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    L?hï6 ã                   @   sè  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
mZ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mZmZ d d	lmZmZ d d
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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„ Z.dhdi„ Z/djdk„ Z0dldm„ Z1dndo„ Z2dpdq„ Z3drds„ Z4dtdu„ Z5dvdw„ Z6dxdy„ Z7dzd{„ Z8ed|d}„ ƒZ9d~d„ Z:d€d„ Z;d‚dƒ„ Z<d„d…„ Z=d†d‡„ Z>dˆd‰„ Z?dŠd‹„ Z@dŒd„ ZAdŽd„ ZBdd‘„ ZCd’d“„ ZDd”d•„ ZEd–d—„ ZFd˜d™„ ZGedšd›„ ƒZHedœd„ ƒZIdždŸ„ ZJd d¡„ ZKd¢d£„ ZLd¤d¥„ ZMd¦d§„ ZNd¨d©„ ZOdªd«„ ZPd¬d­„ ZQd®d¯„ ZRd°d±„ ZSd²d³„ ZTd´dµ„ ZUd¶d·„ ZVd¸d¹„ ZWdºd»„ ZXd¼d½„ ZYd¾d¿„ ZZdÀdÁ„ Z[edÂdÃ„ ƒZ\dÄdÅ„ Z]dÆdÇ„ Z^dÈdÉ„ Z_dS (Ë  é    N)ÚSumÚ	summation)ÚAdd)ÚTuple)ÚExpr)Ú
DerivativeÚFunctionÚLambdaÚdiff)Ú
EulerGamma)ÚEÚIÚRationalÚnanÚooÚpiÚzooÚ	all_close)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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er`   Úoptions© rh   úV/var/www/html/venv/lib/python3.8/site-packages/sympy/integrals/tests/test_integrals.pyÚNS3   s    rj   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prh   rh   ri   Útest_poly_deprecated7   s     rr   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   rn   Úprincipal_valuerh   ©Úgrh   ri   Ú<lambda>F   ó    z&test_principal_value.<locals>.<lambda>c                      s   t ˆ ƒ ¡ S rt   )rW   ru   rh   rv   rh   ri   rx   G   ry   é   c                      s   t ˆ tt dfƒ ¡ S ©Nrs   )rW   rn   r   ru   rh   )Úlrh   ri   rx   K   ry   rk   éþÿÿÿé   )rn   rW   r   ru   ro   Úyr   rZ   Ú
ValueErrorÚtogetherr-   r   r"   r1   )ÚdÚvÚsrc   rh   )rw   r|   ri   Útest_principal_valueA   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expandro   )ÚiZsymsr„   rh   rh   ri   Ú	diff_test^   s    *rŠ   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   rs   éÿÿÿÿr}   rk   )rH   r"   rn   ro   r   r    rh   rh   rh   ri   Útest_improper_integralh   s    rŒ   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 )Nrs   rk   é
   é   )
rW   r`   Úlimitsr   ro   r   rn   r   rO   r   )Ús1Ús2Zs3Zs4Zs5Zs6Zs7rh   rh   ri   Útest_constructorn   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   rs   rk   é   rz   r`   F©Zcommutative)rW   rn   ro   r   r   ÚNaNr
   r   ÚtrH   r‡   rˆ   ÚaZatomsrc   ÚZeroÚOnerŠ   r    Úis_commutativer   ©rf   r`   rh   rh   ri   Útest_basics„   sR    ÿ
þÿ
ÿÿ
ÿ6ÿ
,20,"$8rœ   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_wrtrš   rh   rh   rh   ri   ÚTest³   s   r    rs   rk   r   rz   c                   S   s   t td td ƒS r{   ©rH   rn   rh   rh   rh   ri   rx   »   ry   ztest_diff_wrt.<locals>.<lambda>c                   S   s   t td td ddfƒS )Nrs   r   r¡   rh   rh   rh   ri   rx   ¼   ry   )r   rH   ro   r   rZ   r€   )r    r–   rh   rh   ri   Útest_diff_wrt²   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 )Nrz   rŽ   rk   rs   )rŠ   rW   rn   r   ro   rh   rh   rh   ri   Útest_basics_multiple¿   s    2,. $r£   c                  C   sô   t ddd\} }tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ksHt‚| ¡  ¡ | ¡  ¡ ksdt‚| ¡  ¡ | ¡  ¡ ks€t‚tddd}t| | |fƒ}| ¡  ¡ | ¡  ¡ ks¸t‚| ¡  ¡ | ¡  ¡ ksÔt‚| ¡  ¡ | ¡  ¡ ksðt‚d S )NzA BFr”   rn   T)Úcomplex©Úreal)r   r   rW   Zadjointr‡   ro   Ú	conjugateZ	transpose)ÚAÚBrn   rq   rh   rh   ri   Útest_conjugate_transposeÉ   s    rª   c                  C   sD  t dtdtfƒdkst‚t dtdtfƒdt ks4t‚t ttdtfƒtd d ksTt‚t dt tdtfƒdtd  d ks|t‚t dtd  tdtfƒtd ks t‚t dt tdtfƒttƒksÀt‚t dtd  tdtfƒdt d ksèt‚t td dt  d tdtfƒtd d dtd  d  dt  ks2t‚t td tƒtd d ksRt‚t dt t d tƒdt d td  d ks†t‚td	ƒ} td
ƒ}t tt tdtfƒttd  d ksÀt‚t ttd  tdtfƒttd  d ksît‚t ttd  | t  | tdtfƒttd  d | td  d  |t  ks@t‚d S )Nr   rz   rk   rs   r‹   rŽ   é   é   ÚbÚcr~   )rH   r–   rn   ro   r"   r   r—   )r­   r®   rh   rh   ri   Útest_integrationÙ   s     ($ (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 )	Nrk   r   rs   r‹   é	   rz   r«   r~   )rH   rn   r   r   ro   r"   r3   rh   rh   rh   ri   Útest_multiple_integrationì   s    06Fÿr±   c                   C   s"   t tt ƒtdtfƒdkst‚d S ©Nr   rs   )rH   r    rn   r   ro   rh   rh   rh   ri   Útest_issue_3532ô   s    r³   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 )Nrz   rk   rŽ   rs   r}   )rH   r-   rn   ro   rh   rh   rh   ri   Útest_issue_3560ø   s    *&r´   c                   C   s   t tdd„ ƒ d S )Nc                   S   s   t ttfƒS rt   r¡   rh   rh   rh   ri   rx   ÿ   ry   z"test_issue_18038.<locals>.<lambda>)rZ   ÚAttributeErrorrh   rh   rh   ri   Útest_issue_18038þ   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 )Nrk   rz   Frm   Tr~   )rK   rn   r   r\   rW   r]   r^   rH   Ú
isinstancero   ÚgensÚas_expr)rq   ZqxZqyrh   rh   ri   Útest_integrate_poly  s     4rº   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 )	Nrk   rz   r   rs   Frm   Tr~   )rK   rn   r   r\   rW   r]   r^   rH   r   r·   ro   r¸   r¹   r   ÚHalf)rq   ZQxZQyrh   rh   ri   Útest_integrate_poly_definite  s     "r¼   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   rk   c                   S   s   t dƒS ©Nrk   rG   rh   rh   rh   ri   rx   0  ry   z)test_integrate_omit_var.<locals>.<lambda>c                      s   t tˆ  ƒS rt   r¡   rh   ©r   rh   ri   rx   1  ry   )r   rH   rn   ro   rZ   r€   rh   rh   r¾   ri   Útest_integrate_omit_var+  s    r¿   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   rk   iè  ié  )r   rH   rn   r3   ro   r¾   rh   rh   ri   Útest_integrate_poly_accurately4  s    *rÀ   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   rk   r‹   rs   )r   rH   rn   ro   r¾   rh   rh   ri   Útest_issue_3635=  s    rÁ   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condsrs   rk   )r   rH   rn   ro   r    r3   r¾   rh   rh   ri   Útest_integrate_linearterm_powE  s
