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    —9%eB- ã                   @   sœ  d dl Z d dlmZmZ d dlmZ d dlmZ d dlm	Z	 d dl
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d„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zedd„ ƒZ	dd„ Z
dd„ Zdd„ Zd d!„ Zd"d#„ Zd$d%„ Zd&d'„ Zd(d)„ Zed*d+„ ƒZed,d-„ ƒZd.d/„ Zd0d1„ Zd2d3„ Zed4d5„ ƒZd6d7„ Zd8d9„ Zd:d;„ Zd<d=„ Zd>d?„ Zd@dA„ ZdBdC„ ZdDdE„ ZdFdG„ Z dHdI„ Z!dJdK„ Z"dLdM„ Z#dNdO„ Z$dPdQ„ Z%dRdS„ Z&dTdU„ Z'dVdW„ Z(edXdY„ ƒZ)dZd[„ Z*d\d]„ Z+d^d_„ Z,d`da„ Z-dbdc„ Z.ddde„ Z/dfdg„ Z0dhdi„ Z1djdk„ Z2dldm„ Z3dndo„ Z4dpdq„ Z5drds„ Z6dtdu„ Z7dvdw„ Z8dxdy„ Z9dzd{„ Z:ed|d}„ ƒZ;d~d„ Z<d€d„ Z=d‚dƒ„ Z>d„d…„ Z?d†d‡„ Z@dˆd‰„ ZAdŠd‹„ ZBdŒd„ ZCdŽd„ ZDdd‘„ ZEd’d“„ ZFd”d•„ ZGd–d—„ ZHd˜d™„ ZIedšd›„ ƒZJedœd„ ƒZKdždŸ„ ZLd d¡„ ZMd¢d£„ ZNd¤d¥„ ZOd¦d§„ ZPd¨d©„ ZQdªd«„ ZRd¬d­„ ZSd®d¯„ ZTd°d±„ ZUd²d³„ ZVd´dµ„ ZWd¶d·„ ZXd¸d¹„ ZYdºd»„ ZZd¼d½„ Z[dS (¿  é    N)ÚSumÚ	summation)ÚAdd)ÚTuple)ÚExpr)Ú
DerivativeÚFunctionÚLambdaÚdiff)Ú
EulerGamma)ÚEÚFloatÚIÚRationalÚnanÚooÚpiÚzoo)ÚEqÚNe)ÚS)ÚSymbolÚsymbols)Úsympify)ÚAbsÚimÚ
polar_liftÚreÚsign)ÚLambertWÚexpÚ	exp_polarÚlog)ÚacoshÚasinhÚcoshÚcothÚcschÚsinhÚtanhÚsech)ÚMaxÚMinÚsqrt)Ú	Piecewise)ÚacosÚasinÚatanÚcosÚsinÚsincÚtanÚsec)Ú
DiracDeltaÚ	Heaviside)ÚCiÚEiÚSiÚerfÚerfcÚerfiÚfresnelcÚli)ÚgammaÚ	polygamma)ÚhyperÚmeijerg)ÚSingularityFunction)Úlerchphi©Ú	integrate)ÚAnd)ÚMatrix)ÚPolyÚfactor)Ússtr)ÚO)ÚInterval)Ú	gammasimp)Úsimplify)Útrigsimp)ÚIdxÚIndexedBase)Ú	unchanged)Úfloor)ÚIntegral)ÚNonElementaryIntegral)Úunits)ÚraisesÚslowÚskipÚON_CIÚwarns_deprecated_sympyÚwarns)ÚSymPyDeprecationWarning)Úverify_numericallyzx y z a b c d e s t x_1 x_2ÚnT©ÚintegerÚfé   c                 K   s   t t| ƒj|f|ŽddS )NT)Z	full_prec)rM   r   Úevalf)Úerb   Úoptions© rj   úc/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/integrals/tests/test_integrals.pyÚNS4   s    rl   c               	   C   sx   t dt tƒ} |  t¡t td tddks.t‚ttdd t| tƒ W 5 Q R X ttdd t| tfƒ W 5 Q R X d S )Né   ZQQ)ÚdomainF©Ztest_stacklevel)rK   ÚxrH   ÚAssertionErrorr_   r`   rW   ©Úprj   rj   rk   Útest_poly_deprecated8   s     rt   c                     s8  dt  ‰ tˆ t t tfƒ ¡ dks&t‚tˆ tt tfƒ ¡ ttdt  ƒ ksPt‚tt‡ fdd„ƒ tt‡ fdd„ƒ dt d d  ‰tˆt t tfƒ ¡  	¡ t
dƒ t d ks´t‚tt‡fdd„ƒ dt d d  } t| t t tfƒ ¡ dksôt‚t| t d	dfƒ ¡ tdƒ kst‚t t d d  }t|t t tfƒ ¡ dksHt‚t|t d	dfƒ ¡ dksft‚t d t d d  }t|t t tfƒ ¡ tksšt‚t|t d	dfƒ ¡ tdƒ d
 ksÂt‚dt d d dt d    }t|t t tfƒ ¡ t d kst‚t|t d	dfƒ ¡ tdƒ tdƒd  ks4t‚d S )Né   r   c                      s   t ˆ tƒ ¡ S ©N)rW   rp   Úprincipal_valuerj   ©Úgrj   rk   Ú<lambda>G   ó    z&test_principal_value.<locals>.<lambda>c                      s   t ˆ ƒ ¡ S rv   )rW   rw   rj   rx   rj   rk   rz   H   r{   é   c                      s   t ˆ tt dfƒ ¡ S ©Nru   )rW   rp   r   rw   rj   )Úlrj   rk   rz   L   r{   rm   éþÿÿÿé   )rp   rW   r   rw   rq   Úyr   rZ   Ú
ValueErrorÚtogetherr-   r   r"   r1   )ÚdÚvÚsre   rj   )ry   r~   rk   Útest_principal_valueB   s(    *0$  (&r‡   c                 C   s<   | j }|D ],}|  |¡ ¡ |  ¡  |¡  ¡ dks
t‚q
|S )zºReturn the set of symbols, s, which were used in testing that
    i.diff(s) agrees with i.doit().diff(s). If there is an error then
    the assertion will fail, causing the test to fail.r   )Úfree_symbolsr
   ÚdoitÚexpandrq   )ÚiZsymsr†   rj   rj   rk   Ú	diff_test_   s    *rŒ   c                   C   sd   t ttƒtddfƒdkst‚t td tdtfƒdks8t‚t ddttƒ  tdtfƒtdƒks`t‚d S )Nr   ru   éÿÿÿÿr   rm   )rH   r"   rp   rq   r   r    rj   rj   rj   rk   Útest_improper_integrali   s    rŽ   c                  C   s  t ttƒ} | jttƒfkst‚t ttfƒ}|jttƒfks>t‚t tttdtfƒƒ}|jttƒfksft‚t tttƒƒ}|jttƒfksˆt‚t tttddƒfƒ}|jttddƒfks´t‚t ttdkƒ}|jttdt	ƒfksÚt‚t ttdktdk @ ƒ}|jttddƒfks
t‚d S )Nru   rm   é
   é   )
rW   rb   Úlimitsr   rq   r   rp   r   rO   r   )Ús1Ús2Zs3Zs4Zs5Zs6Zs7rj   rj   rk   Útest_constructoro   s    
r”   c                  C   sØ  t dtƒdkst‚t ttddfƒdks*t‚t ttƒtks<t‚t tjtƒtjksRt‚tt ttƒtƒdksjt‚tt ttddfƒtƒdksˆt‚tt ttƒtƒtks t‚tt ttdtfƒtƒtks¾t‚td d } tt	| tdtfƒtƒtt | tdtfƒtƒ 
¡  ¡   krdt d  ¡ ks n t‚tt	| tdtfƒtƒtt | tdtfƒtƒ  kr\dksbn t‚tt	| tdtfƒtƒtt | tdtfƒtƒ  krždks¤n t‚tt	| tƒtƒtt | tƒtƒ  krÔdksÚn t‚t	| tttfƒ t¡t | tttfƒ t¡ 
¡  ¡ kst‚t | tttfƒ t¡ 
¡ dt d ks@t‚t	| tttfƒ t¡ 
¡ dt d   ¡ ksrt‚t	td ttdt fƒ t¡dtd  ks¢t‚t ttƒ ¡ thks¼t‚t ttƒtddfƒ ¡ tjtjthksèt‚tt ttdt fƒƒthks
t‚tt ttdt fƒƒtthks.t‚t	ttttfƒdksHt‚t	ttt t fƒdksft‚t	tt ttƒ tƒtt td d  ttƒ ksžt‚t tƒjs®t‚tddd}t |t tƒjdksÔt‚d S )	Nr   ru   rm   é   r|   rb   F©Zcommutative)rW   rp   rq   r   r   ÚNaNr
   r   ÚtrH   r‰   rŠ   ÚaZatomsre   ÚZeroÚOnerŒ   r    Úis_commutativer   ©rh   rb   rj   rj   rk   Útest_basics…   sR    ÿ
þÿ
ÿÿ
ÿ6ÿ
,20,"$8rž   c                  C   sz   G dd„ dt ƒ} | ƒ }t|d |ƒ|d d | ks8t‚t|d |ddfƒtddƒksZt‚ttdd„ ƒ ttd	d„ ƒ d S )
Nc                   @   s   e Zd ZdZdZdS )ztest_diff_wrt.<locals>.TestTN)Ú__name__Ú
__module__Ú__qualname__Z	_diff_wrtrœ   rj   rj   rj   rk   ÚTest´   s   r¢   ru   rm   r   r|   c                   S   s   t td td ƒS r}   ©rH   rp   rj   rj   rj   rk   rz   ¼   r{   ztest_diff_wrt.<locals>.<lambda>c                   S   s   t td td ddfƒS )Nru   r   r£   rj   rj   rj   rk   rz   ½   r{   )r   rH   rq   r   rZ   r‚   )r¢   r˜   rj   rj   rk   Útest_diff_wrt³   s    ""r¤   c                   C   s  t tttdt dt fttdt fƒƒthks2t‚t tttdt fttdt fƒƒthks^t‚t tttdt fttdt fƒƒtthksŒt‚t ttttƒƒtthks¨t‚t ttt ttƒƒtthksÈt‚t ttt ttdtfƒƒthksìt‚t ttt tttftttfƒƒtthkst‚d S )Nr|   r   rm   ru   )rŒ   rW   rp   r   rq   rj   rj   rj   rk   Útest_basics_multipleÀ   s    2,. $r¥   c                  C   sô   t ddd\} }tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ksHt‚| ¡  ¡ | ¡  ¡ ksdt‚| ¡  ¡ | ¡  ¡ ks€t‚tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks¸t‚| ¡  ¡ | ¡  ¡ ksÔt‚| ¡  ¡ | ¡  ¡ ksðt‚d S )NzA BFr–   rp   T)Úcomplex©Úreal)r   r   rW   Zadjointr‰   rq   Ú	conjugateZ	transpose)ÚAÚBrp   rs   rj   rj   rk   Útest_conjugate_transposeÊ   s    r¬   c                  C   sD  t dtdtfƒdkst‚t dtdtfƒdt ks4t‚t ttdtfƒtd d ksTt‚t dt tdtfƒdtd  d ks|t‚t dtd  tdtfƒtd ks t‚t dt tdtfƒttƒksÀt‚t dtd  tdtfƒdt d ksèt‚t td dt  d tdtfƒtd d dtd  d  dt  ks2t‚t td tƒtd d ksRt‚t dt t d tƒdt d td  d ks†t‚td	ƒ} td
ƒ}t tt tdtfƒttd  d ksÀt‚t ttd  tdtfƒttd  d ksît‚t ttd  | t  | tdtfƒttd  d | td  d  |t  ks@t‚d S )Nr   r|   rm   ru   r   r   é   é   ÚbÚcr€   )rH   r˜   rp   rq   r"   r   r™   )r¯   r°   rj   rj   rk   Útest_integrationÚ   s     ($ (J 4*.r±   c                   C   s  t td td  tddftddfƒtdƒks0t‚t td td  ttƒtddƒtd  td  ksft‚t dtd  dt d  tƒtdt ƒtddƒ tdt ƒtddƒ  tddt  dtd     ksÐt‚t ttt ƒt tddftddfƒtdƒ d kst‚d S )	Nrm   r   ru   r   é	   r|   r­   r€   )rH   rp   r   r   rq   r"   r3   rj   rj   rj   rk   Útest_multiple_integrationí   s    06Fÿr³   c                   C   s"   t tt ƒtdtfƒdkst‚d S )Nr   ru   )rH   r    rp   r   rq   rj   rj   rj   rk   Útest_issue_3532õ   s    r´   c                   C   sz   t ttƒd tƒdttƒd  d ks*t‚t ttƒtƒdttƒd  d ksPt‚t dttƒd  tƒdttƒ ksvt‚d S )Nr|   rm   r   ru   r   )rH   r-   rp   rq   rj   rj   rj   rk   Útest_issue_3560ù   s    *&rµ   c                   C   s   t tdd„ ƒ d S )Nc                   S   s   t ttfƒS rv   r£   rj   rj   rj   rk   rz      r{   z"test_issue_18038.<locals>.<lambda>)rZ   ÚAttributeErrorrj   rj   rj   rk   Útest_issue_18038ÿ   s    r·   c               	   C   s6  t ttd t  td  ttƒ} tƒ  t| tƒ}W 5 Q R X ttdd t| tƒ}W 5 Q R X ttdd t| tƒ}W 5 Q R X t|t ƒdks’t	‚t|t ƒdks¤t	‚|j
ttfks¶t	‚|j
ttfksÈt	‚| ¡ td d td t d  ttd   ksüt	‚| ¡ tt td td  d  td d  ks2t	‚d S )Nrm   r|   Fro   Tr€   )rK   rp   r   r^   rW   r_   r`   rH   Ú
isinstancerq   ÚgensÚas_expr)rs   ZqxZqyrj   rj   rk   Útest_integrate_poly  s     4r»   c               	   C   s2  t ttd t  td  ttƒ} tƒ  t| tddfƒ}W 5 Q R X ttdd t| tddfƒ}W 5 Q R X ttdd t| tdtfƒ}W 5 Q R X t	|t ƒdks¤t
‚t	|t ƒdks¶t
‚|jtfksÆt
‚|jtfksÖt
‚| ¡ tjtd  td  ksøt
‚| ¡ td d tt  td td  d  ks.t
