a
    kº”h}H  ã                   @   sp  d dl 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 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 d d
lmZ d dlmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4 d dl5m6Z6 d dl7m8Z8 d dl9m:Z: d dl;m<Z< d dl=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZF d dlGmHZHmIZImJZJmKZK d dlLmMZM d dlNmOZO d dlPmQZQmRZRmSZSmTZT d dlUmVZVmWZW edddZXdd„ ZYeTdd„ ƒZZdd„ Z[eQd d!„ ƒZ\eQd"d#„ ƒZ]eQd$d%„ ƒZ^d&d'„ Z_eSd(d)„ ƒZ`d*d+„ Zad,d-„ Zbd.d/„ Zcd0d1„ Zdd2d3„ Zed4d5„ Zfd6d7„ Zgd8d9„ ZheSd:d;„ ƒZid<d=„ Zjd>S )?é    )ÚLambda)ÚEÚIÚRationalÚooÚpi)ÚEq)ÚS)ÚDummyÚSymbol)ÚAbsÚre)ÚexpÚlog)Úfrac)Úsqrt)Ú	Piecewise)ÚcosÚcotÚcscÚsecÚsinÚtanÚasinÚacosÚatanÚacotÚasecÚacsc)ÚsinhÚcoshÚtanhÚcothÚsechÚcschÚasinhÚacoshÚatanhÚacothÚasechÚacsch)Úgamma)Úexpint)ÚMatrixSymbol)Úsimplify)	Úfunction_rangeÚcontinuous_domainÚnot_empty_inÚperiodicityÚlcimÚ	is_convexÚstationary_pointsÚminimumÚmaximum)ÚIntervalÚ	FiniteSetÚ
ComplementÚUnion)ÚImageSet)ÚConditionSet)ÚXFAILÚraisesÚ_both_exp_powÚslow)ÚxÚyÚaT)Úrealc                   C   sô  t ttƒttt d td ƒƒtddƒks.J ‚t ttƒttdtƒƒtddƒksRJ ‚t ttƒttdtƒƒtt tƒksxJ ‚t ttƒtttd tƒƒtt dƒks¢J ‚t td td  ttddƒƒttt tddƒƒttd	dƒtƒƒksèJ ‚t dtd  ttddƒƒtdtƒksJ ‚t t	tƒttddƒƒtt	dƒt	dƒƒks@J ‚t t
tƒt ttjƒtt dƒkshJ ‚t tdt d ƒttddƒƒtdtdƒƒksšJ ‚t ttd  td t  ttjƒtdƒksÊJ ‚t ttd  td t  t ttjƒttƒksþJ ‚t ttƒtttdd
ƒtdƒƒƒtttdƒ dƒttdƒƒƒksBJ ‚t ttƒttt dƒƒtddƒksjJ ‚t ttƒttjƒtjksˆJ ‚t tttd d ƒ ttjƒt dd¡ks¸J ‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )Né   éÿÿÿÿé   r   é   éûÿÿÿé   é   é   éýÿÿÿé   éüÿÿÿc                   S   s*   t ttƒttƒttƒ  d t ttjƒS ©NrF   )r/   r   rB   r   r   r	   ÚReals© rS   rS   úL/var/www/auris/lib/python3.9/site-packages/sympy/calculus/tests/test_util.pyÚ<lambda>;   s   $ÿz%test_function_range.<locals>.<lambda>c                   S   s   t ttƒt ttjƒS ©N)r/   r   rB   r	   rR   rS   rS   rS   rT   rU   =   s   ÿc                   S   s   t ttƒttjƒS rV   )r/   r   rB   r	   ÚIntegersrS   rS   rS   rT   rU   ?   s   ÿc                   S   s   t ttƒd ttjƒS rQ   )r/   r   rB   r	   ZNaturalsrS   rS   rS   rT   rU   A   s   ÿ)r/   r   rB   r8   r   r   r   r;   r   r   r   r	   rR   r   r9   rC   r   ÚEmptySetÚopenr?   ÚNotImplementedErrorrS   rS   rS   rT   Útest_function_range   sZ    ÿÿ
ÿ
ÿ"ÿÿ
ÿ

ÿ
ÿ
 ÿ
$ÿ
ÿ
