a
    t@8bÙ=  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}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    ú<lib/python3.9/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sXJ ‚t tttƒjtthksrJ ‚d S ©Né   )r   Zfree_symbolsÚsetr   r   r    r    r    r!   Útest_free_symbols   s
    r&   c                  C   sÆ  t dƒ} tdt ƒttƒks J ‚ttƒd ttƒks8J ‚dttƒ ttƒksPJ ‚tttƒƒttƒkshJ ‚tttƒtƒtttƒttƒksŠJ ‚tdƒtdƒksžJ ‚tttƒƒtdtƒks¸J ‚ttdt ƒƒjtdt ƒksÚJ ‚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sZJ ‚ttd t t tƒtdtƒks€J ‚ttd t t tƒtdtƒks¦J ‚ttdd	„ ƒ tt	d
d	„ ƒ d S )Nr   é   r   éäÿÿÿiéÿÿÿr$   r   c                   S   s   t ttƒttƒS ©N)r   r   r   r    r    r    r!   Ú<lambda>0   ó    ztest_simple_1.<locals>.<lambda>c                   S   s   t tdt ƒS ©Nr'   ©r   r   r    r    r    r!   r*   1   r+   )
r   r   r   r   r   Úexprr   r   Ú
ValueErrorÚ	TypeError)Úor    r    r!   Útest_simple_1!   s     "",$0&&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svJ ‚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sÄJ ‚d S )Nr'   r$   r   éýÿÿÿ)r   r   r   r   r.   r    r    r    r!   Útest_simple_24   s     8r4   c                   C   sØ   t tƒt t tƒksJ ‚t tƒd dt tƒ ks4J ‚t tƒtd  t tƒksPJ ‚t tƒdt  dt t tƒ kstJ ‚t dt ƒdtd   dtd  t dt ƒ ks¨J ‚t tƒtdt ƒ t tƒtdt ƒ ksÔJ ‚d S ©Nr'   r$   ©r   r   r   r    r    r    r!   Útest_simple_3;   s    $4r7   c                   C   s    t tƒd t td ƒksJ ‚d S r,   r-   r    r    r    r!   Útest_simple_4D   s    r8   c                   C   sl   t tƒt td ƒ t tƒks J ‚t tƒt td ƒ t td ƒksDJ ‚t tƒt dt ƒ t dt ƒkshJ ‚d S )Nr'   éþÿÿÿr$   r-   r    r    r    r!   Útest_simple_5H   s     $r:   c                   C   s  t tƒt tƒ t tƒksJ ‚t tƒt dƒ t dƒks8J ‚t tƒt td ƒ t tƒksXJ ‚t dt ƒt dƒ t dt ƒks|J ‚t tƒt tdt ƒƒ t tdt ƒƒks¨J ‚t td ƒt tdt ƒƒ t tdt ƒƒksØJ ‚t td ƒt tdt ƒƒ t tdt ƒƒks
J ‚d S )Nr$   r'   r   r3   r6   r    r    r    r!   Útest_simple_6N   s     $,0r;   c                   C   sp   dt dƒ t dƒksJ ‚dt dƒ t dƒks0J ‚tt dƒ t dƒksHJ ‚dt t dƒ dt t dƒ kslJ ‚d S ©Nr$   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sHJ ‚t td tt d  ƒ ƒt ttddƒ ƒkszJ ‚t ttddƒ tt d ƒ ƒt td ƒksªJ ‚t tdt td   ƒt tt td   ƒksÜJ ‚d S )Nr'   r   r   é	   r9   )r   r   r   r   r   r    r    r    r!   Útest_simple_8_   s
    *20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sFJ ‚t tƒ tdff¡ttdftdfffksrJ ‚t tƒ tdftdff¡ttdftdfffks¤J ‚d S ©Nr   )r   r   Zas_expr_variablesr   r    r    r    r!   Útest_as_expr_variablesg   s     &,rA   c                   C   sR   t dtƒ t dtƒ¡sJ ‚t dtƒ t dƒ¡s2J ‚t dƒ t dtƒ¡du sNJ ‚d S )Nr$   F)r   r   Úcontainsr    r    r    r!   