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   @   s|  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
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tƒtƒd ttƒrJ ‚d S )Né   é   é   é   éÿÿÿÿ)rD   r#   rN   r$   Úur%   r'   r	   r   r   rJ   rP   rP   rP   rQ   Útest_find_substitutions"   s    2(ÿ,ÿÿ8rY   c                   C   s2  t ttƒtt ksJ ‚t tdƒtƒttdƒ ks4J ‚t td tƒtd d ksRJ ‚t dtd  dtd   tƒtd td  ks„J ‚t td d tƒtd d d ksªJ ‚t dt d d tƒdt d d d ksØJ ‚t td d tƒtd d d ksþJ ‚t dt d d tƒdt d d d ks.J ‚d S )NrS   é   rV   é	   )rC   ÚyrN   r   rX   rP   rP   rP   rQ   Ú test_manualintegrate_polynomials+   s    2&.&r]   c                	   C   s8  t tdt ƒtƒtdt ƒd ks&J ‚t dt tƒdt tdƒ ksHJ ‚tdtdtdt ƒ ƒ ttdtdt ƒ ƒd ƒd ttdtdt ƒ ƒd ƒd  ƒ t dt tƒttƒks¼J ‚t ddt d  tƒtdt d ƒd ksêJ ‚t ttƒd t tƒttƒd d ksJ ‚ttt ttƒd  tt ƒ d S )NrS   rT   rZ   )rC   r   rN   r   rR   r   rP   rP   rP   rQ   Ú!test_manualintegrate_exponentials8   s    &">ÿ.,r^   c                  C   sÖ  t ttƒttƒ tƒttƒttƒ d ttƒttƒ d  ksBJ ‚t dt ttƒ tƒdt ttƒ dttƒ  ksxJ ‚t tttƒ tƒtd ttƒ d td d  ks®J ‚t ttƒtƒtttƒ t ksÐJ ‚t dtd  d ttƒ tƒdtd  ttƒ dt ttƒ  dttƒ  ks$J ‚t ttƒtƒtttƒ ttd d ƒd  ksXJ ‚tttƒtƒd kspJ ‚tttƒtƒd ksˆJ ‚ttd tƒd ks J ‚tttƒtƒ} | d ttƒkrÎ| d dksÒJ ‚d S )	NrS   rV   rZ   é   rU   é   rT   r   )rC   r   rN   r&   r"   r   r!   rE   )ÚresultrP   rP   rQ   Útest_manualintegrate_partsE   s    &ÿ66".ÿ
4rb   c                  C   sh  t ttƒtƒttƒ ksJ ‚t ttƒtƒtttƒƒ ks<J ‚t ttƒtƒtttƒttƒ ƒksbJ ‚t ttƒtƒtttƒttƒ ƒ ksŠJ ‚t ttƒttƒ tƒttƒd d ttƒd  d fv sÆJ ‚t ttƒ ttƒ tƒttƒ ksìJ ‚t ttƒttƒ tƒttƒ ksJ ‚t ttƒd tƒttƒks2J ‚t ttƒd tƒttƒ ksTJ ‚t tttd ƒ tƒtttd ƒttd ƒ ƒd ksJ ‚t ttƒtttƒƒ tƒttttƒƒtttƒƒ ƒ ksÎJ ‚t tdt ƒttƒ tƒt tdt ƒ ks J ‚t tdt ƒttƒ tƒdtttƒƒ dtttƒd ƒ  dttƒd   ksTJ ‚t	t
dt ƒtdt ƒd ƒ t	tttd ƒ t
td ƒd ƒ t	ttƒtttƒƒƒ t	ttƒtt
tƒƒƒ ttƒdtttd ƒƒ  } }t | tƒ|ksòJ ‚| t¡|   t¡ ¡ dksJ ‚ttƒtttd ƒƒ } }t | tƒ|ksBJ ‚| t¡|   t¡ ¡ dksdJ ‚d S )NrS   rZ   éýÿÿÿr   )rC   r&   rN   r"   r'   r   r%   r$   r#   rR   r   r   r   r   r   r!   r   Zrewriter   Zsimplifyr   rK   rP   rP   rQ   Ú!test_manualintegrate_trigonometryX   s2     &(<&& "<>22ÿ
""rd   c                   C   sî  t ttƒd ttƒ tƒttƒd d ks.J ‚t ttƒd ttƒd  tƒtd tdt ƒd  kshJ ‚t ttƒttƒd  tƒttƒd  d ks˜J ‚t ttƒd ttƒd  tƒttƒd d ttƒd d  ksÚJ ‚t ttƒd ttƒ tƒttƒd d ttƒ ksJ ‚t ttƒttƒd  tƒttƒd d ksBJ ‚t ttƒd ttƒ tƒttƒd  d dttƒd  d  ttƒ ksJ ‚t ttƒd ttƒd  tƒttƒd  d dttƒd  d  ttƒd d  ksêJ ‚d S )	NrS   rZ   é   rV   é    r_   rU   é   )rC   r&   rN   r"   r'   r%   r#   r$   rP   rP   rP   rQ   Útest_manualintegrate_trigpowersw   s     .ÿ0ÿ80,ÿ
