U
    L?h+W  ã                   @   s¼  d dl mZ d dl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 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mZmZ d d	l m!Z! d d
l"m#Z#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/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5 edƒZ6edddZ7edddZ8eddd\Z9Z:dd„ Z;dd„ Z<dd„ Z=d d!„ Z>d"d#„ Z?d$d%„ Z@e4d&d'„ ƒZAd(d)„ ZBd*d+„ ZCd,d-„ ZDd.d/„ ZEd0d1„ ZFd2d3„ ZGd4S )5é    )ÚAccumBounds)ÚEÚFloatÚIÚRationalÚnanÚooÚpiÚzoo)ÚEqÚGeÚGtÚLeÚLtÚNe)ÚS)ÚSymbolÚsymbols)Ú	factorial)ÚexpÚlog)ÚceilingÚfloorÚfrac)Úsqrt)ÚsinÚcosÚtan)ÚRootOfÚCRootOf)ÚIntegers)ÚInterval)ÚImageSet)ÚLambda)Ú	unchanged)ÚXFAILÚraisesÚxÚiT)Z	imaginaryÚy©Úrealzk,n)Úintegerc                  C   sø  t tƒtkst‚t tƒtks t‚t t ƒt ks4t‚t tƒtksDt‚t dƒdksTt‚t dƒdksdt‚t dƒdkstt‚t tƒdks„t‚t t ƒdks–t‚t dt ƒdksªt‚t dt ƒdks¾t‚t tƒd	ksÎt‚t t ƒd
ksàt‚t tjƒdksòt‚t t	ddƒƒdks
t‚t t	dd	ƒƒdks"t‚t t	dd	ƒƒdks:t‚t t	dd	ƒ ƒdksTt‚t t
dƒƒdksjt‚t t
dƒ ƒdks‚t‚t t
dƒƒdks˜t‚t t
dƒ ƒdks°t‚t tƒtksÂt‚t t ƒt ksØt‚t tƒ} | jt krü| jd tks t‚t tt ƒtt kst‚t t t ƒt t ks8t‚t ttt d ƒt ƒttt d ƒt ksjt‚t dt ƒdt ks„t‚t dt ƒdt ksžt‚t td ƒdks´t‚t t d ƒt ksÎt‚t td ƒdksät‚t td ƒdksút‚t tt ƒdkst‚t tt ƒd	t ks*t‚t t tƒƒd	ks@t‚t t tƒƒt tƒksZt‚t t tƒƒt tƒkstt‚tt tƒs„t‚tt dt ƒs˜t‚tt tt ƒs¬t‚t tƒtks¾t‚t dt ƒdt ksØt‚t tt ƒtt ksòt‚tt td ƒst‚tt tt ƒst‚t td	 ƒt tƒd	 ks8t‚t tt ƒt tƒt ksVt‚t td	 ƒt tƒd	 kstt‚t tt ƒt tƒt ks’t‚t d	tt  t ƒdt tƒt  ks¼t‚t tt ƒtt ksÖt‚tt tt ƒsêt‚t tt ƒtt kst‚t t	ddƒtt  ƒdd	t  ks,t‚t tdƒƒdksBt‚t tdƒƒdksXt‚t tdƒƒdksnt‚t tdƒtdƒ ƒdksŒt‚tt tdƒtdƒ ƒjddƒd	ks¶t‚t tdƒtdƒ ƒdksÔt‚t tƒtk dksêt‚t tƒtkdks t‚t tƒtkdkst‚t tƒtkdks,t‚t tƒtkjs@t‚t tƒtkjsTt‚t tƒtkjsht‚t tƒtkjs|t‚t tƒtkdks’t‚t tƒtk dks¨t‚t tƒt kdksÀt‚t tƒt kdksØt‚t tƒ t¡tttƒ ksøt‚t tƒ t¡tt ƒ kst‚t tƒ t¡ tt ¡t t ƒks@t‚t tƒ t¡ tt¡t tƒksdt‚t tƒ t¡ tt¡tt ƒ ksŒt‚t tƒ t¡ tt ¡ttƒ ks´t‚tt tƒtttƒ ƒsÐt‚tt tƒtt ƒ ƒsìt‚t ddd}t ddd }t d!dd"}t d#dd$}t |ƒdk dks2t‚t |ƒdkdksHt‚t |ƒdkdks^t‚t |ƒdkdkstt‚t |ƒdkdksŠt‚t |ƒdk|dkks¤t‚t |ƒdk |dk ks¾t‚t |ƒdk dksÔt‚t |ƒdkdksêt‚t |ƒdk dk	s t‚t |ƒdk|dk k	st‚t |ƒdk|dkk	s4t‚t |ƒdkdk	sJt‚t |ƒd	k|d	kk	sdt‚t |ƒdkdk	szt‚t |ƒdkdk	st‚t |ƒj!dk	s¤t‚t |ƒj"dk	s¸t‚t |ƒj!dk	sÌt‚t |ƒj"dk	sàt‚t |ƒj!dk	sôt‚t |ƒj"dk
