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    Þ@·f_º  ã                   @   sü  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$d% Zvd&d' Zwd(d) Zxd*d+ Zyd,d- Zzd.d/ Z{d0d1 Z|d2d3 Z}d4d5 Z~d6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZekdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zekdxdy Z dzd{ Z¡d|d} Z¢d~d Z£dd Z€dd Z¥dd ZŠdd Z§dd Zšekdd Z©dd Zªdd Z«dd Z¬dd Z­dd Z®dd Z¯dd Z°dd Z±dd Z²dd Z³d d¡ ZŽd¢d£ Zµd€d¥ Z¶dŠd§ Z·dšd© Zždªd« Z¹d¬d­ Zºd®d¯ Z»d°d± ZŒd²d³ ZœdŽdµ ZŸd¶d· Z¿džd¹ ZÀdºd» ZÁdŒdœ ZÂdŸd¿ ZÃdÀdÁ ZÄdÂdÃ ZÅdÄdÅ ZÆdÆdÇ ZÇdÈdÉ ZÈdÊdË ZÉdÌdÍ ZÊdÎdÏ ZËdÐdÑ ZÌdÒdÓ ZÍdÔdÕ ZÎdÖd× ZÏdØdÙ ZÐdÚdÛ ZÑdÜdÝ ZÒdÞdß ZÓdàdá ZÔdâdã ZÕdädå ZÖdædç Z×dèdé ZØdêdë ZÙdìdí ZÚdîdï ZÛdðdñ ZÜdòdó ZÝdôdõ ZÞdöd÷ Zßdødù Zàdúdû Záekdüdý Zâdþdÿ Zãd d Zädd Zådd Zædd Zçdd	 Zèd
d Zédd Zêdd Zëdd Zìdd Zídd Zîdd Zïdd Zðdd Zñdd Zòdd Zód d! Zôd"d# Zõd$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dxS (y  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kstt ttt t ks,tt t ttt ksDtt td tt tks^tt td  ttt ksztt ttt tddddkstt dt ttdks²tt tttttksÊtt tt ttt ksætt ttt tttkstt dt tt  ttdks(tt tdt  tttksFtt ttd  ttt ksftt dt dtd  tddkstt dt t tdttd t tdksºtt dt t tdddttd t tdddksðtt dt t t tdddtdt t t tdddks.tt tt tt tdt t	t ksZtt t
tt t tdt	t
tt kstt tdt d ttdksªtt tjtt tjksÆtt tdt ttjtjksètt dtd  tdddtks
tt dtd  tdddt ks.tt ddt d  tdddt ksVtt ddt d  tdddtks|tt dtt ttddt ks tt dtt ttddtksÂtt dt
t ttd ddt ksêtt dt
t ttd ddtkstt dttd  tdt tdd ddtksDtt dttd  tdt tdd ddt ksztt dttd  tttdd ddt ks¬tt dttd  tttdd ddtksÜtt ttttttjtjks tt ttttttjtjks$tt ttttttjtjksHtt ttttttjtjksltt ttt tdd	ddkstt td tdd	ddks¬tt dtd  tdd	dtksÎtt dt tdd	dtksìtt ddt  tdtks
tt ddt  tdddt ks.tt td
 tdddtksLtt td tdddt ksltt dtt tdddt t kstt td tddddks²tt tttddddksÐtt tt  tdddt ddt   ksþtt dt
t t tdtt
td t tdks4tt dtt tdddtksVtt dtt tdddt ksztt dtt tdddtkstt dtt tdddt ksÀtt tdt dtt  tdddtksîtt tdt dt  tdddtkstd S )Né   r   ú+©Údiré   ú-é   é   ú+-éþÿÿÿéýÿÿÿéÿÿÿÿ)rH   rT   r   ÚAssertionErrorr   r   r)   rG   rU   r   r1   rB   r   ÚNaNrO   r5   r   r6   r   r2   rL   ÚNegativeInfinityÚInfinityr4   r3   r   r
   r/   r#   © rl   rl   úB/tmp/pip-unpacked-wheel-6uje5nh9/sympy/series/tests/test_limits.pyÚtest_basic1)   sr     $ &.6>,."""$(&$"(&4620$$$$""$ (.6"$"$.rn   c                   C   s  t tt tddddkstt ttd t tddks<tt ddt  ttdksXtt tdt  ttdksvtt ttt  tttkstt tttd   tttks¶tt tttt  tttksØtt ddt  tt  ttdksþtd S )Nr   r]   r^   r`   rg   r\   é   )rH   rT   rh   r   r   rl   rl   rl   rm   Útest_basic2p   s     ""rp   c                   C   s>   t dt tdddtkstt dt tdddt ks:td S )Nr`   r   r]   r^   ra   ©rH   rT   r   rh   rl   rl   rl   rm   Útest_basic3{   s    rr   c                   C   sÐ   t dt tt  tddks tt dt tt  tddt ksDtt dtd  ttd   tddtd  ksttt ttd tt ttdksttdtd d  tdtfdt td d	 ksÌtd S )
Nr\   r   r`   é   rf   re   i   rb   é	   )rH   rT   rU   rh   r)   r   rF   r   rl   rl   rl   rm   Útest_basic4   s
     $0$ru   c                  C   s0  t ddd\} }}t| | t| t|  }| | t¡dksBt||  | t¡dksZt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,td S )Nza b cT©r[   r   ztau xr\   r`   re   ç      à?rb   )r   r   rH   r   rh   r0   r   )ÚaÚbÚcÚAÚtaurT   Úexprrl   rl   rm   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s2td S )Né   rb   r\   re   r]   r`   é   )rH   r(   rT   r   rh   rl   rl   rl   rm   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sðtt|tddkstt|td
dkstd S )Nr\   é   r`   r   Trw   g      À?rt   rc   rg   rb   )r)   rT   r*   r   rH   rh   )Zfunc1Zfunc2Zfunc3rl   rl   rm   Útest_piecewise2   s    @ÿ.ÿ&<r   c                  C   s8   G dd dt } t| tttt| tttks4td S )Nc                   @   s   e Zd Zedd ZdS )ztest_basic5.<locals>.myc                 S   s   |t jkrt jS d S ©N)r   rk   ri   )ÚclsÚargrl   rl   rm   Úevalš   s    
ztest_basic5.<locals>.my.evalN)Ú__name__Ú
__module__Ú__qualname__Úclassmethodr   rl   rl   rl   rm   Úmy§   s   r   )r   rH   rT   r   rG   rh   )r   rl   rl   rm   Útest_basic5Š   s    r   c                   C   s0   t tt tt  tdtt dt  ks,td S ©Nr\   )rH   rT   rU   rV   rh   rl   rl   rl   rm   Útest_issue_3885¯   s    r   c                   C   sf   t ttt tddkstt ttt td ¡ dks<tt ttdddjttdtdfksbtd S )Nr   r`   rd   r^   )rG   r5   rT   rh   ÚdoitÚargsr   rl   rl   rl   rm   Ú
test_Limit³   s     r   c                   C   s$  t tttdddkstt tttdddks4tt tttdddksNtt tttdddkshtt tttdddkstt tttdddkstt tttdddks¶tt tttdddksÐtt tttdddksêtt tttdddkstt tttd	dd	ks"tt tttd	dd
ks>tt ttdt  d tddtddksltt ttd tt ttttj tdd ks€tt tt	tttdksÂtt tt	ttt dksâtt t
t	tttdks tt t
t	ttt dks td S )Nre   r]   ra   rf   rg   r   r`   r\   éø   é÷   rb   rw   )rH   r%   rT   rh   r   r   rL   r   ÚHalfr0   r$   rl   rl   rl   rm   Ú