‚d S )	Nrm   r|   r   ru   Fro   Tr€   )rK   rp   r   r^   rW   r_   r`   rH   r   r¸   rq   r¹   rº   r   ÚHalf)rs   ZQxZQyrj   rj   rk   Útest_integrate_poly_definite  s     "r½   c                      sD   t dƒ‰ ttƒtd d ks t‚ttdd„ ƒ tt‡ fdd„ƒ d S )Nr   rm   c                   S   s   t dƒS ©Nrm   rG   rj   rj   rj   rk   rz   1  r{   z)test_integrate_omit_var.<locals>.<lambda>c                      s   t tˆ  ƒS rv   r£   rj   ©r   rj   rk   rz   2  r{   )r   rH   rp   rq   rZ   r‚   rj   rj   r¿   rk   Útest_integrate_omit_var,  s    rÀ   c                  C   sd   t dƒ} ttt| ƒ tƒtd t| ƒ d ks2t‚ttd t| ƒ tƒtd t| ƒ d ks`t‚d S )Nr   rm   iè  ié  )r   rH   rp   r3   rq   r¿   rj   rj   rk   Útest_integrate_poly_accurately5  s    *rÁ   c                  C   sN   t dƒ} ttd | ƒtd |  ks&t‚ttd | ddfƒdtd  ksJt‚d S )Nr   rm   r   ru   )r   rH   rp   rq   r¿   rj   rj   rk   Útest_issue_3635>  s    rÂ   c                  C   sž   t ddd} tt|  tddt| d  | d  ks6t‚tt| ƒt d|   dt| ƒ  tddt|  ƒt| ƒt d|   dt| ƒ   dt| ƒ  ksšt‚d S )Nr   T©ÚpositiveÚnone©Zcondsru   rm   )r   rH   rp   rq   r    r3   r¿   rj   rj   rk   Útest_integrate_linearterm_powF  s
    *(4ÿrÇ   c                   C   sˆ   t tttƒ tƒdt ttƒd  d ks.t‚t tttƒ tttƒd   tƒdt ttƒd  d dt ttƒd  d  ks„t‚d S )Nrm   r|   r   )rH   r   r-   rp   rq   r   rj   rj   rj   rk   Útest_issue_3618O  s    . .ÿrÈ   c                   C   s$  t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒksJt‚t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒks”t‚t ttd t ƒttd t ƒ tƒttttd  ƒtd  ttd dƒftdfƒttttd  ƒtd  ttd dƒftdfƒ ks t‚d S )Nru   r   T)rH   r2   rb   rp   r.   r3   r   rq   rj   rj   rj   rk   Útest_issue_3623U  s    $ ÿ
$ ÿ
$..ÿÿrÉ   c                  C   s    t dddd} tdt t| t t d ƒ tddgƒdtt|  ƒ t|   ksRt‚ttt| t t d ƒ td	dƒ tddgƒdtt|  ƒ t|   ksœt‚d S )
Nrb   T)rd   Únonzerog      à¿rm   r   r   ç       @r   )r   rH   rp   r3   r   r2   rq   r   ©rb   rj   rj   rk   Útest_issue_3664_  s    &ÿ,ÿrÍ   c                   C   s4   t tdtd dt  d  tddfƒƒdks0t‚d S )Nru   rm   r­   é   r€   z1.10714871779409)rl   rW   rp   rq   rj   rj   rj   rk   Útest_issue_3679g  s    rÏ   c                  C   sb   ddl m}  ddlm} | tttd ƒtƒƒtdƒttƒ |tdƒt ttƒ ƒ d ks^t	‚d S )Nr   ©Úexpand_func)Úfresnelsrm   )
Úsympy.core.functionrÑ   Ú'sympy.functions.special.error_functionsrÒ   rH   r3   rp   r-   r   rq   )rÑ   rÒ   rj   rj   rk   Útest_issue_3686l  s
    *ÿrÕ   c                  C   s@   t j} t j}tt|  | td| d| fƒd|  | ks<t‚d S )Nru   r   é   )rY   Úmr†   rH   rp   rq   )r×   r†   rj   rj   rk   Útest_integrate_unitss  s    rØ   c                   C   s@   t tdt ƒtƒt ttdt ƒ  ttdt ƒ  ks<t‚d S r¾   )rH   r   rp   rq   rj   rj   rj   rk   Útest_transcendental_functionsy  s    $ÿrÙ   c                   C   sd   t tdt ƒt tddfƒtd  d ks.t‚t ttƒdt d  tddfƒtd  d ks`t‚d S )Nru   r   rm   r®   r   )rH   r"   rp   r   rq   rj   rj   rj   rk   Útest_log_polylog~  s    .rÚ   c                  C   s\   dt tƒ dt tƒd   } tt| tƒtƒ}t|  td¡ ¡ | td¡ ¡  ƒdk sXt‚d S )Nr€   rm   é*   g»½×Ùß|Û=)r"   rp   r
   rH   ÚabsÚsubsrg   rq   )re   Úfidrj   rj   rk   Útest_issue_3740ƒ  s    rß   c                   C   s&   t ddtd   tƒttƒks"t‚d S ©Nru   rm   )rH   rp   r1   rq   rj   rj   rj   rk   Útest_issue_3788‰  s    rá   c                      s6   t tƒ‰ tˆ tƒttƒ ks t‚tt‡ fdd„ƒ d S )Nc                      s   t ˆ dt ƒS r¾   r£   rj   ©re   rj   rk   rz     r{   z!test_issue_3952.<locals>.<lambda>)r3   rp   rH   r2   rq   rZ   r‚   rj   rj   râ   rk   Útest_issue_3952  s    rã   c                   C   s6   t dt dt  tƒdt tdƒ td  ks2t‚d S r¾   ©rH   rp   r"   rq   rj   rj   rj   rk   Útest_issue_4516“  s    rå   c                  C   sF   t tdt  t ƒtdtfƒ} t| ƒtjkr>t| ƒt	ddƒksBt
‚d S )Nru   r   r   rm   )rH   r    r   rp   r   r   r   r¼   r   r   rq   )Úansrj   rj   rk   Útest_issue_7450—  s    rç   c                	   C   sÀ   t dtdt ƒ ddtdt ƒ   tdtfƒt d tdƒt d  ksNt‚t dtdt ƒ ddtdt ƒ   ƒt d tdƒttdƒttƒ ƒttttd  t ƒ   d  ks¼t‚d S )Nru   rm   r|   r   r   ©	rH   r2   rp   r   r-   rq   r1   r5   rV   rj   rj   rj   rk   Útest_issue_8623œ  s    NFÿÿré   c                   C   sŒ   t ddttƒ  tdtfƒttdƒ ks,t‚t ddttƒ  ƒdtdƒ ttdƒttd ƒ ƒtttd td  t ƒ   d ksˆt‚d S ©Nru   rm   r   r|   rè   rj   rj   rj   rk   Útest_issue_9569¢  s    ,rë   c                  C   sÀ   t ddd} ttt d  d|  |   ƒtdt |  |  ƒ }t|tttfƒ}t|tdtfƒtdƒ|  ttd  d| d   ƒ dttƒ  tt	tdƒt d|   ƒ d  td  ks¼t
‚d S )Nr†   TrÃ   rm   r   )r   r    Úzr   r-   r   rH   rp   r   r<   rq   )r†   ZpzZpzgxrj   rj   rk   Útest_issue_13733§  s    2>ÿÿrí   c                   C   s   t ddttƒ  tdtfƒttdƒ ks,t‚t ddttƒ  ƒdtdƒ ttdƒttd ƒ d ƒtttd td  t ƒ   d ksŒt‚d S rê   rè   rj   rj   rj   rk   Útest_issue_13749¯  s    ,rî   c                   C   s<   t ttƒdt d  tƒtttƒtd d  tƒks8t‚d S rà   )rH   r    rp   rX   rq   rj   rj   rj   rk   Útest_issue_18133´  s    rï   c                  C   sä   t ddd} t ddd}t|t t|  t t t t ƒ t|  t t t t ƒ tt  t	dt t t| t t t t ƒ dƒftt|  t t t t ƒ dfƒ}t
dt t tt tt   d	  }t|tƒ|ksàt‚d S )
Nz3999999.9999999995é5   )Ú	precisionz2.5000000000000004e-7ç      ð?r   Tr   gŽíµ ÷Æ >)r   r.   r   r    r   r˜   r   rp   rì   r   r   rH   rq   )r™   r¯   ÚrZfunrj   rj   rk   Útest_issue_21741¸  s    D(ÿ þ$rô   c                  C   sZ   t dddd„ ƒ} t| tƒt ttƒ tdt ƒ gtdt ƒ tdt ƒ ggƒksVt‚d S )Nrm   c                 S   s    | | d t | | d t ƒ S r}   )r3   rp   )r‹   Újrj   rj   rk   rz   Ã  r{   ztest_matrices.<locals>.<lambda>r|   )rJ   rH   rp   r2   rq   )ÚMrj   rj   rk   Útest_matricesÂ  s
    
þr÷   c                   C   s¬   t ttƒtƒtttƒtƒks t‚t ttƒtddfƒtttƒtddfƒksLt‚t ttƒtttƒtƒ tƒttƒd d ks|t‚t tttƒtƒttƒ tƒtttƒƒks¨t‚d S ©Nr   ru   rm   )rH   re   rp   rW   rq   r
   r"   rj   rj   rj   rk   Útest_integrate_functionsË  s     ,0rù   c                   C   s‚   t tttƒtƒtƒttƒks t‚t tttƒtƒtƒttttƒtƒ ksJt‚t tttƒtƒd tƒttttƒtƒd tƒks~t‚d S r¾   )rH   r   re   rp   rq   r   rW   rj   rj   rj   rk   Útest_integrate_derivativesÓ  s
     *ÿrú   c                     sâ  t td d tddfƒ} t}dt d }|  ¡ |  ||¡ ¡ ksDt‚|  ||¡ ||¡| ks`t‚dt d }t}|  ||¡ ||¡| ksŒt‚t tdt ƒtddfƒ} |  tdt ¡t ttƒtd  tdtfƒksÔt‚|  tdt ¡ tdt ¡| ksøt‚t ttd  ƒtt tfƒ} |  tdt ¡t dtdtd  ƒ tt tfƒksLt‚t ttƒ t| t ¡ ¡ t t| d  tƒ ¡ ks‚t‚t	dƒ}t ttd| fƒ tdt ¡ ¡ t dtd  tt d| fƒ ¡ ksÔt‚t ttd|fƒ tdt ¡t td td| tfƒkst‚t tt tddftddfƒ‰ ˆ  ttdt  tf¡ ¡ ˆ  ttdt
  tf¡ ¡   krrdksxn t‚t tt| tfƒ‰ ˆ  tdt ¡t dt t| d td fƒksºt‚tt‡ fd	d
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ tt‡ fdd
„ƒ t td tddfƒ‰ tt‡ fdd
„ƒ tddd}tddd}t tt||fƒ‰ ˆ  tdt ¡ ˆ  tdt ¡t dt t|d |d fƒks¤t‚t tt| fƒ‰ ˆ  tdt ¡t dt t| d fƒksÞt‚d S )Nrm   ru   r   r|   r   éüÿÿÿéýÿÿÿr€   c                      s   ˆ   td¡S r}   )Ú	transformrp   rj   ©r‹   rj   rk   rz   ÷  r{   z test_transform.<locals>.<lambda>c                      s   ˆ   ttt ¡S rv   ©rý   rp   r†   r˜   rj   rþ   rj   rk   rz   ø  r{   c                      s   ˆ   tt ¡S rv   ©rý   rp   r†   rj   rþ   rj   rk   rz   ù  r{   c                      s   ˆ   tttf¡S rv   rÿ   rj   rþ   rj   rk   rz   ú  r{   c                      s   ˆ   dt dt ¡S r¾   r   rj   rþ   rj   rk   rz   û  r{   c                      s   ˆ   td t¡S r¾   r   rj   rþ   rj   rk   rz   þ  r{   r™   T)Únegativer¯   rÃ   )rW   rp   r   r‰   rý   rq   r3   r   r    r   rì   r¯   r†   rZ   r‚   r   )r™   ZfxÚfyZ_3ÚamÚbprj   rþ   rk   Útest_transformÚ  sZ    0$8ÿ
  ÿ
ÿ
ÿ
ÿ22r  c                  C   s^   t jttƒ ttdtd  ƒ d  } ttttƒƒtƒ| ks@t‚ttt	tƒƒtƒ| ksZt‚d S rà   )
r   r¼   r0   rp   r-   rH   r2   rq   r3   r/   râ   rj   rj   rk   Útest_issue_4052
  s    &r  c                  C   sŠ  t tttddfƒdƒdkst‚tttd  ƒtt tfƒ} t | dƒdksLt‚t | d t ttddƒ  dƒdkstt‚t	d	ƒ}d
t
dƒ dd|d    }dt
dƒ d| d  t
d|d  | d ƒd  }d|d  d d|d  d|  d d  }t
dƒd|d  d|  d  d|d  d|  d d  }|||  | }t t||ddfƒdƒt dt
dƒ dt  dtt