4ÿrh   c                  C   s:  t ttƒdtdt ƒ  tƒtttƒƒks.J ‚t dddtd    tƒtdt d ƒd ks`J ‚t dddtd    tƒttƒd ksŠJ ‚t ddtd   tƒttd ƒd ks´J ‚t dddtd    tƒtdt ƒd ksâJ ‚tdd	d
} tdd	d
}t d| |td    tƒtttt| | ƒ ƒ|t| | ƒ  | | dkfttt|  | ƒ ƒttt|  | ƒ ƒ dt|ƒ t|  ƒ  d	fƒks’J ‚t dd|td    tƒtttdtd| ƒ  ƒd| td| ƒ  d| dkft ttdtd| ƒ  ƒttdtd| ƒ  ƒ  dt|ƒ  d	fƒks2J ‚t d| dtd    tƒttdt t| ƒ ƒdt| ƒ  | dkfttt|  ƒd  ƒttt|  ƒd  ƒ dt|  ƒ  d	fƒksºJ ‚t dddtd    tƒttƒd ksæJ ‚t dt	t
td    tƒttttt	t
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tt	t
 ƒ  tt	dƒfdt
t  d	fƒksFJ ‚t dtdtd  ƒ tƒttƒksnJ ‚t dtddtd   ƒ tƒttƒd ksžJ ‚t dtddtd   ƒ tƒtdt ƒksÎJ ‚t dtddtd   ƒ tƒtttddƒ ƒd ksJ ‚t dttd d ƒ tƒttƒks0J ‚t dttd d ƒ tƒttd ƒks\J ‚t dtdtd  d ƒ tƒttƒd ksŒJ ‚t dtdtd  d ƒ tƒtdt ƒd ksÀJ ‚t dt| td  d ƒ tƒtttt|  ƒ ƒt|  ƒ | dk ftt| ƒt ƒt| ƒ | dkftd	fƒks0J ‚t dt| td  ƒ tƒttttd|  ƒ ƒ| dkftdt dt| td  ƒ  ƒd	fƒks’J ‚t dttd d ƒ tƒtdt dttd d ƒ  ƒksÒJ ‚t dttd d ƒ tƒtdt dttd d ƒ  ƒksJ ‚t dtdtd  d ƒ tƒtdt dtdtd  d ƒ  ƒd ks^J ‚t dtdtd  d ƒ tƒtdt dtdtd  d ƒ  ƒd ksªJ ‚t dt| td  d ƒ tƒttdt| ƒ t| td  d ƒ d|  t  ƒt| ƒ t| dƒft t d d	fƒks$J ‚t dt|  dtd   ƒ tƒttdt td|  ƒ ƒd | dk ftdt dt|  dtd   ƒ  ƒd d	fƒksžJ ‚t ttƒtƒtttƒ tdtd  ƒ ksÎJ ‚t tt	t ƒtƒtt	t tt	t ƒ tt	d  td  d ƒ t	 tt	dƒfdƒks(J ‚t ttt	t ƒ tƒt	 tt tt	d  td  d ƒ dt	d   tdt	d  t dtt	d  ƒ tt	d  td  d ƒ  ƒdt	d  tt	d  ƒ   tt	d dƒftd d d	fƒ d td tt	t ƒ d  k	sJ ‚t ttƒtƒtttƒ tdtd  ƒ k	s<J ‚t tt	t ƒtƒtt	t tt	t ƒ tt	d  td  d ƒ t	 tt	dƒftt d d	fƒk	s¢J ‚t ttt	t ƒ tƒt	tt tt	d  td  d ƒ dt	d   tdt	d  t dtt	d  ƒ tt	d  td  d ƒ  ƒdt	d  tt	d  ƒ   tt	d dƒftd d d	fƒ d td tt	t ƒ d  k
s„J ‚t ttƒtƒtttƒ ttd d ƒd  k
s¸J ‚t tt	t ƒtƒtt	t tt	t ƒ tt	d td  d ƒd  t	 tt	dƒfdƒksJ ‚t ttt	t ƒ tƒt	 tt	d  tttt	d ƒ ƒt	d tt	d ƒ    d td tt	t ƒ d  ks†J ‚t ttƒtƒtttƒ tdttddtd   ƒ  tƒ ksÈJ ‚t tt	t ƒtƒttt	t ƒ tdttddt	d td    ƒ  tƒt	  ksJ ‚t ttt	t ƒ tƒtd tt	t ƒ d tdtddt	d td    ƒ tƒdt	   ks€J ‚t ttƒtƒtttƒ tdttddtd   ƒ  tƒ ksÂJ ‚t tt	t ƒtƒttt	t ƒ tdttddt	d td    ƒ  tƒt	  ksJ ‚t ttt	t ƒ tƒtd tt	t ƒ d tdtddt	d td    ƒ tƒdt	   kszJ ‚t ttƒtƒtttƒ ttd d ƒd  ks®J ‚t tt	t ƒtƒtt	t tt	t ƒ tt	d td  d ƒd  t	 tt	dƒftt d d	fƒksJ ‚t ttt	t ƒ tƒt	tt	d  tttt	d ƒ ƒt	d tt	d ƒ    d td tt	t ƒ d  ks†J ‚t dt| |td   ƒ tƒtttt||  ƒ ƒt|ƒ t| dk | dkƒfttt| |  ƒ ƒt| ƒ t| dk| dkƒftd| t dt| ƒ t| |td   ƒ  ƒt| ƒ t|dƒftt| ƒ d	fƒksbJ ‚t dt| |td   ƒ tƒtttt| |  ƒ ƒt| ƒ t| dk|dk ƒfttt||  ƒ ƒt|ƒ t| dk|dkƒftdt|ƒ t| |td   ƒ d| t  ƒt|ƒ t|dƒftt| ƒ d	fƒks6J ‚d S )NrT   rS   rV   r[   rZ   rU   é   ÚaT©ÚrealÚbr   rW   re   é   )r   Téþÿÿÿ)rC   r   rN   r!   r   r   r   r   r   rj   rm   r   r    r	   r   r   r
   r   r@   r   r   rB   )ÚraÚrbrP   rP   rQ   Ú test_manualintegrate_inversetrig‰   sä    .2**.0Dÿÿ