test_floor¹   s$    .8 r   c                   C   s  t ttttdddkstt ttttdddks<tt ttttdddksZtt ttttdddksxtt tdtt tdddkstt tdtt tdddksŒtt tdtt tdddksÞtt tdtt tdddkstd S )Nr   r]   ra   rg   rc   r   )rH   r%   r5   rT   rh   r1   rl   rl   rl   rm   Ú&test_floor_requires_robust_assumptionsÒ   s    """r   c                   C   sš  t tttdddkstt tttdddks4tt tttdddksNtt tttdddkshtt tttdddkstt tttdddkstt tttdddks¶tt tttdddksÐtt tttdddksêtt tttdddkstt tttd	dd
ks"tt tttd	dd	ks>tt ttdt  d tddtddksltt ttd tt ttttj tdd ks€td S )Nre   r]   rg   ra   r   r`   r\   rb   r   éù   rw   )	rH   r$   rT   rh   r   r   rL   r   r   rl   rl   rl   rm   Útest_ceilingÝ   s    .r   c                   C   s  t ttttdddkstt ttttdddks<tt ttttdddksZtt ttttdddksxtt tdtt tdddkstt tdtt tdddksŒtt tdtt tdddksÞtt tdtt tdddkstd S )Nr   r]   r`   ra   rc   r   )rH   r$   r5   rT   rh   r1   rl   rl   rl   rm   Ú(test_ceiling_requires_robust_assumptionsð   s    """r   c                   C   s°  t tttttddkstt ttdt  tttddksDtt ttdt  tt tdtksltt ttt tttdtkstt ttttdddks¬tt ttttdddksÊtt ttttdddksètt ttd tdddksttt	dd  t td	t d tdddks:tt td	t d tdddks^tt ttt
j tddt
dd kstt tdt tdtddks¬td S )
Nr   r`   r]   ra   rd   r\   c                   S   s   t tttddS ©Nr   rd   )rH   r&   rT   rl   rl   rl   rm   Ú<lambda>  ó    ztest_frac.<locals>.<lambda>re   )rH   r&   rT   r   rL   rh   r5   r1   rQ   Ú
ValueErrorr   r   rl   rl   rl   rm   Ú	test_fracû   s    &(" $$*r   c                   C   s   t tttt tdddks"tt tttt tdddksDtt ttt t tdddkshtt ttt t tdddkstd S )Nr   r]   ra   re   )rH   r%   r5   rT   rh   r6   rl   rl   rl   rm   Útest_issue_14355  s    ""$r    c                  C   sd   t ddd} tt| td|   | ddks0ttt| t| d  t|  | ttd ks`td S )NrT   T©Úrealr`   r   r\   )r   rH   r0   r5   rh   r)   r   r   ©rT   rl   rl   rm   Ú	test_atan  s    $r€   c                  C   s  t tttddkstt ttttddks4tt ttttddksPtt tttd tdtdksttt ttt ttt  dt  tdttksštt tt	ttd  tt
dksÌtt ttt	ttd  tt	td td d   d  tt
dkstt tt	td d d tddt
ksBtt tt	ttdt
ks`tt tt	tttdt
ksttddd} t tt	| d t	|  | t
dksžtt | td|  t ttd|     d | ddksòtt t| t|  | td	d
kstd S )Nr   r`   r\   rb   r]   rV   Trv   ra   rg   )rH   ÚabsrT   rh   r5   r1   r   rU   r   r   r   r   r   ©rV   rl   rl   rm   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s8tttdtt| ttd|    | dtdksptd S )	NrT   Tr¡   r`   r   r]   rg   r\   )	r   rN   r5   r0   rL   rh   rH   r   r)   r£   rl   rl   rm   Útest_heuristic8  s    ,rš   c                  C   sN   t ddd} d|  t|  t  }t|ttdks6t| tt¡dksJtd S )NrV   Trv   rg   r   )r   r   rT   rH   r   rh   )rV   Úfrl   rl   rm   Útest_issue_3871>  s    rª   c                  C   s   t d} t ddd}td||   |  | tt|ks8ttd|d|    |  | tt|d ksdttd|d|  d   |  | tt|d kstt|d |d  | |ttdksŒttddd|  |  |tdtj ksættdd|  | d| |  |tttd	kstd S )
NrX   rT   Tr¡   r`   r\   re   r   z1/3)r   rH   r   r   rh   r   ÚExp1©rX   rT   rl   rl   rm   Útest_exponentialE  s    $,0(*r­   c                  C   s8   t d} tdt| t|    |  | tttks4td S )NrX   r`   )r   rH   rT   r5   r   r   rh   )rX   rl   rl   rm   Útest_exponential2P  s    r®   c                  C   s.   t dt t} t| tt}| ¡ tks*td S r   ©rE   rT   rG   r   r   rh   ©r©   Úlrl   rl   rm   Ú	test_doitU  s    r²   c                  C   sÒ  t ttttd  tttddks*tt ttttd  d tttddksXtt tttttt  tttddkstdtd d } dtd d }tt| |ddtd  dd}t tt	tt
 t¡t
d	tf ¡  t¡tt|ksþtttdtdd  tdd d ddtd  }t tt	tt
 t¡t
d	tf ¡  t¡tt|ksltt ttd d t tttd	tkstdt  ttd t  }t |tttd	tksÎtd S )
Nr`   re   r\   rg   rb   rf   F)Úevaluater   )rH   r5   rW   r   rL   rh   r1   rM   rJ   r   rX   Úrewriter   r   rT   )ÚloÚhiÚt1Út2Úerl   rl   rm   Útest_series_AccumBounds[  s    *.. 84:,rº   c                   C   s  t tdtttdkstt tdttt dks6tt tdtttt tt ksXtt tdttt t t t ks~tt tdtttdkstt tdttt dksŽtt tdtttt t ksÔtt tdttt t t ksött tdttttkstt tdttt t ks2tt tdtttt dksRtt tdttt t dksttt tdtttdkstt tdttt t t ksŽtt tdtttt dksÔtt tdttt t dksött tdtttdkstd S ©Nr`   r   )	rH   r9   rT   r   rh   r
   r8   r7   r:   rl   rl   rl   rm   Ú!test_bessel_functions_at_infinityr  s"    "& "  "$ "rŒ   c                  C   s2   t dt t} t| tt}|jdd|ks.td S )Nr\   F©Údeepr¯   r°   rl   rl   rm   Ú
test_doit2  s    r¿   c                   C   s.   t ttt ttd  tt dks*td S r»   ©rH   rT   r   r   rh   rl   rl   rl   rm   Útest_issue_2929  s    rÁ   c                   C   s   t dtt td  ttjddttj  ks4tt tttd d tdtdtd ksdtt tttd d tddtd kstd S )Nr`   r\   r   r   )rH   r1   rT   r   r   rh   r5   r¥   rl   rl   rl   rm   Útest_issue_3792  s    40rÂ   c                   C   sš   t dtd  tdtddks"tt dtt  tdtjdt  ksHtt tttd d  tdtdd ksttt tttd t  tdtddt  ks€td S )Nr`   rb   r\   rc   é   r   )rH   rT   r   rh   r   r   ÚOner   rl   rl   rl   rm   Útest_issue_4090  s    "&,rÅ   c                   C   s@   t tttdddtkstt ttttd dddks<td S )Nr   r]   r^   r\   )rH   r2   rT   r   rh   r   rl   rl   rl   rm   Útest_issue_4547€  s    rÆ   c                   C   s   t td tttd   kr$tks*n tt td tddksBtt td tddksZtt td ttdksrtt td tdtjkstd S )Nrw   é   r   r   g      à¿)rH   rT   r   rh   r   r   rl   rl   rl   rm   Útest_issue_5164©  s