ÿ
0r[   c                   C   s<   t ttƒd tdt ƒd  d ttjƒtdtƒks8J ‚d S )NrF   rI   rH   )r/   r   rB   r	   rR   r8   r   rS   rS   rS   rT   Útest_function_range1E   s    r\   c                  C   s  t ttƒttddt ƒƒtddt ƒks,J ‚t ttƒttddt ƒƒttdtd ddƒttd ttddƒ ddƒtttddƒ dt ddƒƒks”J ‚t ttƒttddt ƒƒtt 	dt¡t 	tdt ¡ƒksÐJ ‚t td td d  tt
jƒttt dddƒtdtddƒƒksJ ‚t ttƒtdt d ƒ tt
jƒttddƒtddƒksPJ ‚t dttd ƒ tt
jƒtdtddƒks~J ‚t dt d tt
jƒtt 	t d¡t 	dt¡ƒks¶J ‚t dtd d  d tt
jƒtt 	t d¡t 	dd¡t 	dt¡ƒks J ‚t td t tt
jƒtd	tƒks&J ‚t td td  tt
jƒtd	tƒksPJ ‚t tt tt
jƒtdtƒksrJ ‚t td ttd ƒ tt
jƒtt d	d¡t 	dt¡ƒks°J ‚t tttƒd d ƒtt
jƒ} |  dt d ¡ræJ ‚|  d
¡söJ ‚tdddd}t td|  tt
jƒtdtƒks*J ‚tdƒ}t dttƒ tt
jƒ tt
jttt|d| t t ƒt
jƒtt|d| t ƒt
jƒƒƒ¡s’J ‚t ttƒttƒ tt
jƒt
jks¸J ‚t ttƒtt
jƒtd	dƒksÚJ ‚t dtttƒƒ tt
jƒt td	ƒt¡ks
J ‚t ttƒttƒ tt
jƒt
jks0J ‚t ttƒt tƒ tt
jƒt
jksVJ ‚t t!tƒt"tƒ tt
jƒt
jks|J ‚t t#tƒtt
jƒtdtƒksžJ ‚t t$tƒtt
jƒt 	d	d¡ksÂJ ‚t t$tƒt#tƒ tt
jƒt
j%ksèJ ‚t t&tƒtt
jƒt 'dd¡ksJ ‚t t(tƒtt
jƒtt 	t d	¡t 	dt¡ƒks@J ‚t t)tƒtt
jƒttt d	ƒtdtƒƒkspJ ‚t t*tƒtt
jƒttt d	ƒtdtƒƒks J ‚t+t,t-fD ]:}t |tƒtt
jƒtt 	t d¡t 	dt¡ƒksªJ ‚qªt t.tƒtt
jƒ d¡dksJ ‚t dttƒt  tt
jƒtt
jt/tt0t ttƒ dƒt
jƒƒksNJ ‚t t1td ƒttdd	ƒƒtt 	dtdƒ ¡t 	tdƒ d	¡t 	tdƒ tdƒ ¡ƒksªJ ‚t t1tƒtt
jƒtt
jt
jƒksÐJ ‚t2t3dd„ ƒ t2t3dd„ ƒ t tt4tƒ tt
jƒt
jksJ ‚d S )Nr   rF   FTrI   rH   rO   éþÿÿÿrG   rK   Úd)ZevenZzeroÚnc                   S   s   t dtd d  ttjƒS ©NrH   rF   )r0   rB   r	   Z	ComplexesrS   rS   rS   rT   rU   ƒ   s   ÿz(test_continuous_domain.<locals>.<lambda>c                   S   s   t ttƒttddƒƒS )NrJ   r   )r0   r+   rB   r8   rS   rS   rS   rT   rU   …   s   ÿ)5r0   r   rB   r8   r   r   r;   r   r   rY   r	   rR   r   r   r   ÚRopenÚcontainsr   r
   Zdummy_eqr:   r<   r   rW   r   r   r   r   r   r   r    r!   r#   r   r%   r&   r'   rX   r)   ÚLopenr(   r   r   r"   r*   r$   r   r=   r   r   r?   rZ   r+   )Údomainr^   r_   ÚfrS   rS   rT   Útest_continuous_domainJ   s˜    ,,ÿÿÿ
ÿ
 ÿ
.ÿ
$ÿ
&*"ÿ&"ÿÿ&"0&&&"$&$ÿÿÿÿ" ÿ þÿrf   c                  C   s>   t tttƒ tdk fttƒdfƒ} t| ttjƒtjks:J ‚d S )Nr   T)r   r   r   rB   r0   r	   rR   )Z	acot_contrS   rS   rT   Útest_continuous_domain_acotŠ   s    "rg   c                   C   s$   t ttƒttjƒ d¡dks J ‚d S )NrG   F)r0   r+   rB   r	   rR   rb   rS   rS   rS   rT   Útest_continuous_domain_gamma   s    rh   c                   C   s.   t td dt  ttjƒt dt¡ks*J ‚d S )NrF   rH   )r0   rB   r	   rR   r8   rY   r   rS   rS   rS   rT   Ú test_continuous_domain_neg_power“   s    ri   c                	   C   sD  t ttdt ƒ tddddƒ¡tƒttjdddƒks8J ‚t tttd ƒ tddƒ¡tƒtttdƒ dƒtddƒƒksxJ ‚t ttd t tƒ tddƒ¡tƒtttdƒ d tj dƒtdt	ddƒtdƒd  ƒtddƒƒksàJ ‚t tttd  ƒ tj
