o
    Ð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$„ Znd%d&„ Zod'd(„ Zpd)d*„ Zqd+d,„ Zrd-d.„ Zsd/d0„ Ztd1d2„ Zud3d4„ Zvd5d6„ Zwd7d8„ Zxd9d:„ Zyd;d<„ Zzd=d>„ Z{d?d@„ Z|dAdB„ Z}dCdD„ Z~dEdF„ ZdGdH„ Z€dIdJ„ ZdKdL„ Z‚dMdN„ ZƒdOdP„ Z„dQdR„ Z…eedSdT„ ƒZ†dUdV„ Z‡dWdX„ ZˆdYdZ„ Z‰d[d\„ ZŠd]d^„ Z‹d_d`„ ZŒdadb„ Zdcdd„ ZŽdedf„ Zdgdh„ Zdidj„ Z‘dkdl„ Z’dmdn„ Z“dodp„ Z”dqdr„ Z•dsdt„ Z–eedudv„ ƒZ—dwdx„ Z˜dydz„ Z™d{d|„ Zšd}d~„ Z›dd€„ Zœdd‚„ Zdƒd„„ Zžd…d†„ ZŸeed‡dˆ„ ƒZ d‰dŠ„ Z¡d‹dŒ„ Z¢ddŽ„ Z£dd„ Z¤d‘d’„ Z¥d“d”„ Z¦d•d–„ Z§d—d˜„ Z¨d™dš„ Z©d›dœ„ Zªddž„ Z«dŸd „ Z¬d¡d¢„ Z­d£d¤„ Z®d¥d¦„ Z¯d§d¨„ Z°d©dª„ Z±d«d¬„ Z²d­d®„ Z³d¯d°„ Z´d±d²„ Zµd³d´„ Z¶dµd¶„ Z·d·d¸„ Z¸d¹dº„ Z¹d»d¼„ Zºd½d¾„ Z»d¿dÀ„ Z¼dÁdÂ„ Z½dÃdÄ„ Z¾dÅdÆ„ Z¿dÇdÈ„ ZÀdÉdÊ„ ZÁdËdÌ„ ZÂdÍdÎ„ ZÃdÏdÐ„ ZÄdÑdÒ„ ZÅdÓdÔ„ ZÆdÕdÖ„ ZÇd×dØ„ ZÈdÙdÚ„ ZÉdÛdÜ„ ZÊdÝdÞ„ ZËdßdà„ ZÌdádâ„ ZÍdãdä„ ZÎdådæ„ ZÏdçdè„ ZÐdédê„ ZÑdëdì„ ZÒdídî„ ZÓdïdð„ ZÔdñdò„ ZÕdódô„ ZÖdõdö„ Z×eed÷dø„ ƒZØdùdú„ ZÙdûdü„ ZÚdýdþ„ ZÛdÿd „ ZÜdd„ ZÝdd„ ZÞdd„ Zßdd„ Zàd	d
„ Zádd„ Zâdd„ Zãdd„ Zädd„ Zådd„ Zædd„ Zçdd„ Zèdd„ Zédd„ Zêdd„ Zëdd „ Zìd!d"„ Zíd#d$„ 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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dt   ksxJ ‚t dt	tƒ t tdƒtt	tƒd t tdƒks“J ‚t dttƒ tdddtks¤J ‚t dttƒ tdddt ks¶J ‚t dttƒ tdddtksÇJ ‚t dttƒ tdddt ksÙJ ‚t tdt ƒdttƒ  tdddtksðJ ‚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)rD   rN   r
   r   r   r%   rC   rO   r   r-   r>   r   ÚNaNrK   r1   r   r2   r	   r.   rH   ÚNegativeInfinityÚInfinityr0   r/   r   r   r+   r   © re   re   úND:\Projects\ConvertPro\env\Lib\site-packages\sympy/series/tests/test_limits.pyÚtest_basic1%   sr    "$,4>,."""$(&$"(&4620$$$$""$ (.6"$"$..rg   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   rW   rX   rZ   ra   rV   é   ©rD   rN   r   r
   re   re   re   rf   Útest_basic2l   s    ""*rj   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 )NrZ   r   rW   rX   r[   ©rD   rN   r
   re   re   re   rf   Útest_basic3w   s   "rl   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 )
NrV   r   rZ   é   r`   r_   i   r\   é	   )rD   rN   rO   r%   r
   rB   r   re   re   re   rf   Útest_basic4|   s
    $0$8ro   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©rU   r   ztau xrV   rZ   r_   ç      à?r\   )r   r   rD   r
   r,   r   )ÚaÚbÚcÚAÚtaurN   Úexprre   re   rf   Útest_log„   s"   8ÿÿ(ÿÿÿ0rx   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   r\   rV   r_   rW   rZ   é   )rD   r$   rN   r	   re   re   re   rf   Útest_piecewise“   s   6r{   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 )NrV   é   rZ   r   Trq   g      À?rn   r]   ra   r\   )r%   rN   r&   r   rD   )Zfunc1Zfunc2Zfunc3re   re   rf   Útest_piecewise2˜   s   @ÿ.ÿ&<r}   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   rd   rb   )ÚclsÚargre   re   rf   Úeval¤   s   
ÿztest_basic5.<locals>.my.evalN)Ú__name__Ú
__module__Ú__qualname__Úclassmethodr   re   re   re   rf   Úmy£   s    r†   )r   rD   rN   r
   rC   )r†   re   re   rf   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 ©NrV   )rD   rN   rO   rP   re   re   re   rf   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   rZ   r^   rX   )rC   r1   rN   ÚdoitÚargsr   re   re   re   rf   Ú
test_Limit¯   s    *r   c                   C   s  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 ‚t tttƒƒttƒdksÛJ ‚t tttƒƒtt ƒdksêJ ‚t t	ttƒƒttƒdksøJ ‚t t	ttƒƒtt ƒdksJ ‚d S )Nr_   rW   r[   r`   ra   r   rZ   rV   éø   é÷   r\   rq   )
rD   r!   rN   r	   r
   rH   r   ÚHalfr,   r    re   re   re   rf   Ú
test_floorµ   s$   ,6$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   rW   r[   ra   r]   r|   )rD   r!   r1   rN   r-   re   re   re   rf   Ú&test_floor_requires_robust_assumptionsÎ   ó   """&r’   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 )Nr_   rW   ra   r[   r   rZ   rV   r\   rŽ   éù   rq   )rD   r    rN   r	   r
   rH   r   r   re   re   re   rf   Útest_ceilingÙ   s   ,: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   rW   rZ   r[   r]   ry   )rD   r    r1   rN   r-   re   re   re   rf   Ú(test_ceiling_requires_robust_assumptionsì   r“   r–   c                   C   sž  t ttƒttƒtddƒksJ ‚t ttƒdt  ttƒtddƒks"J ‚t ttƒdt  tt ƒtdtƒks6J ‚t ttƒt ttƒtdtƒksGJ ‚t tttƒƒtddƒdksVJ ‚t tttƒƒtddƒdkseJ ‚t tttƒƒtddƒdkstJ ‚t ttd ƒtddƒdksƒJ ‚ttdd„ ƒ t td	t d ƒtddƒdks›J ‚t td	t d ƒtddƒdks¬J ‚t ttt	j
