a
    kº”h=@  ã                   @   sÀ  d dl 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 d dlmZmZ d dlmZ d dlmZmZmZmZ d d	lmZmZ d d
lmZmZmZ d dl m!Z! d dl"m#Z# d dl$m%Z%m&Z&m'Z'm(Z( d dl)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/ d dl0m1Z1m2Z2m3Z3m4Z4 edddZ5edddZ6dZ7dd„ Z8e4dd„ ƒZ9dd„ Z:e4dd„ ƒZ;dd„ Z<e1dd „ ƒZ=d!d"„ Z>e1d#d$„ ƒZ?d%d&„ Z@d'd(„ ZAd)d*„ ZBd+d,„ ZCd-d.„ ZDd/d0„ ZEd1d2„ ZFd3d4„ ZGd5d6„ ZHd7d8„ ZId9d:„ ZJd;d<„ ZKd=d>„ ZLd?d@„ ZMdAdB„ ZNdCdD„ ZOdEdF„ ZPdGdH„ ZQdIdJ„ ZRdKdL„ ZSdMdN„ ZTdOdP„ ZUdQdR„ ZVdSdT„ ZWe1dUdV„ ƒZXdWdX„ ZYdYdZ„ ZZd[d\„ Z[d]d^„ Z\d_d`„ Z]dadb„ Z^dcdd„ Z_dedf„ Z`e1dgdh„ ƒZadidj„ Zbdkdl„ Zcdmdn„ Zddodp„ Zedqdr„ ZfdsS )té    )Ú
EulerGamma)ÚFunction)ÚEÚIÚIntegerÚRationalÚooÚpi)ÚS)ÚSymbol)ÚexpÚlog)Úsqrt)ÚacotÚatanÚcosÚsin)ÚEiÚerf)ÚdigammaÚgammaÚloggamma)Úzeta)Úcancel)ÚcoshÚcothÚsinhÚtanh)ÚcompareÚmrvÚrewriteÚmrv_leadtermÚgruntzÚsign)ÚXFAILÚraisesÚskipÚslowÚxT)ÚrealÚmFc                   C   s   t stdƒ d S )Nr'   )Úrunslowr&   © r,   r,   úL/var/www/auris/lib/python3.9/site-packages/sympy/series/tests/test_gruntz.pyÚ_sskip#   s    r.   c                   C   sþ  t ttƒtdt tt ƒ ƒtdt ƒ  ttƒdks:J ‚t ttƒtdt tt ƒ ttd  ƒ ƒtdt tttƒ ƒ ƒ  ttƒdksJ ‚t ttttt ƒ ƒddt   ƒtttƒƒ ttƒtu sÎJ ‚t tttttt ƒ ƒƒƒttttƒƒƒ ttƒtu s
J ‚t ttttƒƒƒtttttttƒ ƒ ƒƒƒ ttƒtu sJJ ‚t ttttƒƒƒttttttttƒƒ ƒ ƒƒƒ ttƒdksŽJ ‚t tttƒƒtttttttƒƒ ƒ ƒƒ ttƒdksÊJ ‚t ttƒd ttttƒƒtttƒƒd  tttttƒƒƒttttƒƒƒd  ƒ ƒ ttƒ ttƒdks8J ‚t tttƒ ttttƒ td  ƒd  tttd dttdtd  ttƒ ƒƒ  ƒƒ ttƒtddƒks¨J ‚t tttt ƒ tt ƒtdtd  td  ƒ  ƒttƒ t ttƒtdƒ ks J ‚t dt dt  dt  ttƒdks*J ‚t ttttttdƒttƒ  ƒ ƒ ttƒtu s`J ‚t ttdttd t ƒ tttƒƒ ƒƒttdttƒ tttƒƒ ƒƒ ttƒtu sºJ ‚t tttddƒttd	d
ƒ  tddƒttddƒ   dtd   tddƒttddƒ   ƒƒd ttttddƒttd	dƒ  ƒ ƒƒtd
dƒ  ttƒtu s\J ‚t tdt tt ƒ dttƒ dtdtd  td  ƒ   ƒttƒ ttƒd  ttƒdksÀJ ‚t tttt ƒ tt ƒtdtd  td  ƒ  ƒttƒ ttƒdksJ ‚t ttƒtttƒtttƒƒ ƒtttƒƒ  tttƒttttƒƒƒ ƒ ttƒdkshJ ‚t tttttttƒtttƒƒ ƒ ƒƒtttttƒt ttƒ ƒƒƒ ƒttƒtksÂJ ‚t tttttt ƒ ƒƒƒtttƒƒ ttƒtu súJ ‚d S )Né   éÿÿÿÿé   é   r   éþÿÿÿé   é
   éûÿÿÿé   é   é   é   é   iøÿÿÿé6   é   é1   é-   é   é   )r"   r   r(   r   r   r   r   r   r,   r,   r,   r-   Útest_gruntz_evaluation(   s²    :*ÿÿÿ><.ÿÿ
2ÿÿ
<(&ÿÿþþ
(.ÿÿÿ
@ÿÿ
*6(ÿÿÿ
4
ÿÿÿ.þþþ
F
ÿÿÿ
Bÿ
,ÿÿÿ
&ÿÿÿ
rB   c                
