o
    ŗ„g°ō  ć                   @   s$  d dl mZ d dlmZ d dlmZ d dlmZ d dlm	Z	 d dl
mZmZmZ d dlmZ d dlmZ d d	lmZmZmZmZmZmZ d d
lmZmZmZmZ d dlmZ d dl m!Z!m"Z" d dl#m$Z$ d dl%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z, d dl-m.Z.m/Z/ d dl0m1Z1m2Z2m3Z3 d dl4m5Z5m6Z6m7Z7m8Z8m9Z9 d dl:m;Z;m<Z< d dl=m>Z>m?Z? d dl@mAZA d dlBmCZCmDZD d dlEmFZFmGZGmHZHmIZI d dlJmKZK d dlLmMZM d dlNmOZO d dlPmQZQ d dlRmSZS d dlTmUZUmVZV d dlWmXZX e"d\ZYZZZ[Z\Z]Z^e"dd d!Z_d"d# Z`d$d% Zad&d' Zbd(d) ZceVd*d+ ZdeVd,d- Zed.d/ Zfd0d1 Zgd2d3 ZheVd4d5 Zid6d7 Zjd8d9 Zkd:d; Zld<d= Zmd>d? Znd@dA ZodBdC ZpdDdE ZqdFdG ZrdHdI ZsdJdK ZtdLdM ZudNdO ZvdPdQ ZwdRdS ZxdTdU ZydVdW ZzdXdY Z{dZd[ Z|d\d] Z}d^d_ Z~d`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZeVdd Zdd Zdd Zdd Zdd Zd d” Zd¢d£ Z d¤d„ Z”d¦d§ Z¢dØS )©é    )ŚSum)ŚAdd)ŚBasic)ŚTuple)Ś	unchanged)ŚFunctionŚdiffŚexpand)ŚMul)ŚMod)ŚFloatŚIŚRationalŚooŚpiŚzoo)ŚEqŚGeŚGtŚNe)ŚS)ŚSymbolŚsymbols)Ś	factorial)ŚAbsŚadjointŚargŚ	conjugateŚimŚreŚ	transpose)ŚexpŚlog)ŚMaxŚMinŚsqrt)Ś	PiecewiseŚpiecewise_foldŚpiecewise_exclusiveŚ	UndefinedŚExprCondPair)ŚcosŚsin)Ś
DiracDeltaŚ	Heaviside)ŚKroneckerDelta)ŚIntegralŚ	integrate)ŚAndŚITEŚNotŚOr)ŚMatrixSymbol)Śsrepr)ŚContains)ŚInterval)Śsolve)ŚraisesŚslow)Ślambdifyz	a:d, x, yŚzT)Śnonzeroc                  C   s  t ttdk f d”sJ tt tttdk tddsJ t ttdk fdt tttdk tddks5J t ttdk fddt ttdk fdksJJ t ttdk fdddd	kft ttdk fksbJ t ttdk fdtdk fdt ttdk fdks{J t ttdk fdtd	k fdt ttdk fdksJ t ttdk fttd	k fdt tttdk td	k fdks²J t ttdk fttd	k ftdftksĘJ t tdftksŠJ ttd
d  t d	t tdk ftdft d	t tdk ftdfdd  krt d	t tdk fksJ  J t tdftksJ ttdd  t tdftks$J ttdd  ttdd  ttdd  t dt	dd	ksEJ t dtdk fdt
k } t d| ft dttdk t
dkt
d	kfksiJ t dtdkfd	ttdktdkft dtdkfd	tdkfksJ t dtdkfd	tdk tdk@ ft dtdkfks§J t dttdktdktttjfd}| tt”dksÅJ | td	”dksŠJ | td”dksŪJ t dtdk ftd	 tdk ftttdkf}t dtd	 dk ftd td	 dk fttd	 td	 dkf}| ttd	 ”|ksJ | td”dks'J | td”dks2J | td”tdks?J t dttk fdtd	t k fdtd	t kf}t dttdfdt df}t dttdfd	dt d	kf}| td	”dks~J | td”dksJ | td”dksJ | td”dksJ | td”dksŖJ tdtd\}}}	t |ttdk f|t|	t d	 tdkf}
t |ttdk f|t|	t d	 tdkf}| ||”|
ksģJ t dttdfd td”dks’J t dttdfd td”dksJ t dttt
fd tt
”dks%J t dtttfd tt”dks8J t dtttttfd tt”t dtttttfdks[J t dtttt
 dfd}| t
d”t dtttdfdks~J t dt
dk fdtdk fdttdfd td”t dt
dk fdks¢J t dttd	 dfd	tdk f tt”dks»J t ttdkf}tddd}| t|”tksŌJ | ” t dtdk ftd	 tdk fttdfksļJ |jtdid dksüJ |jtdid dks	J |jtdid tdksJ |jtdid tks%J t tttddftdk f}| ” t tjtdk fksCJ t}t| }t dtdk fd	t tdk fdt tdkf}t| | }t|t|ksoJ t|| t|ks{J t| |ksJ t| | |t|  ksJ || || ksJ || || ks©J || ||  ksµJ t dtdk fdtd	  tdk fdtd	  tdkf}|d	 |ksŲJ tt
 d	 }tt
d	  d! }t |tdk f|tdkf}| td”| td” | td” | td” }| tdd”dksJ | tdd”|ks#J t |tdk f|df}| tdd”dks:J | tdd”| ksGJ | tdd”| td”| td” ks]J | tdd”|ksiJ | td d”| td”ksyJ | tdd ”| td” ksJ |  ” t t tdk ftd! d! t!dd! tdk fttt t t!dd! dfks¶J t ttdk ftd	 dtkftd!tk f}t |tdd	ft!d"dksŚJ t |td	dft!ddksźJ t dtdk fdtdk fdtd	k fdtd!k fd}t |tt" t"fd	ksJ t ttd#k ftd	 tdkftdtk f}t |tdd	ftks1J t#|t r=|j$du s?J d S )$Ng      š?é   r   T©r   T©r@   T)r   Fé’’’’é   c                   S   s   t  S ©N©r&   © rG   rG   śf/var/www/visachat/venv/lib/python3.10/site-packages/sympy/functions/elementary/tests/test_piecewise.pyŚ<lambda>8   s    z!test_piecewise1.<locals>.<lambda>F©Śevaluatec                   S   s   t tS rE   ©r&   ŚxrG   rG   rG   rH   rI   >   s    c                   S   s   t tdfS ©NrD   rL   rG   rG   rG   rH   rI   @   ó    c                   S   s   t ttd fS rN   rL   rG   rG   rG   rH   rI   A   s    c                   S   s   t dgdfS ©Nr@   TrF   rG   rG   rG   rH   rI   B   ó    ))r@   rD   T©rD   Té   é   é   éū’’’é
   ē        zf,g,h)ŚclsŚn)Śnegativeg      šæéž’’’)Śsubsé   é   éö’’’)%r&   rM   Śhasr   r*   r5   r;   Ś	TypeErrorr)   r   Śyr3   r2   r8   r   ŚIntegersr]   r   r"   r   r   r   r>   r!   r+   r   Śevalfr0   ŚdoitŚHalfr   Ś_eval_intervalr1   r   r   Ś
isinstanceŚis_commutative)ŚcondŚpwiseŚpŚp_x2Śp2Śp3Śp4ŚfŚgŚhŚpfŚpgŚp5Śp6rZ   Śf_intŚfpŚdpŚfp_dxŚdp2Śf1Śf2ŚpevalŚpeval_intervalŚpeval2rG   rG   rH   Śtest_piecewise1$   s   
’’’’’’(
’ž

’"
’ 
’ž,<, ..&&&&"
’*&
’26 ,4’
’
’
’, "ż(  0( r   c                  C   s.   t ttdk ftdf} | jttthksJ d S )Nr   T)r&   rM   Śarc   Śfree_symbols©rr   rG   rG   rH   Śtest_piecewise_free_symbols¾   s   r   c                  C   s²  t ddd\} }t| d d | dkfd}t|| ddftdd	ks$J t| d
 d
 | dkf|df}t|| ddftdd	ksBJ t|| dd
ftddksQJ |t| d
