U
    	Ç-eç¬  ã                   @   s`  d dl mZ d dlmZ d dlmZmZ d dlmZ d dl	m
Z
mZmZmZmZmZ d dlmZ d dlmZmZ d dlmZmZmZ d d	lmZmZmZ d d
lmZmZm Z  d dl!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z( d dl)m*Z*m+Z+m,Z, d dl-m.Z.m/Z/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z? d dl@mAZAmBZBmCZCmDZD d dlEmFZFmGZGmHZHmIZImJZJmKZK d dlLmMZMmNZNmOZO d dlPmQZQ d dlRmSZSmTZT d dlUmVZVmWZW d dlXmYZYmZZZ d dl[m\Z\ d dl]m^Z^ d dl_m`Z` d dlUmaZa d dlbmcZc d dldmeZemfZf d dlgmhZhmiZimjZjmkZk edddd Zld!d" Zmd#d$ Znd%d& Zod'd( Zpd)d* Zqd+d, Zrd-d. Zsd/d0 Ztd1d2 Zud3d4 Zvd5d6 Zwd7d8 Zxd9d: Zyd;d< Zzd=d> Z{d?d@ Z|dAdB Z}dCdD Z~dEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZeedSdT ZdUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zeedudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zeedd Z dd Z¡dd Z¢dd Z£dd Z€dd Z¥dd ZŠdd Z§dd Zšdd Z©dd Zªdd Z«dd  Z¬d¡d¢ Z­d£d€ Z®d¥dŠ Z¯d§dš Z°d©dª Z±d«d¬ Z²d­d® Z³d¯d° ZŽd±d² Zµd³dŽ Z¶dµd¶ Z·d·dž Zžd¹dº Z¹d»dŒ ZºdœdŸ Z»d¿dÀ ZŒdÁdÂ ZœdÃdÄ ZŸdÅdÆ Z¿dÇdÈ ZÀdÉdÊ ZÁdËdÌ ZÂdÍdÎ ZÃdÏdÐ ZÄdÑdÒ ZÅdÓdÔ ZÆdÕdÖ ZÇd×dØ ZÈdÙdÚ ZÉdÛdÜ ZÊdÝdÞ ZËdßdà ZÌdádâ ZÍdãdä ZÎdådæ ZÏdçdè ZÐdédê ZÑdëdì ZÒdídî ZÓdïdð ZÔdñdò ZÕdódô ZÖdõdö Z×eed÷dø ZØdùdú ZÙdûdü ZÚdýdþ ZÛdÿd  ZÜdd ZÝdd ZÞdd Zßdd Zàd	d
 Zádd Zâdd Zãdd Zädd Zådd Zædd Zçdd Zèdd Zédd Zêdd Zëdd  Zìd!d" Zíd#d$ Zîd%d& Zïd'd( Zðd)d* Zñd+d, Zòd-d. Zód/d0 Zôd1d2 Zõd3d4 Zöd5d6 Z÷d7d8 Zød9d: Zùd;d< Zúd=d> Zûd?d@ ZüdAdB ZýdCdD ZþdEdF ZÿdGdH Z dIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX ZdYdZ Z	d[d\ Z
d]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh ZdiS (j  é    )Úproduct)ÚSum)ÚFunctionÚdiff)Ú
EulerGamma)ÚEÚIÚRationalÚooÚpiÚzoo)ÚS)ÚSymbolÚsymbols)ÚbinomialÚ	factorialÚsubfactorial)ÚAbsÚreÚsign)ÚLambertWÚexpÚlog)ÚacoshÚacothÚacschÚasechÚatanhÚsinhÚtanh)ÚceilingÚfloorÚfrac)ÚcbrtÚ	real_rootÚsqrt)Ú	Piecewise)ÚacosÚacotÚacscÚasecÚasinÚatanÚcosÚcotÚcscÚsecÚsinÚtan)ÚbesseliÚbesselyÚbesseljÚbesselk)ÚEiÚerfÚerfcÚerfiÚfresnelcÚfresnels)ÚdigammaÚgammaÚ
uppergamma)Úmeijerg)ÚIntegralÚ	integrate)ÚLimitÚlimit)Ú
logcombineÚsimplify)Úhyperexpand)ÚAccumBounds)ÚMul)Ú
heuristics)ÚOrder)ÚXFAILÚraises)ÚxÚyÚzÚkÚnT©ÚintegerÚpositivec                   C   s  t tttt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$tt ttttttjtjksHtt ttttttjtjksltt ttt tdd	ddkstt td tdd	ddks¬tt dtd  tdd	dtksÎtt dt tdd	dtksìtt ddt  tdtks
tt ddt  tdddt ks.tt td
 tdddtksLtt td tdddt ksltt dtt tdddt t kstt td tddddks²tt tttddddksÐtt tt  tdddt ddt   ksþtt dt
t t tdtt
td t tdks4tt dtt tdddtksVtt dtt tdddt ksztt dtt tdddtkstt dtt tdddt ksÀtt tdt dtt  tdddtksîtt tdt dt  tdddtkstd S )Né   r   ú+©Údiré   ú-é   é   ú+-éþÿÿÿéýÿÿÿéÿÿÿÿ)rD   rN   r
   ÚAssertionErrorr   r   r%   rC   rO   r   r-   r>   r   ÚNaNrK   r1   r   r2   r	   r.   rH   ÚNegativeInfinityÚInfinityr0   r/   r   r   r+   r   © rf   rf   ú_/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/series/tests/test_limits.pyÚtest_basic1%   sr     $ &.6>,."""$(&$"(&4620$$$$""$ (.6"$"$.rh   c                   C   s  t tt tddddkstt ttd t tddks<tt ddt  ttdksXtt tdt  ttdksvtt ttt  tttkstt tttd   tttks¶tt tttt  tttksØtt ddt  tt  ttdksþtd S )Nr   rW   rX   rZ   ra   rV   é   )rD   rN   rb   r   r
   rf   rf   rf   rg   Útest_basic2l   s     ""rj   c                   C   s>   t dt tdddtkstt dt tdddt ks:td S )NrZ   r   rW   rX   r[   ©rD   rN   r
   rb   rf   rf   rf   rg   Útest_basic3w   s    rl   c                   C   sÐ   t dt tt  tddks tt dt tt  tddt ksDtt dtd  ttd   tddtd  ksttt ttd tt ttdksttdtd d  tdtfdt td d	 ksÌtd S )
NrV   r   rZ   é   r`   r_   i   r\   é	   )rD   rN   rO   rb   r%   r
   rB   r   rf   rf   rf   rg   Útest_basic4|   s
     $0$ro   c                  C   s0  t ddd\} }}t| | t| t|  }| | t¡dksBt||  | t¡dksZtt ddd\}}|d |d |d  t|d  |d d d  d|d d |d    d| t||  |d d d	 t|d |d    |d d d    }t||tt|d
  |d d d  ks,td S )Nza b cT©rU   r   ztau xrV   rZ   r_   ç      à?r\   )r   r   rD   r
   rb   r,   r   )ÚaÚbÚcÚAÚtaurN   Úexprrf   rf   rg   Útest_log   s"    8ÿÿ(ÿÿÿrx   c                   C   s6   t ttd dd td  tddtddks2td S )Né   r\   rV   r_   rW   rZ   é   )rD   r$   rN   r	   rb   rf   rf   rf   rg   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 )NrV   é   rZ   r   Trq   g      À?rn   r]   ra   r\   )r%   rN   r&   r   rD   rb   )Zfunc1Zfunc2Zfunc3rf   rf   rg   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   re   rc   )ÚclsÚargrf   rf   rg   Úeval€   s    