Útest_contains_0n   s    rC   c                   C   sz  t tƒ t tƒ¡sJ ‚t tƒ t td ƒ¡s0J ‚t td ƒ t tƒ¡rJJ ‚t tƒ t dt ƒ¡rdJ ‚t dt ƒ t tdt ƒƒ¡r†J ‚t tƒ t tdt ƒƒ¡r¤J ‚t dt ƒ t tƒ¡s¾J ‚t tdt ƒƒ t tƒ¡sÜJ ‚t tdt ƒƒ t dt ƒ¡sþJ ‚t tdt ƒƒ t tdt ƒƒ¡s&J ‚t tdt ƒƒ t tdt ƒƒ¡sNJ ‚t tdt ƒƒ t tdt ƒƒ¡rvJ ‚d S r5   )r   r   rB   r   r    r    r    r!   Útest_contains_1t   s    ""((rD   c                   C   sŠ   t tƒ t tƒ¡d u sJ ‚t tƒ t tt ƒ¡s4J ‚t tt ƒ t tƒ¡sNJ ‚t tƒ t tt ƒ¡shJ ‚t tƒ t td t ƒ¡s†J ‚d S r,   )r   r   rB   r   r    r    r    r!   Útest_contains_2ƒ   s
    rE   c                   C   sX   t ttd  ƒ t td t ƒ¡d u s*J ‚t td t ƒ t ttd  ƒ¡d u sTJ ‚d S r,   )r   r   r   rB   r    r    r    r!   Útest_contains_3‹   s    *rF   c                   C   sh   t tdtd  ƒƒ t tdtd  ƒƒ¡du s2J ‚t tdtd  ƒƒ t tdtd  ƒƒ¡du sdJ ‚d S )Nr$   r'   T)r   r   r   rB   r   r    r    r    r!   Útest_contains_4   s    2rG   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$   c                   S   s    t ttd  ƒt td t ƒv S r,   ©r   r   r   r    r    r    r!   r*   ˜   r+   ztest_contains.<locals>.<lambda>)r   r   r   r0   r    r    r    r!   Útest_contains•   s    rI   c                   C   sú   t tt ƒt tƒksJ ‚t dt dtd   ƒt tƒks<J ‚t dt ƒt dtƒksVJ ‚t ddt  ƒt dt ƒksvJ ‚t ttƒdttƒ  ƒt ttƒƒksžJ ‚t tdt ƒt ƒt tdt ƒƒksÆJ ‚t tdt ƒdtd   ƒt tdt ƒƒksöJ ‚d S )Nr   r'   r$   é   )r   r   r   r   r    r    r    r!   Ú
test_add_1›   s    $ ((rK   c                   C   s”   t ttƒƒt tdt ƒƒ t ttƒƒks,J ‚t ttƒƒt ttd ƒƒ t ttƒƒksXJ ‚t ttt ƒƒt ttƒttƒ ƒ t ttt ƒƒksJ ‚d S )Nr'   r   )r   r   r   r   r    r    r    r!   Útest_ln_args¥   s    ,,rL   c                   C   s  t tt ƒjtt ksJ ‚t ttd  ƒjttd  ks<J ‚t tt tƒjtksTJ ‚t ttd  tƒjtd kstJ ‚t tt t ƒjtt t ks–J ‚t tt ƒjtt ks°J ‚t ttdt ƒ ƒjttdt ƒ ksÚJ ‚t ttƒtdt ƒ ƒjttƒtdt ƒ ksJ ‚d S r5   )r   r   r   r.   r   r   r    r    r    r!   Útest_multivar_0«   s    " "*rM   c                   C   s>   t tdt ƒtdt ƒ ƒjtdt ƒtdt ƒ ks:J ‚d S r#   )r   r   r   r   r.   r    r    r    r!   Útest_multivar_0a¶   s    rN   c                   C   sÔ   t tt ƒjtt ksJ ‚t tdt  ƒjtt ks8J ‚t tt ƒt jtt ksVJ ‚t tt ƒtd  t tt ƒkszJ ‚t tt ƒdt  dt t tt ƒ ks¦J ‚t td tt  ƒjtd tt  ksÐJ ‚d S r5   ©r   r   r   r.   r    r    r    r!   Útest_multivar_1º   s    $,rP   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,   rO   r    r    r    r!   Útest_multivar_2Ã   s    rQ   c                   C   s0   t tt ƒt t td tt  ttƒks,J ‚d S r,   rH   r    r    r    r!   Útest_multivar_mul_1Ç   s    rR   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 s6J ‚t tƒt tƒ t tt ƒ t tt ƒksbJ ‚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 sÈJ ‚t td t ƒt tt ƒ t tt ƒksôJ ‚d S r,   )r   r   r   Úargsr    r    r    r!   Útest_multivar_3Ë   s    þ
, þ