 d
 | dkf|| dk fksfJ t| d
 d
 d| kf|| dk f}t|| ddftdd	ksJ t|| dd
ftddksJ |t| d
 d
 d| kf|dfksØJ t| d
 d
 d| kfd| df}t|| ddftdd	ksČJ t|| dd
ftddks×J d S )Nśx yT©ŚrealrD   r   rB   r\   é   r^   r_   rU   é+   rS   iCż’’é   i_ż’’)r   r&   r1   r   )rM   rc   rr   rs   rG   rG   rH   Śtest_piecewise_integrate1Ć   s   *"&""r   c                  C   s2  t dtdkfdttdfdtdk f} t| tddfdksJ t dtt dk fd} t| tt dftdt ks;J |  td” tt df”dksLJ t| tdt ftdtks\J t| tdtftdt t ksnJ t| tt dftdt d ksJ t| tt tft t ksJ t dtdk fttdkfd} |  ttdf”}|  tdtf”}dt	j
d	fD ]"}|  t|df”| t|”ksĒJ |  td|f”| t|”ks×J qµ|t tdtdtd	  d	 t	j
 tdk ft d d
fksųJ |t tdtdtd	 d	 t	j
 tdk ftd d
fksJ d S )Nr@   r   rC   rA   éż’’’r^   é*   rB   rD   T)r&   rM   r   r1   rc   r   r$   r]   r#   r   rg   )rs   Śgy1Śg1yŚyyrG   rG   rH   Śtest_piecewise_integrate1bŚ   s.   &"" $&  "&
ž$
žr   c                  C   s  t ddd} tdt tdd t”fdt tdd t”fd}| t| df”}| td| f”}| tddf”| | d”ks@J | tddf”| | d”ksPJ | tddf”| | d”ks`J | tddf”| | d”kspJ | td	df”| | d	”ksJ | tdd	f”| | d	”ksJ t| t” 	” td| dkf| d	  d	 |  t
j | dkf| d	 d	 |  t
j | dk fdksĮJ t| t” 	” td| dkf| d	 d	 |  t
j | dkf| d	  d	 |  t
j | dk fdksņJ |ttdtd| d	  d	 tdtd|  tdtd| d	  t
j | dk fdks J |ttdtd| d	 d	 tdtd|  tdtd| d	  t
j | dk fdksMJ d S )
Nrc   Tr   r@   r   rC   rA   r\   rD   )r   r&   rM   r9   Ścontainsr1   r]   r'   ŚrewriteŚsimplifyr   rg   r$   r#   ©rc   rs   r   r   rG   rG   rH   Śtest_piecewise_integrate1caō   sd   ż      
ü’
ü’(’’žü&’’žür   c                  C   s  t ddd} tdttdktdkfdt tdkfdt df}| t| df”}| td| f”}| tddf”| | d”ks?J | tddf”| | d”ksOJ | tddf”| | d”ks_J | tddf”| | d”ksoJ | tddf”| | d”ksJ | tddf”| | d”ksJ t| t” ” td| dkf| d  d |  t	j
 | dkf| d d |  t	j
 | dk fd	ksĄJ t| t” ” td| dkf| d d |  t	j
 | dkf| d  d |  t	j
 | dk fd	ksńJ |ttdtd| d  d tdtd|  tdtd| d  t	j
 | dk fd	ksJ |ttdtd| d d tdtd|  tdtd| d  t	j
 | dk fd	ksLJ d S )
Nrc   Tr   r   rC   r@   r\   rD   rA   )r   r&   r5   rM   r1   r]   r'   r   r   r   rg   r$   r#   r   rG   rG   rH   Śtest_piecewise_integrate1cb  sd   
ż      
ü’
ü’	(’’žü&’’žür   c               
   C   s  ddl m}  tttt}tdttk fdttkfd}| 	|”}|tt dt  dt
tttt  t
ttttt ttk fdt t dt
tttt  t
ttttt dfks]J | dD ]}ttttttf|}| |” 	| |””| |”ksJ qad S )	Nr   ©Śpermutationsr@   rD   ©r^   Tr\   T)r@   rD   r^   rU   )Ś	itertoolsr   r   rM   ŚcŚdr&   r   Śbr1   r$   r#   ŚdictŚzipr]   )r   Ślimrm   ŚqŚvŚrrG   rG   rH   Śtest_piecewise_integrate2L  s   
:4
ž&žrØ   c                   C   s*   t dtdk fd ttdf”dksJ d S )Nr@   rU   rA   r   )r&   rM   r1   r   rG   rG   rG   rH   Śtest_meijer_bypassY  s   *r©   c                  C   s  ddl m}  tddf}d}tdttkfdttkfd}| |”}| |ddD ]\}}ttttf||f}| 	|”| 	|” |”ksDJ q&| 	td	” 	td”d
ksSJ tdttkfdttk fd}| |”}| |ddD ]\}}ttttf||f}| 	|”| 	|” |”ksJ qld S )Nr   )Ścartesr_   )r\   rC   r   r@   rD   r_   rS   rT   r@   rD   rA   )ŚrepeatrU   rT   )
Śsympy.utilities.iterablesrŖ   rM   r&   r   r”   r1   r¢   r£   r]   )rŖ   r¤   ŚNrm   ŚansŚiŚjŚrepsrG   rG   rH   Ś/test_piecewise_integrate3_inequality_conditions_  s   

 
 žr²   c                  C   sd  t ddd} t ddd}t ddd}t ddd}tdt|| k ||kfd}td|| k fd||kfd}td||kfd|| k fd}td|| k fd	||k fd
}td||kfd	|| kfd
}td	t| |k ||k fd
}	t|t |}
||||||	fD ]B}| |
”}tdD ]6}| d	|d||i}| |”| |” |
 |””ks¢J | d|d	||i}| |”| |” |
 |””ks¼J qq{t||t}
||||||	fD ]C}| |
”}tdD ]7}| d	|d||i}| |”| |” |
 |””ksóJ | d|d	||i}| |”| |” |
 |””ksJ q×qĢtd|t	| |kf|t	| | ||kf|t	| | df}||||fD ]}| |”|ks?J q3| |”td|| k f|  | |t
| |kf|  t
| | dfkseJ |	 |”td|| kf|  | |t
| |kf|  t
| | dfksJ td|| k ftj||kfd}ttj||kfd|| k fd}td|| k fd	||k ftjdf}ttj||kfd	|| kfd
}td	t| |k ||k ftj||kfd
}	t|t |}
|||||	fD ]F}| |
”}tdD ]9}| d	|d||i}| |”| |” |
 |””ksJ | d|d	||i}| |”| |” |
 |””ks,J qōqéd S )Nr   Tr   r”   rM   rc   r   rB   r@   rA   r_   r^   )r   r&   r5   r2   r   r   r1   Śranger]   r$   r#   r   rg   )r   r”   rM   rc   Śp0Śp1ro   rp   rq   rw   r¤   rm   r®   rÆ   r±   rG   rG   rH   Ś-test_piecewise_integrate4_symbolic_conditionsy  sx   
$&ü
$(üż

ż

ż"(
&*üžr¶   c                  C   sP   t dttdftt df} t| tddft dttdfdt dfks&J d S )Nr   Tr@   r^   rU   )r&   r   rc   rM   r1   ©rm   rG   rG   rH   Ś0test_piecewise_integrate5_independent_conditionsŗ  s   4rø   c                  C   s  t dttt dkdt dt  dkB dttt dkdt d dk dt dt  dkft dttt dkddt dt  dkfdt dtt dkftdf dfdfdt dttt dkdt dt  dkB dttt dkdt d dk dt dt  dkft dttt dkddt dt  dkfdt dtt dkftdf dfdf  } t| t dtt tjktt dkB fdt d tt dkfdt dt  dfks×J t| dk t”ttt tjktt dkB dttt dkdt d dkdt dt  dkks
