U
    —9%eÅi  ã                   @   sN  d dl mZmZmZmZmZmZmZmZm	Z	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lmZ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# d dl$m%Z% d d	l&m'Z'm(Z( d d
l)m*Z*m+Z+m,Z, d dl-m.Z. d dl/m0Z0m1Z1m2Z2m3Z3 d dl4m5Z5m6Z6m7Z7m8Z8 d dl9m:Z: d dl;m<Z<m=Z= d dl>m?Z? d dl@mAZA d dlBmCZC d dlDmEZE d dlFmGZG d dlHmIZImJZJmKZKmLZL d dlMmNZNmOZOmPZPmQZQmRZRmSZS e#dƒ\ZTZUZVdd„ ZWdd„ ZXdd„ ZYeJeIdd„ ƒƒZZd d!„ Z[d"d#„ Z\eJd$d%„ ƒZ]eJd&d'„ ƒZ^eJd(d)„ ƒZ_d*d+„ Z`d,d-„ Zad.d/„ Zbd0d1„ Zcd2d3„ Zdd4d5„ Zed6d7„ Zfd8S )9é    )Úmellin_transformÚinverse_mellin_transformÚfourier_transformÚinverse_fourier_transformÚsine_transformÚinverse_sine_transformÚcosine_transformÚinverse_cosine_transformÚhankel_transformÚinverse_hankel_transformÚFourierTransformÚSineTransformÚCosineTransformÚInverseFourierTransformÚInverseSineTransformÚInverseCosineTransformÚIntegralTransformError)Úlaplace_transformÚinverse_laplace_transform)ÚFunctionÚ
expand_mul)Ú
EulerGamma)ÚIÚRationalÚooÚpi)ÚS)ÚSymbolÚsymbols)Ú	factorial)ÚreÚ
unpolarify)ÚexpÚ	exp_polarÚlog)Úsqrt)ÚatanÚcosÚsinÚtan)ÚbesseliÚbesseljÚbesselkÚbessely)Ú	Heaviside)ÚerfÚexpint)Úgamma)Úmeijerg)Ú	gammasimp)Úhyperexpand)Útrigsimp)ÚXFAILÚslowÚskipÚraises)ÚxÚsÚaÚbÚcÚdznu beta rhoc                  C   s„   ddl m}  tdƒ}t|tƒttƒ| |tƒttƒks8t‚t|tƒtt ƒ ttƒ| |tƒttƒttd ƒt  dt	fdfks€t‚d S )Nr   )ÚMellinTransformÚfé   T)
Úsympy.integrals.transformsr@   r   r   r:   r;   ÚAssertionErrorr"   r1   r   )r@   rA   © rE   úd/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/integrals/tests/test_transforms.pyÚtest_undefined_function$   s    $(ÿrG   c                  C   sJ   t dƒ} t| tƒttƒjthks$t‚t| tƒt ttƒjtthksFt‚d S )NrA   )r   r   r:   r;   Zfree_symbolsrD   r<   )rA   rE   rE   rF   Útest_free_symbols,   s    rH   c                  C   sŠ  ddl m}  tdƒ}t|tƒttƒ d¡| ttd  |tƒ tdtfƒksNt‚t	|tƒttƒ d¡| |tƒt
dt t t t ƒ tt tfƒks–t‚t|tƒttdd d¡| |tƒt
