o
    *Ī®c»ä  ć                   @   sų  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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l.m/Z/m0Z0m1Z1 d dl2m3Z3m4Z4m5Z5m6Z6m7Z7 d dl8m9Z9m:Z: d dl;m<Z<m=Z= d dl>m?Z? d dl@mAZAmBZB d dlCmDZDmEZEmFZFmGZG d dlHmIZI d dlJmKZK d dlLmMZM d dlNmOZO d dlPmQZQ d dlRmSZSmTZT d dlUmVZV e d\ZWZXZYZZZ[Z\e ddd Z]d!d" Z^d#d$ Z_d%d& Z`d'd( ZaeTd)d* ZbeTd+d, Zcd-d. Zdd/d0 Zed1d2 ZfeTd3d4 Zgd5d6 Zhd7d8 Zid9d: Zjd;d< Zkd=d> Zld?d@ ZmdAdB ZndCdD ZodEdF ZpdGdH ZqdIdJ ZrdKdL ZsdMdN ZtdOdP ZudQdR ZvdSdT ZwdUdV ZxdWdX ZydYdZ Zzd[d\ Z{d]d^ Z|d_d` Z}dadb Z~dcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz 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eTdd Zdd Zdd Zdd Zdd Zdd Zdd ZdS ) é    )ŚSum)ŚAdd)ŚBasic)ŚTuple)Ś	unchanged)ŚFunctionŚdiffŚexpand)ŚMul)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   sd  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s(J tttdk fddtttdk fdks=J tttdk fddddkftttdk fksUJ tttdk fdtdk fdtttdk fdksnJ 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s„J tttdk fttdk ftdftks¹J ttdftksĆJ 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rõtdt tdk fksųJ  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s6J 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sZJ 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s¶J | td”dksĮJ | td”dksĢJ 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s#J | td”tdks0J 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soJ | td”dkszJ | td”dksJ | td”dksJ | td”dksJ 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sŻJ tdttdfd td”dksšJ 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s)J tdtttttfd tt”tdtttttfdksLJ tdtttt	 dfd}| t	d”tdtttdfdksoJ 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sÅJ | ” tdtdk ftd tdk fttdfksąJ |jtdiddksķJ |jtdiddksśJ |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s4J t}t| }tdtdk fdt tdk fdt tdkf}t| | }t|t|ks`J t|| t|kslJ t| |ksuJ t| | |t|  ksJ || || ksJ || || ksJ || ||  ks¦J tdtdk fdtd  tdk fdtd  tdkf}|d |ksÉJ 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s8J | tdd”| td”| td” ksNJ | tdd”|ksZJ | td d”| td”ksjJ | 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sĖJ t|tddft ddksŪJ 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s"J t"|tr.|j#du s0J d S )#Né   r   T©r   T©r?   T)r   Fé’’’’é   c                   S   s   t  S ©N©r%   © rF   rF   śV/tmp/pip-target-vg8gfxp4/lib/python/sympy/functions/elementary/tests/test_piecewise.pyŚ<lambda>6   s    z!test_piecewise1.<locals>.<lambda>F©Śevaluatec                   S   s   t tS rD   ©r%   ŚxrF   rF   rF   rG   rH   <   s    c                   S   s   t tdfS ©NrC   rK   rF   rF   rF   rG   rH   >   ó    c                   S   s   t ttd fS rM   rK   rF   rF   rF   rG   rH   ?   s    c                   S   s   t dgdfS ©Nr?   TrE   rF   rF   rF   rG   rH   @   ó    ))r?   rC   T©rC   Té   é   é   éū’’’é