¡tƒttj
tdƒƒksJ ‚t tttd  ƒ tj
¡tƒttj
tdƒƒksHJ ‚t ttd d	t  d td  ƒ tj
¡tƒttj
tdƒƒksŒJ ‚t td	dttd  ƒ tdd	ƒ¡tƒtt tƒksÄJ ‚t tdttd  ƒ tdd	ƒ¡tƒttd	ƒd dƒks J ‚t tttd d  ƒ tj
¡tƒttj
tddƒƒks:J ‚t tttd ƒ ttdd	ddƒtdd
ƒƒ¡tƒtttd
ƒ dƒttd	ƒ dddƒtdd	ddƒtdd
ƒƒksªJ ‚t tdƒ td	dƒ¡tƒtjksÐJ ‚t ttd td  ƒ tdtƒ¡tƒttddddƒtdtƒƒksJ ‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )NrF   rH   TFrG   rO   é   r]   rI   rK   c                   S   s   t tƒS rV   )r1   rB   rS   rS   rS   rT   rU   ³   ó    z#test_not_empty_in.<locals>.<lambda>c                   S   s   t tddƒtƒS )Nr   rH   )r1   r8   rB   rS   rS   rS   rT   rU   ´   rk   c                   S   s   t ttƒ tj¡ttƒS rV   )r1   r9   rB   Ú	intersectr	   rR   rD   rS   rS   rS   rT   rU   ¶   rk   )r1   r9   rB   rl   r8   r	   ÚHalfr;   r   r   rR   r:   rD   r   rX   r?   Ú
ValueErrorrZ   rS   rS   rS   rT   Útest_not_empty_in˜   s^    "ÿÿ""ÿÿÿ
ÿ
,ÿ
$
ÿ
"ÿ
 ÿ
ÿÿ"ÿþ
&$ÿ
ÿro   c                     sâ  t tdt ƒtƒtksJ ‚t dtdt ƒ tƒtd ks<J ‚t ttƒd tƒdt ksZJ ‚t dtdt ƒ tƒtd ks|J ‚t ttƒttƒ tƒdt ksžJ ‚t ttƒttƒ tƒdt ksÀJ ‚t ttƒttƒ tƒdt ksâJ ‚t tdt ƒtdt ƒ t tƒtd ksJ ‚t ttƒttƒ tƒtks2J ‚t ttƒtdt ƒ tƒdt ksZJ ‚t ttƒd tƒdt kszJ ‚t tdt ƒttƒttƒ  tƒtks¦J ‚t t	ttƒƒtƒdt ksÆJ ‚t t
tdt ƒƒttdt ƒƒ tƒtksöJ ‚t tdt ƒt	ttƒtdt ƒ ƒ tƒtks*J ‚t tttƒtdt ƒ ƒtƒdt ksVJ ‚t ttdt ƒƒtƒtksvJ ‚t dttƒd  tƒtks–J ‚t ttd ƒtƒdks²J ‚t ttƒd tƒdt ksÒJ ‚t tdt d d ƒtƒtddƒksüJ ‚t tdƒtd  t d tƒdtdƒd  ks0J ‚t td d t tƒd u sPJ ‚t tttƒƒtƒdt kspJ ‚t ttƒd ttƒd  tƒtju sšJ ‚t ttƒtƒtju s´J ‚t ttƒtttƒ  tƒdt ksÜJ ‚t ttdt ƒ tƒtksüJ ‚t t	tƒtƒd u sJ ‚t t	tt ƒtƒdt ks4J ‚t t	tt ƒtƒdt ksTJ ‚t t	tƒtƒd u slJ ‚t t	t
ttƒttdt ƒ  ƒddtƒdt ks¤J ‚t t	t
tdt ƒtttƒ  ƒddtƒdt ksÜJ ‚t t	ttƒƒtƒdt ksüJ ‚t t	dt t ƒtƒtksJ ‚t t	ttttƒ  ƒtƒd u s@J ‚t t	ttd ƒttƒ ƒtƒdt kslJ ‚t t
tƒtƒd u s„J ‚t t	tƒttƒ tƒd u s¤J ‚t ttƒt tƒd u sÀJ ‚t tttttƒƒƒƒtƒtksäJ ‚tdd	„ ttttttfD ƒƒsJ ‚t ttttƒƒƒtƒtks(J ‚t ttttƒttƒ ƒƒtƒdt ksTJ ‚t ttƒtjktƒdt ksvJ ‚t tdktƒd u sŽJ ‚t td td  d tƒd u s²J ‚t ttƒtƒd u sÊJ ‚t ttd d ƒtƒd u sêJ ‚t td d d tƒd u s
