o
    *Î®c‘š  ã                   @   sz  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$Z$ d dl%m&Z&m'Z'm(Z( d dl)m*Z*m+Z+m,Z, d dl-m.Z. d dl/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z; d dl<m=Z=m>Z> d dl?m@Z@mAZAmBZBmCZCmDZDmEZE d dlFmGZGmHZHmIZI d dlJmKZKmLZL d dlMmNZNmOZO d dlPmQZQmRZR d dlSmTZT d dlUmVZV d dlMmWZW d dlXmYZY d dlZm[Z[m\Z\ d dl]m^Z^m_Z_m`Z`maZa eddddZbdd „ Zcd!d"„ Zdd#d$„ Zed%d&„ Zfd'd(„ Zgd)d*„ Zhd+d,„ Zid-d.„ Zjd/d0„ Zkd1d2„ Zld3d4„ Zmd5d6„ Znd7d8„ Zod9d:„ Zpd;d<„ Zqd=d>„ Zrd?d@„ ZsdAdB„ ZtdCdD„ ZudEdF„ ZvdGdH„ ZwdIdJ„ ZxdKdL„ Zye[dMdN„ ƒZzdOdP„ Z{dQdR„ Z|dSdT„ Z}dUdV„ Z~dWdX„ ZdYdZ„ Z€d[d\„ Zd]d^„ Z‚d_d`„ Zƒdadb„ Z„dcdd„ Z…dedf„ Z†dgdh„ Z‡didj„ Zˆdkdl„ Z‰dmdn„ ZŠe[dodp„ ƒZ‹dqdr„ ZŒdsdt„ Zdudv„ ZŽdwdx„ Zdydz„ Zd{d|„ Z‘d}d~„ Z’dd€„ Z“e[dd‚„ ƒZ”dƒd„„ Z•d…d†„ Z–d‡dˆ„ Z—d‰dŠ„ Z˜d‹dŒ„ Z™ddŽ„ Zšdd„ Z›d‘d’„ Zœd“d”„ Zd•d–„ Zžd—d˜„ ZŸd™dš„ Z d›dœ„ Z¡ddž„ Z¢dŸd „ Z£d¡d¢„ Z¤d£d¤„ Z¥d¥d¦„ Z¦d§d¨„ Z§d©dª„ Z¨d«d¬„ Z©d­d®„ Zªd¯d°„ Z«d±d²„ Z¬d³d´„ Z­dµd¶„ Z®d·d¸„ Z¯d¹dº„ Z°d»d¼„ Z±d½d¾„ Z²d¿dÀ„ Z³dÁdÂ„ Z´dÃdÄ„ ZµdÅdÆ„ Z¶dÇdÈ„ Z·dÉdÊ„ Z¸dËdÌ„ Z¹dÍdÎ„ ZºdÏdÐ„ Z»dÑdÒ„ Z¼dÓdÔ„ Z½dÕdÖ„ Z¾d×dØ„ Z¿dÙdÚ„ ZÀdÛdÜ„ ZÁdÝdÞ„ ZÂdßdà„ ZÃdádâ„ ZÄdãdä„ ZÅe[dådæ„ ƒZÆdçdè„ ZÇdédê„ ZÈdëdì„ ZÉdídî„ ZÊdïdð„ ZËdñdò„ ZÌdódô„ ZÍdõdö„ ZÎd÷dø„ ZÏdùdú„ ZÐdûdü„ ZÑdýdþ„ ZÒdÿd „ ZÓdd„ ZÔdd„ ZÕdd„ ZÖdd„ Z×d	d
„ ZØdd„ ZÙdd„ ZÚdd„ ZÛdd„ ZÜdd„ ZÝdd„ ZÞdd„ Zßdd„ Zàdd„ Zádd„ Zâdd „ Zãd!d"„ Zäd#d$„ Zåd%d&„ Zæd'd(„ Zçd)d*„ Zèd+d,„ Zéd-d.„ Zêd/d0„ Zëd1d2„ Zìd3d4„ Zíd5d6„ Zîd7d8„ Zïd9d:„ Zðd;d<„ Zñd=d>„ Zòd?d@„ ZódAdB„ ZôdCdD„ ZõdEdF„ ZödGdH„ Z÷dIdJ„ ZødKdL„ ZùdMdN„ ZúdOS (P  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acothÚatanhÚ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besseljÚbesselk)ÚEiÚerfÚerfcÚerfiÚfresnelcÚfresnels)ÚdigammaÚgammaÚ
uppergamma)ÚIntegralÚ	integrate)ÚLimitÚlimit)Ú
logcombineÚsimplify)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ƒtu s
J ‚t ttt ƒt u sJ ‚t t ttƒt u s"J ‚t td tt ƒtu s/J ‚t td  ttƒt u s=J ‚t tttƒ tddddksMJ ‚t dt ttƒdksYJ ‚t ttƒttƒtu seJ ‚t ttƒ ttƒt u ssJ ‚t ttƒt ttƒtu sJ ‚t dt tt ƒ ttƒdks’J ‚t tdt  ttƒtu s J ‚t ttd  ttƒt u s¯J ‚t dt dtdƒ  tdƒdksÁJ ‚t dt t tdƒttd t tdƒ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ƒ tdƒt ttƒ ks&J ‚t t	tt ƒt tdƒtt	tƒƒt ks=J ‚t t
dt d ƒttƒdksNJ ‚t tjtt ƒtju s\J ‚t tdƒt ttjƒ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 sJ ‚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ƒ ttddt u sÉJ ‚t dttƒ ttddtu sÚJ ‚t dt	tƒ ttd ddt u sîJ ‚t dt	tƒ ttd ddtu sJ ‚t dttd ƒ tdt tddƒ ddtu sJ ‚t dttd ƒ tdt tddƒ ddt u s6J ‚t dttƒd  tttddƒ ddt u sOJ ‚t dttƒd  tttddƒ ddtu sgJ ‚t ttƒttƒttjtjƒksyJ ‚t ttƒttƒttjtjƒks‹J ‚t ttƒttƒttjtjƒksJ ‚t ttƒttƒttjtjƒks¯J ‚t ttƒ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ƒ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ƒ tdddt t ksCJ ‚t td tddddksRJ ‚t ttƒtddddksaJ ‚t tt  tdddtdt  ksuJ ‚t dt	tƒ t tdƒtt	tƒd t tdƒksJ ‚t dttƒ tdddtks¡J ‚t dttƒ tdddt ks³J ‚t dttƒ tdddtksÄJ ‚t dttƒ tdddt ksÖJ ‚t tdt ƒdttƒ  tdddtksíJ ‚t tdt ƒdt  tdddtksJ ‚d S )Né   r   ú+©Údiré   ú-é   é   ú+-éþÿÿÿéýÿÿÿéÿÿÿÿ)r=   rF   r
   r   r   r!   r<   rG   r   r)   r8   r   ÚNaNrC   r-   r   r.   r	   r*   r@   ÚNegativeInfinityÚInfinityr,   r+   r   r   r'   r   © r]   r]   úE/tmp/pip-target-vg8gfxp4/lib/python/sympy/series/tests/test_limits.pyÚtest_basic1#   sr    "$,4>,."""$(&$"(&4620$$$$""$ ((6"$"$..r_   c                   C   s  t tt tddddksJ ‚t ttƒd t tdƒdksJ ‚t ddt  ttƒdks,J ‚t tdt ƒ ttƒdks;J ‚t ttt ƒ ttƒtu sJJ ‚t tttd  ƒ ttƒtu s[J ‚t ttttƒ ƒ ttƒtu slJ ‚t ddt  tt ƒ ttƒdksJ ‚d S )Nr   rO   rP   rR   rY   rN   é   ©r=   rF   r   r
   r]   r]   r]   r^   Útest_basic2j   s    ""*rb   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 )NrR   r   rO   rP   rS   ©r=   rF   r
   r]   r]   r]   r^   Útest_basic3u   s   "rd   c                   C   sÐ   t dt tt  tdƒdksJ ‚t dt tt  tdƒdt ks"J ‚t dtd  ttd   tdƒdtd  ks:J ‚t ttd ƒttƒ ttƒdksLJ ‚tdtd d  tdtfƒdt tdƒ d	 ksfJ ‚d S )
NrN   r   rR   é   rX   rW   i   rT   é	   )r=   rF   rG   r!   r
   r;   r   r]   r]   r]   r^   Útest_basic4z   s
    $0$8rg   c                  C   s.  t ddd\} }}t| | ƒt| ƒt|ƒ  }| | t¡dks!J ‚||  | t¡dks-J ‚t ddd\}}|d |d |d  t|d ƒ |d d d  d|d d |d    d| t|| ƒ |d d d	 t|d |d  ƒ  |d d d    }t||tƒt|d
  |d d d  ks•J ‚d S )Nza b cT©rM   r   ztau xrN   rR   rW   ç      à?rT   )r   r   r=   r
   r(   r   )ÚaÚbÚcÚAÚtaurF   Úexprr]   r]   r^   Útest_log‚   s"   8ÿÿ(ÿÿÿ0rp   c                   C   s6   t ttd dƒd td  tddƒtddƒksJ ‚d S )Né   rT   rN   rW   rO   rR   é   )r=   r    rF   r	   r]   r]   r]   r^   Útest_piecewise‘   s   6rs   c               
   C   s  dt tƒ tdt d tt dddt d d   ƒƒ dt d dkfddt  tt dddt d d   ƒƒ dfƒ } ttd d tdkftd d dfƒ}ttd d	 td
