a
    {þdé‚  ã                   @   s˜  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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mZmZmZmZmZmZ d dl m!Z!m"Z"m#Z# d d	l$m%Z% d d
l&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z- d dl.m/Z/m0Z0 d dl1m2Z2 d dl3m4Z4 d dl5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z; d dl<m=Z= d dl>m?Z? d dl m@Z@ d dlmAZA d dlBmCZCmDZDmEZE dd„ ZFdd„ ZGdd„ ZHdd„ ZIdd „ ZJeCd!d"„ ƒZKd#d$„ ZLd%d&„ ZMd'd(„ ZNd)d*„ ZOd+d,„ ZPd-d.„ ZQd/d0„ ZRd1d2„ ZSd3d4„ ZTd5d6„ ZUd7d8„ ZVeEd9d:„ ƒZWd;d<„ ZXd=d>„ ZYd?d@„ ZZdAdB„ Z[dCdD„ Z\dEdF„ Z]dGdH„ Z^eCdIdJ„ ƒZ_dKdL„ Z`eCdMdN„ ƒZadOdP„ ZbdQdR„ ZcdSdT„ ZddUdV„ ZeeEdWdX„ ƒZfdYS )Zé    )ÚExpr)Ú
DerivativeÚFunctionÚLambdaÚexpand)ÚEÚIÚRationalÚcompÚnanÚooÚpiÚzoo)ÚEq)ÚS)ÚSymbolÚsymbols)ÚAbsÚadjointÚargÚ	conjugateÚimÚreÚsignÚ	transpose)ÚexpÚ	exp_polarÚlog)Úsqrt)Ú	Piecewise)ÚacosÚatanÚatan2ÚcosÚsin)Ú
DiracDeltaÚ	Heaviside)ÚIntegral)ÚMatrix)ÚFunctionMatrix)ÚMatrixSymbol)ÚImmutableMatrixÚImmutableSparseMatrix)ÚSparseMatrix)ÚInterval)Ú	unchanged)ÚArgumentIndexError)ÚXFAILÚraisesÚ_both_exp_powc                 C   s   t |  ¡ | ¡ dƒS )z7Check whether two complex numbers are numerically closegíµ ÷Æ°>)r
   Ún)ÚaÚb© r7   úx/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/functions/elementary/tests/test_complexes.pyÚN_equals   s    r9   c                  C   s  t dƒ\} }t ddd\}}tddd}tddd}ttƒtu sDJ ‚ttƒtu sTJ ‚tt ƒt u shJ ‚tdƒdksxJ ‚td	ƒd	ksˆJ ‚td
ƒd
ks˜J ‚ttƒtks¨J ‚tt ƒt ks¼J ‚tt| ƒsÊJ ‚t| t ƒt| ƒ ksäJ ‚t|t ƒdksøJ ‚t|ƒ|ks
J ‚t|t ƒt| ks$J ‚t|ƒdks6J ‚t| | ƒt| ƒt|ƒ ksXJ ‚t| | ƒt| ƒ| ksvJ ‚tt| ƒƒt| ƒksJ ‚tdt ƒdks¦J ‚t| t ƒt| ƒksÀJ ‚t| |t  ƒt| ƒt|ƒ ksæJ ‚t| |t  ƒt| ƒksJ ‚tt	dt ƒƒt	dƒks"J ‚tdt d ƒj
dddksDJ ‚tt| ƒƒt| ƒks^J ‚tt| ƒƒt| ƒksxJ ‚t| ƒ ¡ t| ƒdfks–J ‚t|| |  ƒ |¡t||  ƒks¾J ‚t|| |  ƒ |¡t| t| ƒ ksêJ ‚tt||t  ƒƒ|d |d  td	dƒ tt||ƒd ƒ ks0J ‚t|d|t   ƒd| ksRJ ‚td	t||t  ƒ d ƒ|d |d  td	dƒ tt||ƒd ƒ d tj ksªJ ‚t| ƒ t¡| tjt| ƒ  ksÐJ ‚| t|ƒ  tt¡| | tjt|ƒ  ks J ‚tddd}tddd}tdƒ} t|ƒjs0J ‚t| ƒjd u sDJ ‚t|ƒjdu sXJ ‚ttjƒtju snJ ‚t dƒ\}}}	td||ƒ}
t|
ƒtj|
t|
ƒ  ks¨J ‚td	dt  dgddt ggƒ}
t|
ƒtd	dgddggƒksêJ ‚td	dt  ddt  gddt ggƒ}
t|
ƒtd	dgddggƒks4J ‚tdd„ tdƒD ƒƒ}t|ƒtg d¢g d¢g d¢g d¢g d¢gƒ t d¡ksˆJ ‚t|ƒtg d ¢g d ¢g d ¢g d ¢g d ¢gƒ t d¡ksÆJ ‚tddt ||f||t  ƒƒ}t|ƒtg d!¢g d"¢g d#¢gƒksJ ‚d S )$Núx,yúa,bT©ÚrealÚrÚi©Ú	imaginaryr   é   éÿÿÿÿé   ©Úcomplexé   é   r5   ©Z	algebraicÚt©ZtranscendentalÚxFún m lÚAéýÿÿÿc                    s"   g | ]‰ ‡ fd d„t dƒD ƒ‘qS )c                    s   g | ]}d ˆ  |t   ‘qS )rD   ©r   ©Ú.0r?   ©Újr7   r8   Ú
