a
    {þd¼>  ã                   @   s¬  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 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l0m1Z1m2Z2m3Z3 edddZ4edddZ5dZ6dd„ Z7e3dd„ ƒZ8dd„ Z9e3dd„ ƒZ:dd„ Z;e1dd „ ƒZ<d!d"„ Z=e1d#d$„ ƒZ>d%d&„ Z?d'd(„ Z@d)d*„ ZAd+d,„ ZBd-d.„ ZCd/d0„ ZDd1d2„ ZEd3d4„ ZFd5d6„ ZGd7d8„ ZHd9d:„ ZId;d<„ ZJd=d>„ ZKd?d@„ ZLdAdB„ ZMdCdD„ ZNdEdF„ ZOdGdH„ ZPdIdJ„ ZQdKdL„ ZRdMdN„ ZSdOdP„ ZTdQdR„ ZUdSdT„ ZVe1dUdV„ ƒZWdWdX„ ZXdYdZ„ ZYd[d\„ ZZd]d^„ Z[d_d`„ Z\dadb„ Z]dcdd„ Z^dedf„ Z_e1dgdh„ ƒZ`didj„ Zadkdl„ Zbdmdn„ ZcdoS )pé    )Ú
EulerGamma)ÚEÚIÚIntegerÚRationalÚooÚpi)ÚS)ÚSymbol)ÚexpÚlog)Úsqrt)ÚacotÚatanÚcosÚsin©Úsign)ÚEiÚerf)ÚdigammaÚgammaÚloggamma)Úzeta)Úcancel)ÚcoshÚcothÚsinhÚtanh)ÚcompareÚmrvÚrewriteÚmrv_leadtermÚgruntzr   )ÚXFAILÚskipÚslowÚxT)ÚrealÚmFc                   C   s   t stdƒ d S )Nr&   )Úrunslowr%   © r+   r+   úg/var/www/html/stable-diffusion-webui/venv/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
rA   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.   r0   )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þrC   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.   r0   r2   r/   )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
rE   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.   r0   é   r   )r-   r#   r   r'   r   r   r   r	   rD   r   r   r+   r+   r+   r,   Útest_gruntz_eval_special_slow€   s    (ÿÿÿrG   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    rI   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 )Nr/   )r#   r   r'   r   r   r+   r+   r+   r,   Útest_gruntz_EiŽ   s    rJ   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 )Nr0   r.   )r#   r   r   r'   r   r   r+   r+   r+   r,   Útest_gruntz_eval_special_fail’   s
    0ÿÿrK   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 )Nr0   r.   r/   )r#   r   r'   r   r   r   r   r   r+   r+   r+   r,   Útest_gruntz_hyperbolic›   s    $&$&rL   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 )Nr0   ú<r.   ú>r1   ú=r5   )r   r'   r   r)   r+   r+   r+   r,   Útest_compare1ª   s0     $ $ $&,(rP   c                   C   sd  t ttƒtd tƒdksJ ‚t ttd ƒttƒd tƒdks@J ‚t ttƒtttt ƒ ƒtƒdksfJ ‚t tttt ƒ ƒttƒtƒdksŒJ ‚t tttt ƒ ƒtt ƒtƒdks´J ‚t tt ƒttƒdksÎJ ‚t ttt ƒtƒdksèJ ‚t ttdt  ƒttƒdks
J ‚t tttƒ ƒttƒtƒdks.J ‚t ttttƒ ƒt ƒtttƒ ƒtƒdks`J ‚d S )Nr3   rN   r0   rO   rM   r.   ©r   r   r'   r+   r+   r+   r,   Útest_compare2Ê   s    $&&("$rR   c                   C   s2   t tttƒƒtttttƒ ƒ ƒtƒdks.J ‚d S )NrN   rQ   r+   r+   r+   r,   Útest_compare3×   s    rS   c                   C   s<  t tdƒtƒdksJ ‚t tdƒtƒdks,J ‚t tdƒtƒdksBJ ‚t ttƒtƒdksXJ ‚t tt ƒtƒdkspJ ‚t ttƒtƒdks†J ‚t ttƒ tƒdksžJ ‚t ddt  tƒdks¸J ‚t ddt  tƒdksÒJ ‚t tdt ƒtƒdksìJ ‚t ttdƒ tƒdksJ ‚t td tƒdks J ‚t td tƒdks8J ‚d S )	Nr   r1   r.   r5   r/   éýÿÿÿr0   r3   )r   r   r'   r   r   r   r   r+   r+   r+   r,   Ú