    *rÈ   c                  C   s,   ddt   dt   } t| t dtks(td S )Nç      ð?r   )rT   rH   r	   rh   )Úfuncrl   rl   rm   Útest_issue_5383±  s    rË   c                  C   sp   t tdd  tt  t  tdt d  ttt  tddt    t d  } t| t ttdd ksltd S )Nr`   r\   r   rb   ih  )rT   r   r   r   r   rH   r   rh   ©r}   rl   rl   rm   Útest_issue_14793¶  s    *
ÿÿÿrÍ   c            
       C   s0  t ttt gddgddtjtddgddg} ttt tt t tt dtdd  tddddddddtttt tt t tt dtdd  ddddddddf }t| t|ksžt	t
t| |D ]d\}\}}|\}}}}|||  }	zt|	td|d|kst	W qÆ t	k
r(   d s$t	Y qÆX qÆd S )	Nrg   r`   r\   rb   ra   r]   r   r^   )Úlistr   rT   r   r   r   r   r
   Úlenrh   Ú	enumerateÚziprH   Úprint)
ÚtestsÚresultsÚir   ÚresrU   Úsr¹   ÚdÚeqrl   rl   rm   Útest_issue_5183Œ  sN    ý(                     ýrÚ   c                  C   sº   t ttt ttdkstt tttttd ks8tt tttttksPtt ttt ttdksltt tttt	j
ttksttddd} t | td|   | ddks¶td S )Nr   r\   ÚrTr¡   r`   )rH   r5   rT   r   rh   r0   r   rB   r1   r   r   r)   r   ©rÛ   rl   rl   rm   Útest_issue_5184Ô  s    rÝ   c                   C   s*   t dt dt  tj tddks&td S r»   )rH   rU   r   r«   rh   rl   rl   rl   rm   Útest_issue_5229ß  s    rÞ   c            	      C   sì   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tt	t
| |D ]X\}\}}|\}}}|t}zt|t||d|ksÆtW q tk
rä   d sàtY qX qd S )Nr\   r   rb   ra   r]   r^   )rÎ   r   r2   r6   r   r   r   rÏ   rh   rÐ   rÑ   rT   rH   rÒ   )	rÓ   rÔ   rÕ   r   rÖ   r©   r±   rØ   rÙ   rl   rl   rm   Útest_issue_4546ã  s0    
 þ         ÿ
rß   c                   C   sX   t dttd  dt  tddks(tt ddt  ddt   t tddksTtd S )Nr`   rb   r   rc   )rH   rT   r   rh   rl   rl   rl   rm   Útest_issue_3934ø  s    (rà   c                   C   sX   t ttdd dttdd   ttdks0tt td dtd   ttdksTtd S )NéM   rb   r`   gfffffFY@)rH   rT   r   r   rh   rl   rl   rl   rm   Útest_calculate_seriesý  s    0râ   c                   C   s   t td dtd   ttdks$tt td dtd   ttdksHtt td dtd   ttdksltt td td d tt   ttdkstd S )NrÇ   r`   éd   i]  éè  )rH   rT   r   rh   r   rl   rl   rl   rm   Útest_issue_5955	  s    $$$rå   c                   C   s0   t tdtt ttt tddks,td S r»   )rH   r   r5   rT   r2   rh   rl   rl   rl   rm   Útest_newissue  s    ræ   c                   C   sŒ   t tt ttttt ttks$tt dttt  t tdtdttt  t tdks`tt tt ttttt ttkstt tt dt  ttttt dt  ttksžtd S r»   )rH   rT   r   rG   rh   r5   rl   rl   rl   rm   Útest_extended_real_line  s    $<$rç   c                  C   sJ   t ddd} t| t td| ks&ttt| d d  | ttksFtd S )NrT   Trv   r`   r\   r   )r   rO   r   rh   rH   r£   rl   rl   rm   Útest_order_oo  s    rè   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttt ttS r   ©rH   r   rT   rU   r   rl   rl   rl   rm   r   #  r   z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ttS r   ré   rl   rl   rl   rm   r   $  r   ©rQ   ÚNotImplementedErrorrl   rl   rl   rm   Útest_issue_5436"  s    rì   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   rl   rl   rl   rm   r   (  r   z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   Ú0r^   rí   rl   rl   rl   rm   r   )  r   )rQ   Ú	TypeErrorr   rl   rl   rl   rm   Útest_Limit_dir'  s    rð   c                   C   s^   t td d td d d  ttdks,tt td d td d d  tt dksZtd S )Nr`   rä   rq   rl   rl   rl   rm   Útest_polynomial,  s    ,rñ   c                   C   s   t dt dtt  ttt  t  t  tttd tt  ksDtt dt dtt  ttt  t  t  tt td tt  kstd S ©Nr`   )rH   rU   rT   rV   r   rh   rl   rl   rl   rm   Útest_rational1  s    Dró   c                   C   s<   t ttt tdt t  tdtttt  ks8td S ©Nr\   r   )rH   r   rT   rV   rU   r   r   rh   rl   rl   rl   rm   Útest_issue_57406  s    rõ   c                  C   s^   t dddd} | d t| d   t| d  d  ttd   }t|td ¡ | d ksZtd S )NrX   TrY   r`   r\   )r   rT   rH   Úcancelrh   )rX   rÛ   rl   rl   rm   Útest_issue_6366:  s    0r÷   c                  C   s   t t} t| tttksttt|  ttdks4tt| tdt t tt t   ttdksdtt| tt tt kstd S )Nr   r\   r`   )	r   rT   rH   r   rh   r)   r   r	   rB   ©r©   rl   rl   rm   Útest_factorial@  s
    0rù   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sŽtd S )	Nrc   rb   r   r\   é#   rs   é   r`   )rT   r   rU   r   r   rH   r   rh   ©r¹   rl   rl   rm   Útest_issue_6560J  s    4ÿÿÿ
ÿrý   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sàtt  ||¡t ¡ d	|d
  |  d
 | d
 |d