rT   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 sLJ ‚|jd u sZJ ‚d S )Nr   T)Únegativer   )ÚcomplexF)r   r   r   Zis_positive)r   r   r    r    r!   Útest_issue_3468Ö   s    rW   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shJ ‚dt   t ¡dtdt ƒffksŠJ ‚dt d   t ¡dtdt ƒffks°J ‚dt d   t ¡dtdt ƒffksÖJ ‚t t d   t ¡t tt ƒffksúJ ‚d S )Nr$   r   r'   )r   Úextract_leading_orderr   r    r    r    r!   Útest_leading_orderä   s    <,"&&rY   c                   C   sˆ   t dt td   t¡ƒttdtƒftdƒtdtƒfhks>J ‚t dt tt  td   t¡ƒdt ttƒftt ttƒfhks„J ‚d S r5   )r%   r	   r   rX   r   r
   r    r    r    r!   Útest_leading_order2í   s    $ÿ
.ÿrZ   c                   C   s&   t td ƒ t¡t td ƒks"J ‚d S r,   )r   r   Z_eval_as_leading_termr    r    r    r!   Útest_order_leadtermô   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sZJ ‚d S r<   )r   r   r   r   r   )Úer    r    r!   Útest_order_symbolsø   s      r]   c                   C   s&   t tƒtu sJ ‚t tƒ t¡r"J ‚d S r)   )r   r   r   rB   r    r    r    r!   Útest_nanþ   s    r^   c                   C   s:   t dtƒt t tƒksJ ‚t dtƒt t dtƒks6J ‚d S r#   )r   r   r   r    r    r    r!   Útest_O1  s    r_   c                   C   s‚   t tƒ ¡ dksJ ‚t tttƒ ƒ ¡ dks0J ‚t td ttƒd  ƒ ¡ dksTJ ‚t tttƒ ƒ ¡ dkspJ ‚ttdd„ ƒ d S )Nr$   r'   c                   S   s   t tƒt tƒ  ¡ S r)   ©r   r   r   Úgetnr    r    r    r!   r*     r+   ztest_getn.<locals>.<lambda>)r   r   ra   r   r   ÚNotImplementedErrorr    r    r    r!   Ú	test_getn  s
    $rc   c                   C   s"   t td ƒ t¡t tƒksJ ‚d S r,   )r   r   Zdiffr    r    r    r!   Ú	test_diff  s    rd   c                   C   sª   t  ¡ d u sJ ‚t  ¡ t ks J ‚tt ƒ ¡ tt ƒks8J ‚tt ƒ ¡ dksLJ ‚ttt ƒ ttƒ  ¡ tt ƒttƒ ksxJ ‚ttt ƒ ttƒ  ¡ tks˜J ‚ttdd„ ƒ d S )Nr   c                   S   s   t tƒt tƒ  ¡ S r)   r`   r    r    r    r!   r*     r+   ztest_getO.<locals>.<lambda>)r   ZgetOZremoveOr   r   r   r   rb   r    r    r    r!   Ú	test_getO  s    , re   c                  C   s8   ddl m}  td| dt ƒ ƒtdttƒ ƒks4J ‚d S )Nr   ©Údigammar$   )Z'sympy.functions.special.gamma_functionsrg   r   r   r   rf   r    r    r!   Útest_leading_term  s    rh   c                   C   s–   t tƒ t tƒd¡dksJ ‚t tƒ tt¡t tƒks8J ‚t tƒ tt¡t tƒksTJ ‚t tƒ ttt ¡t tt tt fƒks€J ‚tdƒt js’J ‚d S r#   )r   r   Úsubsr   r   Zis_Powr    r    r    r!   Ú	test_eval$  s
    ,rj   c                  C   s
  t dƒ\} }t| | |ƒtd| |ƒ td| |ƒks4J ‚t|| |ƒtd| |ƒ td| |ƒks\J ‚t| | | |ƒtd| |ƒ td| |ƒksˆJ ‚td| |ƒt| | |ƒ td| |ƒks°J ‚td| |ƒt|| |ƒ td| |ƒksØJ ‚td| |ƒt| | | |ƒ td| |ƒksJ ‚d S )Nza br$   )r   r   )ÚaÚbr    r    r!   Útest_issue_4279,  s    ((,((rm   c                  C   sˆ   dt dƒ t dƒksJ ‚dt tƒ t dt ƒks4J ‚dt tttfƒ t dt ttfƒks\J ‚tdƒ} dt | tƒƒ t dt ƒks„J ‚d S )Nr$   Úf)r   r   r   r   )rn   r    r    r!   Útest_issue_48556  s