test_sign1Û   s    rU   c                  C   sŠ   t ttƒdksJ ‚t t tƒdks&J ‚tddd} t | tƒdksDJ ‚t |  tƒdksXJ ‚t | t tƒdksnJ ‚t |  t tƒdks†J ‚d S )Nr.   r/   ÚyT©Úpositive)r   r'   r
   ©rV   r+   r+   r,   Ú
test_sign2ë   s    rZ   c                 C   s   t t| |ƒd  ¡ ƒS ©Nr   )Úsetr    Úkeys)ÚaÚbr+   r+   r,   Úmmrvõ   s    r`   c                   C   s  t ttƒthksJ ‚t tdt  tƒthks0J ‚t td tƒthksHJ ‚t ttƒtƒthks`J ‚t ttƒtƒttƒhks|J ‚t tt ƒtƒtt ƒhksœJ ‚t ttd ƒtƒttd ƒhksÀJ ‚t tdt ƒ tƒthksÞJ ‚t ttdt  ƒtƒttdt  ƒhksJ ‚d S rB   )r`   r'   r   r   r+   r+   r+   r,   Ú	test_mrv1ù   s     $ra   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 rH   ©r`   r   r'   r+   r+   r+   r,   Ú
test_mrv2a  s    08rc   c                   C   s4   t ttttd  ƒ ƒtƒttd  ƒhks0J ‚d S )Nr0   rb   r+   r+   r+   r,   Ú
test_mrv2b  s    rd   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 rB   rb   r+   r+   r+   r,   Ú
test_mrv2c  s
    &ÿ"ÿre   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 )Nr0   r.   r1   )r`   r   r'   r   r+   r+   r+   r,   Ú	test_mrv3  s4    @*ÿÿ&ÿÿÿ**ÿÿ
 ÿ ÿ
>rf   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 rH   )r   r`   r'   r   )Úlnr+   r+   r,   Ú	test_mrv4)  s    Hÿÿ@ÿrh   c                 C   s   t | d | d ||ƒS ©Nr.   r   )r!   )r^   r_   Úcr+   r+   r,   Úmrewrite1  s    rk   c                  C   sô   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dtt tƒ  dt  t fksðJ ‚d S rB   ©r   r'   rk   r    r)   ©Úer+   r+   r,   Útest_rewrite15  s    $(, ro   c                  C   s`   t tƒttt tƒƒƒ } t| tƒt tƒhks0J ‚tt| tƒttƒdt ttƒ t fks\J ‚d S rH   )r   r'   r   r`   rk   r    r)   rm   r+   r+   r,   Útest_rewrite2@  s    rp   c                  C   sž   t t dtd   ƒt tdt  ƒ } tt| tƒttƒdt tt dt dtd   ƒ  t dt  ftdt t dt td  ƒ  td t ffv sšJ ‚d S )Nr.   r0   r/   r2   rl   rm   r+   r+   r,   Útest_rewrite3H  s    &ÿÿ*ÿrq   c                   C   s”   t tdt ƒ tƒdksJ ‚t dtt tt ƒ ƒ ttƒ tƒdksJJ ‚t tdt tt ƒ ƒtdt ƒ ttƒ tƒtdt ƒ dfksJ ‚d S )Nr.   )r/   r   r   )r"   r   r'   r+   r+   r+   r,   Útest_mrv_leadterm1O  s    .*ÿÿrr   c                   C   sB   t tttƒt ƒt tttƒttƒ ƒ ttƒ tƒdks>J ‚d S )N)r.   r   )r"   r   r   r'   r+   r+   r+   r,   Útest_mrv_leadterm2V  s    4ÿrs   c                   C   sŠ   t tt tt ƒtt ttƒ ƒ  ƒtƒtt tttƒ  ƒhksHJ ‚ttt tt ƒtt ttƒ ƒ  ƒtƒtt ƒdfks†J ‚d S r[   )r`   r   r'   r   r"   r+   r+   r+   r,   Útest_mrv_leadterm3\  s    Hrt   c                   C   sJ  t tttƒtu sJ ‚t ttt ƒt u s,J ‚t t ttƒt u sDJ ‚t td tt ƒtu s^J ‚t td  ttƒt u szJ ‚t tttƒ tddddksšJ ‚t dt ttƒdks²J ‚t ttƒttƒtu sÊJ ‚t ttƒ ttƒt u sæJ ‚t ttƒt ttƒtu sJ ‚t dt tt ƒ ttƒdks(J ‚t tdt  ttƒtu sFJ ‚d S )Nr0   r   ú+©Údirr.   )r#   r'   r   r   r   r+   r+   r+   r,   Útest_limit1b  s     $rx   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   ru   rv   r.   r/   r0   é   )r#   r'   r   r   r+   r+   r+   r,   Útest_limit2q  s     ""rz   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
