a
    rÀh!R  ã                   @   sp  d Z ddlmZ ddlmZ ddl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 ddlmZ ddl m!Z!m"Z"m#Z# ddl$m%Z% ddl&m'Z'm(Z( ddl)m*Z*m+Z+ ddl,m-Z-m.Z.m/Z/ ddl0m1Z1m2Z3m4Z4m5Z6m7Z7m8Z8 ddl9m:Z: ddl;m<Z< ddl=m>Z> ddl?m@Z@ ddlAmBZBmCZC ddlDmEZEmFZF e G¡ ZHdd„ ZIdd„ ZJdd„ ZKdd„ ZLd d!„ ZMd"d#„ ZNd$d%„ ZOd&d'„ ZPd(d)„ ZQd*d+„ ZRd,d-„ ZSd.d/„ ZTd0d1„ ZUd2d3„ ZVd4d5„ ZWd6d7„ ZXeFd8d9„ ƒZYd:d;„ ZZd<d=„ Z[d>d?„ Z\d@dA„ Z]dBdC„ Z^eFdDdE„ ƒZ_dFdG„ Z`dHdI„ ZadJdK„ ZbdLdM„ ZcdNdO„ ZddPdQ„ ZedRdS„ ZfdTS )UzFTests for tools for solving inequalities and systems of inequalities. é    )ÚSum)ÚFunction)ÚIÚRationalÚooÚpi)ÚEqÚGeÚGtÚLeÚLtÚNe)ÚS)ÚDummyÚSymbol)ÚAbs)ÚexpÚlog)ÚrootÚsqrt)Ú	Piecewise)ÚcosÚsinÚtan)ÚIntegral)ÚAndÚOr)ÚPolyÚPurePoly)Ú	FiniteSetÚIntervalÚUnion)Úreduce_inequalitiesÚsolve_poly_inequalityÚreduce_rational_inequalitiesÚsolve_univariate_inequalityÚreduce_abs_inequalityÚ_solve_inequality)Úrootof)Úsolve)Úsolveset)ÚMod)ÚxÚy)ÚraisesÚXFAILc                   C   sd   t tdtƒdƒtjgksJ ‚t tdtƒdƒtjgks8J ‚t ttd tƒdƒtdtddƒgks`J ‚d S )Nr   z==é   ú>éÿÿÿÿTF)	Úpsolver   r,   r   ÚRealsÚEmptySetr   r    r   © r6   r6   úa/var/www/html/assistant/venv/lib/python3.9/site-packages/sympy/solvers/tests/test_inequalities.pyÚtest_solve_poly_inequality$   s    r8   c               	   C   sÞ  t ttd dƒggtddtdƒks(J ‚t ttd dƒggtddtdƒksPJ ‚t ttd dƒggtddtjksvJ ‚tjr t t	td dƒggtddtj
ks°ntt tƒs°J ‚t ttd dƒggtddtdƒ tj
¡ksàJ ‚t ttd dƒggtddtdƒ tj
¡ksJ ‚t ttd dƒggtddtddƒks>J ‚t ttd dƒggtddtddƒksjJ ‚t ttd dƒggtddtddddƒksšJ ‚t t	td dƒggtddttt dƒtdtƒƒksÔJ ‚t ttd dƒggtddtddƒ tj
¡ksJ ‚t ttd dƒggtddtddƒ tj
¡ks<J ‚t ttd dƒggtddtd	dƒ ¡ kslJ ‚t ttd dƒggtddtd	dƒks˜J ‚t ttd dƒggtddtd	dddƒksÈJ ‚t t	td dƒggtddttt d	ƒtdtƒƒksJ ‚t ttd dƒggtddttt d	dd
tdtddƒksDJ ‚t ttd dƒggtddtd	dƒ tj
¡ksxJ ‚tdƒ} t ttd d dƒttd d dƒggtddtjks¼J ‚t ttd d dƒt	td d dƒggtddtddƒksüJ ‚t ttd d dƒt	td d dƒggtddtt|  dddƒtd| ddƒƒksRJ ‚t ttd d dƒttd d dƒggtddtt|  dddƒtd| ddƒƒks¨J ‚t ttd d dƒt	td d dƒggtddtt|  dddƒtd| ddƒƒksþJ ‚t ttd d dƒttd d dƒggtddtt|  dddƒtd| ddƒƒksTJ ‚t ttd d dƒttd d dƒggtddtt|  dddƒtddddƒtd| ddƒƒks¶J ‚t ttd d	ƒggtƒtju sÚJ ‚d S )Né   r   F©Z
relationalr0   r2   Tç      ð?g      ð¿)Z
right_open)Z	left_open)r$   r   r,   r   r   r   r   r5   Zis_realr	   r4   r    r   r
   Z
complementr   r!   ÚevalfÚinfr   Úfalse)Úsr6   r6   r7   Ú+test_reduce_poly_inequalities_real_interval*   s$   ÿÿÿÿÿÿþÿþ