   ē        zf,g,h)ŚclsŚn)Śnegativeg      šæéž’’’)Śsubsé   é   éö’’’)$r   r%   r)   rL   r4   r:   Ś	TypeErrorr(   r   Śyr2   r1   r7   r   ŚIntegersr\   r   r!   r   r   r   r=   r    r*   r   Śevalfr/   ŚdoitŚHalfr   Ś_eval_intervalr0   r   r   Ś
isinstanceŚis_commutative)ŚcondŚpwiseŚpŚp_x2Śp2Śp3Śp4ŚfŚgŚhŚpfŚpgŚp5Śp6rY   Śf_intŚfpŚdpŚfp_dxŚdp2Śf1Śf2ŚpevalŚpeval_intervalŚpeval2rF   rF   rG   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%   rL   Śara   Śfree_symbols©rp   rF   rF   rG   Śtest_piecewise_free_symbols¼   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$J t| d
 d
 | dkf|df}t|| ddftdd	ksBJ t|| dd
ftddksQJ |t| d
 d
 | dkf|| dk fksfJ t| d
 d
 d| kf|| dk f}t|| ddftdd	ksJ t|| dd
ftddksJ |t| d
 d
 d| kf|dfksØJ t| d
 d
 d| kfd| df}t|| ddftdd	ksČJ t|| dd
ftddks×J d S )Nśx yT©ŚrealrC   r   rA   r[   é   r]   r^   rT   é+   rR   iCż’’é   i_ż’’)r   r%   r0   r   )rL   ra   rp   rq   rF   rF   rG   Śtest_piecewise_integrate1Į   s   *"&""r   c                  C   s2  t dtdkfdttdfdtdk f} t| tddfdksJ t dtt dk fd} t| tt dftdt ks;J |  td” tt df”dksLJ t| tdt ftdtks\J t| tdtftdt t ksnJ t| tt dftdt d ksJ t| tt tft t ksJ t dtdk fttdkfd} |  ttdf”}|  tdtf”}dt	j
d	fD ]"}|  t|df”| t|”ksĒJ |  td|f”| t|”ks×J qµ|t tdtdtd	  d	 t	j
 tdk ft d d
fksųJ |t tdtdtd	 d	 t	j
 tdk ftd d
fksJ d S )Nr?   r   rB   r@   éż’’’r]   é*   rA   rC   T)r%   rL   r   r0   ra   r   r#   r\   r"   r   re   )rq   Śgy1Śg1yŚyyrF   rF   rG   Śtest_piecewise_integrate1bŲ   s.   &"" $&  "&
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 )
Nra   Tr   r?   r   rB   r@   r[   rC   )r   r%   rL   r8   Ścontainsr0   r\   r&   ŚrewriteŚsimplifyr   re   r#   r"   ©ra   rq   r   r   rF   rF   rG   Śtest_piecewise_integrate1caņ   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 )
Nra   Tr   r   rB   r?   r[   rC   r@   )r   r%   r4   rL   r0   r\   r&   r   r   r   re   r#   r"   r   rF   rF   rG   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?   rC   ©r]   Tr[   T)r?   rC   r]   rT   )Ś	itertoolsr   r   rL   ŚcŚdr%   r   Śbr0   r#   r"   ŚdictŚzipr\   )r   Ślimrk   ŚqŚvŚrrF   rF   rG   Śtest_piecewise_integrate2J  s   
:4
ž&žr¦   c                   C   s*   t dtdk fd ttdf”dksJ d S )Nr?   rT   r@   r   )r%   rL   r0   r   rF   rF   rF   rG   Śtest_meijer_bypassW  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[   rB   r   r?   rC   r^   rR   rS   r?   rC   r@   )ŚrepeatrT   rS   )
Śsympy.utilities.iterablesrØ   rL   r%   r   r   r0   r    r”   r\   )rØ   r¢   ŚNrk   ŚansŚiŚjŚrepsrF   rF   rG   Ś/test_piecewise_integrate3_inequality_conditions]  s   

 
 žr°   c                  C   sV  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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||kfd
}	t|t |}
|||||	fD ]F}| |
”}tdD ]9}| d	|d||i}| |”| |” |
 |””ks
J | d|d	||i}| |”| |” |
