U
    ZÊ¹j}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.t‚t ttƒttdtƒƒtddƒksRt‚t ttƒttdtƒƒtt tƒksxt‚t ttƒtttd tƒƒtt dƒks¢t‚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sèt‚t dtd  ttddƒƒtdtƒk�st‚t t
tƒttddƒƒtt
dƒt
dƒƒk�s@t‚t ttƒt ttjƒtt dƒk�sht‚t tdt d ƒttddƒƒtdtdƒƒk�sšt‚t ttd  td t  ttjƒtdƒk�sÊt‚t ttd  td t  t ttjƒttƒk�sþt‚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�sBt‚t ttƒttt dƒƒtddƒk�sjt‚t ttƒttjƒtjk�sˆt‚t tttd d ƒ ttjƒt dd¡k�s¸t‚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   ú]/var/www/html/bwave/python/venv/lib/python3.8/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   ÚAssertionErrorr   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s8t‚d S )NrF   rI   rH   )r/   r   rB   r	   rR   r8   r   rX   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,t‚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”t‚t t	tƒttddt ƒƒtt 
dt¡t 
tdt ¡ƒksÐt‚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t‚t ttƒtdt d ƒ ttjƒttddƒtddƒk�sPt‚t dttd ƒ ttjƒtdtddƒk�s~t‚t dt d ttjƒtt 
t d¡t 
dt¡ƒk�s¶t‚t dtd d  d ttjƒtt 
t d¡t 
dd¡t 
dt¡ƒk�s t‚t td t ttjƒtd	tƒk�s&t‚t td td  ttjƒtd	tƒk�sPt‚t tt ttjƒtdtƒk�srt‚t td ttd ƒ ttjƒtt d	d¡t 
dt¡ƒk�s°t‚t tttƒd d ƒttjƒ} |  dt d ¡�ræt‚|  d
¡�söt‚tdddd�}t td|  ttjƒtdtƒk�s*t‚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’t‚t ttƒttƒ ttjƒtjk�s¸t‚t ttƒttjƒtd	dƒk�sÚt‚t dtttƒƒ ttjƒt td	ƒt¡k�s
t‚t ttƒttƒ ttjƒtjk�s0t‚t t tƒt!tƒ ttjƒtjk�sVt‚t t"tƒt#tƒ ttjƒtjk�s|t‚t t$tƒttjƒtdtƒk�sžt‚t t%tƒttjƒt 
d	d¡k�sÂt‚t t%tƒt$tƒ ttjƒtj&k�sèt‚t t'tƒttjƒt (dd¡k�st‚t t)tƒttjƒtt 
t d	¡t 
dt¡ƒk�s@t‚t t*tƒttjƒttt d	ƒtdtƒƒk�spt‚t t+tƒttjƒttt d	ƒtdtƒƒk�s t‚t,t-t.fD ]:}t |tƒttjƒtt 
t d¡t 
dt¡ƒk�sªt‚�qªt t/tƒttjƒ d¡dk�st‚t dttƒt  ttjƒttjt0tt1t ttƒ dƒtjƒƒk�sNt‚t t2t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�sªt‚t t2tƒttjƒttjtjƒk�sÐt‚t3t4dd„ ƒ t3t4dd„ ƒ t tt5tƒ ttjƒtjk�st‚d S )Nr   rF   FTrI   rH   rO   éþÿÿÿrG   rK   Úd)ZevenÚ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)6r0   r   rB   r8   r   rX   r   r;   r   r   rZ   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'   rY   r)   ÚLopenr(   r   r   r"   r*   r$   r   r=   r   r   r?   r[   r+   )Údomainr_   ra   ÚfrS   rS   rT   Útest_continuous_domainJ   s¬    ,,ÿÿ
 ÿ
ÿ
 ÿ
.ÿ
$ÿ
&*"
 
ÿ& ÿÿ&"0&&&"$&$ 
ÿ
 ÿ
 ÿ 
