o
    jgÅi  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sJ ‚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@J ‚d S )Nr   )ÚMellinTransformÚfé   T)	Úsympy.integrals.transformsr@   r   r   r:   r;   r"   r1   r   )r@   rA   © rD   ú]/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/integrals/tests/test_transforms.pyÚtest_undefined_function$   s   $(ÿrF   c                  C   sJ   t dƒ} t| tƒttƒjthksJ ‚t| tƒt ttƒjtthks#J ‚d S )NrA   )r   r   r:   r;   Úfree_symbolsr<   )rA   rD   rD   rE   Útest_free_symbols,   s   &rH   c                  C   s„  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s'J ‚t|tƒttƒ d¡| |tƒt	dt
 t t t ƒ tt tfƒksKJ ‚t|tƒttdd d¡| |tƒt	t t ƒ tdtfƒkskJ ‚td	t t
 t|tƒttttfƒ d¡ ƒd
ks…J ‚td	t t
 t|tƒttƒ d¡ ƒdksœJ ‚t|tƒttƒ d¡| |tƒt	d	t
 t t t ƒ tt tfƒksÀJ ‚d S )Nr   )ÚIntegralrA   rI   rB   éþÿÿÿT©Ú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)))Úsympy.integrals.integralsrI   r   r   r:   r;   Úrewriter   r   r"   r   r   r   Ústrr   r<   r=   r   r   )rI   rA   rD   rD   rE   Útest_as_integral2   s(   ÿ,ÿ ÿ*ÿ$ÿ,ÿrQ   c                  C   sÜ  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skJ ‚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s¹J ‚| | 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sìJ ‚d S )NzRisch takes forever.r=   T©ÚpositiverM   éÿÿÿÿrB   )r8   r   r   r%   r:   r=   r<   Úsubsr;   r1   r    r   ÚHalfr   r   )ÚMTÚbposÚexprrD   rD   rE   Útest_mellin_transform_failE   s<   (:ÿ
ÿþÿ*ÿ
ÿÿýÿ4ÿÿrZ   c                  C   s¸  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/J ‚|tt tdt ƒ ttƒdtt  t
tƒ t	fdfksMJ ‚|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sxJ ‚|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s¬J ‚|dt t  ttƒttƒttt ƒ ttƒ dt
tƒfdfksÎJ ‚|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J ‚|dt td  tdt ƒ ttd td   ttd ƒ  ttƒ}|d sKJ |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~J ‚|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sÁJ ‚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J ‚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s]J ‚|tt ƒttƒttƒdt	fdfksrJ ‚|tdt ƒttƒtt ƒt	 dfdfksŠJ ‚|ttƒd	 tdt ƒ ttƒd
td  dt	fdfks¨J ‚|ttƒd ttd ƒ ttƒdtd	  t	 dfdfksÇJ ‚|ttd ƒttƒttttt ƒ  ddfksáJ ‚|tdt d ƒttƒttttt ƒ  ddfksýJ ‚|ttdt ƒƒttƒttttt ƒ  ddfksJ ‚|ttddt  ƒƒttƒttttt ƒ  ddfks7J ‚|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sZJ ‚d S )Nr   ©ÚMaxÚMinr=   TrR   rB   rT   rM   é   é   é   é   é   ©rT   r   ©r   rB   )Ú(sympy.functions.elementary.miscellaneousr\   r]   r   r   r:   Únur.   r;   r   r    Úbetar1   ÚrhoÚabsr(   r   r'   r<   r=   r%   rU   r   rV   r"   r$   r)   r/   r   )r\   r]   rW   rX   ÚmtrY   rD   rD   rE   Útest_mellin_transformc   s’   ÿÿ",ÿ""ÿÿ(ÿÿÿ
