o
    jgt@  ã                   @   s   d dl mZ d dlmZmZ d dl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 d dlmZ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 d dl m!Z! d dl"m#Z# d dl$m%Z%m&Z&m'Z'm(Z( dd„ Z)dd„ Z*dd„ Z+dd„ Z,dd„ Z-dd„ Z.dd„ Z/dd„ Z0dd „ Z1d!d"„ Z2d#d$„ Z3d%d&„ Z4d'd(„ Z5d)d*„ Z6d+d,„ Z7d-d.„ Z8d/d0„ Z9d1d2„ Z:d3d4„ Z;d5d6„ Z<d7d8„ Z=d9d:„ Z>d;d<„ Z?d=d>„ Z@d?d@„ ZAdAdB„ ZBdCdD„ ZCdEdF„ ZDdGdH„ ZEdIdJ„ ZFdKdL„ ZGdMdN„ ZHdOdP„ ZIdQdR„ ZJdSdT„ ZKdUdV„ ZLdWdX„ ZMdYdZ„ ZNd[d\„ ZOd]d^„ ZPd_d`„ ZQdadb„ ZRdcdd„ ZSdedf„ ZTdgdh„ ZUdidj„ ZVdkdl„ ZWdmdn„ ZXdodp„ ZYdqdr„ ZZdsdt„ Z[dudv„ Z\dwdx„ Z]dydz„ Z^d{d|„ Z_d}d~„ Z`dS )€é    )ÚAdd)ÚFunctionÚexpand)ÚIÚRationalÚnanÚooÚpi)ÚS)ÚSymbolÚsymbols)Ú	conjugateÚ	transpose)ÚexpÚlog)Úsqrt)ÚcosÚsin)ÚIntegral)ÚOÚOrder)Ú	unchanged)Úraises)ÚwÚxÚyÚzc                   C   s.   t tƒ t tdt tdƒ tdƒ  tƒ d S )Néÿÿÿÿé   é   )r   r   r   r   © r    r    úU/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/series/tests/test_order.pyÚtest_caching_bug   s   &r"   c                   C   sv   t dƒjtƒ ks
J ‚t tƒjthksJ ‚t dtƒjthksJ ‚t tt ƒjtthks,J ‚t tttƒjtthks9J ‚d S ©Né   )r   Úfree_symbolsÚsetr   r   r    r    r    r!   Útest_free_symbols   s
   r'   c                  C   s¼  t dƒ} tdt ƒttƒksJ ‚ttƒd ttƒksJ ‚dttƒ ttƒks(J ‚tttƒƒttƒks4J ‚tttƒtƒtttƒttƒksEJ ‚tdƒtdƒksOJ ‚tttƒƒtdtƒks\J ‚ttdt ƒƒjtdt ƒksmJ ‚tttdt ƒ ƒjttdt ƒ ks‚J ‚tt| d  ƒjt| d  ks“J ‚tt| t ddƒ  ƒjt| t ddƒ  ksªJ ‚ttd t t tƒtdtƒks¼J ‚ttd t t tƒtdtƒksÎJ ‚ttdd	„ ƒ tt	d
d	„ ƒ d S )Nr   é   r   éäÿÿÿiéÿÿÿr$   r   c                   S   s   t ttƒttƒS ©N)r   r   r   r    r    r    r!   Ú<lambda>0   s    ztest_simple_1.<locals>.<lambda>c                   S   s   t tdt ƒS ©Nr(   ©r   r   r    r    r    r!   r+   1   s    )
r   r   r   r   r   Úexprr   r   Ú
ValueErrorÚ	TypeError)Úor    r    r!   Útest_simple_1!   s    ""*".$$r2   c                   C   sÈ   t dt ƒt t td ƒksJ ‚t dt ƒt t dtƒksJ ‚t dt ƒt tdt ƒ t td tdt ƒ ƒks;J ‚t dt ƒt tdt ƒ ttƒd  jtd tdt ƒ ttƒd  ksbJ ‚d S )Nr(   r$   r   éýÿÿÿ)r   r   r   r   r.   r    r    r    r!   Útest_simple_24   s    8Rr4   c                   C   sØ   t tƒt t tƒksJ ‚t tƒd dt tƒ ksJ ‚t tƒtd  t tƒks(J ‚t tƒdt  dt t tƒ ks:J ‚t dt ƒdtd   dtd  t dt ƒ ksTJ ‚t tƒtdt ƒ t tƒtdt ƒ ksjJ ‚d S ©Nr(   r$   ©r   r   r   r    r    r    r!   