<listcomp>m   ó    z&test_re.<locals>.<listcomp>.<listcomp>é   ©Úrange)rR   r7   rS   r8   rU   m   rV   ztest_re.<locals>.<listcomp>rW   )r   r   r   r   r   )rD   rD   rD   rD   rD   )rH   rH   rH   rH   rH   )é   rZ   rZ   rZ   rZ   )é   r[   r[   r[   r[   )r   rB   rD   rG   rH   )r   r   r   )rB   rB   rB   )rD   rD   rD   )!r   r   r   r   r   r   r/   r   r   r   r   r   Úas_real_imagÚdiffr   r	   r#   r"   r   ÚHalfÚrewriteÚImaginaryUnitÚis_algebraicÚComplexInfinityÚNaNr*   r(   r+   r-   rY   Úzerosr)   r   )rL   Úyr5   r6   r>   r?   rJ   r4   ÚmÚlrN   ÚXr7   r7   r8   Útest_re   s˜    "&"(,ÿ*ÿ
"4ÿ
&0  "("üü
üü
ri   c                  C   s  t dƒ\} }t ddd\}}tddd}tddd}ttƒtu sDJ ‚ttt ƒtu sXJ ‚tt t ƒt u spJ ‚tdƒdks€J ‚td	ƒdksJ ‚td
ƒdks J ‚ttt ƒtks´J ‚tt t ƒt ksÌJ ‚tt| ƒsÚJ ‚t| t ƒt| ƒksòJ ‚t|t ƒ|ksJ ‚t|ƒdksJ ‚t|t ƒdks0J ‚t|ƒt | ksHJ ‚t| | ƒt| ƒt|ƒ ksjJ ‚t| | ƒt| ƒks„J ‚t| |t  ƒt| ƒ| ks¦J ‚tt| ƒt ƒt| ƒksÄJ ‚tdt ƒd	ksÚJ ‚t| t ƒt| ƒd	 ksøJ ‚t| |t  ƒt| ƒt|ƒ ksJ ‚t| |t  ƒt| ƒ| ks@J ‚tt	dt ƒƒt
d ks^J ‚tdt d ƒjdddks€J ‚tt| ƒƒt| ƒ ksœJ ‚tt| ƒƒt| ƒks¶J ‚t| ƒ ¡ t| ƒdfksÔJ ‚t|| |  ƒ |¡t||  ƒksüJ ‚t|| |  ƒ |¡t t||  ƒ ks*J ‚tt||t  ƒƒ|d |d  td	dƒ tt||ƒd ƒ kspJ ‚t|d|t   ƒ|| ks’J ‚td	t||t  ƒ d ƒ|d |d  td	dƒ tt||ƒd ƒ d ksäJ ‚t| ƒ t¡tj | t| ƒ  ksJ ‚| t|ƒ  tt¡| tj|t|ƒ   ks<J ‚tddd}tddd}tdƒ} t|ƒjslJ ‚t| ƒjd u s€J ‚t|ƒjdu s”J ‚ttjƒtju sªJ ‚t dƒ\}}}	td||ƒ}
t|
ƒtjdt  |
t|
ƒ  ksìJ ‚td	dt  dgddt ggƒ}
t|
ƒtddgddggƒks.J ‚td	dt  ddt  gddt ggƒ}
t|
ƒtddgddggƒksxJ ‚tdd„ tdƒD ƒƒ}tdd„ tdƒD ƒƒ}t|ƒ  ¡ |ksºJ ‚t!ddt"||f||t  ƒƒ}t|ƒtg d¢g d¢g d¢gƒks J ‚d S )Nr:   r;   Tr<   r>   r?   r@   r   rB   rC   rD   rE   rH   r5   rI   rJ   rK   rL   FrM   rN   rO   rG   éþÿÿÿc                 S   s   g | ]}d d„ t dƒD ƒ‘qS )c                 S   s   g | ]}|t  | ‘qS r7   rP   rQ   r7   r7   r8   rU   Ð   rV   z&test_im.<locals>.<listcomp>.<listcomp>rW   rX   rQ   r7   r7   r8   rU   Ð   rV   ztest_im.<locals>.<listcomp>rW   c                 S   s   g | ]}t td ƒƒ‘qS )rW   )ÚlistrY   rQ   r7   r7   r8   rU   Ñ   rV   )r   rB   rD   )#r   r   r   r   r   r   r   r/   r   r   r   r   r   r\   r]   r   r	   r$   r"   r_   r   r`   ra   rb   rc   r*   ZOner(   r+   r,   rY   r-   Zas_immutabler)   r   )rL   re   r5   r6   r>   r?   rJ   r4   rf   rg   rN   rh   ÚYr7   r7   r8   Útest_im~   s‚    ""&""(.ÿ*ÿ
".ÿ
(0( "("ÿrm   c            
      C   s´	  t dƒdksJ ‚t dƒdks J ‚t dt ƒtks4J ‚t dt ƒt ksJJ ‚t dƒdksZJ ‚t ddd	 ¡ dksrJ ‚t tdd	 ¡ dksŠJ ‚t tƒtu sšJ ‚t d
d
t  ƒ ¡ td
ƒd
d
t   d ksÊJ ‚t d
dt  ƒ ¡ t d
dt  ƒksòJ ‚t d
d
t  ƒ ¡ t dt ƒksJ ‚t ttdtdƒ ƒƒƒdks:J ‚t tdtdƒ ƒƒtksXJ ‚tdƒ} t | ƒj	du stJ ‚t | ƒj
du sˆJ ‚t | ƒjd u sœJ ‚t | ƒjd u s°J ‚t | ƒjd u sÄJ ‚t | ƒjd u sØJ ‚t | ƒ ¡ t | ƒksòJ ‚t d|  ƒt | ƒksJ ‚t d
|  ƒt | ƒks&J ‚t t|  ƒtt | ƒ ksDJ ‚t dt |  ƒt t | ƒ kshJ ‚t t| ƒƒtt | ƒƒks†J ‚tddd}tddd}tddd}t d