st‚t |ƒj!d k
st‚t |ƒj"d k
s0t‚t ddd%dkdk
sJt‚t ddd%dkdk
sdt‚t ddd%dkdk
s~t‚t ddd%dk dk
s˜t‚t ddd%dkdk
s²t‚t ddd%dkdk
sÌt‚t ddd%dkdk
sæt‚t ddd%dk dks t‚t ddd%dkdkst‚t ddd%dkdks4t‚t ddd%dkdksNt‚t ddd%dk dksht‚t tƒd&kt#t tƒd&dd%ksŒt‚t tƒd'kt$t tƒd'dd%ks°t‚t tƒd(k t%t tƒd(dd%ksÔt‚t tƒd)kt&t tƒd)dd%ksøt‚t tƒd&ktdk kst‚t tƒd'ktdkks,t‚t tƒd(k td	k ksFt‚t tƒd)ktdkks`t‚t tƒtkttd k ks~t‚t tƒtkttkks˜t‚t tƒtk ttk ks²t‚t tƒtkttd kksÐt‚t t'td	 d*t  dƒƒdksôt‚d S )+Nr   é   éÿÿÿÿé   éýÿÿÿé   éþÿÿÿiúÿÿÿé   éüÿÿÿé   éùÿÿÿç      1@é   éïÿÿÿçÃõ(\Â@iøÿÿÿé   é   é   é   é
   é   T©Zchopé2   l    'öª~$DæA®7YáD3':ÿ^îXf FÚneg©ÚnegativeÚnn©ÚnonnegativeÚpos©ÚpositiveÚnp©Únonpositive©Úevaluateç      @çš™™™™™	Àç333333@ç333333û¿é   )(r   r   ÚAssertionErrorr   r
   r   r	   r   ÚHalfr   r   r   r(   ÚfuncÚargsr   r)   r'   r$   ÚkÚnr   r   ÚintÚevalfr   Úis_RelationalÚrewriter   r   Úsubsr   r   Zis_negativeZis_nonnegativer   r   r   r   r   )ÚerC   rF   rI   rL   © rb   ú`/var/www/html/venv/lib/python3.8/site-packages/sympy/functions/elementary/tests/test_integers.pyÚ
test_floor   s    2*(*ÿ
  ($(($$$$rd   c                     s°  t tƒtkst‚t tƒtks t‚t t ƒt ks4t‚t tƒtksDt‚t dƒdksTt‚t dƒdksdt‚t dƒdkstt‚t tƒdks„t‚t t ƒdks–t‚t dt ƒdksªt‚t dt ƒdks¾t‚t tƒd	ksÎt‚t t ƒd
ksàt‚t tjƒdksòt‚t t	ddƒƒdks
t‚t t	ddƒƒdks"t‚t t	ddƒ ƒdks<t‚t t
dƒƒdksRt‚t t
dƒ ƒdksjt‚t t
dƒƒdks€t‚t t
dƒ ƒdks˜t‚t tƒtksªt‚t t ƒt ksÀt‚t tƒ} | jt krä| jd tksèt‚t tt ƒtt kst‚t t t ƒt t ks t‚t ttt d	 ƒt ƒttt d	 ƒt ksRt‚t dt ƒdt kslt‚t dt ƒdt ks†t‚t td ƒtksœt‚t t d ƒdks´t‚t td ƒdksÊt‚t td ƒdksàt‚t tt ƒdksöt‚t tt ƒtd	 kst‚t t tƒƒd	ks&t‚t t tƒƒt tƒks@t‚t t tƒƒt tƒksZt‚tt tƒsjt‚tt dt ƒs~t‚tt tt ƒs’t‚t tƒtks¤t‚t dt ƒdt ks¾t‚t tt ƒtt ksØt‚tt td ƒsìt‚tt tt ƒs t‚t td ƒt tƒd kst‚t td ƒt tƒd ks<t‚t tdt  ƒt tƒdt  ksbt‚t tt ƒt tƒt ks€t‚t td ƒt tƒd ksžt‚t tt ƒt tƒt ks¼t‚t dt tt  ƒdt tƒt  ksæt‚t tt ƒtt ks t‚tt tt ƒst‚t tt ƒtt ks.t‚t t	ddƒtt  ƒddt  ksVt‚t tdƒƒdkslt‚t tdƒƒdks‚t‚t tdƒƒdks˜t‚t tdƒ tdƒ ƒdks¸t‚tt tdƒ tdƒ ƒjddƒd