    *(4ÿrÆ   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 )Nrk   rz   rŽ   )rH   r   r-   rn   ro   r   rh   rh   rh   ri   Útest_issue_3618N  s    . .ÿrÇ   c                   C   s$  t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒksJt‚t ttd t ƒtƒttttd  ƒtd  ttd dƒftdfƒks”t‚t ttd t ƒttd t ƒ tƒttttd  ƒtd  ttd dƒftdfƒttttd  ƒtd  ttd dƒftdfƒ ks t‚d S )Nrs   r   T)rH   r2   r`   rn   r.   r3   r   ro   rh   rh   rh   ri   Útest_issue_3623T  s    $ ÿ
$ ÿ
$..ÿÿrÈ   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 )
Nr`   T)rb   Únonzerog      à¿rk   r}   r   ç       @r‹   )r   rH   rn   r3   r   r2   ro   r   ©r`   rh   rh   ri   Útest_issue_3664^  s    &ÿ,ÿrÌ   c                   C   s4   t tdtd dt  d  tddfƒƒdks0t‚d S )Nrs   rk   r«   é   r~   z1.10714871779409)rj   rW   rn   ro   rh   rh   rh   ri   Útest_issue_3679f  s    rÎ   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fresnelsrk   )
Úsympy.core.functionrÐ   Ú'sympy.functions.special.error_functionsrÑ   rH   r3   rn   r-   r   ro   )rÐ   rÑ   rh   rh   ri   Útest_issue_3686k  s
    *ÿrÔ   c                  C   s@   t j} t j}tt|  | td| d| fƒd|  | ks<t‚d S )Nrs   rŽ   é   )rY   Úmr„   rH   rn   ro   )rÖ   r„   rh   rh   ri   Útest_integrate_unitsr  s    r×   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 r½   )rH   r   rn   ro   rh   rh   rh   ri   Útest_transcendental_functionsx  s    $ÿrØ   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 )Nrs   r   rk   r¬   r‹   )rH   r"   rn   r   ro   rh   rh   rh   ri   Útest_log_polylog}  s    .rÙ   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~   rk   é*   g»½×Ùß|Û=)r"   rn   r
   rH   ÚabsÚsubsre   ro   )rc   Zfidrh   rh   ri   Útest_issue_3740‚  s    rÝ   c                   C   s&   t ddtd   tƒttƒks"t‚d S ©Nrs   rk   )rH   rn   r1   ro   rh   rh   rh   ri   Útest_issue_3788ˆ  s    rß   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 r½   r¡   rh   ©rc   rh   ri   rx     ry   z!test_issue_3952.<locals>.<lambda>)r3   rn   rH   r2   ro   rZ   r€   rh   rh   rà   ri   Útest_issue_3952Œ  s    rá   c                   C   s6   t dt dt  tƒdt tdƒ td  ks2t‚d S r½   ©rH   rn   r"   ro   rh   rh   rh   ri   Útest_issue_4516’  s    rã   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 )Nrs   r   r‹   rk   )rH   r    r   rn   r   r   r   r»   r   r   ro   )Úansrh   rh   ri   Útest_issue_7450–  s    rå   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 )Nrs   rk   rz   r   rŽ   ©	rH   r2   rn   r   r-   ro   r1   r5   rV   rh   rh   rh   ri   Útest_issue_8623›  s    NFÿÿrç   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 ©Nrs   rk   r   rz   ræ   rh   rh   rh   ri   Útest_issue_9569¡  s    ,ré   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„   TrÂ   rk   r   )r   r    Úzr   r-   r   rH   rn   r   r<   ro   )r„   ZpzZpzgxrh   rh   ri   Útest_issue_13733¦  s    2>ÿÿrë   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 rè   ræ   rh   rh   rh   ri   Útest_issue_13749®  s    ,rì   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 rÞ   )rH   r    rn   rX   ro   rh   rh   rh   ri   Útest_issue_18133³  s    rí   c                  C   s¶   d} d}t |t t|  t t t t ƒ t|  t t t t ƒ tt  ttdƒftt|  t t t t ƒ dfƒ}t	dt t tt tt   d  }t
t|tƒ|ƒs²t‚d S )Ng    €„NAgíµ ÷Æ>r   Tr}   gŽíµ ÷Æ >)r.   r   r    r   r–   r   rn   rê   r   r   r   rH   ro   )r—   r­   ÚrZfunrh   rh   ri   Útest_issue_21741·  s    N ÿ$rï   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 )Nrk   c                 S   s    | | d t | | d t ƒ S r{   )r3   rn   )r‰   Újrh   rh   ri   rx   Á  ry   ztest_matrices.<locals>.<lambda>rz   )rJ   rH   rn   r2   ro   )ÚMrh   rh   ri   Útest_matricesÀ  s
    
þrò   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   rs   rk   )rH   rc   rn   rW   ro   r
   r"   rh   rh   rh   ri   Útest_integrate_functionsÉ  s     ,0rô   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 r½   )rH   r   rc   rn   ro   r   rW   rh   rh   rh   ri   Útest_integrate_derivativesÑ  s
     *ÿrõ   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 )Nrk   rs   r‹   rz   r   éüÿÿÿéýÿÿÿr~   c                      s   ˆ   td¡S r{   )Ú	transformrn   rh   ©r‰   rh   ri   rx   õ  ry   z test_transform.<locals>.<lambda>c                      s   ˆ   ttt ¡S rt   ©rø   rn   r„   r–   rh   rù   rh   ri   rx   ö  ry   c                      s   ˆ   tt ¡S rt   ©rø   rn   r„   rh   rù   rh   ri   rx   ÷  ry   c                      s   ˆ   tttf¡S rt   rú   rh   rù   rh   ri   rx   ø  ry   c                      s   ˆ   dt dt ¡S r½   rû   rh   rù   rh   ri   rx   ù  ry   c                      s   ˆ   td t¡S r½   rû   rh   rù   rh   ri   rx   ü  ry   r—   T)Únegativer­   rÂ   )rW   rn   r   r‡   rø   ro   r3   r   r    r   rê   r­   r„   rZ   r€   r   )r—   ZfxÚfyZ_3ÚamÚbprh   rù   ri   Útest_transformØ  sZ    0$8ÿ
  ÿ
ÿ
ÿ
ÿ22r   c                  C   s^   t jttƒ ttdtd  ƒ d  } ttttƒƒtƒ| ks@t‚ttt	tƒƒtƒ| ksZt‚d S rÞ   )
r   r»   r0   rn   r-   rH   r2   ro   r3   r/   rà   rh   rh   ri   Útest_issue_4052  s    &r  c                  C   sŠ  t tttddfƒdƒdkst‚tttd  ƒtt tfƒ} t | dƒdksLt‚t | d t ttddƒ  dƒdkstt‚t	d	ƒ}d
t
dƒ dd|d    }dt
dƒ d| d  t
d|d  | d ƒd  }d|d  d d|d  d|  d d  }t