| |  ƒt | ƒksÈJ ‚t ||  ƒt | ƒ ksäJ ‚t || |  ƒt | ƒksJ ‚tddd} t | ƒjdu s"J ‚t | ƒjdu s6J ‚t | ƒjdu sJJ ‚t | ƒjdu s^J ‚t | ƒ | ¡d
tt |  ƒ ks„J ‚t | ƒ ¡ | t| ƒ ks¢J ‚tt | ƒƒt | ƒ ks¾J ‚tddd} t | ƒjdu sÞJ ‚t | ƒjdu sòJ ‚t | ƒjdu sJ ‚t | ƒjd u sJ ‚t | ƒ | ¡d
t| ƒ ks:J ‚t | ƒ ¡ t | ƒksTJ ‚tt | ƒƒt | ƒksnJ ‚tddd} t | ƒjdu sŽJ ‚t | ƒjdu s¢J ‚t | ƒjdu s¶J ‚t | ƒjdu sÊJ ‚t | ƒ ¡ | t| ƒ ksèJ ‚t t| ƒƒdksþJ ‚tt | ƒƒdksJ ‚tddd} t | ƒjdu s4J ‚t | ƒjdu sHJ ‚t | ƒjdu s\J ‚t | ƒjdu spJ ‚t | ƒ ¡ | t| ƒ ksŽJ ‚t t| ƒƒdks¤J ‚tt | ƒƒdksºJ ‚d} t | ƒjdu sÒJ ‚t | ƒjdu sæJ ‚t | ƒjdu súJ ‚t | ƒjdu sJ ‚t | ƒ ¡ dks$J ‚t t| ƒƒdks:J ‚tt | ƒƒdksPJ ‚tdddd}t |ƒjdu srJ ‚t |ƒjdu s†J ‚t |ƒjdu sšJ ‚t |ƒjdu s®J ‚t |ƒd
 dksÄJ ‚t |ƒd jt |ƒdfksäJ ‚t tdddƒjsüJ ‚t tdddƒjd u sJ ‚t tdddƒjd u s4J ‚t tdddƒjsLJ ‚t tdddƒjd u shJ ‚t tdddƒjd u s„J ‚t tddddƒjd u s¢J ‚tdddtdƒ } }tdƒ}t | ƒ t¡td| dkfd| dk fdƒksðJ ‚t |ƒ t¡t |ƒksJ ‚t | ƒ t¡d
t| tdƒd
 d d ks<J ‚t |ƒ t¡t |ƒksXJ ‚t |ƒ t¡tdt|dƒf|t|ƒ dfƒksŒJ ‚t ||ƒƒ t¡tdt||ƒdƒf||ƒt||ƒƒ dfƒksÐJ ‚t ttt ƒt ƒtju sðJ ‚td d!tdƒ  ƒ tdtdƒ ƒ tddtdƒ  ƒ }t |ƒjt u 	sLt |ƒdk	sLJ ‚dtd
ƒ d
tdƒ  d"td!ƒ  }t |d ƒt!ddƒ }|| }	t |	ƒjt u 	s°t |	ƒdk	s°J ‚d S )#Ng333333ó?rB   g333333ó¿rC   rG   rO   r   F)ÚevaluaterD   rH   rL   Trj   Úp©Zpositiver4   ©Únegativerf   r@   r<   )ÚnonzeroÚnz)rs   Úinteger)Únonnegative)Únonpositive)r=   Úzerore   Úf)r   T)ZH0é
   rZ   é3  )"r   r   Údoitr   r   r   Úsimplifyr   r   Ú	is_finiteZ
is_complexZis_imaginaryÚ
is_integerÚis_realÚis_zeror   r]   r%   r   ÚargsÚis_nonnegativeZis_nonpositiver   r_   r   r&   r   r   r   r   ZNegativeOneÚfuncr   r	   )
rL   ro   r4   rf   rt   re   ry   ÚeqÚqÚdr7   r7   r8   Ú	test_sign×   sÎ    0(&"$&  ÿ
04D :"$rˆ   c                  C   sÜ  t d } |  ¡ | dfksJ ‚tdƒ}t|ƒ ¡ t|ƒd t|ƒd  tddƒ ttt|ƒt|ƒƒd ƒ t|ƒd t|ƒd  tddƒ t	tt|ƒt|ƒƒd ƒ fks¬J ‚t
ddd	\}}dt||t  ƒ d  ¡ |d |d  tddƒ tt||ƒd ƒ d tj |d |d  tddƒ t	t||ƒd ƒ d fksDJ ‚t|d ƒ ¡ t|d ƒdfksjJ ‚t
d
dd}t|d ƒ ¡ dt|ƒfks˜J ‚dt dt   ¡ dks¶J ‚dt d dt   ¡ dksØJ ‚d S )Néè  r   rL   rD   rB   rH   r;   Tr<   r?   r@   )r   rB   rG   )rj   r   )r   r\   r   r   r   r   r	   r#   r"   r$   r   r   r   r^   Úabs)r4   rL   r5   r6   r?   r7   r7   r8   Útest_as_real_imagQ  s6    
::ÿÿÿÿÿÿ.ýÿ
&"r‹   c                  C   s€   t d } t| ƒ}tdƒ}| |  ¡ dks,J ‚t| | ƒdks@J ‚| | jd||iddks^J ‚| | jd||iddks|J ‚d S )Nr‰   rL   rB   ©Úsubsr   rD   )r   Úintr   Úroundr   r4   )r4   r?   rL   r7   r7   r8   Útest_sign_issue_3068o  s    r   c                     sÞ  t tdd„ ƒ tdƒ\‰ } ttˆ ƒƒtˆ ƒks2J ‚tˆ |  ƒjtu sHJ ‚tdƒdksXJ ‚tdƒdkshJ ‚tdƒdksxJ ‚ttƒdksˆJ ‚tt ƒdksšJ ‚ttƒtu sªJ ‚ttƒt	u sºJ ‚ttt
 ƒt
ksÎJ ‚tt t
 ƒt
ksäJ ‚ttˆ  ƒtˆ ƒksüJ ‚tt ˆ  ƒtˆ ƒksJ ‚tdˆ  ƒdtˆ ƒ ks6J ‚td	ˆ  ƒd
tˆ ƒ ksTJ ‚tdt
 ˆ  |  ƒdt
 tˆ |  ƒ ks‚J ‚ttˆ ƒƒtˆ ƒksœJ ‚ttˆ ƒƒtˆ ƒks¶J ‚tˆ ƒjddttˆ ƒd tˆ ƒd  ƒksèJ ‚tddd}tdt