ÿÿýÿÿ4":
ÿ:"ÿ
ÿDÿ
ÿ(*ÿÿþ
ÿ*0<>488<*ÿrk   c                  C   sâ   t } | ttƒtd  ttƒ}|dd … dksJ ‚t|d dd t¡r%J ‚| ttƒd td  ttƒ}|dd … dks=J ‚t|d dd t¡rJJ ‚| ttƒtd d  ttƒ}|dd … dksbJ ‚t|d dd t¡roJ ‚d S )NrB   )rd   Tr   T)Úallow_hyperrM   ))r   rM   T)r   r$   r:   r;   r4   Úhasr2   )rW   rj   rD   rD   rE   Útest_mellin_transform2¢   s   rn   c               	   C   s˜  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s6J ‚|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†J ‚|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sÑJ ‚|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	J ‚|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sDJ ‚|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‹J ‚|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séJ ‚|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sJ ‚|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sWJ ‚|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sÇJ ‚|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s1J ‚|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sxJ ‚|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sùJ ‚|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J ‚|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sPJ ‚|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sJ ‚|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sÞJ ‚|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sWJ ‚|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s³J ‚|dd … | t	tƒ t	tƒƒtfdfksÊJ ‚d S )Nr   ©r\   rM   rB   ra   r^   TrJ   z3/2©Úfunc)re   r\   r   r+   r<   r%   r:   r;   r1   r    r   r(   r   rV   r'   r   r=   r-   r,   r   r*   r"   r3   r5   Úexpand)r\   rW   rj   Úmt0rD   rD   rE   Útest_mellin_transform_bessel²   s:  <ÿ .(ÿÿþÿ (*ÿÿþÿ"ÿþ
ÿ$&ÿ
þ
ÿ&*ÿþ
ÿ"*.ÿÿý
ÿ4
ÿ8&ÿ
ÿ .ÿÿ.þ.ý
ÿ N2ÿ&þ
ÿ".ÿþ
ÿ"4ÿÿ:þ4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$,@ÿ2rt   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s7J ‚tttƒt tt
dtfƒ t¡ ¡ |t
ƒksOJ ‚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spJ ‚|ttttƒ|t d
  tt
d
| tfƒ t¡jddƒƒt|t
ƒks•J ‚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sÁJ ‚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sêJ ‚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sJ ‚tdt  ttƒ ttƒ dt tt tj ƒ  t|dƒ ¡ |t|ƒƒks>J ‚d S )Nr   ro   )ÚCiÚE1ÚSi©Úsimplifyr<   T©ÚnegativeÚu)ÚpolarrB   rp   rM   rc   rd   r^   )re   r\   Ú'sympy.functions.special.error_functionsru   rv   rw   Úsympy.simplify.simplifyry   r   r   r:   r;   r1   r   r   rO   r0   rr   r<   r    r!   r%   r   r   rV   )r\   ru   rv   rw   ry   Úanegr|   rD   rD   rE   Útest_expint  s\   *ÿÿ*ÿ
ÿ
ÿÿý"ÿÿÿ"ÿÿþ:
ÿ0þþr   c               