 ƒtddƒd
ks¼J ‚t tdt ƒtdƒtddƒksÍJ ‚d S )Nr   rZ   rW   r[   r^   rV   c                   S   s   t ttƒtddƒS ©Nr   r^   )rD   r"   rN   re   re   re   rf   Ú<lambda>   s    ztest_frac.<locals>.<lambda>r_   rq   )rD   r"   rN   r
   rH   r1   r-   rM   Ú
ValueErrorr   r   re   re   re   rf   Ú	test_frac÷   s   &(""" &rš   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   rW   r[   r_   )rD   r!   r1   rN   r2   re   re   re   rf   Útest_issue_14355  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 )NrN   T©ÚrealrZ   r   rV   )r   rD   r,   r1   r%   r
   r   ©rN   re   re   rf   Ú	test_atan  s   $4rŸ   c                  C   s  t ttƒtdƒdksJ ‚t tttƒƒtdƒdksJ ‚t tttƒƒtdƒdks(J ‚t tttd ƒƒtdƒtdƒks:J ‚t ttt ƒttt ƒ dt  tdƒttƒksTJ ‚t tttƒtd  ƒtt	ƒdksfJ ‚t ttttƒtd  ƒtttd ƒtd d  ƒ d  tt	ƒdksŠJ ‚t tttd ƒd d ƒtddƒt	ksŸJ ‚t tttƒƒtdƒt	ks­J ‚t ttttƒƒƒtdƒt	ks½J ‚t
ddd} t tt| ƒd ƒt| ƒ | t	ƒdks×J ‚t | td|  t ƒttd|   ƒ  d | dƒdksóJ ‚t t| ƒt| ƒ | td	ƒd
ksJ ‚d S )Nr   rZ   rV   r\   rW   rP   Trp   r[   ra   )rD   ÚabsrN   r1   r-   r   rO   r   r   r
   r   r   ©rP   re   re   rf   Útest_set_signs  s   $4$H* (8(r¢   c                  C   st   t ddd} ttd|  ƒt| ƒ | ddƒtddƒksJ ‚ttdtt| ƒƒttd|  ƒƒ  ƒ| dƒtdƒks8J ‚d S )	NrN   Trœ   rZ   r   rW   ra   rV   )r   rJ   r1   r,   rH   rD   r   r%   rž   re   re   rf   Útest_heuristic4  s   ,<r£   c                  C   sN   t ddd} d|  t|  t ƒ }t|ttƒdksJ ‚| tt¡dks%J ‚d S )NrP   Trp   ra   r   )r   r   rN   rD   r
   )rP   Úfre   re   rf   Útest_issue_3871:  s   r¥   c                  C   s  t dƒ} t ddd}td||   |  | tƒt|ƒksJ ‚td|d|    |  | tƒt|d ƒks2J ‚td|d|  d   |  | tƒt|d ƒksJJ ‚t|d |d  | |tƒtdƒks^J ‚tddd|  |  |tƒdtj kssJ ‚tdd|  | d| |  |tƒttd	ƒƒksJ ‚d S )
NrR   rN   Trœ   rZ   rV   r_   ry   z1/3)r   rD   r
   r   r   ÚExp1©rR   rN   re   re   rf   Útest_exponentialA  s   $,0(*8r¨   c                  C   s8   t dƒ} tdt| t| ƒ   |  | tƒttƒksJ ‚d S )NrR   rZ   )r   rD   rN   r1   r
   r   )rR   re   re   rf   Útest_exponential2L  s   0r©   c                  C   s.   t dt tƒ} t| ttƒ}| ¡ tu sJ ‚d S rˆ   ©rA   rN   rC   r
   r‹   ©r¤   Úlre   re   rf   Ú	test_doitQ  s   r­   c                  C   sÌ  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d d t ttƒtd	tƒksÊJ ‚dt  ttƒd t  }t |ttƒtd	tƒksäJ ‚d S )
NrZ   r_   rV   ra   r\   r`   F)Úevaluater   )rD   r1   rQ   r
   rH   r-   rI   rF   r   rR   Úrewriter   r‹   rN   )ÚloÚhiÚt1Út2Úere   re   rf   Útest_series_AccumBoundsW  s   *.. 848*rµ   c                   C   s  t tdtƒttƒdksJ ‚t tdtƒtt ƒdksJ ‚t tdtƒttt ƒtt ks,J ‚t tdtƒtt t ƒt t ks?J ‚t tdtƒttƒdksLJ ‚t tdtƒtt ƒdksZJ ‚t tdtƒttt ƒt ksjJ ‚t tdtƒtt t ƒt ks{J ‚t tdtƒttƒtksˆJ ‚t tdtƒtt ƒt ks—J ‚t tdtƒttt ƒdks¦J ‚t tdtƒtt t ƒdks¶J ‚t tdtƒttƒdksÃJ ‚t tdtƒtt ƒt t ksÔJ ‚t tdtƒttt ƒdksãJ ‚t tdtƒtt t ƒdksóJ ‚t tdtƒttƒdksJ ‚d S ©NrZ   r   )rD   r5   rN   r
   r   r4   r3   r6   re   re   re   rf   Ú!test_bessel_functions_at_infinityn  s"   "& " "  r·   c                  C   s2   t dt tƒ} t| ttƒ}|jdd|ksJ ‚d S )NrV   F©Údeeprª   r«   re   re   rf   Ú
test_doit2‡  s   rº   c                   C   s.   t tttƒ ttƒd  tt ƒdksJ ‚d S r¶   ri   re   re   re   rf   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 )NrZ   rV   r|   r   )rD   r-   rN   r   r   r1   r    re   re   re   rf   Útest_issue_3792“  s   400r½   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$J ‚t ttƒtd d  tdƒtdƒd ks:J ‚t ttƒtd t  tdƒtdƒdt  ksRJ ‚d S )NrZ   r\   rV   r]   é   r|   )rD   rN   r	   r   r   ÚOner   re   re   re   rf   Útest_issue_4090™  s   "&,4rÀ   c                   C   s@   t ttƒtdddtu sJ ‚t ttƒttd dddksJ ‚d S )Nr   rW   rX   rV   )rD   r.   rN   r
   r   re   re   re   rf   Útest_issue_4547   s   $rÁ   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 )Nrq   é   r   g      à¿r|   )rD   rN   r
   r   re   re   re   rf   Útest_issue_5164¥  s