Útest_simple_3;   s   $40r7   c                   C   s    t tƒd t td ƒksJ ‚d S r,   r-   r    r    r    r!   Útest_simple_4D   s    r8   c                   C   sl   t tƒt td ƒ t tƒksJ ‚t tƒt td ƒ t td ƒks"J ‚t tƒt dt ƒ t dt ƒks4J ‚d S )Nr(   éþÿÿÿr$   r-   r    r    r    r!   Útest_simple_5H   s    $(r:   c                   C   s  t tƒt tƒ t tƒksJ ‚t tƒt dƒ t dƒksJ ‚t tƒt td ƒ t tƒks,J ‚t dt ƒt dƒ t dt ƒks>J ‚t tƒt tdt ƒƒ t tdt ƒƒksTJ ‚t td ƒt tdt ƒƒ t tdt ƒƒkslJ ‚t td ƒt tdt ƒƒ t tdt ƒƒks„J ‚d S )Nr$   r(   r   r3   r6   r    r    r    r!   Útest_simple_6N   s    $,04r;   c                   C   sp   dt dƒ t dƒksJ ‚dt dƒ t dƒksJ ‚tt dƒ t dƒks$J ‚dt t dƒ dt t dƒ ks6J ‚d S ©Nr$   r(   )r   r   r    r    r    r!   Útest_simple_7X   s   (r=   c                   C   sà   t tt ƒƒt ttƒƒksJ ‚t td ttƒ ƒt ttddƒ ƒks$J ‚t td tt d  ƒ ƒt ttddƒ ƒks=J ‚t ttddƒ tt d ƒ ƒt td ƒksUJ ‚t tdt td   ƒt tt td   ƒksnJ ‚d S )Nr(   r   r   é	   r9   )r   r   r   r   r   r    r    r    r!   Útest_simple_8_   s
   *206r?   c                   C   s¨   t tƒ d ¡ttdfffksJ ‚t tƒ tdff¡ttdfffks#J ‚t tƒ tdff¡ttdftdfffks9J ‚t tƒ tdftdff¡ttdftdfffksRJ ‚d S ©Nr   )r   r   Úas_expr_variablesr   r    r    r    r!   Útest_as_expr_variablesg   s    &,6rB   c                   C   sR   t dtƒ t dtƒ¡sJ ‚t dtƒ t dƒ¡sJ ‚t dƒ t dtƒ¡du s'J ‚d S )Nr$   F)r   r   Úcontainsr    r    r    r!   Útest_contains_0n   s    rD   c                   C   st  t tƒ t tƒ¡sJ ‚t tƒ t td ƒ¡sJ ‚t td ƒ t tƒ¡r%J ‚t tƒ t dt ƒ¡r2J ‚t dt ƒ t tdt ƒƒ¡rCJ ‚t tƒ t tdt ƒƒ¡rRJ ‚t dt ƒ t tƒ¡s_J ‚t tdt ƒƒ t tƒ¡snJ ‚t tdt ƒƒ t dt ƒ¡sJ ‚t tdt ƒƒ t tdt ƒƒ¡s’J ‚t tdt ƒƒ t tdt ƒƒ¡s¥J ‚t tdt ƒƒ t tdt ƒƒ¡r¸J ‚d S r5   )r   r   rC   r   r    r    r    r!   Útest_contains_1t   s   ""&&*rE   c                   C   sŠ   t tƒ t tƒ¡d u sJ ‚t tƒ t tt ƒ¡sJ ‚t tt ƒ t tƒ¡s'J ‚t tƒ t tt ƒ¡s4J ‚t tƒ t td t ƒ¡sCJ ‚d S r,   )r   r   rC   r   r    r    r    r!   Útest_contains_2ƒ   s
   "rF   c                   C   sX   t ttd  ƒ t td t ƒ¡d u sJ ‚t td t ƒ t ttd  ƒ¡d u s*J ‚d S r,   )r   r   r   rC   r    r    r    r!   Útest_contains_3‹   s   *.rG   c                   C   sh   t tdtd  ƒƒ t tdtd  ƒƒ¡du sJ ‚t tdtd  ƒƒ t tdtd  ƒƒ¡du s2J ‚d S )Nr$   r(   T)r   r   r   rC   r   r    r    r    r!   Útest_contains_4   s   26rH   c                   C   s>   t dtƒt dƒvsJ ‚t dƒt dtƒv sJ ‚ttdd„ ƒ d S )Nr$   c                   S   s    t ttd  ƒt td t ƒv S r,   ©r   r   r   r    r    r    r!   r+   ˜   s     ztest_contains.<locals>.<lambda>)r   r   r   r0   r    r    r    r!   Útest_contains•   s   rJ   c                   C   s
  t tt ƒt tƒksJ ‚t dt dtd   ƒt tƒksJ ‚t dt ƒt dtƒks+J ‚t ddt  ƒt dt ƒks;J ‚t ttƒdttƒ  ƒt ttƒd d ttƒ ƒksWJ ‚t tdt ƒt ƒt tdt ƒƒkskJ ‚t tdt ƒdtd   ƒt tdt ƒƒksƒJ ‚d S )Nr   r(   r$   é   )r   r   r   r   r    r    r    r!   Ú
test_add_1›   s   $ 8(4rL   c                   C   sœ   t ttƒƒt tdt ƒƒ t ttƒƒksJ ‚t ttƒƒt ttd ƒƒ t ttƒƒks,J ‚t ttt ƒƒt ttƒttƒ ƒ t ttƒttƒ ttƒksLJ ‚d S )Nr(   r   )r   r   r   r   r    r    r    r!   Útest_ln_args©   s   ,,DrM   c                   C   s  t tt ƒjtt ksJ ‚t ttd  ƒjttd  ksJ ‚t tt tƒjtks*J ‚t ttd  tƒjtd ks:J ‚t tt t ƒjtt t ksKJ ‚t tt ƒjtt ksXJ ‚t ttdt ƒ ƒjttdt ƒ ksmJ ‚t ttƒtdt ƒ ƒjttƒtdt ƒ ks†J ‚d S r5   )r   r   r   r.   r   r   r    r    r    r!   Útest_multivar_0¯   s   " "*6rN   c                   C   s>   t tdt ƒtdt ƒ ƒjtdt ƒtdt ƒ ksJ ‚d S r#   )r   r   r   r   r.   r    r    r    r!   Útest_multivar_0aº   s   >rO   c                   C   sÔ   t tt ƒjtt ksJ ‚t tdt  ƒjtt ksJ ‚t tt ƒt jtt ks+J ‚t tt ƒtd  t tt ƒks=J ‚t tt ƒdt  dt t tt ƒ ksSJ ‚t td tt  ƒjtd tt  kshJ ‚d S r5   ©r   r   r   r.   r    r    r    r!   Útest_multivar_1¾   s   $,.rQ   c                   C   sB   t td t td t  ttƒjtd t td t  ksJ ‚d S r,   rP   r    r    r    r!   Útest_multivar_2Ç   s   BrR   c                   C   s0   t tt ƒt t td tt  ttƒksJ ‚d S r,   rI   r    r    r    r!   Útest_multivar_mul_1Ë   ó   0rS   c                   C   sø   t tƒt tƒ jt tƒt tƒft tƒt tƒffv sJ ‚t tƒt tƒ t tt ƒ t tt ƒks1J ‚t td t ƒt td t ƒ jt ttd  ƒt ttd  ƒft ttd  ƒt ttd  ƒffv sdJ ‚t td t ƒt tt ƒ t tt ƒkszJ ‚d S r,   )r   r   r   Úargsr    r    r    r!   Útest_multivar_3Ï   s   
þ, 