ztest_basic5.<locals>.my.evalN)Ú__name__Ú
__module__Ú__qualname__Úclassmethodr   rf   rf   rf   rg   Úmy£   s   r   )r   rD   rN   r
   rC   rb   )r   rf   rf   rg   Útest_basic5¢   s    r   c                   C   s0   t tt tt  tdtt dt  ks,td S ©NrV   )rD   rN   rO   rP   rb   rf   rf   rf   rg   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   rZ   r^   rX   )rC   r1   rN   rb   ÚdoitÚargsr   rf   rf   rf   rg   Ú
test_Limit¯   s     r   c                   C   s$  t tttdddkstt tttdddks4tt tttdddksNtt tttdddkshtt tttdddkstt tttdddkstt tttdddks¶tt tttdddksÐtt tttdddksêtt tttdddkstt tttd	dd	ks"tt tttd	dd
ks>tt ttdt  d tddtddksltt ttd tt ttttj tdd ks€tt tt	tttdksÂtt tt	ttt dksâtt t
t	tttdks tt t
t	ttt dks td S )Nr_   rW   r[   r`   ra   r   rZ   rV   éø   é÷   r\   rq   )rD   r!   rN   rb   r	   r
   rH   r   ÚHalfr,   r    rf   rf   rf   rg   Ú
test_floorµ   s$    .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   rW   r[   ra   r]   r|   )rD   r!   r1   rN   rb   r-   rf   rf   rf   rg   Ú&test_floor_requires_robust_assumptionsÎ   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 )Nr_   rW   ra   r[   r   rZ   rV   r\   r   éù   rq   )	rD   r    rN   rb   r	   r
   rH   r   r   rf   rf   rf   rg   Útest_ceilingÙ   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   rW   rZ   r[   r]   ry   )rD   r    r1   rN   rb   r-   rf   rf   rf   rg   Ú(test_ceiling_requires_robust_assumptionsì   s    """r   c                   C   sš  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d
kstt tdt tdtddks€td S )Nr   rZ   rW   r[   r^   rV   c                   S   s   t tttddS ©Nr   r^   )rD   r"   rN   rf   rf   rf   rg   Ú<lambda>   ó    ztest_frac.<locals>.<lambda>r_   rq   )rD   r"   rN   r
   rH   rb   r1   r-   rM   Ú
ValueErrorr   r   rf   rf   rf   rg   Ú	test_frac÷   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   rW   r[   r_   )rD   r!   r1   rN   rb   r2   rf   rf   rf   rg   Útest_issue_14355  s    ""$r   c                  C   sd   t ddd} tt| td|   | ddks0ttt| t| d  t|  | ttd ks`td S )NrN   T©ÚrealrZ   r   rV   )r   rD   r,   r1   rb   r%   r
   r   ©rN   rf   rf   rg   Ú	test_atan  s    $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   rZ   rV   r\   rW   rP   Trp   r[   ra   )rD   ÚabsrN   rb   r1   r-   r   rO   r   r   r
   r   r   ©rP   rf   rf   rg   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 )	NrN   Tr   rZ   r   rW   ra   rV   )	r   rJ   r1   r,   rH   rb   rD   r   r%   r   rf   rf   rg   Útest_heuristic4  s    ,r¢   c                  C   sN   t ddd} d|  t|  t  }t|ttdks6t| tt¡dksJtd S )NrP   Trp   ra   r   )r   r   rN   rD   r
   rb   )rP   Úfrf   rf   rg   Útest_issue_3871:  s    r€   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 )
NrR   rN   Tr   rZ   rV   r_   ry   z1/3)r   rD   r
   r   rb   r   ÚExp1©rR   rN   rf   rf   rg   Útest_exponentialA  s    $,0(*r§   c                  C   s8   t d} tdt| t|    |  | tttks4td S )NrR   rZ   )r   rD   rN   r1   r
   r   rb   )rR   rf   rf   rg   Útest_exponential2L  s    rš   c                  C   s.   t dt t} t| tt}| ¡ tks*td S r   ©rA   rN   rC   r
   r   rb   ©r£   Úlrf   rf   rg   Ú	test_doitQ  s    r¬   c                  C   sÒ  t ttttd  tttddks*tt ttttd  d tttddksXtt tttttt  tttddkstdtd d } dtd d }tt| |ddtd  dd}t tt	tt
 t¡t
d	tf ¡  t¡tt|ksþtttdtdd  tdd d ddtd  }t tt	tt
 t¡t
d	tf ¡  t¡tt|ksltt ttd d t tttd	tkstdt  ttd t  }t |tttd	tksÎtd S )
NrZ   r_   rV   ra   r\   r`   F)Úevaluater   )rD   r1   rQ   r
   rH   rb   r-   rI   rF   r   rR   Úrewriter   r   rN   )ÚloÚhiÚt1Út2Úerf   rf   rg   Útest_series_AccumBoundsW  s    *.. 84:,rŽ   c                   C   s  t tdtttdkstt tdttt dks6tt tdtttt tt ksXtt tdttt t t t ks~tt tdtttdkstt tdttt dksŽtt tdtttt t ksÔtt tdttt t t ksött tdttttkstt tdttt t ks2tt tdtttt dksRtt tdttt t dksttt tdtttdkstt tdttt t t ksŽtt tdtttt dksÔtt tdttt t dksött tdtttdkstd S ©NrZ   r   )	rD   r5   rN   r
   rb   r   r4   r3   r6   rf   rf   rf   rg   Ú!test_bessel_functions_at_infinityn  s"    "& "  "$ "r¶   c                  C   s2   t dt t} t| tt}|jdd|ks.td S )NrV   F©Údeepr©   rª   rf   rf   rg   Ú