8Dÿÿ
(<ÿÿ
,Fÿ(00:ÿ

ÿ

ÿ
ÿ
Jÿ
@ÿ
@@LLTÿ
Rÿ
0Z0Xÿÿþþþÿ
0f.Xÿÿþþþÿ
4\rBVbBVb4hp02Dýÿ
2,@ýÿrr   c                	   C   s–  t tdtd  d ƒt tƒttdtd  d ƒdtddt  ƒ  tttddƒk ttddƒkƒfƒkslJ ‚t dtd tdtd  ƒ  tƒtttd  d d ƒ d	t  td  d d dtj  d
td    ttdk tdkƒfƒksðJ ‚t td dtd  d dtj   tƒdtd  d dtj  d dtd  d dtj  d  dtdtd  d ƒ d  ddtdtd  d ƒ   ks’J ‚d S )Nri   rS   r[   rZ   rV   rc   rT   é   é}   é   r_   éûÿÿÿrg   é1   iÅÑ·iÁöW )	rC   r   rN   r   r   rB   r	   r   ÚHalfrP   rP   rP   rQ   Ú&test_manualintegrate_trig_substitutionì   s*    (ÿÿ  &ÿÿÿ&ÿþþÿry   c                  C   sˆ   t ttƒtt ƒ t tƒtt ƒ ttƒ ks4J ‚tdƒ} t | tƒ| t ƒ t tƒt| t ƒt tƒ t| tƒt tƒ ks„J ‚d S )NrJ   )rC   r   rN   r.   r   r@   ©rJ   rP   rP   rQ   Ú)test_manualintegrate_trivial_substitutionø   s
    4&ÿr{   c                   C   sz   t ddtd   tƒttd ƒ d ttd ƒd  ks<J ‚t ddtd   tƒttd ƒd ttd ƒd  ksvJ ‚d S )NrT   rV   rS   rW   )rC   rN   r   rP   rP   rP   rQ   Útest_manualintegrate_rationalÿ   s    <r|   c                  C   s,  dt td  d ƒ dtdƒ ttƒ ttdƒt d ƒ  } }t| |ƒ dt dtd  ƒ dttƒ tdt ƒ d  } }t| |ƒ ttddƒ t t d ƒ dttddƒtd ƒ  } }t| |ƒ t dt ƒt t	dt ƒ } }t| |ƒ t ddt  td  ƒttƒt dƒ ttd ƒ d  } }t| |ƒ t
td dt  d ƒ} tdƒttƒ t
dƒ ttdƒdt d  dttƒ  ƒ tdƒttdƒdt d  dttƒ  ƒ   d }t| |ƒ tdtd  ƒtdƒttƒ tdtdƒ t ttƒ ƒ d  } }t| |ƒ t
dt d ƒt t
dƒtdt ƒ tdƒtdt ƒ   } }t| |ƒ tdt d ƒt tdƒ tdt ƒ tdƒtdt ƒ   } }t| |ƒ dtdt d ƒ t dtdƒ tdt ƒ dt
dƒ tdt ƒ   } }t| |ƒ ttd ƒt ttd ƒ } }t| |ƒ ttd ƒt ttd ƒd  } }t| |ƒ dtdt d ƒ tdt d ƒd  } }t| |ƒ tddt ƒt tddt ƒ } }t| |ƒ dtddt
tƒd   ƒ dtdƒ tttddƒƒ d  } }t| |ƒ tddt
tƒd   ƒdtttd	dƒƒ  } }t| |ƒ d S )
NrV   rS   rZ   rT   re   iðÿÿÿr_   r[   i÷ÿÿÿ)r   rN   r   r
   r1   rR   r2   r	   r6   r.   r&   r3   r"   r4   r-   r0   r   r,   r   r/   r   r5   r?   r+   r*   rK   rP   rP   rQ   Útest_manualintegrate_special  sJ    @
2
6

:
:*ÿÿ
B
>
@
J

"
*
"
>
.r}   c                   C   s´   t tttd dt  d ƒ tƒttd dt  d  ks>J ‚t ttd dt  d tƒtƒtttd dt  d tƒƒks€J ‚t tttƒttttƒtƒtttƒtttƒks°J ‚d S )NrS   rZ   )rC   r
   r   rN   r\   r@   r&   rP   rP   rP   rQ   Útest_manualintegrate_derivative)  s     ÿÿÿr~   c                  C   sö  t tdt d ƒtdt d ƒd ƒ t tdt dƒtdt ƒd ƒ ttttt  dƒtƒttttt  ƒt ttdƒftttdƒ dfƒks”J ‚t ttd d dƒdttd d dƒ ƒ tttƒtƒtttƒ ksÜJ ‚tttdƒ tƒtd d ksþJ ‚tttdƒ tƒdksJ ‚ttttƒ tƒtd ttƒ d ksFJ ‚tttt ƒ tƒtd tt ƒ d ksvJ ‚ttdt d ƒtƒtd tdt d ƒ ksªJ ‚ttttƒ tƒtd ttƒ d ksÖJ ‚tttd ƒtdt ƒ td  tƒtd d t	ddƒ ttd ƒ t	ddƒ tt d ƒ ks<J ‚t
dƒ} ttd	t ƒtdt d	 ƒ tƒttd	 ƒ tt	d
dƒƒ tdt td	ƒ ƒ ksœJ ‚tt| t ƒtdt |  ƒ tƒt| t	ddƒ ƒtt|  ƒ tdt |  ƒ ksòJ ‚d S )NrZ   rS   r   rT   Tro   rV   r\   rg   é   )rR   r)   rN   r(   rC   rj   rm   r   r   r	   r   r&   r"   r   )r\   rP   rP   rQ   Útest_manualintegrate_Heaviside2  s.    & 0ÿ*",04,$8ÿ