þÿþÿþ
ÿÿ
ÿÿ
ÿÿ
ÿþ
ÿþ
ÿþ
ÿÿÿ
ÿÿ
ÿÿÿ
ÿþ
ÿÿþ
ÿÿþ
ÿÿÿÿ
ÿÿÿ
(ÿþ
(ÿþ
(ÿþ
(ÿþ
(ÿÿþ
r@   c               
   C   s&  t ttd dƒggtddttdƒks*J ‚t ttd dƒggtddttdƒksTJ ‚t ttd dƒggtdddksxJ ‚t ttd dƒggtddttt tƒtttƒƒks°J ‚t ttd dƒggtddtttt ƒtttƒt	tdƒƒksðJ ‚t t	td dƒggtddtttt ƒtttƒt	tdƒƒks2J ‚t
jt
dƒfD ]Þ} | t }t ttd | ƒggtddttt|  ƒtt| ƒƒksˆJ ‚t ttd | ƒggtddttt|  tƒtt| ƒƒƒksÆJ ‚t ttd | ƒggtddttt|  tƒtt| ƒƒƒksJ ‚t ttd | ƒggtddtttt| tƒtt|ƒƒttt|  ƒt| tƒƒƒƒks\J ‚t ttd | ƒggtddtttt| tƒtt|  ƒƒtt| tƒtt|ƒƒƒƒks´J ‚t t	td | ƒggtddttt| tƒtt|  ƒƒtt|  tƒtt| ƒƒtt| tƒtt|ƒƒƒks@J ‚q@d S )Nr9   r   Tr:   Fr;   )r$   r   r,   r   r   r	   r   r   r
   r   r   ÚOner   )Úoner=   r6   r6   r7   Ú0test_reduce_poly_inequalities_complex_relationalu   s‚    ÿÿÿÿÿÿÿÿÿþÿþ
ÿþ
ÿþ
ÿþ
ÿ4þ
ÿ4þ
ÿþþrC   c                   C   s\  t g tƒdksJ ‚t td dt  d td d  dkggtddtt t d¡tdd	ƒt d
t¡ƒkslJ ‚t dt d dt  td d td d   dk ggtddtt dd¡t dd¡ƒksÈJ ‚t td td  dkggtddt d	d¡ksúJ ‚t td d
t  d td  dkggtddtt dd	¡t dt¡ƒksHJ ‚t td d td d  dk ggtddtt dd¡t dd
¡ƒks’J ‚t dt d td
  dkggtddtt t d¡t tddƒt¡ƒksàJ ‚t td t dt kggtddtt t d¡t dd
¡ƒks$J ‚t ttk tdkt tk ggtddtdtƒksXJ ‚d S )NFr9   é   é   r   r:   éüÿÿÿéþÿÿÿr2   é   é
   é   éûÿÿÿr0   éýÿÿÿé   )	r$   r,   r!   r    Úopenr   ÚRopenr   ÚLopenr6   r6   r6   r7   Ú1test_reduce_rational_inequalities_real_relational   sT    *ÿ"þ4þýÿ
þ&ÿþ
"ÿþ
ÿ þ
ÿþ
ÿÿrQ   c               	      s¨  t td ƒdk } ttdtƒttdƒƒ}t| ƒ|ks6J ‚t| tƒ|ksHJ ‚tt td ƒƒttdƒksfJ ‚tt dt d ƒdkƒttttddƒtƒttt	ƒƒttttddƒƒtt	 tƒƒƒks¾J ‚tt td ƒt dt d ƒ dk ƒttt
jtƒttdƒƒksþJ ‚tt td ƒt dt tƒ d ƒ dk ƒttt
dƒtk td	k ƒtt
jtk tdk ƒƒksXJ ‚td
dd‰ tt‡ fdd„ƒ ttdk tˆ gdtt	 tk tdk ƒks¤J ‚d S )NrJ   rD   r9   rM   iõÿÿÿrH   é   rG   r2   ÚnrF)Zextended_realc                      s   t tˆ d ƒdk ƒS )NrJ   rD   )r"   Úabsr6   ©rS   r6   r7   Ú<lambda>Ð   ó    z.test_reduce_abs_inequalities.<locals>.<lambda>©Úsymbols)rT   r,   r   r   r"   r   r   r   r   r   r   ÚHalfr   r.   Ú	TypeError)ÚeÚansr6   rU   r7   Útest_reduce_abs_inequalitiesÁ   s2    ÿÿÿ
ÿÿÿ&*ÿ
r^   c                   C   s`   t ttdƒt dƒƒttdƒd tkttk ƒks4J ‚t td dkƒttjtk ttk ƒks\J ‚d S )Nr9   r0   r   )r"   r	   r   r,   r   r   r   ÚNegativeOner6   r6   r6   r7   Ú test_reduce_inequalities_generalÔ   s    4r`   c                   C   s`   t ttd dƒdgƒttdƒks$J ‚t ttd dƒdgƒdksBJ ‚t td dkƒtju s\J ‚d S )Nr9   r   TF)r"   r   r,   r   Útruer6   r6   r6   r7   Ú test_reduce_inequalities_booleanÙ   s    ÿÿrb   c                