k ftd d	 tdkft ttd ƒƒdfƒ}t| tdƒdksxJ ‚t|tdƒdks‚J ‚t|td
ƒdksŒJ ‚d S )NrN   é   rR   r   Tri   g      À?rf   rU   rY   rT   )r!   rF   r"   r   r=   )Úfunc1Úfunc2Úfunc3r]   r]   r^   Útest_piecewise2–   s   @ÿ.ÿ&<rx   c                  C   s8   G dd„ dt ƒ} t| tƒttƒt| tƒttƒksJ ‚d S )Nc                   @   s   e Zd Zedd„ ƒZdS )ztest_basic5.<locals>.myc                 S   s   |t ju rt jS d S ©N)r   r\   rZ   )ÚclsÚargr]   r]   r^   Úeval¢   s   
ÿztest_basic5.<locals>.my.evalN)Ú__name__Ú
__module__Ú__qualname__Úclassmethodr|   r]   r]   r]   r^   Úmy¡   s    r   )r   r=   rF   r
   r<   )r   r]   r]   r^   Útest_basic5    s   (r‚   c                   C   s0   t tt tt  tdƒtt dt  ksJ ‚d S ©NrN   )r=   rF   rG   rH   r]   r]   r]   r^   Útest_issue_3885©   ó   0r„   c                   C   sf   t ttƒt tdƒdksJ ‚t ttƒt tdƒ ¡ dksJ ‚t ttdddjttdtdƒfks1J ‚d S )Nr   rR   rV   rP   )r<   r-   rF   ÚdoitÚargsr   r]   r]   r]   r^   Ú
test_Limit­   s    *rˆ   c                   C   sž  t ttƒtddƒdksJ ‚t ttƒtddƒdksJ ‚t ttƒtddƒdks'J ‚t ttƒtddƒdks4J ‚t ttƒtddƒdksAJ ‚t ttƒtddƒdksNJ ‚t ttƒtddƒdks[J ‚t ttƒtddƒdkshJ ‚t ttƒtddƒdksuJ ‚t ttƒtddƒdks‚J ‚t ttƒtd	dƒd	ksJ ‚t ttƒtd	dƒd
ksœJ ‚t ttdt ƒ d tddƒtddƒks²J ‚t ttd ƒttƒ ttƒttj tdƒd ƒksÍJ ‚d S )NrW   rO   rS   rX   rY   r   rR   rN   éø   é÷   rT   ri   )r=   r   rF   r	   r
   r@   r   ÚHalfr]   r]   r]   r^   Ú
test_floor³   ó   ,:rŒ   c                   C   s  t tttƒƒtddƒdksJ ‚t tttƒƒtddƒdksJ ‚t tttƒƒtddƒdks-J ‚t tttƒƒtddƒdks<J ‚t tdttƒ ƒtddƒdksMJ ‚t tdttƒ ƒtddƒdks^J ‚t tdttƒ ƒtddƒdksoJ ‚t tdttƒ ƒtddƒdks€J ‚d S )Nr   rO   rS   rY   rU   rt   )r=   r   r-   rF   r)   r]   r]   r]   r^   Ú&test_floor_requires_robust_assumptionsÆ   ó   """&rŽ   c                   C   sž  t ttƒtddƒdksJ ‚t ttƒtddƒdksJ ‚t ttƒtddƒdks'J ‚t ttƒtddƒdks4J ‚t ttƒtddƒdksAJ ‚t ttƒtddƒdksNJ ‚t ttƒtddƒdks[J ‚t ttƒtddƒdkshJ ‚t ttƒtddƒdksuJ ‚t ttƒtddƒdks‚J ‚t ttƒtd	dƒd
ksJ ‚t ttƒtd	dƒd	ksœJ ‚t ttdt ƒ d tddƒtddƒks²J ‚t ttd ƒttƒ ttƒttj tdƒd ƒksÍJ ‚d S )NrW   rO   rY   rS   r   rR   rN   rT   r‰   éù   ri   )r=   r   rF   r	   r
   r@   r   r‹   r]   r]   r]   r^   Útest_ceilingÑ   r   r‘   c                   C   s  t tttƒƒtddƒdksJ ‚t tttƒƒtddƒdksJ ‚t tttƒƒtddƒdks-J ‚t tttƒƒtddƒdks<J ‚t tdttƒ ƒtddƒdksMJ ‚t tdttƒ ƒtddƒdks^J ‚t tdttƒ ƒtddƒdksoJ ‚t tdttƒ ƒtddƒdks€J ‚d S )Nr   rO   rR   rS   rU   rq   )r=   r   r-   rF   r)   r]   r]   r]   r^   Ú(test_ceiling_requires_robust_assumptionsä   r   r’   c                   C   s   t tttƒt ƒtddƒdksJ ‚t tttƒt ƒtddƒdks"J ‚t tttƒ t ƒtddƒdks4J ‚t tttƒ t ƒtddƒdksFJ ‚d S )Nr   rO   rS   rW   )r=   r   r-   rF   r.   r]   r]   r]   r^   Útest_issue_14355ï   s   ""$(r“   c                  C   sd   t ddd} tt| ƒtd|  ƒ | dƒdksJ ‚tt| ƒt| d ƒ t| ƒ | tƒtd ks0J ‚d S )NrF   T©ÚrealrR   r   rN   )r   r=   r(   r-   r!   r
   r   ©rF   r]   r]   r^   Ú	test_atan÷   s   $4r—   c                  C   s  t ttƒtdƒdksJ ‚t tttƒƒtdƒdksJ ‚t tttƒƒtdƒdks(J ‚t tttd ƒƒtdƒtdƒks:J ‚t ttt ƒttt ƒ dt  tdƒttƒksTJ ‚t tttƒtd  ƒtt	ƒdksfJ ‚t ttttƒtd  ƒtttd ƒtd d  ƒ d  tt	ƒdksŠJ ‚t tttd ƒd d ƒtddƒt	ksŸJ ‚t tttƒƒtdƒt	ks­J ‚t ttttƒƒƒtdƒt	ks½J ‚t
ddd} t tt| ƒd ƒt| ƒ | t	ƒdks×J ‚t | td|  t ƒttd|   ƒ  d | dƒdksóJ ‚t t| ƒt| ƒ | td	ƒd
ksJ ‚d S )Nr   rR   rN   rT   rO   rH   Trh   rS   rY   )r=   ÚabsrF   r-   r)   r   rG   r   r   r
   r   r   ©rH   r]   r]   r^   Útest_set_signsý   s   $4$H* (8(rš   c                  C   st   t ddd} ttd|  ƒt| ƒ | ddƒtddƒksJ ‚ttdtt| ƒƒttd|  ƒƒ  ƒ| dƒtdƒks8J ‚d S )	NrF   Tr”   rR   r   rO   rY   rN   )r   rB   r-   r(   r@   r=   r   r!   r–   r]   r]   r^   Útest_heuristic  s   ,<r›   c                  C   sN   t ddd} d|  t|  t ƒ }t|ttƒdksJ ‚| tt¡dks%J ‚d S )NrH   Trh   rY   r   )r   r   rF   r=   r
   )rH   Úfr]   r]   r^   Útest_issue_3871"  s   r   c                  C   s  t dƒ} t ddd}td||   |  | tƒt|ƒksJ ‚td|d|    |  | tƒt|d ƒks2J ‚td|d|  d   |  | tƒt|d ƒksJJ ‚t|d |d  | |tƒtdƒks^J ‚tddd|  |  |tƒdtj kssJ ‚tdd|  | d| |  |tƒttd	ƒƒksJ ‚d S )
NrJ   rF   Tr”   rR   rN   rW   rq   z1/3)r   r=   r
   r   r   ÚExp1)rJ   rF   r]   r]   r^   Útest_exponential)  s   $,0(*8rŸ   c                  C   s8   t dƒ} tdt| t| ƒ   |  | tƒttƒksJ ‚d S )NrJ   rR   )r   r=   rF   r-   r
   r   )rJ   r]   r]   r^   Útest_exponential24  s   0r    c                  C   s.   t dt tƒ} t| ttƒ}| ¡ tu sJ ‚d S rƒ   ©r:   rF   r<   r
   r†   ©rœ   Úlr]   r]   r^   Ú	test_doit9  s   r¤   c                  C   sî  t ttƒttd ƒ ttƒtddƒksJ ‚t ttƒttd ƒ d ttƒtddƒks,J ‚t ttƒttƒttƒ  ttƒtddƒksCJ ‚dtdƒ d } dtdƒ d }tt| |ƒddtdƒ  dd}t tttt	ƒ 
t¡t	d	tfƒ ¡  
t¡ƒttƒ|ksJ ‚ttdtdƒd  tdƒd d ƒddtdƒ  ƒ}t tttt	ƒ 
t¡t	d	tfƒ ¡  
t¡ƒttƒ|ksµJ ‚t ttƒt ttƒtd	tƒksÆJ ‚t ttƒd d t ttƒtd	tƒksÛJ ‚dt  ttƒd t  }t |ttƒtd	tƒksõJ ‚d S )