t t ƒ tdtfƒksÖt‚td	t t t|tƒttttfƒ d¡ ƒd
kst‚td	t t t|tƒttƒ d¡ ƒdks<t‚t|tƒttƒ d¡| |tƒt
d	t t t t ƒ tt tfƒks†t‚d S )Nr   )ÚIntegralrA   rI   rB   éþÿÿÿT©Znocondsé   z.Integral(f(s)/x**s, (s, _c - oo*I, _c + oo*I))z2Integral(f(s)*exp(s*x), (s, _c - oo*I, _c + oo*I)))Zsympy.integrals.integralsrI   r   r   r:   r;   Úrewriter   rD   r   r"   r   r   r   Ústrr   r<   r=   r   r   )rI   rA   rE   rE   rF   Útest_as_integral2   s(    ÿ,ÿ ÿ*ÿ
$ÿ
,ÿrO   c                  C   sà  t dƒ t} tddd}tttd  ƒt t tttd  ƒ }| | t| ¡ttƒdtd  dtdt    |tdt  d   t	tt ƒ t	dt dt  ƒ t	dt ƒ t
tƒ t
tƒ d tj fdfksÖt‚tttd  ƒt t }| | t| ¡ttƒdtdt   t |tdt    t	t dt  ƒ t	tt ƒ t	t d ƒ t
tƒ t
tƒ d fdfkstt‚| | t| tdi¡ttƒ|dt d   t	tƒ t	t tj ƒ dttƒ  dtddƒfdfksÜt‚d S )NzRisch takes forever.r=   T©ZpositiverL   éÿÿÿÿrB   )r8   r   r   r%   r:   r=   r<   Úsubsr;   r1   r    r   ÚHalfrD   r   r   )ÚMTÚbposÚexprrE   rE   rF   Útest_mellin_transform_failE   sB    (:ÿ
ÿ þÿ*ÿ
ÿÿ ýÿ
4 ÿÿrW   c                  C   s¼  ddl m} m} t}tddd}|tt ttd ƒ ttƒdtt  t	 t
tƒ fdfks^t‚|tt tdt ƒ ttƒdtt  t
tƒ t	fdfksšt‚|dt td  tdt ƒ ttƒttƒttƒ ttt ƒ dt	ft
tƒdkfksðt‚|td td  ttd ƒ ttƒttƒtdt t ƒ tdt ƒ t	 dt
tƒ ft
tƒdkfksZt‚|dt t  ttƒttƒttt ƒ ttƒ dt
tƒfdfks t‚|tdt ƒt  ttƒdttt d ƒ tdt ƒ ttttd   ƒ ttƒ ttt ƒ t dt
tƒft
tƒdk fks"t‚|dt td  tdt ƒ ttd td   ttd ƒ  ttƒ}|d sšt|d dt
tƒ d ft
tƒdkfkƒ‚|tt tt  tt  ttƒd tttt d   ttt ƒ ttt ƒtttt  ƒ  ks t‚|tt |t  t|  ttƒt|tt d   ttt ƒ ttt ƒtttt  ƒ  | dt
tƒ ƒ|ddt
tƒ ƒfdfks†t‚tttd  ƒt t }|| t|¡ttƒt d| tdt    ttƒ tt dt  ƒ tt t d ƒ dt
tƒ d fdfkst‚tttd  ƒt t tttd  ƒ }|| t|¡ttƒdtdt   |tdt  d   ttƒ tdt dt  ƒ tdt t ƒ dt
tƒ d tj fdfks¾t‚|tt ƒttƒttƒdt	fdfksèt‚|tdt ƒttƒtt ƒt	 dfdfkst‚|ttƒd	 tdt ƒ ttƒd