 ˆ  | ƒdt
 | tˆ ƒ ks"J ‚tdt
 t ˆ  | ƒdt
 | tˆ ƒ ksTJ ‚tddd‰ tddd}td| ƒdks‚J ‚ˆ d|  tˆ ƒd|  ks¤J ‚tˆ ƒ ˆ ¡tˆ ƒksÀJ ‚tˆ ƒtˆ ƒksÖJ ‚tˆ ƒd ˆ d tˆ ƒ ksøJ ‚tˆ ƒd ˆ d ksJ ‚tˆ ƒd|  jtˆ ƒd| fks:J ‚dtˆ ƒ jtˆ ƒdfksZJ ‚dtˆ ƒd  dˆ d tˆ ƒ  ks„J ‚tˆ ƒd tˆ ƒˆ d  ks¦J ‚tˆ d ƒˆ d tˆ ƒ ksÈJ ‚ttt ƒtt
 d ƒksèJ ‚tddt  ddt   ƒdtdttddƒƒ ƒ ks$J ‚tddd} tt|  ƒdksFJ ‚tdƒ} tt|  ƒtt
 t| ƒ d ƒksvJ ‚tddd‰ tˆ ƒ ˆ ¡tˆ ƒ ks J ‚tddtdƒ  ƒ tdtdƒ ƒ tddtdƒ  ƒ }t|ƒjtu süt|ƒdksüJ ‚dtdƒ dtdƒ  dtdƒ  }t|d ƒtddƒ }|| }t|ƒjtu s`t|ƒdks`J ‚tdtt
t d ƒ ƒdks‚J ‚tddt  ƒdksœJ ‚tddt  ƒdtt
ƒ ks¾J ‚tt	ƒt	u sÐJ ‚tt	 ƒt	u säJ ‚tt	t ƒt	u súJ ‚tt	tt	  ƒt	u sJ ‚tddd }td!dd"}tdƒ‰ t|ƒjsDJ ‚tˆ ƒjd u sXJ ‚t|ƒjd#u slJ ‚tˆ ƒ ¡ tˆ ƒks†J ‚t t‡ fd$d„ƒ ttdt ƒtdt ƒ ƒ}t|ƒ|ksÆJ ‚tdˆ  ƒdtˆ ƒ ksäJ ‚tdˆ d  ƒ}	|	jr|	dtˆ d ƒ ksJ ‚tt| ˆ  ƒs*J ‚ttˆ ˆ d  ƒsBJ ‚ttˆ |  ƒsVJ ‚td%dd}tˆ | ƒtˆ ƒ| ks€J ‚tttddd|  ƒsœJ ‚td&dd}
t|
ˆ ƒd ƒ|
ˆ ƒksÆJ ‚tttd'ƒƒsÚJ ‚d S )(Nc                   S   s   t tddƒƒS )NrD   rG   )r   r.   r7   r7   r7   r8   Ú<lambda>~  rV   ztest_Abs.<locals>.<lambda>r:   r   rB   rC   rj   rD   g       Àg       @TrE   r5   rp   rL   r<   r4   ©ru   rG   rH   rO   rW   rZ   é   i9 éùÿÿÿre   r@   rz   r{   é	   rI   rJ   rK   Fc                      s   t ˆ ƒ d¡S )NrD   )r   Úfdiffr7   ©rL   r7   r8   r‘   Ì  rV   ro   ry   zim(acos(-i + acosh(-g + i))))r2   Ú	TypeErrorr   r   r„   r   r   r   r   r   r   r   r   r   r   r   r   r]   rŠ   r‚   r   r!   r	   ra   r–   r0   r    Zis_Mulr/   r   r   )re   r5   r4   r…   r†   ro   r‡   rJ   r   Úery   r7   r—   r8   Útest_Abs}  s¦    .2.2""ÿÿ
 *"" <(:"$""""rš   c                  C   s   t ddd} t| ƒ t¡ ¡ }|| t| ƒ | t|  ƒ  ks@J ‚dD ]}| | |¡t|ƒksDJ ‚qDt dƒ}t|ƒ t¡t|ƒks„J ‚t dddt dƒ } }t| ƒ t¡t| | dkf|  dfƒksÄJ ‚t|ƒ t¡t|ƒksÞJ ‚t|ƒ t¡|t|ƒ ksüJ ‚t ddd}t|ƒ t¡tt	| t	| dkft	 | dfƒks@J ‚t|ƒ t
¡t|t
|ƒ ƒksdJ ‚t|ƒ t
¡t|d	  ƒks†J ‚t ddd
}ttt	 |  ƒtt	 | ƒ ƒd	  t
¡tt	|  ƒ tt	 | ƒ d	 tt	 |  ƒtt	| ƒ  ksüJ ‚d S )NrL   Tr<   )rj   rC   r   rB   rD   re   r   r?   r@   rD   ©Zextended_real)r   r   r_   r&   r   r   rŠ   r   r   r   r   r   r   )rL   r5   r?   re   r7   r7   r8   Útest_Abs_rewriteå  s&    "*8$"(8ÿrœ   c                  C   sº   t ddd} t| d ƒt| ƒks$J ‚t| d ƒ| d ks<J ‚t ddd} t| d ƒt| ƒks`J ‚t| d ƒ| d ksxJ ‚t dddd}t dddd	}t|ƒ|ks¤J ‚t|ƒ| ks¶J ‚d S )
NrL   TrE   rD   r<   Únn)rv   r=   Únp)rw   r=   ©r   r   r   )rL   r   rž   r7   r7   r8   Útest_Abs_realÿ  s    r    c            
      C   s„  t dƒ} t| ƒjd u sJ ‚t| ƒjdu s,J ‚t| ƒjd u s>J ‚t| ƒjd u sPJ ‚t| ƒjd u sbJ ‚t| ƒjd u stJ ‚t| ƒjdu s†J ‚t ddd}t|ƒjdu s¤J ‚t|ƒjdu s¶J ‚t|ƒjd u sÈJ ‚t|ƒjd u sÚJ ‚t|ƒjdu sìJ ‚t|ƒjd u sþJ ‚t|ƒjdu sJ ‚t dddd}t|ƒjdu s4J ‚t|ƒjdu sHJ ‚t|ƒjd u s\J ‚t|ƒjdu spJ ‚t|ƒjdu s„J ‚t|ƒj	du s˜J ‚t ddd}t|ƒjdu s¸J ‚t|ƒjdu sÌJ ‚t|ƒjd u sàJ ‚t|ƒjdu sôJ ‚t|ƒj	du sJ ‚t d	dd