   C   s  t ƒ  tttttƒddt   ƒƒttttƒddt  ttƒttƒ    ƒƒ ttƒt u sbJ ‚tttt dtt ƒ  ƒƒtt dtt dtt ƒ  ƒ  ƒ ttt tt dtt ƒ  ƒ ƒƒ tt dtt ƒ  ƒd  ttƒ t ttƒdksJ ‚d S ©Nr/   r1   )r.   r"   r   r(   r   r   r,   r,   r,   r-   Útest_gruntz_evaluation_slowa   s*    ,ÿÿÿB$ÿþþþþþrD   c                   C   s†  t ttƒtdt tt ƒ ƒtdt ttd  ƒ ƒ  ttƒdksHJ ‚t tttttƒ ƒ ƒttƒ tttƒƒ ttd ƒ ttƒdttƒ ks–J ‚t tttƒƒttdt tttƒ ƒ ƒƒttdt ƒƒ  ttƒdksàJ ‚t ttƒtttt ƒ ƒttƒ  ttƒtu sJ ‚t ttt	t	tƒƒƒƒt ttƒtt
ddƒƒksHJ ‚t ttt	ttƒƒƒƒt ttƒtt
ddƒƒks|J ‚t t	t	t	tƒƒƒttƒtu sžJ ‚t tttƒƒttƒtu s¼J ‚t ttdttƒ  ƒttƒ ttƒ tdt ƒ t ttƒ ttƒt
ddƒksJ ‚t tttdttƒ  ƒttƒ ttƒ  ttƒtjksLJ ‚t ttdttƒ  ƒttƒ ttƒ ttƒdks‚J ‚d S )Nr/   r1   r3   r0   )r"   r   r(   r   r   r   r   r	   r   r   r   r   r   r   r
   ÚHalfr,   r,   r,   r-   Útest_gruntz_eval_speciall   s:    H6ÿ
ÿ:ÿÿ444"0ÿÿÿÿ
.ÿ
rF   c                   C   sŒ   t ƒ  tttd ƒtdt ƒ tt ƒtttj  tttj  d    tt	ƒt	u sXJ ‚ttttt
t
t
tƒƒƒƒƒƒt tt	ƒdksˆJ ‚d S )Nr/   r1   é   r   )r.   r"   r   r(   r   r	   r   r
   rE   r   r   r,   r,   r,   r-   Útest_gruntz_eval_special_slow€   s    (ÿÿÿrH   c                   C   sH   t ƒ  tttttt ƒ ƒtdt ƒ ƒtttƒƒ ttƒtu sDJ ‚d S ©Nr/   )r.   r"   r   r   r(   r   r,   r,   r,   r-   Ú,test_grunts_eval_special_slow_sometimes_fail‡   s    rJ   c                   C   sL   t tttttƒ ƒ ƒttƒ tt ƒ tttƒƒ t ttƒdksHJ ‚d S )Nr0   )r"   r   r(   r   r   r,   r,   r,   r-   Útest_gruntz_EiŽ   s    rK   c                   C   sH   t ttdƒd t ƒtttt ƒ ƒttƒ  ttƒtdƒ ksDJ ‚d S )Nr1   r/   )r"   r   r   r(   r   r   r,   r,   r,   r-   Útest_gruntz_eval_special_fail’   s
    0ÿÿrL   c                   C   sj  t ttƒttƒtu sJ ‚t ttƒtt ƒtu s2J ‚t ttƒttƒtu sJJ ‚t ttƒtt ƒt u sfJ ‚t dttƒ ttƒ ttƒtu sŠJ ‚t dttƒ ttƒ tt ƒdks°J ‚t dttƒ ttƒ ttƒtu sÔJ ‚t dttƒ ttƒ tt ƒdksúJ ‚t ttƒttƒdksJ ‚t ttƒtt ƒdks0J ‚t ttƒttƒdksJJ ‚t ttƒtt ƒdksfJ ‚d S )Nr1   r/   r0   )r"   r   r(   r   r   r   r   r   r,   r,   r,   r-   Útest_gruntz_hyperbolic›   s    $&$&rM   c                   C   sØ  t dttƒdksJ ‚t tttƒtƒdks,J ‚t ttƒttd ƒtƒdksLJ ‚t ttd ƒtttƒƒtƒdkspJ ‚t dtttƒƒtƒdksŒJ ‚t tdtƒdks J ‚t ttƒttƒdks¸J ‚t ttd ƒttƒtƒdksØJ ‚t tttƒƒttd ƒtƒdksüJ ‚t tttƒƒdtƒdksJ ‚t ddtƒdks0J ‚t ddtƒdksFJ ‚t ddtƒdks\J ‚t ttd tƒdksvJ ‚t td td tƒdks”J ‚t td dt tƒdks²J ‚t dt tt tƒdksÐJ ‚t tt t tƒdksìJ ‚t ttƒtt ƒtƒdksJ ‚t tt ƒtdt ƒtƒdks0J ‚t tdt ƒttƒd tƒdksVJ ‚t ttƒd tttt ƒ ƒtƒdks‚J ‚t ttƒtttt ƒ ƒtƒdksªJ ‚t ttd ƒdttd ƒ tƒdksÔJ ‚d S )Nr1   ú<r/   ú>r2   ú=r6   )r   r(   r   r*   r,   r,   r,   r-   Útest_compare1ª   s0     $ $ $&,(rQ   c                   C   sd  t ttƒtd tƒdksJ ‚t ttd ƒttƒd tƒdks@J ‚t ttƒtttt ƒ ƒtƒdksfJ ‚t tttt ƒ ƒttƒtƒdksŒJ ‚t tttt ƒ ƒtt ƒtƒdks´J ‚t tt ƒttƒdksÎJ ‚t ttt ƒtƒdksèJ ‚t ttdt  ƒttƒdks
J ‚t tttƒ ƒttƒtƒdks.J ‚t ttttƒ ƒt ƒtttƒ ƒtƒdks`J ‚d S )Nr4   rO   r1   rP   rN   r/   ©r   r   r(   r,   r,   r,   r-   Útest_compare2Ê   s    $&&("$rS   c                   C   s2   t tttƒƒtttttƒ ƒ ƒtƒdks.J ‚d S )NrO   rR   r,   r,   r,   r-   Útest_compare3×   s    rT   c                   C   s<  t tdƒtƒdksJ ‚t tdƒtƒdks,J ‚t tdƒtƒdksBJ ‚t ttƒtƒdksXJ ‚t tt ƒtƒdkspJ ‚t ttƒtƒdks†J ‚t ttƒ tƒdksžJ ‚t ddt  tƒdks¸J ‚t ddt  tƒdksÒJ ‚t tdt ƒtƒdksìJ ‚t ttdƒ tƒdksJ ‚t td tƒdks J ‚t td tƒdks8J ‚d S )	Nr   r2   r/   r6   r0   éýÿÿÿr1   r4   )r#   r   r(   r   r   r   r   r,   r,   r,   r-   Ú
test_sign1Û   s    rV   c                  C   sŠ   t ttƒdksJ ‚t t tƒdks&J ‚tddd} t | tƒdksDJ ‚t |  tƒdksXJ ‚t | t tƒdksnJ ‚t |  t tƒdks†J ‚d S )Nr/   r0   ÚyT©Úpositive)r#   r(   r   ©rW   r,   r,   r-   Ú
test_sign2ë   s    r[   c                 C   s   t t| |ƒd  ¡ ƒS ©Nr   )Úsetr   Úkeys)ÚaÚbr,   r,   r-   Úmmrvõ   s    ra   c                   C   s  t ttƒthksJ ‚t tdt  tƒthks0J ‚t td tƒthksHJ ‚t ttƒtƒthks`J ‚t ttƒtƒttƒhks|J ‚t tt ƒtƒtt ƒhksœJ ‚t ttd ƒtƒttd ƒhksÀJ ‚t tdt ƒ tƒthksÞJ ‚t ttdt  ƒtƒttdt  ƒhksJ ‚d S rC   )ra   r(   r   r   r,   r,   r,   r-   Ú	test_mrv1ù   s     $rb   c                   C   s˜   t tttttƒ ƒ ƒtƒtttƒ ƒhks0J ‚t tttt ƒ ƒtƒtttt ƒ ƒtt ƒhkshJ ‚t tdt tt ƒ ƒtƒtt ƒhks”J ‚d S rI   ©ra   r   r(   r,   r,   r,   r-   Ú
test_mrv2a  s    08rd   c                   C   s4   t ttttd  ƒ ƒtƒttd  ƒhks0J ‚d S )Nr1   rc   r,   r,   r,   r-   Ú
test_mrv2b  s    re   c                   C   sX   t tt dtd   ƒttdt  ƒ tƒttdt  ƒtdtd  t ƒhksTJ ‚d S rC   rc   r,   r,   r,   r-   Ú
test_mrv2c  s
    &ÿ"ÿrf   c                	   C   s