td  dt	fdfksTt‚|ttƒd ttd ƒ ttƒdtd	  t	 dfdfks’t‚|ttd ƒttƒttttt ƒ  ddfksÆt‚|tdt d ƒttƒttttt ƒ  ddfksþt‚|ttdt ƒƒttƒttttt ƒ  ddfks6t‚|ttddt  ƒƒttƒttttt ƒ  ddfksrt‚|tttƒƒttƒtttj ƒ ttƒt  tddƒdfdfks¸t‚d S )Nr   ©ÚMaxÚMinr=   TrP   rB   rQ   rL   é   é   é   é   é   ©rQ   r   ©r   rB   )Ú(sympy.functions.elementary.miscellaneousrY   rZ   r   r   r:   Únur.   r;   r   r    rD   Úbetar1   ÚrhoÚabsr(   r   r'   r<   r=   r%   rR   r   rS   r"   r$   r)   r/   r   )rY   rZ   rT   rU   ÚmtrV   rE   rE   rF   Útest_mellin_transformc   sž    ÿÿ",ÿ"" 
ÿÿ
(ÿ
ÿÿ
ÿÿ
 
ýÿ ÿ4":ÿ
:  ÿÿ
D ÿÿ
(*ÿÿ þÿ
*0<>488<*ÿrh   c                  C   sâ   t } | ttƒtd  ttƒ}|dd … dks0t‚t|d dd t¡rJt‚| ttƒd td  ttƒ}|dd … dkszt‚t|d dd t¡r”t‚| ttƒtd d  ttƒ}|dd … dksÄt‚t|d dd t¡rÞt‚d S )NrB   )ra   Tr   T)Zallow_hyperrL   ))r   rL   T)r   r$   r:   r;   rD   r4   Úhasr2   )rT   rg   rE   rE   rF   Útest_mellin_transform2¢   s    rj   c               	   C   sœ  ddl m}  t}|ttdttƒ ƒttƒttd t ƒttd t d ƒ t	tƒ d t
ddƒfdfkslt‚|tttƒƒttttƒƒ ttƒdt tdt tj ƒ ttd t tj ƒ tt d t d ƒttdt  d ƒ  t	tƒ d tj t
ddƒfdfkst‚|tttƒƒttttƒƒ ttƒdt ttd t ƒ tdt tj ƒ tt d t tj ƒttdt  d ƒ  t	tƒ d t
ddƒfdfks¦t‚|ttttƒƒd ttƒttt ƒttjt ƒ ttƒtdt ƒ tdt t ƒ  t	tƒ tjfdfkst‚|ttttƒƒtt ttƒƒ ttƒttƒttjt ƒ ttƒtdt t ƒ tdt t ƒ  dtjfdfksŒt‚|ttd ttƒƒttttƒƒ ttƒtdt ƒttt tj ƒ ttƒtt
ddƒt ƒ ttt tj ƒ  tjt	tƒ tjfdfkst‚|ttttƒƒttttƒƒ ttƒdt tddt  ƒ ttt d t ƒ tdt tt d  ƒtdt tt d  ƒ tdt tt d  ƒ  t	tƒt	tƒ  d tjfdfksÖt‚|ttttƒƒd tt ttƒƒd  ttƒdd … | t	tƒt	tƒ ƒtjfdfks0t‚|ttdttƒ ƒttƒtttd t  ƒ tttd  ƒ tttd  ƒ t | t	tƒ d t	tƒd ƒt
ddƒfdfks²t‚|tttƒƒttttƒƒ ttƒdt  tttd t  ƒ ttjdt  ƒ tdt d t ƒ tdt d t ƒ ttƒtdt td  ƒ tdt td  ƒ  | t	tƒd  d t	tƒd d ƒt
ddƒfdfks’t‚|tttƒƒttttƒƒ ttƒdt  tttd t  ƒ tttd  ƒ tttd  ƒ ttjdt  ƒ ttƒttjt td  ƒ ttjt td  ƒ  | t	tƒ d t	tƒd ƒt
ddƒfdfksft‚|ttttƒƒttttƒƒ ttƒttt ƒ ttƒ ttt ƒ ttjt ƒ ttd	ƒ tdt t ƒ  | t	tƒ dƒtjfdfksôt‚|ttttƒƒttttƒƒ ttƒdt  tttd td  t  ƒ tddt  ƒ ttd td  t ƒ ttd td  t ƒ tttd td  t d ƒ ttd td  t d ƒ  | t	tƒ t	tƒ d t	tƒ t	tƒ d ƒtjfdfksöt‚|ttttƒƒd ttƒdd … | t	tƒ dt	tƒƒtjfdfks>t‚|ttdttƒ ƒttƒtttd  ƒtttd  ƒ d | t	tƒ d t	tƒd ƒtfdfks¤t‚|ttdtdttƒ ƒ ƒttdtdttƒ ƒ ƒ ttƒdt  tdt ƒ ttd t ƒ dttd t d ƒ  | dt	tƒ d ƒtfdfk	s>t‚|ttttƒƒttttƒƒ ttƒttƒttt ƒ tt tj ƒ dttƒ ttt d ƒ  | t	tƒ dƒtjfdfk	sÀt‚|ttttƒƒttttƒƒ ttƒddt d  tdt d ƒ tt d td  t ƒ ttd td  t ƒ tt d td  t d ƒttd td  t d ƒ  | t	tƒ d t	tƒd  t	tƒd t	tƒd  ƒtjfdfk