 .ÿ
 ,ÿr€   c                  C   sx  t dƒ} dtdd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g}|D ]}t|tƒ}dD ]N}z| | |¡}W n ty¦   Y q|Y n0 | | |¡ t¡|  ¡ dks|J ‚q|t| tdt d ¡ }t|tƒ}d	D ].}| | |¡ t¡| | |¡  ¡ dksòJ ‚qòt d
ƒ}	tt|jƒd ƒD ]4}
t|jƒ}|	||
< tt|j|Ž |	ƒtƒs<J ‚q<qhd S )NÚnrg   r_   rZ   )ro   rW   r   rT   rZ   r_   re   r   rS   rT   )rS   rV   rg   Út)r   r	   r<   rN   r:   r8   r9   r>   r;   r=   r7   rC   ÚsubsÚ
ValueErrorr   r   ÚrangeÚlenÚargsÚlistÚ
isinstanceÚfuncr@   )r   rj   rm   ZpolysÚpZintegralÚdegZp_subbedÚqr‚   ÚiÚnew_argsrP   rP   rQ   Ú$test_manualintegrate_orthogonal_polyJ  s.     
þ


$
,
r   c                  C   sê   t td ¡ ƒ\} }}tdddd}t|||  ƒt|| ƒ }|t tf}t||ƒ|| d td| | ƒd  t|| ƒ t|| ƒt|| ƒd  d  | ks¨J ‚| t||ƒ ¡  t | t|| ƒ ksÒJ ‚t||ƒ 	t
¡ræJ ‚d S )Nzr x phir   T)ÚintegerÚpositiverS   rV   )Úmapr   Úsplitr"   r
   rC   r&   rA   ZtrigsimpÚhasr   )ÚrrN   Úphir   Ú	integrandZlimitsrP   rP   rQ   Útest_issue_6799h  s    Nÿ*r™   c                   C   sB   t tt tƒtttd  td  ttdƒfttƒdfƒks>J ‚d S )NrT   rW   T)rC   rN   r\   r   r   r   rP   rP   rP   rQ   Útest_issue_12251u  s    &ÿrš   c                   C   sr   t ttttd  ƒƒtƒtttd  ƒks.J ‚ttttd ƒ tddt ttƒ tttd  ƒ d ksnJ ‚d S )NrS   rV   F)Zrisch)	rC   r   r   rN   rA   r   r   r
   r1   rP   rP   rP   rQ   Útest_issue_3796z  s    .r›   c                   C   sŠ   t ttƒttƒ tddttƒttƒ d ttƒttƒ d  ksFJ ‚t ttƒttƒ tddttƒd d ttƒd  d fv s†J ‚d S )NT©ZmanualrS   )rA   r   rN   r&   r"   rP   rP   rP   rQ   Útest_manual_true  s    &ÿ ÿr   c               
   C   s  t dƒ} t dƒ}t| t tƒt| t t| ƒ tt| ƒdƒftdfƒksJJ ‚t| |t  tƒtt| |t  t| ƒ tt| ƒdƒf|t dfƒ| t|dƒftdfƒks¨J ‚tt|t ƒtƒtt|t ƒ| t|dƒftdfƒksâJ ‚t ddd} t| d t tƒ| d t t| d ƒ ksJ ‚t ddd} t| d t tƒtksFJ ‚t dƒ} t ddd}t| |t  tƒt| |t  t| ƒ tt| ƒdƒf|t dfƒ| ks¦J ‚t ddd} t| d |t  tƒ| d |t  |t| d ƒ  ksîJ ‚t d	dd
}t dƒ}td||td    tƒttt|| ƒ ƒ|t|| ƒ  ksFJ ‚t ddd
}td||td    tƒttt| ƒtd| ƒ  ƒ|t| ƒ td| ƒ  ksªJ ‚tdt| | |  d t|td  d ƒ  tƒ| |  t	t|  | |  t|td  d ƒ t|  t|td  d ƒ  dt|   | |   t|td  d ƒ   tƒ ksdJ ‚tdtd d tdtd  d ƒ  tƒt	dtd d tdtd  d ƒ  tƒks¾J ‚tdt|t  t|d    tƒt	d|t  |d t  t  tƒks
J ‚d S )Nr\   r   r   T©r’   rT   )Zzero)Znonzerorj   ©Únegativerm   rS   rW   rV   )
r   rC   rN   r   r   r   r   r!   r   r@   )r\   r   rj   rm   rP   rP   rQ   Útest_issue_6746†  sp    "ÿ
 
þýýû
ÿ
0*ÿÿÿ
D6ÿ
0.ÿ*ÿÿÿ
((ÿ