þ0rV   c                  C   s^   t ddd} t ddd}ttƒ t| ƒ t|ƒ tjd u sJ ‚| jdu s&J ‚|jd u s-J ‚d S )Nr   T)Únegativer   )ÚcomplexF)r   r   r   Úis_positive)r   r   r    r    r!   Útest_issue_3468Ú   s   rZ   c                   C   sþ   t d dt d    t ¡dt d  tdt d  ƒffksJ ‚ddt    t ¡dt  tdt  ƒffks4J ‚dt   t ¡dtdt ƒffksEJ ‚dt d   t ¡dtdt ƒffksXJ ‚dt d   t ¡dtdt ƒffkskJ ‚t t d   t ¡t tt ƒffks}J ‚d S )Nr$   r   r(   )r   Úextract_leading_orderr   r    r    r    r!   Útest_leading_orderè   s   <,"&&(r\   c                   C   sˆ   t dt td   t¡ƒttdtƒftdƒtdtƒfhksJ ‚t dt tt  td   t¡ƒdt ttƒftt ttƒfhksBJ ‚d S r5   )r&   r	   r   r[   r   r
   r    r    r    r!   Útest_leading_order2ñ   s   $
ÿ.ÿr]   c                   C   s&   t td ƒ t¡t td ƒksJ ‚d S r,   )r   r   Ú_eval_as_leading_termr    r    r    r!   Útest_order_leadtermø   s   &r_   c                  C   s^   t t tt ƒ tt t ddfƒ } t| ƒtt d t t tƒks J ‚t| t ƒtt d ƒks-J ‚d S r<   )r   r   r   r   r   )Úer    r    r!   Útest_order_symbolsü   s     ra   c                   C   s&   t tƒtu sJ ‚t tƒ t¡rJ ‚d S r*   )r   r   r   rC   r    r    r    r!   Útest_nan  s   rb   c                   C   s:   t dtƒt t tƒksJ ‚t dtƒt t dtƒksJ ‚d S r#   )r   r   r   r    r    r    r!   Útest_O1  s    rc   c                   C   s‚   t tƒ ¡ dks
J ‚t tttƒ ƒ ¡ dksJ ‚t td ttƒd  ƒ ¡ dks*J ‚t tttƒ ƒ ¡ dks8J ‚ttdd„ ƒ d S )Nr$   r(   c                   S   ó   t tƒt tƒ  ¡ S r*   ©r   r   r   Úgetnr    r    r    r!   r+     ó    ztest_getn.<locals>.<lambda>)r   r   rf   r   r   ÚNotImplementedErrorr    r    r    r!   Ú	test_getn  s
   $ri   c                   C   s"   t td ƒ t¡t tƒksJ ‚d S r,   )r   r   Údiffr    r    r    r!   Ú	test_diff  s   "rk   c                   C   sª   t  ¡ d u sJ ‚t  ¡ t ksJ ‚tt ƒ ¡ tt ƒksJ ‚tt ƒ ¡ dks&J ‚ttt ƒ ttƒ  ¡ tt ƒttƒ ks<J ‚ttt ƒ ttƒ  ¡ tksLJ ‚ttdd„ ƒ d S )Nr   c                   S   rd   r*   re   r    r    r    r!   r+      rg   ztest_getO.<locals>.<lambda>)r   ÚgetOÚremoveOr   r   r   r   rh   r    r    r    r!   Ú	test_getO  s   , rn   c                  C   s8   ddl m}  td| dt ƒ ƒtdttƒ ƒksJ ‚d S )Nr   ©Údigammar$   )Ú'sympy.functions.special.gamma_functionsrp   r   r   r   ro   r    r    r!   Útest_leading_term#  s   ,rr   c                   C   s–   t tƒ t tƒd¡dksJ ‚t tƒ tt¡t tƒksJ ‚t tƒ tt¡t tƒks*J ‚t tƒ ttt ¡t tt tt fƒks@J ‚tdƒt jsIJ ‚d S r#   )r   r   Úsubsr   r   Úis_Powr    r    r    r!   Ú	test_eval(  s