  t ttd ƒtttƒ  ttƒt t  tƒttd ƒhks@J ‚t ttƒtdt tt ƒ ƒtdt ƒ  tƒttƒtt ƒhks†J ‚t ttd dttdtd  ttƒ ƒƒ  ƒtƒttdtd  ttƒ ƒƒhksÚJ ‚t ttttƒ ƒttƒ tƒthksJ ‚t tdt tt ƒ ƒtdt ƒ ttƒ tƒttƒtt ƒhksLJ ‚t dtt tt ƒ ƒ ttƒ tƒttƒtt ƒtttt ƒ ƒhksšJ ‚t tttttttƒ ƒ d ƒƒtƒttttƒ ƒhksØJ ‚t tttttƒdt  ƒƒƒtƒthksJ ‚d S )Nr1   r/   r2   )ra   r   r(   r   r,   r,   r,   r-   Ú	test_mrv3  s4    @*ÿÿ&ÿÿÿ**ÿÿ
 ÿ ÿ
>rg   c                  C   s¸   t } t| | tƒ| | tƒƒ ƒ| | tƒƒ | | tƒ| | | tƒƒƒ ƒ | tƒ tƒthks\J ‚tt t tttttƒ ƒ d ƒƒttt t tƒdt  ƒƒƒ tƒttttƒ ƒhks´J ‚d S rI   )r   ra   r(   r   )Úlnr,   r,   r-   Ú	test_mrv4)  s    Hÿÿ@ÿri   c                 C   s   t | d | d ||ƒS ©Nr/   r   )r    )r_   r`   Úcr,   r,   r-   Úmrewrite1  s    rl   c                  C   s   t tƒ} tt| tƒttƒdt t fks,J ‚t td ƒ} tt| tƒttƒdt td  fks`J ‚t tdt  ƒ} tt| tƒttƒdt t dt  fksœJ ‚dt t t t ƒ ƒ t tƒ } tt| tƒttƒt t tƒ t t t ƒ td  t fksüJ ‚d S rC   ©r   r(   rl   r   r*   ©Úer,   r,   r-   Útest_rewrite15  s    $(, rp   c                  C   s`   t tƒttt tƒƒƒ } t| tƒt tƒhks0J ‚tt| tƒttƒdt ttƒ t fks\J ‚d S rI   )r   r(   r   ra   rl   r   r*   rn   r,   r,   r-   Útest_rewrite2@  s    rq   c                  C   s¢   t t dtd   ƒt tdt  ƒ } tt| tƒttƒdt tt td t td  ƒ  t dt  ftd t td t td  ƒ t td t ffv sžJ ‚d S )Nr/   r1   r0   r2   r3   rm   rn   r,   r,   r-   Útest_rewrite3H  s    &ÿÿ.ÿrr   c                   C   s”   t tdt ƒ tƒdksJ ‚t dtt tt ƒ ƒ ttƒ tƒdksJJ ‚t tdt tt ƒ ƒtdt ƒ ttƒ tƒtdt ƒ dfksJ ‚d S )Nr/   )r0   r   r   )r!   r   r(   r,   r,   r,   r-   Útest_mrv_leadterm1O  s    .*ÿÿrs   c                   C   sB   t tttƒt ƒt tttƒttƒ ƒ ttƒ tƒdks>J ‚d S )N)r/   r   )r!   r   r   r(   r,   r,   r,   r-   Útest_mrv_leadterm2V  s    4ÿrt   c                   C   sŠ   t tt tt ƒtt ttƒ ƒ  ƒtƒtt tttƒ  ƒhksHJ ‚ttt tt ƒtt ttƒ ƒ  ƒtƒtt ƒdfks†J ‚d S r\   )ra   r   r(   r   r!   r,   r,   r,   r-   Útest_mrv_leadterm3\  s    Hru   c                   C   sJ  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 sDJ ‚t td tt ƒtu s^J ‚t td  ttƒt u szJ ‚t tttƒ tddddksšJ ‚t dt ttƒdks²J ‚t ttƒttƒtu sÊJ ‚t ttƒ ttƒt u sæJ ‚t ttƒt ttƒtu sJ ‚t dt tt ƒ ttƒdks(J ‚t tdt  ttƒtu sFJ ‚d S )Nr1   r   ú+©Údirr/   )r"   r(   r   r   r   r,   r,   r,   r-   Útest_limit1b  s     $ry   c                   C   s  t tt tddddksJ ‚t ttƒd t tdƒdks<J ‚t ddt  ttƒdksXJ ‚t tdt ƒ ttƒdksvJ ‚t ttt ƒ ttƒtu s”J ‚t tttd  ƒ ttƒtu s¶J ‚t ttttƒ ƒ ttƒtu sØJ ‚t ddt  tt ƒ ttƒdksþJ ‚d S )Nr   rv   rw   r/   r0   r1   é   )r"   r(   r   r   r,   r,   r,   r-   Útest_limit2q  s     ""r{   c                  C   sœ   t dƒ} tttdttƒ ƒ ttƒdks,J ‚ttt| ttƒ ƒ ttƒdksPJ ‚tttƒdttƒ  ttƒdkstJ ‚tttƒ| ttƒ  ttƒdks˜J ‚d S )Nr_   r/   r   )r   r"   r(   r   r   r   )r_   r,   r,   r-   Útest_limit3|  s