dƒd|d  d|  d  d|d  d|  d d  }|||  | }t t||ddfƒdƒt dt
dƒ dt  dtt
dƒƒ  d dƒksŽt‚t tttdt ƒƒdt td   tddfƒdƒt ddƒksÐt‚t ttt
td d ƒƒt
td d ƒtd d   tddfƒdƒt dtd  d dƒks.t‚t ttttt ƒtt t ƒ td d   tdtfƒdƒt ddƒkszt‚t tttttƒttƒ ƒƒttd td fƒdddt ddƒksÀt‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks t‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks@t‚t dttdttd ƒ ƒtt tfƒ dddt ddƒks€t‚t tdtd tddfƒ  dd!dd"d#ks®t‚tttƒtd  tdtfƒjdd$}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 ).Nrk   rŽ   rd   z10.5000000000000z1.77245385090552rs   l      Fµx:^V )z2.71828182845904e-20z2.71828182845905e-20r–   r«   rz   é   r~   é   éù   é6   éA   r   é2   é1   é¢   rÕ   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)rÍ   é   é   zsqrt(1-x**2)é   )Úmaxnr  )z0.0Ú0)r  g\Âõ(\ß?gR¸…ëQà?Úosc)Zquadz0.504067061906928r‹   z0.276374705640365zIntegral(x, x)zIntegral(x, (x, y)))rj   rW   rn   ro   r    r   r   r   r   r   r-   r1   r"   r3   r2   re   r   )Úgaussr–   r—   r­   r®   r‚   rc   rh   rh   ri   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 )	Nrs   rŽ   r~   Tr  )z-0.000976138910649103z0.965906660135753z1.93278945918216rk   z0.0144361088886740)rj   rH   rn   rÜ   ro   rW   rh   rh   rh   ri   Útest_evalf_issue_939C  s    $ÿ( ÿÿr  c                  C   sŠ   t ttƒtt  tddftddfƒ} t| dƒdks6t‚| tddƒdtdƒ d  ksXt‚t tttt  ƒtddftddfƒtj	ks†t‚d S )	Nrs   rk   r‹   rd   z2.43790283299492rö   rz   r«   )
rH   r-   rn   r   rj   ro   r   r3   r   r˜   ©Úresrh   rh   ri   Ú(test_double_previously_failing_integralsR  s    $"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 )Nrz   rŽ   r‹   r~   r   r   iúÿÿÿr}   rs   rk   rö   r“   r«   )rE   rn   r—   rH   ro   r   rU   rW   r‡   r   rc   )	Zin_1Zout_1Zin_2Zout_2Zin_3Zout_3_1Zout_3_2Zin_4Zout_4rh   rh   ri   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   rk   r~   rs   r   ée   )
rH   r7   rn   rc   r   ro   r   r    r   r-   rp   rh   rh   ri   Útest_integrate_DiracDeltaz  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 )Nrs   r‹   Tr   rk   ©r   T)rH   rn   r   r.   r   r"   ro   r    r`   r2   r3   rê   r   r–   r-   rh   rh   rh   ri   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 )Nrn   Tr¥   rk   r   rz   r~   r  rÕ   rs   r}   r®   )Zextended_real)r   rH   r,   ro   r+   r   r    r.   r   r-   r   r<   )rn   r®   Zint1Zint2Zint3rh   rh   ri   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$t‚t
ddd\} }t t| ƒ| ƒt| d  d | dkf| d d dfƒkspt‚t td|  d ƒ| ƒt| d  d|   | dkf| d d|   d dfƒksÀt‚t t| |d  ƒ| ddfƒd|d  td|d ƒ d|d   td|d ƒd  d kst‚t tt| ƒ ƒ| ƒtt| ƒ| dkfdt|  ƒ dfƒks\t‚t td|  d ƒ| ƒt|  | dk f| d dfƒks”t‚t d|  t| d d ƒ | ƒt| d | dk f| d  d | dk f| d dfƒksêt‚t t| ƒ| |d fƒt|d |d dkf| d |d dk fdƒks4t‚d S )Nr}   rs   rŽ   rk   r   rz   r~   éñÿÿÿrd   iÓ  r‹   r  zt sTr¥   r¬   é   r  )rH   r   rn   r   ro   r   r»   r   r3   r   r   r.   rÛ   r,   r    )r–   r„   rh   rh   ri   Útest_integrate_Abs_sign»  sL    "&$(&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 ©Nrz   r   rs   rk   r}   )rW   r    rn   r   rÜ   ro   r	   r   ©rf   rc   Úconvrh   rh   ri   Ú
test_subs1Ö  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    rn   r   r–   rÜ   ro   r	   r   r#  rh   rh   ri   Ú
test_subs2à  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   rs   rz   rk   r}   r&  r#  rh   rh   ri   Ú
test_subs3ê  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#  rh   rh   ri   Ú
test_subs4ò  s
    ,&r*  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 )Nrk   rŽ   rs   r   )	rW   r    rn   r   rÜ   ro   r   r‡   Úis_zero©rf   rh   rh   ri   Ú
test_subs5ú  s    (*(**r-  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 brs   )r   rW   rn   r   rc   rÜ   ro   )r—   r­   rf   rh   rh   ri   Ú
test_subs6  s    ,(,<>,r.  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 rÞ   )rW   rn   r   rÜ   ro   r3   r,  rh   rh   ri   Ú
test_subs7  s     ÿ*ÿr/  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 )Nrk   rs   T)Úforce)rW   rc   rn   r   rˆ   ro   r   r,  rh   rh   ri   Útest_expand"  s     8 ÿr1  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 ©Nrk   rz   )rW   r    rn   rh   rh   rh   ri   rx   ,  ry   z+test_integration_variable.<locals>.<lambda>c                   S   s   t ttd  ƒdt tfƒS r2  )rW   r    rn   r   rh   rh   rh   ri   rx   -  ry   )rZ   r€   rh   rh   rh   ri   Útest_integration_variable+  s    r3  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 )Nrk   rs   r   )rW   r2   rn   r3   rˆ   ro   rh   rh   rh   ri   Útest_expand_integral0  s    *"ÿÿ$ÿÿr4  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 )Nrz   rs   rk   r   Úmidpoint©Úmethodr«   éÙ   r~   r  rÕ   é9   i	  é   iIÎ  iÚ  r“   éV   r¬   é   g      à?r   c                      s
   ˆ   d¡S )Nr~   ©Úas_sumrh   r,  rh   ri   rx   D  ry   z'test_as_sum_midpoint1.<locals>.<lambda>)
rW   r-   rn   r>  ro   rÛ   r`   r   rZ   ÚNotImplementedErrorrh   rh   r,  ri   Útest_as_sum_midpoint19  s$    *ÿÿ

ÿ
ÿ
ÿ
((r@  c                  C   s  t tt d tddfƒ} tdddd}| jddd ¡ tdd	ƒt td  ksRt‚| jddd ¡ td
dƒt td  ks~t‚| jddd ¡ tddƒt td  ksªt‚| jd	dd ¡ tddƒt td  ksÖt‚| j|dd ¡ td t tddƒ dd|d    kst‚d S )Nrk   r   rs   r`   T©rÃ   rb   r5  r6  r~   rŽ   r  rz   é#   él   é   é@   rÕ   )rW   rn   r   r   r>  rˆ   r   ro   r›   rh   rh   ri   Útest_as_sum_midpoint2G  s    ,,,,$ÿrF  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$t‚| jdddd t	¡s@t‚d S )Nrk   r   rs   Úleftr6  r«   rz   rŽ   r:  r~   r“   é    r¬   r   F)r7  Úevaluate)