ÿ" ÿ þ ÿrh   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:t‚d S )Nr   T)r   r   r   rB   r0   r	   rR   rX   )Z	acot_contrS   rS   rT   Útest_continuous_domain_acotŠ   s    "ri   c                   C   s$   t ttƒttjƒ d¡dks t‚d S )NrG   F)r0   r+   rB   r	   rR   rd   rX   rS   rS   rS   rT   Útest_continuous_domain_gamma�   s    rj   c                   C   s.   t td dt  ttjƒt dt¡ks*t‚d S )NrF   rH   )r0   rB   r	   rR   r8   rZ   r   rX   rS   rS   rS   rT   Ú test_continuous_domain_neg_power“   s    rk   c                	   C   sD  t ttdt ƒ tddddƒ¡tƒttjdddƒks8t‚t tttd ƒ tddƒ¡tƒttt	dƒ dƒtddƒƒksxt‚t ttd t tƒ tddƒ¡tƒttt	dƒ d tj dƒtdt
ddƒt	dƒd  ƒtddƒƒksàt‚t tttd  ƒ tj¡tƒttjtdƒƒk�st‚t tttd  ƒ tj¡tƒttjtdƒƒk�sHt‚t ttd d	t  d td  ƒ tj¡tƒttjtdƒƒk�sŒt‚t td	dttd  ƒ tdd	ƒ¡tƒtt tƒk�sÄt‚t tdttd  ƒ tdd	ƒ¡tƒttd	ƒd dƒk�s t‚t tttd d  ƒ tj¡tƒttjtddƒƒk�s:t‚t tttd ƒ ttdd	ddƒtdd
ƒƒ¡tƒttt	d
ƒ dƒtt	d	ƒ dddƒtdd	ddƒtdd
ƒƒk�sªt‚t tdƒ td	dƒ¡tƒtjk�sÐt‚t ttd td  ƒ tdtƒ¡tƒttddddƒtdtƒƒk�st‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )NrF   rH   TFrG   rO   é   r^   rI   rK   c                   S   s   t tƒS rV   )r1   rB   rS   rS   rS   rT   rU   ³   ó    z#test_not_empty_in.<locals>.<lambda>c                   S   s   t tddƒtƒS )Nr   rH   )r1   r8   rB   rS   rS   rS   rT   rU   ´   rm   c                   S   s   t ttƒ tj¡ttƒS rV   )r1   r9   rB   Ú	intersectr	   rR   rD   rS   rS   rS   rT   rU   ¶   rm   )r1   r9   rB   rn   r8   r	   ÚHalfrX   r;   r   r   rR   r:   rD   r   rY   r?   Ú
ValueErrorr[   rS   rS   rS   rT   Útest_not_empty_in˜   sb    "ÿÿ" ÿÿÿ
ÿ
,ÿ
$
ÿ
"ÿ
 ÿ
ÿÿ" ÿþ
&$ÿ
ÿrq   c                     sâ  t tdt ƒtƒtkst‚t dtdt ƒ tƒtd ks<t‚t ttƒd tƒdt ksZt‚t dtdt ƒ tƒtd ks|t‚t ttƒttƒ tƒdt ksžt‚t ttƒttƒ tƒdt ksÀt‚t ttƒttƒ tƒdt ksât‚t tdt ƒtdt ƒ t tƒtd k�st‚t ttƒt	tƒ tƒtk�s2t‚t ttƒtdt ƒ tƒdt k�sZt‚t ttƒd tƒdt k�szt‚t tdt ƒttƒttƒ  tƒtk�s¦t‚t t
ttƒƒtƒdt k�sÆt‚t tt	dt ƒƒttdt ƒƒ tƒtk�söt‚t tdt ƒt
ttƒtdt ƒ ƒ tƒtk�s*t‚t tttƒtdt ƒ ƒtƒdt k�sVt‚t ttdt ƒƒtƒtk�svt‚t dttƒd  tƒtk�s–t‚t ttd ƒtƒdk�s²t‚t ttƒd tƒdt k�sÒt‚t tdt d d ƒtƒtddƒk�süt‚t tdƒtd  t d tƒdtdƒd  k�s0t‚t td d t tƒd k�sPt‚t tttƒƒtƒdt k�spt‚t ttƒd ttƒd  tƒtjk�sšt‚t ttƒtƒtjk�s´t‚t ttƒtttƒ  tƒdt k�sÜt‚t ttdt ƒ tƒtk�süt‚t t
tƒtƒd k�st‚t t
tt ƒtƒdt k�s4t‚t t
tt ƒtƒdt k�sTt‚t t
tƒtƒd k�slt‚t t
tttƒttdt ƒ  ƒdd�tƒdt k�s¤t‚t t
ttdt ƒtttƒ  ƒdd�tƒdt k�sÜt‚t t
ttƒƒtƒdt k�süt‚t t
dt t ƒtƒtk�st‚t t
ttttƒ  ƒtƒd k�s@t‚t t
ttd ƒttƒ ƒtƒdt k�slt‚t ttƒtƒd k�s„t‚t t
tƒttƒ tƒd k�s¤t‚t ttƒt tƒd k�sÀt‚t tttttƒƒƒƒtƒtk�sät‚tdd	„ tttttt	fD ƒƒ�st‚t ttttƒƒƒtƒtk�s(t‚t ttttƒttƒ ƒƒtƒdt k�sTt‚t ttƒtjktƒdt k�svt‚t tdktƒd k�sŽt‚t td td  d tƒd k�s²t‚t ttƒtƒd k�sÊt‚t ttd d ƒtƒd k�sêt‚t td d d tƒd k�s
t‚t tt d tƒd k�s&t‚t ttdtƒƒtdtƒ tƒd k�sNt‚td