J ‚t tt d tƒd u s&J ‚t ttdtƒƒtdtƒ tƒd u sNJ ‚td
tdk ftd tdkft
tƒdfƒ} t | tƒd u sŠJ ‚tdddƒ‰ tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ d S )NrF   r]   rO   rI   rH   F)Úevaluatec                 s   s$   | ]}t t|tƒƒtƒtkV  qd S rV   )r2   r   rB   r   )Ú.0re   rS   rS   rT   Ú	<genexpr>ç   rk   z#test_periodicity.<locals>.<genexpr>r   rG   TÚmc                      s   t tˆ ƒˆ ƒS rV   ©r2   r   rS   ©rs   rS   rT   rU   û   rk   z"test_periodicity.<locals>.<lambda>c                      s   t tˆ d ƒˆ ƒS ©N)r   r   rt   rS   ru   rS   rT   rU   ü   rk   c                      s   t tˆ ƒˆ d ƒS rv   rt   rS   ru   rS   rT   rU   ý   rk   c                      s   t tˆ d ƒˆ d ƒS rv   rt   rS   ru   rS   rT   rU   þ   rk   )r2   r   rB   r   r   r   r   rC   r   r   r   r   r   r   r   r	   ZZeror   rD   r   Úallrm   r   r,   r   r-   r?   rZ   )ÚprS   ru   rT   Útest_periodicity¹   s|    """""0 ( , 04,   *4  *(   88  $, $ÿ ,"$  ((ry   c                   C   s¢   t ttƒtddtksJ ‚t ttƒttƒ tdddt ks@J ‚t ttƒtƒdt ksZJ ‚t ttt ƒtƒdt ttƒ ks€J ‚t t	tttƒƒƒtƒtksžJ ‚d S )NT)ÚcheckrF   )
r2   r   rB   r   r   r   r   rC   Úabsr   rS   rS   rS   rT   Útest_periodicity_check  s
    &&r|   c                   C   s¾   t tjtdƒtdƒgƒdks J ‚t td td tgƒtks>J ‚t dt td gƒdt ks^J ‚t tjdt gƒd u sxJ ‚t tdƒdt  td tddƒ tjt gƒtdƒdt  ksºJ ‚d S )NrF   rI   é   rO   rH   )r3   r	   rm   r   ÚOner   r   rS   rS   rS   rT   Ú	test_lcim	  s
      r   c                   C   s6  t dt tt dt¡ddks"J ‚t dt ttt dƒddksDJ ‚t td ttdtƒddksdJ ‚t dtd  tt dt¡ddksŠJ ‚t dtd  tt t d¡ddks²J ‚t ttƒtƒdksÈJ ‚t td td  ttƒdksèJ ‚t t	tƒt	tƒ tƒdksJ ‚t d	td  dtd   ttƒdks2J ‚d S )
NrH   r   )rd   TFrF   rI   rG   rM   )
r4   rB   r8   rY   r   rc   ra   r   rC   r   rS   rS   rS   rT   Útest_is_convex  s    "" &(  r€   c                   C   st  t ttƒttt d td ƒƒt d td hks6J ‚t ttƒtt dtd ¡ƒtju s\J ‚t ttƒtƒtju stJ ‚t ttƒt	tƒ ttdtƒƒtd tt
ddƒ hks¬J ‚t ttƒttdtƒƒdthksÎJ ‚t td td  tƒtt
ddƒƒksöJ ‚t td td  ttddƒƒtju s J ‚t td d td  tƒdtdƒ dtdƒ hksXJ ‚t td d td  ttddƒƒdtdƒ hksŽJ ‚t td td  dtd   ttjƒtd	dt
ddƒƒksÌJ ‚t ttƒtƒtju sæJ ‚t ttƒt ttjƒd
hksJ ‚t t	tƒtttddƒtddƒƒƒdt thks<J ‚t tttjƒtjksVJ ‚t tttjƒtjkspJ ‚d S )NrF   r   rO   rI   rG   rJ   rK   rL   r]   rH   éúÿÿÿrN   )r5   r   rB   r8   r   ra   r	   rX   r   r   r   r   r9   r   rR   r   r   r;   rC   rS   rS   rS   rT   Útest_stationary_points  sV    ÿÿÿÿÿÿÿ