      sf  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s4J ‚|tt ƒttt dfƒtdt ƒksIJ ‚ˆ|tdtd  d  ttdtfƒƒtd d	 td	t ƒ d
t  ksnJ ‚|d	td d	  ttdƒt tt d	 ƒ d ttd	 ƒdt   ks“J ‚|d	td d	  ttdƒt tt d	 ƒ d ttd	 ƒdt   ks¸J ‚|ttƒttd	 ƒ ttd	tfƒtd	 tt ƒ t ksÖJ ‚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J ‚tddd\}}||t |  tt| ƒ t ttdtfƒt| t|  ƒks1J ‚|t|| t|  ƒ|t  tt| tfƒt| tt|  ƒ ksUJ ‚‡ ‡fdd„}tddd}	|d|	t  ttt d fƒt|	 ttd	 ƒ ks}J ‚|d	|	t  ttd tfƒt|	 td	t ƒ ks—J ‚||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¿J ‚||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sìJ ‚||ttƒttt ƒ ttƒ ttdƒƒd	td	  t ksJ ‚||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s[J ‚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s J ‚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J ‚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sWJ ‚|dtd  ttdtfƒt tƒd
 td	t ƒ kssJ ‚| |dtd
  ttt dfƒddt tƒd ttd	 ƒ ks”J ‚|ttttt ƒ  ttdƒt td	 ƒks¬J ‚|ttttt d ƒ  ttdƒt td d	 ƒksÈJ ‚|tttdt t ƒ  ttt!ddƒdfƒt ttƒd	 ƒkséJ ‚|ttttt ƒ  ttdƒt d	d	t  ƒksJ ‚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v s[J ‚|
|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v s³J ‚|ttt#j$ ƒ ttƒt  ttt!ddƒdfƒt%ttƒƒksÔJ ‚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J ‚ˆ|dt tt#j$dt  ƒ tttd	 d  ƒ td	t td  ƒtd	dt  t ƒ  ttttƒd	  d t!d	d
ƒfƒƒtttƒƒt&tttƒƒ ksQJ ‚ˆ|dt ttd t ƒ tt#j$dt  ƒ tt#j$t td  ƒtd	dt  t ƒ  ttttƒ d t!d	d
ƒfƒƒt'ttƒƒt&tttƒƒ ksœJ ‚ˆ|ttt ƒtt#j$t ƒ ttƒtd	t ƒ td	t t ƒ  ttttƒ t#j$fƒƒt&tttƒƒd ksÔJ ‚ˆ|ttƒtt#j$t ƒ ttƒtd	t t ƒ td	t t ƒ  ttdt#j$fƒƒt&t ttƒƒt&tttƒƒ ksJ ‚ˆ|d
t td t d	 ƒ ttd td  t ƒ tt d td  t d	 ƒttd td  t d	 ƒ ttd td  t d	 ƒ  ttttƒttƒ  d t#j$fƒƒt&tttƒƒt&tttƒƒ ksvJ ‚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$fƒƒt&tttƒƒt&t ttƒƒt&tttƒƒt'tt ƒ    ttt ƒ ksJ ‚|tt'tt ƒ ttdt#j$fƒttƒtd	  ks1J ‚d S )!Nr   ©rr   r[   )Úcot©Úpowsimprx   rT   rM   rB   r^   )rT   N©NrB   ÚrT©Úrealza brR   c                    s    ˆˆ t | ddddƒ tt¡S )NF)ÚdeepT©Úforce)r   Úreplacer#   r"   )rY   ©r…   ry   rD   rE   Ú	simp_powsW  ó    z0test_inverse_mellin_transform.<locals>.simp_powsrf   )r   Nr_   r`   rb   r‹   ra   rc   )rJ   r   rd   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‹   )rŒ   rŠ   )	Úsympy.core.functionrr   Úsympy.simplify.powsimpr…   r   r‘   r   r#   r"   )rY   rr   r…   r‘   rD   rD   rE   Úmysimp‚  s   þþz-test_inverse_mellin_transform.<locals>.mysimprJ   )(r’   rr   re   r\   r]   Ú(sympy.functions.elementary.trigonometricrƒ   r“   r…   r   ry   r   r1   r;   r:   r   r"   r.   r   rU   rO   r(   r   rg   rh   r?   r>   r   r    r%   r<   r=   r$   r   r)   r   rV   r/   r+   r'   )rr   r\   r]   rƒ   ÚIMTr‡   Ú_aÚ_br   rf   r”   rD   rŽ   rE   Útest_inverse_mellin_transform5  sP  $*$ÿ*ÿ*ÿ<"
þDH64,
ÿ&ÿ
þ(
ÿ"ÿ
ÿ
ÿÿÿ$þ
ý4ÿÿþ
ýBÿÿDÿ
ÿ
þBÿÿ"
þ8"
ÿ08B4$.4ÿÿþ 68ÿÿþ.