   , $rÃ   c                  C   s,   ddt   dt   } t| t dƒtksJ ‚d S )Nç      ð?r   )rN   rD   r   )Úfuncre   re   rf   Útest_issue_5383­  s   rÆ   c                  C   sp   t tdƒd  tt ƒ t  tdt ƒd  ttt ƒƒ tdƒdt    t d  } t| t tƒtdƒd ks6J ‚d S )NrZ   rV   rz   r\   ih  )rN   r   r   r   r   rD   r
   ©rw   re   re   rf   Útest_issue_14793²  s   *
ÿÿÿ rÈ   c            
   
   C   sb  t ttt gddgddtjtddƒgddgƒƒ} g t‘t‘t ‘t‘t t ‘t‘t dtddƒ  ‘t‘d‘d‘d‘d‘d‘d‘d‘d‘t‘t‘t‘t ‘t‘t t ‘t‘t dtddƒ  ‘d‘d‘d‘d‘d‘d‘d‘d‘R }t| ƒt|ƒks}J ‚t	t
| |ƒƒD ]*\}\}}|\}}}}|||  }	zt|	td|d|ks£J ‚W q„ ty®   	 J ‚w d S )	Nra   rZ   rV   r\   r[   rW   r   rX   )Úlistr   rN   r   r   r	   r
   r   ÚlenÚ	enumerateÚziprD   ÚAssertionErrorÚprint)
ÚtestsÚresultsÚirŒ   ÚresrO   Úsr´   ÚdÚeqre   re   rf   Útest_issue_5183¸  s‚   ý:ÿÿÿÿÿÿÿÿþþþþþþþþýýýýýýýýûûrÖ   c                  C   sº   t ttƒt ttƒdksJ ‚t ttƒttƒtd ksJ ‚t ttƒttƒtu s(J ‚t ttƒt ttƒdks6J ‚t ttƒttj	ƒt
tƒksEJ ‚tddd} t | td|  ƒ | dƒdks[J ‚d S )Nr   rV   ÚrTrœ   rZ   )rD   r1   rN   r
   r,   r   r>   r-   r   r   r%   r   ©r×   re   re   rf   Útest_issue_5184Ð  s   $rÙ   c                   C   s*   t dt dt  tj tdƒdksJ ‚d S r¶   )rD   rO   r   r¦   re   re   re   rf   Útest_issue_5229Û  ó   *rÚ   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 )NrV   r   r\   r[   rW   rX   )rÉ   r   r.   r2   r   r	   r
   rÊ   rË   rÌ   rN   rD   rÍ   rÎ   )	rÏ   rÐ   rÑ   rŒ   rÒ   r¤   r¬   rÔ   rÕ   re   re   rf   Útest_issue_4546ß  s$   
 þÿ
ûûrÜ   c                   C   sX   t dttdƒ  dt  tdƒdksJ ‚t ddt  ddt   t tdƒdks*J ‚d S )NrZ   r\   r   r]   )rD   rN   r   re   re   re   rf   Útest_issue_3934ô  s   (0rÝ   c                   C   sX   t ttddƒ dttddƒ   ttƒdksJ ‚t td dtd   ttƒdks*J ‚d S )NéM   r\   rZ   gfffffFY@)rD   rN   r	   r
   re   re   re   rf   Útest_calculate_seriesù  s   0(rß   c                   C   sž   t td dtd   ttƒdksJ ‚t td dtd   ttƒdks$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 )NrÂ   rZ   éd   i]  éè  ©rD   rN   r
   r   re   re   re   rf   Útest_issue_5955  s   $$$2rã   c                   C   s0   t tdttƒ ƒtttƒƒ tdƒdksJ ‚d S r¶   )rD   r   r1   rN   r.   re   re   re   rf   Útest_newissue  rŠ   rä   c                   C   s¼   t tt ttƒttt ttƒksJ ‚t dtttƒ  t tdƒtdtttƒ  t tdƒks0J ‚t tt ttƒttt ttƒksBJ ‚t tt dt  ttƒttt dt  ttƒks\J ‚d S r¶   )rD   rN   r
   rC   r1   re   re   re   rf   Útest_extended_real_line  s   $<$8rå   c                  C   sJ   t ddd} t| ƒt td| ƒksJ ‚tt| d d  | tƒtu s#J ‚d S )NrN   Trp   rZ   rV   r|   )r   rK   r
   rD   rž   re   re   rf   Útest_order_oo  s   $ræ   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 r~   ©rD   r   rN   rO   r
   re   re   re   rf   r˜     ó    z!test_issue_5436.<locals>.<lambda>c                   S   s   t tt t ƒttƒS r~   rè   re   re   re   rf   r˜      s    ©rM   ÚNotImplementedErrorre   re   re   rf   Útest_issue_5436  ó   rì   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   rX   ©rC   rN   re   re   re   rf   r˜   $  ó    z test_Limit_dir.<locals>.<lambda>c                   S   s   t ttdddS )Nr   Ú0rX   rî   re   re   re   rf   r˜   %  rï   )rM   Ú	TypeErrorr™   re   re   re   rf   Útest_Limit_dir#  rí   rò   c                   C   s^   t td d td d d  ttƒdksJ ‚t td d td d d  tt ƒdks-J ‚d S )NrZ   rá   rk   re   re   re   rf   Útest_polynomial(  s   ,2ró   c                   C   sŽ   t dt dtt  ttt  t  t  ttƒtd tt  ks"J ‚t dt dtt  ttt  t  t  tt ƒtd tt  ksEJ ‚d S ©NrZ   )rD   rO   rN   rP   r
   re   re   re   rf   Útest_rational-  s   DJrõ   c                   C   s<   t ttƒt tdt ƒt  tdƒtttt ƒ ksJ ‚d S ©NrV   r   )rD   r   rN   rP   rO   r
   r   re   re   re   rf   Útest_issue_57402  ó   <r÷   c                  C   s^   t dddd} | d t| d   t| d  d  ttd   }t|tdƒ ¡ | d ks-J ‚d S )NrR   TrS   rZ   rV   )r   rN   rD   Úcancel)rR   r×   re   re   rf   Útest_issue_63666  s   0 rú   c                  C   s„   t tƒ} t| ttƒtu sJ ‚tt|  ttƒdksJ ‚t| tdt t ƒtt t   ttƒdks2J ‚t| tt ƒtt ƒks@J ‚d S )Nr   rV   rZ   )r   rN   rD   r
   r%   r   r   r>   ©r¤   re   re   rf   Útest_factorial<  s