 "ÿr¡   c                   C   s€  t ttƒttƒ tƒt ttƒ ttd  d ƒ tttƒ ttd  d ƒ ttƒ  tttd  d ƒt tƒ ks|J ‚t ttƒttƒ tƒt ttƒ ttd  d ƒ tttƒ ttd  d ƒ ttƒ  tttd  d ƒt tƒ ksøJ ‚t ttƒttƒ tƒt ttƒ tttƒ ttd d ƒd  ttƒ  ttd d ƒd  tttd d ƒt tƒd  ks|J ‚d S )NrS   rT   )rC   r    rN   r   r   r@   r   r!   rP   rP   rP   rQ   Útest_issue_2850®  s&    2$ÿÿ
2$ÿÿ
*ÿÿÿÿr¢   c                	   C   s  t tdt ƒttƒ tƒttƒtdt ƒ d dttƒ tdt ƒ d  ksRJ ‚ttdt ƒttƒ tƒ ¡ rtJ ‚t td td dt  d d  tƒtttd dtd   dtd   dt  d  tƒdtdtd dtd   dtd   dt  d  tƒ  ksJ ‚d S )NrS   r_   rZ   rV   re   rT   )rC   r&   rN   r   r"   rF   Zcontains_dont_knowr@   rP   rP   rP   rQ   Útest_issue_9462¸  s    R"$48ÿÿr£   c                  C   s   t tƒttd ƒ } dttd ƒ ttƒ d dttd ƒ t tƒ d  }t| tƒ|krh| t¡| kslJ ‚tt tƒ ttd ƒ } tdttd ƒ ttƒ d dttd ƒ t tƒ d   dttd ƒ ttƒ d  dttd ƒ t tƒ d  }t| tƒ|kr| t¡| ksJ ‚d S )NrV   ri   é   é€   é!  éð   )r"   rN   r   r&   rC   r   rK   rP   rP   rQ   Útest_cyclic_partsÀ  s    8 :ÿÿr¨   c                   C   s¾   t dtd  dtd   dtd   dt  d td dtd   dtd   dtd   dtd   dt  d	  tƒdt td d	  dttƒ  d	td d	   dtd	   ksºJ ‚d S )
NrV   rZ   ri   rS   é   re   rU   r_   rT   )rC   rN   r!   rP   rP   rP   rQ   Útest_issue_10847_slowÊ  s    0Bÿÿ:þrª   c                  C   s 	  t td td t  tƒtttttt ƒ ƒtt ƒ ttdƒfdt dfƒ t ksZJ ‚tddd} t td td |   tƒ| tttt|  ƒ ƒt|  ƒ | dk ftt| ƒ t ƒtt| ƒt ƒ dt| ƒ  dfƒ t ksäJ ‚t ttt	 ƒtt
t ƒ tƒdt	d  ttttt	 ƒtt	ƒ ƒtt	ƒ tt	dƒfdttt	 ƒ dfƒ d dt	 ttt	 ƒ d  dtt	 tddƒ  tt
t ƒ d  dtt	 tddƒ  d	  ks°J ‚td
dd}tddd}t tt| ƒt|t ƒ tƒd|d  tttt| ƒt|ƒ ƒt|ƒ |dkftt| ƒ tt| ƒ ƒtt| ƒtt| ƒ ƒ dt| ƒ  dfƒ d d| tt| ƒ d  dt| tddƒ  t|t ƒ d  dt| tddƒ  d	  ksÆJ ‚t ttƒttƒ tƒdttddƒ  ttƒ d dttddƒ  d	  ksJ ‚t ttt t ƒt tƒ}|tdt ttttt t ƒtt ƒ ƒ tt ƒ ttdƒfdttt t ƒ dfƒ dttt t ƒ  ttdƒfttƒttƒ dfƒksÄJ ‚t|ƒtdt tttt t ƒtt ƒ ƒ tt ƒ dttt t ƒ  ttdƒttdƒ@ fdt ttt t ƒ dttt t ƒ  ttdƒfttƒttƒ dfƒkstJ ‚tddd}tddd}t t|t | ƒt tƒtd| ttt|t | ƒt| ƒ ƒ t| ƒ |dk ft tt|ƒ t|t | ƒ ƒtt|ƒt|t | ƒ ƒ  dt| ƒ  dfƒ dt|t | ƒ  t|dƒft|ƒttƒ dfƒksnJ ‚tt t|t | ƒt|   tƒƒtd| |  ttt|t | ƒt||  | ƒ ƒt||  | ƒ ||  | dkftt| |  | ƒ t|t | ƒ ƒdt| |  | ƒ  tt| |  | ƒt|t | ƒ ƒdt| |  | ƒ   dfƒ d| ttt|t | ƒt||  | ƒ ƒt||  | ƒ ||  | dkftt| |  | ƒ t|t | ƒ ƒdt| |  | ƒ  tt| |  | ƒt|t | ƒ ƒdt| |  | ƒ   dfƒ  dt|t | ƒ  t|dƒft|ƒt| t ƒ dfƒksjJ ‚t tdt d ƒtd  tƒdtdt d ƒ ttdt d ƒd ƒ ttdt d ƒd ƒ ksÒJ ‚t tdt d ƒd t tƒdt d tddƒ d dt d tddƒ d  ks*J ‚t ttddƒ ttƒ tƒdttddƒ  ttƒ d dttddƒ  d  ks€J ‚t td ttƒ tƒttƒ dtd   ddtd    ksÂJ ‚t tt	ƒt	d ddt	    t	ƒtt	ƒtddt	  ƒ ttddt	  ƒt	 t	ƒ k	sJ ‚d S )NrS   r   rW   TÚcrk   rV   rZ   r[   r\   Úzro   rT   rj   rm   r_   é   rs   rc   )rC   rN   r«   r   r!   r   r   r   r   r\   r¬   r	   rj   rm   r   r   r   r@   )ÚrcZryZrzra   rp   rq   rP   rP   rQ   Útest_issue_10847Ñ  sÊ    :ÿ&0ÿÿÿ4ÿÿÿ$þþÿ
2Fÿÿþ$þýÿ
P2þþþýV4ý0Pþýýûÿ