test_doit2  s    r¹   c                   C   s.   t ttt ttd  tt dks*td S rµ   ©rD   rN   r   r
   rb   rf   rf   rf   rg   Útest_issue_2929  s    r»   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 )NrZ   rV   r|   r   )rD   r-   rN   r   r   rb   r1   r   rf   rf   rf   rg   Útest_issue_3792  s    40rŒ   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 )NrZ   r\   rV   r]   é   r|   )rD   rN   r	   rb   r   r   ÚOner   rf   rf   rf   rg   Útest_issue_4090  s    "&,r¿   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   rW   rX   rV   )rD   r.   rN   r
   rb   r   rf   rf   rf   rg   Útest_issue_4547   s    rÀ   c                   C   s   t td tttd   kr$tks*n tt td tdtdd ksJtt td tddksbtt td ttdksztt td tdtdd kstd S )Nrq   é   r   g      à¿r|   )rD   rN   r
   rb   r   rf   rf   rf   rg   Útest_issue_5164¥  s
    * rÂ   c                  C   s,   ddt   dt   } t| t dtks(td S )Nç      ð?r   )rN   rD   r   rb   )Úfuncrf   rf   rg   Útest_issue_5383­  s    rÅ   c                  C   sp   t tdd  tt  t  tdt d  ttt  tddt    t d  } t| t ttdd ksltd S )NrZ   rV   rz   r\   ih  )rN   r   r   r   r   rD   r
   rb   ©rw   rf   rf   rg   Útest_issue_14793²  s    *
ÿÿÿrÇ   c            
       C   s0  t ttt gddgddtjtddgddg} ttt tt t tt dtdd  tddddddddtttt tt t tt dtdd  ddddddddf }t| t|ksžt	t
t| |D ]d\}\}}|\}}}}|||  }	zt|	td|d|kst	W qÆ t	k
r(   d s$t	Y qÆX qÆd S )	Nra   rZ   rV   r\   r[   rW   r   rX   )Úlistr   rN   r   r   r	   r
   r   Úlenrb   Ú	enumerateÚziprD   Úprint)
ÚtestsÚresultsÚir   ÚresrO   Úsr³   ÚdÚeqrf   rf   rg   Útest_issue_5183ž  sN    ý(                     ýrÔ   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   rV   ÚrTr   rZ   )rD   r1   rN   r
   rb   r,   r   r>   r-   r   r   r%   r   ©rÕ   rf   rf   rg   Útest_issue_5184Ð  s    r×   c                   C   s*   t dt dt  tj tddks&td S rµ   )rD   rO   r   r¥   rb   rf   rf   rf   rg   Útest_issue_5229Û  s    rØ   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 )NrV   r   r\   r[   rW   rX   )rÈ   r   r.   r2   r   r	   r
   rÉ   rb   rÊ   rË   rN   rD   rÌ   )	rÍ   rÎ   rÏ   r   rÐ   r£   r«   rÒ   rÓ   rf   rf   rg   Útest_issue_4546ß  s0    
 þ         ÿ
rÙ   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 )NrZ   r\   r   r]   )rD   rN   r   rb   rf   rf   rf   rg   Útest_issue_3934ô  s    (rÚ   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   r\   rZ   gfffffFY@)rD   rN   r	   r
   rb   rf   rf   rf   rg   Útest_calculate_seriesù  s    0rÜ   c                   C   s   t td dtd   ttdks$tt td dtd   ttdksHtt td dtd   ttdksltt td td d tt   ttdkstd S )NrÁ   rZ   éd   i]  éè  )rD   rN   r
   rb   r   rf   rf   rf   rg   Útest_issue_5955  s    $$$rß   c                   C   s0   t tdtt ttt tddks,td S rµ   )rD   r   r1   rN   r.   rb   rf   rf   rf   rg   Útest_newissue  s    rà   c                   C   sŒ   t tt ttttt ttks$tt dttt  t tdtdttt  t tdks`tt tt ttttt ttkstt tt dt  ttttt dt  ttksžtd S rµ   )rD   rN   r
   rC   rb   r1   rf   rf   rf   rg   Útest_extended_real_line  s    $<$rá   c                  C   sJ   t ddd} t| t td| ks&ttt| d d  | ttksFtd S )NrN   Trp   rZ   rV   r|   )r   rK   r
   rb   rD   r   rf   rf   rg   Útest_order_oo  s    râ   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttt ttS r~   ©rD   r   rN   rO   r
   rf   rf   rf   rg   r     r   z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ttS r~   rã   rf   rf   rf   rg   r      r   ©rM   ÚNotImplementedErrorrf   rf   rf   rg   Útest_issue_5436  s    ræ   c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t ttdddS )Nr   rX   ©rC   rN   rf   rf   rf   rg   r   $  r   z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   Ú0rX   rç   rf   rf   rf   rg   r   %  r   )rM   Ú	TypeErrorr   rf   rf   rf   rg   Útest_Limit_dir#  s    rê   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 )NrZ   rÞ   rk   rf   rf   rf   rg   Útest_polynomial(  s    ,rë   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 ©NrZ   )rD   rO   rN   rP   r
   rb   rf   rf   rf   rg   Útest_rational-  s    Drí   c                   C   s<   t ttt tdt t  tdtttt  ks8td S ©NrV   r   )rD   r   rN   rP   rO   r