   ,ru   c                  C   s  t dƒ\} }t| | |ƒtd| |ƒ td| |ƒksJ ‚t|| |ƒtd| |ƒ td| |ƒks.J ‚t| | | |ƒtd| |ƒ td| |ƒksDJ ‚td| |ƒt| | |ƒ td| |ƒksXJ ‚td| |ƒt|| |ƒ td| |ƒkslJ ‚td| |ƒt| | | |ƒ td| |ƒks‚J ‚d S )Nza br$   )r   r   )ÚaÚbr    r    r!   Útest_issue_42790  s   ((,((0rx   c                  C   sˆ   dt dƒ t dƒksJ ‚dt tƒ t dt ƒksJ ‚dt tttfƒ t dt ttfƒks.J ‚tdƒ} dt | tƒƒ t dt ƒksBJ ‚d S )Nr$   Úf)r   r   r   r   )ry   r    r    r!   Útest_issue_4855:  s
   ($rz   c                  C   s  t ddd} t ddd}tt| ƒƒtt| ƒƒksJ ‚tt|ƒƒtt|ƒƒks(J ‚tt| d ƒƒtt| ƒd ƒks:J ‚tt|d ƒƒtt|ƒd ƒksLJ ‚tt| ƒƒtt| ƒƒksZJ ‚tt|ƒƒtt|ƒƒkshJ ‚tt| d ƒƒtt| ƒd ƒkszJ ‚tt|d ƒƒtt|ƒd ƒksŒJ ‚d S )Nr   T)Úrealr   )Ú	imaginaryr(   )r   r   r   r   )r   r   r    r    r!   Útest_order_conjugate_transposeC  s   $$$(r}   c                  C   s  t ddd} t| | t  tƒtdtƒksJ ‚| | t  ttƒ ttƒks&J ‚| t ttƒ ttd tƒks7J ‚tdttƒ |  |  t ƒ| |  t ttd tƒ ksTJ ‚t| |  ttƒ t ƒ| |  t ttd tƒ ksoJ ‚t| ttƒ |  t ƒ| |  t ttd tƒ ksŠJ ‚d S )NÚAF)Úcommutativer$   r(   )r   r   r   r   )r~   r    r    r!   Útest_order_noncommutativeP  s     ":6:r€   c                   C   s(   dt d  d tt ƒ tt ƒksJ ‚d S )Nr$   r(   i'  )r   r   r    r    r    r!   Útest_issue_6753Z  s   (r   c                   C   s$  t dt ttfƒt tttfƒksJ ‚t dt ttfƒt tttfƒks$J ‚t tttfƒd t tttfƒks6J ‚dt tttfƒ t tttfƒksHJ ‚t t tttfƒttfƒt tttfƒks]J ‚t t tttfƒttfƒt tttfttfƒksuJ ‚t dttfƒt dttfƒks…J ‚t td t t ttfƒttd ttfƒksJ ‚t td t t ttfƒttttfƒks³J ‚t dt ttfƒt t td ttfƒksÉJ ‚t dt ttfƒt t dttfƒksÝJ ‚t dt ttfƒt tdt ƒ t td tdt ƒ ttfƒksÿJ ‚t dt ttfƒt tdt ƒ ttƒd  t td tdt ƒ ttƒd  ttfƒks.J ‚t tttfƒdt  dt t tttfƒ   krRt tttfƒksUJ ‚ J ‚t tttfƒd dt tttfƒ   krut tttfƒksxJ ‚ J ‚t tttfƒt tt tttfƒ   kr˜t tttfƒks›J ‚ J ‚t tttfƒtd  td t tttfƒ ks´J ‚t dt ttfƒdtd   dtd  t dt ttfƒ   krât dt ttfƒksåJ ‚ J ‚t tttfƒtdt ƒ tdt ƒt tttfƒ ksJ ‚t tttfƒd t td ttfƒksJ ‚t tttfƒt td ttfƒ t td ttfƒks3J ‚t tttfƒt td ttfƒ t tttfƒksMJ ‚t tttfƒt dt ttfƒ t tttfƒksgJ ‚t tttfƒt tttfƒ t tttfƒksJ ‚t tttfƒt dttfƒ t tttfƒks—J ‚t tttfƒt td ttfƒ t td ttfƒks³J ‚t dt ttfƒt dttfƒ t dttfƒksÍJ ‚t tttfƒt tdt ƒttfƒ t tttfƒkséJ ‚t td ttfƒt tdt ƒttfƒ t td ttfƒks	J ‚t td ttfƒt tdt ƒttfƒ t tdt ƒttfƒks+J ‚t ttƒttfƒjt dttƒ ttfƒj  krLttƒksOJ ‚ J ‚t tt ttfƒjt dtt  ttfƒj  krtttttƒ ƒkswJ ‚ J ‚t dt ddt d   ttfƒjtd ksJ ‚d S )Nr$   r   r)   r(   r3   r9   )r   r   r   r   r   r   r   r.   r    r    r    r!   