J d S )Nr   r@   rD   FrC   TrU   )r&   r3   rM   rc   r'   r   rg   r   r·   rG   rG   rH   Śtest_issue_22917æ  s4   &.’( ’’ž(.’( ’’žü$
ž,.’r¹   c            
      C   s  t td d td  ttdt  td  dfdt d df} |  ” t tttdfdtd  dfks6J t ttttdttt dfd ” t dtttdttdfdks\J t dt tt tt	tt	 t   tt	dtt	 t d@ fdtt tt	tt	 t   tt	dtt	 t d@ fd ” t dt tttdtt	dfdtttdtt	dfdks¾J dtttdt
t	dftdff}t |  ” t | ksŪJ dttdfttt dff}t |  ” t | ksöJ t dt	 tttdtt	dftdf ” tksJ tdttdfttd t df}ttt d }td}t |  ” |ks:J t | t|t”  ” | t|t”ksQJ td	dd
}tddd
}tddd}t | d|  td| df|dd|   |d| d   | d|   df}| ” | d|  ksJ t d|dk |dk @ |dk @ f|d d |d  |d  |dk |dk @ ftj|d  d|  |d  |dk |dk @ |dk @ f|d | |d d  tj|d  d|    |dk |dk @ |dk @ |dk @ f|d tj|d  d|  |d d |d    |dk |dk @ f|d | |d d  tj|d  d|    |dk |dk @ |dk @ fd|dk |dk @ f|d d |d  |d  |dk f|d | |d d  tj|d  |d    |dk |dk |dk B @ ftj|d  d|  |d  |dk |dk |dk B @ fdt d|dk |dk @ |dk @ fd| |d tj  |d  |dk |dk @ fd| d|d   d|  |dk |dk @ |dk @ fd| d| |d tj  d|d  d|    |dk |dk @ |dk @ |dk @ fd| d|d  d|  |d tj |d    |dk |dk @ fd| d| |d tj  d|d  d|    |dk |dk @ |dk @ fd|dk |dk @ fd| |d tj  |d  |dk fd| |d|d   d| |d tj    |dk |dk |dk B @ fd| d|d   d|  |dk |dk |dk B @ fd } |  ” t d|dk f|d |d d  d |dk fd|d  d d|d  d  d |dk fd|d  d d|d  d  d |dk fd| |d d  d |dk fdksōJ t}t dtdkfdtdk fdtdkf ” t dtdkfdtdk fdksJ t dtdk fdtdk fd ” t dtdk fdks7J t dtdkf ” t dtdkf|dfksOJ t dtdkttk @ f ” t dtdkttk @ f|dfksoJ t dtdk fdtdktdk @ fd ” t dtdk fdtdk fdksJ t dtdk fdtdktdk@ fd ” t dtdk fdtdkfdks¹J t dtdk fdtdktdk @ fd ” t dtdk fdtdktdk @ fdksāJ t dtdk fdtdktdk@ fd ” t dtdk fdtdkfdksJ t dtdk fdtdktdk@ fd ” t dtdk fdtdktdk@ fdks0J t tttdktdk@ ftdf ” t tttdktdk@ ftdfksWJ t dtdktdk @ fdtdktdk @ f ” t dtdktdk @ fdtdktdk @ f|dfksJ t dtdktdk@ fdtdktdk @ f ” t dtdktdk@ fdtdktdk @ f|dfks»J tddd}	t |tdkfdtdk|	tk@ |	t dk@ ft|	d  |	tk|	t dk@ f|	d t tdk|	tk@ fd|	tkf|df} |  ” t |tdkf|	d t |	tkf|dfksJ |  |	t	” ” t |tdkft t	d  ttdt	k fdtt	k f|dfks?J d S )NrD   r@   r   rC   TrB   rA   rr   r    ©ŚintegerrZ   Śt©ŚpositiverU   r\   r   r^   r_   r   ŚL)Śnonnegative)r&   rM   r   r   r   r   r2   r”   r   rc   r   r,   r   r   r]   r   r   rg   r)   r   r"   r#   )
rm   Śargsr®   rr   r    rZ   r¼   ŚexprŚnanræ   rG   rG   rH   Śtest_piecewise_simplifyĻ  sŌ  .’’’’ž&’’’žżż"&
’$.P(’’’’’’’’(’’’4’’’’’$’’’’÷	’’"’’&’’’’’’’(’’’’’’’ ’’’’ö÷6’’’,’
’’’ż&
’
’’ 
’"
’"
’""’
’"
’""’
’ $
’(’’
’(’’
’*ż"’4’rÄ   c                     sb  t t tdkfttdkf} |  ttd ” t tdgks J t d tddgks-J t td d tdkfd t tdgksDJ t td d tdkf df}t|tddgks^J t td d tdkf tdk f}t|tddgkszJ t td d tdkf tdk f}t|tdgksJ t td d tdkf df}t|tdgks®J t td d tdkf dfd	}t|tdgksČJ t td d tdkft d td dkftd td dkf}t|tdgksńJ tt td tdkfdt dfd d
dgksJ t td d tdkfd tt fdd dd }t td d ttk ftd df}t|t}|dd |D dgksJJ |dd |D ddgksZJ |dd |D ddgksjJ |t dtdkftjdft dtdkftjdft dtdkftjdfgksJ t td dtd kfdt dtd kf}t|t tt t d t dk ftjdft td tdkftjdfgksĻJ t	ddd}t|| t| d |d gksčJ t
d tt t t dtdkfd tt d
tdkfdgksJ t dtd  tdtk tdk fd t d dtd gks/J d S )Nr   rD   r@   r^   rB   r_   rU   T)rW   FrC   rA   c                      s
   t  tS rE   )r:   rM   rG   r   rG   rH   rI   [  ó   
 z&test_piecewise_solve.<locals>.<lambda>c                 S   s   t tdd | S )Nc                 S   s
   | t juS rE   )r   ŚNaN©rM   rG   rG   rH   rI   ^  rÅ   z4test_piecewise_solve.<locals>.nona.<locals>.<lambda>)ŚlistŚfilter)r®   rG   rG   rH   Śnona]  ó   z"test_piecewise_solve.<locals>.nonac                 S   ó   g | ]}|  td ”qS )r\   ©r]   rc   ©Ś.0rÆ   rG   rG   rH   Ś
<listcomp>a  ó    z(test_piecewise_solve.<locals>.<listcomp>c                 S   rĢ   )rD   rĶ   rĪ   rG   rG   rH   rŠ   b  rŃ   r\   c                 S   rĢ   )r^   rĶ   rĪ   rG   rG   rH   rŠ   c  rŃ   rm   r½   rr   rR   )r&   rM   r]   r:   r;   ŚNotImplementedErrorrc   r   rĘ   r   r   r   r2   r%   )Śabs2rs   rŹ   rm   r®   Śabsxm3rG   r   rH   Śtest_piecewise_solve;  sd   "" &’4"
  żžž&&
’$$rÕ   c                  C   s8  t ttdk fddtkf} tt|  t td tdk ftdtkfks$J t| |  t dt tdk fddtkfks;J tt dtdk fdt dtdk fd t dtdk fdksZJ t dtdk fttdkfd	}t dtdk fdt tdkfd	}d
| d|  } tt| tt tftdt d tddfksJ tt dtdkft dtdkf dft dtdkfdtdkfks¼J tt tttdktdk tdkft ttdktdk B tdktdkB @ fksäJ t dttdfd	t ttt t dfdtt t dfd	}}tt||ddtt||ddksJ d S )Nr@   rD   r   rR   rW   )r`   Té   )ių’’’TrA   rU   Tr\   FrJ   )	r&   rM   r'   r1   r   rc   r3   r   r