   r   rb   rf   rf   rf   rg   Útest_issue_57402  s    rï   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 )NrR   TrS   rZ   rV   )r   rN   rD   Úcancelrb   )rR   rÕ   rf   rf   rg   Útest_issue_63666  s    0rñ   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   rV   rZ   )	r   rN   rD   r
   rb   r%   r   r   r>   ©r£   rf   rf   rg   Útest_factorial<  s
    0ró   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 )	Nr]   r\   r|   rV   é#   rm   é   rZ   )rN   r	   rO   r   r   rD   r
   rb   ©r³   rf   rf   rg   Útest_issue_6560F  s    4ÿÿÿ
ÿ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sàtt  ||¡t ¡ d	|d
  |  d
 | d
 |d
   ks"td S )NrR   rÕ   Trp   rt   ÚpÚm)ÚnegativerV   rZ   c                      s   t  tS r~   )rD   r
   rf   ©rw   rR   rf   rg   r   U  r   z!test_issue_5172.<locals>.<lambda>)r   ÚsubsrM   rå   rD   r
   rb   rF   )rÕ   rt   rø   rù   rf   rû   rg   Útest_issue_5172K  s$    *.ÿÿ
ÿ"ÿrý   c                  C   s,   t d} tttt|   ttdks(td S )Nrr   rZ   )r   rD   r%   rN   r
   rb   ©rr   rf   rf   rg   Útest_issue_7088[  s    rÿ   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 )NrV   r   r[   r_   rZ   ra   r\   )rD   r+   r   rN   r   rb   r'   r,   r   r
   r(   r   r   r*   r)   r   r%   r#   rf   rf   rf   rg   Útest_branch_cuts`  sT    (&&,&&&0*2.."&">>:B"6:@:6<<:&***"&&&.22r   c                  C   sj   t d} tdtdt t| d   tdt t| d    }t|tddt| d tj  ksftd S )Nrr   rZ   rV   r   )	r   rP   r%   r1   r-   rD   r   r   rb   )rr   r³   rf   rf   rg   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 rî   )rD   r   r7   rN   r   rb   rf   rf   rf   rg   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 )Nrr   r   )r   rD   rN   r
   r   rb   rþ   rf   rf   rg   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dxrZ   r   rV   )r   rD   r%   r   rN   rb   )r  rf   rf   rg   Útest_issue_4503¢  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 )Nrf   )rZ   )r   r   r^   )r@   rN   rG   rD   rb   r
   )ÚGÚgrf   rf   rg   Útest_issue_6052š  s    r  c                  C   sj   t ttdt dt  } ttt| tt |  tddks>tttt| tt |  td ¡ dksftd S )NrZ   rm   r   rV   g       @)r%   rN   r3   rD   r   rb   ZevalfrÆ   rf   rf   rg   Útest_issue_7224¯  s    $r	  c                   C   s&   t ttddd  ttdks"td S )NrZ   g    eÍÍAr   )rD   rR   r	   r
   rb   rf   rf   rf   rg   Útest_issue_8208µ  s    r
  c                   C   s<   t ttdd d ttd tdd  tddks8td S )NrZ   r|   rV   r\   rÁ   r   )rD   rN   r	   r%   rb   rf   rf   rf   rg   Útest_issue_8229¹  s    r  c                  C   s4   t ddd\} }ttd||   |tdks0td S )Nzd tTrp   rZ   ra   )r   rD   r8   r
   rb   )rÒ   Útrf   rf   rg   Útest_issue_8433œ  s    r  c                  C   sH   t dddd} t ddd}t||  t|  t|  | tdksDtd S )NrQ   T)rT   ZnonnegativeÚlamdarp   r   )r   rD   r   r   r
   rb   )rQ   r  rf   rf   rg   Útest_issue_8481Â  s    r  c                   C   sJ   t tttd tttkstt tttd dt   ttdksFtd S )NrV   r\   r   )rD   r   rR   r
   rb   rf   rf   rf   rg   Útest_issue_8462È  s    r  c                  C   s@   t dddd} t d}t||  |t ttd|   ks<td S )NrR   TrS   rN   ra   )r   rD   r
   r   rb   rŠ   rf   rf   rg   Útest_issue_8634Í  s    r  c                  C   s  t ddd} t ddd}t| t | td   | tdks<tt| t | td   | ttks`tt| t | td   | ttkstt| t | t| d	   | ttks¬tt ddd} t| t | td	   | ttksÜtt| t | td
   | tt kstd S )NrN   Tr   rQ   rp   r   r]   g      @rZ   rV   )r   rD   rR   r
   rb   )rN   rQ   rf   rf   rg   Útest_issue_8635_18176Ó  s    $$$($r  c                   C   s   t tttttkstd S r~   )rD   r   rN   r
   rb   rf   rf   rf   rg   Útest_issue_8730ß  s    r  c                      s`   t dddt ddd ttt  d    tdksHttt fdd	 d S )
NrR   T)rT   rt   rp   rZ   r   c                      s$   t tt     tS r~   )rD   r   r
   rf   ©rt   rR   rf   rg   r   è  r   z!test_issue_9252.<locals>.<lambda>)r   rD   r   r
   rb   rM   rå   rf   rf   r  rg   Útest_issue_9252ã  s    0r  c                   C   s"   t ttd tdddkstd S )Nrõ   r   r[   )rD   r1   rN   rb   rf   rf   rf   rg   Útest_issue_9558ë  s    r  c                   C   s2   t dt ttdt td   tttks.td S )NrÁ   rV   )rD   rQ   r   r
   r   rb   rf   rf   rf   rg   Útest_issue_10801ï  s    r  c                  C   s8   t ddd\} }tt| | t|  | d|ks4td S )Nzs xTr   r   )r   rD   r8   rb   )rÑ   rN   rf   rf   rg   Útest_issue_10976ô  s    r  c                   C   s<   t ttttd t tdt t   ttdks8td S ©NrZ   rV   )rD   r   rR   r   r%   r   r