   0 rü   c                  C   s¸   dt d  d t tddƒ  tdt d  d tj  dt d  d  dt d  d  tddƒ dtd    } t| ttƒdt d  d dt d  d  dt  d  tddƒ ksZJ ‚d S )	Nr]   r\   r|   rV   é#   rm   é   rZ   )rN   r	   rO   r   r   rD   r
   ©r´   re   re   rf   Útest_issue_6560F  s   4ÿÿÿ
ÿJr   c                     s$  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 )NrR   r×   Trp   rt   ÚpÚm)ÚnegativerV   rZ   c                      s   t ˆ ˆtƒS r~   )rD   r
   re   ©rw   rR   re   rf   r˜   U  s    z!test_issue_5172.<locals>.<lambda>)r   ÚsubsrM   rë   rD   r
   rF   )r×   rt   r  r  re   r  rf   Útest_issue_5172K  s$   *.ÿÿ
ÿ"ÿr  c                  C   s,   t dƒ} tttt|   ƒttƒdksJ ‚d S )Nrr   rZ   )r   rD   r%   rN   r
   ©rr   re   re   rf   Útest_issue_7088[  s   $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 )NrV   r   r[   r_   rZ   ra   r\   )rD   r+   r   rN   r   r'   r,   r   r
   r(   r   r   r*   r)   r   r%   r#   re   re   re   rf   Útest_branch_cuts`  sT   (&&,&&$.(0,,"&">>:B"6:@:6<<:&***"&&&.226r	  c                  C   sj   t dƒ} tdtdt ƒt| ƒd   tdt ƒt| ƒd    }t|tdƒdt| ƒd tj  ks3J ‚d S )Nrr   rZ   rV   r   )r   rP   r%   r1   r-   rD   r   r   )rr   r´   re   re   rf   Útest_issue_6364  s   8*r
  c                   C   s6   t tdtt ƒ ƒtd  tdƒtdt ƒksJ ‚d S rö   )rD   r   r7   rN   r   re   re   re   rf   Útest_issue_6682–  ó   6r  c                  C   s”   t dƒ} t| t tdƒtt| ƒ ksJ ‚t|  t tdƒt t| ƒ ks&J ‚t|  t ttƒt t| ƒ ks8J ‚t| t ttƒtt| ƒ ksHJ ‚d S )Nrr   r   )r   rD   rN   r
   r   r  re   re   rf   Útest_issue_4099š  s
    $$$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dxrZ   r   rV   )r   rD   r%   r   rN   )r  re   re   rf   Útest_issue_4503¢  s   .ÿr  c                  C   sJ   t ddddt ƒ} t| ƒ}t|tddƒdksJ ‚t|ttƒt ks#J ‚d S )Nre   )rZ   )r   r   r^   )r@   rN   rG   rD   r
   )ÚGÚgre   re   rf   Útest_issue_6052¨  s   r  c                  C   sj   t tƒtdt dt ƒƒ } ttt| ttƒ |  tdƒdksJ ‚ttt| ttƒ |  tdƒ ¡ dks3J ‚d S )NrZ   rm   r   rV   g       @)r%   rN   r3   rD   r   ZevalfrÇ   re   re   rf   Útest_issue_7224¯  s   $,r  c                   C   s&   t ttddƒd  ttƒdksJ ‚d S )NrZ   g    eÍÍAr   )rD   rR   r	   r
   re   re   re   rf   Útest_issue_8208µ  ó   &r  c                   C   s<   t ttddƒ d ttƒd tddƒ  tdƒdksJ ‚d S )NrZ   r|   rV   r\   rÂ   r   )rD   rN   r	   r%   re   re   re   rf   Útest_issue_8229¹  rø   r  c                  C   s4   t ddd\} }ttd||   ƒ|tƒdksJ ‚d S )Nzd tTrp   rZ   ra   )r   rD   r8   r
   )rÔ   Útre   re   rf   Útest_issue_8433½  s   $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 )NrQ   T)rT   ZnonnegativeÚlamdarp   r   )r   rD   r   r   r
   )rQ   r  re   re   rf   Útest_issue_8481Â  s   .r  c                   C   sJ   t tttd ƒttƒtksJ ‚t tttd ƒdt   ttƒdks#J ‚d S )NrV   r\   r   )rD   r   rR   r
   re   re   re   rf   Útest_issue_8462È  s   ,r  c                  C   s@   t dddd} t dƒ}t||  |t ƒttd|  ƒ ksJ ‚d S )NrR   TrS   rN   ra   )r   rD   r
   r   r§   re   re   rf   Útest_issue_8634Í  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 )NrN   Trœ   rQ   rp   r   r]   g      @rZ   rV   )r   rD   rR   r
   )rN   rQ   re   re   rf   Útest_issue_8635_18176Ó  s   $$$($*r  c                   C   s   t ttƒttƒtu sJ ‚d S r~   )rD   r   rN   r
   re   re   re   rf   Útest_issue_8730ß  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$J ‚tt‡ ‡fdd	„ƒ d S )
NrR   T)rT   rt   rp   rZ   r   c                      s$   t tˆƒˆtˆƒ  ˆ ˆ  ˆtƒS r~   )rD   r   r
   re   ©rt   rR   re   rf   r˜   è  s   $ z!test_issue_9252.<locals>.<lambda>)r   rD   r   r
   rM   rë   re   re   r   rf   Útest_issue_9252ã  s   0r!  c                   C   s"   t ttƒd tddƒdksJ ‚d S )Nrþ   r   r[   )rD   r1   rN   re   re   re   rf   Útest_issue_9558ë  s   "r"  c                   C   s2   t dt ttdt tƒd   ttƒtksJ ‚d S )NrÂ   rV   )rD   rQ   r   r
   r   re   re   re   rf   Útest_issue_10801ï  s   2r#  c                  C   s8   t ddd\} }tt| | ƒt| ƒ | dƒ|ksJ ‚d S )Nzs xTrœ   r   )r   rD   r8   )rÓ   rN   re   re   rf   Útest_issue_10976ô  s   (r$  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 ©NrZ   rV   )rD   r   rR   r   r%   r   r