    (ro   c                  C   s  t ddd} t ddd}tt| ƒƒtt| ƒƒks4J ‚tt|ƒƒtt|ƒƒksPJ ‚tt| d ƒƒtt| ƒd ƒkstJ ‚tt|d ƒƒtt|ƒd ƒks˜J ‚tt| ƒƒtt| ƒƒks´J ‚tt|ƒƒtt|ƒƒksÐJ ‚tt| d ƒƒtt| ƒd ƒksôJ ‚tt|d ƒƒtt|ƒd ƒksJ ‚d S )Nr   T)Úrealr   )Z	imaginaryr'   )r   r   r   r   )r   r   r    r    r!   Útest_order_conjugate_transpose?  s    $$$rq   c                  C   s  t ddd} t| | t  tƒtdtƒks,J ‚| | t  ttƒ ttƒksLJ ‚| t ttƒ ttd tƒksnJ ‚tdttƒ |  |  t ƒ| |  t ttd tƒ ks¨J ‚t| |  ttƒ t ƒ| |  t ttd tƒ ksÞJ ‚t| ttƒ |  t ƒ| |  t ttd tƒ ksJ ‚d S )NÚAF)Zcommutativer$   r'   )r   r   r   r   )rr   r    r    r!   Útest_order_noncommutativeL  s      ":6rs   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_6753V  s    rt   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sHJ ‚t tttfƒd t tttfƒkslJ ‚dt tttfƒ t tttfƒksJ ‚t t tttfƒttfƒt tttfƒksºJ ‚t t tttfƒttfƒt tttfttfƒksêJ ‚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s>J ‚t td t t ttfƒttttfƒkslJ ‚t dt ttfƒt t td ttfƒksšJ ‚t dt ttfƒt t dttfƒksÄJ ‚t dt ttfƒt tdt ƒ t td tdt ƒ ttfƒks
J ‚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shJ ‚t tttfƒdt  dt t tttfƒ   kr®t tttfƒks´n J ‚t tttfƒd dt tttfƒ   kròt tttfƒksøn J ‚t tttfƒt tt tttfƒ   kr6t tttfƒks<n J ‚t tttfƒtd  td t tttfƒ ksnJ ‚t dt ttfƒdtd   dtd  t dt ttfƒ   krÈt dt ttfƒksÎn 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s2J ‚t tttfƒt td ttfƒ t td ttfƒksjJ ‚t tttfƒt td ttfƒ t tttfƒksžJ ‚t tttfƒt dt ttfƒ t tttfƒksÒJ ‚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s2J ‚t tttfƒt td ttfƒ t td ttfƒksjJ ‚t dt ttfƒt dttfƒ t dttfƒksžJ ‚t tttfƒt tdt ƒttfƒ t tttfƒksÖJ ‚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sZJ ‚t ttƒttfƒjt dttƒ ttfƒj  kršttƒks n J ‚t tt ttfƒjt dtt  ttfƒj  krètttƒt ƒksîn J ‚t dt ddt d   ttfƒjtd ks J ‚d S )Nr$   r   r(   r'   r3   r9   )r   r   r   r   r   r   r   r.   r    r    r    r!   Útest_order_at_infinityZ  sB    $$$$*0"2..*F^LDD2`:*84400848@DFNru   c                   C   s¾   t ttdfƒt tttfƒ js"J ‚t ttdfƒt tttfƒ t tttfƒt ttdfƒ ks^J ‚t t tttfƒƒt tttfƒks‚J ‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )Nr   c                   S   s   t ttdfƒt tttfƒ S r@   ©r   r   r   r    r    r    r!   r*   Œ  r+   z8test_mixing_order_at_zero_and_infinity.<locals>.<lambda>c                   S   s   t tttfƒt ttdfƒ S r@   rv   r    r    r    r!   r*     r+   c                   S   s   t t tttfƒtƒS r)   )r   r   r   r   r    r    r    r!   r*   Ž  r+   c                   S   s   t t tƒttfƒS r)   rv   r    r    r    r!   r*     r+   )r   r   r   Úis_Addr   rb   r    r    r    r!   Ú&test_mixing_order_at_zero_and_infinity†  s    "<$rx   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sLJ ‚t t d tdfƒt td tdfƒksvJ ‚t td tdfƒd t td d tdfƒks¦J ‚t td tdfƒttd tdfƒ t td tdfƒksàJ ‚d S r<   )r   r   r   r    r    r    r!   Útest_order_at_some_point’  s