rW   rn   r   r>  rˆ   ro   r   r`   Úhasr   r,  rh   rh   ri   Útest_as_sum_leftR  s    0668ÿ
rK  c                  C   s:  t tt d tddfƒ} | jddd ¡ ddt  td  ksBt‚| jddd ¡ tddƒttddƒ  td  ksxt‚| jddd ¡ td	d
ƒttddƒ  td  ks®t‚| jddd ¡ tddƒttddƒ  td  ksät‚| jtdd ¡ td t tddƒ tt  ddt   ddtd    ks6t‚d S )Nrk   r   rs   Úrightr6  rŽ   r«   rz   r<  r:  r~   rd   rH  r¬   )rW   rn   r   r>  rˆ   ro   r   r`   r,  rh   rh   ri   Útest_as_sum_right]  s    *6668ÿrM  c                  C   s.  t tt d tddfƒ} | jddd ¡ td t tj ks@t‚| jddd ¡ td t tddƒ kslt‚| jddd ¡ td t tdd	ƒ ks˜t‚| jd
dd ¡ td t tddƒ ksÄt‚| jt	dd ¡ td t tddƒ ddt	d    kst‚t t
tƒtddfƒ dd¡tjks*t‚d S )Nrk   r   rs   Z	trapezoidr6  rz   r«   é   r  r~   r  rH  r¬   )rW   rn   r   r>  rˆ   r   r»   ro   r   r`   r   r,  rh   rh   ri   Útest_as_sum_trapezoidg  s    (,,,$ÿ
rO  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 )
Nrk   r   rs   c                      s
   ˆ   d¡S )Nr‹   r=  rh   r,  rh   ri   rx   t  ry   z$test_as_sum_raises.<locals>.<lambda>c                      s
   ˆ   d¡S ©Nr   r=  rh   r,  rh   ri   rx   u  ry   c                   S   s   t tƒ d¡S )Nrz   )rW   rn   r>  rh   rh   rh   ri   rx   v  ry   c                      s
   ˆ   t¡S rt   )r>  r   rh   r,  rh   ri   rx   w  ry   c                      s   ˆ j dddS )Nrz   Zxxxx2r6  r=  rh   r,  rh   ri   rx   x  ry   )rW   rn   r   rZ   r€   rh   rh   r,  ri   Útest_as_sum_raisesr  s    rQ  c                  C   s4   t t ttƒtƒ} t tttƒ}|  ¡ | ¡ ks0t‚d S rt   )rW   rn   r‡   ro   ©rf   rc   rh   rh   ri   Útest_nested_doit{  s    rS  c                  C   s   t td td dfƒ} t td tdd fƒ}|  ¡ tddƒks>t‚| ¡ tddƒksTt‚t tt td tfƒ tt¡t tt td tfƒksˆt‚t tt ttd fƒ tt¡t tt ttd fƒks¼t‚ttd td dfƒtddƒksÞt‚ttd tdd fƒtddƒkst‚tddƒtddƒkst‚d S )Nrk   rs   rz   r‹   zx**2)rn   Ú1N)	rW   rn   r‡   r   ro   r   rÜ   r–   rH   rR  rh   rh   ri   Útest_issue_4665  s    44"$rU  c                  C   s*   t td tddfƒ} | t | jŽ ks&t‚d S )Nrk   r‹   rs   )rW   rn   Úargsro   r,  rh   rh   ri   Útest_integral_reconstructŽ  s    rW  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 )	Nrk   r   rs   rz   F©Údeeprc   r~   )
rW   rn   r‡   r   ro   r   r—   r    ÚlistÚreversed)rf   rc   r   rh   rh   ri   Útest_doit_integrals“  s     & r\  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 )Nrs   rk   rŽ   rd   r~   T)rH   r-   rn   r.   r   r   ro   r"   rh   rh   rh   ri   Útest_issue_4884¢  s    Bÿ>ÿÿýÿr]  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 )Nrk   rs   r‹   T)rH   rn   r`   r"   r.   r   ro   rh   rh   rh   ri   Útest_issue_18153«  s    *&ÿÿþýÿr^  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   ©rn   r   rê   Frs   Trk   rÊ   rz   )Ú	sympy.abcrn   r   rê   rW   Z	is_numberro   r`   r   r3   r2   rc   )rn   r   rê   r‰   rh   rh   ri   Útest_is_number´  s0    ((((.ra  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   r_  rs   rk   )	r`  rn   r   rê   rW   r†   ro   Úsetrc   r_  rh   rh   ri   Útest_free_symbolsÔ  s:     ÿ
ÿ
 ÿ
 ÿ
 ÿ
&rc  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   )rn   rÖ   rs   rk   FT)r`  rn   rÖ   rW   r+  ro   r   r    r   r3   r   )rn   rÖ   r‰   rh   rh   ri   Útest_is_zeroð  s     $rd  c                     s\   ddl m}  tt| ƒ| | fƒ}| | ¡‰ |j| dd ¡ t‡ fdd„tdƒD ƒŽ ksXt	‚d S )Nr   ©rn   r«   rË   c                    s   g | ]}t ˆ ƒ‘qS rh   )Únext)Ú.0rð   r,  rh   ri   Ú
<listcomp>  s     ztest_series.<locals>.<listcomp>r~   )
r`  rn   rW   r2   ZlseriesZnseriesZremoveOr   Úrangero   )rn   r‰   rh   r,  ri   Útest_series  s    
rj  c                  C   sV   t dƒ} tdt| ƒ |  | ƒt| ƒt| ƒ ks2t‚tt| ƒd |  | ƒ t¡sRt‚d S )Nrn   rs   rk   )	r   rH   r3   r"   r;   ro   r2   rJ  r9   re  rh   rh   ri   Ú!test_trig_nonelementary_integrals
  s    *rk  c               	   C   s4  t dƒ} t dƒ}t ddd}tt| d |d  ƒ| ƒ|d t| | ƒ d | t| d |d  ƒ d  ksnt‚tt| d |d  ƒ| ƒ| t| d |d  ƒ d |d t| t| d |d  ƒ ƒ d  ksÐt‚t ddd} t ddd}td| d |d  td	ƒ  | ƒ| |d t| d |d  ƒ  ks0t‚d S )
Nrn   r   rê   TrÂ   rk   r¥   rs   z3/2)r   rH   r-   r$   ro   r"   r   r_  rh   rh   ri   Útest_issue_4403  s    2ÿBÿ ÿrl  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 )Nrk   r~   r}   rö   )rH   r-   rn   r1   ro   rh   rh   rh   ri   Útest_issue_4403_2#  s    2ÿrm  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RTrÂ   rk   r   r~   )r   rH   r-   rn   r   ro   )rn  rh   rh   ri   Útest_issue_4100(  s    ro  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wrn   r   rê   rc   rk   rs   )r`  rp  rn   r   rê   r   rW   ro   rV  r   rH   r‡   )rp  rn   r   rê   rc   rh   rh   ri   Útest_issue_5167-  s(    (",.0ÿ
*,>"":&:ÿrq  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 )Nrê   TrÂ   rk   rs   r~   r‹   )r   rH   r    r"   rn   r-   r   r   r<   r   r»   ro   r>   ©rê   rh   rh   ri   Útest_issue_4890D  s    *ÿ*ÿFÿrs  c                   C   s,   t dttdtd  ƒ  tƒ t¡r(t‚d S rÞ   )rH   rn   r-   rJ  rW   ro   rh   rh   rh   ri   Útest_issue_4551N  s    rt  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 )Nr`   T©rb   rÃ   rs   r   rk   )r   rQ   rH   rn   r   r»   ro   rË   rh   rh   ri   Útest_issue_4376R  s    "Nÿÿrv  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 )Nrz   rs   r¬   r“   r  )rH   r-   rn   r   ro   rh   rh   rh   ri   Útest_issue_4517X  s    "*ÿrw  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 mTra   r   rk   r  )r   rH   r3   rn   r   rQ   r.   r   ro   rI   r2   )ÚkrÖ   rh   rh   ri   Útest_issue_4527]  s$    &($ýÿ \X**ÿÿüry  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   TrÂ   rk   rÄ   rÅ   )	r   rH   r    r   r   rn   r   rW   ro   )Zyposrh   rh   ri   Útest_issue_4199r  s    .*ÿrz  c                  C   s²  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||d d|    ƒ t