 |””ks%J qķqād S )Nr   Tr   r   rL   ra   r   rA   r?   r@   r^   r]   ē      ą?)r±   T)r   r%   r4   r1   r   r   r0   Śranger\   r#   r"   )r   r   rL   ra   Śp0Śp1rm   rn   ro   ru   r¢   rk   r¬   r­   rÆ   rF   rF   rG   Ś-test_piecewise_integrate4_symbolic_conditionsw  sx   
$&ü
$(üż

ż

ż&
&*üžrµ   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]   rT   )r%   r   ra   rL   r0   ©rk   rF   rF   rG   Ś0test_piecewise_integrate5_independent_conditionsø  s   4r·   c            
      C   sT
  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}	|	 ” j|	jksJ t dtdk fdtdk fd ” t dtdk fdks/J t dtdkf ” t dtdkf|dfksGJ t dtdkttk @ f ” t dtdkttk @ f|dfksgJ 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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sŚJ 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s(J d S )NrC   r?   r   rB   TrA   r@   rp   r   ©ŚintegerrY   Śt©ŚpositiverT   r[   r   r]   r^   r   )r%   rL   r   r   r   r   r1   r   r   ra   r   r+   r   r   r\   r   r   re   r(   Śargsr   )
rk   r½   r¬   rp   r   rY   rŗ   ŚexprŚnanŚcoveredrF   rF   rG   Śtest_piecewise_simplify½  s  .’’’’ž&’’’žżż"&
’$.P(’’’’’’’’(’’’4’’’’’$’’’’÷	’’"’’&’’’’’’’(’’’’’’’ ’’’’ö÷6’’’,’
’’’ż$
’’ 
’"
’"
’""’
’"
’""’’rĮ   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   rC   r?   r]   rA   r^   rT   T)rV   FrB   r@   c                      s
   t  tS rD   )r9   rL   rF   r   rF   rG   rH   4  ó   
 z&test_piecewise_solve.<locals>.<lambda>c                 S   s   t tdd | S )Nc                 S   s
   | t juS rD   )r   ŚNaN©rL   rF   rF   rG   rH   7  rĀ   z4test_piecewise_solve.<locals>.nona.<locals>.<lambda>)ŚlistŚfilter)r¬   rF   rF   rG   Śnona6  ó   z"test_piecewise_solve.<locals>.nonac                 S   ó   g | ]}|  td ”qS )r[   ©r\   ra   ©Ś.0r­   rF   rF   rG   Ś
<listcomp>:  ó    z(test_piecewise_solve.<locals>.<listcomp>c                 S   rÉ   )rC   rŹ   rĖ   rF   rF   rG   rĶ   ;  rĪ   r[   c                 S   rÉ   )r]   rŹ   rĖ   rF   rF   rG   rĶ   <  rĪ   rk   r»   rp   rQ   )r%   rL   r\   r9   r:   ŚNotImplementedErrorra   r   rĆ   r   r   r   r1   r$   )Śabs2rq   rĒ   rk   r¬   Śabsxm3rF   r   rG   Śtest_piecewise_solve  sd   "" &’4"
  żžž&&
’$$rŅ   c                  C   s8  t ttdk fddtkf} tt|  t td tdk ftdtkfks$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?   rC   r   rQ   rV   )r_   Té   )ių’’’Tr@   rT   Tr[   FrI   )	r%   rL   r&   r0   r   ra   r2   r   r