NrR   rW   rN   rY   rT   rX   F)Úevaluater   )r=   r-   rI   r
   r@   r)   rA   r?   r   rJ   Úrewriter   r†   r   rF   )ÚloÚhiÚt1Út2Úer]   r]   r^   Útest_series_AccumBounds?  s   *.. 848"*r¬   c                  C   s2   t dt tƒ} t| ttƒ}|jdd|ksJ ‚d S )NrN   F©Údeepr¡   r¢   r]   r]   r^   Ú
test_doit2W  s   r¯   c                   C   s.   t tttƒ ttƒd  tt ƒdksJ ‚d S ©NrR   r   ra   r]   r]   r]   r^   Útest_issue_2929_  ó   .r±   c                   C   s”   t dttƒ td  ttjƒddttjƒ  ksJ ‚t tttd ƒd ƒtdƒtdtdƒ ƒks2J ‚t tttd ƒd ƒtdƒdtdƒ ksHJ ‚d S )NrR   rN   rt   r   )r=   r)   rF   r   r‹   r-   r˜   r]   r]   r]   r^   Útest_issue_3792c  s   400r³   c                   C   s¨   t dtd  tdƒtddƒksJ ‚t dtt  tdƒtjdt  ks$J ‚t ttƒtd d  tdƒtdƒd ks:J ‚t ttƒtd t  tdƒtdƒdt  ksRJ ‚d S )NrR   rT   rN   rU   é   rt   )r=   rF   r	   r   r   ÚOner   r]   r]   r]   r^   Útest_issue_4090i  s   "&,4r¶   c                   C   s@   t ttƒtdddtu sJ ‚t ttƒttd dddksJ ‚d S )Nr   rO   rP   rN   )r=   r*   rF   r
   r   r]   r]   r]   r^   Útest_issue_4547p  s   $r·   c                   C   s    t td ttƒtd   krtu sJ ‚ J ‚t td tdƒtdƒd ks&J ‚t td tdƒdks2J ‚t td ttƒdks>J ‚t td tdƒtdƒd ksNJ ‚d S )Nri   é   r   g      à¿rt   )r=   rF   r
   r   r]   r]   r]   r^   Útest_issue_5164u  s
   , $r¹   c                  C   s,   ddt   dt   } t| t dƒtksJ ‚d S )Nç      ð?r   )rF   r=   r   )Úfuncr]   r]   r^   Útest_issue_5383}  s   r¼   c                  C   sp   t tdƒd  tt ƒ t  tdt ƒd  ttt ƒƒ tdƒdt    t d  } t| t tƒtdƒd ks6J ‚d S )NrR   rN   rr   rT   ih  )rF   r   r   r   r   r=   r
   ©ro   r]   r]   r^   Útest_issue_14793‚  s   *
ÿÿÿ r¾   c            
   
   C   sb  t ttt gddgddtjtddƒgddgƒƒ} g t‘t‘t ‘t‘t t ‘t‘t dtddƒ  ‘t‘d‘d‘d‘d‘d‘d‘d‘d‘t‘t‘t‘t ‘t‘t t ‘t‘t dtddƒ  ‘d‘d‘d‘d‘d‘d‘d‘d‘R }t| ƒt|ƒks}J ‚t	t
| |ƒƒD ]*\}\}}|\}}}}|||  }	zt|	td|d|ks£J ‚W q„ ty®   	 J ‚w d S )	NrY   rR   rN   rT   rS   rO   r   rP   )Úlistr   rF   r   r‹   r	   r
   r   ÚlenÚ	enumerateÚzipr=   ÚAssertionErrorÚprint)
ÚtestsÚresultsÚir‡   ÚresrG   Úsr«   ÚdÚeqr]   r]   r^   Útest_issue_5183ˆ  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ûrÌ   c                  C   sº   t ttƒt ttƒdksJ ‚t ttƒttƒtd ksJ ‚t ttƒttƒtu s(J ‚t ttƒt ttƒdks6J ‚t ttƒttj	ƒt
tƒksEJ ‚tddd} t | td|  ƒ | dƒdks[J ‚d S )Nr   rN   ÚrTr”   rR   )r=   r-   rF   r
   r(   r   r8   r)   r   r‹   r!   r   ©rÍ   r]   r]   r^   Útest_issue_5184   s   $rÏ   c                   C   s*   t dt dt  tj tdƒdksJ ‚d S r°   )r=   rG   r   rž   r]   r]   r]   r^   Útest_issue_5229«  ó   *rÐ   c            	      C   sâ   t tttgt d dtd tttddƒ gddgƒƒ} ddt tddt tddtt ddtt ddtt f}t| ƒt|ƒks@J ‚tt	| |ƒƒD ]'\}\}}|\}}}|t
ƒ}zt|t
||d|kscJ ‚W qG tyn   	 J ‚w d S )NrN   r   rT   rS   rO   rP   )r¿   r   r*   r.   r   r	   r
   rÀ   rÁ   rÂ   rF   r=   rÃ   rÄ   )	rÅ   rÆ   rÇ   r‡   rÈ   rœ   r£   rÊ   rË   r]   r]   r^   Útest_issue_4546¯  s$   
 þÿ
ûûrÒ   c                   C   sX   t dttdƒ  dt  tdƒdksJ ‚t ddt  ddt   t tdƒdks*J ‚d S )NrR   rT   r   rU   )r=   rF   r   r]   r]   r]   r^   Útest_issue_3934Ä  s   (0rÓ   c                   C   sX   t ttddƒ dttddƒ   ttƒdksJ ‚t td dtd   ttƒdks*J ‚d S )NéM   rT   rR   gfffffFY@)r=   rF   r	   r
   r]   r]   r]   r^   Útest_calculate_seriesÉ  s   0(rÕ   c                   C   sž   t td dtd   ttƒdksJ ‚t td dtd   ttƒdks$J ‚t td dtd   ttƒdks6J ‚t td td d tt ƒ  ttƒdksMJ ‚d S )Nr¸   rR   éd   i]  éè  ©r=   rF   r
   r   r]   r]   r]   r^   Útest_issue_5955Ð  s   $$$2rÙ   c                   C   s0   t tdttƒ ƒtttƒƒ tdƒdksJ ‚d S r°   )r=   r   r-   rF   r*   r]   r]   r]   r^   Útest_newissue×  r…   rÚ   c                   C   s¼   t tt ttƒttt ttƒksJ ‚t dtttƒ  t tdƒtdtttƒ  t tdƒks0J ‚t tt ttƒttt ttƒksBJ ‚t tt dt  ttƒttt dt  ttƒks\J ‚d S r°   )r=   rF   r
   r<   r-   r]   r]   r]   r^   Útest_extended_real_lineÛ  s   $<$8rÛ   c                  C   sJ   t ddd} t| ƒt td| ƒksJ ‚tt| d d  | tƒtu s#J ‚d S )NrF   Trh   rR   rN   rt   )r   rC   r
   r=   r–   r]   r]   r^   Útest_order_ooâ  s   $rÜ   c                   C   ó    t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t ttt ƒttƒS ry   ©r=   r   rF   rG   r
   r]   r]   r]   r^   Ú<lambda>ê  ó    z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ƒttƒS ry   rÞ   r]   r]   r]   r^   rß   ë  s    ©rE   ÚNotImplementedErrorr]   r]   r]   r^   Útest_issue_5436é  ó   rã   c                   C   s    t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t ttdddS )Nr   rP   ©r<   rF   r]   r]   r]   r^   rß   ï  ó    z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   Ú0rP   rå   r]   r]   r]   r^   rß   ð  ræ   )rE   Ú	TypeErrorÚ