tdk ftd tdkfttƒdfƒ} t | tƒd k�sŠt‚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.0rg   rS   rS   rT   Ú	<genexpr>ç   s     z#test_periodicity.<locals>.<genexpr>r   rG   TÚmc                      s   t tˆ ƒˆ ƒS rV   ©r2   r   rS   ©ru   rS   rT   rU   û   rm   z"test_periodicity.<locals>.<lambda>c                      s   t tˆ d ƒˆ ƒS ©N)r   r   rv   rS   rw   rS   rT   rU   ü   rm   c                      s   t tˆ ƒˆ d ƒS rx   rv   rS   rw   rS   rT   rU   ý   rm   c                      s   t tˆ d ƒˆ d ƒS rx   rv   rS   rw   rS   rT   rU   þ   rm   )r2   r   rB   r   rX   r   r   r   rC   r   r   r   r   r   r   r   r	   ZZeror   rD   r   Úallro   r   r,   r   r-   r?   r[   )ÚprS   rw   rT   Útest_periodicity¹   s†    """""0 ( , 04,   *4  *(   88  $, $     ÿ ,"$  ((r{   c                   C   s¢   t ttƒtdd�tkst‚t ttƒttƒ tdd�dt ks@t‚t ttƒtƒdt ksZt‚t ttt ƒtƒdt t	tƒ ks€t‚t t
tttƒƒƒtƒtksžt‚d S )NT)ÚcheckrF   )r2   r   rB   r   rX   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 t‚t td td tgƒtks>t‚t dt td gƒdt ks^t‚t tjdt gƒd ksxt‚t tdƒdt  td tddƒ tjt gƒtdƒdt  ksºt‚d S )NrF   rI   é   rO   rH   )r3   r	   ro   rX   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"t‚t dt ttt dƒd�dksDt‚t td ttdtƒd�dksdt‚t dtd  tt dt¡d�dksŠt‚t dtd  tt t d¡d�dks²t‚t ttƒtƒdksÈt‚t td t	d  tt	ƒdksèt‚t t
tƒt
t	ƒ tƒdk�st‚t d	td  dt	d   tt	ƒdk�s2t‚d S )
NrH   r   )rf   TFrF   rI   rG   rM   )r4   rB   r8   rZ   r   rX   re   rc   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s6t‚t ttƒtt dtd ¡ƒtjks\t‚t t	tƒtƒtjkstt‚t ttƒt
tƒ ttdtƒƒtd ttddƒ hks¬t‚t ttƒttdtƒƒdthksÎt‚t td td  tƒttddƒƒksöt‚t td td  ttddƒƒtjk�s t‚t td d td  tƒdtdƒ dtdƒ hk�sXt‚t td d td  ttddƒƒdtdƒ hk�sŽt‚t td td  dtd   ttjƒtd	dtddƒƒk�sÌt‚t ttƒtƒtjk�sæt‚t ttƒt ttjƒd
hk�st‚t t
tƒtttddƒtddƒƒƒdt thk�s<t‚t tttjƒtjk�sVt‚t tttjƒtjk�spt‚d S )NrF   r   rO   rI   rG   rJ   rK   rL   r^   rH   éúÿÿÿrN   )r5   r   rB   r8   r   rX   rc   r	   rY   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kst‚t ttƒttddƒƒtdƒks:t‚t ttƒtƒtksPt‚t ttƒttt	 d t	d ƒƒtjkszt‚t ttƒt
tƒ ttjƒtjksžt‚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sät‚t td td  tƒtk�st‚t td td  ttddƒƒtd	ƒk�s0t‚t td td  ttddƒƒtdd
ƒk�s^t‚tt td  td  td  d tƒƒdtdƒ d tddƒ k�s¦t‚t ttƒttt dƒƒtdƒk�sÌt‚t ttƒt ttjƒtjk�sît‚t t
tƒtttddƒtddƒƒƒtjk�st‚t t
tƒttƒ ttjƒtdƒk�sDt‚t tttjƒtk�s\t‚t ttd t ƒttddƒƒdk�s„t‚t tdtd  dt  ƒttddƒƒdk�s´t‚t tdt dtd  d  ƒttddƒƒdk�sèt‚t tttd d ƒ ttjƒdk�st‚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+  rƒ   rN   é<   é   i  é   c                   S   s   t ttƒttjƒS rV   )r7   r   rB   r	   rY   rS   rS   rS   rT   rU   U  rm   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	   rY   rS   rS   rS   rT   rU   V  rm   c                   S   s"   t dtd td  d  ttjƒS rb   )r7   