o
    jg_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u s
J t ttt t u sJ t t ttt u s"J t td tt tu s/J t td  ttt u s=J t ttt tddddksMJ t dt ttdksYJ t tttttu seJ t tt ttt u ssJ 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 s J t ttd  ttt u s¯J t dt dtd  tddksÁJ t dt t tdttd t tdks×J t dt t tdddttd t tdddksñJ 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s&J t t	tt t tdtt	tt ks=J t t
dt d ttdksNJ t tjtt tju s\J t tdt ttjtju smJ 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 s€J t ddt d  tdddtu s·J t dtt ttddt u sÉJ t dtt ttddtu sÚJ t dt	t ttd ddt u sîJ 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 sJ t dttd  tdt tdd ddt u s6J t dttd  tttdd ddt u sOJ t dttd  tttdd ddtu sgJ t ttttttjtjksyJ 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s¯J t ttt tdd	ddksÀJ t td tdd	ddksÏJ t dtd  tdd	dtu sàJ t dt tdd	dtu sïJ t ddt  tdtu sþJ t ddt  tdddt u sJ t td
 tdddtu sJ t td tdddt u s/J t dtt tdddt t ksCJ t td tddddksRJ t tttddddksaJ t tt  tdddt ddt   ksxJ t dt	t t tdtt	td t tdksJ t dtt tdddtks€J t dtt tdddt ks¶J t dtt tdddtksÇJ t dtt tdddt ksÙJ t tdt dtt  tdddtksðJ 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   úV/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/series/tests/test_limits.pyÚtest_basic1)   sr    "$,4>,."""$(&$"(&4620$$$$""$ (.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s,J t tdt  ttdks;J t ttt  tttu sJJ t tttd   tttu s[J t tttt  tttu slJ t ddt  tt  ttdksJ 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s"J t dtd  ttd   tddtd  ks:J t ttd tt ttdksLJ tdtd d  tdtfdt td d	 ksfJ 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
    $0$8ru   c                  C   s.  t ddd\} }}t| | t| t|  }| | t¡dks!J ||  | t¡dks-J 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ÿ0r~   c                   C   s6   t ttd dd td  tddtddksJ d S )Né   rb   r\   re   r]   r`   é   )rH   r(   rT   r   rk   rk   rk   rl   Útest_piecewise   s   6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sxJ 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   )Úfunc1Úfunc2Ú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sJ 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   
ÿz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¯   ó   0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s1J 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sJ 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sAJ t tttdddksNJ t tttdddks[J t tttdddkshJ t tttdddksuJ 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s²J t ttd tt ttttj tdd ksÍJ t tttttdksÛJ t ttttt dksêJ t t	ttttdksøJ 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$   rk   rk   rk   rl   Ú
test_floor¹   s$   ,6$r   c                   C   s  t ttttdddksJ t ttttdddksJ t ttttdddks-J t ttttdddks<J t tdtt tdddksMJ t tdtt tdddks^J t tdtt tdddksoJ t tdtt tdddksJ d S )Nr   r]   ra   rg   rc   r   )rH   r%   r5   rT   r1   rk   rk   rk   rl   Ú&test_floor_requires_robust_assumptionsÒ   ó   """&r   c                   C   s  t tttdddksJ t tttdddksJ t tttdddks'J t tttdddks4J t tttdddksAJ t tttdddksNJ t tttdddks[J t tttdddkshJ t tttdddksuJ t tttdddksJ t tttd	dd
ksJ t tttd	dd	ksJ t ttdt  d tddtddks²J t ttd tt ttttj tdd ksÍJ d S )Nre   r]   rg   ra   r   r`   r\   rb   r   éù   rw   )rH   r$   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s-J t ttttdddks<J t tdtt tdddksMJ t tdtt tdddks^J t tdtt tdddksoJ t tdtt tdddksJ d S )Nr   r]   r`   ra   rc   r   )rH   r$   r5   rT   r1   rk   rk   rk   rl   Ú(test_ceiling_requires_robust_assumptionsð   r   r   c                   C   sŠ  t tttttddksJ t ttdt  tttddks"J t ttdt  tt tdtks6J t ttt tttdtksGJ t ttttdddksVJ t ttttdddkseJ t ttttdddkstJ t ttd tdddksJ ttdd  t td	t d tdddksJ t td	t d tdddks¬J t ttt	j
 tddt	dd ksÀJ t tdt tdtddksÑJ d S )
Nr   r`   r]   ra   rd   r\   c                   S   s   t tttddS ©Nr   rd   )rH   r&   rT   rk   rk   rk   rl   Ú<lambda>  ó    ztest_frac.<locals>.<lambda>re   )rH   r&   rT   r   rL   r5   r1   rQ   Ú
ValueErrorr   r   rk   rk   rk   rl   Ú	test_fracû   s   &("""(&r€   c                   C   s   t tttt tdddksJ t tttt tdddks"J t ttt t tdddks4J t ttt t tdddksFJ d S )Nr   r]   ra   re   )rH   r%   r5   rT   r6   rk   rk   rk   rl   Útest_issue_14355  s   ""$(r¥   c                  C   sd   t ddd} tt| td|   | ddksJ tt| t| d  t|  | ttd ks0J d S )NrT   T©Úrealr`   r   r\   )r   rH   r0   r5   r)   r   r   ©rT   rk   rk   rl   Ú	test_atan  s   $4r©   c                  C   s  t tttddksJ t ttttddksJ t ttttddks(J t tttd tdtdks:J t ttt ttt  dt  tdttksTJ t ttttd  tt	dksfJ t tttttd  tttd td d   d  tt	dksJ t tttd d d tddt	ksJ t ttttdt	ks­J t tttttdt	ksœJ t