   ks"td S )NrX   rÛ   Trv   rz   ÚpÚm©Únegativer\   r`   c                      s   t  tS r   )rH   r   rl   ©r}   rX   rl   rm   r   Y  r   z!test_issue_5172.<locals>.<lambda>)r   ÚsubsrQ   rë   rH   r   rh   rJ   )rÛ   rz   rþ   rÿ   rl   r  rm   Útest_issue_5172O  s$    *.ÿÿ
ÿ"ÿr  c                  C   s,   t d} tttt|   ttdks(td S )Nrx   r`   )r   rH   r)   rT   r   rh   ©rx   rl   rl   rm   Útest_issue_7088_  s    r  c                   C   s  t ttt d tdttd ks(tt ttt d tddtdksNtt ttt d tdtd ksttt ttt d tddt td ks tt ttt d tdtd ksÆtt ttt d tddtdksìtt ttt d tdtdkstt ttt d tdddt td ksBtt ttdt  tdttd ksltt ttdt  tddt ttd  kstt ttdt  tdtttd  ksÌtt ttdt  tddt td ksútt tdt tdtd kstt tdt tddt d ksBtt tttt	td ks`tt tttt	 t d kstt t
ttdd t  tdttttdd   ksÀtt t
ttdd t  tddt ttdd  ksþtt t
ttdd t  tdtttdd  ks8tt t
ttdd t  tddt tttdd   ksztt t
ttdtd kstt t
ttddt d ksºtt ttt tdd  tdttdd ksðtt ttt tdd  tddttdd  ks*tt ttt tdd  tddt ttd d  ksjtt ttt tdd  tddttd d ks€tt ttt tdd  tdttdd ksÚtt ttt tdd  tddtttdd  kstt ttt tdd  tdt ttdd  ksRtt ttt tdd  tddttdd  kstt ttt d tdtt ks²tt ttt d tddt t ksÜtt tt t d tdt t kstt tt t d tddtt ks0tt ttt d tdtksRtt ttt d tddt ksxtt tt t d tdt kstt tt t d tddtksÄtt ttt d tddtdd  ksòtt ttt d tdddtdd   ks$tt tt t d tddtdd   ksVtt tt t d tdddtdd  kstd S )Nr\   r   ra   re   r`   rg   rb   )rH   r/   r
   rT   r   rh   r+   r0   r   r   r,   r   r   r.   r-   r   r)   r'   rl   rl   rl   rm   Útest_branch_cutsd  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sftd S )Nrx   r`   r\   r   )	r   rV   r)   r5   r1   rH   r   r   rh   )rx   r¹   rl   rl   rm   Útest_issue_6364  s    8r  c                   C   s6   t tdtt  td  tdtdt ks2td S rô   )rH   r   r;   rT   r   rh   rl   rl   rl   rm   Útest_issue_6682  s    r	  c                  C   s   t d} t| t tdtt|  ks(tt|  t tdt t|  ksLtt|  t ttt t|  ksptt| t tttt|  kstd S )Nrx   r   )r   rH   rT   r   r   rh   r  rl   rl   rm   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sXtd S )NÚdxr`   r   r\   )r   rH   r)   r   rT   rh   )r  rl   rl   rm   Útest_issue_4503Š  s    .ÿr  c                  C   sJ   t ddddt } t| }t|tdddks0tt|ttt ksFtd S )Nrl   )r`   )r   r   rd   )rD   rT   rK   rH   rh   r   )ÚGÚgrl   rl   rm   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>tttt| tt |  td ¡ dksftd S )Nr`   rs   r   r\   g       @)r)   rT   r7   rH   r   rh   ZevalfrÌ   rl   rl   rm   Útest_issue_7224³  s    $r  c                   C   s&   t ttddd  ttdks"td S )Nr`   g    eÍÍAr   )rH   rX   r   r   rh   rl   rl   rl   rm   Útest_issue_8208¹  s    r  c                   C   s<   t ttdd d ttd tdd  tddks8td S )Nr`   r   r\   rb   rÇ   r   )rH   rT   r   r)   rh   rl   rl   rl   rm   Útest_issue_8229œ  s    r  c                  C   s4   t ddd\} }ttd||   |tdks0td S )Nzd tTrv   r`   rg   )r   rH   r<   r   rh   )rØ   Útrl   rl   rm   Útest_issue_8433Á  s    r  c                  C   sH   t dddd} t ddd}t||  t|  t|  | tdksDtd S )NrW   T)rZ   ZnonnegativeÚlamdarv   r   )r   rH   r   r   r   rh   )rW   r  rl   rl   rm   Útest_issue_8481Æ  s    r  c                   C   sJ   t tttd tttkstt tttd dt   ttdksFtd S )Nr\   rb   r   )rH   r   rX   r   rh   rl   rl   rl   rm   Útest_issue_8462Ì  s    r  c                  C   s@   t dddd} t d}t||  |t ttd|   ks<td S )NrX   TrY   rT   rg   )r   rH   r   r   rh   r¬   rl   rl   rm   Útest_issue_8634Ñ  s    r  c                  C   s  t ddd} t ddd}t| t | td   | tdks<tt| t | td   | ttks`tt| t | td   | ttkstt| t | t| d	   | ttks¬tt ddd} t| t | td	   | ttksÜtt| t | td
   | tt kstd S )NrT   Tr¡   rW   rv   r   rc   g      @r`   r\   )r   rH   rX   r   rh   )rT   rW   rl   rl   rm   Útest_issue_8635_18176×  s    $$$($r  c                   C   s   t tttttkstd S r   )rH   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_8730ã  s    r  c                      s`   t dddt ddd ttt  d    tdksHttt fdd	 d S )
NrX   T©rZ   rz   rv   r`   r   c                      s$   t tt     tS r   )rH   r   r   rl   ©rz   rX   rl   rm   r   ì  r   z!test_issue_9252.<locals>.<lambda>)r   rH   r   r   rh   rQ   rë   rl   rl   r  rm   Útest_issue_9252ç  s    0r  c                   C   s"   t ttd tdddkstd S )Nrû   r   ra   )rH   r5   rT   rh   rl   rl   rl   rm   Útest_issue_9558ï  s    r  c                   C   s2   t dt ttdt td   tttks.td S )NrÇ   r\   )rH   rW   r   r   r   rh   rl   rl   rl   rm   Útest_issue_10801ó  s    r  c                  C   s8   t ddd\} }tt| | t|  | d|ks4td S )Nzs xTr¡   r   )r   rH   r<   rh   )r×   rT   rl   rl   rm   Útest_issue_10976ø  s    r   c                   C   s<   t ttttd t tdt t   ttdks8td S ©Nr`   r\   )rH   r   rX   r   r)   r   r   rh   rl   rl   rl   rm   Útest_issue_9041ý  s    r"  c                  C   s   t d\} }}t| | |j|hks&tt| | |dj|hks@tt| | | | |j|hks`tt| d  | | d |j||hkstd S )Nzx, y, ara   r\   )r   rG   Zfree_symbolsrh   )rT   rU   rx   rl   rl   rm   Útest_issue_9205  s