   rb   rf   rf   rf   rg   Útest_issue_9041ù  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, ar[   rV   )r   rC   Zfree_symbolsrb   )rN   rO   rr   rf   rf   rg   Útest_issue_9205ý  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   r\   rZ   )rD   r   rR   r
   rb   rf   rf   rf   rg   Útest_issue_9471  s    &r  c                   C   s$   t ttdt ttdks td S r  )rD   r9   r   rN   r
   rb   rf   rf   rf   rg   Útest_issue_11496
  s    r  c                   C   s<   t ttt t tt  t tdtttd   ks8td S )Nr   rZ   )rF   rD   rN   rO   rR   rb   rf   rf   rf   rg   Útest_issue_11879  s    r  c                  C   sF   t d} td|  | tdks ttdd|   | ttddksBtd S )NrQ   rÃ   rZ   g333333Ó?r\   é
   )r   rD   r
   rb   r	   )rQ   rf   rf   rg   Útest_limit_with_Float  s    r!  c                   C   sD   t dt dt d   td d  td  tttddks@td S ©Nr\   rZ   rV   )rD   rN   r
   r	   rb   rf   rf   rf   rg   Útest_issue_10610  s    r#  c                   C   s  t tttt tddtdks&tt tttt tddtddt t  ksXtttdd  t tttt tt	t	kstt ttt
t tddtdks¬tt ttt
t tddt	 ksÐtttdd  t ttt
t tt	t	ksþtd S )Nr   rW   rV   r[   c                   S   s   t tttt tddS r   )rD   r   rN   r   rf   rf   rf   rg   r     r   z"test_issue_10868.<locals>.<lambda>c                   S   s   t tttt tddS r   )rD   r   rN   r   rf   rf   rf   rg   r   #  r   )rD   r   rN   r   rb   r   r   rM   r   r
   r   rf   rf   rf   rg   Útest_issue_10868  s    &2 &$r$  c                   C   s$   t ttt t ttdks td S rì   )rD   rR   r-   r
   rb   rf   rf   rf   rg   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 )Nr\   rV   r   rº   rf   rf   rf   rg   Útest_issue_12555+  s    6r&  c                  C   sÔ  t ddd\} }}t dddd\}}}}}}}	|| ||  |  | t|d |d|   |d  |d  |d|  |d  |d  |d   |d|  |d|   |d  |d  |d d|  d   d|d|   ||d   | |  | |d d|  d   d||d   |d|   | |  | |d d|  d   d||d   ||d   |d  |d   |d |d d|  d    ||  | |  d  }
|
 ||¡jddt|
||jddksÐtd S )	Nzr z xTr   za b s0 K F0 s T)rU   r   rV   rZ   r·   )r   r%   rü   ÚfactorrD   rb   )rÕ   rP   rN   rr   rs   Ús0ÚKZF0rÑ   ÚTÚfxrf   rf   rg   Útest_issue_127690  s$    :"ÿ:ÿ:þ:ý*üüür,  c                   C   sz   t tdddt d   dt t  dt d dt dtj    dt d dt dtj    tttd	d
ksvtd S )Né   r]   éûÿÿÿrZ   i@¶  rV   ry   iúÿÿÿé   é$   )rD   r%   rN   r   r   r
   r	   rb   rf   rf   rf   rg   Útest_issue_13332<  s    Bÿ ÿÿr1  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   )rD   rN   r1   r-   r
   rb   Úexpandrf   rf   rf   rg   Útest_issue_12564A  s    .,$$&r3  c                   C   s    t tdd  t tdd  d S )Nc                   S   s   t tttt ¡ S r~   )rC   r   rN   r   r   rf   rf   rf   rg   r   K  r   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  tt ¡ S )NrV   rZ   )rC   rN   r   r   rf   rf   rf   rg   r   L  r   rä   rf   rf   rf   rg   Útest_issue_14456J  s    r4  c                   C   sB   t dtdt t td   tdt dt d  t ks>td S )Nr\   r|   é   rV   )rD   r0   r   rN   r
   rb   rf   rf   rf   rg   Útest_issue_14411O  s    r6  c                   C   s8   t ttd d d td d  d  ttdks4td S r  rk   rf   rf   rf   rg   Útest_issue_13382S  s    r7  c                   C   s<   t tdtttd  d ttt    ttdks8td S )Nra   rZ   ©rD   rN   r   r
   rb   rf   rf   rf   rg   Útest_issue_13403W  s    r9  c                   C   sb   t td  ttd  td td d  ttd d   td ttd   ttdks^td S r"  r8  rf   rf   rf   rg   Útest_issue_13416[  s    r:  c                   C   sx   t td dt dddt   t  d  t td  d td  t   tttd d td d  td  ksttd S )NrV   rZ   r|   r\   r5  rm   rz   )rD   rR   rN   r
   rb   rf   rf   rf   rg   Útest_issue_13462_  s    r;  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 )Nrr   ra   )r   rD   r8   rN   r
   rb   r%   rþ   rf   rf   rg   Útest_issue_13750c  s    r<  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
isinstancerD   r1   rN   r   r
   rC   rb   r-   r   rf   rf   rf   rg   Útest_issue_14276i  s    """r>  c                   C   s0   t dtttt  dt  ttdks,td S rì   )rD   r   rN   r
   rb   rf   rf   rf   rg   Útest_issue_14514p  s    r?  c                   C   s~  t ttd tt tttt  ttttj	tj
ks>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   )rD   r1   rN   r-   r2   r/   r