Útest_order_at_infinity^  sB   $$$$*0 0,,(D^NFF2b:*84400848@DHP6r‚   c                   C   s¾   t ttdfƒt tttfƒ jsJ ‚t ttdfƒt tttfƒ t tttfƒt ttdfƒ ks/J ‚t t tttfƒƒt tttfƒksAJ ‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )Nr   c                   S   s   t ttdfƒt tttfƒ S r@   ©r   r   r   r    r    r    r!   r+     ó    z8test_mixing_order_at_zero_and_infinity.<locals>.<lambda>c                   S   s   t tttfƒt ttdfƒ S r@   rƒ   r    r    r    r!   r+   ‘  r„   c                   S   s   t t tttfƒtƒS r*   )r   r   r   r   r    r    r    r!   r+   ’  rg   c                   S   s   t t tƒttfƒS r*   rƒ   r    r    r    r!   r+   “  s    )r   r   r   Úis_Addr   rh   r    r    r    r!   Ú&test_mixing_order_at_zero_and_infinityŠ  s   "<$r†   c                   C   sä   t ttdfƒt dtdfƒksJ ‚t dt d tdfƒt td tdfƒks&J ‚t t d tdfƒt td tdfƒks;J ‚t td tdfƒd t td d tdfƒksSJ ‚t td tdfƒttd tdfƒ t td tdfƒkspJ ‚d S r<   )r   r   r   r    r    r    r!   Útest_order_at_some_point–  s
    ,*0>r‡   c                   C   sÜ   dt tƒ  tdt ¡dt dt ttfƒ ksJ ‚dt tƒ  td¡dks'J ‚tt td ƒ t  td¡dks9J ‚t td ƒ ttd ¡t td d tdfƒksRJ ‚t dtd  tdfƒ ttd ¡t dtdfƒkslJ ‚d S )Nr$   r   r(   é
   r   )r   r   rs   r   Úlimitr   r    r    r    r!   Útest_order_subs_limitsž  s
   2$28rŠ   c                   C   s4   t tƒ tdd¡t dƒttd tdfƒ ksJ ‚d S )Nrˆ   r$   )r   r   Úseriesr   r    r    r    r!   Útest_issue_9351©  s   4rŒ   c                   C   s<   t dƒt dƒ t dƒksJ ‚t dƒt dƒ t dƒksJ ‚d S r#   )r   r    r    r    r!   Útest_issue_9192­  s    r   c                   C   s<   t tttƒ ttƒ ttfƒt tttƒ ttfƒksJ ‚d S r*   )r   r   r   r   r   r    r    r    r!   Útest_issue_9910²  s   <rŽ   c                  C   sD   dd„ t dƒD ƒ} |  ttd ƒ¡ t| Ž  td¡tdƒks J ‚d S )Nc                 S   s   g | ]}t | ‘qS r    )r   )Ú.0Úir    r    r!   Ú
<listcomp>·  rg   z4test_performance_of_adding_order.<locals>.<listcomp>iè  ié  r$   )ÚrangeÚappendr   r   r   rs   )Úlr    r    r!   Ú test_performance_of_adding_order¶  s    r•   c                   C   s  t d t d  t d  tt d t tfƒ  ¡ t d t d  t d  tt d t tfƒ t d	 fks2J ‚t d