ddd} t tt| d t|  | t	dks×J t | td|  t ttd|     d | ddksóJ t t| t|  | td	d
ksJ d S )Nr   r`   r\   rb   r]   rV   Trv   ra   rg   )rH   ÚabsrT   r5   r1   r   rU   r   r   r   r   r   ©rV   rk   rk   rl   Útest_set_signs  s   $4$H* (8(r¬   c                  C   st   t ddd} ttd|  t|  | ddtddksJ ttdtt| ttd|    | dtdks8J d S )	NrT   TrŠ   r`   r   r]   rg   r\   )r   rN   r5   r0   rL   rH   r   r)   rš   rk   rk   rl   Útest_heuristic8  s   ,<r­   c                  C   sN   t ddd} d|  t|  t  }t|ttdksJ | tt¡dks%J d S )NrV   Trv   rg   r   )r   r   rT   rH   r   )rV   Úfrk   rk   rl   Útest_issue_3871>  s   r¯   c                  C   s  t d} t ddd}td||   |  | tt|ksJ td|d|    |  | tt|d ks2J td|d|  d   |  | tt|d ksJJ t|d |d  | |ttdks^J tddd|  |  |tdtj kssJ tdd|  | d| |  |tttd	ksJ d S )
NrX   rT   TrŠ   r`   r\   re   r   z1/3)r   rH   r   r   r   ÚExp1©rX   rT   rk   rk   rl   Útest_exponentialE  s   $,0(*8r²   c                  C   s8   t d} tdt| t|    |  | tttksJ d S )NrX   r`   )r   rH   rT   r5   r   r   )rX   rk   rk   rl   Útest_exponential2P  s   0r³   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   r·   c                  C   sÌ  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s,J t tttttt  tttddksCJ 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sJ 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sµJ t ttd d t tttd	tksÊJ dt  ttd t  }t |tttd	tksäJ 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8*r¿   c                   C   s  t tdtttdksJ t tdttt dksJ t tdtttt tt ks,J t tdttt t t t ks?J t tdtttdksLJ t tdttt dksZJ t tdtttt t ksjJ t tdttt t t ks{J t tdttttksJ t tdttt t ksJ t tdtttt dksŠJ t tdttt t dks¶J t tdtttdksÃJ t tdttt t t ksÔJ t tdtttt dksãJ t tdttt t dksóJ 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"   "& " "  rÁ   c                  C   s2   t dt t} t| tt}|jdd|ksJ d S )Nr\   F©ÚdeeprŽ   rµ   rk   rk   rl   Ú
test_doit2  s   rÄ   c                   C   s.   t ttt ttd  tt dksJ d S rÀ   ro   rk   rk   rk   rl   Útest_issue_2929  ó   .rÅ   c                   C   s   t dtt td  ttjddttj  ksJ t tttd d tdtdtd ks2J t tttd d tddtd ksHJ d S )Nr`   r\   r   r   )rH   r1   rT   r   r   r5   rª   rk   rk   rk   rl   Útest_issue_3792  s   400rÇ   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s$J t tttd d  tdtdd ks:J t tttd t  tdtddt  ksRJ d S )Nr`   rb   r\   rc   é   r   )rH   rT   r   r   r   ÚOner   rk   rk   rk   rl   Útest_issue_4090  s   "&,4rÊ   c                   C   s@   t tttdddtu sJ t ttttd dddksJ d S )Nr   r]   r^   r\   )rH   r2   rT   r   r   rk   rk   rk   rl   Útest_issue_4547€  s   $rË   c                   C   s   t td tttd   krtu sJ  J t td tddks"J t td tddks.J t td ttdks:J t td tdtjksGJ d S )Nrw   é   r   r   g      à¿)rH   rT   r   r   r   rk   rk   rk   rl   Útest_issue_5164©  s
   ,rÍ   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   rÐ   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s6J 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 rÒ   c            
   
   C   sb  t ttt gddgddtjtddgddg} 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R }t| t|ks}J t	t
| |D ]*\}\}}|\}}}}|||  }	zt|	td|d|ks£J W q ty®   	 J w d 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srŸ   ÚdÚeqrk   rk   rl   Útest_issue_5183Œ  s   ý:ÿÿÿÿÿÿÿÿþþþþþþþþýýýýýýýýûûrà   c                  C   sº   t ttt ttdksJ t tttttd ksJ t tttttu s(J t ttt ttdks6J t ttttj	t
tksEJ tddd} t | td|   | ddks[J d S )Nr   r\   ÚrTrŠ   r`   )rH   r5   rT   r   r0   r   rB   r1   r   r   r)   r   ©rá   rk   rk   rl   Útest_issue_5184Ô  s   $rã   c                   C   s*   t dt dt  tj tddksJ d S rÀ   )rH   rU   r   r°   rk   rk   rk   rl   Útest_issue_5229ß  ó   *rä   c            	      C   sâ   t tttgt d dtd tttdd gddg} ddt tddt tddtt ddtt ddtt f}t| t|ks@J tt	| |D ]'\}\}}|\}}}|t
}zt|t
||d|kscJ W qG tyn   	 J w d S )Nr\   r   rb   ra   r]   r^   )rÓ   r   r2   r6   r   r   r   rÔ   rÕ   rÖ   rT   rH   r×   rØ   )	rÙ   rÚ   rÛ   r   rÜ   r®   r¶   rÞ   rß   rk   rk   rl   Útest_issue_4546ã  s$   
 þÿ