   rH   r   rd   re   rb   r.   rŸ   rf   rf   rf   rg   Útest_issues_14525t  s    >>..04r@  c                   C   s4   t tttttd   td  ttdks0td S )NrV   rZ   r   )rD   r%   rN   r-   r
   rb   rf   rf   rf   rg   Útest_issue_14574~  s    rA  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 )Nr\   r]   rV   ra   r|   r_   )	rD   r<   rN   r
   r   r   rb   r	   r;   rf   rf   rf   rg   Útest_issue_10102  s    "" rB  c                   C   s   t tdd  d S )Nc                   S   s    t ttt ttt  ttS r~   )rD   r   r   rN   r1   r   r
   rf   rf   rf   rg   r     r   z"test_issue_14377.<locals>.<lambda>rä   rf   rf   rf   rg   Útest_issue_14377  s    rC  c                  C   s   t d dt d  dt d d  t d  tt d d   dt d d  t d  tt d t  d   t  d  } t| t ttdd kstd S )NrV   r_   r\   rZ   )rN   r=   rD   r
   r   rb   rö   rf   rf   rg   Útest_issue_15146  s    8*ÿÿÿrD  c                  C   s°   dt  ddt   ddt   t  d    t d  t d  } t| t ttdk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 )NrV   r_   rZ   rœ   r   r]   r\   )rN   rD   r
   r   rb   r   r   rö   rf   rf   rg   Útest_issue_15202  s    :FrE  c                   C   s0   t td td d  td  ttdks,td S )NiÐ  rZ   iÏ  i0øÿÿrk   rf   rf   rf   rg   Útest_issue_15282  s    rF  c                   C   s2   t t tttd  t ttdddks.td S )NrZ   r[   rX   r   )rD   rN   r   r   r
   rb   rf   rf   rf   rg   Útest_issue_15984¡  s    rG  c                   C   s&   t ttdtt ttdks"td S rì   )rD   r?   rN   r>   r
   rb   rf   rf   rf   rg   Útest_issue_13571¥  s    rH  c                   C   s*   t ttttdtttjks&td S rì   )rD   r'   r:   rN   r   rŸ   rb   rf   rf   rf   rg   Útest_issue_13575©  s    rI  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   r^   rX   rZ   rV   )rC   r1   rN   r   rb   r
   r   rf   rf   rf   rg   Útest_issue_17325­  s    $ $rJ  c                   C   s   t t td¡dkstd S )Nr   )r   rN   rD   rb   rf   rf   rf   rg   Útest_issue_10978Ž  s    rK  c                   C   s    t ttd tttkstd S r   )rD   r!   rR   r
   rb   rf   rf   rf   rg   Útest_issue_14313_commentž  s    rL  c                  C   s2   ddt   t   t ¡} t| t ddddks.td S )NrZ   rW   rX   )rN   r   rD   rb   )rÒ   rf   rf   rg   Útest_issue_15323Œ  s    rM  c                   C   s,   t ttt  tt tddks(td S rì   )rD   r   r   rN   rb   rf   rf   rf   rg   Útest_issue_12571Â  s    rN  c                   C   sH   t td td t t  td td  td   tttdksDtd S r"  ©rD   rN   r
   r   rb   rf   rf   rf   rg   Útest_issue_14590Æ  s    rP  c                  C   sR   t d\} }tt| t|  t|  t|    tt|t|  |   |  ksNtd S )Núa b)r   rD   rN   rO   rb   ©rr   rs   rf   rf   rg   Útest_issue_14393Ê  s    rS  c                   C   s@   t ttd dtd   ttdt   tttdks<td S )NrZ   ra   )rD   r   rR   r
   r   rb   rf   rf   rf   rg   Útest_issue_14556Ï  s    rT  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 )NrZ   rV   r\   r|   ©rD   r   rN   r
   rb   rf   rf   rf   rg   Útest_issue_14811Ó  s    rV  c                   C   s    t tttdtdkstd S )Ni Ê;)rD   r   rN   rb   rf   rf   rf   rg   Útest_issue_16222×  s    rW  c                   C   sD   t ttd  td t  ttd   t ttttdks@td S rì   rO  rf   rf   rf   rg   Útest_issue_16714Û  s    rX  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 )NrP   Trp   rZ   )rU   rT   )r   rD   r   rR   r
   r>   rb   r    rf   rf   rg   Útest_issue_16722ß  s    4rY  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 )NrZ   rV   r   r\   )rD   rR   r   r
   rb   rf   rf   rf   rg   Útest_issue_17431æ  s&    $ÿÿÿ ÿÿ0 ÿÿrZ  c                   C   s2   t ttt tttt  tdtks.td S rì   )rD   r7   r   rN   r   rb   rf   rf   rf   rg   Útest_issue_17671î  s    r[  c                  C   sf   t ddd\} }}}t| d | t| d d |d  ||  |  |t| d|  d  ksbtd S )Nza b c xTrp   rZ   rV   )r   rD   r%   r
   rb   )rr   rs   rt   rN   rf   rf   rg   Útest_issue_17751ò  s    r\  c                   C   s@   t tttt tdt t  tttdtt ks<td S r  )rD   r   rR   r%   r   r
   r   rb   rf   rf   rf   rg   Útest_issue_17792÷  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d S )Nr   r[   ra   rW   rZ   )rD   r   r1   rN   rb   rf   rf   rf   rg   Útest_issue_18118û  s    r^  c                   C   s.   t tttttt tdddks*td S )Nr   rW   rZ   )rD   r1   r%   rN   rb   rf   rf   rf   rg   Útest_issue_18306   s    r_  c                   C   s<   t ttdt t ttttd   ttdks8td S )Nr\   rÝ   )rD   r   r   rN   r