ÿ
 ÿ
$ÿ
ÿ
ÿ
 
ÿ
ÿ
r‚   c                
   C   sh  t ttƒtƒtju sJ ‚t ttƒttddƒƒtdƒks:J ‚t ttƒtƒtu sPJ ‚t ttƒttt d td ƒƒtju szJ ‚t ttƒt	tƒ ttj
ƒtjksžJ ‚tt ttƒt	tƒ ttttddƒ ttddƒ ƒƒƒtdƒd ksäJ ‚t td td  tƒtu sJ ‚t td td  ttddƒƒtd	ƒks0J ‚t td td  ttddƒƒtdd
ƒks^J ‚tt td  td  td  d tƒƒdtdƒ d tddƒ ks¦J ‚t ttƒttt dƒƒtdƒksÌJ ‚t ttƒt ttj
ƒtju sîJ ‚t t	tƒtttddƒtddƒƒƒtju sJ ‚t t	tƒttƒ ttj
ƒtdƒksDJ ‚t tttj
ƒtks\J ‚t ttd t ƒttddƒƒdks„J ‚t tdtd  dt  ƒttddƒƒdks´J ‚t tdt dtd  d  ƒttddƒƒdksèJ ‚t tttd d ƒ ttj
ƒdksJ ‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )Nr   rH   rO   rI   rM   rK   rF   rJ   é   rL   é
   é)   i   i+  r   rN   é<   é   i  é   c                   S   s   t ttƒttjƒS rV   )r7   r   rB   r	   rX   rS   rS   rS   rT   rU   U  rk   ztest_maximum.<locals>.<lambda>c                   S   s   t tttƒƒttjƒS rV   )r7   r   r   rB   r	   rX   rS   rS   rS   rT   rU   V  rk   c                   S   s"   t dtd td  d  ttjƒS r`   )r7   rB   rC   r	   rX   rS   rS   rS   rT   rU   W  rk   c                   S   s   t ttƒttƒƒS rV   )r7   r   rB   rS   rS   rS   rT   rU   X  rk   c                   S   s   t ttƒtt tjƒS rV   )r7   r   rB   rC   r	   rX   rS   rS   rS   rT   rU   Y  rk   c                   S   s   t ttƒtjƒS rV   )r7   r   rB   r	   r~   rS   rS   rS   rT   rU   Z  rk   )r7   r   rB   r	   r~   r8   r   r   r   r   rR   rm   r.   r   r   r   r   ÚNegativeOner;   rC   r{   rD   r?   rn   rS   rS   rS   rT   Útest_maximum=  s>    "*$4
ÿ ,.&ÿ
&" ÿ
((04(rŠ   c                
   C   s¦  t ttƒtƒtju sJ ‚t ttƒttddƒƒtdƒks:J ‚t ttƒtƒt u sRJ ‚t ttƒttt d td ƒƒtju s|J ‚t ttƒt	tƒ ttj
ƒtddƒks¤J ‚tt ttƒt	tƒ ttttddƒ ttddƒ ƒƒƒtdƒ d ksìJ ‚t td td  tƒtddƒksJ ‚t td td  ttd	d
ƒƒtddƒks@J ‚t td td  td  d tƒtdƒkspJ ‚t ttƒttdtƒƒtdƒks”J ‚t ttƒt ttj
ƒt u s¶J ‚t t	tƒtttd
dƒtddƒƒƒtju säJ ‚t t	tƒttƒ ttj
ƒtdƒ ksJ ‚t tttj
ƒtks&J ‚t tttd d ƒ ttj
ƒdksNJ ‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )NrH   rO   rG   rF   rI   rM   rK   içÿÿÿrJ   r   rN   r„   r]   r   c                   S   s   t ttƒttjƒS rV   )r6   r   rB   r	   rX   rS   rS   rS   rT   rU   p  rk   ztest_minimum.<locals>.