   )rk   r“   rm   r   r   rF   rF   rG   Śtest_piecewise_foldW  s<   ..’ž ’’"’ž"&’*’’rŌ   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   r@   TrC   r?   rT   rA   rB   r   )	r%   r*   rL   r   r   r\   r   r&   r²   )	r“   rm   ro   r¬   r­   Śr1ru   rv   Śp7rF   rF   rG   Ś%test_piecewise_fold_piecewise_in_condt  s(    ’r×   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   r@   r?   T)r%   r*   rL   r   r   r&   )r“   rm   rn   rF   rF   rG   Ś'test_piecewise_fold_piecewise_in_cond_2  s   żrŲ   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   FTr@   rI   )r%   r8   r   rL   r&   r	   )r“   rm   ri   rF   rF   rG   Śtest_piecewise_fold_expand  s   "’’ rŁ   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_   rC   rB   r?   )r%   rL   r½   r¶   rF   rF   rG   Śtest_piecewise_duplicate£  s   (rŚ   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?   rC   rB   r]   F©Śdeep)r%   rL   r/   rd   r   ra   r   )r“   rm   rF   rF   rG   Ś	test_doitØ  s   (,rŻ   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?   r@   g      ąær±   rC   T)	r%   rL   r8   r   r\   r   r0   r   re   )r“   rF   rF   rG   Śtest_piecewise_interval²  s   (

żrŽ   c                  C   s$  t dtdk ftjtdkfd} t| t dtdk ftjttdfdtdkfddks+J t| d t dtdk ftjttdfdtdkfddd ksKJ tt dtdkft dtdkf dft dtdkft dtdkftjtdk fdd tdkfddksJ tt dttkft dttkftjttkfddksJ tt dttkfddt dttkfks±J td	dd
\}}t d|dk fddd}t d|dk fd|dkfdd}t ||dk fddd}t ||dk fd|dkfdd}t ||dk fd|dkfdd}t||ksJ t|dd|ksJ d S )Nr   rA   r?   FrI   rC   T)Śskip_nanzxr, yrr   rQ   r   r]   rŪ   )	r%   rL   r   re   r'   r   ra   rĆ   r   )rk   ŚxrŚyrr“   Śp1xrm   Śp2xŚp2xxrF   rF   rG   Śtest_piecewise_exclusive½  sL    ’$’
’’’’žžž’’rå   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 rD   )rg   r%   r½   )r­   rF   rF   rG   Ś	canonicalį  s   

z*test_piecewise_collapse.<locals>.canonicalrC   r]   ©rT   T©r^   T)r   rC   rV   rJ   Fzr1:5rT   )rR   Tr   )r?   rC   r]   rT   g      @rQ   )r%   rL   Śreversedr\   r   r4   r   Śtruer1   r    r”   )r   r   rę   r½   r­   rÕ   Śr2Śr3Śr4r   r   rF   rF   rG   Śtest_piecewise_collapseŪ  s   &( ū’
ž’
’’’ž
’’’
’’’
ž’’’’’’
ž
’
’
’,rī   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 )NrC   r   r?   FTr@   g       Ąg      @rW   r±   g       @)r%   rL   r8   r   r<   )rk   rp   rF   rF   rG   Śtest_piecewise_lambdify  s   ü
rļ   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OrC   r?   )rY   )Śsympy.series.orderrš   r%   r+   rL   r*   Śnseries)rš   r“   rm   rF   rF   rG   Śtest_piecewise_series  s   "2ró   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?   r@   Tr   )r%   rL   Śas_leading_term)r“   rm   rn   ro   ru   rv   rÖ   Śp8rF   rF   rG   Śtest_piecewise_as_leading_term  s    rö   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 )NrC   r   r?   TF)r%   rL   r   r   r&   Śis_imaginaryŚis_realŚas_real_imag)r“   rm   rn   ro   rF   rF   rG   Śtest_piecewise_complex1  s   $rś   c                  C   sč   t ddd\} }t| |d  tdkf| d | df}| ” tt| |d  tdkft| d | dfks8J | ” tt| |d  tdkft| d | dfksUJ | ” tt| |d  tdkft| d | dfksrJ d S )NśA BF)ŚcommutativerC   r   T)r   r%   rL   r   r   r   )ŚAŚBrk   rF   rF   rG   Śtest_conjugate_transposeF  s   &,’,’,’r’   c                  C   s    t tdftks