ValueErrorr]   r]   r]   r^   Útest_Limit_dirî  rä   rê   c                   C   s^   t td d td d d  ttƒdksJ ‚t td d td d d  tt ƒdks-J ‚d S )NrR   r×   rc   r]   r]   r]   r^   Útest_polynomialó  s   ,2rë   c                   C   sŽ   t dt dtt  ttt  t  t  ttƒtd tt  ks"J ‚t dt dtt  ttt  t  t  tt ƒtd tt  ksEJ ‚d S ©NrR   )r=   rG   rF   rH   r
   r]   r]   r]   r^   Útest_rationalø  s   DJrí   c                   C   s<   t ttƒt tdt ƒt  tdƒtttt ƒ ksJ ‚d S ©NrN   r   )r=   r   rF   rH   rG   r
   r   r]   r]   r]   r^   Útest_issue_5740ý  ó   <rï   c                  C   s^   t dddd} | d t| d   t| d  d  ttd   }t|tdƒ ¡ | d ks-J ‚d S )NrJ   TrK   rR   rN   )r   rF   r=   Úcancel)rJ   rÍ   r]   r]   r^   Útest_issue_6366  s   0 rò   c                  C   s„   t tƒ} t| ttƒtu sJ ‚tt|  ttƒdksJ ‚t| tdt t ƒtt t   ttƒdks2J ‚t| tt ƒt t ƒks@J ‚d S )Nr   rN   rR   )r   rF   r=   r
   r!   r   r   ©rœ   r]   r]   r^   Útest_factorial  s
   0 rô   c                  C   s¸   dt d  d t tddƒ  tdt d  d tj  dt d  d  dt d  d  tddƒ dtd    } t| ttƒdt d  d dt d  d  dt  d  tddƒ ksZJ ‚d S )	NrU   rT   rt   rN   é#   re   é   rR   )rF   r	   rG   r   r‹   r=   r
   ©r«   r]   r]   r^   Útest_issue_6560  s   4ÿÿÿ
ÿJrø   c                     s$  t dƒ‰t ddd} t dƒ}t ddd}t ddd}d	ˆ ˆ|  d
  ˆ| ˆ|  d
    | | d
 ˆˆ|  d	  ˆ| ˆ|  d
    |   ˆ ˆ| ˆ  ‰ ˆ  ||d
 ¡‰ tt‡ ‡fdd„ƒ tˆ  ||¡ˆtƒd
kspJ ‚tˆ  ||¡ˆtƒ ¡ d	|d
  |  d
 | d
 |d
   ksJ ‚d S )NrJ   rÍ   Trh   rl   ÚpÚm)ÚnegativerN   rR   c                      s   t ˆ ˆtƒS ry   )r=   r
   r]   ©ro   rJ   r]   r^   rß      s    z!test_issue_5172.<locals>.<lambda>)r   ÚsubsrE   râ   r=   r
   r?   )rÍ   rl   rù   rú   r]   rü   r^   Útest_issue_5172  s$   *.ÿÿ
ÿ"ÿrþ   c                  C   s,   t dƒ} tttt|   ƒttƒdksJ ‚d S )Nrj   rR   )r   r=   r!   rF   r
   ©rj   r]   r]   r^   Útest_issue_7088&  s   $r   c                   C   s€  t ttt d ƒtdƒttdƒ ksJ ‚t ttt d ƒtddƒtdƒks'J ‚t ttt d ƒtdƒtdƒ ks:J ‚t ttt d ƒtddƒt tdƒ ksPJ ‚t ttt d ƒtdƒtdƒ kscJ ‚t ttt d ƒtddƒtdƒksvJ ‚t ttt d ƒtdƒtdƒksˆJ ‚t ttt d ƒtddƒdt tdƒ ksŸJ ‚t ttdt  ƒtdƒttdƒ ks³J ‚t ttdt  ƒtddƒt ttdƒ  ksËJ ‚t ttdt  ƒtdƒtttdƒ  ksáJ ‚t ttdt  ƒtddƒt tdƒ ks÷J ‚t tdt ƒtdƒtd ksJ ‚t tdt ƒtddƒt d ksJ ‚t ttƒttƒtd ks*J ‚t ttƒtt ƒt d ks;J ‚t t	tt
dƒd t  ƒtdƒtttt
dƒd ƒ  ksZJ ‚t t	tt
dƒd t  ƒtddƒt tt
dƒd ƒ ksyJ ‚t t	tt
dƒd t  ƒtdƒttt
dƒd ƒ ks–J ‚t t	tt
dƒd t  ƒtddƒt ttt
dƒd ƒ  ks·J ‚t t	tƒtdƒtd ksÆJ ‚t t	tƒtddƒt d ks×J ‚t ttt t
dƒd  ƒtdƒtt
dƒd ƒksòJ ‚t ttt t
dƒd  ƒtddƒtt
dƒd ƒ ksJ ‚t ttt t
dƒd  ƒtdƒdt tt
dƒ d ƒ ks/J ‚t ttt t
dƒd  ƒtddƒtt
dƒ d ƒksLJ ‚t ttt t
dƒd  ƒtdƒtt
dƒd ƒksgJ ‚t ttt t
dƒd  ƒtddƒttt
dƒd ƒ ks…J ‚t ttt t
dƒd  ƒtdƒt tt
dƒd ƒ ks£J ‚t ttt t
dƒd  ƒtddƒtt
dƒd ƒ ksÀJ ‚t ttt d ƒtdƒtt ksÓJ ‚t ttt d ƒtddƒt t ksèJ ‚t tt t d ƒtdƒt t ksýJ ‚t tt t d ƒtddƒtt ksJ ‚t ttt d ƒtdƒtks#J ‚t ttt d ƒtddƒt ks6J ‚t tt t d ƒtdƒt ksIJ ‚t tt t d ƒtddƒtks\J ‚t ttt d ƒtdƒdt
dƒd  kssJ ‚t ttt d ƒtddƒdt
dƒd   ksŒJ ‚t tt t d ƒtdƒdt
dƒd   ks¥J ‚t tt t d ƒtddƒdt
dƒd  ks¾J ‚d S )NrN   r   rS   rW   rR   rY   rT   )r=   r'   r   rF   r   r#   r(   r   r
   r$   r   r   r&   r%   r   r!   r   r]   r]   r]   r^   Útest_branch_cuts+  sT   (&&,&&$.(0,,"&">>:B"6:@:6<<:&***"&&&.226r  c                  C   sj   t dƒ} tdtdt ƒt| ƒd   tdt ƒt| ƒd    }t|tdƒdt| ƒd tj  ks3J ‚d S )Nrj   rR   rN   r   )r   rH   r!   r-   r)   r=   r   r‹   )rj   r«   r]   r]   r^   Útest_issue_6364[  s   8*r  c                   C   s6   t tdtt ƒ ƒtd  tdƒtdt ƒksJ ‚d S rî   )r=   r   r1   rF   r   r]   r]   r]   r^   Útest_issue_6682a  ó   6r  c                  C   s”   t dƒ} t| t tdƒtt| ƒ ksJ ‚t|  t tdƒt t| ƒ ks&J ‚t|  t ttƒt t| ƒ ks8J ‚t| t ttƒtt| ƒ ksHJ ‚d S )Nrj   r   )r   r=   rF   r
   r   rÿ   r]   r]   r^   Útest_issue_4099e  s
    $$$r  c                  C   s\   t dƒ} ttdtt|  ƒ ƒtdttƒ ƒ |  | dƒttƒdtttƒd ƒ  ks,J ‚d S )NÚdxrR   r   rN   )r   r=   r!   r   rF   )r  r]   r]   r^   Útest_issue_4503m  s   .ÿr  c                   C   s&   t ttddƒd  ttƒdksJ ‚d S )NrR   g    eÍÍAr   )r=   rJ   r	   r
   r]   r]   r]   r^   Útest_issue_8208s  ó   &r  c                   C   s<   t ttddƒ d ttƒd tddƒ  tdƒdksJ ‚d S )NrR   rt   rN   rT   r¸   r   )r=   rF   r	   r!   r]   r]   r]   r^   Útest_issue_8229w  rð   r
  c                  C   s4   t ddd\} }ttd||   ƒ|tƒdksJ ‚d S )Nzd tTrh   rR   rY   )r   r=   r2   r
   )rÊ   Útr]   r]   r^   Útest_issue_8433{  s   $r  c                  C   sH   t dddd} t ddd}t||  t| ƒ t| ƒ | tƒdks"J ‚d S )NrI   T)rL   ÚnonnegativeÚlamdarh   r   )r   r=   r   r   r
   )rI   r  r]   r]   r^   Útest_issue_8481€  s   .r  c                  C   s  t ddd} t ddd}t| t | td   | tƒdksJ ‚t| t | td   | tƒtks0J ‚t| t | td   | tƒtksBJ ‚t| t | t| d	   | tƒtksVJ ‚t ddd} t| t | td	   | tƒtksnJ ‚t| t | td
   | tƒt ksJ ‚d S )NrF   Tr”   rI   rh   r   rU   g      @rR   rN   )r   r=   rJ   r