   rb   rf   rf   rf   rg   Útest_issue_18378  s    r`  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 )NrZ   rV   r\   )rD   r   rN   r
   r   rb   rf   rf   rf   rg   Útest_issue_18399  s    ,ra  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 )NrV   r[   rX   )rD   r2   rN   r%   r   r
   rC   rb   rf   rf   rf   rg   Útest_issue_18442  s    rb  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   rZ   r[   )rD   r   r   rN   rb   rf   rf   rf   rg   Útest_issue_18452  s     rc  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 )NrZ   r[   rX   rV   r   r   )	rD   r1   rN   r
   rC   rb   r-   r2   rH   rf   rf   rf   rg   Útest_issue_18473  s    888$$B,,,..rd  c                   C   s@   t dtdt  tdt d  dt  tttdks<td S ©NrV   r\   rZ   )rD   r   rN   r
   rb   rf   rf   rf   rg   Útest_issue_18482&  s    rf  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 )NrZ   r   rV   rW   rX   r[   )rD   r1   rN   r%   r-   rb   rf   rf   rf   rg   Útest_issue_18508*  s    ,0rg  c                   C   s   t tdd  d S )Nc                   S   s   t tdt t ttS r   )rD   r   rR   rN   r
   rf   rf   rf   rg   r   1  r   z"test_issue_18521.<locals>.<lambda>rä   rf   rf   rf   rg   Útest_issue_185210  s    rh  c                  C   sT   t ddd\} }tt| | |t|ks,tttt| | |tt|ksPtd S )NrQ  Trp   )r   rD   r   rb   r   rR  rf   rf   rg   Útest_issue_189694  s    ri  c                   C   s,   t tttdt   tttdks(td S rì   )rD   rR   r   r
   r   rb   rf   rf   rf   rg   Útest_issue_18992:  s    rj  c                  C   s<   t d} tt| t| d t| d   | ddks8td S )NrN   rZ   rV   r   ra   )r   rD   r>   rb   r   rf   rf   rg   Útest_issue_19067>  s    rk  c                   C   s*   t tdt dt    ttdks&td S re  rk   rf   rf   rf   rg   Útest_issue_19586C  s    rl  c                  C   s0   t d} t ddd}t| | | ddks,td S )NrR   rø   T)Úzeror   )r   rD   rb   )rR   rø   rf   rf   rg   Útest_issue_13715G  s    rn  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"  )rD   rR   r1   r
   rb   rf   rf   rf   rg   Útest_issue_15055M  s    ro  c                  C   s   t ddd\} }t d\}}}t|| | t| td| | | | |d     | |  ||  |d|||  | ks~td S )Nzm viTrp   zB ti dr_   rV   r   )r   rD   r%   rb   )rù   ÚviÚBÚtirÒ   rf   rf   rg   Útest_issue_16708Q  s    rs  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 )NrZ   r\   rV   r_   )rD   r3   rN   r
   r%   r   rb   rf   rf   rf   rg   Útest_issue_19154W  s    @rt  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betaTrp   Úhrù   Úomegar  rZ   r\   rV   rq   r|   r   )r   r   r   r   rD   r
   rb   rF   )ru  rv  rù   Úwr  r³   Úqrø   rÑ   ÚZr   rf   rf   rg   Útest_issue_19453\  s    (Lÿ"r{  c                   C   s&   t td d t ttdks"td S )NrZ   r|   r   rU  rf   rf   rf   rg   Útest_issue_19739o  s    r|  c                   C   s2   t dt  tdtd  d  ttdks.td S )NrV   r|   rZ   )rD   rN   r%   r
   rb   rf   rf   rf   rg   Útest_issue_19766s  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 )
Nrù   r[   rX   Tr   )Znonzerora   rZ   r   )r   rD   r-   rN   r
   rC   rb   rH   )rù   rf   rf   rg   Útest_issue_19770w  s    88"r~  c                   C   s  t ttttt ttd tttttt ttd ddk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 )NrV   rW   rX   r[   r^   ra   rZ   )	rD   r2   rN   r1   r   rC   rb   rH   r
   rf   rf   rf   rg   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 )NrZ   r   rV   )rD   rN   r   rb   rf   rf   rf   rg   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 )NrZ   rV   r   )rD   rN   r+   r   rb   rf   rf   rf   rg   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 )Nr\   rz   r|   )rD   r1   r   rN   rb   rf   rf   rf   rg   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 )NrZ   r   rW   r[   r^   )r   rN   r1   rD   rb   rÆ   rf   rf   rg   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logxrZ   )r   rN   ZnseriesrO   rb   rò   rf   rf   rg   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 rµ   )rN   r-   rD   rb   r2  )r   rf   rf   rg   Útest_issue_21415º  s    r  c                   C   s(   t ttd tt tttks$td S rì   )rD   r   rR   r