 P<:ÿÿÿJ<:ÿÿÿýúúúÿ
	hXVB 0ÿr¯   c                   C   sd   t tttƒ t¡tƒtttttƒtƒtƒks0J ‚t tttƒ t¡ t¡tƒttttƒtƒks`J ‚d S rM   )rC   rJ   rN   r\   r   r@   r   rP   rP   rP   rQ   Útest_issue_12899  s    0r°   c                   C   s2   t tttddfƒtƒttttddfƒ ks.J ‚d S )NrT   rS   )rC   r@   r\   rN   rP   rP   rP   rQ   Ú#test_constant_independent_of_symbol  s    ÿr±   c                   C   s´   t tdt ƒtƒtdt ƒ d ks(J ‚t ttƒtdt ƒ tƒdttƒd  d ksZJ ‚t tdt ƒttƒ dttƒ  tƒdtttƒd ƒ ttƒd  dttƒ  ks°J ‚d S )NrS   ro   rZ   rT   )rC   r&   rN   r"   r   rP   rP   rP   rQ   Útest_issue_12641  s
    (2$*ÿr²   c                   C   s4   t ttƒttƒd  tƒttƒd  d ks0J ‚d S )Nr_   rU   )rC   r&   rN   r"   rP   rP   rP   rQ   Útest_issue_13297   s    r³   c                   C   sB   t dtttd ƒ  tttd ƒd ƒtttd ƒd ƒ ƒ d S )NrT   )rR   rN   r   r   rP   rP   rP   rQ   Útest_issue_14470%  s    r´   c                  C   sÒ  t ttƒtttƒƒ tƒtttƒƒks*J ‚t tdt ƒtttƒƒ tƒttƒtttƒƒ tttƒƒ kslJ ‚t tdt ƒtttƒƒ tƒ} |  t¡r˜J ‚|  t¡tdt ƒtttƒƒ ks¾J ‚t tdd„ t	ddƒD ƒƒtƒttdt ƒ d ttdt ƒ d  ttd	t ƒ d	  ttd
t ƒ d
  ttdt ƒ d  ttdt ƒ d  tttƒ  tdt ƒd  tdt ƒd  td	t ƒd  td
t ƒd  tdt ƒd  tdt ƒd
  ttƒ ksÎJ ‚d S )NrS   é
   c                 s   s   | ]}t t|t  ƒ V  qd S rM   )rN   r   )Ú.0ÚkrP   rP   rQ   Ú	<genexpr>2  ó    z"test_issue_9858.<locals>.<genexpr>rT   re   rg   rU   r_   rV   rZ   rw   é$   rs   ri   r[   )
rC   r   rN   r"   r&   r•   r@   r   Úsumr…   )ÚresrP   rP   rQ   Útest_issue_9858)  s<    *ÿ&Nÿÿ
ÿÿÿþþþþþÿr½   c                  C   s”   t ttd d  tƒttd ƒd ks*J ‚t td td d  tƒttd d ƒd ks\J ‚td	td  d d  } t | tƒ t¡ ¡ | ksJ ‚d S )
NrV   rT   rS   rU   rs   rZ   r_   ru   r[   )rC   rN   r!   r   Zfactorrz   rP   rP   rQ   Útest_issue_85208  s    *2r¾   c                      sŽ   t dƒ\‰‰tˆƒtˆƒ ‰ tˆ tˆƒˆƒˆttˆƒƒ ks@J ‚tˆ tˆƒˆƒtˆƒˆ ks`J ‚tt‡ ‡fdd„ƒ tt‡ ‡‡fdd„ƒ d S )Nzx yc                      s
   t ˆ ˆƒS rM   )rG   rP   )ÚexprrN   rP   rQ   Ú<lambda>G  r¹   z"test_manual_subs.<locals>.<lambda>c                      s   t ˆ tˆƒˆˆƒS rM   )rG   r   rP   ©r¿   rN   r\   rP   rQ   rÀ   H  r¹   )r   r   r   rG   rH   r„   rP   rP   rÁ   rQ   Útest_manual_subs?  s    $ rÂ   c                  C   sÀ   t tƒtt tƒƒ ttddƒ  } 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  }t| |ƒ d S )	NrZ   rV   i€ÿÿÿrT   r¦   r§   ri   r¤   )r   rN   r"   r	   r&   rR   rK   rP   rP   rQ   Útest_issue_15471K  s    "rÃ   c               	   C   sÞ   dt  d dt d  dt   d  } t| t ƒdtdt d  dt   d ƒ d dtdƒ tdtdƒ t tddƒ  d ƒ d	  ksˆJ ‚ddt d  dt   d  }t|t ƒdtd
t  d ƒ dtd
t  d