   )rF   rI   r]   r]   r^   Útest_issue_8635_18176†  s   $$$($*r  c                   C   s   t ttƒttƒtu sJ ‚d S ry   )r=   r   rF   r
   r]   r]   r]   r^   Útest_issue_8730’  ó   r  c                      s`   t ddd‰t ddd‰ ttˆƒˆtˆƒ  dˆ  ˆ  ˆtƒdks$J ‚tt‡ ‡fdd	„ƒ d S )
NrJ   T)rL   rl   rh   rR   r   c                      s$   t tˆƒˆtˆƒ  ˆ ˆ  ˆtƒS ry   )r=   r   r
   r]   ©rl   rJ   r]   r^   rß   ›  s   $ z!test_issue_9252.<locals>.<lambda>)r   r=   r   r
   rE   râ   r]   r]   r  r^   Útest_issue_9252–  s   0r  c                   C   s"   t ttƒd tddƒdksJ ‚d S )Nrö   r   rS   )r=   r-   rF   r]   r]   r]   r^   Útest_issue_9558ž  s   "r  c                   C   s2   t dt ttdt tƒd   ttƒtksJ ‚d S )Nr¸   rN   )r=   rI   r   r
   r   r]   r]   r]   r^   Útest_issue_10801¢  s   2r  c                  C   s8   t ddd\} }tt| | ƒt| ƒ | dƒ|ksJ ‚d S )Nzs xTr”   r   )r   r=   r2   )rÉ   rF   r]   r]   r^   Útest_issue_10976§  s   (r  c                   C   s<   t ttƒttdƒ t tdt t ƒ  ttƒdksJ ‚d S ©NrR   rN   )r=   r   rJ   r   r!   r   r
   r]   r]   r]   r^   Útest_issue_9041¬  rð   r  c                  C   sŒ   t dƒ\} }}t| | |ƒj|hksJ ‚t| | |dƒj|hks J ‚t| | | | |ƒj|hks0J ‚t| d  | | d |ƒj||hksDJ ‚d S )Nzx, y, arS   rN   )r   r<   Úfree_symbols)rF   rG   rj   r]   r]   r^   Útest_issue_9205°  s
    ,r  c                   C   sT   t dttdƒ td  ttƒdksJ ‚t dttdƒd  td  ttƒdks(J ‚d S )Né   rT   rR   )r=   r   rJ   r
   r]   r]   r]   r^   Útest_issue_9471¸  s   &.r  c                   C   s$   t ttdt ƒƒttƒdksJ ‚d S r  )r=   r3   r   rF   r
   r]   r]   r]   r^   Útest_issue_11496½  ó   $r  c                   C   s<   t ttt t tt  t tdƒƒtttd   ksJ ‚d S )Nr   rR   )r?   r=   rF   rG   rJ   r]   r]   r]   r^   Útest_issue_11879Á  rð   r   c                  C   sF   t dƒ} td|  | tƒdksJ ‚tdd|   | tƒtddƒks!J ‚d S )NrI   rº   rR   g333333Ó?rT   é
   )r   r=   r
   r	   )rI   r]   r]   r^   Útest_limit_with_FloatÅ  s   &r"  c                   C   sD   t dt dt d   td d  td  ttƒtddƒks J ‚d S ©NrT   rR   rN   )r=   rF   r
   r	   r]   r]   r]   r^   Útest_issue_10610Ë  ó   Dr$  c                   C   s$   t tttƒ t ttƒdksJ ‚d S rì   )r=   rJ   r)   r
   r]   r]   r]   r^   Útest_issue_6599Ï  r  r&  c                   C   sn   t dt dtd   td ttƒ  tt ƒdksJ ‚t dt dtd   td ttƒ  ttƒtu s5J ‚d S )NrT   rN   r!  ra   r]   r]   r]   r^   Útest_issue_12555Ó  s   68r'  c                  C   sÒ  t ddd\} }}t dddd\}}}}}}}	|| ||  |  | t|d |d|   |d  |d  |d|  |d  |d  |d   |d|  |d|   |d  |d  |d d|  d   d|d|   ||d   | |  | |d d|  d   d||d   |d|   | |  | |d d|  d   d||d   ||d   |d  |d   |d |d d|  d   ƒ ||  | |  d  }
|
 ||¡jddt|
||ƒjddksçJ ‚d S )	Nzr z xTr”   za b s0 K F0 s T)rM   r•   rN   rR   r­   )r   r!   rý   Úfactorr=   )rÍ   rH   rF   rj   rk   Ús0ÚKÚF0rÉ   ÚTÚfxr]   r]   r^   Útest_issue_12769Ø  s$   :"ÿ:ÿ:þ:ý*üüü0r.  c                   C   sz   t tdƒ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ƒtd	d
ƒks;J ‚d S )Né   rU   éûÿÿÿrR   i@¶  rN   rq   iúÿÿÿé   é$   )r=   r!   rF   r   r‹   r
   r	   r]   r]   r]   r^   Útest_issue_13332ä  s   Bÿÿÿr3  c                   C   sò   t td tttƒ  ttƒ tt ƒtu sJ ‚t td tttƒ  ttƒ ttƒtu s-J ‚t tttƒ d  ¡ ttƒtu s?J ‚t tttƒ d  ¡ ttƒtu sQJ ‚t tttƒ d  ¡ tt ƒtu sdJ ‚t tttƒ d  ¡ tt ƒtu swJ ‚d S rƒ   )r=   rF   r-   r)   r
   Úexpandr]   r]   r]   r^   Útest_issue_12564é  s   .,$$&*r5  c                   C   rÝ   )Nc                   S   s   t ttƒttƒ ¡ S ry   )r<   r   rF   r   r†   r]   r]   r]   r^   rß   ó  rà   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  ttƒ ¡ S )NrN   rR   )r<   rF   r   r†   r]   r]   r]   r^   rß   ô  s    rá   r]   r]   r]   r^   Útest_issue_14456ò  rä   r6  c                   C   sB   t dtdt t td  ƒ tdt dt d  ƒt u sJ ‚d S )NrT   rt   é   rN   )r=   r,   r   rF   r
   r]   r]   r]   r^   Útest_issue_14411÷  s   Br8  c                   C   s8   t ttd d d td d  d  ttƒdksJ ‚d S r  rc   r]   r]   r]   r^   Útest_issue_13382û  s   8r9  c                   C   s<   t tdtttd ƒ d tttƒ    ttƒdksJ ‚d S )NrY   rR   ©r=   rF   r   r
   r]   r]   r]   r^   Útest_issue_13403ÿ  rð   r;  c                   C   sb   t td  ttƒd  td td d  ttd ƒd   td ttƒd   ttƒdks/J ‚d S r#  r:  r]   r]   r]   r^   Útest_issue_13416  s   br<  c                   C   sx   t td dt dddt   t  d  t td  d td  t   ttƒtd d td d  td  ks:J ‚d S )NrN   rR   rt   rT   r7  re   rr   )r=   rJ   rF   r
   r]   r]   r]   r^   Útest_issue_13462  s   xr=  c                  C   sH   t dƒ} tt| t ƒttƒdksJ ‚ttttƒt ƒttƒdks"J ‚d S )Nrj   rY   )r   r=   r2   rF   r
   r!   rÿ   r]   r]   r^   Útest_issue_13750  s   $r>  c                   C   s0   t dttƒttƒ  dt  ttƒdksJ ‚d S rì   )r=   r   rF   r