   )rm   rµ   ro   r   r”   rG   rG   rH   Śtest_piecewise_fold~  s<   ..’ž ’’"’ž"&’*’’r×   c            	      C   s|  t tttdk fd} t dt| df| t|  df}| tt d ”dks(J | td”dks2J | tt d ”dks?J t dt| dfd}t|}tddD ]}| t|”| t|”ksbJ qRdt dtdk fd	k }t|}tdD ]}| t|”| t|”ksJ qvt dtdk fd	}t dtdk fd	}t d||k fd}t|}tddD ]}| t|”| t|”ks»J q«d S )
Nr   rA   TrD   r@   rU   rB   rC   r   )	r&   r+   rM   r   r   r]   r   r'   r³   )	rµ   ro   rq   r®   rÆ   Śr1rw   rx   Śp7rG   rG   rH   Ś%test_piecewise_fold_piecewise_in_cond  s(    ’rŚ   c                  C   s|   t tttdk fd} t dt| dfd|  df}t dtdktttdB fdtt tdk ftdf}t||ks<J d S )Nr   rA   r@   T)r&   r+   rM   r   r   r'   )rµ   ro   rp   rG   rG   rH   Ś'test_piecewise_fold_piecewise_in_cond_2³  s   żrŪ   c                  C   sź   t dtdddd t”fd} ttdt |  }tdktdk @ }ttdt |  ddt dt |ft |fd|fdddksAJ ttdt |  d dt dt |fdksXJ |t dt |fdkseJ |ttdt |  kssJ d S )Nr@   r   FTrA   rJ   )r&   r9   r   rM   r'   r	   )rµ   ro   rk   rG   rG   rH   Śtest_piecewise_fold_expand½  s   "’’ rÜ   c                  C   s>   t ttdk ftd tdkftdtk f} | t | j ksJ d S )Nr`   rD   rC   r@   )r&   rM   rĮ   r·   rG   rG   rH   Śtest_piecewise_duplicateŹ  s   (rŻ   c                  C   s¤   t ttdk ftd dtkftdtk f} t ttdk ftdt dtkftdtk f}| ” | ks2J |jdd|ks<J ttt tdtf ” } |  ” | ksPJ d S )Nr@   rD   rC   r^   F©Śdeep)r&   rM   r0   rf   r   rc   r   )rµ   ro   rG   rG   rH   Ś	test_doitĻ  s   (,rą   c                  C   s¦   t ttdd t”fd} |  td”dksJ |  td”dks!J |  t”t dtdd t”fdks5J t| tt dtdkftd d tdkftjdfksQJ d S )Nr   r@   rA   g      ąæē      ą?rD   T)	r&   rM   r9   r   r]   r   r1   r   rg   )rµ   rG   rG   rH   Śtest_piecewise_intervalŁ  s   (

żrā   c                  C   s$  t dtdk ftjtdkfd} t| t dtdk ftjttdfdtdkfddks+J t| d t dtdk ftjttdfdtdkfddd ksKJ tt dtdkft dtdkf dft dtdkft dtdkftjtdk fdd tdkfddksJ tt dttkft dttkftjttkfddksJ tt dttkfddt dttkfks±J td	dd
\}}t d|dk fddd}t d|dk fd|dkfdd}t ||dk fddd}t ||dk fd|dkfdd}t ||dk fd|dkfdd}t||ksJ t|dd|ksJ d S )Nr   rB   r@   FrJ   rD   T)Śskip_nanzxr, yrr   rR   r   r^   rŽ   )	r&   rM   r   rg   r(   r   rc   rĘ   r   )rm   ŚxrŚyrrµ   Śp1xro   Śp2xŚp2xxrG   rG   rH   Śtest_piecewise_exclusiveä  sL    ’$’
’’’’žžž’’ré   c               	   C   sd  t tdftks
J tdk } t t| ftd | ft t| fks!J t t| ftd | jft t| fks5J tdk }dd }d| ft d| fd|f|ffd| ft d| fd|jf|ffd| ft d| fd|f|fdfd| ft d| fd|fd|ffd| ft d| fd|fd|fd	ffD ] }d
D ]}|t |ddi t|”|t |  t|”ks©J qqtd\}}}}t|k } t|k }t|k }	t|k }
t d| ft d| fd|fd|	f|fd|	ft d| fd|fd|	fksēJ t d| ft d| fd|fd|	fd|	fd|
ft d| ft d|fd|	f|	fd|
fksJ t dt| |
ft d|
fd|fd|	f|fd|	ft dt| |
ft d|
fd|f|fd|	fksFJ t d|	fd|	 fdtjft d|	fdtjfksaJ t d|	fdt|	 |fdt d|	fd|fdks|J t d|	fdt|	 |fd t	t
||||tfd”dksJ t d|	fd|	 ft d|	fdks°J d S )NTr@   r_   c                 S   s   t | tr
t| j S | S rE   )ri   r&   rĮ   )rÆ   rG   rG   rH   Ś	canonical  s   

z*test_piecewise_collapse.<locals>.canonicalrD   r^   ©rU   T©r_   T)r   rD   rW   rK   Fzr1:5rU   )rS   Tr   )r@   rD   r^   rU   g      @rR   )r&   rM   Śreversedr]   r   r5   r   Śtruer2   r¢   r£   )r   r”   rź   rĮ   rÆ   rŲ   Śr2Śr3Śr4r   r    rG   rG   rH   Śtest_piecewise_collapse  s   &( ū’
ž’
’’’ž
’’’
’’’
ž’’’’’’
ž
’
’
’,rņ   c                  C   s   t td tdk fttdddd t”fdt tdkfd} tt| }|ddks*J |d	d	ks2J |d
d
ks:J |dd	ksBJ d S )NrD   r   r@   FTrA   g       Ąg      @rX   rį   g       @)r&   rM   r9   r   r=   )rm   rr   rG   rG   rH   Śtest_piecewise_lambdify/  s   ü
ró   c                  C   sz   ddl m}  ttttdk ftttdkf}tt| td  tdk fd| td  tdkf}|jtdd|ks;J d S )Nr   )ŚOrD   r@   )rZ   )Śsympy.series.orderrō   r&   r,   rM   r+   Śnseries)rō   rµ   ro   rG   rG   rH   Śtest_piecewise_series>  s   "2r÷   c                  C   sd  t dt tdkfd} t ttdkfd}t dt tdkftdf}t ttdkfdt df}t dt tdkftdf}t dt tdk ftdf}t ttdk fdt df}t ttdkfdt df}|  t”dkskJ | t”dkstJ | t”tks}J | t”dt ksJ | t”tksJ | t”dt ksJ | t”tks„J | t”dt ks°J d S )Nr@   rA   Tr   )r&   rM   Śas_leading_term)rµ   ro   rp   rq   rw   rx   rŁ   Śp8rG   rG   rH   Śtest_piecewise_as_leading_termE  s    rś   c                  C   s6  t dtdk fddtkf} t dt tdk ftdtkf}t tt tdkfdt df}t t tt tdkfdt df}t| | ksEJ t|t| ksPJ t||ksXJ | jdu s_J | jdu sfJ |jdu smJ |jdu stJ |jd u s{J |jd u sJ |  ” | dfksJ | ” dt | fksJ d S )NrD   r   r@   TF)r&   rM   r   r   r'   Śis_imaginaryŚis_realŚas_real_imag)rµ   ro   rp   rq   rG   rG   rH   Śtest_piecewise_complexX  s   $rž   c                  C   sč   t ddd\} }t| |d  tdkf| d | df}| ” tt| |d  tdkft| d | dfks8J | ” tt| |d  tdkft| d | dfksUJ | ” tt| |d  tdkft| d | dfksrJ d S )NśA BF)ŚcommutativerD   r   T)r   r&   rM   r   r   r    )ŚAŚBrm   rG   rG   rH   Śtest_conjugate_transposem  s   &,’,’,’r  c                  C   s    t tdftks