 ƒ  ksÚJ ‚d S )Nr_   rS   rZ   re   rU   r`   é   rT   éE   rV   )rN   rC   r   r   r!   r	   )rJ   ÚgrP   rP   rQ   Útest_quadratic_denomR  s    $drÇ   c                   C   s"   t ttƒtƒtttƒ ksJ ‚d S rM   )rC   r&   rN   r\   rP   rP   rP   rQ   Útest_issue_22757X  s    rÈ   c                  C   s0   t ttƒtƒ} | jj}|j|j|j ks,J ‚d S rM   )rF   r'   rN   Zsubstepr˜   ZconstantÚother)ZstepsZconstant_times_steprP   rP   rQ   Útest_issue_23348\  s    rÊ   c                  C   sf   t dttd d ƒ tddfƒjdd} | tddtdƒ  ƒ tdƒ ksNJ ‚t|  ¡ ƒd	ksbJ ‚d S )
NrT   rS   ro   rW   Trœ   rV   rZ   z1.31695789692482)r@   r   rN   Zdoitr   Ústrr   )rŽ   rP   rP   rQ   Útest_issue_23566b  s    (&rÌ   c                  C   s   t ddd} t ddd}ttttd  t ƒtƒttƒttƒ tttƒt ƒ dttƒ  ksbJ ‚tt| td  t ƒtƒttƒttƒ tt| ƒt ƒ dt| ƒ  ks¬J ‚tt|td  t ƒtƒttƒ ttƒ t	|t t| ƒ ƒ dt| ƒ  ksJ ‚tt
ttd  t ƒtƒtdƒttƒ t
tƒttdƒttƒ t ttƒ ƒ ttƒttdƒttƒ t ttƒ ƒ   dttƒ  ksŽJ ‚ttttd  t ƒtƒtdƒttƒ t
tƒ ttdƒttƒ t ttƒ ƒ ttƒttdƒttƒ t ttƒ ƒ   dttƒ  ksJ ‚d S )NÚapTrž   ÚanrŸ   rS   )r   rC   r   rj   rN   rm   r   r
   r2   r1   r&   r3   r"   r4   )rÍ   rÎ   rP   rP   rQ   Útest_issue_25093h  s&    JJV4&ÿ
ÿÿ
6&ÿ
ÿÿrÏ   c                  C   s¸  t ttd ƒtttd ƒ d ƒ t tttdƒd  ƒdt tttdƒd  ƒ d ƒ t dttd ƒ tttƒ ttd ƒ ƒ t tttd ƒ td ttd ƒ ttƒ ƒ tttt  t  t	 } tttt  t  t	 tt t  tt	 d  }tttt  t  t	 tt t  ttt t ƒ }t
| tƒtt|ttt	 dƒf|d	fƒttd
ƒfttt t t	  d	fƒks|J ‚| t¡ | ¡s’J ‚| t¡ tt	 d¡ | ¡s´J ‚d S )NrS   r_   rZ   rU   r`   rT   éüÿÿÿrW   Tr   )rR   r   rN   r   r   r«   rj   rm   ÚdÚerC   r   r   r   rO   rƒ   )rJ   ZF1ZF2rP   rP   rQ   Útest_nested_powv  s    "6*.04>ÿ
rÓ   c                
   C   sŒ  t dtd  d tddt  ƒ ddt d tdƒd   d ddt d tdƒd   d  d	dt d tdƒd   d
  dtdt d ƒ d
  ƒ tttttt  ƒd  tƒttdtd ttttt  ƒ tttt  ƒ ƒt	tdƒftd dttdƒd    dfƒksJ ‚t tdt d ƒd dt d dtdƒ  d  dtdƒ dt d tdƒd   d dtdƒ dt d tdƒd   d  dtdƒ dt d tj
d   d  ddt d tdƒd   d  ddt d tj
d   d  tdƒtdt d ƒ d  dtdt d tj
d  d ƒ d  dtdƒ tdt d tj
d  ƒ d  ƒ t tttt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  ƒ t tdt d tdt d ƒ ƒd 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 ƒ d S )Nr_   rZ   rV   rS   rµ   rg   i7  é   é(   éQ   éˆ   ro   r   TrT   rU   é   r©   re   r[   r`   )rR   rN   r   r   rC   rj   rm   r   r   r   ZOner   r!   rP   rP   rP   rQ   Ú test_manualintegrate_sqrt_linear„  sF     >ÿÿÿZÿ