   re   re   re   rf   Útest_issue_9041ù  rø   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, ar[   rV   )r   rC   Zfree_symbols)rN   rO   rr   re   re   rf   Útest_issue_9205ý  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   r\   rZ   )rD   r   rR   r
   re   re   re   rf   Útest_issue_9471  s   &.r)  c                   C   s$   t ttdt ƒƒttƒdksJ ‚d S r%  )rD   r9   r   rN   r
   re   re   re   rf   Útest_issue_11496
  ó   $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   rZ   )rF   rD   rN   rO   rR   re   re   re   rf   Útest_issue_11879  rø   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 )NrQ   rÄ   rZ   g333333Ó?r\   é
   )r   rD   r
   r	   )rQ   re   re   rf   Útest_limit_with_Float  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 ©Nr\   rZ   rV   )rD   rN   r
   r	   re   re   re   rf   Útest_issue_10610  ó   Dr0  c                   C   s  t ttƒttƒ tddƒtdƒksJ ‚t ttƒttƒ tddƒtdƒdt t  ks,J ‚ttdd„ ƒ t ttƒttƒ ttƒtksCJ ‚t ttƒt	tƒ tddƒtdƒksVJ ‚t ttƒt	tƒ tddƒt kshJ ‚ttdd„ ƒ t ttƒt	tƒ ttƒtksJ ‚d S )Nr   rW   rV   r[   c                   S   ó   t ttƒttƒ tddƒS r—   )rD   r   rN   r   re   re   re   rf   r˜     ó    z"test_issue_10868.<locals>.<lambda>c                   S   r2  r—   )rD   r   rN   r   re   re   re   rf   r˜   #  r3  )
rD   r   rN   r   r   r   rM   r™   r
   r   re   re   re   rf   Útest_issue_10868  s   &2 &$$r4  c                   C   s$   t tttƒ t ttƒdksJ ‚d S rô   )rD   rR   r-   r
   re   re   re   rf   Útest_issue_6599'  r+  r5  c                   C   sn   t dt dtd   td ttƒ  tt ƒdksJ ‚t dt dtd   td ttƒ  ttƒtu s5J ‚d S )Nr\   rV   r-  ri   re   re   re   rf   Útest_issue_12555+  s   68r6  c                  C   sÒ  t ddd\} }}t dddd\}}}}}}}	|| ||  |  | t|d |d|   |d  |d  |d|  |d  |d  |d   |d|  |d|   |d  |d  |d d|  d   d|d|   ||d   | |  | |d d|  d   d||d   |d|   | |  | |d d|  d   d||d   ||d   |d  |d   |d |d d|  d   ƒ ||  | |  d  }
|
 ||¡jddt|
||ƒjddksçJ ‚d S )	Nzr z xTrœ   za b s0 K F0 s T)rU   r   rV   rZ   r¸   )r   r%   r  ÚfactorrD   )r×   rP   rN   rr   rs   Ús0ÚKZF0rÓ   ÚTÚfxre   re   rf   Útest_issue_127690  s$   :"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   r]   éûÿÿÿrZ   i@¶  rV   ry   iúÿÿÿé   é$   )rD   r%   rN   r   r   r
   r	   re   re   re   rf   Útest_issue_13332<  s   BÿÿÿrA  c                   C   sò   t td tttƒ  ttƒ tt ƒtu sJ ‚t td tttƒ  ttƒ ttƒtu s-J ‚t tttƒ d  ¡ ttƒtu s?J ‚t tttƒ d  ¡ ttƒtu sQJ ‚t tttƒ d  ¡ tt ƒtu sdJ ‚t tttƒ d  ¡ tt ƒtu swJ ‚d S rˆ   )rD   rN   r1   r-   r
   Úexpandre   re   re   rf   Útest_issue_12564A  s   .,$$&*rC  c                   C   rç   )Nc                   S   s   t ttƒttƒ ¡ S r~   )rC   r   rN   r   r‹   re   re   re   rf   r˜   K  ré   z"test_issue_14456.<locals>.<lambda>c                   S   s   t td td  ttƒ ¡ S )NrV   rZ   )rC   rN   r   r‹   re   re   re   rf   r˜   L  s    rê   re   re   re   rf   Útest_issue_14456J  rí   rD  c                   C   sB   t dtdt t td  ƒ tdt dt d  ƒt u sJ ‚d S )Nr\   r|   é   rV   )rD   r0   r   rN   r
   re   re   re   rf   Útest_issue_14411O  s   BrF  c                   C   s8   t ttd d d td d  d  ttƒdksJ ‚d S r%  rk   re   re   re   rf   Útest_issue_13382S  s   8rG  c                   C   s<   t tdtttd ƒ d tttƒ    ttƒdksJ ‚d S )Nra   rZ   ©rD   rN   r   r
   re   re   re   rf   Útest_issue_13403W  rø   rI  c                   C   sb   t td  ttƒd  td td d  ttd ƒd   td ttƒd   ttƒdks/J ‚d S r/  rH  re   re   re   rf   Útest_issue_13416[  s   brJ  c                   C   sx   t td dt dddt   t  d  t td  d td  t   ttƒtd d td d  td  ks:J ‚d S )NrV   rZ   r|   r\   rE  rm   rz   )rD   rR   rN   r
   re   re   re   rf   Útest_issue_13462_  s   xrK  c                  C   sH   t dƒ} tt| t ƒttƒdksJ ‚ttttƒt ƒttƒdks"J ‚d S )Nrr   ra   )r   rD   r8   rN   r
   r%   r  re   re   rf   Útest_issue_13750c  s   $rL  c                   C   sž   t tttƒttƒ ttƒtƒsJ ‚t tttƒttƒ ttƒtƒs"J ‚t tttttƒƒƒttƒtƒs3J ‚tddtd ttƒ   td t  ttƒtksMJ ‚d S r%  )	Ú
isinstancerD   r1   rN   r   r
   rC   r-   r   re   re   re   rf   Útest_issue_14276i  s   """8rN  c                   C   s0   t dttƒttƒ  dt  ttƒdksJ ‚d S rô   )rD   r   rN   r