ûûræ   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s*J d S )Nr`   rb   r   rc   )rH   rT   r   rk   rk   rk   rl   Útest_issue_3934ø  s   (0rç   c                   C   sX   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 )NéM   rb   r`   gfffffFY@)rH   rT   r   r   rk   rk   rk   rl   Útest_calculate_seriesý  s   0(ré   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s$J t td dtd   ttdks6J t td td d tt   ttdksMJ d S )NrÌ   r`   éd   i]  éè  ©rH   rT   r   r   rk   rk   rk   rl   Útest_issue_5955	  s   $$$2rí   c                   C   s0   t tdtt ttt tddksJ d S rÀ   )rH   r   r5   rT   r2   rk   rk   rk   rl   Útest_newissue  r   rî   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s0J t tt ttttt ttksBJ t tt dt  ttttt dt  ttks\J d S rÀ   )rH   rT   r   rG   r5   rk   rk   rk   rl   Útest_extended_real_line  s   $<$8rï   c                  C   sJ   t ddd} t| t td| ksJ tt| d d  | ttu s#J d S )NrT   Trv   r`   r\   r   )r   rO   r   rH   rš   rk   rk   rl   Útest_order_oo  s   $rð   c                   C   ó    t tdd  t tdd  d S )Nc                   S   s   t ttt ttS r   ©rH   r   rT   rU   r   rk   rk   rk   rl   r¡   #  ó    z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ttS r   rò   rk   rk   rk   rl   r¡   $  s    ©rQ   ÚNotImplementedErrorrk   rk   rk   rl   Útest_issue_5436"  ó   rö   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¡   (  ó    z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   Ú0r^   rø   rk   rk   rk   rl   r¡   )  rù   )rQ   Ú	TypeErrorr£   rk   rk   rk   rl   Útest_Limit_dir'  r÷   rü   c                   C   s^   t td d td d d  ttdksJ t td d td d d  tt dks-J d S )Nr`   rë   rq   rk   rk   rk   rl   Útest_polynomial,  s   ,2rý   c                   C   s   t dt dtt  ttt  t  t  tttd tt  ks"J t dt dtt  ttt  t  t  tt td tt  ksEJ d S ©Nr`   )rH   rU   rT   rV   r   rk   rk   rk   rl   Útest_rational1  s   DJrÿ   c                   C   s<   t ttt tdt t  tdtttt  ksJ d S ©Nr\   r   )rH   r   rT   rV   rU   r   r   rk   rk   rk   rl   Útest_issue_57406  ó   <r  c                  C   s^   t dddd} | d t| d   t| d  d  ttd   }t|td ¡ | d ks-J d S )NrX   TrY   r`   r\   )r   rT   rH   Úcancel)rX   rá   rk   rk   rl   Útest_issue_6366:  s   0 r  c                  C   s   t t} t| tttu sJ tt|  ttdksJ t| tdt t tt t   ttdks2J 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_factorial@  s
   0 r  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sZJ d S )	Nrc   rb   r   r\   é#   rs   é   r`   )rT   r   rU   r   r   rH   r   ©rŸ   rk   rk   rl   Útest_issue_6560J  s   4ÿÿÿ
ÿJr
  c                     s$  t dt ddd} t d}t ddd}t ddd}d	 |  d
  | |  d
    | | d
 |  d	  | |  d
    |    |      ||d
 ¡ tt fdd t  ||¡td
kspJ t  ||¡t ¡ d	|d
  |  d
 | d
 |d
   ksJ d S )NrX   rá   Trv   rz   ÚpÚm©Únegativer\   r`   c                      s   t  tS r   )rH   r   rk   ©r}   rX   rk   rl   r¡   Y  s    z!test_issue_5172.<locals>.<lambda>)r   ÚsubsrQ   rõ   rH   r   rJ   )rá   rz   r  r  rk   r  rl   Útest_issue_5172O  s$   *.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_7088_  s   $r  c                   C   s  t ttt d tdttd ksJ t ttt d tddtdks'J t ttt d tdtd ks:J t ttt d tddt td ksPJ t ttt d tdtd kscJ t ttt d tddtdksvJ 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sJ t ttdt  tdttd ks³J t ttdt  tddt ttd  ksËJ t ttdt  tdtttd  ksáJ t ttdt  tddt td ks÷J t tdt tdtd ksJ t tdt tddt d ksJ 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sZJ t t	tt
dd t  tddt tt
dd  ksyJ t t	tt
dd t  tdttt
dd  ksJ t t	tt
dd t  tddt ttt
dd   ks·J t t	ttdtd ksÆJ t t	ttddt d ks×J t ttt t
dd  tdtt
dd ksòJ 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s/J t ttt t
dd  tddtt
d d ksLJ t ttt t
dd  tdtt
dd ksgJ 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s£J t ttt t
dd  tddtt
dd  ksÀJ t ttt d tdtt ksÓJ t ttt d tddt t ksèJ t tt t d tdt t ksýJ t tt t d tddtt ksJ t ttt d tdtks#J t ttt d tddt ks6J t tt t d tdt ksIJ t tt t d tddtks\J t ttt d tddt
dd  kssJ 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s¥J t tt t d tdddt
dd  ksŸJ 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_cutsd  sT   (&&,&&$.(0,,"&">>:B"6:@:6<<:&***"&&&.226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s3J d S )Nrx   r`   r\   r   )r   rV   r)   r5   r1   rH   r   r   )rx   rŸ   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sJ d S r   )rH   r   r;   rT   r   rk   rk   rk   rl   Útest_issue_6682  ó   6r  c                  C   s   t d} t| t tdtt|  ksJ t|  t tdt t|  ks&J t|  t ttt t|  ks8J t| t tttt|  ksHJ d S )Nrx   r   )r   rH   rT   r   r   r  rk   rk   rl   Útest_issue_4099  s