dƒƒ  d dƒksŽt‚t tttdt ƒƒdt td   tddfƒdƒt ddƒksÐt‚t ttt
td d ƒƒt
td d ƒtd d   tddfƒdƒt dtd  d dƒks.t‚t ttttt ƒtt t ƒ td d   tdtfƒdƒt ddƒkszt‚t tttttƒttƒ ƒƒttd td fƒdddt ddƒksÀt‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks t‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks@t‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks€t‚t tdtd tddfƒ  dd!dd"d#ks®t‚tttƒtd  tdtfƒjdd$}d%|  k rêd&k sðn t‚t tttƒtd  tdtfƒd'd(d)kst‚t tttt d ƒt tt d*fƒd'd(d+ksRt‚t tttƒƒd,ksjt‚t ttttfƒƒd-ks†t‚d S ).Nrm   r   rf   z10.5000000000000z1.77245385090552ru   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r˜   r­   r|   é   r€   é   éù   é6   éA   r   é2   é1   é¢   rÖ   z*pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))é`   zlog(2)/2-1/4T©Úchopzpi/4*log(4*pi**3/gamma(1/4)**4)rÎ   é   é   zsqrt(1-x**2)é   )Úmaxnr  )z0.0Ú0)r  g\Âõ(\ß?gR¸…ëQà?Úosc)Úquadz0.504067061906928r   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rl   rW   rp   rq   r    r   r   r   r   r   r-   r1   r"   r3   r2   rg   r   )Úgaussr˜   r™   r¯   r°   r„   re   rj   rj   rk   Útest_evalf_integrals  s¼     ÿÿÿ4,<,ÿ
0ÿ
4 ÿÿÿ
ÿ
ÿÿÿÿ
4ÿ
$  ÿÿ
$  ÿÿ
$  ÿÿ
 ÿ  ÿÿ
$ ÿÿ
 
ÿÿÿ
r  c                   C   s†   t tdtd d  tƒ td¡dddks.t‚t tdtd d  tddfƒƒdksVt‚t tdtd d  tddfƒdddks‚t‚d S )	Nru   r   r€   Tr  )z-0.000976138910649103z0.965906660135753z1.93278945918216rm   z0.0144361088886740)rl   rH   rp   rÝ   rq   rW   rj   rj   rj   rk   Útest_evalf_issue_939E  s    $ÿ( ÿÿr  c                  C   sŠ   t ttƒtt  tddftddfƒ} t| dƒdks6t‚| tddƒdtdƒ d  ksXt‚t tttt  ƒtddftddfƒtj	ks†t‚d S )	Nru   rm   r   rf   z2.43790283299492rû   r|   r­   )
rH   r-   rp   r   rl   rq   r   r3   r   rš   ©Úresrj   rj   rk   Ú(test_double_previously_failing_integralsT  s    $"r  c            	      C   s¬  t ttdƒt tddƒ } t ttdƒd t tddƒ }t| tƒ|ksFt‚dt tddƒ dt tddƒ  }dt tdd	ƒ dt tddƒ  }t|tƒ|ks˜t‚d
td
  t dt tddƒ  d
t tddƒ  }d
td  t d d
t t tddƒ  dt tddƒ d  }td
 td
  dt t tddƒ  d
t tddƒ  }t|tƒ|ksLt‚t|tƒ|ks`t‚tt|tfƒstt‚t|tƒt|tfƒkst‚t|tƒ ¡ |ks¨t‚dt tddƒ d
t tddƒ  }dt tddƒ d d
t tddƒ  }t|tt	 tfƒ|kst‚tt tddƒtƒt tddƒks,t‚tt tddƒtt	 t	fƒd	ksPt‚tdt tddƒ tt	 t	fƒdksxt‚tt tddƒt
tƒ tt	 t	fƒt
dƒks¨t‚d S )Nr|   r   r   r€   r   r   iúÿÿÿr   ru   rm   rû   r•   r­   )rE   rp   r™   rH   rq   r   rU   rW   r‰   r   re   )	Zin_1Zout_1Zin_2Zout_2Zin_3Zout_3_1Zout_3_2Zin_4Zout_4rj   rj   rk   Ú"test_integrate_SingularityFunction_  s*      0<4 $$$(r  c                  C   s   t ttƒttƒ tt tfƒtdƒks*t‚t ttƒd tt tfƒtdƒksPt‚t t ddt  tt  dt  ttƒ ttd ƒ tddfƒtddfƒdks t‚ttd td   ƒt } t | ttdt  ƒ tt tftt tfƒt | ttdt  ƒ tt tftt tfƒ  kr–t | tdt t ƒ tt tftt tfƒ  kr–t | tdt t ƒ tt tftt tfƒ  kr–dt	dt ƒ ksœn t‚d S )Nr   rm   r€   ru   r   ée   )
rH   r7   rp   re   r   rq   r   r    r   r-   rr   rj   rj   rk   Útest_integrate_DiracDelta|  s.    *&ÿ
ÿÿÿÿ**ÿ
*þ
*ý
ür!  c                	   C   sj  t tt tƒtttd  td  ttdƒfttƒdfƒks>t‚t tt tƒttt ttƒ tttƒdƒftdfƒksxt‚t ttt ƒtƒtttt ƒt ttdƒftdfƒks²t‚t tttt ƒ tƒttt d ttt ƒ td  ttd dƒftd d dfƒkst‚t ttt  tƒtttt d  tt d  ttt dƒfttƒdfƒks^t‚t ttt  tƒtttt  tttƒ  ttttƒ dƒftdfƒksªt‚t t	tt ƒtƒtt
tt ƒt ttdƒftdfƒksæt‚t t	tt ƒd tƒttt d t
tt ƒt	tt ƒ d  t ttdƒftdfƒksBt‚t tt	tt ƒ tƒttt
tt ƒ t t	tt ƒtd   ttdƒftd d dfƒks¢t‚t t
tt ƒtƒtt	tt ƒ t ttdƒfdƒksÜt‚t t
tt ƒd tƒttt d t
tt ƒt	tt ƒ d  t ttdƒfdƒks4t‚t tt
tt ƒ tƒtt t	tt ƒ t t
tt ƒtd   ttdƒfdƒksŠt‚t ttt ƒtdtfƒtttt ƒt dt  tt kttk @ ttdƒ@ ftdfƒksæt‚t ttƒtt ttt ƒ ƒ tƒtttƒ ttt ƒttttt ƒ ƒ ttttt ƒ ƒ  tttd ƒftdfƒksft‚d S )Nru   r   Tr   rm   ©r   T)rH   rp   r   r.   r   r"   rq   r    rb   r2   r3   rì   r   r˜   r-   rj   rj   rj   rk   Ú test_integrate_returns_piecewise  st     
ÿ
 ÿ
 ÿ
, ÿ( 
ÿ( ÿ ÿ4 ÿ0 ÿ ÿ4 ÿ2 ÿ2 ÿ$<ÿþr#  c                  C   sv  t ddd} tt| dƒ| ddfƒdks*t‚tt| d | d ƒ| ddfƒtdd	ƒksVt‚ttt| ƒt|  ƒƒd | ƒttd|  ƒd | dkfd
td|  ƒd  dfƒksªt‚t ddd}tt|| ƒt| d  ƒ | t tfƒ}t|t| d  ƒ | t |fƒ}t| t| d  ƒ | |tfƒ}|||   krlt	t
ƒ| t|ƒ d t	t
ƒ| d  t|d  ƒd  ksrn t‚d S )Nrp   Tr§   rm   r   r|   r€   r  rÖ   ru   r   r°   )Zextended_real)r   rH   r,   rq   r+   r   r    r.   r   r-   r   r<   )rp   r°   Zint1Zint2Zint3rj   rj   rk   Útest_integrate_max_min®  s     , ÿ
& (ÿÿr$  c                  C   s8  t ttƒtddfƒtddƒks"t‚t ttƒtddfƒtjks@t‚t ttd ƒtddfƒtddƒksft‚t ttd d ƒtddfƒdksŠt‚t ttd dt  ƒtdd	fƒd
ks²t‚t ttƒtddfƒdksÎt‚t ttƒttƒ tt	 t	fƒdksôt‚t ttd ƒtd  tddfƒtddƒks$t‚t
ddd\} }t t| ƒ| ƒt| d  d | dkf| d d dfƒkspt‚t td|  d ƒ| ƒt| d  d|   | dkf| d d|   d dfƒksÀt‚t t| |d  ƒ| ddfƒd|d  td|d ƒ d|d   td|d ƒd  d kst‚t tt| ƒ ƒ| ƒtt| ƒ| dkfdt|  ƒ dfƒks\t‚t td|  d ƒ| ƒt|  | dk f| d dfƒks”t‚t d|  t| d d ƒ | ƒt| d | dk f| d  d | dk f| d dfƒksêt‚t t| ƒ| |d fƒt|d |d dkf| d |d dk fdƒks4t‚d S )Nr   ru   r   rm   r   r|   r€   éñÿÿÿrf   iÓ  r   r  zt sTr§   r®   é   r"  )rH   r   rp   r   rq   r   r¼   r   r3   r   r   r.   rÜ   r,   r    )r˜   r†   rj   rj   rk   Útest_integrate_Abs_sign½  sL    "&$(&0 ÿ ÿ:ÿ
 ÿ 
ÿ  
ÿ  ÿr'  c                  C   sÞ   t ttt ƒtƒ} |  td¡t ttd ƒtƒks4t‚t ttt ƒtddfƒ} |  td¡t ttd ƒtddfƒkstt‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tfƒ}| tdi¡t tdtd  ƒtt tfƒksÚt‚d S ©Nr|   r   ru   rm   r   )rW   r    rp   r   rÝ   rq   r	   r   ©rh   re   Úconvrj   rj   rk   Ú
test_subs1Ø  s    "("r+  c                  C   s  t ttt ƒttƒ} |  td¡t ttd ƒttƒks8t‚t ttt ƒtddftddfƒ} |  td¡t ttd ƒtddftddfƒksˆt‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tftddfƒ}| tdi¡t tdtd  ƒtt tftddfƒksþt‚d S r(  ©	rW   r    rp   r   r˜   rÝ   rq   r	   r   r)  rj   rj   rk   Ú
test_subs2â  s    $ 0*r-  c                  C   sÊ   t ttt ƒtdtfttdfƒ} |  td¡t ttd ƒtddftddfƒksPt‚ttttd  ƒƒ}t |tt ƒ|tƒ tt tfttdfƒ}| tdi¡t tdtd  ƒtt tftddfƒksÆt‚d S ©Nr   ru   r|   rm   r   r,  r)  rj   rj   rk   Ú
test_subs3ì  s
     0*r/  c                  C   s¾   t ttƒtdtfttdfƒ} |  td¡t ttƒtddftddfƒksHt‚ttttd  ƒƒ}t |tƒ|tƒ tt tfttdfƒ}| tdi¡t tdtd  ƒtt tftddfƒksºt‚d S r.  r,  r)  rj   rj   rk   Ú
test_subs4ô  s
    ,&r0  c                  C   sÀ  t ttd  ƒtt tfƒ} |  td¡| ks0t‚t ttd  t ƒtƒ} |  td¡t ttd  d ƒtƒkspt‚t ttd  t ƒttfƒ} |  td¡t tttd  ƒtdfƒks¶t‚|  td¡t ttd  d ƒtƒksÞt‚t ttd  t ƒtt tftt tfƒ} |  td¡| kst‚|  td¡| ks4t‚t ttd  ƒttfƒ} |  td¡t ttd  ƒtdfƒksvt‚t ttƒtƒ} |  td¡|  td¡ t ttƒtddfƒ  ¡ js¼t‚d S )Nrm   r   ru   r   )	rW   r    rp   r   rÝ   rq   r   r‰   Úis_zero©rh   rj   rj   rk   Ú
test_subs5ü  s    (*(**r3  c                  C   s  t dƒ\} }ttt tttƒttƒfƒ}| td¡ttt ttdƒttƒfƒksTt‚| td¡tttttƒtdƒfƒks|t‚ttt tttƒttƒftttƒttƒfƒ}| td¡ttt ttdƒttƒfttdƒttƒfƒksät‚| td¡ttt tttƒttƒftttƒtdƒfƒks"t‚ttt tttƒt| ƒftttƒt| ƒfƒ}| | d¡ttt tttƒtdƒftttƒtdƒfƒksŒt‚d S )Nza bru   )r   rW   rp   r   re   rÝ   rq   )r™   r¯   rh   rj   rj   rk   Ú
test_subs6  s    ,(,<>,r4  c                  C   s¶   t ttdtftddfƒ} |  tdtdi¡| ks2t‚t ttƒttƒ tttƒttƒftddfƒ} |  ttƒd¡| ksvt‚|  ttƒd¡t ttƒttƒ tdttƒftddfƒks²t‚d S rà   )rW   rp   r   rÝ   rq   r3   r2  rj   rj   rk   Ú
test_subs7  s     ÿ*ÿr5  c                  C   sÈ   t ttƒttd ƒ tdtfƒ} |  ¡ t ttƒtdtfƒt ttd ƒtdtfƒ ksXt‚t ttƒttd ƒ tdtfƒ} |  ¡ | ksˆt‚| jddt ttƒtdtfƒt ttd ƒtdtfƒ ksÄt‚d S )Nrm   ru   T)Úforce)rW   re   rp   r   rŠ   rq   r   r2  rj   rj   rk   Útest_expand$  s     8 ÿr7  c                   C   s    t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t ttd  ƒdƒS ©Nrm   r|   )rW   r    rp   rj   rj   rj   rk   rz   .  r{   z+test_integration_variable.<locals>.<lambda>c                   S   s   t ttd  ƒdt tfƒS r8  )rW   r    rp   r   rj   rj   rj   rk   rz   /  r{   )rZ   r‚   rj   rj   rj   rk   Útest_integration_variable-  s    r9  c                   C   sÊ   t ttd ƒttd ƒd  tddfƒ ¡ t ttd ƒttd ƒ tddfƒt ttd ƒtddfƒ kslt‚t ttd ƒttd ƒd  tƒ ¡ t ttd ƒttd ƒ tƒt ttd ƒtƒ ksÆt‚d S )Nrm   ru   r   )rW   r2   rp   r3   rŠ   rq   rj   rj   rj   rk   Útest_expand_integral2  s    *"ÿÿ$ÿÿr:  c                      sN  t ttd d ƒtddfƒ‰ ˆ jddddtdƒ ks:t‚ˆ jdddd	td