s²t‚|tt d ƒtttd ƒ ttƒ}ttt|d jdd
ƒƒƒ}|dtt
ddƒ  ttt ƒ ttjt ƒ tdt t ƒtdt t ƒ tt t d ƒ ttt d ƒ  ksjt‚|dd … | t	tƒ t	tƒƒtfdfks˜t‚d S )Nr   ©rY   rL   rB   r^   r[   TrJ   z3/2©Úfunc)rb   rY   r   r+   r<   r%   r:   r;   r1   r    r   rD   r(   r   rS   r'   r   r=   r-   r,   r   r*   r"   r3   r5   Úexpand)rY   rT   rg   Zmt0rE   rE   rF   Útest_mellin_transform_bessel²   sZ   <ÿ .(ÿ ÿþÿ
 (*ÿ ÿþÿ
"ÿ þÿ
$&ÿ þÿ
&*ÿ þÿ
"*.ÿÿ ýÿ
4ÿ
8$ ÿÿ
 .ÿÿ.þ, ýÿ
 N2ÿ$ þÿ
".ÿ þÿ
"4ÿÿ:þ2 ýÿ
 ÿ

ÿÿÿ ÿÿ
 ÿ ÿÿÿ ÿÿ
"ÿÿÿ þÿ
"8ÿÿÿÿÿýÿ
$,@ÿro   c                  C   s†  ddl m}  ddlm}m}m} ddlm} tddd}tddd	}t	|t
ƒt
tƒttƒt dtfdfksnt‚tttƒt tt
dtfƒ t¡ ¡ |t
ƒksžt‚t	ttt
ƒt
tƒttƒtt d
  | d
ttƒ dƒtfdfksàt‚|ttttƒ|t d
  tt
d
| tfƒ t¡jddƒƒt|t
ƒks,t‚t	|t
ƒt
tƒdt  ttƒ ttd tj ƒ dt tt d d
 ƒ  ddfks†t‚tdt  ttƒ ttd
 d ƒ dt tt d d
 ƒ  tt
dƒ|t
ƒksÚt‚t	|tt
ƒƒt
tƒddt d
   ttƒ ttƒ ttt tj ƒ  ddfks0t‚tdt  ttƒ ttƒ dt tt tj ƒ  t|dƒ ¡ |t|ƒƒks‚t‚d S )Nr   rk   )ÚCiÚE1ÚSi©Úsimplifyr<   T©ÚnegativeÚu)ZpolarrB   rl   rL   r`   ra   r[   )rb   rY   Ú'sympy.functions.special.error_functionsrp   rq   rr   Úsympy.simplify.simplifyrt   r   r   r:   r;   r1   r   rD   r   rM   r0   rn   r<   r    r!   r%   r   r   rS   )rY   rp   rq   rr   rt   Zanegrw   rE   rE   rF   Útest_expint  sn    *ÿÿÿ*ÿ
ÿÿÿÿý
"ÿ ÿÿ
"ÿ  ÿþ
:ÿ
0  þ
þrz   c               
      sl  ddl m}  ddlm}m} ddlm} ddlm‰  ddl	m
‰ t}|ttƒttdtfƒtt ƒksht‚|tt ƒttt dfƒtdt ƒks’t‚ˆ|tdtd  d  ttdtfƒƒtd d	 td	t ƒ d
t  ksÜt‚|d	td d	  ttdƒt tt d	 ƒ d ttd	 ƒdt   ks(t‚|d	td d	  ttdƒt tt d	 ƒ d ttd	 ƒdt   kstt‚|ttƒttd	 ƒ ttd	tfƒtd	 tt ƒ t ks²t‚tddd}|d	td d	  ttt ƒd tfƒ t|¡ t¡ 