   re   re   re   rf   Útest_issue_14514p  rŠ   rO  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 rˆ   )rD   r1   rN   r-   r2   r/   r
   rH   r   rc   rd   r.   r¿   re   re   re   rf   Útest_issues_14525t  s   >>...2@rP  c                   C   s4   t ttƒtttd  ƒ td  ttƒdksJ ‚d S )NrV   rZ   r   )rD   r%   rN   r-   r
   re   re   re   rf   Útest_issue_14574~  ó   4rQ  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 )Nr\   r]   rV   ra   r|   r_   )rD   r<   rN   r
   r   r   r	   r;   re   re   re   rf   Útest_issue_10102‚  s   "" "rS  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 r~   )rD   r   r   rN   r1   r   r
   re   re   re   rf   r˜   Œ  s     z"test_issue_14377.<locals>.<lambda>rê   re   re   re   rf   Útest_issue_14377‹  ó   rU  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 )NrV   r_   r\   rZ   )rN   r=   rD   r
   r   rÿ   re   re   rf   Útest_issue_15146  s   8*ÿÿÿ rW  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 )NrV   r_   rZ   r¾   r-  r]   r\   )rN   rD   r
   r   r   r   rÿ   re   re   rf   Útest_issue_15202•  s   :FrX  c                   C   s0   t td td d  td  ttƒdksJ ‚d S )NiÐ  rZ   iÏ  i0øÿÿrk   re   re   re   rf   Útest_issue_15282  rŠ   rY  c                   C   s2   t t tttƒd ƒ t ttdddksJ ‚d S )NrZ   r[   rX   r   )rD   rN   r   r   r
   re   re   re   rf   Útest_issue_15984¡  ó   2rZ  c                   C   s&   t ttdƒttƒ ttƒdksJ ‚d S rô   )rD   r?   rN   r>   r
   re   re   re   rf   Útest_issue_13571¥  r  r\  c                   C   s*   t tttƒƒtdƒtttjƒƒksJ ‚d S rô   )rD   r'   r:   rN   r   r¿   re   re   re   rf   Útest_issue_13575©  rÛ   r]  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   r^   rX   rZ   rV   )rC   r1   rN   r‹   r
   r   re   re   re   rf   Útest_issue_17325­  s   $ $$r^  c                   C   s   t tƒ td¡dksJ ‚d S )Nr   )r   rN   rD   re   re   re   rf   Útest_issue_10978´  r  r_  c                   C   s    t ttd ƒttƒtu sJ ‚d S rˆ   )rD   r!   rR   r
   re   re   re   rf   Útest_issue_14313_comment¸  ó    r`  c                  C   s2   ddt   t   t ¡} t| t ddddksJ ‚d S )NrZ   rW   rX   )rN   r   rD   )rÔ   re   re   rf   Útest_issue_15323¼  s   rb  c                   C   s,   t tttƒ ƒ ttƒ tdƒdksJ ‚d S rô   )rD   r   r   rN   re   re   re   rf   Útest_issue_12571Â  ó   ,rc  c                   C   sH   t td td t t  td td  td   ttƒtdƒks"J ‚d S r/  râ   re   re   re   rf   Útest_issue_14590Æ  ó   Hre  c                  C   sR   t dƒ\} }tt| t|  t|  t|    ttƒ|t|  |   |  ks'J ‚d S )Núa b)r   rD   rN   rO   ©rr   rs   re   re   rf   Útest_issue_14393Ê  s   Fri  c                   C   s@   t ttd ƒdtd   ttƒdt   ttƒtdƒksJ ‚d S )NrZ   ra   )rD   r   rR   r
   r   re   re   re   rf   Útest_issue_14556Ï  ó   @rj  c                   C   sL   t dtdƒd td   dt  dtdƒd td    ttƒtks$J ‚d S )NrZ   rV   r\   r|   ©rD   r   rN   r
   re   re   re   rf   Útest_issue_14811Ó  s   Lrm  c                   C   s    t ttƒtdƒtdƒksJ ‚d S )Ni Êš;)rD   r   rN   re   re   re   rf   Útest_issue_16222×  ra  rn  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 rô   râ   re   re   re   rf   Útest_issue_16714Û  r1  ro  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 )NrP   Trp   rZ   )rU   rT   )r   rD   r   rR   r
   r>   r¡   re   re   rf   Útest_issue_16722ß  s   48rp  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 )NrZ   rV   r   r\   )rD   rR   r   r
   re   re   re   rf   Útest_issue_17431æ  s"   $ÿÿÿÿÿ0ÿÿ4rq  c                   C   s2   t tttƒ ƒtttƒƒt  tdƒtksJ ‚d S rô   )rD   r7   r   rN   r   re   re   re   rf   Útest_issue_17671î  r[  rr  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 xTrp   rZ   rV   )r   rD   r%   r
   )rr   rs   rt   rN   re   re   rf   Útest_issue_17751ò  s   Rrs  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%  )rD   r   rR   r%   r   r
   r   re   re   re   rf   Útest_issue_17792÷  rk  rt  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   r[   ra   rW   rZ   )rD   r   r1   rN   re   re   re   rf   Útest_issue_18118û  s   "ru  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   rW   rZ   )rD   r1   r%   rN   re   re   re   rf   Útest_issue_18306   r¼   rv  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 )Nr\   rà   )rD   r   r   rN   r