    $$$r  c                  C   s\   t d} ttdtt|   tdtt  |  | dttdtttd   ks,J d S )NÚdxr`   r   r\   )r   rH   r)   r   rT   )r  rk   rk   rl   Útest_issue_4503Š  s   .ÿr  c                  C   sJ   t ddddt } t| }t|tdddksJ t|ttt ks#J d S )Nrk   )r`   )r   r   rd   )rD   rT   rK   rH   r   )ÚGÚgrk   rk   rl   Útest_issue_6052¬  s   r  c                  C   sj   t ttdt dt  } ttt| tt |  tddksJ ttt| tt |  td ¡ dks3J d S )Nr`   rs   r   r\   g       @)r)   rT   r7   rH   r   ÚevalfrÑ   rk   rk   rl   Útest_issue_7224³  s   $,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_8208¹  ó   &r   c                   C   s<   t ttdd d ttd tdd  tddksJ d S )Nr`   r   r\   rb   rÌ   r   )rH   rT   r   r)   rk   rk   rk   rl   Útest_issue_8229œ  r  r"  c                  C   s4   t ddd\} }ttd||   |tdksJ d S )Nzd tTrv   r`   rg   )r   rH   r<   r   )rÞ   Útrk   rk   rl   Útest_issue_8433Á  s   $r$  c                  C   sH   t dddd} t ddd}t||  t|  t|  | tdks"J d S )NrW   T)rZ   ÚnonnegativeÚlamdarv   r   )r   rH   r   r   r   )rW   r&  rk   rk   rl   Útest_issue_8481Æ  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s#J d S )Nr\   rb   r   )rH   r   rX   r   rk   rk   rk   rl   Útest_issue_8462Ì  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_8634Ñ  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s0J t| t | td   | ttksBJ t| t | t| d	   | ttksVJ t ddd} t| t | td	   | ttksnJ t| t | td
   | tt ksJ d S )NrT   TrŠ   rW   rv   r   rc   g      @r`   r\   )r   rH   rX   r   )rT   rW   rk   rk   rl   Útest_issue_8635_18176×  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_8730ã  ó   r+  c                      s`   t dddt ddd ttt  d    tdks$J tt fdd	 d S )
NrX   T©rZ   rz   rv   r`   r   c                      s$   t tt     tS r   )rH   r   r   rk   ©rz   rX   rk   rl   r¡   ì  s   $ z!test_issue_9252.<locals>.<lambda>)r   rH   r   r   rQ   rõ   rk   rk   r.  rl   Útest_issue_9252ç  s   0r/  c                   C   s"   t ttd tdddksJ d S )Nr  r   ra   )rH   r5   rT   rk   rk   rk   rl   Útest_issue_9558ï  s   "r0  c                   C   s2   t dt ttdt td   tttksJ d S )NrÌ   r\   )rH   rW   r   r   r   rk   rk   rk   rl   Útest_issue_10801ó  s   2r1  c                  C   s8   t ddd\} }tt| | t|  | d|ksJ d S )Nzs xTrŠ   r   )r   rH   r<   )rÝ   rT   rk   rk   rl   Útest_issue_10976ø  s   (r2  c                   C   s<   t ttttd t tdt t   ttdksJ d S ©Nr`   r\   )rH   r   rX   r   r)   r   r   rk   rk   rk   rl   Útest_issue_9041ý  r  r4  c                  C   s   t d\} }}t| | |j|hksJ t| | |dj|hks J t| | | | |j|hks0J t| d  | | d |j||hksDJ d S )Nzx, y, ara   r\   )r   rG   Úfree_symbols)rT   rU   rx   rk   rk   rl   Útest_issue_9205  s
    ,r6  c                   C   sT   t dttd td  ttdksJ t dttdd  td  ttdks(J d S )Né   rb   r`   )rH   r   rX   r   rk   rk   rk   rl   Útest_issue_9471	  s   &.r8  c                   C   ó(   t ttd tt tttksJ d S rþ   )rH   r   rX   r   r   rk   rk   rk   rl   Útest_issue_10382  ó   (r:  c                   C   s$   t ttdt ttdksJ d S r3  )rH   r=   r   rT   r   rk   rk   rk   rl   Útest_issue_11496  ó   $r<  c                   C   s<   t ttt t tt  t tdtttd   ksJ d S ©Nr   r`   )rJ   rH   rT   rU   rX   rk   rk   rk   rl   Útest_issue_11879  r  r?  c                  C   sF   t d} td|  | tdksJ tdd|   | ttddks!J d S )NrW   rÎ   r`   g333333Ó?rb   é
   )r   rH   r   r   )rW   rk   rk   rl   Útest_limit_with_Float  s   &rA  c                   C   sD   t dt dt d   td d  td  tttddks J d S ©Nrb   r`   r\   )rH   rT   r   r   rk   rk   rk   rl   Útest_issue_10610   ó   DrC  c                   C   s  t tttt tddtdksJ t tttt tddtddt t  ks,J ttdd  t tttt tttksCJ t ttt	t tddtdksVJ t ttt	t tddt kshJ ttdd  t ttt	t tttksJ d S )Nr   r]   r\   ra   c                   S   ó   t tttt tddS r    )rH   r   rT   r!   rk   rk   rk   rl   r¡   '  ó    z"test_issue_10868.<locals>.<lambda>c                   S   rE  r    )rH   r   rT   r    rk   rk   rk   rl   r¡   +  rF  )
rH   r   rT   r!   r