     ,*0ry   c                   C   sÜ   dt tƒ  tdt ¡dt dt ttfƒ ks2J ‚dt tƒ  td¡dksNJ ‚tt td ƒ t  td¡dksrJ ‚t td ƒ ttd ¡t td d tdfƒks¤J ‚t dtd  tdfƒ ttd ¡t dtdfƒksØJ ‚d S )Nr$   r   r'   é
   r   )r   r   ri   r   Úlimitr   r    r    r    r!   Útest_order_subs_limitsš  s
    2$2r|   c                   C   s4   t tƒ tdd¡t dƒttd tdfƒ ks0J ‚d S )Nrz   r$   )r   r   Zseriesr   r    r    r    r!   Útest_issue_9351¥  s    r}   c                   C   s<   t dƒt dƒ t dƒksJ ‚t dƒt dƒ t dƒks8J ‚d S r#   )r   r    r    r    r!   Útest_issue_9192©  s    r~   c                   C   s<   t tttƒ ttƒ ttfƒt tttƒ ttfƒks8J ‚d S r)   )r   r   r   r   r   r    r    r    r!   Útest_issue_9910®  s    r   c                  C   sH   t dd„ tdƒD ƒƒ} |  ttd ƒ¡ t| Ž  td¡tdƒksDJ ‚d S )Nc                 s   s   | ]}t | V  qd S r)   )r   )Ú.0Úir    r    r!   Ú	<genexpr>³  r+   z3test_performance_of_adding_order.<locals>.<genexpr>iè  ié  r$   )ÚlistÚrangeÚappendr   r   r   ri   )Úlr    r    r!   Ú test_performance_of_adding_order²  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sdJ ‚t d
 tt d t tfƒ js„J ‚tt d t tfƒ t d
 ¡du s¨J ‚tt t tfƒ tt t dfƒ¡d u sÎJ ‚tt t dfƒ tt t tfƒ¡d u sôJ ‚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   rB   r   r    r    r    r!   r*   ¾  r+   z"test_issue_14622.<locals>.<lambda>)r   r   r   Zas_numer_denomrw   rB   r   rb   r    r    r    r!   Útest_issue_14622·  s    ,.ÿ
 $&&rŒ   c                   C   sð   t dtd  dtd   tt fƒt dtd  tt fƒks@J ‚t dtd  ttƒ tt fƒt dtd  tt fƒks|J ‚t dtd  tt ƒ tt fƒt tt ƒtt fƒks¸J ‚t dt ttfƒ tt ¡t dt tt fƒksìJ ‚d S )Nr$   r'   r‰   r   )r   r   r   r   ri   r    r    r    r!   Útest_issue_15539Á  s    @<<r   c                   C   s   t tdƒsJ ‚d S r@   )r   r   r    r    r    r!   Útest_issue_18606Ç  s    rŽ   c                   C   s   t ttƒƒ d¡sJ ‚d S r,   )r   r   r   rB   r    r    r    r!   Útest_issue_22165Ë  s    r   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_9917Ï  s    r   N)`Zsympy.core.addr   Zsympy.core.functionr   r   Zsympy.core.numbersr   r   r   r   r	   Zsympy.core.singletonr
   Zsympy.core.symbolr   r   Z$sympy.functions.elementary.complexesr   r   Z&sympy.functions.elementary.exponentialr   r   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   Zsympy.integrals.integralsr   Zsympy.series.orderr   r   Zsympy.core.exprr   Zsympy.testing.pytestr   Z	sympy.abcr   r   r   r   r"   r&   r2   r4   r7   r8   r:   r;   r=   r?   rA   rC   rD   rE   rF   rG   rI   rK   rL   rM   rN   rP   rQ   rR   rT   rW   rY   rZ   r[   r]   r^   r_   rc   rd   re   rh   rj   rm   ro   rq   rs   rt   ru   rx   ry   r|   r}   r~   r   r‡   rŒ   r   rŽ   r   r   r    r    r    r!   Ú<module>   sˆ   	
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