J t tdfddtksJ t dtdtfjdttdffks*J t dtdtfddjdtdtffks@J t tdfdd} | tksNJ d S )NTrI   r?   F)r%   rL   r   r½   r¶   rF   rF   rG   Śtest_piecewise_evaluateQ  s   (
’r   c                   C   s   t ttdkft tdkf ” ttdtddft tt dfgks$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   TrC   r@   )r%   rL   Śas_expr_set_pairsr8   r   rF   rF   rF   rG   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 )NrV   r   )é   T)r%   r   rL   r   r6   )rk   r£   rF   rF   rG   Śtest_S_srepr_is_identitye  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?   rT   rC   r]   rB   r   rU   r^   é   r   )r%   rL   r3   r0   ra   r²   r\   )rk   r¢   r¬   r­   rF   rF   rG   Śtest_issue_12587k  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?   rC   r]   r@   r   r   r^   rT   rR   rQ   rB   TrS   é   rV   é   )r0   rL   r$   r   r%   r1   r4   r   r   r(   ra   r#   r   re   r\   r3   rĆ   )rk   ræ   r­   rF   rF   rG   Śtest_issue_11045v  s   0$’’’"’"’’"’$’
’ 
’"*’ü"*
ż$
’&
’&
’$’r	  c                  C   s  t } tdtdk f t”tttdk f| dfksJ tdttdktdk f t”t| tdk fttdk f| dfks<J tdttdktdk f tddf”| u sSJ tdttdktdk f tddf”dksjJ td\}}tddd	\}}t|ttdk |dk f|ttdk |dkf t”t|t |dkft|t tdk f|t tdk f| df|dk ft|t tdk f| dfdfksĆJ d S )
Nr?   rC   Tr   r]   rT   rū   za br   )r(   r%   rL   r0   r1   r   r4   )ræ   rż   rž   r   r   rF   rF   rG   Ś
test_holesĄ  s$   
’ 
’..,.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$   t d| dk fd| d  | dk fdS )Nr   rB   r?   rC   r@   rE   rÄ   rF   rF   rG   rp   Õ  ó   $ztest_issue_11922.<locals>.fc                    s     t  t |    t ddf”S )NrB   r?   ©rL   r0   ©Śkr   rF   rG   rH   ×  s    z"test_issue_11922.<locals>.<lambda>gffffffž?r   r  c                    s$   dt d   t |    t ddf”S )Nr?   rC   rB   r  r  r   rF   rG   rH   Ū  r  r]   Tr»   r?   rV   )r   r\   r%   rL   r0   )Śautocorrr  Śgood_autocorrr   rF   r   rG   Śtest_issue_11922Ō  s    ’r  c               	   C   sä   dt dtdk fdt d tdk ft dtdkfd	t d
tdkfd tdkfdt d tdk fd } t| tt tf}|t| tt tf ” ksJJ t|dksRJ t dtt dk fd t”t dttkft t dfkspJ d S )Ngż©§J¢j?r   gf'vb'6TĄgČlAwæg¶3ŲPõ?rC   g333333Ó?é{   )gffffffę?TgŁ?)g333333ć?Tgš%Ń½æg%JMć× @g$I$Éw@r@   z1.00195081676351r?   T)r%   rL   r0   r   r/   rd   Śstrra   )rp   r­   rF   rF   rG   Śtest_issue_5227ę  s(   ’’’’ū ’r  c            
      C   sl  t ddd} t ddd}t ddd}t ddd}tdt|| k ||kfd}tdt| |k||k fd}t|||tft|||tfksFJ td	td|k || k fd
}td	t| |k|dkfd
}t||}|td|dkf||td| kftd| dfksJ t||}	|	|ksJ | |ddf”tdtd| d ks J | |ddf”tdtd| d ks“J d S )Nr   Tr   r   rL   ra   r   rA   r?   r@   rC   rT   )r   r%   r4   r0   r   r1   r"   r#   )
r   r   rL   ra   r³   r“   rn   ro   Śip3Śip4rF   rF   rG   Śtest_issue_10137ō  s&   $


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?   rB   r@   rE   rÄ   rF   rF   rG   rH   
  ó    z-test_stackoverflow_43852159.<locals>.<lambda>c                    s$   t  | t  t tt t