   C   sŽ   t ttd dƒttd dƒgƒtttttjtƒt	tt
ƒƒtttdƒt	t
 tƒƒƒttttjtƒt	tt
ƒƒtttdƒt	t
 tƒƒƒƒksŠJ ‚d S )Nr9   r0   r2   )r"   r	   r,   r-   r   r   r   r   rA   r   r   r6   r6   r6   r7   Ú%test_reduce_inequalities_multivariateà   s     00þrc   c                   C   s    t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t tttƒt dƒƒS ©Nr0   )r"   r	   r   r,   r6   r6   r6   r7   rV   ç   rW   z1test_reduce_inequalities_errors.<locals>.<lambda>c                   S   s   t ttd t t dƒƒS ©Nr9   r0   )r"   r	   r,   r-   r6   r6   r6   r7   rV   è   rW   )r.   ÚNotImplementedErrorr6   r6   r6   r7   Útest_reduce_inequalities_errorsæ   s    rg   c                   C   s¦   t tt dk tgdtdt k ks&J ‚t tt dktgdttk tt d k@ ksVJ ‚t tdtt ƒtgdtttƒks|J ‚t tdtt ƒtgdtttƒks¢J ‚d S )Nr0   rX   r   )r"   r,   r-   r   r   r   r6   r6   r6   r7   Útest__solve_inequalitiesë   s    &0&rh   c                  C   st   dt d  d t tddƒ  tddƒ dk} t| ƒtt tddƒtdƒd  k tdƒ d td	dƒ t k ƒkspJ ‚d S )
NrL   r9   é-   rH   é!   r   iñÿÿÿi‘  é   )r,   r   r"   r   r   )Úeqr6   r6   r7   Útest_issue_6343ò   s    ,6ÿrm   c                  C   sr  t td d dk ƒttjtk tdk ƒks,J ‚t td d dkƒttjtktdkƒksXJ ‚t td d dkƒttt tk tdk ƒtttk tjtk ƒƒksšJ ‚t td d dkƒttt tk tdkƒttjtkttk ƒƒksÜJ ‚td t d } t| dkƒ}ttt	| dƒtkttk ƒtt tk tt	| dƒkƒƒ}||ks:J ‚tt
t d d ƒdk ƒttjtk tdk ƒksnJ ‚d S )Nr9   r0   r   r2   rM   é	   )r"   r,   r   r   r_   r   r   rA   r)   r(   r   ÚZero)rl   ZsolZtrur6   r6   r7   Útest_issue_8235ø   s"    ÿÿ(ÿ(ÿ4rp   c                  C   s¬   t dtttd tddfƒ d ktgƒtttd tddfƒ d kksJJ ‚tdƒ} t| tƒtddfƒ}t dt| td  ktgƒttd  t| tƒtddfƒ kks¨J ‚d S )Nr   r9   r0   rD   Úf)r"   r,   r   r-   r   r   )rq   r\   r6   r6   r7   Útest_issue_5526  s    ÿÿþ ÿrr   c                     s  t td dktddttt dƒtdtƒƒks2J ‚t td dktƒtttdtƒtttƒƒtttdƒtt tƒƒƒksxJ ‚t td td  td  dktddttddƒtdtƒƒks¸J ‚t td td  td  dktƒtttdtƒttdƒƒttdtƒtttƒƒƒksJ ‚t td td  td  dk tt	ddƒd	tt
tdƒt
tdƒƒksVJ ‚t td dt  d dktddttd
tdƒ d tj ddƒttjtdƒd  tddƒƒksºJ ‚t td td  t d dktddtdtdƒksòJ ‚t tt tdt   dk tƒt
tdƒks J ‚t td td  t td td  dt   dk tƒtt
tdƒt
tdƒƒksrJ ‚t td td  t td td  dt   td  dktƒt