<lambda>c                   S   s   t tttƒƒttjƒS rV   )r6   r   r   rB   r	   rX   rS   rS   rS   rT   rU   q  rk   c                   S   s"   t dtd td  d  ttjƒS r`   )r6   rB   rC   r	   rX   rS   rS   rS   rT   rU   r  rk   c                   S   s   t ttƒttƒƒS rV   )r6   r   rB   rS   rS   rS   rT   rU   s  rk   c                   S   s   t ttƒtt tjƒS rV   )r6   r   rB   rC   r	   rX   rS   rS   rS   rT   rU   t  rk   c                   S   s   t ttƒtjƒS rV   )r6   r   rB   r	   r~   rS   rS   rS   rT   rU   u  rk   )r6   r   rB   r	   r‰   r8   r   r   r   r   rR   r   r.   r   r   r   r;   rC   r?   rn   rS   rS   rS   rT   Útest_minimum]  s2    "*(4ÿ&.0$" ÿ
*(r‹   c                   C   s>   t tdƒtd  dttd d ƒ  tƒtdƒd ks:J ‚d S )NrI   rH   rF   )r7   r   rB   rS   rS   rS   rT   Útest_issue_19869x  s    (
ÿrŒ   c                  C   s,   t tƒ} t| ttjƒtdtddƒks(J ‚d S )Nr   FT)r{   rD   r/   r	   rR   r8   r   )re   rS   rS   rT   Útest_issue_16469}  s    r   c                   C   s0   t ttt td tjd   ƒtƒdks,J ‚d S )NrO   rF   rM   )r2   r   r   r   rB   r	   rm   rS   rS   rS   rT   Útest_issue_18747‚  s    rŽ   c                   C   s0   t tƒtd k ¡ t dtdƒd ¡ks,J ‚d S )NrI   rG   rH   rF   )r   rB   r   Zas_setr8   ra   r	   rS   rS   rS   rT   Útest_issue_25942‡  s    r   N)kZsympy.core.functionr   Zsympy.core.numbersr   r   r   r   r   Zsympy.core.relationalr   Zsympy.core.singletonr	   Zsympy.core.symbolr
   r   Z$sympy.functions.elementary.complexesr   r   Z&sympy.functions.elementary.exponentialr   r   Z#sympy.functions.elementary.integersr   Z(sympy.functions.elementary.miscellaneousr   Z$sympy.functions.elementary.piecewiser   Z(sympy.functions.elementary.trigonometricr   r   r   r   r   r   r   r   r   r   r   r   Z%sympy.functions.elementary.hyperbolicr   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   Z'sympy.functions.special.gamma_functionsr+   Z'sympy.functions.special.error_functionsr,   Z"sympy.matrices.expressions.matexprr-   Zsympy.simplify.simplifyr.   Zsympy.calculus.utilr/   r0   r1   r2   r3   r4   r5   r6   r7   Zsympy.sets.setsr8   r9   r:   r;   Zsympy.sets.fancysetsr<   Zsympy.sets.conditionsetr=   Zsympy.testing.pytestr>   r?   r@   rA   Z	sympy.abcrB   rC   rD   r[   r\   rf   rg   rh   ri   ro   ry   r|   r   r€   r‚   rŠ   r‹   rŒ   r   rŽ   r   rS   rS   rS   rT   Ú<module>   s\   88,'
@


!
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