   r]   r]   r]   r^   Útest_issue_14514  r…   r?  c                   C   sx  t ttƒd ttƒ ttƒttƒ  ttƒttj	tj
ƒksJ ‚t ttƒd ttƒ ttƒttƒ  ttƒttj	tj
ƒks>J ‚t ttƒttƒd  ttƒttj	tj
ƒksUJ ‚t ttƒttƒd  ttƒttj	tjƒkslJ ‚t ttƒttƒd  ttƒttj	tjƒksƒJ ‚t ttƒd ttƒd  ttƒttj	tjƒksœJ ‚t ttƒd ttƒd  ttƒ ttƒttj tj
ƒksºJ ‚d S rƒ   )r=   r-   rF   r)   r.   r+   r
   r@   r   r[   r\   r*   rµ   r]   r]   r]   r^   Útest_issues_14525  s   >>...2@r@  c                   C   s4   t ttƒtttd  ƒ td  ttƒdksJ ‚d S )NrN   rR   r   )r=   r!   rF   r)   r
   r]   r]   r]   r^   Útest_issue_14574  ó   4rA  c                   C   sº   t ttƒttƒtjksJ ‚t dttƒ ttƒdtj ksJ ‚t dttƒ ttƒtddƒks/J ‚t ttƒttƒtjks<J ‚t ttƒtt ƒtddƒksLJ ‚t dttƒ tt ƒdks[J ‚d S )NrT   rU   rN   rY   rt   rW   )r=   r6   rF   r
   r   r‹   r	   r5   r]   r]   r]   r^   Útest_issue_10102#  s   "" "rC  c                   C   ó   t tdd„ ƒ d S )Nc                   S   s    t ttt ƒttt ƒ ttƒS ry   )r=   r   r   rF   r-   r   r
   r]   r]   r]   r^   rß   -  s     z"test_issue_14377.<locals>.<lambda>rá   r]   r]   r]   r^   Útest_issue_14377,  ó   rE  c                  C   s   t d dt d  dt d d  t d  tt d d ƒ  dt d d  t d  tt d t  d ƒ  t  d  } t| t tƒtdƒd ksFJ ‚d S )NrN   rW   rT   rR   )rF   r7   r=   r
   r   r÷   r]   r]   r^   Útest_issue_151460  s   8*ÿÿÿ rG  c                  C   s°   dt  ddt   ddt   t  d    t d  t d  } t| t tƒtdƒks)J ‚tt dƒd dt  tt ƒ  dt   tt d ƒdtt ƒ  dt    } t| t tƒdksVJ ‚d S )NrN   rW   rR   r´   r!  rU   rT   )rF   r=   r
   r   r   r   r÷   r]   r]   r^   Útest_issue_152026  s   :FrH  c                   C   s0   t td td d  td  ttƒdksJ ‚d S )NiÐ  rR   iÏ  i0øÿÿrc   r]   r]   r]   r^   Útest_issue_15282>  r…   rI  c                   C   s2   t t tttƒd ƒ t ttdddksJ ‚d S )NrR   rS   rP   r   )r=   rF   r   r   r
   r]   r]   r]   r^   Útest_issue_15984B  ó   2rJ  c                   C   s&   t ttdƒttƒ ttƒdksJ ‚d S rì   )r=   r9   rF   r8   r
   r]   r]   r]   r^   Útest_issue_13571F  r	  rL  c                   C   s*   t tttƒƒtdƒtttjƒƒksJ ‚d S rì   )r=   r#   r4   rF   r   rµ   r]   r]   r]   r^   Útest_issue_13575J  rÑ   rM  c                   C   sŒ   t ttƒ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   rV   rP   rR   rN   )r<   r-   rF   r†   r
   r   r]   r]   r]   r^   Útest_issue_17325N  s   $ $$rN  c                   C   s   t tƒ td¡dksJ ‚d S ©Nr   )r   rF   r=   r]   r]   r]   r^   Útest_issue_10978U  r  rP  c                   C   s    t ttd ƒttƒtu sJ ‚d S rƒ   )r=   r   rJ   r
   r]   r]   r]   r^   Útest_issue_14313_commentY  ó    rQ  c                  C   s2   ddt   t   t ¡} t| t ddddksJ ‚d S )NrR   rO   rP   )rF   r   r=   )rÊ   r]   r]   r^   Útest_issue_15323]  s   rS  c                   C   s,   t tttƒ ƒ ttƒ tdƒdksJ ‚d S rì   )r=   r   r   rF   r]   r]   r]   r^   Útest_issue_12571c  ó   ,rT  c                   C   sH   t td td t t  td td  td   ttƒtdƒks"J ‚d S r#  rØ   r]   r]   r]   r^   Útest_issue_14590g  ó   HrV  c                  C   sR   t dƒ\} }tt| t|  t|  t|    ttƒ|t|  |   |  ks'J ‚d S )Núa b)r   r=   rF   rG   ©rj   rk   r]   r]   r^   Útest_issue_14393k  s   FrZ  c                   C   s@   t ttd ƒdtd   ttƒdt   ttƒtdƒksJ ‚d S )NrR   rY   )r=   r   rJ   r
   r   r]   r]   r]   r^   Útest_issue_14556p  ó   @r[  c                   C   sL   t dtdƒd td   dt  dtdƒd td    ttƒtks$J ‚d S )NrR   rN   rT   rt   ©r=   r   rF   r
   r]   r]   r]   r^   Útest_issue_14811t  s   Lr^  c                   C   s   t tdtƒttƒdksJ ‚d S rO  )r=   r0   rF   r
   r]   r]   r]   r^   Útest_issue_14874x  s   r_  c                   C   s    t ttƒtdƒtdƒksJ ‚d S )Ni Êš;)r=   r   rF   r]   r]   r]   r^   Útest_issue_16222|  rR  r`  c                   C   sD   t ttd  td t  ttd   t ttƒttdƒƒks J ‚d S rì   rØ   r]   r]   r]   r^   Útest_issue_16714€  r%  ra  c                  C   s†   t ddd} ttt|  tƒt|    ttƒdt| d ƒ ks J ‚t dddd} ttt|  tƒt|    ttƒdt| d ƒ ksAJ ‚d S )NrH   Trh   rR   )rM   rL   )r   r=   r   rJ   r
   r8   r™   r]   r]   r^   Útest_issue_16722„  s   48rb  c                   C   sÀ   t td d td d ttd ƒ  td  ttƒ td  ttƒdks&J ‚t td d ttƒ td td  ttd ƒ  ttƒdksFJ ‚t td ttƒ tttd ƒ  ttƒdks^J ‚d S )NrR   rN   r   rT   )r=   rJ   r   r
   r]   r]   r]   r^   Útest_issue_17431‹  s"   $ÿÿÿÿÿ0ÿÿ4rc  c                   C   s2   t tttƒ ƒtttƒƒt  tdƒtksJ ‚d S rì   )r=   r1   r   rF   r   r]   r]   r]   r^   Útest_issue_17671“  rK  rd  c                  C   sf   t ddd\} }}}t| d | t| d d |d  ||  | ƒ |tƒ| d|  d  ks1J ‚d S )Nza b c xTrh   rR   rN   )r   r=   r!   r
   )rj   rk   rl   rF   r]   r]   r^   Útest_issue_17751—  s   Rre  c                   C   s@   t ttƒttƒ tdƒt t  ttƒtdƒttƒ ksJ ‚d S r  )r=   r   rJ   r!   r   r
