J t tttt tddtksÔJ t ttdt tddt t d ksJ t ttdt tdddks&J t tttt tddtdtd ksVJ t ttdt tddtkszJ t ttdt tdddksJ t tttt tdddksÂJ t ttdt tddtksæJ t ttdt tddtt d ksJ t tttt tddtks6J t ttdt tdddksZJ t ttdt tddt t d ksJ t tttt tdddks¬J t ttdt tddtt d ksØJ t ttdt tddtksüJ t tttt tddtdtd ks,J t ttdt tdddksPJ t ttdt tddtkstJ d S )Nr   rd   r   r`   r]   r\   ra   )rH   r0   r5   rT   r   r   r/   r   r
   r+   r,   r.   r-   r   r   r   r)   r   r   r!   r    rk   rk   rk   rl   Útest_issue_25847?  sH    &&"&("$((($($((($*$.$0$$$$,$$.$,$0$r«  c                   C   s.   t tdtd tdt tttjks*J d S r*  )rH   r7   rT   r   r   r«   rk   rk   rk   rl   Útest_issue_26040}  s    r¬  c                  C   sî   t dt td dt  d  } tdt td dt  d  }ddtd   | d  d td dt  d |  | d  }td td dtd   td  dtd   td  dtd   td   }t|| td	td d ksêJ d S )
Nr   r\   r`   rb   rs   rÂ   r   rc   r   )rR   rT   rS   r   rH   r   )r¹   rW   r  r  rk   rk   rl   Útest_issue_26250  s
      <Lr­  c                   C   s`   t tt td  t tttdks*J t ttd  t tttdksNJ ttdd  d S )Nr`   rg   c                   S   s   t t td  t ttS ró   rq   rk   rk   rk   rl   r     r   z"test_issue_26513.<locals>.<lambda>)rH   r¥   rT   r   r   rQ   rê   rk   rk   rk   rl   Útest_issue_26513  s    *$r®  c                   C   sL   t tttt  tt
 dks$J t tttt  tt dksHJ d S rW  )rH   r;   rT   r   r   rk   rk   rk   rl   Útest_issue_26916  s    $r¯  c                   C   sî   t ttdt  d dttdt    tttks8J t ddt  t tddt  dtddt      tddddksJ t ttdt  dttdt    ttdksŽJ t ttdt  d ttdt    tttksêJ d S rZ  )rH   r   r	   rT   r)   r   rk   rk   rk   rl   Útest_issue_22982_15323  s    8H4r°  c                   C   sD   t ttd ttdt  tt d  ttdtd ks@J d S )Nr   gžëQž?rw   r`   )rH   rT   r#   r"   r   rk   rk   rk   rl   Útest_issue_26991  s    r±  c                  C   s\   dt tt d t    t  t d tt d t d   t d   d } t| t tdksXJ d S )Nr`   rb   r   )rT   r   rH   r   rË   rk   rk   rl   Útest_issue_27278  s    Dr²  N(&  Ú	itertoolsr   Zsympy.concrete.summationsr   Zsympy.core.functionr   r   Z
sympy.corer   r   Zsympy.core.modr   Zsympy.core.numbersr	   r
   r   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z%sympy.functions.combinatorial.numbersr   Z(sympy.functions.combinatorial.factorialsr   r   r   Z$sympy.functions.elementary.complexesr   r   r   Z&sympy.functions.elementary.exponentialr   r   r   Z%sympy.functions.elementary.hyperbolicr   r   r   r   r    r!   r"   r#   Z#sympy.functions.elementary.integersr$   r%   r&   Z(sympy.functions.elementary.miscellaneousr'   r(   r)   Z$sympy.functions.elementary.piecewiser*   Z(sympy.functions.elementary.trigonometricr+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   Zsympy.functions.special.besselr7   r8   r9   r:   Z'sympy.functions.special.error_functionsr;   r<   r=   r>   r?   r@   Z'sympy.functions.special.gamma_functionsrA   rB   rC   Zsympy.functions.special.hyperrD   Zsympy.integrals.integralsrE   rF   Zsympy.series.limitsrG   rH   Zsympy.simplify.simplifyrI   rJ   Zsympy.simplify.hyperexpandrK   Z!sympy.calculus.accumulationboundsrL   Zsympy.core.mulrM   rN   Zsympy.series.orderrO   Zsympy.testing.pytestrP   rQ   ZsympyrR   rS   Z	sympy.abcrT   rU   rV   rW   rX   rm   rp   rr   ru   r~   r   r   r   r   r   r   r   r   r   r   r    r€   r§   rš   rª   r­   r®   r²   rº   rŒ   r¿   rÀ   rÁ   rÄ   rÅ   rÇ   rÊ   rÌ   rÚ   rÝ   rÞ   rß   rà   rä   rå   ræ   rç   rë   rï   rò   rô   rö   rø   rú   rþ   r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r$  r%  r'  r(  r)  r+  r-  r/  r0  r1  r2  r7  r<  r>  r?  rA  rB  rD  rE  rF  rG  rI  rJ  rK  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rX  rY  r[  r\  r]  r`  ra  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rs  rt  ru  rv  rw  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   r¡  r¢  r£  r€  r¥  r§  rš  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  rk   rk   rk   rl   Ú<module>   sŠ   (8 G
	



0	
		
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