     r#  c                   C   sT   t dttd td  ttdks&tt dttdd  td  ttdksPtd S )Né   rb   r`   )rH   r   rX   r   rh   rl   rl   rl   rm   Útest_issue_9471	  s    &r%  c                   C   s(   t ttd tt tttks$td S rò   )rH   r   rX   r   r   rh   rl   rl   rl   rm   Útest_issue_10382  s    r&  c                   C   s$   t ttdt ttdks td S r!  )rH   r=   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_11496  s    r'  c                   C   s<   t ttt t tt  t tdtttd   ks8td S ©Nr   r`   )rJ   rH   rT   rU   rX   rh   rl   rl   rl   rm   Útest_issue_11879  s    r)  c                  C   sF   t d} td|  | tdks ttdd|   | ttddksBtd S )NrW   rÉ   r`   g333333Ó?rb   é
   )r   rH   r   rh   r   )rW   rl   rl   rm   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@td S ©Nrb   r`   r\   )rH   rT   r   r   rh   rl   rl   rl   rm   Útest_issue_10610   s    r-  c                   C   s  t tttt tddtdks&tt tttt tddtddt t  ksXtttdd  t tttt tt	t	kstt ttt
t tddtdks¬tt ttt
t tddt	 ksÐtttdd  t ttt
t tt	t	ksþtd S )Nr   r]   r\   ra   c                   S   s   t tttt tddS r   )rH   r   rT   r!   rl   rl   rl   rm   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    rl   rl   rl   rm   r   +  r   )rH   r   rT   r!   rh   r
   r   rQ   r   r   r    rl   rl   rl   rm   Útest_issue_10868$  s    &2 &$r.  c                   C   s$   t ttt t ttdks td S rò   )rH   rX   r1   r   rh   rl   rl   rl   rm   Útest_issue_6599/  s    r/  c                   C   sn   t dt dtd   td tt  tt dks6tt dt dtd   td tt  tttksjtd S )Nrb   r\   r*  rÀ   rl   rl   rl   rm   Útest_issue_125553  s    6r0  c                  C   sÔ  t ddd\} }}t dddd\}}}}}}}	|| ||  |  | t|d |d|   |d  |d  |d|  |d  |d  |d   |d|  |d|   |d  |d  |d d|  d   d|d|   ||d   | |  | |d d|  d   d||d   |d|   | |  | |d d|  d   d||d   ||d   |d  |d   |d |d d|  d    ||  | |  d  }
|
 ||¡jddt|
||jddksÐtd S )	Nzr z xTr¡   za b s0 K F0 s T)r[   r¢   r\   r`   rœ   )r   r)   r  ZfactorrH   rh   )rÛ   rV   rT   rx   ry   Ús0ÚKZF0r×   ÚTÚfxrl   rl   rm   Útest_issue_127698  s$    :"ÿ:ÿ:þ:ý*üüür5  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svtd S )Né   rc   éûÿÿÿr`   i@¶  r\   r   iúÿÿÿé   é$   )rH   r)   rT   r   r   r   r   rh   rl   rl   rl   rm   Útest_issue_13332D  s    Bÿ ÿÿr:  c                   C   sò   t td ttt  tt tt tks.tt td ttt  tt tttksZtt ttt d  ¡ tttks~tt ttt d  ¡ tttks¢tt ttt d  ¡ tt tksÈtt ttt d  ¡ tt tksîtd S r   )rH   rT   r5   r1   r   rh   Úexpandrl   rl   rl   rm   Útest_issue_12564I  s    .,$$&r<  c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t tttt ¡ S r   )rG   r   rT   r   r   rl   rl   rl   rm   r   S  r   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  tt ¡ S )Nr\   r`   )rG   rT   r   r   rl   rl   rl   rm   r   T  r   rê   rl   rl   rl   rm   Útest_issue_14456R  s    r=  c                   C   sB   t dtdt t td   tdt dt d  t ks>td S )Nrb   r   é   r\   )rH   r4   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_14411W  s    r?  c                   C   s8   t ttd d d td d  d  ttdks4td S r!  rq   rl   rl   rl   rm   Útest_issue_13382[  s    r@  c                   C   s<   t tdtttd  d ttt    ttdks8td S )Nrg   r`   ©rH   rT   r   r   rh   rl   rl   rl   rm   Útest_issue_13403_  s    rB  c                   C   sb   t td  ttd  td td d  ttd d   td ttd   ttdks^td S r,  rA  rl   rl   rl   rm   Útest_issue_13416c  s    rC  c                   C   sx   t td dt dddt   t  d  t td  d td  t   tttd d td d  td  ksttd S )Nr\   r`   r   rb   r>  rs   r   )rH   rX   rT   r   rh   rl   rl   rl   rm   Útest_issue_13462g  s    rD  c                  C   sH   t d} tt| t ttdks$tttttt ttdksDtd S )Nrx   rg   )r   rH   r<   rT   r   rh   r)   r  rl   rl   rm   Útest_issue_13750k  s    rE  c                   C   s   t ttttt ttts"tt ttttt tttsDtt ttttttttsfttddtd tt   td t  ttt	kstd S r!  )
Ú
isinstancerH   r5   rT   r   r   rG   rh   r1   r	   rl   rl   rl   rm   Útest_issue_14276q  s    """rG  c                   C   s0   t dtttt  dt  ttdks,td S rò   )rH   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_14514x  s    rH  c                   C   s~  t ttd tt tttt  ttttj	tj
ks>tt ttd tt tttt  ttttj	tj
ks|tt ttttd  ttttj	tj
ksªtt ttttd  ttttj	tjksØtt ttttd  ttttj	tjkstt ttd ttd  ttttj	tjks<tt ttd ttd  tt ttttj tj