J t tdfddtksJ t dtdtfjdttdffks*J t dtdtfddjdtdtffks@J t tdfdd} | tksNJ d S )NTrJ   r@   F)r&   rM   r   rĮ   r·   rG   rG   rH   Śtest_piecewise_evaluatex  s   (
’r  c                   C   s   t ttdkft tdkf ” ttdtddft tt dfgks$J t td d tdkfd ” td d tdtfdtt dddfgksJJ d S )Nr   TrD   rA   )r&   rM   Śas_expr_set_pairsr9   r   rG   rG   rG   rH   Śtest_as_expr_set_pairs  s   "’(’r  c                  C   s0   t dttdfd} tt| }| |ksJ d S )NrW   r   )é   T)r&   r   rM   r   r7   )rm   r„   rG   rG   rH   Śtest_S_srepr_is_identity  s   r  c                  C   s¦   t dtdkfdttdktdk@ fd} |  tddf”d	ks J t dtdkfdttk fd} td
df}|  |”}tddD ]}| t|”|  t|” |”ksPJ q=d S )Nr@   rU   rD   r^   rC   r   rV   r_   é   r   )r&   rM   r4   r1   rc   r³   r]   )rm   r¤   r®   rÆ   rG   rG   rH   Śtest_issue_12587  s   (

$’r
  c                  C   sĄ  t dtttd d   tddftd ksJ tdtttdk tdktdk fd  tddf”dks5J tdtdkfdttd kfd  tddf”dksOJ tdtdkfdtdtfd  tddf”d	kshJ tdtdt td ktdk fd  tddf”dksJ tdtdt td ktdk fd  tddf”dks J tdtdkfdttd kfd  tddf”dksŗJ tdtdt tdt d  fd  tddf”d	ksÖJ tdttdk tdkfdtdkfd  tddf”d	ksóJ tdttdfd
  tddf”dksJ tttdktdk @ fdtdk f  tddf”dks$J tttdktdk @ fdtdk f} t	}|   tdt
f”}|tt
d t
dk ftdt
d d tdt
 tdt
 tj t
tdt
kf|dfksmJ |   tddf”| t
d”ks~J |   tddf”dksJ |   tddf”|u sJ tdtdkfdtttdktdk fd} |   tddf”dksŗJ tdtdtktdkfdttdk tdkfdtdk f} |   tddf”dksćJ tdtdk fdtttdtdkf  tddf”tju sJ tdtdk fdtttdtdkfd  tddf”dks!J tdtdk fdtttdtdk fd  tddf”dks@J tdtdk fdttdt
tk @ fd  tddf”dks^J d S )Nr@   rD   r^   rA   r   r   r_   rU   rS   rR   rC   TrT   é   rW   é   )r1   rM   r%   r   r&   r2   r5   r   r   r)   rc   r$   r   rg   r]   r4   rĘ   )rm   rĆ   rÆ   rG   rG   rH   Śtest_issue_11045  s   0$’’’"’"’’"’$’
’ 
’"*’ü"*
ż$
’&
’&
’$’r  c                  C   s  t } tdtdk f t”tttdk f| dfksJ tdttdktdk f t”t| tdk fttdk f| dfks<J tdttdktdk f tddf”| u sSJ tdttdktdk f tddf”dksjJ td\}}tddd	\}}t|ttdk |dk f|ttdk |dkf t”t|t |dkft|t tdk f|t tdk f| df|dk ft|t tdk f| dfdfksĆJ d S )
Nr@   rD   Tr   r^   rU   r’   za br   )r)   r&   rM   r1   r2   r   r5   )rĆ   r  r  r   r”   rG   rG   rH   Ś
test_holesē  s$   
’ 
’..,.ż’r  c                     sĄ   dd   fdd} | ddksJ t d} fdd}||}| |d	”dks*J t dd
d}||}| |d	”dks>J tdtdk fdtdkf ” tdtdk fdt d d
fks^J d S )Nc                 S   s$   t d| dk fd| d  | dk fdS )Nr   rC   r@   rD   rA   rF   rĒ   rG   rG   rH   rr   ü  ó   $ztest_issue_11922.<locals>.fc                    s     t  t |    t ddf”S )NrC   r@   ©rM   r1   ©Śkr   rG   rH   rI   ž  s    z"test_issue_11922.<locals>.<lambda>gffffffž?r   r  c                    s$   dt d   t |    t ddf”S )Nr@   rD   rC   r  r  r   rG   rH   rI     r  r^   Tr½   r@   rW   )r   r]   r&   rM   r1   )Śautocorrr  Śgood_autocorrr   rG   r   rH   Śtest_issue_11922ū  s    ’r  c               	   C   sä   dt dtdk fdt d tdk ft dtdkfd	t d
tdkfd tdkfdt d tdk fd } t| tt tf}|t| tt tf ” ksJJ t|dksRJ t dtt dk fd t”t dttkft t dfkspJ d S )Ngż©§J¢j?r   gf'vb'6TĄgČlAwæg¶3ŲPõ?rD   g333333Ó?é{   )gffffffę?TgŁ?)g333333ć?Tgš%Ń½æg%JMć× @g$I$Éw@rA   z1.00195081676351r@   T)r&   rM   r1   r   r0   rf   Śstrrc   )rr   rÆ   rG   rG   rH   Śtest_issue_5227  s(   ’’’’ū ’r  c            
      C   sl  t ddd} t ddd}t ddd}t ddd}tdt|| k ||kfd}tdt| |k||k fd}t|||tft|||tfksFJ td	td|k || k fd
}td	t| |k|dkfd
}t||}|td|dkf||td| kftd| dfksJ t||}	|	|ksJ | |ddf”tdtd| d ks J | |ddf”tdtd| d ks“J d S )Nr   Tr   r”   rM   rc   r   rB   r@   rA   rD   rU   )r   r&   r5   r1   r   r2   r#   r$   )
r   r”   rM   rc   r“   rµ   rp   rq   Śip3Śip4rG   rG   rH   Śtest_issue_10137  s&   $


ż
(,r  c                     s   dd   fdd} | t }| t d”| t d”ksJ | t d”dks&J t t t  t tdtd	ktdk@ t t d	k@ t t dk@ fd
ksMJ d S )Nc                 S   s   t d| dk| dk@ fdS )Nr@   rC   rA   rF   rĒ   rG   rG   rH   rI   1  ó    z-test_stackoverflow_43852159.<locals>.<lambda>c                    s$   t  | t  t tt t