    $$$r{   c                   C   sX   t dt dt  dt  ttƒdks(J ‚t ddt  ddt   t tdƒdksTJ ‚d S )Nr1   r3   r.   r   ©r#   r'   r   r+   r+   r+   r,   Útest_limit4„  s    (r}   c               	   C   sš   t t dt t ƒ  ƒ} t | ƒt t d|   ƒ t t t |  ƒƒ | d  t tƒ t }t|tƒd|  t t ƒt tƒt t|  ƒt td|   ƒhks–J ‚d S rB   )r   r'   r`   )ÚhÚexprr+   r+   r,   Útest_MrvTestCase_page47_ex3_21‹  s    @r€   c                  C   s®   t dƒ} ttt ttƒtt ks$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| ƒt t ksªJ ‚d S )NrV   r1   )	r
   r#   r   r'   r   r   Úsimplifyr!   Ú_signrY   r+   r+   r,   Útest_gruntz_I’  s
    $(rƒ   c                   C   s,   t td dttd ƒ  ttƒtks(J ‚d S rH   )r#   r'   r   r   r   r+   r+   r+   r,   Útest_issue_4814š  s    r„   c                   C   s  t dttƒ ttƒdksJ ‚t dttƒ ttƒdks8J ‚t ttƒttƒ ttƒtu sXJ ‚t tttƒƒttƒ ttƒtu s|J ‚t ttƒtdƒdks”J ‚t ttddƒdt  ƒttƒttddƒƒksÄJ ‚t ttt ƒtttƒƒ ttƒdksìJ ‚t ttttƒƒƒttƒ ttƒtu sJ ‚d S )Nr.   r   r1   r0   r6   )r#   r   r'   r   r   r   r   r   r+   r+   r+   r,   Útest_intractablež  s     $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 ri   )
r   r#   r   r   r'   r   r   r	   rD   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 )Nr6   r.   r0   r/   r|   r+   r+   r+   r,   Útest_issue_3644³  s    rˆ   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integerrX   r.   r0   )r
   r'   r#   r   )r‰   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 rH   )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 )Nr‰   r‹   TrW   rj   Úpr)   )Únegativer0   r.   )r
   Úsubsr#   r   r   )r‰   r‹   rj   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 ri   )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 )Nr0   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-rv   r/   )Zsympy.functionsr   r#   r'   r   r   r   r+   r+   r,   Útest_issue_7096Ú  s    r•   N)dZ
sympy.corer   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$sympy.functions.elementary.complexesr   r‚   Z'sympy.functions.special.error_functionsr   r   Z'sympy.functions.special.gamma_functionsr   r   r   Z&sympy.functions.special.zeta_functionsr   Zsympy.polys.polytoolsr   Z%sympy.functions.elementary.hyperbolicr   r   r   r   Zsympy.series.gruntzr   r    r!   r"   r#   Zsympy.testing.pytestr$   r%   r&   r'   r)   r*   r-   rA   rC   rE   rG   rI   rJ   rK   rL   rP   rR   rS   rU   rZ   r`   ra   rc   rd   re   rf   rh   rk   ro   rp   rq   rr   rs   rt   rx   rz   r{   r}   r€   rƒ   r„   r…   r†   r‡   rˆ   rŒ   r   r‘   r’   r“   r•   r+   r+   r+   r,   Ú<module>   sˆ     
8


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