    $$$r|   c                   C   sX   t dt dt  dt  ttƒdks(J ‚t ddt  ddt   t tdƒdksTJ ‚d S )Nr2   r4   r/   r   ©r"   r(   r   r,   r,   r,   r-   Útest_limit4„  s    (r~   c               	   C   sš   t t dt t ƒ  ƒ} t | ƒt t d|   ƒ t t t |  ƒƒ | d  t tƒ t }t|tƒd|  t t ƒt tƒt t|  ƒt td|   ƒhks–J ‚d S rC   )r   r(   ra   )ÚhÚexprr,   r,   r-   Útest_MrvTestCase_page47_ex3_21‹  s    @r   c                  C   s    t dƒ} ttt ttƒtt ks$J ‚t| t t ttƒ| t t ksHJ ‚t| d t t ttƒ| t t kspJ ‚t| d ttƒ t ttƒ| t t ksœJ ‚d S )NrW   r2   )r   r"   r   r(   r   r   rZ   r,   r,   r-   Útest_gruntz_I’  s
    $(r‚   c                   C   s,   t td dttd ƒ  ttƒtks(J ‚d S rI   )r"   r(   r   r   r   r,   r,   r,   r-   Útest_issue_4814š  s    rƒ   c                   C   s  t dttƒ ttƒdksJ ‚t dttƒ ttƒdks8J ‚t ttƒttƒ ttƒtu sXJ ‚t tttƒƒttƒ ttƒtu s|J ‚t ttƒtdƒdks”J ‚t ttddƒdt  ƒttƒttddƒƒksÄJ ‚t ttt ƒtttƒƒ ttƒdksìJ ‚t ttttƒƒƒttƒ ttƒtu sJ ‚d S )Nr/   r   r2   r1   r7   )r"   r   r(   r   r   r   r   r   r,   r,   r,   r-   Útest_intractablež  s     $0(r„   c                   C   s^   t tdtttƒƒ ttƒdttƒttjƒ   ƒdks:J ‚tdt	tƒ tt ƒt u sZJ ‚d S rj   )
r   r"   r   r   r(   r   r	   r
   rE   r   r,   r,   r,   r-   Útest_aseries_trig©  s    ÿÿr…   c                   C   s,   t ttttttƒ ƒƒ ttƒtu s(J ‚d S )N)r"   r(   r   r   r   r,   r,   r,   r-   Útest_exp_log_series¯  s    r†   c                   C   s<   t td t d dt td   dt  ttƒdks8J ‚d S )Nr7   r/   r1   r0   r}   r,   r,   r,   r-   Útest_issue_3644³  s    r‡   c                  C   s^   t dddd} | d t| d   t| d  d  ttd   }t|tdƒ ¡ | d ksZJ ‚d S )NÚnT)ÚintegerrY   r/   r1   )r   r(   r"   Úsimplify)rˆ   Úrr,   r,   r-   Útest_issue_6843·  s    0rŒ   c                   C   s&   t ttdt ƒ ttƒtjks"J ‚d S rI   )r"   r(   r   r   r
   r   r,   r,   r,   r-   Útest_issue_4190½  s    r   c                  C   s  t dƒ} t ddd}t dƒ}t ddd}t ddd}d	|  | | d
  | || | d
    | |d