rB   rC   r	   rY   rS   rS   rS   rT   rU   W  rm   c                   S   s   t ttƒttƒƒS rV   )r7   r   rB   rS   rS   rS   rT   rU   X  rm   c                   S   s   t ttƒtt tjƒS rV   )r7   r   rB   rC   r	   rY   rS   rS   rS   rT   rU   Y  rm   c                   S   s   t ttƒtjƒS rV   )r7   r   rB   r	   r€   rS   rS   rS   rT   rU   Z  rm   )r7   r   rB   r	   r€   rX   r8   r   r   r   r   rR   ro   r.   r   r   r   r   ÚNegativeOner;   rC   r}   rD   r?   rp   rS   rS   rS   rT   Útest_maximum=  s>    "*$4
ÿ ,.&ÿ
&" ÿ
((04(rŒ   c                
   C   s¦  t ttƒtƒtjkst‚t ttƒttddƒƒtdƒks:t‚t ttƒtƒt ksRt‚t ttƒttt	 d t	d ƒƒtjks|t‚t ttƒt
tƒ ttjƒtddƒks¤t‚tt ttƒt
tƒ ttt	tddƒ t	tddƒ ƒƒƒtdƒ d ksìt‚t td td  tƒtddƒk�st‚t td td  ttd	d
ƒƒtddƒk�s@t‚t td td  td  d tƒtdƒk�spt‚t ttƒttdtƒƒtdƒk�s”t‚t ttƒt ttjƒt k�s¶t‚t t
tƒtttd
dƒtddƒƒƒtjk�sät‚t t
tƒttƒ ttjƒtdƒ k�st‚t tttjƒtk�s&t‚t tttd d ƒ ttjƒdk�sNt‚ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ d S )NrH   rO   rG   rF   rI   rM   rK   içÿÿÿrJ   r   rN   r†   r^   rƒ   c                   S   s   t ttƒttjƒS rV   )r6   r   rB   r	   rY   rS   rS   rS   rT   rU   p  rm   ztest_minimum.<locals>.<lambda>c                   S   s   t tttƒƒttjƒS rV   )r6   r   r   rB   r	   rY   rS   rS   rS   rT   rU   q  rm   c                   S   s"   t dtd td  d  ttjƒS rb   )r6   rB   rC   r	   rY   rS   rS   rS   rT   rU   r  rm   c                   S   s   t ttƒttƒƒS rV   )r6   r   rB   rS   rS   rS   rT   rU   s  rm   c                   S   s   t ttƒtt tjƒS rV   )r6   r   rB   rC   r	   rY   rS   rS   rS   rT   rU   t  rm   c                   S   s   t ttƒtjƒS rV   )r6   r   rB   r	   r€   rS   rS   rS   rT   rU   u  rm   )r6   r   rB   r	   r‹   rX   r8   r   r   r   r   rR   r   r.   r   r   r   r;   rC   r?   rp   rS   rS   rS   rT   Útest_minimum]  s2    "*(4ÿ&.0$" 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:t‚d S )NrI   rH   rF   )r7   r   rB   rX   rS   rS   rS   rT   Útest_issue_19869x  s    (
ÿrŽ   c                  C   s,   t tƒ} t| ttjƒtdtddƒks(t‚d S )Nr   FT)r}   rD   r/   r	   rR   r8   r   rX   )rg   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,t‚d S )NrO   rF   rM   )r2   r   r   r   rB   r	   ro   rX   rS   rS   rS   rT   Útest_issue_18747‚  s    r�   c                   C   s0   t tƒtd k ¡ t dtdƒd ¡ks,t‚d S )NrI   rG   rH   rF   )r   rB   r   Zas_setr8   rc   r	   rX   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]   rh   ri   rj   rk   rq   r{   r~   r�   r‚   r„   rŒ   r�   rŽ   r�   r�   r‘   rS   rS   rS   rT   Ú<module>   s\   88,'
@


!
G  