 fS rD   )r0   ra   r   rÄ   r   rF   rG   rH     s   $ g      ųæg      ų?r]   r   r?   rB   r@   )rL   r\   r&   ra   r%   )ŚConvŚcxrF   r   rG   Śtest_stackoverflow_43852159	  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))))
    rL   Tr   r  )r¹   Śfinitec                 S   s   t |  | dkf| | dkfS ©Nr   rE   rÄ   rF   rF   rG   rH   3  s    z"test_issue_12557.<locals>.<lambda>rC   rB   r   N)r   r0   r   r*   r$   r%   r   )rL   r  rŠ   ŚfuncrF   rF   rG   Śtest_issue_12557  s   "2’r  c               	   C   s¤  ddl m}  td\}}}}td||k ftt||k||k fd||kf}| |”}|td||kf|t |t  |t||kf| t tt||  dfksQJ | tdD ]*}t	t
||f|}tddD ]}	| |” ||	”| |” |” ||	”ksJ qgqWt|||}
| |
”}t| t tt|t||  ||kfd}| tdD ] }t	t
|||f|}| |” |
 |””}|| |”ksÉJ q©||ksŠJ d S )	Nr   r   z
t0, t1 T tTrC   rB   r]   r@   )r   r   r   r%   rL   r1   r0   r"   r²   r    r”   Śxreplacer\   r   r#   )r   Śt0Śt1ŚTrŗ   rp   rq   r­   rÆ   Śttr¢   r¬   ŚtrurF   rF   rG   Śtest_issue_69009  s6   .


ż
’’
$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   )	r9   ŚabsrL   r4   r1   r   r   ŚZeroŚOnerF   rF   rF   rG   Śtest_issue_10122S  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?   TrC   rB   )
r%   rL   r   r\   ra   r"   r0   r	   r!   r   )ŚuŚeŚMrF   rF   rG   Śtest_issue_4313X  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ėr.  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 )NrC   r]   Tr?   rA   r@   r   r[   )rB   r   r?   r   )r   r?   r?   r   )r%   rL   r   Ś
_intervalsr   r   r   r*   r+   r   r   rF   rF   rF   rG   Śtest__intervals{  s*   (&żż
’""’’’’r0  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?   rC   r]   rT   r^   r?   TrC   r   rT   )r%   rL   r   r0   r   )r   r   r   r   r,  rk   rF   rF   rG   Śtest_containment  s   .’
ūr1  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   rC   r@   rA   )r,   rL   r0   r   r%   r   r-   )Śd1rF   rF   rG   Śtest_piecewise_with_DiracDelta  s   "’r3  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?   rA   rB   Fr   T)Śzeror]   rQ   )	r%   rL   Śis_zeror   Ś
is_nonzeror   Ś	is_finiter   r&   ©r   r   r   rF   rF   rG   Śtest_issue_10258„  s    $  r9  c                  C   s   t ttdkfdt ttdkfd} }| | }t|}dD ]}| t|”| t|”ks-J q| | }t|}dD ]}| t|”| t|”ksHJ q8d S )Nr?   rQ   r]   r   )r   rC   rT   )r%   rL   r&   r\   )r   r   Śmrp   r­   rF   rF   rG   Śtest_issue_10087ŗ  s   &’r;  c                  C   są  t d} t d}t| d |dk f| d df}t| d |tddk f| d df}t|| |ddf| d | d  d d| d  | d  d  | d | d   ksSJ td|dk fd	}td|dk fd
}t|| |ddfdkssJ t ddd}t ddd\}}} }}ttd||k|dk B || kB f|df|d|f}| ” }	|	td|| kf|t|| |td|  dfks¼J dD ]/}
tddD ]'}t| d|D ]}|| k|