ksztd S r   )rH   r5   rT   r1   r6   r3   r   rL   r   rj   rk   rh   r2   rÄ   rl   rl   rl   rm   Útest_issues_14525|  s    >>..04rI  c                   C   s4   t tttttd   td  ttdks0td S )Nr\   r`   r   )rH   r)   rT   r1   r   rh   rl   rl   rl   rm   Útest_issue_14574  s    rJ  c                   C   sº   t tttttjkstt dtt ttdtj ks<tt dtt tttddks^tt tttttjksxtt tttt tddkstt dtt tt dks¶td S )Nrb   rc   r\   rg   r   re   )	rH   r@   rT   r   r   r   rh   r   r?   rl   rl   rl   rm   Útest_issue_10102  s    "" rK  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   rl   rl   rl   rm   r     r   z"test_issue_14377.<locals>.<lambda>rê   rl   rl   rl   rm   Útest_issue_14377  s    rL  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td S )Nr\   re   rb   r`   )rT   rA   rH   r   r   rh   rü   rl   rl   rm   Útest_issue_15146  s    8*ÿÿÿrM  c                  C   s°   dt  ddt   ddt   t  d    t d  t d  } t| t ttdksRttt dd dt  tt   dt   tt d dtt   dt    } t| t tdks¬td S )Nr\   re   r`   rÃ   r*  rc   rb   )rT   rH   r   r   rh   r   r   rü   rl   rl   rm   Útest_issue_15202  s    :FrN  c                   C   s0   t td td d  td  ttdks,td S )NiÐ  r`   iÏ  i0øÿÿrq   rl   rl   rl   rm   Útest_issue_15282¥  s    rO  c                   C   s2   t t tttd  t ttdddks.td S )Nr`   ra   r^   r   )rH   rT   r   r   r   rh   rl   rl   rl   rm   Útest_issue_15984©  s    rP  c                   C   s&   t ttdtt ttdks"td S rò   )rH   rC   rT   rB   r   rh   rl   rl   rl   rm   Útest_issue_13571­  s    rQ  c                   C   s*   t ttttdtttjks&td S rò   )rH   r+   r>   rT   r   rÄ   rh   rl   rl   rl   rm   Útest_issue_13575±  s    rR  c                   C   s   t ttt tddd ¡ dks$tt td tddd ¡ dksDtt dtd  tddd ¡ tkshtt dt tddd ¡ tkstd S )Nr   rd   r^   r`   r\   )rG   r5   rT   r   rh   r   r   rl   rl   rl   rm   Útest_issue_17325µ  s    $ $rS  c                   C   s   t t td¡dkstd S )Nr   )r   rT   rH   rh   rl   rl   rl   rm   Útest_issue_10978Œ  s    rT  c                   C   s    t ttd tttkstd S r   )rH   r%   rX   r   rh   rl   rl   rl   rm   Útest_issue_14313_commentÀ  s    rU  c                  C   s2   ddt   t   t ¡} t| t ddddks.td S )Nr`   r]   r^   )rT   r   rH   rh   )rØ   rl   rl   rm   Útest_issue_15323Ä  s    rV  c                   C   s,   t ttt  tt tddks(td S rò   )rH   r   r   rT   rh   rl   rl   rl   rm   Útest_issue_12571Ê  s    rW  c                   C   sH   t td td t t  td td  td   tttdksDtd S r,  ©rH   rT   r   r   rh   rl   rl   rl   rm   Útest_issue_14590Î  s    rY  c                  C   sR   t d\} }tt| t|  t|  t|    tt|t|  |   |  ksNtd S )Núa b)r   rH   rT   rU   rh   ©rx   ry   rl   rl   rm   Útest_issue_14393Ò  s    r\  c                   C   s@   t ttd dtd   ttdt   tttdks<td S )Nr`   rg   )rH   r   rX   r   r   rh   rl   rl   rl   rm   Útest_issue_14556×  s    r]  c                   C   sL   t dtdd td   dt  dtdd td    tttksHtd S )Nr`   r\   rb   r   ©rH   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_14811Û  s    r_  c                   C   s    t tttdtdkstd S )Ni Ê;)rH   r   rT   rh   rl   rl   rl   rm   Útest_issue_16222ß  s    r`  c                   C   sD   t ttd  td t  ttd   t ttttdks@td S rò   rX  rl   rl   rl   rm   Útest_issue_16714ã  s    ra  c                  C   s   t ddd} ttt|  tt|    ttdt| d  ks@tt dddd} ttt|  tt|    ttdt| d  kstd S )NrV   Trv   r`   )r[   rZ   )r   rH   r   rX   r   rB   rh   rŠ   rl   rl   rm   Útest_issue_16722ç  s    4rb  c                   C   sÀ   t td d td d ttd   td  tt td  ttdksLtt td d tt td td  ttd   ttdkstt td tt tttd   ttdksŒtd S )Nr`   r\   r   rb   )rH   rX   r   r   rh   rl   rl   rl   rm   Útest_issue_17431î  s&    $ÿÿÿ ÿÿ0 ÿÿrc  c                   C   s2   t ttt tttt  tdtks.td S rò   )rH   r;   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_17671ö  s    rd  c                  C   sf   t ddd\} }}}t| d | t| d d |d  ||  |  |t| d|  d  ksbtd S )Nza b c xTrv   r`   r\   )r   rH   r)   r   rh   )rx   ry   rz   rT   rl   rl   rm   Útest_issue_17751ú  s    re  c                   C   s@   t tttt tdt t  tttdtt ks<td S r!  )rH   r   rX   r)   r   r   r   rh   rl   rl   rl   rm   Útest_issue_17792ÿ  s    rf  c                   C   s@   t ttttdddkstt ttttdddks<td S )Nr   ra   rg   r]   r`   )rH   r   r5   rT   rh   rl   rl   rl   rm   Útest_issue_18118  s    rg  c                   C   s.   t tttttt tdddks*td S )Nr   r]   r`   )rH   r5   r)   rT   rh   rl   rl   rl   rm   Útest_issue_18306  s    rh  c                   C   s<   t ttdt t ttttd   ttdks8td S )Nrb   rã   )rH   r   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_18378  s    ri  c                   C   sJ   t dtdd t  dt  tttks,tt t t tttksFtd S )Nr`   r\   rb   )rH   r   rT   r   r   rh   rl   rl   rl   rm   Útest_issue_18399  s    ,rj  c                   C   sH   t ttdtt  ttddtttdtt  ttddksDtd S )Nr\   ra   r^   )rH   r6   rT   r)   r   r   rG   rh   rl   rl   rl   rm   Útest_issue_18442  s    rk  c                   C   sF   t tttt tddks tt tttt tdddksBtd S )Nr   r`   ra   )rH   r¥   r   rT   rh   rl   rl   rl   rm   Útest_issue_18452  s     rl  c                   C   sD  t ttdt  tttttdt  ttddks8tt ttdt  tttttdt  ttddksptt ttdt  tttttdt  ttddksštt ttd dt  ttdksÌtt ttd dt  ttdksðtt ttd dt  tttttd dt  ttddks2tt ttd dt  tttddks^tt ttd dt  tttdtkstt ttd dt  tttddks¶tt ttd dt  tt tdtksätt ttd dt  tt tdtkstt ttd dt  tt tdtks@td S )Nr`   ra   r^   r\   r*  r   )	rH   r5   rT   r   rG   rh   r1   r6   rL   rl   rl   rl   rm   Útest_issue_18473  s    888$$B,,,..rm  c                   C   s@   t dtdt  tdt d  dt  tttdks<td S ©Nr\   rb   r`   )rH   r   rT   r   rh   rl   rl   rl   rm   Útest_issue_18482.  