d|  t | dt| ƒ  ƒ dt| ƒ  ¡sàt‚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sHt‚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s®t‚d S )
Nza:dTrÂ   rk   r~   r   )Ú
expand_mul)rx  za d)r   rH   r    rn   r   r-   r   r<   ro   Úequalsr>   rÒ   r{  r`  rx  r   )r—   r­   r®   r‚   r{  rx  rh   rh   ri   Útest_issue_3940y  s     2ÿ"Jÿ.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 r½   )rH   r—   rn   r   r"   ro   rh   rh   rh   ri   Útest_issue_5413‰  s    r~  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)rÉ   rk   rs   )r   r   r    r–   r3   rn   r2   r   rH   r"   ro   )r¨   rê   r®   ZP1ZP2Zh1Zh2rh   rh   ri   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 )Nrz   rk   rÕ   r   )	r3   r   rn   r2   rR   rL   rH   r
   ro   )Úexprrh   rh   ri   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   rk   )	rH   r3   rn   rc   r   rê   r   rW   ro   rh   rh   rh   ri   Útest_issue_5178±  s    , ÿrƒ  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   rk   r~   é   r¬   iÐ  r«   i€  i _7 r  rŽ   )r3   rn   ÚseriesrN   rH   ro   r
   ©rc   rw   rh   rh   ri   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heurischrs   )Zsympy.integrals.heurischr‰  rD   rn   ro   rˆ  rh   rh   ri   Útest_atom_bugÀ  s    rŠ  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 )Nrê   F©Úzeror   rk   )r   rH   r3   rn   r   r   r   r"   r9   r   ro   rr  rh   rh   ri   Útest_limit_bugÅ  s    &*ÿr  c                  C   s,   t dƒ} tttƒ| tƒ tƒ t¡s(t‚d S )Nrw   )r   rH   r    rn   rJ  rW   ro   rv   rh   rh   ri   Útest_issue_4703Ë  s    rŽ  c                  C   s.   t dƒ} t| tƒ t¡d tƒ t¡s*t‚d S )Nrc   rk   )r   rH   rn   r
   rJ  rW   ro   rà   rh   rh   ri   Útest_issue_1888Ð  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 )Nrk   r   )rH   r2   rn   r   r   r;   ro   rh   rh   rh   ri   Útest_issue_3558×  s    r  c                   C   s6   t dtddtd   ƒ tƒttd ƒd ks2t‚d S )Nrs   r  r~   rk   )rH   r-   rn   r$   ro   rh   rh   rh   ri   Útest_issue_4422Û  s    r‘  c                   C   sN   t tttddt  ƒ tƒƒtdt d ƒdtd  t d  d ksJt‚d S )Nrs   rk   r¬   rd   )rQ   rH   rn   r-   ro   rh   rh   rh   ri   Útest_issue_4493ß  s    &ÿr’  c                   C   sh   t ttƒt tt tfƒtks"t‚t ttƒt tdtfƒtd ksFt‚t ttƒt tƒttƒksdt‚d S r‚  )rH   r3   rn   r   r   ro   r;   rh   rh   rh   ri   Útest_issue_4737ä  s    "$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   rÏ   r—   TrÂ   rs   )rÒ   rÐ   r   rQ   rH   r    rn   r"   r   rB   rA   ro   )rÐ   r—   rh   rh   ri   Útest_issue_4992ê  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
lowergammars   )Ú'sympy.functions.special.gamma_functionsr–  rQ   rH   r    rn   r   ro   r•  rh   rh   ri   Útest_issue_4487ò  s    r˜  c                  C   s,   t dƒ} td| d  | ddfƒtks(t‚d S )Nrn   rs   rk   r‹   )r   rH   r   ro   re  rh   rh   ri   Útest_issue_4215÷  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 )Nr`   Tru  rk   rs   )r   rH   rn   r"   ro   rË   rh   rh   ri   Útest_issue_4400ü  s    Rÿÿrš  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 )Nrs   rk   T©rD   )rH   r-   rn   rW   ro   rh   rh   rh   ri   Útest_issue_6253  s    (&ÿrœ  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 )Nrs   r   iôÿÿÿrz   r¬   rk   r«   rŽ   r“   r~   r:  r  é/   )rH   rn   r   rê   r"   ro   rh   rh   rh   ri   Útest_issue_4153
  s    .B& *ýrž  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 hrk   )r   rH   rn   r-   rJ  r   ro   rW   )rn  r­   Úhrf   rh   rh   ri   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 r2  râ   rh   rh   rh   ri   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 )Nrs   T)ÚmanualrD   r¡   rh   rh   rh   ri   rx      ry   z$test_manual_option.<locals>.<lambda>rs   r   T©r¢  )rZ   r€   rH   r"   rn   rJ  rW   ro   rh   rh   rh   ri   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 )Nrs   T)rD   Úrischr¡   rh   rh   rh   ri   rx   &  ry   z%test_meijerg_option.<locals>.<lambda>Tr›  )rZ   r€   rH   r5   rn   rW   ro   rh   rh   rh   ri   Útest_meijerg_option%  s    r¦  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 )Nrs   r   T©r¥  )rH   r"   rn   r   rh   rh   rh   ri   rx   -  ry   z#test_risch_option.<locals>.<lambda>rk   Tr§  rs   )rZ   r€   rH   r    rn   rX   ro   r"   r   r<   rW   rh   rh   rh   ri   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 )Nrs   T)r¥  r‰  r¡   rh   rh   rh   ri   rx   6  ry   z&test_heurisch_option.<locals>.<lambda>rk   Trˆ  rz   r~   Fi€ÿÿÿrs   i!  éð   r  rÍ   )rZ   r€   rH   r    rn   r-   r   r>   ro   rW   r"   r2   r   r3   rh   rh   rh   ri   Útest_heurisch_option4  s    .,*BJÿÿrª  c                  C   s:   ddt d  d  } t| t ƒ t ¡}t| |dds6t‚d S )Nrs   gHáz®Gñ?rk   g333333@gê-™—q=)Ztol)rn   rH   r
   r_   ro   r†  rh   rh   ri   Útest_issue_6828A  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    rn   r2   r—   ro   )r¬  rh   rh   ri   Útest_issue_4803G  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 rÞ   )rH   r-   r5   rn   ro   rh   rh   rh   ri   Útest_issue_4234M  s    r®  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 )
Nrk   rŽ   TrX  rd   rz   é   r«   iøÿÿÿ)