   r   rQ   r£   r   r    rk   rk   rk   rl   Útest_issue_10868$  s   &2 &$$rG  c                   C   s$   t ttt t ttdksJ d S rþ   )rH   rX   r1   r   rk   rk   rk   rl   Útest_issue_6599/  r=  rH  c                   C   sn   t dt dtd   td tt  tt dksJ t dt dtd   td tt  tttu s5J d S )Nrb   r\   r@  ro   rk   rk   rk   rl   Útest_issue_125553  s   68rI  c                  C   sÒ  t ddd\} }}t dddd\}}}}}}}	|| ||  |  | t|d |d|   |d  |d  |d|  |d  |d  |d   |d|  |d|   |d  |d  |d d|  d   d|d|   ||d   | |  | |d d|  d   d||d   |d|   | |  | |d d|  d   d||d   ||d   |d  |d   |d |d d|  d    ||  | |  d  }
|
 ||¡jddt|
||jddksçJ d S )	Nzr z xTrŠ   za b s0 K F0 s T)r[   r§   r\   r`   rÂ   )r   r)   r  ÚfactorrH   )rá   rV   rT   rx   ry   Ús0ÚKÚF0rÝ   ÚTÚfxrk   rk   rl   Útest_issue_127698  s$   :"ÿ:ÿ:þ:ý*üüü0rP  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s;J d S )Né   rc   éûÿÿÿr`   i@¶  r\   r   iúÿÿÿé   é$   )rH   r)   rT   r   r   r   r   rk   rk   rk   rl   Útest_issue_13332D  s   BÿÿÿrU  c                   C   sò   t td ttt  tt tt tu sJ t td ttt  tt tttu s-J t ttt d  ¡ tttu s?J t ttt d  ¡ tttu sQJ t ttt d  ¡ tt tu sdJ t ttt d  ¡ tt tu swJ d S r   )rH   rT   r5   r1   r   Úexpandrk   rk   rk   rl   Útest_issue_12564I  s   .,$$&*rW  c                   C   rñ   )Nc                   S   s   t tttt ¡ S r   )rG   r   rT   r   r   rk   rk   rk   rl   r¡   S  ró   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  tt ¡ S )Nr\   r`   )rG   rT   r   r   rk   rk   rk   rl   r¡   T  s    rô   rk   rk   rk   rl   Útest_issue_14456R  r÷   rX  c                   C   sB   t dtdt t td   tdt dt d  t u sJ d S )Nrb   r   é   r\   )rH   r4   r   rT   r   rk   rk   rk   rl   Útest_issue_14411W  s   BrZ  c                   C   s8   t ttd d d td d  d  ttdksJ d S r3  rq   rk   rk   rk   rl   Útest_issue_13382[  s   8r[  c                   C   s<   t tdtttd  d ttt    ttdksJ d S )Nrg   r`   ©rH   rT   r   r   rk   rk   rk   rl   Útest_issue_13403_  r  r]  c                   C   sb   t td  ttd  td td d  ttd d   td ttd   ttdks/J d S rB  r\  rk   rk   rk   rl   Útest_issue_13416c  s   br^  c                   C   sx   t td dt dddt   t  d  t td  d td  t   tttd d td d  td  ks:J d S )Nr\   r`   r   rb   rY  rs   r   )rH   rX   rT   r   rk   rk   rk   rl   Útest_issue_13462g  s   xr_  c                  C   sH   t d} tt| t ttdksJ ttttt ttdks"J d S )Nrx   rg   )r   rH   r<   rT   r   r)   r  rk   rk   rl   Útest_issue_13750k  s   $r`  c                   C   s   t ttttt tttsJ t ttttt ttts"J t tttttttts3J tddtd tt   td t  tttksMJ d S r3  )	Ú
isinstancerH   r5   rT   r   r   rG   r1   r	   rk   rk   rk   rl   Útest_issue_14276q  s   """8rb  c                   C   s0   t dtttt  dt  ttdksJ d S rþ   )rH   r   rT   r   rk   rk   rk   rl   Útest_issue_14514x  r   rc  c                   C   sx  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sUJ t ttttd  ttttj	tjkslJ 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sºJ d S r   )rH   r5   rT   r1   r6   r3   r   rL   r   ri   rj   r2   rÉ   rk   rk   rk   rl   Útest_issues_14525|  s   >>...2@rd  c                   C   s4   t tttttd   td  ttdksJ d S )Nr\   r`   r   )rH   r)   rT   r1   r   rk   rk   rk   rl   Útest_issue_14574  ó   4re  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s<J t tttt tddksLJ 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   "" "rg  c                   C   ó   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¡     s     z"test_issue_14377.<locals>.<lambda>rô   rk   rk   rk   rl   Útest_issue_14377  ó   ri  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sFJ d S )Nr\   re   rb   r`   )rT   rA   rH   r   r   r	  rk   rk   rl   Útest_issue_15146  s   8*ÿÿÿ rk  c                  C   s°   dt  ddt   ddt   t  d    t d  t d  } t| t ttdks)J tt dd dt  tt   dt   tt d dtt   dt    } t| t tdksVJ d S )Nr\   re   r`   rÈ   r@  rc   rb   )rT   rH   r   r   r   r   r	  rk   rk   rl   Útest_issue_15202  s   :Frl  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¥  r   rm  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_15984©  ó   2rn  c                   C   s&   t ttdtt ttdksJ d S rþ   )rH   rC   rT   rB   r   rk   rk   rk   rl   Útest_issue_13571­  r!  rp  c                   C   s*   t ttttdtttjksJ d S rþ   )rH   r+   r>   rT   r   rÉ   rk   rk   rk   rl   Útest_issue_13575±  rå   rq  c                   C   s   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 s4J t dt tddd ¡ tu sDJ d S )Nr   rd   r^   r`   r\   )rG   r5   rT   