U
    	Ç-e¼>  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+   ú_/var/www/html/Darija-Ai-Train/env/lib/python3.8/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:t‚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st‚t ttttt ƒ ƒddt   ƒtttƒƒ ttƒtksÎt‚t tttttt ƒ ƒƒƒttttƒƒƒ ttƒtks
t‚t ttttƒƒƒtttttttƒ ƒ ƒƒƒ ttƒtksJt‚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sŽt‚t tttƒƒtttttttƒƒ ƒ ƒƒ ttƒdksÊt‚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s8t‚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¨t‚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 t‚t dt dt  dt  ttƒdks*t‚t ttttttdƒttƒ  ƒ ƒ ttƒtks`t‚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ksºt‚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ks\t‚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sÀt‚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t‚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sht‚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sÂt‚t tttttt ƒ ƒƒƒtttƒƒ ttƒtksút‚d S )Né   éÿÿÿÿé   é   r   éþÿÿÿé   é
   éûÿÿÿé   é   é   é   é   iøÿÿÿé6   é   é1   é-   é   é   )	r#   r   r'   r   ÚAssertionErrorr   r   r   r   r+   r+   r+   r,   Útest_gruntz_evaluation(   sÈ    :*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 ksbt‚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t‚d S ©Nr.   r0   )r-   r#   r   r'   r   r   rA   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sHt‚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–t‚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sàt‚t ttƒt	ttt ƒ ƒt	tƒ  ttƒtkst‚t ttt
t
tƒƒƒƒt ttƒttddƒƒksHt‚t ttt
ttƒƒƒƒt ttƒttddƒƒks|t‚t t
t
t
tƒƒƒttƒtksžt‚t tttƒƒttƒtks¼t‚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t‚t tt	tdt	tƒ  ƒt	tƒ ttƒ  ttƒtjksLt‚t t	tdt	tƒ  ƒt	tƒ ttƒ ttƒdks‚t‚d S )Nr.   r0   r2   r/   )r#   r   r'   r   r   rA   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	ksXt
‚ttttttttƒƒƒƒƒƒt tt	ƒdksˆt
‚d S )Nr.   r0   é   r   )r-   r#   r   r'   r   r   r   r	   rE   r   rA   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ksDt‚d S ©Nr.   )r-   r#   r   r   r'   r   rA   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sHt‚d S )Nr/   )r#   r   r'   r   r   rA   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sDt‚d S )Nr0   r.   )r#   r   r   r'   r   r   rA   r+   r+   r+   r,   Útest_gruntz_eval_special_fail’   s    ,  ÿÿrL   c                   C   sj  t ttƒttƒtkst‚t ttƒtt ƒtks2t‚t ttƒttƒtksJt‚t ttƒtt ƒt ksft‚t dttƒ ttƒ ttƒtksŠt‚t dttƒ ttƒ tt ƒdks°t‚t dttƒ ttƒ ttƒtksÔt‚t dttƒ ttƒ tt ƒdksút‚t ttƒttƒdkst‚t ttƒtt ƒdks0t‚t ttƒttƒdksJt‚t ttƒtt ƒdksft‚d S )Nr0   r.   r/   )	r#   r   r'   r   rA   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t‚t tttƒtƒdks,t‚t ttƒttd ƒtƒdksLt‚t ttd ƒtttƒƒtƒdkspt‚t dtttƒƒtƒdksŒt‚t tdtƒdks t‚t ttƒttƒdks¸t‚t ttd ƒttƒtƒdksØt‚t tttƒƒttd ƒtƒdksüt‚t tttƒƒdtƒdkst‚t ddtƒdks0t‚t ddtƒdksFt‚t ddtƒdks\t‚t ttd tƒdksvt‚t td td tƒdks”t‚t td dt tƒdks²t‚t dt tt tƒdksÐt‚t tt t tƒdksìt‚t ttƒtt ƒtƒdkst‚t tt ƒtdt ƒtƒdks0t‚t tdt ƒttƒd tƒdksVt‚t ttƒd tttt ƒ ƒtƒdks‚t‚t ttƒtttt ƒ ƒtƒdksªt‚t ttd ƒdttd ƒ tƒdksÔt‚d S )Nr0   ú<r.   ú>r1   ú=r5   )r   r'   rA   r   r)   r+   r+   r+   r,   Útest_compare1ª   s0     $ $ $&,(rQ   c                   C   sd  t ttƒtd tƒdkst‚t ttd ƒttƒd tƒdks@t‚t ttƒtttt ƒ ƒtƒdksft‚t tttt ƒ ƒttƒtƒdksŒt‚t tttt ƒ ƒtt ƒtƒdks´t‚t tt ƒttƒdksÎt‚t ttt ƒtƒdksèt‚t ttdt  ƒttƒdks