¡ t|ƒtd	t| ƒ ƒ kst‚tddd\}}||t |  tt| ƒ t ttdtfƒt| t|  ƒksht‚|t|| t|  ƒ|t  tt| tfƒt| tt|  ƒ ks°t‚‡ ‡fdd„}tddd}	|d|	t  ttt d fƒt|	 ttd	 ƒ ks t‚|d	|	t  ttd tfƒt|	 td	t ƒ ks4t‚||ttƒttƒ ttt ƒ ttdtfƒƒd	t td	  td	t ƒ ks„t‚||ttƒtd	t t ƒ td	t ƒ ttt d fƒƒtd	 td	  ttd	 ƒ ksÞt‚||ttƒttt ƒ ttƒ ttdƒƒd	td	  t kst‚||tt ttd	   ttt ƒ ttƒ ttt ƒ td	t ƒ td	t t ƒ t tt|ttƒ dƒ|d	ttƒ d	ƒfƒƒtt tt  tt  ks¼t‚ˆ|d	ttƒ t d  ttƒ td	t d t ƒ tt d t ƒ td	t t ƒ ttdttƒ d fƒƒd	ttd	 ƒ t ksFt‚ˆ|dtdt   t tdt  d	   ttƒ td	t dt  ƒ td	t t ƒ ttdttƒ d	 d fƒƒt td	  t d td	tt d   ƒd	 t  ttd	tt d   ƒd	 td	     t d t  kst‚ˆ|dtdt    t t tdt    ttƒ tt dt  ƒ tt t d	 ƒ ttdttƒ d fƒƒt t td	tt d   ƒd	 t  ks´t‚|dtd  ttdtfƒt!tƒd
 td	t ƒ ksìt‚| |dtd
  ttt dfƒddt!tƒd ttd	 ƒ ks.t‚|ttttt ƒ  ttdƒt!td	 ƒks^t‚|ttttt d ƒ  ttdƒt!td d	 ƒks–t‚|tttdt t ƒ  ttt"ddƒdfƒt!ttƒd	 ƒksØt‚|ttttt ƒ  ttdƒt!d	d	t  ƒkst‚dd„ }
|
|
|ttt#tt ƒ  ttdƒƒƒt!d	t ƒtd	t ƒ t!td	 ƒttd	 ƒ  t!tƒttd	 ƒ t!d	d	t  ƒttd	 ƒ  t!t d	 ƒtt d	 ƒ  fks¼t‚|
|t|tt ƒ t ttdƒƒt!d	t d	 ƒtd	t ƒ t!d	d	t  ƒttd	 ƒ  t!tƒ tt d	 ƒ t!d	d	t  ƒttd	 ƒ  t!t d	 ƒtt d	 ƒ  fk	slt‚|ttt$j% ƒ ttƒt  ttt"ddƒdfƒt&ttƒƒk	s®t‚ˆ|ttd t ƒttd t d	 ƒ ttttƒ d t"dd
ƒfƒƒt'tdttƒ ƒk
st‚ˆ|dt tt$j%dt  ƒ tttd	 d  ƒ td	t td  ƒtd	dt  t ƒ  ttttƒd	  d t"d	d
ƒfƒƒtttƒƒt'tttƒƒ k
s¨t‚ˆ|dt ttd t ƒ tt$j%dt  ƒ tt$j%t td  ƒtd	dt  t ƒ  ttttƒ d t"d	d
ƒfƒƒt(ttƒƒt'tttƒƒ ks>t‚ˆ|ttt ƒtt$j%t ƒ ttƒtd	t ƒ td	t t ƒ  ttttƒ t$j%fƒƒt'tttƒƒd ks®t‚ˆ|ttƒtt$j%t ƒ ttƒtd	t t ƒ td	t t ƒ  ttdt$j%fƒƒt't ttƒƒt'tttƒƒ ks$t‚ˆ|d
t td t d	 ƒ ttd t d  t ƒ tt d t d  t d	 ƒttd t d  t d	 ƒ ttd t d  t d	 ƒ  ttttƒtt ƒ  d t$j%fƒƒt'tttƒƒt't ttƒƒ ksòt‚ˆ|ddt   t(tt d tt  d  tt  ƒ td t d	 ƒ ttd t d  t ƒ ttd t d  t ƒ tttd t d  t d	 ƒ ttd t d  t d	 ƒ  tt|ttƒ d tt ƒd  ttƒ d tt ƒd  ƒt$j%fƒƒt'tttƒƒt't  ttƒƒt't ttƒƒt(tt  ƒ    ttt  ƒ ks2t‚|tt(tt ƒ ttdt$j%fƒttƒtd	  ksht‚d S )!Nr   ©rn   rX   )Úcot©Úpowsimprs   rQ   rL   rB   r[   )rQ   N©NrB   ÚrT©Úrealza brP   c                    s    ˆˆ t | ddddƒ tt¡S )NF)ÚdeepT©Úforce)r   Úreplacer#   r"   )rV   ©r~   rt   rE   rF   Ú	simp_powsW  s    z0test_inverse_mellin_transform.<locals>.simp_powsrc   )r   Nr\   r]   r_   r„   r^   r`   )rJ   r   ra   c                 S   sJ   ddl m} ddlm} ddlm} |||| ddddddd tt¡S )Nr   r{   r}   )Ú