   re   re   re   rf   Útest_issue_18378  rø   rw  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 )NrZ   rV   r\   )rD   r   rN   r
   r   re   re   re   rf   Útest_issue_18399  s   ,rx  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 )NrV   r[   rX   )rD   r2   rN   r%   r   r
   rC   re   re   re   rf   Útest_issue_18442  rf  ry  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   rZ   r[   )rD   r    r   rN   re   re   re   rf   Útest_issue_18452  s    &rz  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 )NrZ   r[   rX   rV   r-  r   )rD   r1   rN   r
   rC   r-   r2   rH   re   re   re   rf   Útest_issue_18473  s   888$$@***,.2r{  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 ©NrV   r\   rZ   )rD   r   rN   r
   re   re   re   rf   Útest_issue_18482&  rk  r}  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 )NrZ   r   rV   rW   rX   r[   )rD   r1   rN   r%   r-   re   re   re   rf   Útest_issue_18508*  s   ,06r~  c                   C   rT  )Nc                   S   s   t tdt t ƒttƒS rˆ   )rD   r   rR   rN   r
   re   re   re   rf   r˜   1  s    z"test_issue_18521.<locals>.<lambda>rê   re   re   re   rf   Útest_issue_185210  rV  r  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 )Nrg  Trp   )r   rD   r   r   rh  re   re   rf   Útest_issue_189694  s   (r€  c                   C   s,   t tttƒdt   ttƒtdƒksJ ‚d S rô   )rD   rR   r   r
   r   re   re   re   rf   Útest_issue_18992:  rd  r  c                  C   s<   t dƒ} tt| ƒt| d ƒt| d ƒ  | dƒdksJ ‚d S )NrN   rZ   rV   r   ra   )r   rD   r>   rž   re   re   rf   Útest_issue_19067>  s   4r‚  c                   C   s*   t tdt dt    ttƒdksJ ‚d S r|  rk   re   re   re   rf   Útest_issue_19586C  rÛ   rƒ  c                  C   s0   t dƒ} t ddd}t| | | dƒdksJ ‚d S )NrR   r  T)Úzeror   )r   rD   )rR   r  re   re   rf   Útest_issue_13715G  s   r…  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/  )rD   rR   r1   r
   re   re   re   rf   Útest_issue_15055M  s   Tr†  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 viTrp   zB ti dr_   rV   r   )r   rD   r%   )r  ÚviÚBÚtirÔ   re   re   rf   Útest_issue_16708Q  s   drŠ  c                   C   s†   t tddt ƒttdtƒd   ttƒdtdƒ t d ks J ‚t tddt ƒttdtƒd   tt ƒdtdƒ t d ksAJ ‚d S )NrZ   r\   rV   r_   )rD   r3   rN   r
   r%   r   re   re   re   rf   Útest_issue_19154W  s   @Fr‹  c                  C   sN  t ddd} t ddd}t ddd}t ddd}t ddd}td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betaTrp   Úhr  Úomegar  rZ   r\   rV   rq   r|   r   )r   r   r   r   rD   r
   rF   )rŒ  r  r  Úwr  r´   Úqr  rÓ   ÚZr   re   re   rf   Útest_issue_19453\  s   (Lÿ (r’  c                   C   s&   t tdƒ d t ttƒdksJ ‚d S )NrZ   r|   r   rl  re   re   re   rf   Útest_issue_19739o  r  r“  c                   C   s2   t dt  tdtd  d ƒ ttƒdksJ ‚d S )NrV   r|   rZ   )rD   rN   r%   r
   re   re   re   rf   Útest_issue_19766s  r[  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 )
Nr  r[   rX   Trœ   )Znonzerora   rZ   r   )r   rD   r-   rN   r
   rC   rH   )r  re   re   rf   Útest_issue_19770w  s   88"$r•  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$J ‚t ttƒtttƒƒ ttd ddtttƒtttƒƒ ttd ddksJJ ‚t ttƒtttƒƒ ttd ddtttƒtttƒƒ ttd ddkspJ ‚t tttƒƒttd ƒtddƒksƒJ ‚t dtt ƒ  tt tƒks•J ‚tdttƒ  tt tƒks¥J ‚tdtt ƒ  tt tƒks¶J ‚t dttƒ  tt tƒksÇJ ‚d S )NrV   rW   rX   r[   r^   ra   rZ   )rD   r2   rN   r1   r   rC   rH   r
   re   re   re   rf   Útest_issue_7535ƒ  s   HLL&$ "&r–  c                   C   s2   t td dt  t t tdƒt d ksJ ‚d S )NrZ   r   rV   )rD   rN   r   re   re   re   rf   Útest_issue_20365Ž  r[  r—  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 )NrZ   rV   r   )rD   rN   r+   r   re   re   re   rf   Útest_issue_21031’  rf  r˜  c                   C   s0   t ttt ƒdt d  tdƒtd ksJ ‚d S )Nr\   rz   r|   )rD   r1   r   rN   re   re   re   rf   Útest_issue_21038–  rŠ   r™  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 )NrZ   r   rW   r[   r^   )r    rN   r1   rD   rÇ   re   re   rf   Útest_issue_20578š  s   rš  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)ZlogxrZ   )r   rN   ZnseriesrO   rû   re   re   rf   Útest_issue_21227¡  s      $r›  c                  C   sH   t d tdt d  ƒ } |  t d¡dksJ ‚|  ¡  t d¡dks"J ‚d S r¶   )rN   r-   rD   rB  )r   re   re   rf   Útest_issue_21415º  s   rœ  c                   C   s(   t ttd ƒttƒ ttƒtksJ ‚d S rô   )rD   r   rR   r