 fS rE   )r1   rc   r   rĒ   r   rG   rH   rI   2  s   $ g      ųæg      ų?r^   r   r@   rC   rA   )rM   r]   r'   rc   r&   )ŚConvŚcxrG   r   rH   Śtest_stackoverflow_438521590  s   *žr  c                  C   s®   t ddd} t dddd}dd }t|| | t tftd ks"J t||  t| d  }t|| t tftdd	|  |d  d|d   t|d
ftd dfksUJ dS )aD  
    # 3200 seconds to compute the fourier part of issue
    import sympy as sym
    x,y,z,t = sym.symbols('x y z t')
    k = sym.symbols("k", integer=True)
    fourier = sym.fourier_series(sym.cos(k*x)*sym.sqrt(x**2),
                                 (x, -sym.pi, sym.pi))
    assert fourier == FourierSeries(
    sqrt(x**2)*cos(k*x), (x, -pi, pi), (Piecewise((pi**2,
    Eq(k, 0)), (2*(-1)**k/k**2 - 2/k**2, True))/(2*pi),
    SeqFormula(Piecewise((pi**2, (Eq(_n, 0) & Eq(k, 0)) | (Eq(_n, 0) &
    Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) & Eq(k, 0) & Eq(_n, -k)) | (Eq(_n,
    0) & Eq(_n, k) & Eq(k, 0) & Eq(_n, -k))), (pi**2/2, Eq(_n, k) | Eq(_n,
    -k) | (Eq(_n, 0) & Eq(_n, k)) | (Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) &
    Eq(_n, -k)) | (Eq(_n, k) & Eq(_n, -k)) | (Eq(k, 0) & Eq(_n, -k)) |
    (Eq(_n, 0) & Eq(_n, k) & Eq(_n, -k)) | (Eq(_n, k) & Eq(k, 0) & Eq(_n,
    -k))), ((-1)**k*pi**2*_n**3*sin(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
    pi*k**4) - (-1)**k*pi**2*_n**3*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2
    - pi*k**4) + (-1)**k*pi*_n**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
    pi*k**4) - (-1)**k*pi*_n**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
    pi*k**4) - (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(pi*_n**4 -
    2*pi*_n**2*k**2 + pi*k**4) +
    (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
    pi*k**4) + (-1)**k*pi*k**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
    pi*k**4) - (-1)**k*pi*k**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
    pi*k**4) - (2*_n**2 + 2*k**2)/(_n**4 - 2*_n**2*k**2 + k**4),
    True))*cos(_n*x)/pi, (_n, 1, oo)), SeqFormula(0, (_k, 1, oo))))
    rM   Tr   r  )r»   Śfinitec                 S   s   t |  | dkf| | dkfS ©Nr   rF   rĒ   rG   rG   rH   rI   Z  s    z"test_issue_12557.<locals>.<lambda>rD   rC   r   N)r   r1   r   r+   r%   r&   r   )rM   r  rÓ   ŚfuncrG   rG   rH   Śtest_issue_12557;  s   "2’r#  c               	   C   s¤  ddl m}  td\}}}}td||k ftt||k||k fd||kf}| |”}|td||kf|t |t  |t||kf| t tt||  dfksQJ | tdD ]*}t	t
||f|}tddD ]}	| |” ||	”| |” |” ||	”ksJ qgqWt|||}
| |
”}t| t tt|t||  ||kfd}| tdD ] }t	t
|||f|}| |” |
 |””}|| |”ksÉJ q©||ksŠJ d S )	Nr   r   z
t0, t1 T tTrD   rC   r^   rA   )r   r   r   r&   rM   r2   r1   r#   r³   r¢   r£   Śxreplacer]   r   r$   )r   Śt0Śt1ŚTr¼   rr   rs   rÆ   r±   Śttr¤   r®   ŚtrurG   rG   rH   Śtest_issue_6900`  s6   .


ż
’’
$žr*  c                   C   sV   t ttttd  d dktttt tk ttjk ttjtk ttk ks)J d S )Nr@   r   )	r:   ŚabsrM   r5   r2   r   r   ŚZeroŚOnerG   rG   rG   rH   Śtest_issue_10122z  s    *’r.  c                  C   sĢ  t dtdkfdttkftt df} | |  tt” d tt d  }tdt}t|t ” t t dtdkftd  td t td t   ttd   dt tt  td   dt ttt  td   ttd   t|kftd  td  t td |   dt |   dtt   dt tt  td   dt tt |  td   ttd   |td   dfttktdk@ tdktt	 k@ B ft dtt  tdkftd  td t td t   dt t td t td t    td td t td t    dtt  t  dttt  t  dt  ttd   dt tt  td   dt ttt  td   ttd   t|kftd  td  t td |   dt t td  t td |    td td  t td |    dtt  t  dtt |  t  dt  dt tt  td   dt tt |  td   ttd   |td   dfttkft td  td t td t   tdkfttd  ttd   t|kftd td  t td |   td td t td t    dt t td  t td |    dt t td t td t    td td  t td |    td td t td t    ttd   |td   dfdfksdJ d S )Nr   r@   TrD   rC   )
r&   rM   r   r]   rc   r#   r1   r	   r"   r   )ŚuŚeŚMrG   rG   rH   Śtest_issue_4313  sĢ   $ 

F’
’’0
’’’’’
ž
žžü łD’’’ž
žžž
żż8
’ ’žžžżż
ü
üüśõ( ’$’"ž žż
ż
żżżłėr2  c                   C   sJ  t td ttdf t”dg fksJ t dttd kft dttd k fdt dt d k fd t”dt tddfgfksAJ t dtttfd t”dt tddfgfksZJ t tt ttdkfttdf t”ddt	tt dft tttdfgfksJ t dt
td dkfd t”dd	d
t tddfgfks£J d S )NrD   r^   Tr@   rB   rA   r   r\   )rC   r   r@   r   )r   r@   r@   r   )r&   rM   r   Ś
_intervalsr   r   r   r+   r,   r   r   rG   rG   rG   rH   Śtest__intervals¢  s*   (&żż
’""’’’’r4  c                  C   sø   g d¢\} }}}}t |tdkf|dft | ttd dk f|ttd dk f|df }| t” t”t || tdkf| | tdkf| | tdk f|| tdk f|| dfksZJ d S )N)r@   rD   r^   rU   r_   r@   TrD   r   rU   )r&   rM   r   r1   r   )r   r”   r   r    r0  rm   rG   rG   rH   Śtest_containment“  s   .’