logcombineTr„   )r…   rƒ   )	Úsympy.core.functionrn   Úsympy.simplify.powsimpr~   ry   r‰   r†   r#   r"   )rV   rn   r~   r‰   rE   rE   rF   Úmysimp‚  s    þ þz-test_inverse_mellin_transform.<locals>.mysimprJ   ))rŠ   rn   rb   rY   rZ   Ú(sympy.functions.elementary.trigonometricr|   r‹   r~   ry   rt   r   r1   r;   r:   r   r"   rD   r.   r   rR   rM   r(   r   rd   re   r?   r>   r   r    r%   r<   r=   r$   r   r)   r   rS   r/   r+   r'   )rn   rY   rZ   r|   ZIMTr€   Z_aÚ_brˆ   rc   rŒ   rE   r‡   rF   Útest_inverse_mellin_transform5  s‚   $*$ÿ*ÿ
*ÿ
>$ ÿÿþ
DH64,ÿ
&  ÿþ
(ÿ
"ÿ
ÿ
ÿÿÿ   þý
4ÿÿ  þý
Bÿ  ÿDÿ
ÿþ
Bÿ  ÿ"þ
8"ÿ
08B4$.4ÿÿþ 68ÿÿþ.
ÿ
Dÿ
0&ÿ  þý
,(ÿ  þý
"ÿ  þý
&ÿ  þý
28ÿÿ  ýü
Dÿÿ:þ :üÿ
ÿû
r   c            
         s¬  ddl m‰ m‰m‰ ddlm}  ddlm‰ t}t	}‡ ‡‡‡fdd„}dd„ }t
d	d
d}tdƒ}t
dd
d}t
dd
d}t
dd
d}	t|tƒt|ƒt|tƒt|ƒksªt‚t	||ƒ|tƒt||ƒ|tƒksÎt‚||tdtd| t ƒ ƒt|ƒƒ||| ƒ| kst‚||tdt|t ƒ ƒdt|t ƒ  t|ƒƒ||| ƒd | ksRt‚| |t| t ƒttƒ t|ƒtdd|dt t |   ks–t‚|d|dt t t   t|	ddt| |	 ƒd
fksÒt‚|d|dt t t   t|	 dddkst‚|d|dt t t   tt
d	d
ddddks8t‚| |tt| t ƒ ttƒ t|ƒtdd|dt t |  d  ks„t‚|t| t ƒt|t ƒ ttƒ t|ƒ||d |dt t |  d   ksØt‚|t| td  ƒt|ƒttƒttd  |d  | ƒ t|ƒ ks"t‚|tt| ƒtt| d  | ƒ |tƒt| td  ƒksdt‚|t| ttƒ ƒt|ƒd| |d dtd  |d    ks¨t‚d S )Nr   )rn   Úexpand_complexÚexpand_trig)Úfactorrs   c                    s   ˆˆˆˆ | ƒƒƒƒS ©NrE   ©r:   ©rn   r   r‘   rt   rE   rF   ÚsimpÉ  s    z$test_fourier_transform.<locals>.simpc                 S   s   t t|  ƒt|   S r“   )r(   r   r”   rE   rE   rF   ÚsincÌ  s    z$test_fourier_transform.<locals>.sincÚkTr   rA   r<   rP   r=   ÚposkrB   rL   )Ú	extensionFrK   )r   Tru   r[   )rŠ   rn   r   r‘   Zsympy.polys.polytoolsr’   ry   rt   r   r   r   r   r:   r   rD   r   r.   rf   r"   r   r   r(   r%   )
r’   ZFTZIFTr–   r—   r˜   rA   r<   r=   r™   rE   r•   rF   Útest_fourier_transformÂ  sb    $  ÿÿ:J$ÿ