r   r   r   rk   rk   rk   rl   Útest_issue_17325µ  s   $ $$rr  c                   C   s   t t td¡dksJ d S )Nr   )r   rT   rH   rk   rk   rk   rl   Útest_issue_10978Œ  r,  rs  c                   C   s    t ttd tttu sJ d S r   )rH   r%   rX   r   rk   rk   rk   rl   Útest_issue_14313_commentÀ  ó    rt  c                  C   s2   ddt   t   t ¡} t| t ddddksJ d S )Nr`   r]   r^   )rT   r   rH   )rÞ   rk   rk   rl   Útest_issue_15323Ä  s   rv  c                   C   s,   t ttt  tt tddksJ d S rþ   )rH   r   r   rT   rk   rk   rk   rl   Útest_issue_12571Ê  ó   ,rw  c                   C   sH   t td td t t  td td  td   tttdks"J d S rB  rì   rk   rk   rk   rl   Útest_issue_14590Î  ó   Hry  c                  C   sR   t d\} }tt| t|  t|  t|    tt|t|  |   |  ks'J d S )Núa b)r   rH   rT   rU   ©rx   ry   rk   rk   rl   Útest_issue_14393Ò  s   Fr}  c                   C   s@   t ttd dtd   ttdt   tttdksJ d S )Nr`   rg   )rH   r   rX   r   r   rk   rk   rk   rl   Útest_issue_14556×  ó   @r~  c                   C   sL   t dtdd td   dt  dtdd td    tttks$J d S )Nr`   r\   rb   r   ©rH   r   rT   r   rk   rk   rk   rl   Útest_issue_14811Û  s   Lr  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_16222ß  ru  r  c                   C   sD   t ttd  td t  ttd   t ttttdks J d S rþ   rì   rk   rk   rk   rl   Útest_issue_16714ã  rD  r  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sAJ d S )NrV   Trv   r`   )r[   rZ   )r   rH   r   rX   r   rB   r«   rk   rk   rl   Útest_issue_16722ç  s   48r  c                   C   sÀ   t td d td d ttd   td  tt td  ttdks&J t td d tt td td  ttd   ttdksFJ t td tt tttd   ttdks^J d S )Nr`   r\   r   rb   )rH   rX   r   r   rk   rk   rk   rl   Útest_issue_17431î  s"   $ÿÿÿÿÿ0ÿÿ4r  c                   C   s2   t ttt tttt  tdtksJ d S rþ   )rH   r;   r   rT   r   rk   rk   rk   rl   Útest_issue_17671ö  ro  r  c                  C   sf   t ddd\} }}}t| d | t| d d |d  ||  |  |t| d|  d  ks1J d S )Nza b c xTrv   r`   r\   )r   rH   r)   r   )rx   ry   rz   rT   rk   rk   rl   Útest_issue_17751ú  s   Rr  c                   C   s@   t tttt tdt t  tttdtt ksJ d S r3  )rH   r   rX   r)   r   r   r   rk   rk   rk   rl   Útest_issue_17792ÿ  r  r  c                   C   s@   t ttttdddksJ t ttttdddksJ d S )Nr   ra   rg   r]   r`   )rH   r   r5   rT   rk   rk   rk   rl   Útest_issue_18118  s   "r  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  rÆ   r  c                   C   s<   t ttdt t ttttd   ttdksJ d S )Nrb   rê   )rH   r   r   rT   r   rk   rk   rk   rl   Útest_issue_18378  r  r  c                   C   sJ   t dtdd t  dt  tttu sJ t t t tttu s#J d S )Nr`   r\   rb   )rH   r   rT   r   r   rk   rk   rk   rl   Útest_issue_18399  s   ,r  c                   C   sH   t ttdtt  ttddtttdtt  ttddks"J d S )Nr\   ra   r^   )rH   r6   rT   r)   r   r   rG   rk   rk   rk   rl   Útest_issue_18442  rz  r  c                   C   sF   t tttt tddksJ t tttt tdddks!J d S )Nr   r`   ra   )rH   rª   r   rT   rk   rk   rk   rl   Útest_issue_18452  s    &r  c                   C   s:  t ttdt  tttttdt  ttddksJ 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sTJ t ttd dt  ttdksfJ t ttd dt  ttdksxJ t ttd dt  tttttd dt  ttddksJ t ttd dt  tttddks­J t ttd dt  tttdtksÂJ 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síJ 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$$@***,.2r  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.  r  r  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sGJ d S )Nr`   r   r\   r]   r^   ra   )rH   r5   rT   r)   r1   rk   rk   rk   rl   Útest_issue_185082  s   ,06r  c                   C   rh  )Nc                   S   s   t tdt t ttS r   )rH   r   rX   rT   r   rk   rk   rk   rl   r¡   9  s    z"test_issue_18521.<locals>.