ksät‚t tdƒtdƒ ƒdkst‚t tƒtkdkst‚t tƒtkdks.t‚t tƒtk dksDt‚t tƒtkdksZt‚t tƒtkjsnt‚t tƒtk js‚t‚t tƒtkjs–t‚t tƒtk jsªt‚t tƒt kdksÂt‚t tƒt kdksÚt‚t tƒtkdksðt‚t tƒtk dkst‚t tƒ t¡tt ƒ ks&t‚t tƒ t¡ttt ƒ ksHt‚t tƒ t¡ tt ¡ttƒ kspt‚t tƒ t¡ tt¡tt ƒ ks˜t‚t tƒ t¡ tt¡t tƒks¼t‚t tƒ t¡ tt ¡t t ƒksät‚tt tƒttt ƒ ƒst‚tt tƒtt ƒ ƒst‚t ddd}t ddd}t ddd }t d!dd"}t |ƒdkdksdt‚t |ƒdk |dkks~t‚t |ƒdkdks”t‚t |ƒdk|dkks®t‚t |ƒd
k|d
kksÈt‚t |ƒdk|dkksât‚t |ƒdk dksøt‚t |ƒdkdk	st‚t |ƒdk dk	s$t‚t |ƒdkdk	s:t‚t |ƒdkdk	sPt‚t |ƒdkdk	sft‚t |ƒdkdk	s|t‚t |ƒd#k|d#kk	s–t‚t |ƒdkdk	s¬t‚t |ƒdkdk	sÂt‚t |ƒj!dk	sÖt‚t |ƒj"dk	sêt‚t |ƒj!d k	sþt‚t |ƒj"d k
st‚t |ƒj!dk
s&t‚t |ƒj"dk
s:t‚t |ƒj!dk
sNt‚t |ƒj"dk
sbt‚t ddd$dkdk
s|t‚t ddd$dkdk
s–t‚t ddd$dkdk
s°t‚t ddd$dk dk
sÊt‚t ddd$dkdk
sät‚t ddd$dkdk
sþt‚t ddd$dkdkst‚t ddd$dk dks2t‚t ddd$dkdksLt‚t ddd$dkdksft‚t ddd$dkdks€t‚t ddd$dk dksšt‚t tƒd%kt#t tƒd%dd$ks¾t‚t tƒd&kt$t tƒd&dd$ksât‚t tƒd'k t%t tƒd'dd$kst‚t tƒd(kt&t tƒd(dd$ks*t‚t tƒd%ktd#kksDt‚t tƒd&ktd)kks^t‚t tƒd'k tdkksxt‚t tƒd(ktdkks’t‚t tƒtkttkks¬t‚t tƒtkttd kksÊt‚t tƒtk ttd kksèt‚t tƒtkttkkst‚t t'td d*t  dƒƒdks&t‚t(t)ttt*td# td  d dƒ ƒt+ƒ}t*td# td  d dƒ‰ t(t)ttˆ  ƒt+ƒ}| ,t-d+dƒ¡‡ fd,d-„t.d.d/ƒD ƒks¬t‚d S )0Nr   r-   r.   r3   r2   r/   r=   éûÿÿÿr;   r0   r5   r7   r8   r9   r:   r@   r6   é   g      @r>   r?   TrA   rB   l   ¡'öª~$DæA®7YáD3':ÿ^îXf FrC   rD   rF   rG   rI   rJ   rL   rM   r1   rO   rQ   rR   rS   rT   r4   rU   iöÿÿÿc                    s   h | ]}|ˆ  ’qS rb   rb   )Ú.0r(   ©Úfrb   rc   Ú	<setcomp>”  s     ztest_ceiling.<locals>.<setcomp>i÷ÿÿÿé   )/r   r   rV   r   r
   r   r	   r   rW   r   r   r   r(   rX   rY   r   r)   r'   r$   rZ   r[   r   r   r\   r]   r   r^   r_   r   r   r`   r   r   Zis_positiveZis_nonpositiver   r   r   r   r   r"   r#   r   r    Z	intersectr!   Úrange)ra   rC   rF   rI   rL   Úsrb   rh   rc   Útest_ceilingÖ   s    2&*( ,ÿ