   r   re   re   re   rf   Útest_issue_21530À  s   (r  c                  C   sD   t dƒd d } tt|  td t d  t| ƒt dƒd ks J ‚d S )Nr]   rZ   rV   )r%   rD   rN   rØ   re   re   rf   Útest_issue_21550Ä  s   4rž  c                  C   sL   t ttd  ttƒd  d t tdƒ} | tdƒd dtdƒ  ks$J ‚d S )NrZ   é   l   ’Ñqjl   SÍ[	)rD   rN   r   r   )Úoutre   re   rf   Útest_issue_21661É  s   ($r¡  c                   C   s6   t tttƒtt   td¡tdƒtdƒd ksJ ‚d S )Nr¾   r   rZ   i Ø	 )rD   r5   rP   rN   r  r   re   re   re   rf   Útest_issue_21701Î  r  r¢  c                  C   sD   t ddd} tdtdt|  d    tƒ}| tt¡tjks J ‚d S )Nrr   Trœ   rZ   rV   )r   rB   r   rN   rD   r
   r   r   )rr   r   re   re   rf   Útest_issue_21721Ò  s   r£  c                  C   sd   dt dt t t ƒ dt dt t t d ƒ  } |  td¡dks$J ‚t| ƒ td¡dks0J ‚d S )NrZ   r_   r]   r   )r   r   r   rP   rD   r   )Útermre   re   rf   Útest_issue_21756Ø  s   4r¥  c                  C   s@   t dƒ} t| d  td  dtd   ƒ | dd¡tksJ ‚d S )Nrr   rV   rZ   r[   )r   r%   rN   rD   r   r  re   re   rf   Útest_issue_21785Þ  s   8r¦  c                   C   s&   t dt dt   ttƒdksJ ‚d S )Nra   rV   r   rk   re   re   re   rf   Útest_issue_22181ã  r  r§  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=  rV   ry   rþ   r]   é<   r[   r   T)ÚforcerW   )
r%   r,   r2   rN   r   r   rD   r   rE   r
   )Úe1Úe2rw   Úexpr2re   re   rf   Útest_issue_22220ç  s    (6,ÿÿ$$$0.r­  c                  C   sâ   t ddd\} }t|d |  |d | d  || d    |tƒd| d  ks(J ‚t|d |  |d | d  || d    ¡  |tƒd| d  ksJJ ‚t|d |  |||   |d |    |d |    |tƒd| d  ksoJ ‚d S )Nzk, nTrp   rZ   )r   rD   r
   rB  )rQ   rR   re   re   rf   Útest_issue_22334ý  s   @DNr®  c                   C   s0   t tddt  ƒttƒ ttƒtdƒksJ ‚d S r%  )rD   r   rN   r%   r
   re   re   re   rf   Útest_sympyissue_22986  rŠ   r¯  c                  C   s>   dt  dt    dt  dt     } t| t t ƒdksJ ‚d S )NrV   ra   )rN   rD   r
   rû   re   re   rf   Útest_issue_23231  s   $r°  c                   C   s4   t dt td  tdt ƒ tdtfƒtksJ ‚d S )NrZ   rV   ra   r   )rB   rN   r   r
   re   re   re   rf   Útest_issue_23596  rR  r±  c                  C   sº   t t td  t d ƒ} t t td  tt  d ƒ}t| tddƒt dƒ t ks,J ‚t| tddƒt dƒ t ks<J ‚t|tddƒt dƒt ksKJ ‚t|tddƒt dƒ t ks[J ‚d S )NrV   r\   r   rW   r[   )r%   r   rN   rD   )Úexpr1r¬  re   re   rf   Útest_issue_23752  s     $r³  c                  C   s†   t ttd ttƒ ƒƒ t¡} |  tt¡dksJ ‚|  ¡  tt¡dks%J ‚|  	t
¡ tt¡dks2J ‚|  	t
¡ ¡  tt¡dksAJ ‚d S rˆ   )r   r2   r   r   rN   r   rD   r
   rF   r¯   r1   )r;  re   re   rf   Útest_issue_24276  s
   "r´  N(  Ú	itertoolsr   Zsympy.concrete.summationsr   Zsympy.core.functionr   r   Z
sympy.corer   Zsympy.core.numbersr   r   r	   r
   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z(sympy.functions.combinatorial.factorialsr   r   r   Z$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   rg   rj   rl   ro   rx   r{   r}   r‡   r‰   r   r‘   r’   r•   r–   rš   r›   rŸ   r¢   r£   r¥   r¨   r©   r­   rµ   r·   rº   r»   r½   rÀ   rÁ   rÃ   rÆ   rÈ   rÖ   rÙ   rÚ   rÜ   rÝ   rß   rã   rä   rå   ræ   rì   rò   ró   rõ   r÷   rú   rü   r   r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r!  r"  r#  r$  r&  r'  r)  r*  r,  r.  r0  r4  r5  r6  r<  rA  rC  rD  rF  rG  rI  rJ  rK  rL  rN  rO  rP  rQ  rS  rU  rW  rX  rY  rZ  r\  r]  r^  r_  r`  rb  rc  re  ri  rj  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r}  r~  r  r€  r  r‚  rƒ  r…  r†  rŠ  r‹  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r  rž  r¡  r¢  r£  r¥  r¦  r§  r­  r®  r¯  r°  r±  r³  r´  re   re   re   rf   Ú<module>   sŒ    $8 G
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


0	
	

	