<lambda>rô   rk   rk   rk   rl   Útest_issue_185218  rj  r  c                  C   sT   t ddd\} }tt| | |t|ksJ ttt| | |tt|ks(J d S )Nr{  Trv   )r   rH   r   r   r|  rk   rk   rl   Útest_issue_18969<  s   (r  c                   C   s,   t tttdt   tttdksJ d S rþ   )rH   rX   r   r   r   rk   rk   rk   rl   Útest_issue_18992B  rx  r  c                  C   s<   t d} tt| t| d t| d   | ddksJ d S )NrT   r`   r\   r   rg   )r   rH   rB   rš   rk   rk   rl   Útest_issue_19067F  s   4r  c                   C   s*   t tdt dt    ttdksJ d S r  rq   rk   rk   rk   rl   Útest_issue_19586K  rå   r  c                  C   s0   t d} t ddd}t| | | ddksJ d S )NrX   r  T)Úzeror   )r   rH   )rX   r  rk   rk   rl   Útest_issue_13715O  s   r  c                   C   sT   t td t d tdt  td tdtd     t d  ttdks(J d S rB  )rH   rX   r5   r   rk   rk   rk   rl   Útest_issue_15055U  s   T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BÚtirÞ   rk   rk   rl   Útest_issue_16708Y  s   d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sAJ d S )Nr`   rb   r\   re   )rH   r7   rT   r   r)   r   rk   rk   rk   rl   Útest_issue_19154_  s   @Fr  c                  C   sN  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s¥J 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  rŸ   Úqr  rÝ   ÚZr	   rk   rk   rl   Útest_issue_19453d  s   (Lÿ (rŠ  c                   C   s&   t td d t ttdksJ d S )Nr`   r   r   r  rk   rk   rk   rl   Útest_issue_19739w  r!  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_19766{  ro  rš  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sBJ t ddd} tt| t tttddksYJ tt| t t ttd	ksiJ d S )
Nr  ra   r^   TrŠ   )Únonzerorg   r`   r   )r   rH   r1   rT   r   rG   rL   )r  rk   rk   rl   Útest_issue_19770  s   88"$rª  c                   C   s  t ttttt ttd tttttt ttd ddks$J t ttttt ttd ddtttttt ttd ddksJJ t ttttt ttd ddtttttt ttd ddkspJ t tttttd tddksJ t dtt   tt tksJ tdtt  tt tks¥J tdtt   tt tks¶J t dtt  tt tksÇJ d S )Nr\   r]   r^   ra   rd   rg   r`   )rH   r6   rT   r5   r   rG   rL   r   rk   rk   rk   rl   Útest_issue_7535  s   HLL&$ "&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  ro  r¬  c                   C   sH   t dt dt  ddt  ddt    tt tdtd ks"J d S )Nr`   r\   r   )rH   rT   r/   r	   rk   rk   rk   rl   Útest_issue_21031  rz  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  r   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s+J d S )Nr`   r   r]   ra   rd   )rª   rT   r5   rH   rÑ   rk   rk   rl   Útest_issue_20578¢  s   r¯  c                  C   st  t t} | jttdtksJ | jtt dt ksJ t t t } | jttdt t ks1J | jtt dt tks?J t t t} | jttdt tksRJ | jtt dt t ksaJ | jttdt tksnJ t t t dt } | jttdt t t ksJ | jtt dt t tksJ | jttdt t t ksšJ | jtt dt t tksžJ d S )N)Úlogxr`   )r   rT   ÚnseriesrU   r  rk   rk   rl   Útest_issue_21227©  s      $r²  c                  C   sH   t d tdt d   } |  t d¡dksJ |  ¡  t d¡dks"J d S rÀ   )rT   r1   rH   rV  )r   rk   rk   rl   Útest_issue_21415Â  s   r³  c                   C   r9  rþ   )rH   r#   rX   r   r	   rk   rk   rk   rl   Útest_issue_21530È  r;  rŽ  c                  C   sD   t dd d } tt|  td t d  t| t dd ks J d S )Nrc   r`   r\   )r)   rH   rT   râ   rk   rk   rl   Útest_issue_21550Ì  s   4rµ  c                  C   sL   t ttd  ttd  d t td} | tdd dtd  ks$J d S )Nr`   é   l   Ñqjl   SÍ[	)rH   rT   r   r   )Úoutrk   rk   rl   Útest_issue_21661Ñ  s   ($rž  c                   C   s6   t ttttt   td¡tdtdd ksJ d S )NrÈ   r   r`   i Ø	 )rH   r9   rV   rT   r  r   rk   rk   rk   rl   Útest_issue_21701Ö  r  r¹  c                  C   sD   t ddd} tdtdt|  d    t}| tt¡tjks J d S )Nrx   TrŠ   r`   r\   )r   rF   r   rT   rH   r   r   r   )rx   r
   rk   rk   rl   Útest_issue_21721Ú  s   rº  c                  C   sd   dt dt t t  dt dt t t d   } |  td¡dks$J t|  td¡dks0J d S )Nr`   re   rc   r   )r   r
   r   rV   rH   r   )Útermrk   rk   rl   Útest_issue_21756à  s   4rŒ  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_21785æ  s   8rœ  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_22181ë  r!  rŸ  c                  C   sÔ  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s\J t|tt t d t d ksnJ 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rŽtt ks·J  J tttd t  tttd t   }}t|ttddt t ksÝJ t|ttddksèJ d S )NrQ  r\   r   r  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_22220ï  s    (6,ÿÿ$$$0.rÄ  c                  C   sâ   t ddd\} }t|d |  |d | d  || d    |td| d  ks(J t|d |  |d | d  || d    ¡  |td| d  ksJJ t|d |  |||   |d |    |d |    |td| d  ksoJ d S )Nzk, nTrv   r`   )r   rH   r   rV  )rW   rX   rk   rk   rl   Útest_issue_22334  s   @DNrÅ  c                   C   s0   t tddt  tt tttdksJ d S r3  )rH   r   rT   r)   r   rk   rk   rk   rl   Útest_sympyissue_22986  r   rÆ  c                  C   s>   dt  dt    dt  dt     } t| t t dksJ d S )Nr\   rg   )rT   rH   r   r  rk   rk   rl   Útest_issue_23231  s   $rÇ  c                   C   s4   t dt td  tdt  tdtftksJ d S )Nr`   r\   rg   r   )rF   rT   r   r   rk   rk   rk   rl   Útest_issue_23596  rf  rÈ  c                  C   sº   t t td  t d } t t td  tt  d }t| tddt d t ks,J t| tddt d t ks<J t|tddt dt ksKJ t|tddt d t ks[J d S )Nr\   rb   r   r]   ra   )r)   r