 | | | d	  | || | d
    |   |  | | |   }| ||d
 ¡}t| ||¡| tƒd
ksÌJ ‚t| ||¡| tƒ ¡ d	|d
  | d
 |d
 |d
   ksJ ‚d S )Nrˆ   r‹   TrX   rk   Úpr*   )Únegativer1   r/   )r   Úsubsr"   r   rŠ   )rˆ   r‹   rk   rŽ   r*   r€   r,   r,   r-   Útest_issue_5172Á  s"    *.ÿÿ
ÿ"ÿr‘   c                   C   s<   t dttƒ tdƒdksJ ‚t tttƒ tdƒdks8J ‚d S rj   )r"   r   r(   r,   r,   r,   r-   Útest_issue_4109Ñ  s    r’   c                   C   s6   t tdtt ƒ ƒtd  tdƒtdt ƒks2J ‚d S )Nr1   r   )r"   r   r   r(   r   r,   r,   r,   r-   Útest_issue_6682Ö  s    r“   c                  C   s<   ddl m}  ttt  tdddt| dt  ƒ ks8J ‚d S )Nr   ©r#   ú-rw   r0   )Zsympy.functionsr#   r"   r(   r	   r   r”   r,   r,   r-   Útest_issue_7096Ú  s    r–   c                      s0   t dƒ‰ tt‡ fdd„ƒ tt‡ fdd„ƒ d S )NÚfc                      s   t ˆ tƒtdƒS )Nr@   ©r"   r(   r,   ©r—   r,   r-   Ú<lambda>â  ó    z&test_issue_7391_8166.<locals>.<lambda>c                      s,   t tˆ tƒd  td ˆ tƒd   tdƒS )Nr1   r@   r   r˜   r,   r™   r,   r-   rš   ã  r›   )r   r%   Ú
ValueErrorr,   r,   r™   r-   Útest_issue_7391_8166ß  s    r   c                  C   sX   t tƒddt  td   } ttƒ}t| ttƒ|ks8J ‚td|  ttƒd| ksTJ ‚d S rC   )r   r(   r   r   r"   r   )ÚeqZansr,   r,   r-   Útest_issue_24210_25885æ  s    rŸ   N)gZ
sympy.corer   Zsympy.core.functionr   Zsympy.core.numbersr   r   r   r   r   r	   Zsympy.core.singletonr
   Zsympy.core.symbolr   Z&sympy.functions.elementary.exponentialr   r   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   r   r   Z'sympy.functions.special.error_functionsr   r   Z'sympy.functions.special.gamma_functionsr   r   r   Z&sympy.functions.special.zeta_functionsr   Zsympy.polys.polytoolsr   Z%sympy.functions.elementary.hyperbolicr   r   r   r   Zsympy.series.gruntzr   r   r    r!   r"   r#   Zsympy.testing.pytestr$   r%   r&   r'   r(   r*   r+   r.   rB   rD   rF   rH   rJ   rK   rL   rM   rQ   rS   rT   rV   r[   ra   rb   rd   re   rf   rg   ri   rl   rp   rq   rr   rs   rt   ru   ry   r{   r|   r~   r   r‚   rƒ   r„   r…   r†   r‡   rŒ   r   r‘   r’   r“   r–   r   rŸ   r,   r,   r,   r-   Ú<module>   sŒ     
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
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