rQ   rH   rn   r-   rL   r.   r   r#   r0   ro   rh   rh   rh   ri   Útest_issue_4492Q  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 )Nrs   rk   rz   g333333ó?r   g333333ó¿)r—   rê   r"   rX   rW   r‡   ro   rH   r    r`   r„   r–   rn   )rc   Z
integral_frh   rh   ri   Útest_issue_2708Z  s    0ÿ,0ÿÿr±  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)rn   r   r    rH   Ústrro   )rc   rf   rh   rh   ri   Útest_issue_2884h  s     r³  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   rk   rs   r}   )r   r   )r   Tr‹   )Ú$sympy.functions.elementary.complexesrµ  r   rH   r    r„   rn   r%   r   r.   r   rD   r   r»   r   rW   ro   r(   rI   r´  rh   rh   ri   Útest_issue_8368in  sN     ÿÿ

ýüû
õ þòÿ  
ýÿ ÿùÿr·  c                   C   s€   t tdt ƒƒdtdt ƒ ks$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 )Nç      ð?rs   )rH   r(   rn   r%   ro   r)   r"   rh   rh   rh   ri   Útest_issue_8901Ž  s    $4r¹  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 )Nrz   r   rs   r~   rk   )rH   r3   rn   r;   ro   r   r   r2   rh   rh   rh   ri   Útest_issue_8945”  s    >(rº  c                  C   sX   t dƒ\} }}}tt|  t | ƒd ||t    t¡}tt|td|fƒjksTt‚d S )Nzi L a brk   r   )	r   r2   r   rn   Zrewriter    rH   r†   ro   )r‰   ÚLr—   r­   Ú	integrandrh   rh   ri   Útest_issue_7130›  s    *r½  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 trk   )r   rJ   rH   rW   r‡   ro   )r—   r­   r®   r–   Úvtrh   rh   ri   Útest_issue_10567¢  s    r¿  c                   C   s6   t ttd  dt  d ƒtddfƒdt ks2t‚d S )Nrk   r«   é0   r~   rÕ   r  )rH   r-   rn   r   ro   rh   rh   rh   ri   Útest_issue_11742©  s    rÁ  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;   ro   )r–   rh   rh   ri   Útest_issue_11856­  s    rÂ  c                   C   s0   t ttdt ƒƒtddfƒttƒd ks,t‚d S ©Nrs   r   rk   )rH   r-   r"   rn   r   ro   rh   rh   rh   ri   Útest_issue_11876²  s    rÄ  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      (@rŽ   )rH   r    rn   ro   rh   rh   rh   ri   Útest_issue_4950·  s    ,ÿrÅ  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 )Nrk   rŽ   )rH   r3   r"   rn   r2   ro   rh   rh   rh   ri   Útest_issue_4968¼  s    rÆ  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 )Nrs   rk   r‹   r}   )rH   rn   r   ro   rh   rh   rh   ri   Útest_singularitiesÀ  s
    " $"rÇ  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¥   rz   rk   )r   rH   r3   r-   r   rW   ro   )rn   r   rh   rh   ri   Útest_issue_12645É  s    "þ&þýrÈ  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 )Nrz   r   r¬   rs   )rH   r3   rn   r2   r   r   ro   rh   rh   rh   ri   Útest_issue_12677Ó  s    rÉ  c                   C   s6   t tdt ƒttƒ t tdtfƒtdƒ ks2t‚d S )Nrz   r   )rH   r2   rn   r   r"   ro   rh   rh   rh   ri   Útest_issue_14078×  s    rÊ  c                   C   s(   t dttƒ tdtfƒtd ks$t‚d S rÃ  )rH   r%   rn   r   r   ro   rh   rh   rh   ri   Útest_issue_14064Û  s    rË  c                	   C   sp   t ddtttj ƒdttƒ    tƒtttjƒtttƒttjƒdttjƒ   ƒ ttjƒt   kslt‚d S r{   )rH   r    rn   r   r»   r"   r   ro   rh   rh   rh   ri   Útest_issue_14027ß  s    &>ÿrÌ  c                   C   s&   t ttƒtdtd fƒtjks"t‚d S r‚  )rH   r5   rn   r   r   ÚInfinityro   rh   rh   rh   ri   Útest_issue_8170ä  s    rÎ  c                   C   sD   t dt tddfƒtjkst‚t dtd  tddfƒtjks@t‚d S )Nrs   r‹   r}   rz   )rH   rn   r   r•   ro   rh   rh   rh   ri   Útest_issue_8440_14040è  s    rÏ  c                   C   s”   t dtt d  tddfƒdtd  dt  ks4t‚t ddt t t d  tddftddftddfƒdtdƒ dtdƒ  dtd	ƒ  kst‚d S )
Nrs   rk   r   r‹   rö   r~   r¬   r°   rz   )rH   rn   r   ro   rê   r"   rh   rh   rh   ri   Útest_issue_14096í  s    42"ÿrÐ  c                   C   sh   t tdtdtd  ƒ tddfƒ ¡ d ƒdk s4t‚t ttdtd  ƒtddfƒ ¡ d ƒdk sdt‚d S )Nrs   rz   r   gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?)r   rH   r-   rn   r`   ro   rh   rh   rh   ri   Útest_issue_14144ó  s    4rÑ  c                   C   s(   t ttt ƒttƒ tƒ t¡s$t‚d S rt   )rH   r    r   rn   r"   rJ  r:   ro   rh   rh   rh   ri   Útest_issue_14375ø  s    rÒ  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 )Nrc   r   rs   rk   rz   )r   rn   r   rê   rH   rW   ro   rà   rh   rh   ri   Útest_issue_14437þ  s    ÿrÓ  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    rn   r"   ro   rh   rh   rh   ri   Útest_issue_14470  s    rÕ  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 ©Nrs   rk   rz   )r    rn   rH   ro   rà   rh   rh   ri   Útest_issue_14877  s    LHÿr×  c                  C   sB   t td  d ƒtd  t  } t| tddgƒt d ks>t‚d S )Nrk   rs   r‹   r«   )r-   rn   rH   r   ro   rà   rh   rh   ri   Útest_issue_14782  s     rØ  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 )Nrk   rs   r   rz   r  )r-   rn   rH   r   r™   r   ro   rà   rh   rh   ri   Útest_issue_14782_slow  s     rÙ  c                  C   s4   t tddƒ tt  ƒ } t| t dtgƒtks0t‚d S )Nr÷   rk   r   )rn   r   r    rH   r   ro   rà   rh   rh   ri   Útest_issue_12081  s    rÚ  c                  C   sD   dt  d } d|  td|  ƒ t d  }t|t ddgƒdks@t‚d S )Nrs   r~   r}   rk   r   )rn   r    rH   ro   )r   rc   rh   rh   ri   Útest_issue_15285  s    rÛ  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   rs   T)rH   rn   r`   r    r"   r   rP   r.   rA   rB   r   rW   ro   rh   rh   rh   ri   Útest_issue_15432$  s    *4(þrÜ  c                  C   s„   t dƒ} tdtd\}}tttt | | | |   ƒtddt ttt | |  ƒ ttt | |  ƒ | | | |   ks€t‚d S )NÚomegazm p)ÚclsrÄ   rÅ   )rT   r   rS   rH   r    rn   r   ro   )rÝ  rÖ   rq   rh   rh   ri   Útest_issue_15124*  s