tdƒksÀJ ‚ttdd„ ƒ t td t d dktƒtttd t d dƒtk ttk ƒksJ ‚t dtd  dktƒttdƒtk ttk ƒksDJ ‚td td   ¡ } t td |  dktƒtt ktdk @ ttdƒ@ ksJ ‚tdƒ‰tt‡fdd„ƒ tddd‰ tt‡ ‡fdd„ƒ tddd‰t ˆˆ  dkˆ ƒˆ d ˆ k ksüJ ‚t ˆˆ  dk ˆ ƒdksJ ‚t ˆˆ  dkˆ ƒdks4J ‚tdƒd tdƒd  d ‰tt‡fdd„ƒ tt‡fdd„ƒ ttdd„ ƒ ttdd„ ƒ ttdd„ ƒ td t ttd   ‰t ˆdk tddtju sÔJ ‚t ˆdktddtju sòJ ‚ttdd„ ƒ d S )Nr9   rH   Fr:   rG   r0   rD   r   ©Údomainr2   rJ   Tc                   S   s&   t td dt t  d t dk tƒS )Nr9   rD   r   ©Úisolver,   r   r6   r6   r6   r7   rV   +  rW   z2test_solve_univariate_inequality.<locals>.<lambda>rR   Únc                      s   t ttƒˆ ktddS )NFr:   )rv   r   r,   r6   ©rw   r6   r7   rV   :  rW   Úc1©Zpositivec                      s   t ˆˆ  dk ˆ ƒS ©Nr   )rv   r6   )ry   rw   r6   r7   rV   <  rW   )Únegativec                      s   t td ˆ k tƒS ©Nr9   )rv   r,   r6   ©Úzeror6   r7   rV   C  rW   c                      s   t td ˆ t k tƒS r}   ru   r6   r~   r6   r7   rV   D  s   ÿc                   S   s   t dtt  dk tƒS )Nr0   r9   ©rv   r,   r-   r6   r6   r6   r7   rV   F  rW   c                   S   s   t dtt  dk tƒS )Nr0   r   r€   r6   r6   r6   r7   rV   G  rW   c                   S   s   t tt dk tƒS r{   ru   r6   r6   r6   r7   rV   H  rW   c                   S   s$   t tttƒd ttƒd  dƒtƒS re   )rv   r   r   r,   r   r6   r6   r6   r7   rV   O  s   ÿ)rv   r,   r!   r    r   r   r   r   r   r   r   r   r   rZ   r   r.   Ú
ValueErrorr(   Úexpandr   r   rf   r   r   r[   r5   r4   )Zdenr6   )ry   rw   r   r7   Ú test_solve_univariate_inequality  sj     ÿ
0
ÿ$ÿ ,ÿ
*ÿ
 ÿÿ
$
ÿ
.RN"ÿ
2ÿ
&rƒ   c                	   C   s  t ttƒtjk tddttdtd ddƒt tt	ddƒ dt ¡ƒksJJ ‚t ttƒtjktddttd tt	ddƒ ddƒks‚J ‚t t
tƒtjk tddttd tt	ddƒ ddƒksºJ ‚t t
tƒtjktddttdtd ƒt tt	ddƒ dt ¡ƒksJ ‚t ttƒtjk tddtt dtd	 ¡t td t¡ƒksBJ ‚t ttƒtjktddtttjƒt tdt ¡ƒks|J ‚t ttƒtjktddtjks J ‚t t
tƒtd
ƒk tddtjksÆJ ‚t ttƒtjktddtjksêJ ‚t t
tƒtjktddtjksJ ‚d S )NFr:   r   é   TrJ   r9   rD   rH   rG   )rv   r   r,   r   rZ   r!   r    r   rN   r   r   ro   rO   r   rA   r   r4   r5   r_   r6   r6   r6   r7   Útest_trig_inequalitiesS  s,    ,ÿÿÿ(ÿ
 ÿ
ÿ