ūr5  c                  C   s   t td } t| tt tfdksJ t| tddfdksJ t| ttdfd t”dks0J t| tdk fd t”tttd tdk fdksKJ d S )Nr@   r   rD   rA   rB   )r-   rM   r1   r   r&   r   r.   )Śd1rG   rG   rH   Śtest_piecewise_with_DiracDeltaĄ  s   "’r7  c                  C   sn  t dtdk fdjd u sJ t dtdk fdjdu sJ tddd} t dtdk f| dfjs0J t dtdk f| td	k fjd u sBJ td} t dtdk f| dfjd u sVJ t dtdk fdjd u sdJ t dtdk fd
jspJ t dtdk ftdfjd u sJ t dtdk fdjsJ t }t |tdk fjd u sJ t dtdk fd
d	k }|dks­J t|dksµJ d S )Nr   r@   rB   rC   Fr   T)Śzeror^   rR   )	r&   rM   Śis_zeror   Ś
is_nonzeror   Ś	is_finiter   r'   ©r   r”   r   rG   rG   rH   Śtest_issue_10258Ģ  s    $  r=  c                  C   s   t ttdkfdt ttdkfd} }| | }t|}dD ]}| t|”| t|”ks-J q| | }t|}dD ]}| t|”| t|”ksHJ q8d S )Nr@   rR   r^   r   )r   rD   rU   )r&   rM   r'   r]   )r   r”   Śmrr   rÆ   rG   rG   rH   Śtest_issue_10087į  s   &’r?  c                  C   są  t d} t d}t| d |dk f| d df}t| d |tddk f| d df}t|| |ddf| d | d  d d| d  | d  d  | d | d   ksSJ td|dk fd	}td|dk fd
}t|| |ddfdkssJ t ddd}t ddd\}}} }}ttd||k|dk B || kB f|df|d|f}| ” }	|	td|| kf|t|| |td|  dfks¼J dD ]/}
tddD ]'}t| d|D ]}|| k|
f||f||fg}|	 |”| |” ” ksėJ qĪqÅq¾d S )Nzc:5rM   r@   rD   Tr^   rU   r   rR   rA   rS   rc   r½   z	a,b,c,x,zr   )TF)	r   r&   r   r1   r0   rf   r$   r³   r]   )r   rM   r~   r   rc   r   r”   r>   r   r®   rk   r   Śzzr±   rG   rG   rH   Śtest_issue_8919ķ  s8   $:’žž6ž’’rA  c                  C   sņ   t d} tdt| td dfdtd dk fd}| t”t|tks%J | tddf”t|tddfks7J t|tddf | ttd ” ” dksMJ | t”ttt| tdtdk t| td@ B fdt tt	 ktdk @ fdkswJ d S )	Nrr   r@   r   rD   rW   rA   r_   g      $@)
r   r&   r   rM   r1   r0   r]   rZ   rc   r   )rr   rm   rG   rG   rH   Śtest_unevaluated_integrals  s   *$,
&žrB  c                  C   s\   t d\} }}ttttdk tdkftdkdffttttdktdk tdkfks,J d S )Nza:cr@   r   T)r   r&   rM   rc   r3   r<  rG   rG   rH   Ś%test_conditions_as_alternate_booleans  s   $’rC  c                     s\  t d\} }dd   tdk ftdkfttdk ks#J  tdk fttk fttdk ks:J  tdk fttdk ttk f| tdkfttdk ks[J  tdk fdfttdk kspJ  tdk ftdk f| dfttdk ttdk | ksJ  tdk ftdk f| dfttdk ttdk | ks°J  tdk fttk f| tdk fttdk ksĢJ  tdk f| tdk fttk f|dfttdk ttdk | ksńJ  tdk ftttk tdk fttdk ksJ tt fdd	 tt fd
d	 tt	 fdd	 d S )Nza:dc                  W   s   t |   t”S rE   )r&   r   r3   )rĮ   rG   rG   rH   Ś_ITE   s   z+test_Piecewise_rewrite_as_ITE.<locals>._ITEr@   r   TrD   c                      s    t d t dk ft dfS rP   rĒ   rG   )rD  rG   rH   rI   2  r  z/test_Piecewise_rewrite_as_ITE.<locals>.<lambda>c                      s    t t tk ftt kfS rE   )rM   rc   rG   )rD  r   rG   rH   rI   6  r  c                      s    t dk ft dkfS )NrD   r^   rĒ   rG   ©rD  r   r”   rG   rH   rI   7  r  )
r   rM   r3   r   r5   rc   r;   rb   rŅ   Ś
ValueError)r   r    rG   rE  rH   Śtest_Piecewise_rewrite_as_ITE  s4   ..,’*’’"’(’"
’rG  c                   C   s(   t ttttddt fdksJ d S )Nr   rD   rU   )r1   r+  r,   rM   r   rG   rG   rG   rH   Śtest_issue_14052:  s   (rH  c                   C   sŽ   t tdtfdtfdtdtfd tdtfdtfdksJ t tdtfd	tfd
tdtfd tdtfdtfdks>J t tdd tdD  tdtfdksTJ t tdd tddD  ttdtfdksmJ d S )Nr@   rD   rė   r  )é   Té	   é   )r  Tr^   rģ   rT   )rÖ   Tr   é!   )é7   Tc                 S   ó   g | ]	}t |tfd qS ©rA   ©r&   r   rĪ   rG   rG   rH   rŠ   H  ó    ’z$test_issue_14240.<locals>.<listcomp>é(   i  rA   c                 S   rN  rO  rP  rĪ   rG   rG   rH   rŠ   K  rQ  é)   )r'   r&   r   r”   r   r³   r
   r   rG   rG   rG   rH   Śtest_issue_14240>  s0   ’’ż’’ż
’ž
’žrT  c                  C   s>   t d} t| | dk ftdd df}t| ” dksJ d S )NrM   r@   é:   rT   Tz/Piecewise((x, x < 1), (8.28571428571429, True)))r   r&   r   r  re   ©rM   rr   rG   rG   rH   Śtest_issue_14787P  s   rW  c                     s  t d\} }td| dk|dk@ | dk| dk @ |dk @ B |dk| dk @ tt|dd@ B |dk| dk@ | dk @ tt|dd@ B ftj| dk|dk @ | dk|dk@ | dk @ B |dk| dk @ tt|dd@ B |dk| dk@ | dk @ tt|dd@ B ftj tt|dd|dk| dk @ |dk| dk@ | dk @ B @ fd|dk| dk @ tt|dd@ |dk| dk@ | dk @ tt|dd@ B f}tdt| dt|dB t| dtt|dd@ B fdt| d|dk@ fdt| dtt|dd@ f|tt| dtt|d@ f}t|}| ” }| ” }ddtj dtjddf}|D ]'}|D ]!}	| |||	i  fdd||||fD }
t	t
|
dks@J q qd S )	Nzb erD   r@   r   rC   r\   c                    s   g | ]}|   ”qS rG   )r$  )rĻ   r  ©r§   rG   rH   rŠ   w  s    z$test_issue_21481.<locals>.<listcomp>)r   r&   r   r   r   rg   r   r'   r   ŚlenŚset)r”   r0  ŚCr  r  ŚsaŚsbr¦   rÆ   r°   ŚokrG   rX  rH   Śtest_issue_21481U  s`   ’ž&ż’’ž&ż’&’’&’’ņ0üż’r_  c                  C   s  t d\} }tdt| dft| df}| ” t| ksJ t| t| dfd|  |d d  t| dt| | d@ ft| df}| ” t| ksKJ t| d t| dfd|  |d d  t| dt| | d@ ft| df}| ” tdt| dft| dfksJ d S )Nr   r   TrU   rD   r@   rC   )r   r&   r   r,   r   )rM   rc   rµ   ro   rp   rG   rG   rH   Śtest_issue_8458{  s   FJ,r`  c               	   C   s  t d} ttdttt| dtt| dfdsJ t d}tttj	t|dk fdtt|dkt
t|dftjdfs@J t ddd}ttj	t|dk fdtt|dkt
t|dftjdf}|ttj	|dk fd|dkftjdfd	d
ks|J t| }ttj	t|dk fdtt|dkt
t|dftjdf}|tdt
t|dftjdfd	d
ks³J |tdt
|dftjdfd	d
ksĘJ d S )Nr>   r@   r   rR   rM   Tr§   r   FrJ   )r   r   r&   r5   r   r   r   r   r   ŚPir   rĘ   r   )r>   rM   r§   rm   rÆ   rG   rG   rH   Śtest_issue_16417  s6   .žž

ž
ž
’
’rb  c                     sŹ  t d\} }}}}}t  fdd}tdt| |fd}||d | | ks)J t| t|df|t|df|df}||| d|  d| | d|  | d|  | |  d|  | d|  d|  | d|  kswJ tdt| |fd}	||	d | | ksJ tdt| d	fd