 "(($($$$$$*rn   c            	      C   s¬
  t ttƒtƒst‚ttƒtddƒks(t‚tt ƒtddƒks@t‚ttƒtksPt‚ttƒdks`t‚ttƒtkspt‚tt	ddƒƒt	ddƒksŒt‚tt	ddƒ ƒt	ddƒksªt‚tt	ddƒƒt	ddƒksÆt‚t
ddd	} tt|  ƒtt| ƒ ksît‚tdt|   ƒtt| ƒ kst‚td
t|   ƒd
tt| ƒ  ks6t‚ttt|   ƒtt| ƒ ksXt‚tttt  ƒdksrt‚ttttt  ƒsŠt‚tttt  ƒttƒks¨t‚ttƒ t¡tttƒ ksÈt‚ttƒ t¡ttt ƒ ksêt‚ttƒ t¡ tt¡ttƒkst‚ttƒ t¡ tt ¡tt ƒks6t‚ttƒ t¡ tt ¡tt ƒks^t‚ttƒ t¡ tt¡ttƒks‚t‚tttƒtttƒ ƒsžt‚tttƒttt ƒ ƒs¼t‚t
ddd	} t
dddd}t
dddd}t
dddd}t
dddd}t
ddd}t
ddd}t
dddd}t
dddd}t| ƒ|ksFt‚t| ƒ|krXt‚t| ƒ|k t¡spt‚t| ƒ|k t¡sˆt‚t| ƒ|k sšt‚t| ƒ|k r¬t‚t| ƒ|k r¾t‚t| ƒ|k  t¡sÖt‚t| ƒ|krèt‚t| ƒ|ksút‚t| ƒ|kst‚t| ƒ|k t¡s$t‚t| ƒ|kr6t‚t| ƒ|ksHt‚t| ƒ|k t¡s`t‚t| ƒ|k t¡sxt‚tt| ƒ|ƒrŒt‚tt| ƒ|ƒr t‚tt| ƒ|ƒ t¡sºt‚tt| ƒ|ƒ t¡sÔt‚tt| ƒ|ƒsèt‚tt| ƒ|ƒsüt‚tt| ƒ|ƒ t¡st‚tt| ƒ|ƒ t¡s0t‚t| ƒ|k t¡sHt‚t| ƒ|krZt‚t| ƒ|k t¡srt‚t| ƒ|k t¡sŠt‚t| ƒ|k  t¡s¢t‚t| ƒ|k r´t‚t| ƒ|k rÆt‚t| ƒ|k  t¡sÞt‚t| ƒ|k t¡söt‚t| ƒ|kst‚t| ƒ|kst‚t| ƒ|k t¡s2t‚t| ƒ|k t¡sJt‚t| ƒ|ks\t‚t| ƒ|k t¡stt‚t| ƒ|k t¡sŒt‚tt| ƒ|ƒr t‚tt| ƒ|ƒ t¡sºt‚tt| ƒ|ƒ t¡sÔt‚tt| ƒ|ƒ t¡sît‚tt| ƒ|ƒ t¡st‚tt| ƒ|ƒst‚tt| ƒ|ƒ t¡s6t‚tt| ƒ|ƒ t¡sPt‚t| ƒtk sbt‚t| ƒtkstt‚t| ƒtkr†t‚t| ƒtkr˜t‚t| ƒt k r¬t‚t| ƒt krÀt‚t| ƒt ksÔt‚t| ƒt ksèt‚t| ƒdk sút‚t| ƒdkst‚t| ƒdkrt‚t| ƒdkr0t‚t| ƒdk rBt‚t| ƒdk t¡sZt‚t| ƒdk t¡srt‚t| ƒdks„t‚t| ƒtdƒksšt‚t| ƒtdƒtdƒ k t¡s¾t‚t| ƒtdƒtdƒ krÜt‚t| ƒtdƒkròt‚t| ƒtdƒtdƒ k t¡	st‚t| ƒtdƒtdƒ k	s4t‚tt| ƒtdƒƒ	rLt‚tt| ƒtdƒtdƒ ƒ t¡	srt‚tt| ƒtdƒtdƒ ƒ	r’t‚tt| ƒtdƒƒ	sªt‚tt| ƒtdƒtdƒ ƒ t¡	sÐt‚tt| ƒtdƒtdƒ ƒ	sðt‚t|ddj
st‚t|ddj
st‚t|ddj
s,t‚t|ddj 
s@t‚t| ƒj
sPt‚t| ƒj 
s`t‚t| ƒjd k
stt‚t| ƒjd k
sˆt‚ttƒj
s˜t‚ttƒj 
s¨t‚d S )Nr   r-   r;   r3   r/   r4   ÚrTr*   g      à?Úp_i)r,   rK   )r,   rE   Únp_i)r,   rN   Únn_i)r,   rH   Úp_rrJ   Ún_rrD   Únp_r)r+   rN   Únn_r)r+   rH   FrO   )!Ú
isinstancer   r'   rV   r   r   r
   r   r[   r   r   r   rZ   r$   r_   r   r   r)   r`   r	   r   r   Úhasr   r   r   r   r   r   Úis_zeroÚ	is_finiteÚ