ƒ dtdƒ  ksdt‚ˆ jddddtdƒ d dtdƒ d  dtdƒ d  ks¦t‚ˆ jd	dddtdƒ d	tdƒ  d	tdƒ  dtdƒ  ksèt‚tˆ jd	dd ¡ ˆ  ¡  ƒdk st‚t ttd td  ƒtddftddfƒ‰ tt	‡ fdd„ƒ d S )Nr|   ru   rm   r   Úmidpoint©Úmethodr­   éÙ   r€   r  rÖ   é9   i	  é   iIÎ  iÚ  r•   éV   r®   é   g      à?r   c                      s
   ˆ   d¡S )Nr€   ©Úas_sumrj   r2  rj   rk   rz   F  r{   z'test_as_sum_midpoint1.<locals>.<lambda>)
rW   r-   rp   rD  rq   rÜ   rb   r   rZ   ÚNotImplementedErrorrj   rj   r2  rk   Útest_as_sum_midpoint1;  s$    *ÿÿ

ÿ
ÿ
ÿ
((rF  c                  C   s  t tt d tddfƒ} tdddd}| jddd ¡ tdd	ƒt td  ksRt‚| jddd ¡ td
dƒt td  ks~t‚| jddd ¡ tddƒt td  ksªt‚| jd	dd ¡ tddƒt td  ksÖt‚| j|dd ¡ td t tddƒ dd|d    kst‚d S )Nrm   r   ru   rb   T©rÄ   rd   r;  r<  r€   r   r  r|   é#   él   é   é@   rÖ   )rW   rp   r   r   rD  rŠ   r   rq   r   rj   rj   rk   Útest_as_sum_midpoint2I  s    ,,,,$ÿrL  c                  C   sD  t tt d tddfƒ} | jddd ¡ td ks6t‚| jddd ¡ tddƒtd  td  ksft‚| jddd ¡ tdd	ƒttddƒ  td  ksœt‚| jd
dd ¡ tddƒttdd
ƒ  td  ksÒt‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks$t‚| jdddd t	¡s@t‚d S )Nrm   r   ru   Úleftr<  r­   r|   r   r@  r€   r•   é    r®   r   F)r=  Úevaluate)
rW   rp   r   rD  rŠ   rq   r   rb   Úhasr   r2  rj   rj   rk   Útest_as_sum_leftT  s    0668ÿ
rQ  c                  C   s:  t tt d tddfƒ} | jddd ¡ ddt  td  ksBt‚| jddd ¡ tddƒttddƒ  td  ksxt‚| jddd ¡ td	d
ƒttddƒ  td  ks®t‚| jddd ¡ tddƒttddƒ  td  ksät‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks6t‚d S )Nrm   r   ru   Úrightr<  r   r­   r|   rB  r@  r€   rf   rN  r®   )rW   rp   r   rD  rŠ   rq   r   rb   r2  rj   rj   rk   Útest_as_sum_right_  s    *6668ÿrS  c                  C   s.  t tt d tddfƒ} | jddd ¡ td t tj ks@t‚| jddd ¡ td t tddƒ kslt‚| jddd ¡ td t tdd	ƒ ks˜t‚| jd
dd ¡ td t tddƒ ksÄt‚| jt	dd ¡ td t tddƒ ddt	d    kst‚t t
tƒtddfƒ dd¡tjks*t‚d S )Nrm   r   ru   Z	trapezoidr<  r|   r­   é   r
  r€   r  rN  r®   )rW   rp   r   rD  rŠ   r   r¼   rq   r   rb   r   r2  rj   rj   rk   Útest_as_sum_trapezoidi  s    (,,,$ÿ
rU  c                      sr   t tt d tddfƒ‰ tt‡ fdd„ƒ tt‡ fdd„ƒ ttdd„ ƒ tt‡ fdd„ƒ tt‡ fd	d„ƒ d S )
Nrm   r   ru   c                      s
   ˆ   d¡S )Nr   rC  rj   r2  rj   rk   rz   v  r{   z$test_as_sum_raises.<locals>.<lambda>c                      s
   ˆ   d¡S ©Nr   rC  rj   r2  rj   rk   rz   w  r{   c                   S   s   t tƒ d¡S )Nr|   )rW   rp   rD  rj   rj   rj   rk   rz   x  r{   c                      s
   ˆ   t¡S rv   )rD  r   rj   r2  rj   rk   rz   y  r{   c                      s   ˆ j dddS )Nr|   Zxxxx2r<  rC  rj   r2  rj   rk   rz   z  r{   )rW   rp   r   rZ   r‚   rj   rj   r2  rk   Útest_as_sum_raisest  s    rW  c                  C   s4   t t ttƒtƒ} t tttƒ}|  ¡ | ¡ ks0t‚d S rv   )rW   rp   r‰   rq   ©rh   re   rj   rj   rk   Útest_nested_doit}  s    rY  c                  C   s   t td td dfƒ} t td tdd fƒ}|  ¡ tddƒks>t‚| ¡ tddƒksTt‚t tt td tfƒ tt¡t tt td tfƒksˆt‚t tt ttd fƒ tt¡t tt ttd fƒks¼t‚ttd td dfƒtddƒksÞt‚ttd tdd fƒtddƒkst‚tddƒtddƒkst‚d S )Nrm   ru   r|   r   zx**2)rp   Ú1N)	rW   rp   r‰   r   rq   r   rÝ   r˜   rH   rX  rj   rj   rk   Útest_issue_4665ƒ  s    44"$r[  c                  C   s*   t td tddfƒ} | t | jŽ ks&t‚d S )Nrm   r   ru   )rW   rp   Úargsrq   r2  rj   rj   rk   Útest_integral_reconstruct  s    r]  c                  C   s  t t dt ƒtddfƒ} |  ¡ tddƒks.t‚| jddtddƒksHt‚tdƒ}t |tƒtddfƒ ¡ dkspt‚t dtdt |tƒtƒfƒ ¡ dks–t‚t ttdfƒ ¡ dks°t‚tdttƒftdff}t tf|žŽ  ¡ tddƒksæt‚t tftt	|ƒƒžŽ  ¡ dks
t‚d S )	Nrm   r   ru   r|   F©Údeepre   r€   )
rW   rp   r‰   r   rq   r   r™   r    ÚlistÚreversed)rh   re   r‘   rj   rj   rk   Útest_doit_integrals•  s     & rb  c                   C   sð   t ttƒdt  ƒtdttƒ td d  d dttƒ td  d  dttƒ d  ttd ƒdkfdt tt ƒ td d  d dt tt ƒ td  d  dt tt ƒ d  dfƒksÈt‚t tt dttƒ  ƒtt ksìt‚d S )Nru   rm   r   rf   r€   T)rH   r-   rp   r.   r   r   rq   r"   rj   rj   rj   rk   Útest_issue_4884¤  s    Bÿ>ÿÿýÿrc  c                   C   s²   t tt ttƒ tƒttt tt  ttƒ td dt  d  ttt  ttƒ td dt  d   ttt  td dt  d   ttdƒfttƒd d dfƒks®t‚d S )Nrm   ru   r   T)rH   rp   rb   r"   r.   r   rq   rj   rj   rj   rk   Útest_issue_18153­  s    *&ÿÿþýÿrd  c               	   C   sœ  ddl m} m}m} t| ƒjdks&t‚td| ƒjdks:t‚td| dfƒjdksRt‚td| ddfƒjdkslt‚td| d|fƒjdks†t‚td| |fƒjdksžt‚t| |ƒjdks²t‚t| |d| fƒjdksÌt‚t| |ddfƒjdksæt‚t| | ddfƒjdkst‚t| |ddfƒ}|jdkr,| ¡ dks0t‚t| |||fƒ}|jdkrZ| ¡ dks^t‚td|||d fƒ}|jdkrŒ| ¡ dkst‚t| | | ddf|ddfƒjdks¸t‚t| | | ddf|d|fƒjdksàt‚t| | dfƒjdksút‚t| | dt||ddfƒfƒjdks"t‚tt||ddfƒ| ddfƒjdksJt‚tt	| ƒd t
| ƒd  d | ƒjdksxt‚tt| ƒ| ddfƒjdks˜t‚d S )	Nr   ©rp   r   rì   Fru   Trm   rË   r|   )Ú	sympy.abcrp   r   rì   rW   Z	is_numberrq   rb   r   r3   r2   re   )rp   r   rì   r‹   rj   rj   rk   Útest_is_number¶  s0    ((((.rg  c                  C   sj  ddl m} m}m} td| ƒj| hks*t‚t| ƒj| hks>t‚t| | d |fƒj|hksZt‚t| | |d fƒj|hksvt‚t| | d|fƒj|hks’t‚t| | |dfƒj|hks®t‚t| | | |fƒj| |hksÌt‚t| | |ƒj| |hksæt‚t| | ddfƒjtƒ kst‚t| |ddfƒj| hks"t‚t| |||fƒj| |hksBt‚t| |ddf|d d fƒj| |hksjt‚t| |ddf| d|fƒj|hkst‚td|ddf|d| f| ddfƒjtƒ ks¾t‚td|| df|d| f| ddfƒjtƒ ksìt‚td| ddf|| df|ddfƒj| hkst‚tt| ƒt| ƒd|fƒj|hks@t‚tt| ƒt| ƒd| fƒj| hksft‚d S )Nr   re  ru   rm   )	rf  rp   r   rì   rW   rˆ   rq   Úsetre   re  rj   rj   rk   Útest_free_symbolsÖ  s:     ÿ
ÿ
 ÿ
 ÿ
 ÿ
&ri  c                  C   s2  ddl m} m} td| d| fƒjs&t‚td| ddfƒjs<t‚td| ddftdfƒjdks\t‚t| |dfƒjspt‚t| | |dfƒjd ksŒt‚t||dt| ƒf| dfƒ}|jd ks´t‚t|| df|dt| ƒfƒjdksØt‚t| | ttfƒjsît‚t| | t t fƒjs
t‚tt	| ƒ| ddt
 fƒjd ks.t‚d S )Nr   )rp   r×   ru   rm   FT)rf  rp   r×   rW   r1  rq   r   r    r   r3   r   )rp   r×   r‹   rj   rj   rk   Útest_is_zeroò  s     $rj  c                     s\   ddl m}  tt| ƒ| | fƒ}| | ¡‰ |j| dd ¡ t‡ fdd„tdƒD ƒŽ ksXt	‚d S )Nr   ©rp   r­   rÌ   c                    s   g | ]}t ˆ ƒ‘qS rj   )Únext)Ú.0rõ   r2  rj   rk   Ú
<listcomp>	  s     ztest_series.<locals>.<listcomp>r€   )
rf  rp   rW   r2   ZlseriesZnseriesZremoveOr   Úrangerq   )rp   r‹   rj   r2  rk   Útest_series  s    
rp  c                  C   sV   t dƒ} tdt| ƒ |  | ƒt| ƒt| ƒ ks2t‚tt| ƒd |  | ƒ t¡sRt‚d S )Nrp   ru   rm   )	r   rH   r3   r"   r;   rq   r2   rP  r9   rk  rj   rj   rk   Ú!test_trig_nonelementary_integrals  s    *rq  c               	   C   s4  t dƒ} t dƒ}t ddd}tt| d |d  ƒ| ƒ|d t| | ƒ d | t| d |d  ƒ d  ksnt‚tt| d |d  ƒ| ƒ| t| d |d  ƒ d |d t| t| d |d  ƒ ƒ d  ksÐt‚t ddd} t ddd}td| d |d  td	ƒ  | ƒ| |d t| d |d  ƒ  ks0t‚d S )
Nrp   r   rì   TrÃ   rm   r§   ru   z3/2)r   rH   r-   r$   rq   r"   r   re  rj   rj   rk   Útest_issue_4403  s    2ÿBÿ ÿrr  c                   C   sT   t ttd  d ƒtƒdtttdtd  ƒ ƒ ttdtd  ƒ d  ksPt‚d S )Nrm   r€   r   rû   )rH   r-   rp   r1   rq   rj   rj   rj   rk   Útest_issue_4403_2%  s    2ÿrs  c                  C   sD   t ddd} tt| d td  ƒtd| fƒt| d  d ks@t‚d S )NÚRTrÃ   rm   r   r€   )r   rH   r-   rp   r   rq   )rt  rj   rj   rk   Útest_issue_4100*  s    ru  c                  C   sÐ  ddl m} m}m}m} tdƒ}tt||ƒ|ƒ|ƒt||ƒ||ƒksHt‚t||ƒƒj||ƒt	|ƒfksjt‚tt||ƒƒƒj||ƒt	|ƒt	|ƒfks–t‚tt||ƒƒ|ƒj||ƒt	|ƒt	|ƒfksÄt‚tt||ƒ|ƒ|ƒj||ƒt	|ƒt	|ƒfksôt‚ttt||ƒ|ƒ|ƒ|ƒj||ƒt	|ƒt	|ƒt	|ƒfks2t‚t
t||ƒ|ƒ|ƒt||ƒ||ƒks\t‚t
t||ƒ|ƒ|ƒ|t||ƒ|ƒ ksˆt‚t
t||ƒ|ƒ|ƒt|||ƒ |ƒ|t||ƒ|ƒ fksÆt‚t
td|ƒ|ƒ|d ksät‚t
td|ƒ|ƒd| | kst‚td||ƒjtd||ƒjks(t‚t||ƒ||||ƒ ¡ |d t||ƒ||ƒ d ksbt‚t||ƒ|ddf| d|f|d|fƒ ¡ ||d  t||ƒ|ddfƒ |d t||ƒ|ddfƒ  ksÌt‚d S )Nr   )Úwrp   r   rì   re   rm   ru   )rf  rv  rp   r   rì   r   rW   rq   r\  r   rH   r‰   )rv  rp   r   rì   re   rj   rj   rk   Útest_issue_5167/  s(    (",.0ÿ
*,>"":&:ÿrw  c                  C   s  t ddd} ttttƒd  ƒtƒttƒttddƒƒ tttƒt	j
 ƒ d ksTt‚ttttƒd ƒtƒttƒttddƒƒ tttƒt	j