}t|ƒjdu s(J ‚t|ƒjdu s<J ‚t|ƒj
d u sPJ ‚t|ƒjd u sdJ ‚t|ƒjdu sxJ ‚t ddd}t|ƒjdu s˜J ‚t|ƒj
du s¬J ‚t|ƒjd u sÀJ ‚t|ƒjdu sÔJ ‚t ddd}t dddd}t|ƒjdu sJ ‚t|ƒjdu sJ ‚t|ƒjd u s*J ‚t ddd}t dddd}	t|ƒjdu sXJ ‚t|	ƒjdu slJ ‚t|ƒjd u s€J ‚d S )NrL   T)ÚfiniteÚzF)rF   rx   ro   rp   r†   )Zrationalr?   r’   r4   )ÚevenÚne)r=   r£   )ÚoddÚno)r=   r¥   )r   r   r€   Zis_extended_realZis_rationalZis_positiverƒ   Zis_extended_positiveZis_extended_nonnegativer   r   Zis_evenZis_odd)
rL   ry   r¢   ro   r†   r?   r™   r¤   Úor¦   r7   r7   r8   Útest_Abs_properties  sd    r¨   c                  C   s4   t ddd} ttd|  d  ƒd|  d ks0J ‚d S )Nr5   Trp   rB   rD   )r   rŠ   r   )r5   r7   r7   r8   Útest_absM  s    r©   c                  C   sL  t dƒtu sJ ‚t dƒdks J ‚t dƒtks0J ‚t tƒtd ksDJ ‚t t ƒt d ks\J ‚t dt ƒtd kstJ ‚t dt ƒttddƒ ks’J ‚t dt ƒt d ks¬J ‚t tdt t ƒƒdt ksÌJ ‚t tdt t ƒƒdt ksìJ ‚t tddt t d  ƒƒttd	dƒ ksJ ‚td
ƒ} t | dƒt| dƒ  ƒ t¡rHJ ‚t	dƒ}t t t |ƒƒƒt
juslJ ‚t t t t |ƒƒƒƒt
ju sŒJ ‚t	ddd}t t |ƒƒt
jus°J ‚t t t |ƒƒƒt
ju sÌJ ‚tddd}t ||ƒƒdksîJ ‚t dt ||ƒ ƒt dt ƒksJ ‚t	ddd}t |ƒdks2J ‚t |t ƒtd ksLJ ‚t	ddd}t |ƒtksjJ ‚t |t ƒt d ks†J ‚t	dƒ}tt |ƒƒt |ƒks¨J ‚|t|d   }t |ƒt d|t  ƒksÖJ ‚d| dt |d   }t |ƒt dd| t  ƒksJ ‚tddd}|t|  }t |ƒt |dt  ƒksFJ ‚t || ƒt |dt  ƒkshJ ‚|t|ƒ tt|ƒ t|ƒ  }t |ƒjd |ks J ‚|d t|d d   }t |ƒjd |ksÐJ ‚td
ƒ} d| | dƒd  d| | dƒ  }t |ƒt d| ƒksJ ‚t | dƒƒjt krDt | dƒƒj| dƒfksHJ ‚d S )Nr   rB   rC   rD   rH   rG   r”   rW   rO   ry   rL   r>   Tr›   ro   )Zextended_positiverp   r4   rq   rj   r<   )r   r   r   r   r	   r   r   Zatomsr   r   r   rc   r   r   r#   r   r   r‚   r„   )ry   rL   r>   ro   r4   r™   r7   r7   r8   Útest_argT  s\      0$ &"" $rª   c                  C   sZ   t dt ƒtddƒksJ ‚tddd} tddd}t | t|  ƒ t¡t|| ƒksVJ ‚d S )NrB   rL   Tr<   re   )r   r   r"   r   r_   )rL   re   r7   r7   r8   Útest_arg_rewrite  s    r«   c                  C   s6  t ddd} t ddd}t| ƒ|  ks*J ‚tt|  ƒt|  ksBJ ‚t|ƒ|ksRJ ‚tt| ƒt | kslJ ‚t| | ƒ| |  ks†J ‚tt|  | ƒt| |  ks¦J ‚tdƒ\}}tt|ƒƒ|ksÆJ ‚t|| ƒt|ƒt|ƒ ksæJ ‚t|| ƒt|ƒt|ƒ ksJ ‚t|| ƒt|ƒt|ƒ ks*J ‚t|| ƒt|ƒt|ƒ ksLJ ‚t| ƒt|ƒ ksfJ ‚tddd\}}tt|ƒƒ|ksŒJ ‚t|| ƒt|ƒt|ƒ ks®J ‚t|| ƒt|ƒt|ƒ ksÐJ ‚t|| ƒt|ƒt|ƒ ksòJ ‚t|| ƒd	t|ƒ t|ƒ ksJ ‚t| ƒt|ƒ ks2J ‚d S )
Nr5   T)Zantihermitianr6   )Z	hermitianúx yF©ZcommutativerB   )r   r   r   r   )r5   r6   rL   re   r7   r7   r8   Útest_adjoint˜  s,      """"""&r®   c                  C   sÎ  t ddd} t ddd}t| ƒ| ks(J ‚tt|  ƒt |  ksBJ ‚t|ƒ| ksTJ ‚tt| ƒt| kslJ ‚t| | ƒ|  | ks†J ‚tt|  | ƒt|  | ks¦J ‚tdƒ\}}tt|ƒƒ|ksÆJ ‚t|ƒ ¡ tksÚJ ‚t|| ƒt|ƒt|ƒ ksúJ ‚t|| ƒt|ƒt|ƒ ksJ ‚t|| ƒt|ƒt|ƒ ks>J ‚t|| ƒt|ƒt|ƒ ks`J ‚t| ƒt|ƒ kszJ ‚t ddd} t ddd	}t| ƒjs¢J ‚t|ƒjd u s¶J ‚t|ƒjd