is_integerZis_real)	ro   rp   Zn_irq   rr   rs   rt   ru   rv   rb   rb   rc   Ú	test_frac—  sð    "&" "$(($$$& & r|   c                  C   sì   t dƒ\} }t| ƒ | |d¡t|ƒks*t‚t| ƒ | |d¡t|ƒksHt‚t| ƒ | td¡dksbt‚t| ƒ | td¡dks|t‚t| ƒ | dd¡dks–t‚t| ƒ | dd¡dks°t‚t|  ƒ | dd¡dksÌt‚t|  ƒ | dd¡dksèt‚d S )Nzx,yéd   r3   r;   r   r-   r.   )r   r   ZnseriesrV   r   r	   )r'   r)   rb   rb   rc   Útest_series*  s    r~   c                   C   s  t td t td t  ƒjtdddks.t‚t td t td t  ƒjtdddks\t‚t ttƒd t ƒjtdddks‚t‚t ttƒd t ƒjtdddks¨t‚t ttƒt ƒjtdddksÊt‚t ttƒt ƒjtdddksìt‚t ttƒ t ƒjtdddkst‚t ttƒ t ƒjtdddks8t‚t ttƒt d ƒjtdddks`t‚t ttƒt d ƒjtdddksˆt‚ttd t td t  ƒjtdddks¸t‚ttd t td t  ƒjtdddksèt‚tttƒd t ƒjtdddkst‚tttƒd t ƒjtdddks8t‚tttƒt ƒjtdddks\t‚tttƒt ƒjtdddks€t‚tttƒ t ƒjtdddks¦t‚tttƒ t ƒjtdddksÌt‚tttƒt d ƒjtdddksôt‚tttƒt d ƒjtdddkst‚t ttƒt ƒjtdddddksDt‚t ttƒt ƒjtdddddkslt‚t td t td t  ƒjtdddddks t‚t td t td t  ƒjtdddddksÔt‚tttƒt ƒjtdddddksüt‚tttƒt ƒjtdddddks$t‚ttd t td t  ƒjtdddddksXt‚ttd t td t  ƒjtdddddksŒt‚d S )	Nr3   r/   r-   ©Úcdirr2   r.   r   r}   )	r   r'   Úas_leading_termrV   r   r   r   r   Zseriesrb   rb   rb   rc   Útest_issue_143556  s8    ..&&""&&((00(($$&&((((44((4r‚   c                   C   s|  t tƒ t¡tkst‚t tƒjtddtks0t‚t tƒjtdddksJt‚t ttj ƒjtddtjkslt‚t ttj ƒjtddtjksŽt‚t dt d ƒjtddtjks²t‚t dt d ƒjtdddt ksØt‚t ttƒd ƒjtddtksút‚t ttƒd ƒjtddtjks t‚t ttd ƒd ƒjtddtd ksLt‚t ttd ƒd ƒjtddtd ksxt‚d S )Nr-   r   r.   r2   r1   r/   )r   r'   r   rV   r   rW   ZOner   rb   rb   rb   rc   Útest_frac_leading_termX  s    ""$&"&,rƒ   c                   C   sœ   t dtt  tt  ƒdt tt ƒt  ks0t‚t dt tt  tt  ƒt dt t ƒt ksdt‚t dt tt  tt  ƒdt tt ƒt  ks˜t‚d S )Nr3   r1   )r   r	   r   r)   rV   r   rb   rb   rb   rc   Útest_issue_4149f  s    04r„   c                  C   s2   t dddd} dd|    }tt|ƒtƒs.t‚d S )NrZ   T)rK   r,   r/   )r   rw   r   rV   )rZ   r   rb   rb   rc   Útest_issue_21651m  s    r…   c                   C   sd   