    $<ÿrß  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 )Nrk   Frm   r   rs   )r\   rW   r   rn   r   ro   r‡   r]   r^   rH   r   r»   rh   rh   rh   ri   Útest_issue_152181  s    484(rà  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 )Nrk   r   r¬   )rH   r    rn   r2   r–   r3   r   r·   r.   ro   rP   r-   r   rÜ   r  rh   rh   ri   Útest_issue_15292B  s    >rá  c                   C   s.   t tdt ƒttƒ tƒdttƒ ks*t‚d S r½   )rH   r3   rn   ro   rh   rh   rh   ri   Útest_issue_4514H  s    râ  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¥   rk   rs   rz   r}   r÷   r‹   rŽ   )r   rH   r    r   rÜ   r   ro   )rn   r—   r­   ZdefiniteZ
indefiniterh   rh   ri   Útest_issue_15457L  s    "((rã  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 rt   )rH   rn   r    r"   r:   ro   rh   rh   rh   ri   Útest_issue_15431V  s    *ÿrä  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 )Nrk   rz   r~   )	rn   r"   r:   rH   r
   ro   r-   r   r=   )rc   ÚFrh   rh   ri   Ú"test_issue_15640_log_substitutions[  s     & .ræ  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NTrˆ  )Zsympy.vectorrç  rn   rH   r2   r—   r­   Úx_1Úx_2r.   r3   r   r   ro   )rç  rè  rn   rh   rh   ri   Útest_issue_15509g  s     Dþrë  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 )
Nrn   Tr¥   r°   rk   r~   r÷   éQ   rz   )r   rH   rÛ   r.   r   ro   re  rh   rh   ri   Útest_issue_4311_fastp  s    ".ýrí  c               	   C   sè  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 |d  d	|   ƒ td
t |  | | dt| ƒ tt ƒ  ƒ dt| ƒ tt ƒ  ks¾t‚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snt‚tdtt| ƒd  |ƒ| d tttt| ƒd ƒ d  ks´t‚tdtt| ƒd  |ddt fƒt ksät‚d S )NÚKTrÂ   rn   r¥   rÖ   r–   rk   r~   r}   rs   r   )
r   rH   r    r   r-   r   r>   ro   r"   r<   )rî  rn   rÖ   r–   rh   rh   ri   Ú%test_integrate_with_complex_constantsx  s"    6ÿ,ÿÿ
>"ÿBFrï  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 )Nrn   r`   TrA  rs   rk   )r   rH   rF   r!   r   r   rA   ro   )rn   r`   rh   rh   ri   Útest_issue_14241‡  s
    :ÿrð  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 )Nrk   rŽ   r~   r   )rH   r3   r–   r2   r   ro   rh   rh   rh   ri   Útest_issue_13112Ž  s    rñ  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 )	NrŸ  TrÂ   rs   rk   r   rŽ   r  )r   rH   rn   r/   r   ro   )rŸ  r‰   rh   rh   ri   Útest_issue_14709b’  s    $rò  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 )Nrn   r–   r}   r   rk   )r   rH   r    r   r:   ro   r"   )rn   r–   rh   rh   ri   Útest_issue_8614˜  s    &ró  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„   TrÂ   rk   gš™™™™™ù?rs   gÏRt?,eÀg:Œ0âŽyE>r«   rŽ   iöÿÿÿé   rz   )r   r    rH   r   r•   ro   rÛ   rÜ   )r„   r¼  Zsolutionrh   rh   ri   Útest_issue_15494Ÿ  s    ,
4rõ  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   rk   rz   r   r  )r   rW   r@   rn   r‡   r.   r:   r"   r-   r   ro   r¾   rh   rh   ri   Útest_li_integral¯  s    ,.ÿþþrö  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 )	Nrn   r`   rs   rz   rk   r~   Fr‹  )
r   r   r»   rA   rC   rH   r3   ro   Zxreplacerˆ   )rn   r`   rŸ  rä   ÚgotZ_xZrepsrh   rh   ri   Útest_issue_17473¶  s    ( ÿÿrø  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 )Nrk   rs   rz   r   r°   )rH   r"   rn   r   r   ro   rh   rh   rh   ri   Útest_issue_17671Ã  s    *:rù  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 )Nrp  ÚCr   rs   rk   rz   r~   )r   rH   r   r-   ro   )rp  rú  r   rh   rh   ri   Útest_issue_2975É  s    rû  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 Mrè  Tra   rs   rk   r~   r   r  c                      s   t tˆˆtˆ fƒtƒS rt   ©rH   r   r   rh   ©r`   rn   rh   ri   rx   Ü  ry   z!test_issue_7827.<locals>.<lambda>c                      s   t tˆˆdˆ fƒˆ ƒS r{   )rH   r   rh   rý  rh   ri   rx   Ý  ry   c                      s   t tˆ ˆ dtfƒˆ ƒS r{   rü  rh   re  rh   ri   rx   Þ  ry   )r   r   rH   r   ro   r3   r   r.   r2   r   r   rZ   r€   )rñ   rè  rh   rý  ri   Útest_issue_7827Ð  s,    :ÿ,ÿ"2ÿÿÿÿ
,rþ  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 rÖ  )rn   r-   r"   rH   ro   rà   rh   rh   ri   Útest_issue_4231á  s    Xrÿ  c                  C   s@   t dtd t t  tƒ} t| tƒdtd t t  ks<t‚d S rÞ   )r
   rn   r   rH   ro   rà   rh   rh   ri   Útest_issue_17841æ  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 )Nrn   T©r¦   rÉ   r~   rŽ   rs   rÕ   r¬   rk   rz   )r   r0   r(   r"   r%   r2   rH   ro   r   r-   r1   )rn   Úf1Úf2rh   rh   ri   Útest_issue_21034ë  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 rP  )rH   r"   rn   r    r:   ro   r   r   rh   rh   rh   ri   Útest_issue_4187÷  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»  rê   Úr0ÚR0rk   r~   r   Tr  rŽ   )r   rH   r2   r3   ro   r.   r   r   r   r-   r?   rA   r   r™   )r»  rê   r  r  rp  Zsolrh   rh   ri   Útest_issue_5547ü  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 )Nrs   rk   rz   r   )rH   rn   r   r   ro   rh   rh   rh   ri   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 )Nrn   Tr  r~   rz   rk   rs   r}   r¬   rŽ   éûÿÿÿr«   r   rd   r  r¯  iLÿÿÿéZ   r  rö   )r   r"   r    rH   ro   r)   r(   r   r1   r   r%   rˆ   r3   )rn   rc   rå  ZF_truerh   rh   ri   Útest_issue_21024  s”    (B"ÿÿ(Dd$@*$$ f(4 <<.nÿ