 ƒ d ksšt‚tt|  ttƒd  ƒtƒttƒtdd|   ƒ tt| ƒttƒ ddt| ƒ   ƒ dt| ƒ  kst‚d S )Nrì   TrÃ   rm   ru   r€   r   )r   rH   r    r"   rp   r-   r   r   r<   r   r¼   rq   r>   ©rì   rj   rj   rk   Útest_issue_4890F  s    *ÿ*ÿFÿry  c                   C   s,   t dttdtd  ƒ  tƒ t¡r(t‚d S rà   )rH   rp   r-   rP  rW   rq   rj   rj   rj   rk   Útest_issue_4551P  s    rz  c               	   C   s   t dddd} tt| td|   d  tdtjfƒ| d dd|   | d   | dd|     ddd|    | ddd|        ƒdksŒt‚d S )Nrb   T©rd   rÄ   ru   r   rm   )r   rQ   rH   rp   r   r¼   rq   rÌ   rj   rj   rk   Útest_issue_4376T  s    "Nÿÿr|  c                   C   sX   t ttƒtd  ttddƒ  tƒdttddƒ  d dttddƒ  d  ksTt‚d S )Nr|   ru   r®   r•   r  )rH   r-   rp   r   rq   rj   rj   rj   rk   Útest_issue_4517Z  s    "*ÿr}  c               
   C   sü  t ddd\} }tt| t ƒt|t ƒ tdtfƒ ¡ tdt| dƒt|dƒB ft d t| | ƒt| dƒt|dƒ@ B ftd t| |ƒt| dƒt|dƒ@ B fdƒks¦t‚tt| t ƒt|t ƒ tfƒtdt	t| dƒt|dƒƒft t|t ƒd  d tt
|t ƒd  d  t|t ƒt
|t ƒ d|   t| | ƒftt|t ƒd  d tt
|t ƒd  d  t|t ƒt
|t ƒ d|   t| |ƒf|t| t ƒ t
|t ƒ | d |d   | t|t ƒ t
| t ƒ | d |d    dfƒksøt‚d S )Nzk mTrc   r   rm   r"  )r   rH   r3   rp   r   rQ   r.   r   rq   rI   r2   )Úkr×   rj   rj   rk   Útest_issue_4527_  s$    &($ýÿ \X**ÿÿür  c                  C   sp   t ddd} ttt d t |  t ƒt tt tfddttt d t |  t ƒt tt tfƒkslt‚d S )Nr   TrÃ   rm   rÅ   rÆ   )	r   rH   r    r   r   rp   r   rW   rq   )Zyposrj   rj   rk   Útest_issue_4199t  s    .*ÿr€  c                  C   s¶  t ddd\} }}}tttd  t| t  ƒtƒttƒ t|d  d ƒ tt| d t ƒ d kslt‚tt| td  |t  | ƒtƒttƒt|ƒ t|d  d|   ƒ t	t| ƒt |dt| ƒ   ƒ dt| ƒ  ksät‚ddl
m} ddlm} |tttd  ƒtt| t ƒ tt tfƒƒttƒt|d  d ƒ ksLt‚t d	dd\} }|tt|  td  d| t  ƒtt tfƒƒttƒt|d |  ƒ t| ƒ ks²t‚d S )
Nza:dTrÃ   rm   r€   r   )Ú
expand_mul)r~  za d)r   rH   r    rp   r   r-   r   r<   rq   r>   rÓ   r  rf  r~  r   )r™   r¯   r°   r„   r  r~  rj   rj   rk   Útest_issue_3940{  s     2ÿ Pÿ.ÿ
.ÿr‚  c                   C   sV   t t td td   tƒttt t t ƒ d tttt t ƒ d  ksRt‚d S r¾   )rH   r™   rp   r   r"   rq   rj   rj   rj   rk   Útest_issue_5413‹  s    rƒ  c               
   C   sº  t dƒ\} }tddd}|  t| ƒ }|  |t  ttƒd ttƒd   }ttƒd  ttƒd  }ttƒd  ttƒd  d }t|||  tƒ||  |  t	|t ƒ | | t t| ƒ   ||  |  t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   || | t	|t ƒ | | t t| ƒ   | | t | |  t	tƒ t|ƒ  t| ƒ | | t | |  t	tƒ t|ƒ  t| ƒ fks¶t
‚d S )NzA zr°   T)rÊ   rm   ru   )r   r   r    r˜   r3   rp   r2   r   rH   r"   rq   )rª   rì   r°   ZP1ZP2Zh1Zh2rj   rj   rk   Útest_issue_4892a‘  s    &00,,..úr„  c                  C   s\   t tƒtd  dttƒ td   d td d  } ttt| tƒ t¡|  ƒƒdksXt‚d S )Nr|   rm   rÖ   r   )	r3   r   rp   r2   rR   rL   rH   r
   rq   )Úexprrj   rj   rk   Útest_issue_4892b¦  s    	4r†  c                   C   sX   t ttƒtttƒ tdtftdtftdtfƒdttttƒtdtftdtfƒ ksTt‚d S ©Nr   rm   )	rH   r3   rp   re   r   rì   r   rW   rq   rj   rj   rj   rk   Útest_issue_5178³  s    , ÿrˆ  c                  C   sª   t tƒ tdd¡} td d td d  td d  td d	  td d
  ttd ƒ }t| tƒ|kslt‚tt| tƒtƒ| ks„t‚tttd ƒtƒttd ƒks¦t‚d S )Nr   r   rm   r€   é   r®   iÐ  r­   i€  i _7 r  r   )r3   rp   ZseriesrN   rH   rq   r
   ©re   ry   rj   rj   rk   Útest_integrate_series¸  s
    Hr‹  c                  C   s0   ddl m}  | tg g dgg tƒtƒd ks,t‚d S )Nr   ©Úheurischru   )Zsympy.integrals.heurischr  rD   rp   rq   rŒ  rj   rj   rk   Útest_atom_bugÂ  s    rŽ  c                  C   sh   t ddd} tttt |  ƒtdtftdtfƒ ¡ t| ƒttd |  ƒ t	 dttƒ  |  ksdt
‚d S )Nrì   F©Úzeror   rm   )r   rH   r3   rp   r   r   rƒ   r"   r9   r   rq   rx  rj   rj   rk   Útest_limit_bugÇ  s    &*ÿr‘  c                  C   s,   t dƒ} tttƒ| tƒ tƒ t¡s(t‚d S )Nry   )r   rH   r    rp   rP  rW   rq   rx   rj   rj   rk   Útest_issue_4703Í  s    r’  c                  C   s.   t dƒ} t| tƒ t¡d tƒ t¡s*t‚d S )Nre   rm   )r   rH   rp   r
   rP  rW   rq   râ   rj   rj   rk   Útest_issue_1888Ò  s    r“  c                   C   sF   t ttt ƒtt d td ftdtfƒdttd d ƒ ksBt‚d S )Nrm   r   )rH   r2   rp   r   r   r;   rq   rj   rj   rj   rk   Útest_issue_3558Ù  s    r”  c                   C   s6   t dtddtd   ƒ tƒttd ƒd ks2t‚d S )Nru   r  r€   rm   )rH   r-   rp   r$   rq   rj   rj   rj   rk   Útest_issue_4422Ý  s    r•  c                   C   sN   t tttddt  ƒ tƒƒtdt d ƒdtd  t d  d ksJt‚d S )Nru   rm   r®   rf   )rQ   rH   rp   r-   rq   rj   rj   rj   rk   Útest_issue_4493á  s    &ÿr–  c                   C   sh   t ttƒt tt tfƒtks"t‚t ttƒt tdtfƒtd ksFt‚t ttƒt tƒttƒksdt‚d S r‡  )rH   r3   rp   r   r   rq   r;   rj   rj   rj   rk   Útest_issue_4737æ  s    "$r—  c                  C   sh   ddl m}  tddd}t| ttt ƒttƒ t|  tdtfƒƒƒ|t	d|ƒ d t
|ƒ ksdt‚d S )Nr   rÐ   r™   TrÃ   ru   )rÓ   rÑ   r   rQ   rH   r    rp   r"   r   rB   rA   rq   )rÑ   r™   rj   rj   rk   Útest_issue_4992ì  s
    ,ÿr˜  c                  C   s>   ddl m}  tttt ƒtt  tƒƒ| td tƒks:t‚d S )Nr   ©Ú
lowergammaru   )Ú'sympy.functions.special.gamma_functionsrš  rQ   rH   r    rp   r   rq   r™  rj   rj   rk   Útest_issue_4487ô  s    rœ  c                  C   s,   t dƒ} td| d  | ddfƒtks(t‚d S )Nrp   ru   rm   r   )r   rH   r   rq   rk  rj   rj   rk   Útest_issue_4215ù  s    r  c                  C   s    t dddd} tt|  ttƒ tƒ| t t|   ttƒ | d d|   d  tt|   ttƒ | d d|   d   tt|   | d d|   d   ksœt‚d S )Nrb   Tr{  rm   ru   )r   rH   rp   r"   rq   rÌ   rj   rj   rk   Útest_issue_4400þ  s    Rÿÿrž  c                   C   sZ   t tdt ƒtdt ƒ d t tddttt d ƒttd ƒ d t tƒksVt‚d S )Nru   rm   T©rD   )rH   r-   rp   rW   rq   rj   rj   rj   rk   Útest_issue_6253  s    (&ÿr   c                   C   sè   t ddt t t  tddftddftddfƒdtdƒ dtdƒ d  dtdƒ d  dtdƒ  d	td
ƒ  dtdƒ dtd
ƒ  dtdƒ d  dtdƒ dtdƒ d  dtdƒ dtdƒ d  dtdƒ d  fksät‚d S )Nru   r   iôÿÿÿr|   r®   rm   r­   r   r•   r€   r@  r  é/   )rH   rp   r   rì   r"   rq   rj   rj   rj   rk   Útest_issue_4153  s    .B& *ýr¢  c                  C   sf   t dƒ\} }}t|t|  |  | t| d td  ƒ t| | | fƒ}| t¡rTt‚| t¡rbt‚d S )NzR b hrm   )r   rH   rp   r-   rP  r   rq   rW   )rt  r¯   Úhrh   rj   rj   rk   Útest_issue_4326  s    8r¤  c                   C   s>   t dt dt  tƒdt tdƒ dt tdƒ  ks:t‚d S r8  rä   rj   rj   rj   rk   Útest_powers  s    r¥  c                   C   s<   t tdd„ ƒ ttdt ƒt tddfdd t¡s8t‚d S )Nc                   S   s   t dt tdddS )Nru   T)ÚmanualrD   r£   rj   rj   rj   rk   rz   "  r{   z$test_manual_option.<locals>.<lambda>ru   r   T©r¦  )rZ   r‚   rH   r"   rp   rP  rW   rq   rj   rj   rj   rk   Útest_manual_option!  s    r¨  c                   C   s6   t tdd„ ƒ tttƒtddtttƒtƒks2t‚d S )Nc                   S   s   t dt tdddS )Nru   T)rD   Úrischr£   rj   rj   rj   rk   rz   (  r{   z%test_meijerg_option.<locals>.<lambda>TrŸ  )rZ   r‚   rH   r5   rp   rW   rq   rj   rj   rj   rk   Útest_meijerg_option'  s    rª  c                   C   sª   t tdd„ ƒ tttd  ƒtddtttd  ƒtƒks>t‚ttdt ƒt ttddtd ttdt ƒ d td   ks‚t‚tt	tƒtddt
t	tƒtƒks¦t‚d S )Nc                   S   s   t dttƒ tdtfddS )Nru   r   T©r©  )rH   r"   rp   r   rj   rj   rj   rk   rz   /  r{   z#test_risch_option.<locals>.<lambda>rm   Tr«  ru   )rZ   r‚   rH   r    rp   rX   rq   r"   r   r<   rW   rj   rj   rj   rk   Útest_risch_option-  s    0Dr¬  c                   C   s.  t tdd„ ƒ tttd ƒtddttƒttƒ d ks<t‚tttƒt tddt	ttƒt tƒksht‚tt
tƒtt
tƒƒ ttddƒ  tddd	ttd
dƒ  tt
tƒƒ d dttd
dƒ  tt
tƒƒ d  dttd
dƒ  tt
tƒƒ d dttd
dƒ  tt
tƒƒ d  t
tƒ  ks*t‚d S )Nc                   S   s   t dt tdddS )Nru   T)r©  r  r£   rj   rj   rj   rk   rz   8  r{   z&test_heurisch_option.<locals>.<lambda>rm   TrŒ  r|   r€   Fi€ÿÿÿru   i!  éð   r  rÎ   )rZ   r‚   rH   r    rp   r-   r   r>   rq   rW   r"   r2   r   r3   rj   rj   rj   rk   Útest_heurisch_option6  s    .,*BJÿÿr®  c                  C   s:   ddt d  d  } t| t ƒ t ¡}t| |dds6t‚d S )Nru   gHáz®Gñ?rm   g333333@gê-™—q=)Ztol)rp   rH   r
   ra   rq   rŠ  rj   rj   rk   Útest_issue_6828C  s    r¯  c                  C   sX   t dƒ} ttt t| t  ttƒ ƒ tƒttt|  ttƒ ƒ ttƒ t ksTt‚d S )NÚx_max)	r   rH   r   r   r    rp   r2   r™   rq   )r°  rj   rj   rk   Útest_issue_4803I  s    ""ÿr±  c                   C   s@   t dtdttƒd  ƒ ƒttƒtdttƒd  ƒ ks<t‚d S rà   )rH   r-   r5   rp   rq   rj   rj   rj   rk   Útest_issue_4234O  s    r²  c                	   C   s  t ttd tdtd  ƒ tƒƒjddttdtd  dtd   dt  dttd d ƒ ttdƒt d ƒ   dttd d ƒ  ttdƒkttdƒ k B fdtd  dtd   dt  dtdtd  ƒ ttdƒt d ƒ  d	ttd  d ƒ  dfƒkst	‚d S )