u sÊJ ‚d S )Nr5   Tr<   r6   r@   r¬   rI   rJ   rK   F)r   r   r   r   Zinverser   ra   )r5   r6   rL   re   rJ   r7   r7   r8   Útest_conjugate³  s*      """r¯   c                  C   sÖ   t dƒ} tt| ƒƒt| ƒks J ‚tt| ƒƒt| ƒks8J ‚tt| ƒƒt| ƒksPJ ‚tt| ƒƒt| ƒkshJ ‚tt| ƒƒt| ƒks€J ‚tt| ƒƒt| ƒks˜J ‚G dd„ dtƒ}|ƒ } t| ƒt| ƒksÂJ ‚t| ƒ| ksÒJ ‚d S )NrL   c                   @   s$   e Zd Zdd„ Zdd„ Zdd„ ZdS )z+test_conjugate_transpose.<locals>.Symmetricc                 S   s   d S ©Nr7   ©Úselfr7   r7   r8   Ú_eval_adjoint×  s    z9test_conjugate_transpose.<locals>.Symmetric._eval_adjointc                 S   s   d S r°   r7   r±   r7   r7   r8   Ú_eval_conjugateÚ  s    z;test_conjugate_transpose.<locals>.Symmetric._eval_conjugatec                 S   s   | S r°   r7   r±   r7   r7   r8   Ú_eval_transposeÝ  s    z;test_conjugate_transpose.<locals>.Symmetric._eval_transposeN)Ú__name__Ú
__module__Ú__qualname__r³   r´   rµ   r7   r7   r7   r8   Ú	SymmetricÖ  s   r¹   )r   r   r   r   r   )rL   r¹   r7   r7   r8   Útest_conjugate_transposeÍ  s    	rº   c                  C   s¼  t ddd} t| ƒ| ksJ ‚tt|  ƒt|  ks4J ‚tdƒ\}}tt|ƒƒ|ksTJ ‚t|| ƒt|ƒt|ƒ kstJ ‚t|| ƒt|ƒt|ƒ ks”J ‚t|| ƒt|ƒt|ƒ ks´J ‚t|| ƒt|ƒt|ƒ ksÔJ ‚t| ƒt|ƒ ksìJ ‚tddd\}}tt|ƒƒ|ksJ ‚t|| ƒt|ƒt|ƒ ks4J ‚t|| ƒt|ƒt|ƒ ksVJ ‚t|| ƒt|ƒt|ƒ ksxJ ‚t|| ƒdt|ƒ t|ƒ ksžJ ‚t| ƒt|ƒ ks¸J ‚d S )Nr5   TrE   r¬   Fr­   rB   )r   r   r   r   )r5   rL   re   r7   r7   r8   Útest_transposeä  s"        """&r»   c            
   	   C   sš  ddl m} m} tdƒ}tddd}tdƒ}i }|dƒ| dƒ|fksHJ ‚|d	t ƒ| d	t ƒ|fkshJ ‚|t|ƒd
dt|ƒks„J ‚|d	| d
dd	| ks J ‚||tƒ| d
d|| tƒƒ| ksÈJ ‚||dd| |ƒksàJ ‚||dd|ksôJ ‚|||ƒdd|| |ƒƒksJ ‚|d	| dd| d	| ƒks8J ‚|d	||ƒ dd| d	|| |ƒƒ ƒksfJ ‚|||ƒ| ƒ\}}| |¡||ƒ| ks–J ‚tdƒ}tddd}	|tt	dƒ| t| | d  d|	d   ƒ dt	t
ƒ |	  |t tfƒddtt	dƒ|	tdƒ ttt
 ƒ  t|	tdƒ dttt
 ƒ  ttt
 ƒ | | | ƒdtdƒ   d ƒ tdƒ | |ƒ dt	t
ƒ  |t tfƒks–J ‚d S )Nr   )Ú
polar_liftÚpolarifyrL   r¢   T)Zpolarry   rC   rB   FrŒ   )ZliftÚmuÚsigmarp   rD   )Ú$sympy.functions.elementary.complexesr¼   r½   r   r   r   r   r   r'   r   r   r   r   )
r¼   r½   rL   r¢   ry   ÚESZnewexr   r¾   r¿   r7   r7   r8   Útest_polarifyú  sR     ("".<
ÿþ 4
ÿÿÿþþ
þ
þþrÂ   c                  C   sî  ddl m} m}m} ddlm} ddlm} ddlm	} ddl
m}m} ddlm} tdt ƒd	 }	tdt ƒd	 }
|d	ƒd	ks„J ‚||	ƒ|
ks”J ‚||	d
 ƒ|
d
 ks¬J ‚||	| ƒ|	| ksÄJ ‚||	| ƒ|
| ksÜJ ‚||	| ƒ|
| ksôJ ‚|tt|	ƒƒƒtt|
ƒƒksJ ‚||d
t ƒ}||ƒ|ks6J ‚|t|ƒƒt|ƒksPJ ‚||	|	 dd|	|
 ksnJ ‚||||	|	 ƒƒ|||	|
 ƒks”J ‚|t|	ƒƒt|
ƒks®J ‚|||	ƒƒ||
ƒksÈJ ‚|||	ƒƒ||
ƒksâJ ‚|||	ƒƒ||
ƒksüJ ‚||||	ƒƒ|||	ƒksJ ‚||t|	ƒt|	tdƒ ƒƒƒ|t|
ƒt|
d	 ƒƒksTJ ‚||| dƒd
tdƒ ƒƒ|dd
ƒks~J ‚|t|	dƒƒt|
dƒksœJ ‚|||	dƒƒ||
dƒksºJ ‚|| |ƒdkƒ|dkksØJ ‚|dƒdu sêJ ‚d S )Nr   )r¼   Úprincipal_branchÚ