   rT   rH   )Úexpr1rÃ  rk   rk   rl   Útest_issue_23752  s     $rÊ  c                  C   s   t ttd tt  t¡} |  tt¡dksJ |  ¡  tt¡dks%J |  	t
¡ tt¡dks2J |  	t
¡ ¡  tt¡dksAJ d S r   )r   r6   r   r"   rT   r   rH   r   rJ   r¹   r5   )rO  rk   rk   rl   Útest_issue_24276"  s
   "rË  c                     sÆ   t ddd t ddd} t ddd}t ddd	}tt fd
d ttt| t||  ddks1J ttt| t||  d| ksAJ ttt|t|| d|ksQJ ttt|t|| ddksaJ d S )Nrx   TrŠ   ry   rv   rz   r  rX   r-  c                      s   t tt t S r   )rH   r   rT   rk   r  rk   rl   r¡   .  r¢   z"test_issue_25230.<locals>.<lambda>r]   r   ra   )r   rQ   rõ   rH   r   rT   )ry   rz   rX   rk   r  rl   Útest_issue_25230)  s      $rÌ  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s#J t tttttdtd ks4J t t	ttttddksCJ t t
ttttdtd ksTJ t tttttddkscJ 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   $""""rÍ  c                   C   sj  t tttt tddtd ksJ t ttdt tddtd ks&J t ttdt tdddks7J t tttt tddtd ksJJ t ttdt tddt t ks^J t ttdt tdddksoJ t t	ttt tdddksJ t t	tdt tddtt ksJ t t	tdt tddtd ksŠJ t t
ttt tddtd ks¹J t t
tdt tdddksÊJ t t
tdt tddtd ksÝJ t tttt tdddksîJ t ttdt tddtd ksJ t ttdt tddtt ksJ t tttt tddtd ks*J t ttdt tdddks<J t ttdt tddt t ksQJ t tttt tddtkscJ t ttdt tddt t d kszJ t ttdt tdddksJ t tttt tddtdtd ks€J t ttdt tddtks¶J t ttdt tdddksÈJ t tttt tdddksÚJ t ttdt tddtksìJ t ttdt tddtt d ksJ t tttt tddtksJ t ttdt tdddks&J t ttdt tddt t d ks=J t tttt tdddksOJ t ttdt tddtt d kseJ t ttdt tddtkswJ t tttt tddtdtd ksJ t ttdt tdddks¡J t ttdt tddtks³J d S )Nr   rd   r   r`   r]   r\   ra   )rH   r0   r5   rT   r   r   r/   r   r
   r+   r,   r.   r-   r   r   r   r)   r   r   r!   r    rk   rk   rk   rl   Útest_issue_25847?  sH   &&"&(""&&&"&"((($*$.$0$$$$,$$.$,$0$(rÎ  c                   C   s.   t tdtd tdt tttjksJ d S r>  )rH   r7   rT   r   r   r°   rk   rk   rk   rl   Útest_issue_26040}  rÆ   rÏ  c                  C   sî   t dt td dt  d  } tdt td dt  d  }ddtd   | d  d td dt  d |  | d  }td td dtd   td  dtd   td  dtd   td   }t|| td	td d ksuJ d S )
Nr   r\   r`   rb   rs   rÈ   r   rc   r   )rR   rT   rS   r   rH   r   )rŸ   rW   rÁ  rÂ  rk   rk   rl   Útest_issue_26250  s
     <L&rÐ  N(   Ú	itertoolsr   Úsympy.concrete.summationsr   Úsympy.core.functionr   r   Ú
sympy.corer   r   Úsympy.core.modr   Úsympy.core.numbersr	   r
   r   r   r   r   Úsympy.core.singletonr   Úsympy.core.symbolr   r   Ú%sympy.functions.combinatorial.numbersr   Ú(sympy.functions.combinatorial.factorialsr   r   r   Ú$sympy.functions.elementary.complexesr   r   r   Ú&sympy.functions.elementary.exponentialr   r   r   Ú%sympy.functions.elementary.hyperbolicr   r   r   r   r    r!   r"   r#   Ú#sympy.functions.elementary.integersr$   r%   r&   Ú(sympy.functions.elementary.miscellaneousr'   r(   r)   Ú$sympy.functions.elementary.piecewiser*   Ú(sympy.functions.elementary.trigonometricr+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   Úsympy.functions.special.besselr7   r8   r9   r:   Ú'sympy.functions.special.error_functionsr;   r<   r=   r>   r?   r@   Ú'sympy.functions.special.gamma_functionsrA   rB   rC   Úsympy.functions.special.hyperrD   Úsympy.integrals.integralsrE   rF   Úsympy.series.limitsrG   rH   Úsympy.simplify.simplifyrI   rJ   Úsympy.simplify.hyperexpandrK   Ú!sympy.calculus.accumulationboundsrL   Úsympy.core.mulrM   rN   Úsympy.series.orderrO   Úsympy.testing.pytestrP   rQ   ÚsympyrR   rS   Ú	sympy.abcrT   rU   rV   rW   rX   rm   rp   rr   ru   r~   r   r   r   r   r   r   r   r   r   r€   r¥   r©   r¬   r­   r¯   r²   r³   r·   r¿   rÁ   rÄ   rÅ   rÇ   rÊ   rË   rÍ   rÐ   rÒ   rà   rã   rä   ræ   rç   ré   rí   rî   rï   rð   rö   rü   rý   rÿ   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  r4  r6  r8  r:  r<  r?  rA  rC  rG  rH  rI  rP  rU  rW  rX  rZ  r[  r]  r^  r_  r`  rb  rc  rd  re  rg  ri  rk  rl  rm  rn  rp  rq  rr  rs  rt  rv  rw  ry  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  rª  r«  r¬  r­  r®  r¯  r²  r³  rŽ  rµ  rž  r¹  rº  rŒ  rœ  rŸ  rÄ  rÅ  rÆ  rÇ  rÈ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rk   rk   rk   rl   Ú<module>   s    (8 G
	



0	
	
	
>