f||f||fg}|	 |”| |” ” ksėJ qĪqÅq¾d S )Nzc:5rL   r?   rC   Tr]   rT   r   rQ   r@   rR   ra   r»   z	a,b,c,x,zr   )TF)	r   r%   r   r0   r/   rd   r#   r²   r\   )r   rL   r|   r}   ra   r   r   r=   r   r¬   ri   r   ŚzzrÆ   rF   rF   rG   Śtest_issue_8919Ę  s8   $:’žž6ž’’r=  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 )Nrp   r?   r   rC   rV   r@   r^   )
r   r%   r   rL   r0   r/   r\   rY   ra   r   )rp   rk   rF   rF   rG   Śtest_unevaluated_integralsß  s   *$,
&žr>  c                  C   s\   t d\} }}ttttdk tdkftdkdffttttdktdk tdkfks,J d S )Nza:cr?   r   T)r   r%   rL   ra   r2   r8  rF   rF   rG   Ś%test_conditions_as_alternate_booleansš  s   $’r?  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 rD   )r%   r   r2   )r½   rF   rF   rG   Ś_ITEł  s   z+test_Piecewise_rewrite_as_ITE.<locals>._ITEr?   r   TrC   c                      s    t d t dk ft dfS rO   rÄ   rF   )r@  rF   rG   rH     r  z/test_Piecewise_rewrite_as_ITE.<locals>.<lambda>c                      s    t t tk ftt kfS rD   )rL   ra   rF   )r@  r   rF   rG   rH     r  c                      s    t dk ft dkfS )NrC   r]   rÄ   rF   ©r@  r   r   rF   rG   rH     r  )
r   rL   r2   r   r4   ra   r:   r`   rĻ   Ś
ValueError)r   r   rF   rA  rG   Śtest_Piecewise_rewrite_as_ITEö  s4   ..,’*’’"’(’"
’rC  c                   C   s(   t ttttddt fdksJ d S )Nr   rC   rT   )r0   r'  r+   rL   r   rF   rF   rF   rG   Śtest_issue_14052  s   (rD  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?   rC   rē   r  )é   Té	   é   )r  Tr]   rč   rS   )rÓ   Tr   é!   )é7   Tc                 S   ó   g | ]	}t |tfd qS ©r@   ©r%   r   rĖ   rF   rF   rG   rĶ   !  ó    ’z$test_issue_14240.<locals>.<listcomp>é(   i  r@   c                 S   rJ  rK  rL  rĖ   rF   rF   rG   rĶ   $  rM  é)   )r&   r%   r   r   r   r²   r
   r   rF   rF   rF   rG   Śtest_issue_14240  s0   ’’ż’’ż
’ž
’žrP  c                  C   s>   t d} t| | dk ftdd df}t| ” dksJ d S )NrL   r?   é:   rS   Tz/Piecewise((x, x < 1), (8.28571428571429, True)))r   r%   r   r  rc   ©rL   rp   rF   rF   rG   Śtest_issue_14787)  s   rS  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   TrT   rC   r?   rB   )r   r%   r   r+   r   )rL   ra   r“   rm   rn   rF   rF   rG   Śtest_issue_8458/  s   FJ,rT  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   rQ   rL   Tr„   r   FrI   )r   r   r%   r4   r   r   r   r   r   ŚPir   rĆ   r   )r=   rL   r„   rk   r­   rF   rF   rG   Śtest_issue_16417<  s6   .žž

ž
ž
’
’rV  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$J tdt| d	t|d@ fd}||d d|  d	|  d	 d	|   d ksOJ tdt| dt|d@ fd}||d d|  d|  d kssJ tdt| dt|dB fd}||d d|   d| d ksJ tdt|dt| dB fd}|| d|   d|  d|  d ksæJ tdt| dt|d	B fd}||d d|   d	| d d	|  d ksźJ td	t| dt|dB fd}||d d|   d| d d|   d d|  d ksJ tdt| dt|dB fd}||d d|   d| d ks@J tdt| d	t|dB fd	t| dt|d@ fd}||d d|  d	|   d|   d|  d| d	|   d d|  d|   d|   d| d ksJ tdt||fdtdt||fd tdt|| fd tdt|| fd }|| || ||  ||   ||  ksÜJ tdt|| t||t||B t|| B @ fdt|| fdt||t||B t|| B fd}|| || ||  ||   ||  ks&J tdt|dt| dt| |@ B fd