0N$ÿÿÿþ$þ(ýÿ^ÿ$^ÿÿÿrÙ   c                   C   s¸	  t dttt d d ƒ tdt dttd dt t  d ƒ  dt  ƒƒ t dtdtd  dt  d ƒ tdƒtdtdƒ ttdƒd   d ƒ d ƒ t dtdtd  dt  d ƒ tdƒtdtdƒ ttdƒd   d ƒ d ƒ t dtdtd  dt  d ƒ tdƒtd	t dtdƒ tdtd  dt  d ƒ  d ƒ d ƒ t dtdtd  dt  d ƒ ttj tttj ƒ dtttj d ƒ  ƒ 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¶J ‚t dt d	 tdtd  dt  d 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  ƒ t dt d	 tdtd  dt  d 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  ƒ t dt d	 tdtd  dt  d 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  ƒ 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sôJ ‚t	dtd  td  dt  d ttd dt  d ƒ t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s¤J ‚t tdtd  dt  d 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  ƒ t	tt
ttd   ƒtƒtt
ttdttƒ tt
ttd   ƒ dt t  ƒttƒ tt
d
ƒftttƒ tttd  ƒ dfƒ d ttt
ttd   ƒ d  ttd
ƒftt
ƒt dfƒksâJ ‚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	s>J ‚t tttd dt  d 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  ƒ d S )NrT   rS   rZ   rV   r_   r`   rc   é   rU   r   Trg   r[   iùÿÿÿrf   é   ée   re   é‡   ri   iéÏ  i¬ iåY  i+A  i‰‡¦iQ  iC)  ir+  iÁ  i:§ŠC)rR   r   rN   r   r   r   r   r    rx   rC   rj   rm   r«   r   r   rÑ   rÒ   rP   rP   rP   rQ   Ú#test_manualintegrate_sqrt_quadratic–  s    NRRfP$hH.þÿ
(Vÿ(Vÿ(jÿ,^Bÿÿ"ýýb"ûÿ
<jÿ
.*ÿÿFÿÿÿÿþÿ
 ^Bÿÿ.ýý,ûÿ
VÿrÞ   c                   C   sÚ   t tttƒ ttƒ tttƒ tttƒttƒ ƒ ƒ t tttƒd  tttƒ tttƒƒ ƒ t td tttƒtdfƒ td tttƒtdfƒ dtd  tttƒtdfƒ  dt tttƒtƒ  dttƒ  ƒ d S )NrS   rZ   rV   rU   )rR   rN   r%   r'   r   r"   r   rJ   rP   rP   rP   rQ   Útest_mul_pow_derivativeÅ  s    6*6ÿ
ÿÿrß   N)”Zsympy.core.exprr   Zsympy.core.mulr   Zsympy.core.functionr   r   r   r   Zsympy.core.numbersr   r	   r
   Zsympy.core.relationalr   Zsympy.core.singletonr   Zsympy.core.symbolr   r   r   Z&sympy.functions.elementary.exponentialr   r   Z%sympy.functions.elementary.hyperbolicr   r   r   r   r   r   r   Z(sympy.functions.elementary.miscellaneousr   Z$sympy.functions.elementary.piecewiser   r   Z(sympy.functions.elementary.trigonometricr   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   Z'sympy.functions.special.delta_functionsr(   r)   Z*sympy.functions.special.elliptic_integralsr*   r+   Z'sympy.functions.special.error_functionsr,   r-   r.   r/   r0   r1   r2   r3   r4   r5   Z'sympy.functions.special.gamma_functionsr6   Z#sympy.functions.special.polynomialsr7   r8   r9   r:   r;   r<   r=   r>   Z&sympy.functions.special.zeta_functionsr?   Zsympy.integrals.integralsr@   rA   Zsympy.logic.boolalgrB   Zsympy.integrals.manualintegraterC   rD   rE   rF   rG   Zsympy.testing.pytestrH   rI   rN   r\   r¬   rX   r   rj   rm   r«   rÑ   rÒ   rJ   rR   rY   r]   r^   rb   rd   rh   rr   ry   r{   r|   r}   r~   r€   r   r™   rš   r›   r   r¡   r¢   r£   r¨   rª   r¯   r°   r±   r²   r³   r´   r½   r¾   rÂ   rÃ   rÇ   rÈ   rÊ   rÌ   rÏ   rÓ   rÙ   rÞ   rß   rP   rP   rP   rQ   Ú<module>   s–   $80(	

b%	
(
	


=


/