t t tƒƒt tƒkst‚t ttƒƒttƒks0t‚tt tƒƒt tƒksHt‚tttƒƒttƒks`t‚d S )N©r   r'   rV   r   rb   rb   rb   rc   Útest_issue_11207s  s    r‡   c                   C   sÔ   t t ttd ƒt ƒ ƒt ttd ƒt ƒ ks4t‚tt ttd ƒt ƒ ƒt ttd ƒt ƒ ksht‚t tt ttddƒ t ƒ ƒƒt ttddƒ t ƒ ks¤t‚ttt tƒt ƒ ƒ tt tƒt ƒksÐt‚d S )Nr3   r5   r/   )r   r   r'   r)   rV   r   rb   rb   rb   rc   Útest_nested_floor_ceilingz  s    44<rˆ   c                   C   sp   t t t tƒƒd ƒt tƒd ks$t‚ttttƒƒd ƒttƒd ksHt‚ttt tƒƒd ƒt tƒd kslt‚d S )Nr3   r-   r†   rb   rb   rb   rc   Útest_issue_18689€  s    $$r‰   c                   C   s0   t tdƒƒtjkst‚ttdƒƒtjks,t‚d S )Nr   )r   Úfloatr   ZZerorV   r   rb   rb   rb   rc   Útest_issue_18421…  s    r‹   c                     s@  t ddd‰ t ddd} t ddd}tt‡ fdd	„ƒ tt‡ fd
d	„ƒ tt|  ƒjtdddksft‚tt|  ƒjtdddks„t‚tt| ƒjtdddks¢t‚tt| ƒjtdddksÀt‚tt|  ƒjtdddksÞt‚tt|  ƒjtdddksüt‚tt| ƒjtdddkst‚tt| ƒjtdddks<t‚d S )NÚaTr*   ÚbrJ   ÚcrD   c                      s   t tˆ  ƒjtddS ©Nr-   r   )r   r'   r   rb   ©rŒ   rb   rc   Ú<lambda>  ó    z"test_issue_25230.<locals>.<lambda>c                      s   t tˆ  ƒjtddS r   )r   r'   r   rb   r   rb   rc   r‘   Ž  r’   r-   r   r   r.   )r   r&   ÚNotImplementedErrorr   r'   r   rV   r   )r   rŽ   rb   r   rc   Útest_issue_25230‰  s     r”   N)HZ!sympy.calculus.accumulationboundsr   Zsympy.core.numbersr   r   r   r   r   r   r	   r
   Zsympy.core.relationalr   r   r   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z(sympy.functions.combinatorial.factorialsr   Z&sympy.functions.elementary.exponentialr   r   Z#sympy.functions.elementary.integersr   r   r   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   r   Zsympy.polys.rootoftoolsr   r   Zsympyr    Zsympy.sets.setsr!   Zsympy.sets.fancysetsr"   Zsympy.core.functionr#   Zsympy.core.exprr$   Zsympy.testing.pytestr%   r&   r'   r(   r)   rZ   r[   rd   rn   r|   r~   r‚   rƒ   r„   r…   r‡   rˆ   r‰   r‹   r”   rb   rb   rb   rc   Ú<module>   sJ   (  = B "