s    ro  c                   C   s   t tttdtt  tdtdks,tt tttdtt  tdddtdks\tt tttdtt  tdddtd kstd S )Nr`   r   r\   r]   r^   ra   )rH   r5   rT   r)   r1   rh   rl   rl   rl   rm   Útest_issue_185082  s    ,0rp  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   rl   rl   rl   rm   r   9  r   z"test_issue_18521.<locals>.<lambda>rê   rl   rl   rl   rm   Útest_issue_185218  s    rq  c                  C   sT   t ddd\} }tt| | |t|ks,tttt| | |tt|ksPtd S )NrZ  Trv   )r   rH   r   rh   r   r[  rl   rl   rm   Útest_issue_18969<  s    rr  c                   C   s,   t tttdt   tttdks(td S rò   )rH   rX   r   r   r   rh   rl   rl   rl   rm   Útest_issue_18992B  s    rs  c                  C   s<   t d} tt| t| d t| d   | ddks8td S )NrT   r`   r\   r   rg   )r   rH   rB   rh   r£   rl   rl   rm   Útest_issue_19067F  s    rt  c                   C   s*   t tdt dt    ttdks&td S rn  rq   rl   rl   rl   rm   Útest_issue_19586K  s    ru  c                  C   s0   t d} t ddd}t| | | ddks,td S )NrX   rþ   T)Zzeror   )r   rH   rh   )rX   rþ   rl   rl   rm   Útest_issue_13715O  s    rv  c                   C   sT   t td t d tdt  td tdtd     t d  ttdksPtd S r,  )rH   rX   r5   r   rh   rl   rl   rl   rm   Útest_issue_15055U  s    rw  c                  C   s   t ddd\} }t d\}}}t|| | t| td| | | | |d     | |  ||  |d|||  | ks~td S )Nzm viTrv   zB ti dre   r\   r   )r   rH   r)   rh   )rÿ   ÚviÚBZtirØ   rl   rl   rm   Útest_issue_16708Y  s    rz  c                   C   s   t tddt ttdtd   ttdtd t d ks@tt tddt ttdtd   tt dtd t d kstd S )Nr`   rb   r\   re   )rH   r7   rT   r   r)   r   rh   rl   rl   rl   rm   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(tt|
 ¡ d| |  | tdksNtd S )NÚbetaTrv   Úhrÿ   Úomegar  r`   rb   r\   rw   r   r   )r   r   r   r   rH   r   rh   rJ   )r|  r}  rÿ   Úwr  r¹   Úqrþ   r×   ÚZr	   rl   rl   rm   Útest_issue_19453d  s    (Lÿ"r  c                   C   s&   t td d t ttdks"td S )Nr`   r   r   r^  rl   rl   rl   rm   Útest_issue_19739w  s    r  c                   C   s2   t dt  tdtd  d  ttdks.td S )Nr\   r   r`   )rH   rT   r)   r   rh   rl   rl   rl   rm   Útest_issue_19766{  s    r  c                  C   sÖ   t d} tt| t t tttt| t t ttddks@tt ddd} tt| t t tttt| t t ttddkstt ddd} tt| t tttddks²ttt| t t ttd	ksÒtd S )
Nrÿ   ra   r^   Tr¡   )Znonzerorg   r`   r   )r   rH   r1   rT   r   rG   rh   rL   )rÿ   rl   rl   rm   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sHtt ttttt ttd ddtttttt ttd ddkstt ttttt ttd ddtttttt ttd ddksàtt tttttd tddkstt dtt   tt tks.ttdtt  tt tksPttdtt   tt tksttt dtt  tt tkstd S )Nr\   r]   r^   ra   rd   rg   r`   )	rH   r6   rT   r5   r   rG   rh   rL   r   rl   rl   rl   rm   Útest_issue_7535  s    HLL(&"$r  c                   C   s2   t td dt  t t tdt d ks.td S )Nr`   r   r\   )rH   rT   r	   rh   rl   rl   rl   rm   Útest_issue_20365  s    r  c                   C   sH   t dt dt  ddt  ddt    tt tdtd ksDtd S )Nr`   r\   r   )rH   rT   r/   r	   rh   rl   rl   rl   rm   Útest_issue_21031  s    r  c                   C   s0   t ttt dt d  tdtd ks,td S )Nrb   r   r   )rH   r5   r   rT   rh   rl   rl   rl   rm   Útest_issue_21038  s    r  c                  C   sZ   t ttdt  } t| tdddks*tt| tdddks@tt| tdddksVtd S )Nr`   r   r]   ra   rd   )r¥   rT   r5   rH   rh   rÌ   rl   rl   rm   Útest_issue_20578¢  s    r  c                  C   s|  t t} | jttdtkst| jtt dt ks8tt t t } | jttdt t ksbt| jtt dt tks~tt t t} | jttdt tks€t| jtt dt t ksÂt| jttdt tksÜtt t t dt } | jttdt t t kst| jtt dt t tks4t| jttdt t t ksVt| jtt dt t tksxtd S )N)Zlogxr`   )r   rT   ZnseriesrU   rh   rø   rl   rl   rm   Útest_issue_21227©  s    """r  c                  C   sH   t d tdt d   } |  t d¡dks,t|  ¡  t d¡dksDtd S r»   )rT   r1   rH   rh   r;  )r   rl   rl   rm   Útest_issue_21415Â  s    r  c                   C   s(   t ttd tt tttks$td S rò   )rH   r#   rX   r   r	   rh   rl   rl   rl   rm   Útest_issue_21530È  s    r  c                  C   sD   t dd d } tt|  td t d  t| t dd ks@td S )Nrc   r`   r\   )r)   rH   rT   rh   rÜ   rl   rl   rm   Útest_issue_21550Ì  s    r  c                  C   sL   t ttd  ttd  d t td} | tdd dtd  ksHtd S )Nr`   é   l   Ñqjl   SÍ[	)rH   rT   r   r   rh   )Úoutrl   rl   rm   Útest_issue_21661Ñ  s    (r  c                   C   s6   t ttttt   td¡tdtdd ks2td S )NrÃ   r   r`   i Ø	 )rH   r9   rV   rT   r  r   rh   rl   rl   rl   rm   Útest_issue_21701Ö  s    r  c                  C   sD   t ddd} tdtdt|  d    t}| tt¡tjks@td S )Nrx   Tr¡   r`   r\   )	r   rF   r   rT   rH   r   r   r   rh   )rx   r