ÿÿ
ÿÿ
$ÿÿ
(ÿ
("ÿ
JBr›   c                  C   s  t dƒ} t dƒ}t dƒ}tdƒ}t|| ƒ| |ƒt|| ƒ| |ƒksDt‚t||ƒ|| ƒt||ƒ|| ƒksht‚tdt| ƒ | |ƒdt|ƒ ksŒt‚tdt|ƒ || ƒdt| ƒ ks°t‚tdt| ƒ d | |ƒdt|ƒ ksØt‚t| |  | |ƒd| tj	  ||d   t
| d d ƒ t
|d d ƒ ks.t‚td| tdƒd   ||d   t
| d d ƒ t
|d tj	 ƒ || ƒ| |  ksŒt‚tt| |  ƒ| |ƒtdƒ| ttƒ|d |d    ksÌt‚ttdƒ| ttƒ|d |d    || ƒt| |  ƒkst‚tt| ƒ|  | |ƒtdƒttƒ t|d ƒdt    d ksPt‚t| t| | d  ƒ | |ƒtdƒ| t|d  d|  ƒ d|tddƒ   ks¨t‚ttdƒ| t|d  d|  ƒ d|tddƒ   || ƒ| t| | d  ƒ ks t‚d S )	NÚtÚwr<   rA   rB   r^   rL   r[   )r   r   r   r   rD   r   r   r%   r   rS   r1   r"   r   r$   r   r   )rœ   r   r<   rA   rE   rE   rF   Útest_sine_transformü  s–    $  ÿÿ$$(
ÿ
ÿÿÿ
ÿÿ
ÿÿÿ ÿÿ
  ÿ"ÿ
"  ÿÿ

  ÿ(ÿ
  ÿ2ÿ
2  ÿÿrž   c                  C   s.  ddl m} m} tdƒ}tdƒ}tdƒ}tdƒ}t||ƒ||ƒt||ƒ||ƒksTt‚t||ƒ||ƒt	||ƒ||ƒksxt‚tdt
|ƒ ||ƒdt
|ƒ ksœt‚tdt
|ƒ ||ƒdt
|ƒ ksÀt‚td|d |d   ||ƒt
dƒt
tƒ t| | ƒ d|  kst‚t||  ||ƒd| tj  ||d   t| d d ƒ t|d ƒ ksZt‚td| tdƒd   ||d   t| d tj ƒ t|d ƒ ||ƒ||  ks´t‚tt| | ƒ||ƒt
dƒ| t
tƒ|d |d    ksôt‚tt
dƒ| t
tƒ|d |d    ||ƒt| | ƒks4t‚tt| t
|ƒ ƒt|t
|ƒ ƒ ||ƒ|t|d  d|  ƒ d|td	dƒ   kst‚td||  ||ƒt
dƒd
||| ƒ t t|| ƒ d t|| ƒ| || ƒ   t
tƒ ksöt‚tt
dƒttjdfdftjddftjff|d |d  d ƒ dt  ||ƒd||  ksVt‚tdt
|d |d  ƒ ||ƒt
dƒttjfdfdtjff|d |d  d ƒ dt
tƒ  ks¼t‚tt
dƒttjfdfdtjff|d |d  d ƒ dt
tƒ  ||ƒd|t
|d |d  d ƒ  ks*t‚d S )Nr   )rp   rr   rœ   r   r<   rA   rB   rL   r^   rJ   rE   r[   )r   r   )rx   rp   rr   r   r   r   r   rD   r	   r   r%   r   r"   r   rS   r1   r'   r   r(   r2   )rp   rr   rœ   r   r<   rA   rE   rE   rF   Útest_cosine_transform  s¾    $  ÿÿ$$ÿ ÿ$ÿ
ÿ ÿ8ÿ

ÿÿ
ÿÿ
ÿ ÿÿ
  ÿ"ÿ
"  ÿÿ
ÿ ÿ*ÿ
:ÿÿ
 ÿÿÿ ÿ
ÿ
&
 
 ÿ
ÿrŸ   c                  C   sØ  t dƒ} t dƒ}t dƒ}t dƒ}tdƒ}td|  | |dƒd| ksFt‚td| || dƒd|  ksdt‚td| |  | |dƒd| d  ||d   t| d d ƒ t|d ƒ ks¶t‚td| d  ||d   t| d d ƒ t|d ƒ || dƒ| |  kst‚td| |  | ||ƒdd|   ||d   t| d |d  d ƒ t|d |d  ƒ kslt‚td| d  ||d   t| d |d  d ƒ t|d |d  ƒ || |ƒ| |  ksÎt‚t| | t| |  ƒ | ||ƒd|d  | || d	   |d |d  d | td	ƒd    t|td	dƒ ƒ t	t