}||d d|   d|  | | d d|   | |  d d|  d ksgJ td| dkfd}|||ksyJ tdt| dk | dkfd}|||ksJ tdt| dk| dk fd}|||ks§J tdt|dt| dB t| dt|dB @  fd}|| d| d|   d| d|    d|  d ksćJ d S )Nzx y z n t mc                    s   t |   ”S rD   )r	   r   r¶   ©ŚKrF   rG   rH   _  rP   z5test_eval_rewrite_as_KroneckerDelta.<locals>.<lambda>r   rA   r?   Tr@   r]   rē   rč   rT   rC   r   rR   r^   éü’’’rQ   rB   r[   r   rU   r  )r   r.   r%   r   r   r1   r4   )rL   ra   r=   rY   rŗ   r:  rp   r“   rm   rn   ro   ru   rv   rÖ   rõ   Śp9Śp10Śp11Śp12Śp13Śp14Śp15Śp16Śp17Śp18Śp19Śp20Śp21Śp22rF   rW  rG   Ś#test_eval_rewrite_as_KroneckerDelta\  s   $<’’
’ 4628**28F*4D ’’’&’’6,.’6(Z4Hrh  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.statsri  rj  )ri  rj  rk  rl  rF   rF   rG   Śtest_identical_conds_issueØ  s   rn  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%   rL   r0   r   r  )rp   r¤   rF   rF   rG   Śtest_issue_7370²  s   rp  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 )NrL   ra   Śinpr?   )r   r   r   T)r   r5   r%   r2   r   )rL   ra   rq  Śrep_dictrk   rF   rF   rG   Śtest_issue_14933ø  s   6rs  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%   rL   ra   r  rF   rF   rF   rG   rH   Ä  s    z"test_issue_16715.<locals>.<lambda>)r:   rĻ   rF   rF   rF   rG   Śtest_issue_16715Ć  rČ   rt  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   rY   rø   r   rC   r?   )r   r   r   re   r0   r    r   )rŗ   ŚtaurY   ŚlamŚeqrF   rF   rG   Śtest_issue_20360Ē  s
   Drx  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  )r½   ri   rÄ   rF   rF   rG   rH   Ó  rN   z%test_piecewise_eval.<locals>.<lambda>r]   r   r?   )r%   rL   r   r   r   r   r   rF   rF   rG   Śtest_piecewise_evalĻ  sh   ’’’’’’’’’’
’
’
’
’
’
’*’ry  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 )NrL   Tr   rB   r   r?   )r   r%   r0   r!   rR  rF   rF   rG   Śtest_issue_22533ū  s   2rz  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.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$sympy.functions.elementary.piecewiser%   r&   r'   r(   r)   Ś(sympy.functions.elementary.trigonometricr*   r+   Ś'sympy.functions.special.delta_functionsr,   r-   Ś(sympy.functions.special.tensor_functionsr.   Śsympy.integrals.integralsr/   r0   Śsympy.logic.boolalgr1   r2   r3   r4   Ś"sympy.matrices.expressions.matexprr5   Śsympy.printingr6   Śsympy.sets.containsr7   Śsympy.sets.setsr8   Śsympy.solvers.solversr9   Śsympy.testing.pytestr:   r;   Śsympy.utilities.lambdifyr<   r   r   r   r   rL   ra   r=   r   r   r   r   r   r   r¦   r§   r°   rµ   r·   rĮ   rŅ   rŌ   r×   rŲ   rŁ   rŚ   rŻ   rŽ   rå   rī   rļ   ró   rö   rś   r’   r   r  r  r  r	  r
  r  r  r  r  r  r&  r*  r.  r0  r1  r3  r9  r;  r=  r>  r?  rC  rD  rP  rS  rT  rV  rh  rn  rp  rs  rt  rx  ry  rz  rF   rF   rF   rG   Ś<module>   sÄ     $ 
)
-
@WC

-J%# L
	,