Nrm   r   Tr^  rf   r|   é   r­   iøÿÿÿ)
rQ   rH   rp   r-   rL   r.   r   r#   r0   rq   rj   rj   rj   rk   Útest_issue_4492S  s     "ÿJÿÿFÿÿýÿr´  c                  C   s  dt t ttƒ  } t| tddfƒ}t| tddfƒ ¡ |ks@t‚t| ttƒ tddfƒ|tdƒ tdƒ kspt‚td|  ttƒ tddfƒd| tdƒ tdƒ ks¨t‚ttdt	 t
 t t t  t ƒtdtfƒttdt	 t
 t ƒtdt	 t
 td  t ƒ tdtfƒkst‚d S )Nru   rm   r|   g333333ó?r   g333333ó¿)r™   rì   r"   rX   rW   r‰   rq   rH   r    rb   r†   r˜   rp   )re   Z
integral_frj   rj   rk   Útest_issue_2708\  s    0ÿ,0ÿÿrµ  c                  C   sD   dt  dt  d tdt  ƒ } t| t ddfƒ}t|ƒdks@t‚d S )NgºõJ‡  @gìD” @g      $@gš™™™™™¹?gš™™™™™É?z%1.86831064982608*y + 2.16387491480008)rp   r   r    rH   Ústrrq   )re   rh   rj   rj   rk   Útest_issue_2884j  s     r·  c                  C   s–  ddl m} m} ttt t ƒttƒ tdtfƒt	t
t	t t
td  d   |td ƒdk fdt
t ddtd     |td ƒdk fttjfdfdtjfdfttƒd ƒdfƒ td dkfttt t ƒttƒ tdtfƒdfƒksìt‚ttt t ƒttƒ tdtfƒt	d	td  d dt d  d  t|tƒdk|| tƒƒt
d k || tƒƒt
d kƒfttt t ƒttƒ tdtfƒdfƒks’t‚d S )
Nr   ©Úargr   rm   ru   r   )r   r   )r   Tr   )Ú$sympy.functions.elementary.complexesr¹  r   rH   r    r†   rp   r%   r   r.   r   rD   r   r¼   r   rW   rq   r(   rI   r¸  rj   rj   rk   Útest_issue_8368ip  sN     ÿÿ

ýüû
õ þòÿ  
ýÿ ÿùÿr»  c                   C   s€   t tdt ƒƒdtdt ƒ ks$t‚t tdt ƒƒdt dttdt ƒd ƒ  ksXt‚t ttƒƒttttƒd ƒ ks|t‚d S )Nrò   ru   )rH   r(   rp   r%   rq   r)   r"   rj   rj   rj   rk   Útest_issue_8901  s    $4r¼  c                   C   s¶   t ttƒd t tddfƒtdƒ d dtdƒ d  ks>t‚t ttƒd t tdtfƒtd ksft‚t ttƒd td  tƒtdt ƒ tdt ƒdt   ddt   ks²t‚d S )Nr|   r   ru   r€   rm   )rH   r3   rp   r;   rq   r   r   r2   rj   rj   rj   rk   Útest_issue_8945–  s    >(r½  c                  C   sd   t rtdƒ tdƒ\} }}}tt|  t | ƒd ||t    t¡}tt|td|fƒj	ks`t
‚d S )NzToo slow for CI.zi L a brm   r   )r]   r\   r   r2   r   rp   Úrewriter    rH   rˆ   rq   )r‹   ÚLr™   r¯   Ú	integrandrj   rj   rk   Útest_issue_7130  s
    *rÁ  c                  C   sx   t dƒ\} }}}t| | ||gƒ}t||ƒt||ƒ ¡ ks>t‚t||ƒt| |d  d g|| g|| ggƒkstt‚d S )Nza b c trm   )r   rJ   rH   rW   r‰   rq   )r™   r¯   r°   r˜   Úvtrj   rj   rk   Útest_issue_10567¦  s    rÃ  c                   C   s6   t ttd  dt  d ƒtddfƒdt ks2t‚d S )Nrm   r­   é0   r€   rÖ   r  )rH   r-   rp   r   rq   rj   rj   rj   rk   Útest_issue_11742­  s    rÅ  c                  C   s2   t dƒ} ttt|  ƒ| ƒtt|  ƒt ks.t‚d S )Nr˜   )r   rH   r4   r   r;   rq   )r˜   rj   rj   rk   Útest_issue_11856±  s    rÆ  c                   C   s0   t ttdt ƒƒtddfƒttƒd ks,t‚d S ©Nru   r   rm   )rH   r-   r"   rp   r   rq   rj   rj   rj   rk   Útest_issue_11876¶  s    rÈ  c                   C   sV   t dttƒ dtdt ƒ  tdt ƒ tƒdtdt ƒ dtdt ƒ  ksRt‚d S )NiÄÿÿÿg3333333@r€   g333333Àr­   g      (@r   )rH   r    rp   rq   rj   rj   rj   rk   Útest_issue_4950»  s    ,ÿrÉ  c                   C   sP   t tttd ƒƒƒttttd ƒƒ d dt tttd ƒƒ d  ksLt‚d S )Nrm   r   )rH   r3   r"   rp   r2   rq   rj   rj   rj   rk   Útest_issue_4968À  s    rÊ  c                   C   s²   t dtd  tt tfƒtks"t‚t dtd  tddfƒtksBt‚t dtd d  tddfƒtksft‚t dtd  tddfƒt ksˆt‚t dtd d  tddfƒt ks®t‚d S )Nru   rm   r   r   )rH   rp   r   rq   rj   rj   rj   rk   Útest_singularitiesÄ  s
    " $"rË  c                  C   s¸   t ddd\} }tt| |  |  ||  ƒ| tt||  ƒ tt||  ƒf|ttƒ ttƒfƒtt| d |d  ƒ| t|d  t ƒ t|d  t ƒf|ttƒ ttƒfƒks´t‚d S )Nzx yTr§   r|   rm   )r   rH   r3   r-   r   rW   rq   )rp   r   rj   rj   rk   Útest_issue_12645Í  s    "þ&þýrÌ  c                   C   s6   t ttƒttƒd  tdtd fƒtddƒks2t‚d S )Nr|   r   r®   ru   )rH   r3   rp   r2   r   r   rq   rj   rj   rj   rk   Útest_issue_12677×  s    rÍ  c                   C   s6   t tdt ƒttƒ t tdtfƒtdƒ ks2t‚d S )Nr|   r   )rH   r2   rp   r   r"   rq   rj   rj   rj   rk   Útest_issue_14078Û  s    rÎ  c                   C   s(   t dttƒ tdtfƒtd ks$t‚d S rÇ  )rH   r%   rp   r   r   rq   rj   rj   rj   rk   Útest_issue_14064ß  s    rÏ  c                	   C   sp   t ddtttj ƒdttƒ    tƒtttjƒtttƒttjƒdttjƒ   ƒ ttjƒt   kslt‚d S r}   )rH   r    rp   r   r¼   r"   r   rq   rj   rj   rj   rk   Útest_issue_14027ã  s    &>ÿrÐ  c                   C   s&   t ttƒtdtd fƒtjks"t‚d S r‡  )rH   r5   rp   r   r   ÚInfinityrq   rj   rj   rj   rk   Útest_issue_8170è  s    rÒ  c                   C   sD   t dt tddfƒtjkst‚t dtd  tddfƒtjks@t‚d S )Nru   r   r   r|   )rH   rp   r   r—   rq   rj   rj   rj   rk   Útest_issue_8440_14040ì  s    rÓ  c                   C   s”   t dtt d  tddfƒdtd  dt  ks4t‚t ddt t t d  tddftddftddfƒdtdƒ dtdƒ  dtd	ƒ  kst‚d S )
Nru   rm   r   r   rû   r€   r®   r²   r|   )rH   rp   r   rq   rì   r"   rj   rj   rj   rk   Útest_issue_14096ñ  s    42"ÿrÔ  c                   C   sh   t tdtdtd  ƒ tddfƒ ¡ d ƒdk s4t‚t ttdtd  ƒtddfƒ ¡ d ƒdk sdt‚d S )Nru   r|   r   gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?)r   rH   r-   rp   rb   rq   rj   rj   rj   rk   Útest_issue_14144÷  s    4rÕ  c                   C   s(   t ttt ƒttƒ tƒ t¡s$t‚d S rv   )rH   r    r   rp   r"   rP  r:   rq   rj   rj   rj   rk   Útest_issue_14375ü  s    rÖ  c                  C   sX   t dƒtttƒ} t| tddftddftddfƒt| tddftddftddfƒksTt‚d S )Nre   r   ru   rm   r|   )r   rp   r   rì   rH   rW   rq   râ   rj   rj   rk   Útest_issue_14437  s    ÿr×  c                   C   sR   t dtttƒd ƒ tƒttttƒd ƒd ƒttttƒd ƒd ƒ ksNt‚d S r}   ©rH   r-   r    rp   r"   rq   rj   rj   rj   rk   Útest_issue_14470  s    rÙ  c                  C   s¨   t dt td ƒt  dtd   ƒdtd  t  dt td ƒt  d  } t| tƒt dtd  tt td ƒ  d ƒ tt dtd  ƒ t dtd  ƒ  ks¤t‚d S ©Nru   rm   r|   )r    rp   rH   rq   râ   rj   rj   rk   Útest_issue_14877  s    LHÿrÛ  c                  C   sB   t td  d ƒtd  t  } t| tddgƒt d ks>t‚d S )Nrm   ru   r   r­   )r-   rp   rH   r   rq   râ   rj   rj   rk   Útest_issue_14782  s     rÜ  c                  C   sJ   t td  d ƒtd  t  } t| tddgƒtjd td  ksFt‚d S )Nrm   ru   r   r|   r  )r-   rp   rH   r   r›   r   rq   râ   rj   rj   rk   Útest_issue_14782_slow  s     rÝ  c                  C   s4   t tddƒ tt  ƒ } t| t dtgƒtks0t‚d S )Nrü   rm   r   )rp   r   r    rH   r   rq   râ   rj   rj   rk   Útest_issue_12081  s    rÞ  c                  C   sD   dt  d } d|  td|  ƒ t d  }t|t ddgƒdks@t‚d S )Nru   r€   r   rm   r   )rp   r    rH   rq   )r   re   rj   rj   rk   Útest_issue_15285"  s    rß  c                   C   s”   t tt tt ƒ ttƒ tdtfƒ ¡ tttd ƒt	dtƒ ttd ƒt  t
tƒd dkfttt tt ƒ ttƒ tdtfƒdfƒkst‚d S )Nr   ru   T)rH   rp   rb   r    r"   r   rP   r.   rA   rB   r   rW   rq   rj   rj   rj   rk   Útest_issue_15432(  s    *4(þrà  c                  C   s„   t dƒ} tdtd\}}tttt | | | |   ƒtddt ttt | |  ƒ ttt | |  ƒ | | | |   ks€t‚d S )NÚomegazm p)ÚclsrÅ   rÆ   )rT   r   rS   rH   r    rp   r   rq   )rá  r×   rs   rj   rj   rk   Útest_issue_15124.  s
    $<ÿrã  c                	   C   s2  t ƒ  ttttƒƒ W 5 Q R X t ƒ 0 ttttƒtƒttttƒtttƒƒksRt‚W 5 Q R X t ƒ 4 ttttƒtƒ ¡ ttd d tt ƒks’t‚W 5 Q R X ttdd0 tttƒ 	t¡ttd d tt ƒksÔt‚W 5 Q R X t	tttƒtddfƒtt
jtƒkst‚tttƒ 	tddf¡tt
jtƒks.t‚d S )Nrm   Fro   r   ru   )r^   rW   r   rp   r   rq   r‰   r_   r`   rH   r   r¼   rj   rj   rj   rk   Útest_issue_152185  s    484(rä  c                  C   s€   t ttd  tdt ƒ ƒttd tdt ƒ ƒ tdtfƒ} t| tƒsLt	‚t
| ttƒd ttƒ   ttd ¡ƒdks|t	‚d S )Nrm   r   r®   )rH   r    rp   r2   r˜   r3   r   r¸   r.   rq   rP   r-   r   rÝ   r  rj   rj   rk   Útest_issue_15292F  s    >rå  c                   C   s.   t tdt ƒttƒ tƒdttƒ ks*t‚d S r¾   )rH   r3   rp   rq   rj   rj   rj   rk   Útest_issue_4514L  s    ræ  c                  C   sè   t ddd\} }}ttt| d ƒƒ| ||fƒ}ttt| d ƒƒ| ƒ}| |d|di¡ddt  ksft‚| | d¡| | d¡ ddt  ksŽt‚| |d|d	i¡tdƒ td
ƒ ks¶t‚| | d	¡| | d¡ tdƒ td
ƒ ksät‚d S )Nzx a bTr§   rm   ru   r|   r   rü   r   r   )r   rH   r    r   rÝ   r   rq   )rp   r™   r¯   ZdefiniteZ