   r   rb   rf   rf   rf   rg   Útest_issue_21530À  s    r  c                  C   sD   t dd d } tt|  td t d  t| t dd ks@td S )Nr]   rZ   rV   )r%   rD   rN   rb   rÖ   rf   rf   rg   Útest_issue_21550Ä  s    r  c                  C   sL   t ttd  ttd  d t td} | tdd dtd  ksHtd S )NrZ   é   l   Ñqjl   SÍ[	)rD   rN   r   r   rb   )Úoutrf   rf   rg   Útest_issue_21661É  s    (r  c                   C   s6   t ttttt   td¡tdtdd ks2td S )Nrœ   r   rZ   i Ø	 )rD   r5   rP   rN   rü   r   rb   rf   rf   rf   rg   Útest_issue_21701Î  s    r  c                  C   sD   t ddd} tdtdt|  d    t}| tt¡tjks@td S )Nrr   Tr   rZ   rV   )	r   rB   r   rN   rD   r
   r   r   rb   )rr   r   rf   rf   rg   Útest_issue_21721Ò  s    r  c                  C   sd   dt dt t t  dt dt t t d   } |  td¡dksHtt|  td¡dks`td S )NrZ   r_   r]   r   )r   r   r   rP   rD   rb   r   )Útermrf   rf   rg   Útest_issue_21756Ø  s    4r  c                  C   s@   t d} t| d  td  dtd    | dd¡tks<td S )Nrr   rV   rZ   r[   )r   r%   rN   rD   r   rb   rþ   rf   rf   rg   Útest_issue_21785Þ  s    r  c                   C   s&   t dt dt   ttdks"td S )Nra   rV   r   rk   rf   rf   rf   rg   Útest_issue_22181ã  s    r  c                  C   sÞ  t dtt dttd  d  d } t dt tt dttd  dt d t d   tt dttd  dt d t d  
   d }t| tt t d t d k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 )Nr-  rV   ry   rõ   r]   é<   r[   r   T)ÚforcerW   )r%   r,   r2   rN   r   r   rD   r   rb   rE   r
   )Úe1Úe2rw   Úexpr2rf   rf   rg   Útest_issue_22220ç  s     (6,ÿÿ$$&2. r  c                  C   sâ   t ddd\} }t|d |  |d | d  || d    |td| d  ksPtt|d |  |d | d  || d    ¡  |td| d  kstt|d |  |||   |d |    |d |    |td| d  ksÞtd S )Nzk, nTrp   rZ   )r   rD   r
   rb   r2  )rQ   rR   rf   rf   rg   Útest_issue_22334ý  s    @Dr  c                   C   s0   t tddt  tt tttdks,td S r  )rD   r   rN   r%   r
   rb   rf   rf   rf   rg   Útest_sympyissue_22986  s    r  c                  C   s>   dt  dt    dt  dt     } t| t t dks:td S )NrV   ra   )rN   rD   r
   rb   rò   rf   rf   rg   Útest_issue_23231  s    $r  c                   C   s4   t dt td  tdt  tdtftks0td S )NrZ   rV   ra   r   )rB   rN   r   r
   rb   rf   rf   rf   rg   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 )NrV   r\   r   rW   r[   )r%   r   rN   rD   rb   )Úexpr1r  rf   rf   rg   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   r2   r   r   rN   r   rD   r
   rb   rF   r®   r1   )r+  rf   rf   rg   Útest_issue_24276  s
    r  N(  Ú	itertoolsr   Zsympy.concrete.summationsr   Zsympy.core.functionr   r   Z
sympy.corer   Zsympy.core.numbersr   r   r	   r
   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z(sympy.functions.combinatorial.factorialsr   r   r   Z$sympy.functions.elementary.complexesr   r   r   Z&sympy.functions.elementary.exponentialr   r   r   Z%sympy.functions.elementary.hyperbolicr   r   r   r   r   r   r   Z#sympy.functions.elementary.integersr    r!   r"   Z(sympy.functions.elementary.miscellaneousr#   r$   r%   Z$sympy.functions.elementary.piecewiser&   Z(sympy.functions.elementary.trigonometricr'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   Zsympy.functions.special.besselr3   r4   r5   r6   Z'sympy.functions.special.error_functionsr7   r8   r9   r:   r;   r<   Z'sympy.functions.special.gamma_functionsr=   r>   r?   Zsympy.functions.special.hyperr@   Zsympy.integrals.integralsrA   rB   Zsympy.series.limitsrC   rD   Zsympy.simplify.simplifyrE   rF   Zsympy.simplify.hyperexpandrG   Z!sympy.calculus.accumulationboundsrH   Zsympy.core.mulrI   rJ   Zsympy.series.orderrK   Zsympy.testing.pytestrL   rM   Z	sympy.abcrN   rO   rP   rQ   rR   rh   rj   rl   ro   rx   r{   r}   r   r   r   r   r   r   r   r   r   r   r¡   r¢   r€   r§   rš   r¬   rŽ   r¶   r¹   r»   rŒ   r¿   rÀ   rÂ   rÅ   rÇ   rÔ   r×   rØ   rÙ   rÚ   rÜ   rß   rà   rá   râ   ræ   rê   rë   rí   rï   rñ   ró   r÷   rý   rÿ   r   r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r!  r#  r$  r%  r&  r,  r1  r3  r4  r6  r7  r9  r:  r;  r<  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rP  rS  rT  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  rf  rg  rh  ri  rj  rk  rl  rn  ro  rs  rt  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  rf   rf   rf   rg   Ú<module>   s   $8 G
	



0	
	

	