ÿÿ,r  c                  C   s`   t dƒ} tdtdt|  d    tt tfƒ ¡ tt| ƒd dƒ tt| ƒd dƒ ks\t‚d S )Nr—   rs   rk   r   )	r   rH   r   rn   r   rˆ   r8   r   ro   ©r—   rh   rh   ri   Útest_issue_21721n  s    ($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thetarz   rŽ   r~   r   rk   rÕ   r¬   )r   rH   r2   r   ro   )r  r¼  rh   rh   ri   Útest_issue_21831t  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 )Nrk   rs   r~   r‹   rH  )rH   rn   r   r-   r   ro   rh   rh   rh   ri   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 )Nrs   rk   r‹   rö   rz   )rH   rê   rn   r   r-   r   ro   r   rh   rh   rh   ri   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~   rk   r£  )r   r2   rn   r3   rH   rÜ   rW   ro   )r  r€  Zres_realrh   rh   ri   Útest_issue_18527†  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 )Nrs   rk   r   Tza, brÂ   )r­   r2   rn   r—   r3   r"   r5   r-   r.   r   r   r   rH   ro   r   rÜ   )rc   ZFposrå  Zaprÿ   Úreprh   rh   ri   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 )Nrs   rk   r}   r‹   rz   gC˜qBõ?)rH   r-   rn   r"   ro   ÚmathÚiscloser`   rù   rh   rh   ri   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 )Nrs   rk   T)	rH   r-   rn   r   r.   r#   r   r0   ro   rh   rh   rh   ri   Útest_pr_23583ª  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 rÞ   )rH   r    rn   r-   r$   ro   rh   rh   rh   ri   Útest_issue_7264¯  s    r  c                   C   s.   t ttƒtddfƒdtttjƒƒ ks*t‚d S ró   )rH   r*   rn   r1   r)   r   r»   ro   rh   rh   rh   ri   Útest_issue_11254a³  s    r  c                   C   sB   t ttƒtƒtttd ƒƒks"t‚t ttƒtddfƒtks>t‚d S )Nrk   r   rs   )rH   r'   rn   r"   r)   ro   r   rh   rh   rh   ri   Útest_issue_11254b·  s    "r  c                   C   s|   t dtttt d  ddd  tƒdtdt ƒd  ks>t‚t ttƒd tƒdttd ƒ ttd ƒd d  ksxt‚d S )Nr‹   rk   F©rI  r}   rs   )	rH   r(   rn   r   r   r    ro   r%   r)   rh   rh   rh   ri   Útest_issue_11254d¼  s    >r  c                  C   s   t dtd  td  dt  d ttd dt  d ƒ tddfƒ} | dtdƒ d dtddtdƒ  ƒ d	  ksxt‚t |  ¡ d
¡sŒt‚d S )Nrz   rk   r~   r   rs   i›ÿÿÿr«   é‡   r  g€2É{¢ÙÀ)rH   rn   r-   r"   ro   r  r  r`   rù   rh   rh   ri   Útest_issue_22863Â  s    D4r!  c                   C   s.  t ttttƒ ƒƒdtttƒt ƒ ttƒd td  tdƒd   tdttƒ dtttƒt ƒ  d ƒd  ksxt‚t tdt d tdt d ƒ ƒd ƒtdt tdt d ƒ d ƒdt d	 d
dt d tdƒd   d  tdt d ƒd  dt d d d	  td
ƒd	   d ks*t‚d S )Nrk   rÕ   rz   rs   r«   r~   rŽ   r°   r   r  é(   )rH   r-   rn   r   r"   ro   rh   rh   rh   ri   Útest_issue_9723È  s    ^ÿ&^ÿÿÿr#  c                   C   sl   t ttƒtd  ttd  tt  t  tddtttƒttd  ttd   ttd    tƒksht‚d S )Nrk   Tr§  rz   r~   )rH   r"   rn   r®   r­   r—   rX   ro   rh   rh   rh   ri   Útest_issue_23704Ð  s    00ÿr$  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 rÞ   rÔ  rh   rh   rh   ri   Útest_exp_substitutionØ  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 rÞ   )	rH   r&   rn   r"   r)   ro   r*   r1   r'   rh   rh   rh   ri   Útest_hyperbolicÜ  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 )Nrk   rŽ   rz   r¬   r  rs   rö   )rH   r-   rn   ro   r   r"   rh   rh   rh   ri   Útest_nested_powâ  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 )Nrs   rz   rk   r~   rŽ   r  r÷   rN  r¬   r   Tr“   r°   iùÿÿÿrH  rô  r  r«   r   r  iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rH   r-   rn   r$   r   ro   r0   r"   r»   r—   r­   r®   r.   r   r‚   rf   rh   rh   rh   ri   Útest_sqrt_quadraticé  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 )Nrk   rz   r~   r¬   )	rH   rn   r6   r5   r"   ro   r2   r   rc   rh   rh   rh   ri   Útest_mul_pow_derivative  s
    <2Xÿr)  c                  C   s´   t dtdk fdƒ} t dtdk fdƒ }| | }ttdƒ df}t| |ƒdksPt‚t||ƒdksbt‚t|  |ƒdksvt‚t| |ƒdksŠt‚t||ƒdksœt‚t| |ƒdks°t‚d S )	Nr   g        )rs   Tr¸  ÚInfrs   r‹   g      ð¿)r.   rn   ÚfloatrH   ro   )Zfun1Zfun2Zfun_sumr»  rh   rh   ri   Útest_issue_20782  s    r,  c               	      s˜   dd„ ‰ ‡ fdd„} t tdƒ t f}t| dƒ|ƒ}|dt  tdt ƒ tt tdddd	ƒ ks`t‚t| d
ƒt tdƒ t fƒdt  dtd
t ƒ  ks”t‚d S )Nc                 S   s   t dt| k fdt| kfƒS r²   )r.   rn   r  rh   rh   ri   rx   )  ry   z"test_issue_20781.<locals>.<lambda>c                    s   ˆ t | ƒƒˆ t| ƒƒ S rt   )Úintr+  r  ©ÚPrh   ri   rx   *  ry   r*  rs   rk   r¸  Fr  r   )rn   r+  rH   r,   r+   ro   )rc   r»  r  rh   r.  ri   Útest_issue_20781(  s    .ÿr0  c                  C   sâ   t dƒ} t| d td| d  ƒ | ddfƒtd ks8t‚td| d  td| d  ƒ | ddfƒt d ksnt‚tdtd| d  ƒ | ddfƒtd ksšt‚t| d d| d   d td| d  ƒ | ddfƒdt d ksÞt‚d S )	Nrn   r~   rs   rk   r‹   r  r}   rŽ   )r   rH   r-   r   ro   re  rh   rh   ri   Útest_issue_194274  s
    06,r1  c                  C   s*  t dttdt d  dt d  ƒ tdtfƒ} | jtdddt dttd dtd   dt  d ƒ tdtfƒttd tdfƒ ksŠt‚t dttdt d  dt d  ƒ tdtfƒ}|jtdddt dtdtd  dtd   d	td   d
t  d ƒ tdtfƒttd tdfƒ ks&t‚d S )Nrs   rz   rk   r   rË   r~   rŽ   rH  éÁ   iö  i  )rW   r-   r—   rn   rê   r…  rN   ro   )ÚI1ÚI2rh   rh   ri   Útest_issue_23942B  s    0Z0r5  c                  C   sv   dt  tdt  ƒ } ddt t d dt   tdt t ƒ dtdt ƒ  }t| t tdfƒ}| |tj¡srt‚d S )Nrs   y        >ÚÃT¶üí?r¸  gÇÅzðñ¿g	
šT8ò?gÇÅzðñ?g>ÚÃT¶üí?)	rn   r    r   r   rH   Zis_samer  r  ro   )rc   ZF_exprå  rh   rh   ri   Útest_issue_25886I  s    ÿþþýr6  c                  C   sÄ   t tttd ƒƒt ƒ} | tttd ƒƒd ks4t‚t dtd td  tddƒ  tƒ}|ttd ttd td  d ƒ  ks„t‚t dttƒd  tddt	 fƒ}|dtdƒ t	 d ksÀt‚d S )Nrk   rs   rz   r   )
rH   r2   r"   rn   r3   ro   r   r   r-   r   )r3  r4  ZI3rh   rh   ri   Útest_old_issuesT  s    $, r7  )rd   (`  r  Zsympy.concrete.summationsr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.exprr   rÒ   r   r   r	   r
   Z
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