t‚t tttƒ ƒttƒtƒdks.t‚t ttttƒ ƒt ƒtttƒ ƒtƒdks`t‚d S )Nr3   rO   r0   rP   rN   r.   ©r   r   r'   rA   r+   r+   r+   r,   Útest_compare2Ê   s    $&&("$rS   c                   C   s2   t tttƒƒtttttƒ ƒ ƒtƒdks.t‚d S )NrO   rR   r+   r+   r+   r,   Útest_compare3×   s    rT   c                   C   s<  t tdƒtƒdkst‚t tdƒtƒdks,t‚t tdƒtƒdksBt‚t ttƒtƒdksXt‚t tt ƒtƒdkspt‚t ttƒtƒdks†t‚t ttƒ tƒdksžt‚t ddt  tƒdks¸t‚t ddt  tƒdksÒt‚t tdt ƒtƒdksìt‚t ttdƒ tƒdkst‚t td tƒdks t‚t td tƒdks8t‚d S )	Nr   r1   r.   r5   r/   éýÿÿÿr0   r3   )r   r   r'   rA   r   r   r   r   r+   r+   r+   r,   Ú
test_sign1Û   s    rV   c                  C   sŠ   t ttƒdkst‚t t tƒdks&t‚tddd} t | tƒdksDt‚t |  tƒdksXt‚t | t tƒdksnt‚t |  t tƒdks†t‚d S )Nr.   r/   ÚyT©Úpositive)r   r'   rA   r
   ©rW   r+   r+   r,   Ú
test_sign2ë   s    r[   c                 C   s   t t| |ƒd  ¡ ƒS ©Nr   )Úsetr    Úkeys)ÚaÚbr+   r+   r,   Úmmrvõ   s    ra   c                   C   s  t ttƒthkst‚t tdt  tƒthks0t‚t td tƒthksHt‚t ttƒtƒthks`t‚t ttƒtƒttƒhks|t‚t tt ƒtƒtt ƒhksœt‚t ttd ƒtƒttd ƒhksÀt‚t tdt ƒ tƒthksÞt‚t ttdt  ƒtƒttdt  ƒhkst‚d S rC   )ra   r'   rA   r   r   r+   r+   r+   r,   Ú	test_mrv1ù   s     $rb   c                   C   s˜   t tttttƒ ƒ ƒtƒtttƒ ƒhks0t‚t tttt ƒ ƒtƒtttt ƒ ƒtt ƒhksht‚t tdt tt ƒ ƒtƒtt ƒhks”t‚d S rI   ©ra   r   r'   rA   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s0t‚d S )Nr0   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sTt‚d S rC   rc   r+   r+   r+   r,   Ú
test_mrv2c  s    $ ÿ"ÿrf   c                	   C   s
  t ttd ƒtttƒ  ttƒt t  tƒttd ƒhks@t‚t ttƒtdt tt ƒ ƒtdt ƒ  tƒttƒtt ƒhks†t‚t ttd dttdtd  ttƒ ƒƒ  ƒtƒttdtd  ttƒ ƒƒhksÚt‚t ttttƒ ƒttƒ tƒthkst‚t tdt tt ƒ ƒtdt ƒ ttƒ tƒttƒtt ƒhksLt‚t dtt tt ƒ ƒ ttƒ tƒttƒtt ƒtttt ƒ ƒhksšt‚t tttttttƒ ƒ d ƒƒtƒttttƒ ƒhksØt‚t tttttƒdt  ƒƒƒtƒthkst‚d S )Nr0   r.   r1   )ra   r   r'   r   rA   r+   r+   r+   r,   Ú	test_mrv3  s:    @( ÿÿ&ÿÿÿ*( ÿÿ
 ÿ ÿ
>rg   c                  C   s¸   t } t| | tƒ| | tƒƒ ƒ| | tƒƒ | | tƒ| | | tƒƒƒ ƒ | tƒ tƒthks\t‚tt t tttttƒ ƒ d ƒƒttt t tƒdt  ƒƒƒ tƒttttƒ ƒhks´t‚d S rI   )r   ra   r'   rA   r   )Úlnr+   r+   r,   Ú	test_mrv4)  s    Hÿÿ@ÿri   c                 C   s   t | d | d ||ƒS ©Nr.   r   )r!   )r_   r`   Úcr+   r+   r,   Úmrewrite1  s    rl   c                  C   sô   t tƒ} tt| tƒttƒdt t fks,t‚t td ƒ} tt| tƒttƒdt td  fks`t‚t tdt  ƒ} tt| tƒttƒdt t dt  fksœt‚dt t t t ƒ ƒ t tƒ } tt| tƒttƒdtt tƒ  dt  t fksðt‚d S rC   ©r   r'   rl   r    r)   rA   ©Úer+   r+   r,   Útest_rewrite15  s    $(, rp   c                  C   s`   t tƒttt tƒƒƒ } t| tƒt tƒhks0t‚tt| tƒttƒdt ttƒ t fks\t‚d S rI   )r   r'   r   ra   rA   rl   r    r)   rn   r+   r+   r,   Útest_rewrite2@  s    rq   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ksšt‚d S )Nr.   r0   r/   r2   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t‚t dtt tt ƒ ƒ ttƒ tƒdksJt‚t tdt tt ƒ ƒtdt ƒ ttƒ tƒtdt ƒ dfkst‚d S )Nr.   )r/   r   r   )r"   r   r'   rA   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>t‚d S )N)r.   r   )r"   r   r   r'   rA   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sHt‚ttt tt ƒtt ttƒ ƒ  ƒtƒtt ƒdfks†t‚d S r\   )ra   r   r'   r   rA   r"   r+   r+   r+   r,   Útest_mrv_leadterm3\  s    Hru   c                   C   sJ  t tttƒtkst‚t ttt ƒt ks,t‚t t ttƒt ksDt‚t td tt ƒtks^t‚t td  ttƒt kszt‚t tttƒ tddddksšt‚t dt ttƒdks²t‚t ttƒttƒtksÊt‚t ttƒ ttƒt ksæt‚t ttƒt ttƒtkst‚t dt tt ƒ ttƒdks(t‚t tdt  ttƒtksFt‚d S )Nr0   r   ú+©Údirr.   )r#   r'   r   rA   r   r   r+   r+   r+   r,   Útest_limit1b  s     $ry   c                   C   s  t tt tddddkst‚t ttƒd t tdƒdks<t‚t ddt  ttƒdksXt‚t tdt ƒ ttƒdksvt‚t ttt ƒ ttƒtks”t‚t tttd  ƒ ttƒtks¶t‚t ttttƒ ƒ ttƒtksØt‚t ddt  tt ƒ ttƒdksþt‚d S )Nr   rv   rw   r.   r/   r0   é   )r#   r'   rA   r   r   r+   r+   r+   r,   Útest_limit2q  s     ""r{   c                  C   sœ   t dƒ} tttdttƒ ƒ ttƒdks,t‚ttt| ttƒ ƒ ttƒdksPt‚tttƒdttƒ  ttƒdkstt‚tttƒ| ttƒ  ttƒdks˜t‚d S )Nr_   r.   r   )r
   r#   r'   r   r   r   rA   )r_   r+   r+   r,   Útest_limit3|  s
    $$$r|   c                   C   sX   t dt dt  dt  ttƒdks(t‚t ddt  ddt   t tdƒdksTt‚d S )Nr1   r3   r.   r   ©r#   r'   r   rA   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–t‚d S rC   )r   r'   ra   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$t‚t| t t ttƒ| t t ksHt‚t| d t t ttƒ| t t kspt‚t| d ttƒ t ttƒ ¡  t	¡t	| ƒt t ksªt‚d S )NrW   r1   )
r
   r#   r   r'   r   rA   r   Úsimplifyr!   Ú_signrZ   r+   r+   r,   Útest_gruntz_I’  s
    $(r„   c                   C   s,   t td dttd ƒ  ttƒtks(t‚d S rI   )r#   r'   r   r   r   rA   r+   r+   r+   r,   Útest_issue_4814š  s    r…   c                   C   s  t dttƒ ttƒdkst‚t dttƒ ttƒdks8t‚t ttƒttƒ ttƒtksXt‚t tttƒƒttƒ ttƒtks|t‚t ttƒtdƒdks”t‚t ttddƒdt  ƒttƒttddƒƒksÄt‚t ttt ƒtttƒƒ ttƒdksìt‚t ttttƒƒƒttƒ ttƒtkst‚d S )Nr.   r   r1   r0   r6   )	r#   r   r'   r   rA   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:t	‚tdt
tƒ tt ƒt ksZt	‚d S rj   )r   r#   r   r   r'   r   r   r	   rE   rA   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ks(t‚d S )N)r#   r'   r   r   r   rA   r+   r+   r+   r,   Útest_exp_log_series¯  s    rˆ   c                   C   s<   t td t d dt td   dt  ttƒdks8t‚d S )Nr6   r.   r0   r/   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sZt‚d S )NÚnT)ÚintegerrY   r.   r0   )r
   r'   r#   r‚   rA   )rŠ   Úrr+   r+   r,   Útest_issue_6843·  s    0r   c                   C   s&   t ttdt ƒ ttƒtjks"t‚d S rI   )r#   r'   r   r   r	   r   rA   r+   r+   r+   r,   Útest_issue_4190½  s    rŽ   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sÌt‚t| ||¡| tƒ ¡ d	|d
  | d
 |d
 |d
   kst‚d S )NrŠ   rŒ   TrX   rk   Úpr)   )Únegativer0   r.   )r
   Úsubsr#   r   rA   r‚   )rŠ   rŒ   rk   r   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t‚t tttƒ tdƒdks8t‚d S rj   )r#   r   r'   rA   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s2t‚d S )Nr0   r   )r#   r   r   r'   r   rA   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s8t‚d S )Nr   r   ú-rw   r/   )Zsympy.functionsr   r#   r'   r   r   rA   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   rƒ   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-   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„   r…   r†   r‡   rˆ   r‰   r   rŽ   r’   r“   r”   r–   r+   r+   r+   r,   Ú<module>   sˆ     
8
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
 
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