indefiniterj   rj   rk   Útest_issue_15457P  s    "((rç  c                   C   sN   t tttƒ ttƒ tƒtttƒ ttƒ ttƒ ttƒ ttƒ ksJt‚d S rv   )rH   rp   r    r"   r:   rq   rj   rj   rj   rk   Útest_issue_15431Z  s    *ÿrè  c                  C   sü   t tt ƒ } tdtt ƒ ƒ}t| t ƒ|kr8| t ¡| ks<t‚t d tt ƒd  } t d  tt ƒ dtdtt ƒ ƒ  }t| t ƒ|kr’| t ¡| ks–t‚ttt ƒƒt d  } ttƒ tttt ƒƒƒ d ttt ƒƒt   }t| t ƒ|krô| t ¡| ksøt‚d S )Nrm   r|   r€   )	rp   r"   r:   rH   r
   rq   r-   r   r=   )re   ÚFrj   rj   rk   Ú"test_issue_15640_log_substitutions_  s     & .rê  c                  C   s¨   ddl m}  | dƒ}|j}ttt| t ƒ|ttfddt	t
tt t ƒ t t
tt t ƒt  tt kttk @ ttdƒ@ ft ttƒ tttƒ  dfƒks¤t‚d S )Nr   )Ú
CoordSys3DÚNTrŒ  )Zsympy.vectorrë  rp   rH   r2   r™   r¯   Úx_1Úx_2r.   r3   r   r   rq   )rë  rì  rp   rj   rj   rk   Útest_issue_15509k  s     Dþrï  c                  C   s¢   t ddd} t| td| d  ƒ | ƒt| d d d| d  d  | dkf| d  d d| d  d  tddƒ | d	kf| d d d| d  d  dfƒksžt‚d S )
Nrp   Tr§   r²   rm   r€   rü   éQ   r|   )r   rH   rÜ   r.   r   rq   rk  rj   rj   rk   Útest_issue_4311_fastt  s    ".ýrñ  c               	   C   sæ  t ddd} t ddd}t ddd}t ddd}ttt |  |d  ||  ƒ|ƒttƒttƒ tt |d  d	|   ƒ td
t |  | | dt| ƒ tt ƒ  ƒ dt| ƒ  ks¼t‚tddt|d    |ƒt tt ƒt|ttt ƒ  ƒ d tt ƒt|ttt ƒ  ƒ d   ks*t‚ttt |d  ƒ|ƒttƒt	ttƒ| ƒ dttƒ  kslt‚tdtt| ƒd  |ƒ| d tttt| ƒd ƒ d  ks²t‚tdtt| ƒd  |ddt fƒt ksât‚d S )NÚKTrÃ   rp   r§   r×   r˜   rm   r€   r   ru   r   )
r   rH   r    r   r-   r   r>   rq   r"   r<   )rò  rp   r×   r˜   rj   rj   rk   Ú%test_integrate_with_complex_constants|  s"    >ÿ,ÿ
ÿ
>"ÿBFró  c                  C   sx   t dƒ} t dddd}t|| |d   | d  | ƒ|d | |  t| ttt ƒ d|ƒ t|ƒ t|d ƒ kstt‚d S )Nrp   rb   TrG  ru   rm   )r   rH   rF   r!   r   r   rA   rq   )rp   rb   rj   rj   rk   Útest_issue_14241‹  s
    :ÿrô  c                   C   s<   t ttƒd ddttƒ   tddt gƒtd ks8t‚d S )Nrm   r   r€   r   )rH   r3   r˜   r2   r   rq   rj   rj   rj   rk   Útest_issue_13112’  s    rõ  c                  C   sP   t ddd} tttddt |   ƒ td| fƒ}|d| d  t d ksLt‚d S )	Nr£  TrÃ   ru   rm   r   r   r  )r   rH   rp   r/   r   rq   )r£  r‹   rj   rj   rk   Útest_issue_14709b–  s    $rö  c                  C   sl   t dƒ} t dƒ}tt|ƒ| |t | fƒt| ƒks6t‚tt|  ƒtd|  ƒ |  | dtfƒtdƒksht‚d S )Nrp   r˜   r   r   rm   )r   rH   r    r   r:   rq   r"   )rp   r˜   rj   rj   rk   Útest_issue_8614œ  s    &r÷  c                  C   sò   t ddd} t| d ƒdtd|  ƒ  t| ƒ t| ƒ }t|| ƒ}|tjksPt‚t| | d¡d ƒdkslt‚t| d ƒdttd	ƒd
 |  ƒ  t| ƒ t| ƒ }t|| ƒdtd|  d
 ƒ d dtd|  d ƒ d  td|  ƒd  ksît‚d S )Nr†   TrÃ   rm   gš™™™™™ù?ru   gÏRt?,eÀg:Œ0âŽyE>r­   r   iöÿÿÿé   r|   )r   r    rH   r   r—   rq   rÜ   rÝ   )r†   rÀ  Zsolutionrj   rj   rk   Útest_issue_15494£  s    ,
4rù  c               	   C   s~   t dƒ} tt| td  ƒtƒ ¡ ttttd |  ƒ ttdttd |  ƒ d ƒ ttd |  ƒ  t	| dƒfdƒkszt
‚d S )Nr   rm   r|   r   r"  )r   rW   r@   rp   r‰   r.   r:   r"   r-   r   rq   r¿   rj   rj   rk   Útest_li_integral³  s    ,.ÿþþrú  c                  C   sà   t dƒ} t dƒ}tj}| |d  t|||  ƒ t|||  fd| d| ||  f| d|   d ƒ d| td| ||  ƒ  }tt| | ƒ| ƒ}||ks¤t‚t ddd}| |i}tt|| ƒ|ƒ| |¡ 	¡ ksÜt‚d S )	Nrp   rb   ru   r|   rm   r€   Fr  )
r   r   r¼   rA   rC   rH   r3   rq   ZxreplacerŠ   )rp   rb   r£  ræ   ÚgotZ_xZrepsrj   rj   rk   Útest_issue_17473º  s    ( ÿÿrü  c                   C   s¢   t tttƒƒtd  tdtgƒt ks*t‚t tttƒƒtd  tdtgƒtdƒ d td  ksdt‚t tttƒƒtd  tdtgƒtdƒ d td  ksžt‚d S )Nrm   ru   r|   r   r²   )rH   r"   rp   r   r   rq   rj   rj   rj   rk   Útest_issue_17671Ç  s    *:rý  c                  C   s~   t dƒ} t dƒ}t dƒ}td|d | tdƒd   ||  d | d fƒ| |tdƒd  td| d d|   ƒ  kszt‚d S )Nrv  ÚCr   ru   rm   r|   r€   )r   rH   r   r-   rq   )rv  rþ  r   rj   rj   rk   Útest_issue_2975Í  s    rÿ  c                     sØ  t dƒ\‰‰ } tddd}ttˆˆ  ˆ d|fƒˆƒˆd |d d |d   ksTt‚ttˆtˆ ƒ ˆ d|fƒˆƒtˆd tˆ ƒ d ˆ d|fƒks–t‚tttˆ ˆ ƒˆ d|fƒˆƒtttˆ ˆ ƒ ˆ  t	ˆ dƒfd	ƒˆ d|fƒksæt‚ttttˆ ˆ ƒˆ d|fƒˆƒˆƒttttˆ ˆ ƒ ˆ d  t	ˆ dƒfˆ ˆ  dfƒˆ d|fƒˆ t
 kˆ t
k @ t	ˆ dƒ@ fd	ƒksnt‚ttˆˆ d| fƒˆƒ| ˆd  d ksšt‚tt‡ ‡fd
d„ƒ tt‡ ‡fdd„ƒ tt‡fdd„ƒ d S )Nzx n Mrì  Trc   ru   rm   r€   r   r"  c                      s   t tˆˆtˆ fƒtƒS rv   ©rH   r   r   rj   ©rb   rp   rj   rk   rz   à  r{   z!test_issue_7827.<locals>.<lambda>c                      s   t tˆˆdˆ fƒˆ ƒS r}   )rH   r   rj   r  rj   rk   rz   á  r{   c                      s   t tˆ ˆ dtfƒˆ ƒS r}   r   rj   rk  rj   rk   rz   â  r{   )r   r   rH   r   rq   r3   r   r.   r2   r   r   rZ   r‚   )rö   rì  rj   r  rk   Útest_issue_7827Ô  s,    :ÿ,ÿ"2ÿÿÿÿ
,r  c               	   C   sš   ddt   tt tt ƒ ƒddt     t d  t t tt tt ƒ ƒ  tt tt ƒ ƒ  } t| t ƒdtt tt ƒ ƒ dtt tt tt ƒ ƒ ƒ  ks–t‚d S rÚ  )rp   r-   r"   rH   rq   râ   rj   rj   rk   Útest_issue_4231å  s    Xr  c                  C   s@   t dtd t t  tƒ} t| tƒdtd t t  ks<t‚d S rà   )r
   rp   r   rH   rq   râ   rj   rj   rk   Útest_issue_17841ê  s    r  c                  C   sL  t dddd} | | d  tdƒd  | t| ttdƒƒ ƒ  d  }| ttdƒƒ | | dd|      }t|| ƒ| d  dtdƒd   | d	 t| ttdƒƒ ƒ  d| d	  d	  d	|  t| ttdƒƒ ƒ  d	t| ttdƒƒ ƒ  ksðt‚t|| ƒt| d	 tdƒd  ƒd	 d	t	d
ƒ ttdƒƒ t
d	t	d
ƒ |  ƒ  ksHt‚d S )Nrp   T©r¨   rÊ   r€   r   ru   rÖ   r®   rm   r|   )r   r0   r(   r"   r%   r2   rH   rq   r   r-   r1   )rp   Úf1Úf2rj   rj   rk   Útest_issue_21034ï  s    6$xÿFÿr  c                   C   sd   t ttƒtt ƒ tƒtt ƒtt ƒttƒ  ks8t‚t ttƒtt ƒ tdtfƒt ks`t‚d S rV  )rH   r"   rp   r    r:   rq   r   r   rj   rj   rj   rk   Útest_issue_4187û  s    8r	  c               	   C   s2  t dƒ} t dƒ}t dƒ}t dƒ}t|d t|ƒd  ||  d | d fƒ|d  |  d t| d ƒt| d ƒ d   |d | d t| d ƒt| d ƒ d    ksªt‚t|d t|| ƒd  ||  d | d fƒt|d  |  | d t| | d ƒt| | d ƒ d   | |d | | d t| | d ƒt| | d ƒ d   |  |t k|tk @ t|dƒ@ f| |d  dfƒksˆt‚dt | |  }t	dƒt	| ƒ |d  t
t	dƒt	| ƒ ƒ ttjd ƒ d	ttd
ƒd ƒ  | |d  d  }t|d t|| ƒd  ||  d | d fƒ|ks.t‚d S )Nr¿  rì   Úr0ÚR0rm   r€   r   Tr  r   )r   rH   r2   r3   rq   r.   r   r   r   r-   r?   rA   r   r›   )r¿  rì   r
  r  rv  Zsolrj   rj   rk   Útest_issue_5547   s(    8ÿ*ÿ
.>:ÿÿý^r  c                   C   s6   t dddt d  d  tdtfƒtddƒks2t‚d S )Nru   rm   r|   r   )rH   rp   r   r   rq   rj   rj   rj   rk   Útest_issue_15810  s    r  c                  C   sn  t dddd} t| ƒtd|  ƒ td|  tdƒ ƒ }| t| ƒd  | ddtdƒ    d|  d|  tdƒ  t| ƒ  | tdƒd	  td|  tdƒ ƒ  tdƒtd|  tdƒ ƒ d	  }|t|| ƒksÐt‚| tdƒ | d  }t| ƒtdƒ|   }|t|| ƒkst‚| d td
ƒ |  }| d d td
ƒt| ƒ  }|t|| ƒksPt‚| d|  tdƒ  }| d td|  tdƒ ƒtdƒ d  }|t|| ƒks t‚| tdƒ|   }| d d t| ƒtdƒ  }|t|| ƒksàt‚t| td
ƒ|   ƒ}| t| td
ƒ|   ƒ |  dttd
dƒƒ t| ttddƒƒ ƒ  }|t|| ƒksLt‚| d
 | t	  }| d
 d
 t	| d  d  | d tdƒ d  | d tdƒ d  | tdƒ  td
ƒt| t	 ƒ  }|t|| ƒksÔt‚d|  | td
ƒ  }d|  dt| td
ƒ ƒ td
ƒ  }|t|| ƒks t‚| d d|  tdƒ  }| d d | tdƒ d  td|  tdƒ ƒtdƒd  d  }|t|| ƒksŒt‚| d  | t	  }| d  d t	|   tdƒt| t	 ƒ  }|t|| ƒksÜt‚d|  d td
ƒ |  }d|  td
ƒ dtd
ƒ t| ƒ  }|t|| ƒks,t‚| d t
dƒ|   }| d d d|   t| ƒt
dƒ  }|t|| ƒksxt‚| tdƒ| d   }| d d tdƒd| d    }|t|| ƒksÀt‚d|  td	ƒ |  }d|  td	ƒt| ƒ  }|t|| ƒks t‚| d | td
ƒ d  |  }| d d | d tddƒtd
ƒ   d|  tdƒ  dtdƒ t| td
ƒ ƒ  tdƒ| td
ƒ   }|t|| ƒks–t‚| | tdƒ| d    |  }| d d | d d  tdƒt| ƒ  }|t|| ƒksît‚| | d
|  tdƒ   }| d d | d
  td
|  tdƒ ƒtdƒ d  }|t|| ƒksNt‚| tdƒ d| d  d|    }tdƒt| ƒ d tdƒt| d ƒ d  t| d ƒd  }|t|| ƒ ¡ ksÂt‚t| dtdƒ  ƒ}| t| dtdƒ  ƒ |  dt| dtdƒ  ƒ tdƒ  }|t|| ƒks&t‚|  dtdƒtdƒ|   d  tdƒ |   }| d  tdƒ d dt| ƒ tdƒ  d| d  td
ƒ tdƒ tdƒ d|  tdƒ tdƒ tdƒd   dtdƒ tdƒ tdƒd   d| d    tdƒ }|t|| ƒkst‚d| d  tdƒ d	|   }d| d  d d	tdƒ t| ƒ  tdƒ }|t|| ƒksjt‚d S )Nrp   Tr  r€   r|   rm   ru   r   r®   r   éûÿÿÿr­   r   rf   r  r³  iLÿÿÿéZ   r%  rû   )r   r"   r    rH   rq   r)   r(   r   r1   r   r%   rŠ   r3   )rp   re   ré  ZF_truerj   rj   rk   Útest_issue_21024  s”    (B"ÿÿ(Dd$@*$$ f(4 <<.nÿ