unpolarify)ÚNe)Útanh)Úerf)ÚgammaÚ
uppergammar—   r“   rB   rD   T)Zexponents_only)rÀ   r¼   rÃ   rÄ   Úsympy.core.relationalrÅ   Z%sympy.functions.elementary.hyperbolicrÆ   Z'sympy.functions.special.error_functionsrÇ   Z'sympy.functions.special.gamma_functionsrÈ   rÉ   Z	sympy.abcrL   r   r   r   r   r$   r   r   )r¼   rÃ   rÄ   rÅ   rÆ   rÇ   rÈ   rÉ   rL   ro   ÚurJ   r7   r7   r8   Útest_unpolarify  sF    "&ÿ
ÿ
rÌ   c                  C   s`   t dƒ} t| ƒjddt| ƒks$J ‚t| ƒjddt| ƒks@J ‚t| ƒjddt| ƒks\J ‚d S )NrL   T)Ztrig)r   r   r   r   r   r—   r7   r7   r8   Útest_issue_4035M  s    rÍ   c                  C   s$   t dƒ} tt| ƒƒt| ƒks J ‚d S )NrL   )r   r   r—   r7   r7   r8   Útest_issue_3206T  s    rÎ   c                  C   sv   t ddd} t ddd}tdƒ}|| ƒ ¡  | ¡|| ƒ | ¡ ¡ ksHJ ‚||ƒ ¡  |¡||ƒ |¡ ¡  ksrJ ‚d S )NrL   Tr<   re   r@   ry   )r   r   r   r]   ©rL   re   ry   r7   r7   r8   Ú$test_issue_4754_derivative_conjugateY  s
    (rÐ   c                  C   sâ  t ddd} t ddd}tdƒ}t|| ƒƒ | ¡t|| ƒ | ¡ƒksHJ ‚t|| ƒƒ | ¡t|| ƒ | ¡ƒkspJ ‚t||ƒƒ |¡t t||ƒ |¡ƒ ksžJ ‚t||ƒƒ |¡t t||ƒ |¡ƒ ksÌJ ‚t|| ƒƒ | ¡ || ƒdt|   ¡ ¡ | t	d| d  ƒ ksJ ‚t
|| ƒƒ | ¡ || ƒdt| d   ¡ ¡ d|  d| d	   ksXJ ‚t||ƒƒ |¡ ||ƒd| ¡ ¡ | t	d|d  ƒ ksšJ ‚t
||ƒƒ |¡ ||ƒt|d  ¡ ¡ d| d|d	   ksÞJ ‚d S )
NrL   Tr<   re   r@   ry   rB   rD   rH   )r   r   r   r]   r   r   r   r   r|   r   r   rÏ   r7   r7   r8   Útest_derivatives_issue_4757a  s    ((..DHBrÑ   c               	   C   sR  ddl m}  tdƒ}tdƒ}tdƒ}t|g|g|ggƒ}| ¡ }|t|tt|ƒd t|ƒd  t|ƒd  ƒ g|tt|ƒd t|ƒd  t|ƒd  ƒ g|tt|ƒd t|ƒd  t|ƒd  ƒ ggƒksÔJ ‚t|d |d |d  |d   |d |d |d  |d    |d |d |d  |d    ƒ|_| |jƒdksNJ ‚d S )Nr   ©r}   Úv0Úv1Úv2rD   rB   )Úsympy.simplify.simplifyr}   r   r(   Ú
normalizedr   r   Znorm)r}   rÓ   rÔ   rÕ   ÚVÚUr7   r7   r8   Útest_issue_11413o  s    ,,,ýfrÚ   c                  C   s6  ddl m} m}m}m} tdƒ}tddd}|dt ƒ| dt tƒksJJ ‚|d| ƒ| d| tƒkshJ ‚t|dt d ƒt	d ƒs†J ‚t|dt d ƒt	 d ƒs¦J ‚t| dt d d	t	 ƒt	d ƒsÊJ ‚t| dt d d	t	 ƒt	 d ƒsðJ ‚|||t	ƒƒ| |t	ƒksJ ‚||dt ƒƒ|dt ƒks0J ‚| |dt ƒdt	 ƒ| dt dt	 ƒks^J ‚| |dt ƒd	t	 ƒ| dt d	t	 ƒksŒJ ‚| |dt ƒt	ƒ| |dt ƒt	ƒks¶J ‚||dt ƒƒt	d
 ksÔJ ‚| d| |ƒ| ||ƒksòJ ‚| t	| |ƒ| ||ƒksJ ‚t
|dt ƒƒt
dt ƒks2J ‚d S )Nr   )Úperiodic_argumentr¼   rÃ   Úunbranched_argumentrL   ro   Trp   rD   rB   rG   rH   )rÀ   rÛ   r¼   rÃ   rÜ   r   r   r   r9   r   r   )rÛ   r¼   rÃ   rÜ   rL   ro   r7   r7   r8   Útest_periodic_argument~  s4     $&ÿ
"ÿ
ÿ
ÿ
rÝ   c                  C   s0   ddl m}  t| dt d td ƒdƒs,J ‚d S )Nr   ©rÃ   rB   rD   )rÀ   rÃ   r9   r   r   rÞ   r7   r7   r8   Útest_principal_branch_failœ  s    rß   c                  C   sZ  ddl m} m} tddd}tdƒ}tddd}|| |ƒ|ƒ|||ƒksLJ ‚|| dt ƒ|ƒ|dt |ƒkspJ ‚|d| |ƒd|||ƒ ksJ ‚|d	tƒtdƒks¦J ‚|d
dt ƒttt ƒksÄJ ‚|d