$&$r…   c                   C   s   t td dktddtjks J ‚t td dktddtj t¡ksFJ ‚t td dk tddtjksfJ ‚t td dk tddtj t¡ksŒJ ‚d S )Nr9   r   Fr:   T)rv   r,   r   r4   Zas_relationalr5   r6   r6   r6   r7   Útest_issue_9954j  s     & r†   c                  C   sn   t td td  d dƒ} tttƒdttdƒ  dkƒttdtk t| d k ƒt| d tk ttk ƒƒksjJ ‚d S )NrJ   r9   r0   r   rD   r„   )r(   r,   r)   r   r   r   r   r   )Úrr6   r6   r7   Útest_slow_general_univariateq  s    ,ÿrˆ   c                  C   sn   dt  tdt  ƒ } ttdt ƒtt tƒƒ}t| dt ƒ|ks>J ‚dt  tdt  d ƒ } t| dk ƒ|ksjJ ‚d S )Nr0   ú<r9   r   )r,   rT   r   r   r   r&   r   r"   )rl   r]   r6   r6   r7   Útest_issue_8545x  s
    rŠ   c                   C   sR   t t tk tƒtt tk ttk ƒks(J ‚t ttktƒtt tk ttk ƒksNJ ‚d S )N)rv   r   r,   r   r6   r6   r6   r7   Útest_issue_8974€  s    (r‹   c                	   C   sì   t ddtdt d ƒ  dk ƒtt kttdƒd k @ ttdƒ@ ksHJ ‚t tdttƒ ƒd tƒttdƒkspJ ‚tddtddt  ƒ  dtƒt	t
t tk tdk ƒt
tjtk ttddƒk ƒt
tddƒtk ttk ƒƒksÚJ ‚ttd	d
„ ƒ d S )Nr2   r0   r   r9   rL   r‰   rD   rH   c                   S   s$   t ddtddttƒ  ƒ  dtƒS )NrL   r0   r‰   )r&   rT   r   r,   r6   r6   r6   r7   rV     s   ÿÿz"test_issue_10198.<locals>.<lambda>)r"   rT   r,   r   r   r   r   r   r&   r   r   ro   r   r.   r   r6   r6   r6   r7   Útest_issue_10198…  s    ÿ"ÿ(.ÿÿrŒ   c                   C   s<   t ttƒdk ƒdksJ ‚tttƒdk tjdtjks8J ‚d S )Nr9   Trs   )r)   r   r,   r*   r   r4   r6   r6   r6   r7   Útest_issue_10047‘  s    r   c                   C   s0   t ttƒdk ƒttjtk ttdƒk ƒks,J ‚d S )Niè  )r)   r   r,   r   r   ro   r   r6   r6   r6   r7   Útest_issue_10268œ  s    rŽ   c                  C   sF   t dƒ} tttƒ| ktddttj| dk ft|  | ƒdfƒksBJ ‚d S )Nrw   Fr:   r   T)r   rv   r   r,   r   r   r5   r    rx   r6   r6   r7   Útest_isolve_Sets   s    ÿr   c                  C   sŠ  t ddƒ} tddd}t|d |d  |d  dk || d	t|dƒksJJ ‚tdƒ}t|d dk |tjd	|d
k|t k@ tt|dƒdƒ@ ksJ ‚td| d dk|tjd	|dk|tk @ tt|dƒdƒ@ ksÐJ ‚t|d d|  d dk |tjd	|d
k|dk@ tt|dƒdƒ@ ksJ ‚t|d d|  d dk|tjd	|dk|tk @ tt|dƒdƒ@ |dk|t k@ tt|dƒdƒ@ B ks†J ‚d S )Nr   rD   r,   Fr~   r0   r9   rH   rs   rL   r2   rF   )r   r   rv   r   r   ZIntegersr   r+   )Údomr,   r6   r6   r7   Ú%test_integer_domain_relational_isolve§  s$    
4 ÿÿ"ÿ
" ÿÿr‘   c                  C   s‚   t ttƒttdtƒƒtdtƒks$J ‚tddƒ} t dt  t¡dk t| ƒ| ksPJ ‚t ttd ƒt dktt	j
ƒt dd¡ks~J ‚d S )Nr   r0   rI   r„   rR   )r*   r   r-   r    r   r   r,   Údiffr   r   r4   rP   )Úir6   r6   r7   Útest_issue_10671_12466¹  s    $
"
ÿr”   c                  C   s†  t tttttfD ]:} t| tdƒtƒjtks.J ‚t| t	j
tƒtƒjtksJ ‚qttdt d tƒtƒttdƒksrJ ‚tt	j