   r   r]   r]   r]   r^   Útest_issue_17792œ  r\  rf  c                   C   s@   t tttƒƒtddƒdksJ ‚t tttƒƒtddƒdksJ ‚d S )Nr   rS   rY   rO   rR   )r=   r   r-   rF   r]   r]   r]   r^   Útest_issue_18118   s   "rg  c                   C   s.   t tttƒƒtttƒƒ tddƒdksJ ‚d S )Nr   rO   rR   )r=   r-   r!   rF   r]   r]   r]   r^   Útest_issue_18306¥  r²   rh  c                   C   s<   t ttdt ƒt ƒtttƒtd  ƒ ttƒdksJ ‚d S )NrT   rÖ   )r=   r   r   rF   r
   r]   r]   r]   r^   Útest_issue_18378©  rð   ri  c                   C   sJ   t dtdƒd t  dt  ttƒtu sJ ‚t t t ttƒtu s#J ‚d S )NrR   rN   rT   )r=   r   rF   r
   r   r]   r]   r]   r^   Útest_issue_18399­  s   ,rj  c                   C   sH   t ttƒdttƒ  ttddtttƒdttƒ  ttddks"J ‚d S )NrN   rS   rP   )r=   r.   rF   r!   r   r
   r<   r]   r]   r]   r^   Útest_issue_18442²  rW  rk  c                   C   sF   t tttƒƒt tdƒdksJ ‚t tttƒƒt tddƒdks!J ‚d S )Nr   rR   rS   )r=   r˜   r   rF   r]   r]   r]   r^   Útest_issue_18452¶  s    &rl  c                   C   s:  t ttƒdt  ttƒtttƒdt  ttddksJ ‚t ttƒdt  ttƒtttƒdt  ttddks8J ‚t ttƒdt  ttƒtttƒdt  ttddksTJ ‚t ttƒd dt  ttƒdksfJ ‚t ttƒd dt  ttƒdksxJ ‚t ttƒd dt  ttƒtttƒd dt  ttddks˜J ‚t ttƒd dt  ttƒtddƒks­J ‚t ttƒd dt  ttƒtdtƒksÂJ ‚t ttƒd dt  ttƒtddƒks×J ‚t ttƒd dt  tt ƒtdtƒksíJ ‚t ttƒd dt  tt ƒtdtƒksJ ‚t ttƒd dt  tt ƒtdtƒksJ ‚d S )NrR   rS   rP   rN   r!  r   )r=   r-   rF   r
   r<   r)   r.   r@   r]   r]   r]   r^   Útest_issue_18473»  s   888$$@***,.2rm  c                   C   s@   t dtdt ƒ tdt ƒd  dt  ttƒtdƒksJ ‚d S ©NrN   rT   rR   )r=   r   rF   r
   r]   r]   r]   r^   Útest_issue_18482Ë  r\  ro  c                   C   s’   t ttƒtdttƒ ƒ tdƒtdƒksJ ‚t ttƒtdttƒ ƒ tdddtdƒks.J ‚t ttƒtdttƒ ƒ tdddtdƒ ksGJ ‚d S )NrR   r   rN   rO   rP   rS   )r=   r-   rF   r!   r)   r]   r]   r]   r^   Útest_issue_18508Ï  s   ,06rp  c                   C   rD  )Nc                   S   s   t tdt t ƒttƒS rƒ   )r=   r   rJ   rF   r
   r]   r]   r]   r^   rß   Ö  s    z"test_issue_18521.<locals>.<lambda>rá   r]   r]   r]   r^   Útest_issue_18521Õ  rF  rq  c                  C   sT   t ddd\} }tt| ƒ| |ƒt|ƒksJ ‚ttt| ƒƒ| |ƒtt|ƒƒks(J ‚d S )NrX  Trh   )r   r=   r   r   rY  r]   r]   r^   Útest_issue_18969Ù  s   (rr  c                   C   s,   t tttƒdt   ttƒtdƒksJ ‚d S rì   )r=   rJ   r   r
   r   r]   r]   r]   r^   Útest_issue_18992ß  rU  rs  c                  C   s<   t dƒ} tt| ƒt| d ƒt| d ƒ  | dƒdksJ ‚d S )NrF   rR   rN   r   rY   )r   r=   r8   r–   r]   r]   r^   Útest_issue_19067ã  s   4rt  c                   C   s*   t tdt dt    ttƒdksJ ‚d S rn  rc   r]   r]   r]   r^   Útest_issue_19586è  rÑ   ru  c                  C   s0   t dƒ} t ddd}t| | | dƒdksJ ‚d S )NrJ   rù   T)Úzeror   )r   r=   )rJ   rù   r]   r]   r^   Útest_issue_13715ì  s   rw  c                   C   sT   t td t d tdt ƒ td tdtd  ƒ   t d  ttƒdks(J ‚d S r#  )r=   rJ   r-   r
   r]   r]   r]   r^   Útest_issue_15055ò  s   Trx  c                  C   s‚   t ddd\} }t dƒ\}}}t|| | t| ƒtd| | | | |d   ƒ  | |  ||  |dƒ|||  | ks?J ‚d S )Nzm viTrh   zB ti drW   rN   r   )r   r=   r!   )rú   ÚviÚBÚtirÊ   r]   r]   r^   Útest_issue_16708ö  s   d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ƒ}d	|d
  |  | |d| |  |   }|d
 |d
  }|||  |  d }| d| |  |d
| |d
    ||||  |  d  d
| |d	    |d| |  |  |  }	tt|	ƒ| ƒ }
t|
d| |  | tƒdks“J ‚t|
 ¡ d| |  | tƒdks¥J ‚d S )NÚbetaTrh   Úhrú   ÚomegaÚgrR   rT   rN   ri   rt   r   )r   r   r   r   r=   r
   r?   )r}  r~  rú   Úwr€  r«   Úqrù   rÉ   ÚZr   r]   r]   r^   Útest_issue_19453ü  s   (Lÿ (r„  c                   C   s&   t tdƒ d t ttƒdksJ ‚d S )NrR   rt   r   r]  r]   r]   r]   r^   Útest_issue_19739  r	  r…  c                   C   s2   t dt  tdtd  d ƒ ttƒdksJ ‚d S )NrN   rt   rR   )r=   rF   r!   r
   r]   r]   r]   r^   Útest_issue_19766  rK  r†  c                  C   sÖ   t dƒ} tt| t ƒt ttƒtt| t ƒt ttddks J ‚t ddd} tt| t ƒt ttƒtt| t ƒt ttddksBJ ‚t ddd} tt| t ƒttƒtddƒksYJ ‚tt| t ƒt ttƒd	ksiJ ‚d S )
Nrú   rS   rP   Tr”   )ÚnonzerorY   rR   r   )r   r=   r)   rF   r
   r<   r@   )rú   r]   r]   r^   Útest_issue_19770  s   88"$rˆ  c                   C   s’  t ttƒtttƒƒ ttd ƒtttƒtttƒƒ ttd ddks$J ‚t ttƒtttƒƒ ttd ddtttƒtttƒƒ ttd ddksJJ ‚t ttƒtttƒƒ ttd ddtttƒtttƒƒ ttd ddkspJ ‚t tttƒƒttd ƒtddƒksƒJ ‚t dtt ƒ  tt tƒks•J ‚tdttƒ  tt tƒks¥J ‚tdtt ƒ  tt tƒks¶J ‚t dttƒ  tt tƒksÇJ ‚d S )NrN   rO   rP   rS   rV   rY   rR   )r=   r.   rF   r-   r   r<   r@   r