tƒtdƒksÚJ ‚|tdt t ƒ| dt ƒ|ttt ƒ| dt ƒksJ ‚||ttt ƒ dt ƒ|tt t ƒ ksJJ ‚|tt t d ƒ| |ƒ dt ƒtt t d ƒ| ksŠJ ‚t|d	t d dt ƒdt ƒs°J ‚t|d	t d dt ƒdt ƒsÖJ ‚t|d	t d d	t ƒdt ƒsüJ ‚||tƒj|u sJ ‚||dƒj|u s(J ‚||t	 ƒj|u s@J ‚||t
ƒj|u sVJ ‚d S )Nr   )r¼   rÃ   ro   Trp   rL   rq   rD   rB   rC   rG   éüÿÿÿ)rÀ   r¼   rÃ   r   r   r   r   r9   r„   r   r   )r¼   rÃ   ro   rL   Únegr7   r7   r8   Útest_principal_branch£  s0    $ ÿ
2"ÿ
&&&râ   c            	      C   sÐ   t d } t| ƒ}t| | ƒdks$J ‚t| | ƒ| | ks<J ‚tdƒ}t d }t d }t|ƒd t|ƒd  }|| | | }ddlm} t||ƒƒdksœJ ‚dd	dt	dd
ƒfD ]}t| 
||¡ƒdks®J ‚q®d S )Nr‰   rB   rL   i$úÿÿrD   r   rÒ   éo   é   rz   )r   rŽ   r   rŠ   r   r#   r$   rÖ   r}   r	   r   )	r4   r?   rL   ZepsÚbigZoner™   r}   Úxir7   r7   r8   Útest_issue_6167_6151Á  s    rç   c                  C   s\   ddl m}  tdddƒ}| |d ƒ|d ks0J ‚| |d |d  ƒ|d |d  ksXJ ‚d S )Nr   )rÄ   rN   rD   )r   r   )rB   r   )rÀ   rÄ   r*   )rÄ   rN   r7   r7   r8   Útest_issue_14216Ò  s    rè   c                  C   s6   t ddd} t| td| dkfd|  dfƒ ƒs2J ‚d S )Nr>   Tr<   r   rB   )r   r   r   )r>   r7   r7   r8   Útest_issue_14238Ù  s    ré   c                  C   sL   t dƒ} tdd|   ƒd d|  fD ]"}t|ƒt| ƒ dks$J |ƒ‚q$d S )NrL   r“   rD   rB   r   rŸ   )rL   r5   r7   r7   r8   Útest_issue_22189ß  s     rê   c                  C   s˜   t dddd} t ddd}t dddd}t| ƒjd u s:J ‚t| ƒjdu sLJ ‚t|ƒjd u s^J ‚t|ƒjd u spJ ‚t|ƒjdu s‚J ‚t|ƒjd u s”J ‚d S )	NZnonrealFT)r=   r¡   Znonimaginaryr@   Znonzerononimaginary)rx   rA   )r   r   r   r   )ÚnrÚniZnznir7   r7   r8   Útest_zero_assumptionså  s    rí   c                  C   sJ   t ddd} tddd}tt| |ƒƒ| |ƒƒ}| ¡ t| |ƒƒksFJ ‚d S )Nry   Tr<   rL   )r   r   r   r   r|   r   )ry   rL   r…   r7   r7   r8   Útest_issue_15893õ  s    rî   N)gZsympy.core.exprr   Zsympy.core.functionr   r   r   r   Zsympy.core.numbersr   r   r	   r
   r   r   r   r   rÊ   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   rÀ   r   r   r   r   r   r   r   r   Z&sympy.functions.elementary.exponentialr   r   r   Z(sympy.functions.elementary.miscellaneousr   Z$sympy.functions.elementary.piecewiser   Z(sympy.functions.elementary.trigonometricr    r!   r"   r#   r$   Z'sympy.functions.special.delta_functionsr%   r&   Zsympy.integrals.integralsr'   Zsympy.matrices.denser(   Z%sympy.matrices.expressions.funcmatrixr)   Z"sympy.matrices.expressions.matexprr*   Zsympy.matrices.immutabler+   r,   Zsympy.matricesr-   Zsympy.sets.setsr.   r/   r0   Zsympy.testing.pytestr1   r2   r3   r9   ri   rm   rˆ   r‹   r   rš   rœ   r    r¨   r©   rª   r«   r®   r¯   rº   r»   rÂ   rÌ   rÍ   rÎ   rÐ   rÑ   rÚ   rÝ   rß   râ   rç   rè   ré   rê   rí   rî   r7   r7   r7   r8   Ú<module>   sv   ((`Yz
h<<
#/