tƒ}t|tƒ|ksJ ‚td ttƒttƒttƒ tdt  fD ]@}dD ]6}d| | dk}t|tdd||t	dƒ kksÀJ ‚qÀq¸tdtd  dt  d dk tddttd  t	jk ks8J ‚tttt dƒtƒttt dƒks`J ‚tddd}ttt| dƒtƒttd| ƒks”J ‚tt| dk tƒt| dk ks¸J ‚td	dd
}t|t dktƒt	jtk t|k @ ksîJ ‚t|t dktdddt d| kksJ ‚tdt tdt d  ƒ}t|tƒttdƒksNJ ‚tttdt d  k tƒtt	jk ttdƒ@ ks‚J ‚d S )Nr0   r9   )r   r0   r   T)ZlinearÚnz)ZnonzeroÚarz   )r
   r   r   r	   r   r   r'   r,   Úlhsr   rA   r-   r   r   r   rZ   r   ro   )ÚopZieZfxÚcr\   r•   r–   r6   r6   r7   Útest__solve_inequalityÁ  s2    &,ÿ$ÿ
(($*,rš   c                      sf  ddl m‰  ˆ t tƒdks J ‚ˆ tjtdƒƒdks8J ‚ˆ tjtƒˆ ttjƒ  kr\dksbn J ‚ˆ tjt ƒˆ t tjƒ  krŒtjks’n J ‚ˆ tjtƒˆ ttjƒ  kr¼tddƒksÂn J ‚ˆ tjt ƒˆ t tjƒ  krêdksðn J ‚ˆ ttƒˆ ttƒ  krtd ksn J ‚ˆ tt ƒˆ t tƒ  krJtd ksPn J ‚t	t
‡ fdd	„ƒ d S )
Nr   ©Ú_ptrD   r9   r2   rG   r0   c                      s   ˆ t dddtjƒS )Nr“   T)Zinfinite)r   r   rA   r6   r›   r6   r7   rV   ç  rW   ztest__pt.<locals>.<lambda>)Úsympy.solvers.inequalitiesrœ   r   r   rA   rZ   r_   r   r,   r.   r   r6   r6   r›   r7   Útest__ptÝ  s    *00..2rž   c                   C   s.   t ttdƒdktƒtdktjtk @ ks*J ‚d S )NrD   r9   rn   )r'   r   r,   r   ro   r6   r6   r6   r7   Útest_issue_25697ê  s    rŸ   c                   C   s0   t dttƒk ƒt tttƒk ƒ td¡ks,J ‚d S )NrD   )r"   rT   r,   r   Úsubsr6   r6   r6   r7   Útest_issue_25738î  s    ÿr¡   c                   C   s@   t tttƒ dkƒttkttk @ t tk tt k@ B ks<J ‚d S rd   )r"   r   r   r,   r   r6   r6   r6   r7   Útest_issue_25983ó  s    r¢   N)gÚ__doc__Zsympy.concrete.summationsr   Zsympy.core.functionr   Zsympy.core.numbersr   r   r   r   Zsympy.core.relationalr   r	   r
   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z$sympy.functions.elementary.complexesr   Z&sympy.functions.elementary.exponentialr   r   Z(sympy.functions.elementary.miscellaneousr   r   Z$sympy.functions.elementary.piecewiser   Z(sympy.functions.elementary.trigonometricr   r   r   Zsympy.integrals.integralsr   Zsympy.logic.boolalgr   r   Zsympy.polys.polytoolsr   r   Zsympy.sets.setsr   r    r!   r   r"   r#   r3   r$   r%   rv   r&   r'   Zsympy.polys.rootoftoolsr(   Zsympy.solvers.solversr)   Zsympy.solvers.solvesetr*   Zsympy.core.modr+   Z	sympy.abcr,   r-   Zsympy.testing.pytestr.   r/   r<   r=   r8   r@   rC   rQ   r^   r`   rb   rc   rg   rh   rm   rp   rr   rƒ   r…   r†   rˆ   rŠ   r‹   rŒ   r   rŽ   r   r‘   r”   rš   rž   rŸ   r¡   r¢   r6   r6   r6   r7   Ú<module>   sn     K($
>