d}
||
dd	 d	|   ksØJ td	t| dfdt|dfd}|| d|   d| d d|   d	 ksŅJ tdt| dt|d@ fd}|| d|   d|  d|   d| ksüJ tdt|d	t| d@ fd}|| d|   d	|  d	| d ks$J tdt| d	t|d@ fd}||d d|  d	|  d	 d	|   d ksOJ tdt| dt|d@ fd}||d d|  d|  d kssJ tdt| dt|dB fd}||d d|   d| d ksJ tdt|dt| dB fd}|| d|   d|  d|  d ksæJ tdt| dt|d	B fd}||d d|   d	| d d	|  d ksźJ td	t| dt|dB fd}||d d|   d| d d|   d d|  d ksJ tdt| dt|dB fd}||d d|   d| d ks@J tdt| d	t|dB fd	t| dt|d@ fd}||d d|  d	|   d|   d|  d| d	|   d d|  d|   d|   d| d ksJ tdt||fdtdt||fd tdt|| fd tdt|| fd }|| || ||  ||   ||  ksÜJ tdt|| t||t||B t|| B @ fdt|| fdt||t||B t|| B fd}|| || ||  ||   ||  ks&J tdt|dt| dt| |@ B fd
}||d d|   d|  | | d d|   | |  d d|  d ksgJ td| dkfd}|||ksyJ tdt| dk | dkfd}|||ksJ tdt| dk| dk fd}|||ks§J tdt|dt| dB t| dt|dB @  fd}|| d| d|   d| d|    d|  d ksćJ d S )Nzx y z n t mc                    s   t |   ”S rE   )r	   r   r·   ©ŚKrG   rH   rI   «  rQ   z5test_eval_rewrite_as_KroneckerDelta.<locals>.<lambda>r   rB   r@   TrA   r^   rė   rģ   rU   rD   r   rS   r_   éü’’’rR   rC   r\   r   rV   r  )r   r/   r&   r   r   r2   r5   )rM   rc   r>   rZ   r¼   r>  rr   rµ   ro   rp   rq   rw   rx   rŁ   rł   Śp9Śp10Śp11Śp12Śp13Śp14Śp15Śp16Śp17Śp18Śp19Śp20Śp21Śp22rG   rc  rH   Ś#test_eval_rewrite_as_KroneckerDeltaØ  s   $<’’
’ 4628**28F*4D ’’’&’’6,.’6(Z4Hrt  c                  C   s8   ddl m} m} | ddd}| ddd}|||  d S )Nr   )ŚUniformŚdensityŚu1r@   Śu2)Śsympy.statsru  rv  )ru  rv  rw  rx  rG   rG   rH   Śtest_identical_conds_issueō  s   rz  c                  C   s:   t dtdkf} t| tdtddf}t|dksJ d S )Nr@   i`	  r   z252.4é   z252.400000000000000000000000000)r&   rM   r1   r   r  )rr   r¦   rG   rG   rH   Śtest_issue_7370ž  s   r|  c                  C   s   t d} t d}tddd}||d | |d i}tdt|dk| dk df}| |”tdt|d dk|d dk dfks?J d S )NrM   rc   Śinpr@   )r   r   r   T)r   r6   r&   r3   r$  )rM   rc   r}  Śrep_dictrm   rG   rG   rH   Śtest_issue_14933  s   6r  c                   C   s   t tdd  d S )Nc                   S   s   t ttdk fdtdkf ” S )Nr   r@   )r&   rM   rc   r  rG   rG   rG   rH   rI     s    z"test_issue_16715.<locals>.<lambda>)r;   rŅ   rG   rG   rG   rH   Śtest_issue_16715  rĖ   r  c                  C   s   t ddd\} }t ddd}t|tj  }tt|| |d| f}| ” dtt|  d| d  d  d td| d   ksAJ d S )	Nzt tauTr   rZ   rŗ   r   rD   r@   )r   r   r   rg   r1   r!   r   )r¼   ŚtaurZ   ŚlamŚeqrG   rG   rH   Śtest_issue_20360  s
   Dr  c                  C   s  dd } | t ttt ktdk @ ftt ktdk @ ksJ | t ttt kttk @ ftt kttk @ ks8J | t ttdktdk @ ftdktdk @ ksPJ | t ttdkttk @ ftdkttk @ kshJ | t ttdktt k@ ftdktt k@ ksJ | t ttdktdk@ ftdktdk@ ksJ | t ttdktdk @ ftdktdk @ ks²J | t ttdkttk @ ftdkttk @ ksŹJ | t ttdktdk@ ftdktdk@ ksāJ | t tttktt k@ ftt kttk@ ksüJ | t tttktdk@ ftdkttk@ ksJ | t ttt ktdk @ ftdk tt k@ ks0J | t ttt kttk @ fttk tt k@ ksKJ | t ttt ktdk@ ftdktt k@ ksfJ | t ttt kttk@ fttktt k@ ksJ | t ttdkttk@ ftdkttk@ ksJ | t ttttdktttdk B ftttdktttdk B ksĆJ d S )Nc                 S   s   | j d jS r!  )rĮ   rk   rĒ   rG   rG   rH   rI     rO   z%test_piecewise_eval.<locals>.<lambda>r^   r   r@   )r&   rM   r   r   r   r   r   rG   rG   rH   Śtest_piecewise_eval  sh   ’’’’’’’’’’
’
’
’
’
’
’*’r  c                  C   s\   t ddd} td|  | dkfd|  df}t|| tt|  | dkft| dfks,J d S )NrM   Tr   rC   r   r@   )r   r&   r1   r"   rV  rG   rG   rH   Śtest_issue_22533G  s   2r  c                   C   s>   t dtdkfdtdkfdtdkft dtdkfdksJ d S )Nr@   rD   r^   rR   rL   rG   rG   rG   rH   Śtest_issue_24072M  s   "’r  c                  C   sĘ   t ddd} td| dk ftd|  df}| | t”du sJ | | d”dks)J | | d”dks3J | | d”dks=J | | d	”dksGJ | | td
”dksSJ | | td
dd”dksaJ dS )z9 Issue 24127: Tests eval_is_meromorphic auxiliary method rM   Tr   r@   r   NrC   FrD   r   )r   r&   r%   Śis_meromorphicr   r   rV  rG   rG   rH   Ś#test_piecewise__eval_is_meromorphicR  s    r  N)£Śsympy.concrete.summationsr   Śsympy.core.addr   Śsympy.core.basicr   Śsympy.core.containersr   Śsympy.core.exprr   Śsympy.core.functionr   r   r	   Śsympy.core.mulr
   Śsympy.core.modr   Śsympy.core.numbersr   r   r   r   r   r   Śsympy.core.relationalr   r   r   r   Śsympy.core.singletonr   Śsympy.core.symbolr   r   Ś(sympy.functions.combinatorial.factorialsr   Ś$sympy.functions.elementary.complexesr   r   r   r   r   r   r    Ś&sympy.functions.elementary.exponentialr!   r"   Ś(sympy.functions.elementary.miscellaneousr#   r$   r%   Ś$sympy.functions.elementary.piecewiser&   r'   r(   r)   r*   Ś(sympy.functions.elementary.trigonometricr+   r,   Ś'sympy.functions.special.delta_functionsr-   r.   Ś(sympy.functions.special.tensor_functionsr/   Śsympy.integrals.integralsr0   r1   Śsympy.logic.boolalgr2   r3   r4   r5   Ś"sympy.matrices.expressions.matexprr6   Śsympy.printingr7   Śsympy.sets.containsr8   Śsympy.sets.setsr9   Śsympy.solvers.solversr:   Śsympy.testing.pytestr;   r<   Śsympy.utilities.lambdifyr=   r   r”   r   r    rM   rc   r>   r   r   r   r   r   r   rØ   r©   r²   r¶   rø   r¹   rÄ   rÕ   r×   rŚ   rŪ   rÜ   rŻ   rą   rā   ré   rņ   ró   r÷   rś   rž   r  r  r  r  r
  r  r  r  r  r  r  r#  r*  r.  r2  r4  r5  r7  r=  r?  rA  rB  rC  rG  rH  rT  rW  r_  r`  rb  rt  rz  r|  r  r  r  r  r  r  r  rG   rG   rG   rH   Ś<module>   sĪ     $ 
)
-
@lC

-J%#& L
	,