ƒ ksRt‚td|d  | || d	   |d |d  d | td	dƒ   t|td	dƒ ƒ t	t
ƒ || |ƒ| | t| |  ƒ ksÔt‚d S )
Nr€   r˜   rc   Úmr<   rB   r   rL   r^   )r   r   r
   rD   r   r1   r"   r   r   r%   r   )r€   r˜   rc   r    r<   rE   rE   rF   Útest_hankel_transformI  s|    
   ÿ6ÿ6   ÿÿ
Fÿ
ÿÿÿ  ÿÿ
4ÿÿÿÿÿ
Bÿÿ  þþr¡   c                   C   s    t ddt  ttƒd kst‚d S r   )r   r:   r;   rD   rE   rE   rE   rF   Útest_issue_7181e  s    r¢   c                      sŠ   t t d   ddt d   t d   tdt d  ƒ tt t t ƒ ttttdt d  ƒd ƒ ƒ ttƒ ‰ t	t
‡ fdd„ƒ d S )NrB   r[   rL   c                      s   t ˆ ttdtffdddœŽS )NrQ   T)Z
as_meijergZneedeval)r   r;   r:   r   rE   ©ÚFrE   rF   Ú<lambda>u  s    ÿz!test_issue_8882.<locals>.<lambda>)r<   r;   r%   r"   r   r   r(   r&   r1   r9   r   rE   rE   r£   rF   Útest_issue_8882i  s    
Jÿÿr¦   c                  C   s8   t ddd\} }tt| ƒ| |ƒtt| ƒ| |ƒks4t‚d S )Nzx yTr   )r   r   r"   r   rD   )r:   ÚyrE   rE   rF   Útest_issue_12591z  s    r¨   N)grC   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   Zsympy.integrals.laplacer   r   rŠ   r   r   Z
sympy.corer   Zsympy.core.numbersr   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z(sympy.functions.combinatorial.factorialsr   Z$sympy.functions.elementary.complexesr    r!   Z&sympy.functions.elementary.exponentialr"   r#   r$   rb   r%   r   r&   r'   r(   r)   Zsympy.functions.special.besselr*   r+   r,   r-   Z'sympy.functions.special.delta_functionsr.   rx   r/   r0   Z'sympy.functions.special.gamma_functionsr1   Zsympy.functions.special.hyperr2   Zsympy.simplify.gammasimpr3   Zsympy.simplify.hyperexpandr4   Zsympy.simplify.trigsimpr5   Zsympy.testing.pytestr6   r7   r8   r9   Z	sympy.abcr:   r;   r<   r=   r>   r?   rc   rd   re   rG   rH   rO   rW   rh   rj   ro   rz   r   r›   rž   rŸ   r¡   r¢   r¦   r¨   rE   rE   rE   rF   Ú<module>   sX   L ?
`
!
 :#*