 tt d t tfƒ jsBJ ‚tt d t tfƒ t d
 ¡du sTJ ‚tt t tfƒ tt t dfƒ¡d u sgJ ‚tt t dfƒ tt t tfƒ¡d u szJ ‚ttdd„ ƒ d S )Néüÿÿÿr3   r   iúÿÿÿé   r   é   r(   é   r   Fr   c                   S   s   t td ƒ tt ¡S )Nr   )r   r   rC   r   r    r    r    r!   r+   Â  s    z"test_issue_14622.<locals>.<lambda>)r   r   r   Úas_numer_denomr…   rC   r   rh   r    r    r    r!   Útest_issue_14622»  s   ,.
ÿ $&&r›   c                   C   sð   t dtd  dtd   tt fƒt dtd  tt fƒks J ‚t dtd  ttƒ tt fƒt dtd  tt fƒks>J ‚t dtd  tt ƒ tt fƒt tt ƒtt fƒks\J ‚t dt ttfƒ tt ¡t dt tt fƒksvJ ‚d S )Nr$   r(   r—   r   )r   r   r   r   rs   r    r    r    r!   Útest_issue_15539Å  s   @<<8rœ   c                   C   s   t tdƒsJ ‚d S r@   )r   r   r    r    r    r!   Útest_issue_18606Ë  s   r   c                   C   s   t ttƒƒ d¡sJ ‚d S r,   )r   r   r   rC   r    r    r    r!   Útest_issue_22165Ï  s   rž   c                   C   sè   t tt dt  ttfƒt ttttƒ ƒttfƒksJ ‚t tt td  ttfƒt ttttƒ ƒttfƒks8J ‚t tt dtd   ttfƒt ttttƒ ƒttfƒksVJ ‚t dt dt  ttfƒt tttdƒ ƒttfƒksrJ ‚d S )Nr(   r$   r   )r   r   r   r   r   r    r    r    r!   Útest_issue_23231Ó  s   88<<rŸ   c                   C   s0   t tttƒ d ttfƒt tttfƒksJ ‚d S r#   )r   r   r   r   r    r    r    r!   Útest_issue_9917Ü  rT   r    N)aÚsympy.core.addr   Úsympy.core.functionr   r   Úsympy.core.numbersr   r   r   r   r	   Úsympy.core.singletonr
   Úsympy.core.symbolr   r   Ú$sympy.functions.elementary.complexesr   r   Ú&sympy.functions.elementary.exponentialr   r   Ú(sympy.functions.elementary.miscellaneousr   Ú(sympy.functions.elementary.trigonometricr   r   Úsympy.integrals.integralsr   Úsympy.series.orderr   r   Úsympy.core.exprr   Úsympy.testing.pytestr   Ú	sympy.abcr   r   r   r   r"   r'   r2   r4   r7   r8   r:   r;   r=   r?   rB   rD   rE   rF   rG   rH   rJ   rL   rM   rN   rO   rQ   rR   rS   rV   rZ   r\   r]   r_   ra   rb   rc   ri   rk   rn   rr   ru   rx   rz   r}   r€   r   r‚   r†   r‡   rŠ   rŒ   r   rŽ   r•   r›   rœ   r   rž   rŸ   r    r    r    r    r!   Ú<module>   sŒ    	
			

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,
	