ÿÿ,r  c                  C   s`   t dƒ} tdtdt|  d    tt tfƒ ¡ tt| ƒd dƒ tt| ƒd dƒ ks\t‚d S )Nr™   ru   rm   r   )	r   rH   r   rp   r   rŠ   r8   r   rq   )r™   rj   rj   rk   Útest_issue_21721r  s    ($ÿr  c                  C   s€   t dƒ} ttd|  ƒddt| ƒ   | ddt fƒtd ks@t‚td|  ƒddt| ƒ   }t|| ddt fƒtd ks|t‚d S )	NÚthetar|   r   r€   r   rm   rÖ   r®   )r   rH   r2   r   rq   )r  rÀ  rj   rj   rk   Útest_issue_21831x  s    8r  c                   C   sB   t td tddƒ d tdtd  ƒ tddfƒtd ks>t‚d S )Nrm   ru   r€   r   rN  )rH   rp   r   r-   r   rq   rj   rj   rj   rk   Útest_issue_22033_integral  s    r  c                	   C   sº   t dttd td  dtd  td  fttdtd  ƒ tdtd  ƒftddfƒtks^t‚t ddtd  tdƒd   d dtdtd  ƒ ddtd     tddfƒtks¶t‚d S )Nru   rm   r   rû   r|   )rH   rì   rp   r   r-   r   rq   r   rj   rj   rj   rk   Útest_issue_21671„  s    ^r  c                  C   sp   t ddd} ttƒdttƒd   }t| t| ¡| dd | t¡}t|tdd|  krft|tƒksln t‚d S )NÚxrTr§   r€   rm   r§  )r   r2   rp   r3   rH   rÝ   rW   rq   )r  r…  Zres_realrj   rj   rk   Útest_issue_18527Š  s    r  c               	   C   sÄ  dt ttƒ tttƒ   } tt t  ttd ƒ ttd t d  ƒt   ƒ ttd t d  ƒ tt t  ttd ƒ ttd t d  ƒt   ƒttd t d  ƒ  }tt	tttd ƒd ƒ tttd ƒd ƒ  t
tdƒt
t dƒ@ ftttd ƒƒt t
t dƒft t t  ttƒ t ttƒ   t
tt t  ƒfttt  ttƒ t ttƒ   t
ttt  ƒf|dfƒ}t| tƒ|ks„t‚tddd\}}t|t |i}t|  |¡tƒ| |¡ksÀt‚d S )Nru   rm   r   Tza, brÃ   )r¯   r2   rp   r™   r3   r"   r5   r-   r.   r   r   r   rH   rq   r   rÝ   )re   ZFposré  Zapr  Úreprj   rj   rk   Útest_issue_23718“  s    FDÿ@2,ø
r  c                  C   sR   t dttd d ƒ tddfƒ} | tdtdƒ ƒ ks:t‚t |  ¡ d¡sNt‚d S )Nru   rm   r   r   r|   gC˜qBõ?)rH   r-   rp   r"   rq   ÚmathÚiscloserb   rþ   rj   rj   rk   Útest_issue_23566¨  s     r  c                   C   s\   t dttt d d ƒ ƒtttt ƒttt d ƒdkft ttt ƒ dfƒksXt‚d S )Nru   rm   T)	rH   r-   rp   r   r.   r#   r   r0   rq   rj   rj   rj   rk   Útest_pr_23583®  s    r  c                   C   sX   t ttƒtdtdt ƒ ƒ ƒttdt ƒd ƒttƒ d tttƒƒd  ksTt‚d S rà   )rH   r    rp   r-   r$   rq   rj   rj   rj   rk   Útest_issue_7264³  s    r  c                   C   s.   t ttƒtddfƒdtttjƒƒ ks*t‚d S rø   )rH   r*   rp   r1   r)   r   r¼   rq   rj   rj   rj   rk   Útest_issue_11254a·  s    r  c                   C   sB   t ttƒtƒtttd ƒƒks"t‚t ttƒtddfƒtks>t‚d S )Nrm   r   ru   )rH   r'   rp   r"   r)   rq   r   rj   rj   rj   rk   Útest_issue_11254b»  s    "r   c                   C   sD   t ttƒd  t¡tƒdttd ƒ ttd ƒd d  ks@t‚d S )Nrm   ru   )rH   r*   rp   r¾  r(   r)   rq   rj   rj   rj   rk   Útest_issue_11254dÀ  s    r!  c                  C   s   t dtd  td  dt  d ttd dt  d ƒ tddfƒ} | dtdƒ d dtddtdƒ  ƒ d	  ksxt‚t |  ¡ d
¡sŒt‚d S )Nr|   rm   r€   r   ru   i›ÿÿÿr­   é‡   r  g€2É{¢ÙÀ)rH   rp   r-   r"   rq   r  r  rb   rþ   rj   rj   rk   Útest_issue_22863Ä  s    D4r#  c                   C   s.  t ttttƒ ƒƒdtttƒt ƒ ttƒd td  tdƒd   tdttƒ dtttƒt ƒ  d ƒd  ksxt‚t tdt d tdt d ƒ ƒd ƒtdt tdt d ƒ d ƒdt d	 d
dt d tdƒd   d  tdt d ƒd  dt d d d	  td
ƒd	   d ks*t‚d S )Nrm   rÖ   r|   ru   r­   r€   r   r²   r   r  é(   )rH   r-   rp   r   r"   rq   rj   rj   rj   rk   Útest_issue_9723Ê  s    ^ÿ&^ÿÿÿr%  c                   C   sl   t ttƒtd  ttd  tt  t  tddtttƒttd  ttd   ttd    tƒksht‚d S )Nrm   Tr«  r|   r€   )rH   r"   rp   r°   r¯   r™   rX   rq   rj   rj   rj   rk   Útest_issue_23704Ò  s    00ÿr&  c                   C   sd   t dtdtdt ƒ ƒ ƒttdtdt ƒ ƒd ƒd ttdtdt ƒ ƒd ƒd  ks`t‚d S rà   rØ  rj   rj   rj   rk   Útest_exp_substitutionÚ  s    r'  c                   C   sx   t ttƒƒttttƒd ƒ tttƒƒ ks0t‚t ttƒƒdtttd ƒƒ ksTt‚t ttƒƒtttd ƒƒkstt‚d S rà   )	rH   r&   rp   r"   r)   rq   r*   r1   r'   rj   rj   rj   rk   Útest_hyperbolicÞ  s    0$r(  c                   C   sÌ   t ttd ƒƒtttd ƒ d ks(t‚t tttdƒd  ƒƒdt tttdƒd  ƒ d ksdt‚t dttd ƒ ƒtttƒ ttd ƒ ks”t‚t tttd ƒ ƒtd ttd ƒ ttƒ ksÈt‚d S )Nrm   r   r|   r®   r  ru   rû   )rH   r-   rp   rq   r   r"   rj   rj   rj   rk   Útest_nested_powä  s    (<0r)  c                   C   sè  t dtdtd  dt  d ƒ ƒtdƒtdtdƒ ttdƒd   d ƒ d ksXt‚t dtdtd  dt  d ƒ ƒtdƒtdtdƒ ttdƒd   d ƒ d ks°t‚t dtdtd  dt  d ƒ ƒtdƒtd	t dtdƒ tdtd  dt  d ƒ  d ƒ d kst‚t dtdtd  dt  d ƒ ƒttj tttj ƒ dtttj d ƒ  ksvt‚t dtt	t
t  ttd   ƒ tƒttt
dttƒ tt	t
t  ttd   ƒ  dt t  ƒttƒ ttd
ƒtt	t
d dt   d
ƒ@ ft
dt  t tt
dt  t ƒ ttt
dt  t d  ƒ ttd
ƒfdtt	t
t  ƒ t
 tt
d
ƒfttt	ƒ dfƒks„t‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ tdtdƒ ttdƒd   d ƒ d  kst‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ tdtdƒ ttdƒd   d ƒ d  ks˜t‚t dt d	 tdtd  dt  d ƒ ƒdtdtd  dt  d ƒ d dtdƒ td	t dtdƒ tdtd  dt  d ƒ  d ƒ d  ks6t‚t ttt  tt	t
t  ttd   ƒ tƒtt
 t dt  t ttt
dttƒ tt	t
t  ttd   ƒ  dt t  ƒttƒ tt	t
d dt   d
ƒft
dt  t tt
dt  t ƒ ttt
dt  t d  ƒ dfƒ ttt	t
t  ttd   ƒ t  ttd
ƒfdt tt	t
t  ƒ dt t	 tt	t
t  ƒ t	t
t  tdƒd  d   t
  t
 tt
d
ƒftt ttd  d  tt	ƒ dfƒksÚt‚t dtd  td  dt  d ttd dt  d ƒ ƒttd dt  d ƒtd dt d  tdƒd   dtdt dttd dt  d ƒ  d ƒ d  ksˆt‚t tdtd  dt  d ƒƒtd tdƒd  tdtd  dt  d ƒ dtdƒ tdt d tdƒd  ƒ d  ks
t‚t tt	t
t  ttd   ƒtƒtt	d t
d dt   ttt
dttƒ tt	t
t  ttd   ƒ  dt t  ƒttƒ tt	t
d dt   d
ƒft
dt  t tt
dt  t ƒ ttt
dt  t d  ƒ dfƒ t
dt  td  tt	t
t  ttd   ƒ  ttd
ƒfdt	t
t  tdƒd   dt
  tt
d
ƒftt	ƒt dfƒksft‚t tttd dt  d ƒ ƒtd d td	  tdƒd	  ttd dt  d ƒ dttdƒtd  d ƒ d  ksät‚d S )Nru   r|   rm   r€   r   r  rü   rT  r®   r   Tr•   r²   iùÿÿÿrN  rø  r   r­   r"  r  iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rH   r-   rp   r$   r   rq   r0   r"   r¼   r™   r¯   r°   r.   r   r„   rh   rj   rj   rj   rk   Útest_sqrt_quadraticë  sv    XXnX$hH  þÿ
*Vÿ
*Vÿ
*jÿ
,^Bÿÿ"ýýb"ûÿ
:jÿ
.*ÿÿ
 ^Bÿÿ.ýý,ûÿ
Vÿr*  c                   C   sî   t tttƒ ttƒ ƒtttƒ tttƒttƒ ƒ ks<t‚t tttƒd  tƒtttƒ tttƒƒ ksnt‚t td tttƒtdfƒ ƒtd tttƒtdfƒ dtd  tttƒtdfƒ  dt tttƒtƒ  dttƒ  ksêt‚d S )Nrm   r|   r€   r®   )	rH   rp   r6   r5   r"   rq   r2   r   re   rj   rj   rj   rk   Útest_mul_pow_derivative  s
    <2Xÿr+  )rf   (\  r  Zsympy.concrete.summationsr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.exprr   rÓ   r   r   r	   r
   Z
sympy.corer   Zsympy.core.numbersr   r   r   r   r   r   r   r   Zsympy.core.relationalr   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Zsympy.core.sympifyr   rº  r   r   r   r   r   Z&sympy.functions.elementary.exponentialr   r    r!   r"   Z%sympy.functions.elementary.hyperbolicr#   r$   r%   r&   r'   r(   r)   r*   Z(sympy.functions.elementary.miscellaneousr+   r,   r-   Z$sympy.functions.elementary.piecewiser.   Z(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Z'sympy.functions.special.delta_functionsr7   r8   rÔ   r9   r:   r;   r<   r=   r>   r?   r@   r›  rA   rB   Zsympy.functions.special.hyperrC   rD   Z-sympy.functions.special.singularity_functionsrE   Z&sympy.functions.special.zeta_functionsrF   Zsympy.integrals.integralsrH   Zsympy.logic.boolalgrI   Zsympy.matrices.denserJ   Zsympy.polys.polytoolsrK   rL   Zsympy.printing.strrM   Zsympy.series.orderrN   Zsympy.sets.setsrO   Zsympy.simplify.gammasimprP   Zsympy.simplify.simplifyrQ   Zsympy.simplify.trigsimprR   Zsympy.tensor.indexedrS   rT   rU   Z#sympy.functions.elementary.integersrV   rW   Zsympy.integrals.rischrX   Zsympy.physicsrY   Zsympy.testing.pytestrZ   r[   r\   r]   r^   r_   Zsympy.utilities.exceptionsr`   Zsympy.core.randomra   rp   r   rì   r™   r¯   r°   r„   rh   r†   r˜   rí  rî  rb   re   rl   rt   r‡   rŒ   rŽ   r”   rž   r¤   r¥   r¬   r±   r³   r´   rµ   r·   r»   r½   rÀ   rÁ   rÂ   rÇ   rÈ   rÉ   rÍ   rÏ   rÕ   rØ   rÙ   rÚ   rß   rá   rã   rå   rç   ré   rë   rí   rî   rï   rô   r÷   rù   rú   r  r  r  r  r  r  r!  r#  r$  r'  r+  r-  r/  r0  r3  r4  r5  r7  r9  r:  rF  rL  rQ  rS  rU  rW  rY  r[  r]  rb  rc  rd  rg  ri  rj  rp  rq  rr  rs  ru  rw  ry  rz  r|  r}  r  r€  r‚  rƒ  r„  r†  rˆ  r‹  rŽ  r‘  r’  r“  r”  r•  r–  r—  r˜  rœ  r  rž  r   r¢  r¤  r¥  r¨  rª  r¬  r®  r¯  r±  r²  r´  rµ  r·  r»  r¼  r½  rÁ  rÃ  rÅ  rÆ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rÙ  rÛ  rÜ  rÝ  rÞ  rß  rà  rã  rä  rå  ræ  rç  rè  rê  rï  rñ  ró  rô  rõ  rö  r÷  rù  rú  rü  rý  rÿ  r  r  r  r  r	  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r#  r%  r&  r'  r(  r)  r*  r+  rj   rj   rj   rk   Ú<module>   sú  ((((  


.
			

	0
3!

			
			 


		 	

	Y	*