   rl   rl   rm   Útest_issue_21721Ú  s    r  c                  C   sd   dt dt t t  dt dt t t d   } |  td¡dksHtt|  td¡dks`td S )Nr`   re   rc   r   )r   r
   r   rV   rH   rh   r   )Ztermrl   rl   rm   Útest_issue_21756à  s    4r  c                  C   s@   t d} t| d  td  dtd    | dd¡tks<td S )Nrx   r\   r`   ra   )r   r)   rT   rH   r
   rh   r  rl   rl   rm   Útest_issue_21785æ  s    r  c                   C   s&   t dt dt   ttdks"td S )Nrg   r\   r   rq   rl   rl   rl   rm   Útest_issue_22181ë  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sžtt|tt t d t d ksÜtt| tt dt dt d kstt|tt ddkstttt tt t  }t	|d	d
}t|tt
t|tt
  krntt kstn ttttd t  tttd t   }}t|ttddt t ksÂtt|ttddksÚtd S )Nr6  r\   r   rû   rc   é<   ra   r   T)Úforcer]   )r)   r0   r6   rT   r
   r   rH   r   rh   rI   r   )Úe1Úe2r}   Úexpr2rl   rl   rm   Útest_issue_22220ï  s     (6,ÿÿ$$&2. r  c                  C   sâ   t ddd\} }t|d |  |d | d  || d    |td| d  ksPtt|d |  |d | d  || d    ¡  |td| d  kstt|d |  |||   |d |    |d |    |td| d  ksÞtd S )Nzk, nTrv   r`   )r   rH   r   rh   r;  )rW   rX   rl   rl   rm   Útest_issue_22334  s    @Dr  c                   C   s0   t tddt  tt tttdks,td S r!  )rH   r   rT   r)   r   rh   rl   rl   rl   rm   Útest_sympyissue_22986  s    r  c                  C   s>   dt  dt    dt  dt     } t| t t dks:td S )Nr\   rg   )rT   rH   r   rh   rø   rl   rl   rm   Útest_issue_23231  s    $r  c                   C   s4   t dt td  tdt  tdtftks0td S )Nr`   r\   rg   r   )rF   rT   r   r   rh   rl   rl   rl   rm   Útest_issue_23596  s    r   c                  C   sº   t t td  t d } t t td  tt  d }t| tddt d t ksXtt| tddt d t ksxtt|tddt dt kstt|tddt d t ks¶td S )Nr\   rb   r   r]   ra   )r)   r
   rT   rH   rh   )Úexpr1r  rl   rl   rm   Útest_issue_23752  s      r¢  c                  C   s   t ttd tt  t¡} |  tt¡dks2t|  	¡  tt¡dksJt|  
t¡ tt¡dksdt|  
t¡ 	¡  tt¡dkstd S r   )r   r6   r   r"   rT   r   rH   r   rh   rJ   rŽ   r5   )r4  rl   rl   rm   Útest_issue_24276"  s
    r£  c                     sÆ   t ddd t ddd} t ddd}t ddd	}tt fd
d ttt| t||  ddksbtttt| t||  d| kstttt|t|| d|ks¢tttt|t|| ddksÂtd S )Nrx   Tr¡   ry   rv   rz   r   rX   r  c                      s   t tt t S r   )rH   r   rT   rl   r  rl   rm   r   .  r   z"test_issue_25230.<locals>.<lambda>r]   r   ra   )r   rQ   rë   rH   r   rT   rh   )ry   rz   rX   rl   r  rm   Útest_issue_25230)  s       r€  c                   C   sÊ   t tttttdt t ks$tt tttttdtt ksFtt tttttdt	d kshtt t
ttttddkstt tttttdt	d ksštt tttttddksÆtd S )Nra   r\   r   )rH   r/   r   rT   r   r
   rh   r+   r0   r   r,   r.   r-   rl   rl   rl   rm   Útest_issue_255825  s    $"""r¥  c                   C   sx  t tttt tddtd ks&tt ttdt tddtd ksLtt ttdt tdddksntt tttt tddtd kstt ttdt tddt t	 ksŒtt ttdt tdddksÞtt t
ttt tdddkstt t
tdt tddtt	 ks*tt t
tdt tddtd ksRtt tttt tddtd ksztt ttdt tdddkstt ttdt tddtd ksÆtt tttt tdddksêtt ttdt tddtd kstt ttdt tddtt	 ks:tt tttt tddtd ksbtt ttdt tdddkstt ttdt tddt t	 ks°tt tttt tddtksÔtt ttdt tddt	 t d kstt ttdt tdddks&tt tttt tddtdtd ksVtt ttdt tddtksztt ttdt tdddkstt tttt tdddksÂtt ttdt tddtksætt ttdt tddt	t d kstt tttt tddtks6tt ttdt tdddksZtt ttdt tddt	 t d kstt tttt tdddks¬tt ttdt tddt	t d ksØtt ttdt tddtksütt tttt tddtdtd ks,tt ttdt tdddksPtt ttdt tddtksttd S )Nr   rd   r   r`   r]   r\   ra   )rH   r0   r5   rT   r   rh   r   r/   r   r
   r+   r,   r.   r-   r   r   r   r)   r   r   r!   r    rl   rl   rl   rm   Útest_issue_25847?  sH    &&"&("$((($($((($*$.$0$$$$,$$.$,$0$rŠ  c                   C   s.   t tdtd tdt tttjks*td S r(  )rH   r7   rT   r   r   r«   rh   rl   rl   rl   rm   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sêtd S )
Nr   r\   r`   rb   rs   rÃ   r   rc   r   )rR   rT   rS   r   rH   r   rh   )r¹   rW   r  r  rl   rl   rm   Útest_issue_26250  s
      <Lrš  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   rn   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¿   rÁ   rÂ   rÅ   rÆ   rÈ   rË   rÍ   rÚ   rÝ   rÞ   rß   rà   râ   rå   ræ   rç   rè   rì   rð   rñ   ró   rõ   r÷   rù   rý   r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r"  r#  r%  r&  r'  r)  r+  r-  r.  r/  r0  r5  r:  r<  r=  r?  r@  rB  rC  rD  rE  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rY  r\  r]  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  ro  rp  rq  rr  rs  rt  ru  rv  rw  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§  rš  rl   rl   rl   rm   Ú<module>   s   (8 G
	



0	
	
	
>