   r]   r]   r]   r^   Útest_issue_7535#  s   HLL&$ "&r‰  c                   C   s2   t td dt  t t tdƒt d ksJ ‚d S )NrR   r   rN   )r=   rF   r   r]   r]   r]   r^   Útest_issue_20365.  rK  rŠ  c                   C   sH   t dt dt  ddt  ddt    ttƒ tdƒtd ks"J ‚d S )NrR   rN   r   )r=   rF   r'   r   r]   r]   r]   r^   Útest_issue_210312  rW  r‹  c                   C   s0   t ttt ƒdt d  tdƒtd ksJ ‚d S )NrT   rr   rt   )r=   r-   r   rF   r]   r]   r]   r^   Útest_issue_210386  r…   rŒ  c                  C   sZ   t tƒtdt ƒ } t| tddƒdksJ ‚t| tddƒdks J ‚t| tddƒdks+J ‚d S )NrR   r   rO   rS   rV   )r˜   rF   r-   r=   r½   r]   r]   r^   Útest_issue_20578:  s   r  c                  C   st  t tƒ} | jttdtksJ ‚| jtt dt ksJ ‚t t tƒ ƒ} | jttdt t ƒks1J ‚| jtt dt tƒks?J ‚t t tƒƒ} | jttdt tƒksRJ ‚| jtt dt t ƒksaJ ‚| jttdt tƒksnJ ‚t t t dt ƒƒƒ} | jttdt t t ƒƒksˆJ ‚| jtt dt t tƒƒks˜J ‚| jttdt t t ƒƒks¨J ‚| jtt dt t tƒƒks¸J ‚d S )N)ÚlogxrR   )r   rF   ÚnseriesrG   ró   r]   r]   r^   Útest_issue_21227A  s      $r  c                  C   sH   t d tdt d  ƒ } |  t d¡dksJ ‚|  ¡  t d¡dks"J ‚d S r°   )rF   r)   r=   r4  )r   r]   r]   r^   Útest_issue_21415Z  s   r‘  c                   C   s(   t ttd ƒttƒ ttƒtksJ ‚d S rì   )r=   r   rJ   r
   r   r]   r]   r]   r^   Útest_issue_21530`  s   (r’  c                  C   sD   t dƒd d } tt|  td t d  t| ƒt dƒd ks J ‚d S )NrU   rR   rN   )r!   r=   rF   rÎ   r]   r]   r^   Útest_issue_21550d  s   4r“  c                  C   sL   t ttd  ttƒd  d t tdƒ} | tdƒd dtdƒ  ks$J ‚d S )NrR   é   l   ’Ñqjl   SÍ[	)r=   rF   r   r   )Úoutr]   r]   r^   Útest_issue_21661i  s   ($r–  c                   C   s6   t tttƒtt   td¡tdƒtdƒd ksJ ‚d S )Nr´   r   rR   i Ø	 )r=   r/   rH   rF   rý   r   r]   r]   r]   r^   Útest_issue_21701n  r  r—  c                  C   sD   t ddd} tdtdt|  d    tƒ}| tt¡tjks J ‚d S )Nrj   Tr”   rR   rN   )r   r;   r   rF   r=   r
   r   r‹   )rj   r   r]   r]   r^   Útest_issue_21721r  s   r˜  c                  C   sd   dt dt t t ƒ dt dt t t d ƒ  } |  td¡dks$J ‚t| ƒ td¡dks0J ‚d S )NrR   rW   rU   r   )r   r   r   rH   r=   r   )Útermr]   r]   r^   Útest_issue_21756x  s   4rš  c                  C   s@   t dƒ} t| d  td  dtd   ƒ | dd¡tksJ ‚d S )Nrj   rN   rR   rS   )r   r!   rF   r=   r   rÿ   r]   r]   r^   Útest_issue_21785~  s   8r›  c                   C   s&   t dt dt   ttƒdksJ ‚d S )NrY   rN   r   rc   r]   r]   r]   r^   Útest_issue_22181ƒ  r	  rœ  c                  C   sÔ  t dƒtt dƒttd ƒ d ƒ d } t dƒt tt dƒttd ƒ dt dƒ t d  ƒ tt dƒttd ƒ dt dƒ t d  ƒ
   d }t| tt ƒt dƒ t d ks\J ‚t|tt ƒt dƒ t d ksnJ ‚t| tt dƒt dƒt d ks€J ‚t|tt dƒdksŒJ ‚ttt ƒtt t ƒ }t|d	d
}t|tt	ƒt|tt	ƒ  kr´tt ks·J ‚ J ‚tttd ƒt ƒ tttd ƒt ƒ  }}t|ttdƒdt t ksÝJ ‚t|ttdƒdksèJ ‚d S )Nr/  rN   rq   rö   rU   é<   rS   r   T)ÚforcerO   )
r!   r(   r.   rF   r   r   r=   r   r>   r
   )Úe1Úe2ro   Úexpr2r]   r]   r^   Útest_issue_22220‡  s    (6,ÿÿ$$$0.r¢  c                  C   s>   dt  dt    dt  dt     } t| t t ƒdksJ ‚d S )NrN   rY   )rF   r=   r
   ró   r]   r]   r^   Útest_issue_23231  s   $r£  c                   C   s4   t dt td  tdt ƒ tdtfƒtksJ ‚d S )NrR   rN   rY   r   )r;   rF   r   r
   r]   r]   r]   r^   Útest_issue_23596¢  rB  r¤  N)ûÚ	itertoolsr   Úsympy.concrete.summationsr   Úsympy.core.functionr   r   Ú
sympy.corer   Úsympy.core.numbersr   r   r	   r
   r   r   Úsympy.core.singletonr   Úsympy.core.symbolr   r   Ú(sympy.functions.combinatorial.factorialsr   r   r   Ú$sympy.functions.elementary.complexesr   r   r   Ú&sympy.functions.elementary.exponentialr   r   r   Ú%sympy.functions.elementary.hyperbolicr   r   r   Ú#sympy.functions.elementary.integersr   r   r   Ú(sympy.functions.elementary.miscellaneousr   r    r!   Ú$sympy.functions.elementary.piecewiser"   Ú(sympy.functions.elementary.trigonometricr#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   Úsympy.functions.special.besselr/   r0   Ú'sympy.functions.special.error_functionsr1   r2   r3   r4   r5   r6   Ú'sympy.functions.special.gamma_functionsr7   r8   r9   Úsympy.integrals.integralsr:   r;   Úsympy.series.limitsr<   r=   Úsympy.simplify.simplifyr>   r?   Ú!sympy.calculus.accumulationboundsr@   Úsympy.core.mulrA   rB   Úsympy.series.orderrC   Úsympy.testing.pytestrD   rE   Ú	sympy.abcrF   rG   rH   rI   rJ   r_   rb   rd   rg   rp   rs   rx   r‚   r„   rˆ   rŒ   rŽ   r‘   r’   r“   r—   rš   r›   r   rŸ   r    r¤   r¬   r¯   r±   r³   r¶   r·   r¹   r¼   r¾   rÌ   rÏ   rÐ   rÒ   rÓ   rÕ   rÙ   rÚ   rÛ   rÜ   rã   rê   rë   rí   rï   rò   rô   rø   rþ   r   r  r  r  r  r  r  r
  r  r  r  r  r  r  r  r  r  r  r  r  r   r"  r$  r&  r'  r.  r3  r5  r6  r8  r9  r;  r<  r=  r>  r?  r@  rA  rC  rE  rG  rH  rI  rJ  rL  rM  rN  rP  rQ  rS  rT  rV  rZ  r[  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  ro  rp  rq  rr  rs  rt  ru  rw  rx  r|  r„  r…  r†  rˆ  r‰  rŠ  r‹  rŒ  r  r  r‘  r’  r“  r–  r—  r˜  rš  r›  rœ  r¢  r£  r¤  r]   r]   r]   r^   Ú<module>   sp    8 G
	



0	
	