ÿD
ÿ0&ÿþ
ý,(ÿþ
ý"ÿþ
ý&ÿþ
ý28ÿÿý
üDÿÿ:þ:üÿ
ÿ
û:r™   c            
         s¢  ddl m‰ m‰m‰ ddlm}  ddlm‰ t}t	}‡ ‡‡‡fdd„}dd„ }t
d	d
d}tdƒ}t
dd
d}t
dd
d}t
dd
d}	t|tƒt|ƒt|tƒt|ƒksUJ ‚t	||ƒ|tƒt||ƒ|tƒksgJ ‚||tdtd| t ƒ ƒt|ƒƒ||| ƒ| ksƒJ ‚||tdt|t ƒ ƒdt|t ƒ  t|ƒƒ||| ƒd | ks§J ‚| |t| t ƒttƒ t|ƒtdd|dt t |   ksÈJ ‚|d|dt t t   t|	ddt| |	 ƒd
fksåJ ‚|d|dt t t   t|	 dddksüJ ‚|d|dt t t   tt
d	d
ddddksJ ‚| |tt| t ƒ ttƒ t|ƒtdd|dt t |  d  ks=J ‚|t| t ƒt|t ƒ ttƒ t|ƒ||d |dt t |  d   ksgJ ‚|t| td  ƒt|ƒttƒttd  |d  | ƒ t|ƒ ksŒJ ‚|tt| ƒtt| d  | ƒ |tƒt| td  ƒks­J ‚|t| ttƒ ƒt|ƒd| |d dtd  |d    ksÏJ ‚d S )Nr   )rr   Úexpand_complexÚexpand_trig)Úfactorrx   c                    s   ˆˆˆˆ | ƒƒƒƒS ©NrD   ©r:   ©rr   rš   r›   ry   rD   rE   ÚsimpÉ  ó   z$test_fourier_transform.<locals>.simpc                 S   s   t t|  ƒt|   S r   )r(   r   rž   rD   rD   rE   ÚsincÌ  r¡   z$test_fourier_transform.<locals>.sincÚkTrˆ   rA   r<   rR   r=   ÚposkrB   rM   )Ú	extensionFrK   )r   Trz   r^   )r’   rr   rš   r›   Úsympy.polys.polytoolsrœ   r   ry   r   r   r   r   r:   r   r   r.   ri   r"   r   r   r(   r%   )
rœ   ÚFTÚIFTr    r¢   r£   rA   r<   r=   r¤   rD   rŸ   rE   Útest_fourier_transformÂ  s^   $
ÿÿ8H$ÿÿÿÿÿ$ÿ
ÿ(
ÿ("
ÿJBHr©   c                  C   sþ  t dƒ} t dƒ}t dƒ}tdƒ}t|| ƒ| |ƒt|| ƒ| |ƒks"J ‚t||ƒ|| ƒt||ƒ|| ƒks4J ‚tdt| ƒ | |ƒdt|ƒ ksFJ ‚tdt|ƒ || ƒdt| ƒ ksXJ ‚tdt| ƒ d | |ƒdt|ƒ kslJ ‚t| |  | |ƒd| tj  ||d   t	| d d ƒ t	|d d ƒ ks–J ‚td| tdƒd   ||d   t	| d d ƒ t	|d tj ƒ || ƒ| |  ksÄJ ‚tt
| |  ƒ| |ƒtdƒ| ttƒ|d |d    ksãJ ‚ttdƒ| ttƒ|d |d    || ƒt
| |  ƒksJ ‚tt| ƒ|  | |ƒtdƒttƒ t|d ƒdt    d ks%J ‚t| t
| | d  ƒ | |ƒtdƒ| t
|d  d|  ƒ d|tddƒ   ksQJ ‚ttdƒ| t
|d  d|  ƒ d|tddƒ   || ƒ| t
| | d  ƒ ks}J ‚d S )	NÚtÚwr<   rA   rB   ra   rM   r^   )r   r   r   r   r   r   r%   r   rV   r1   r"   r   r$   r   r   )rª   r«   r<   rA   rD   rD   rE   Útest_sine_transformü  s|   $
ÿÿ$$(
ÿ
ÿÿ
ÿ
ÿÿ
ÿÿÿÿÿÿ"ÿ&ÿ
ÿÿ(
ÿÿ2
ÿ6ÿÿr¬   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s*J ‚t||ƒ||ƒt||ƒ||ƒks<J ‚tdt	|ƒ ||ƒdt	|ƒ ksNJ ‚tdt	|ƒ ||ƒdt	|ƒ ks`J ‚td|d |d   ||ƒt	dƒt	t
ƒ t| | ƒ d|  ksƒJ ‚t||  ||ƒd| tj  ||d   t| d d ƒ t|d ƒ ks«J ‚td| tdƒd   ||d   t| d tj ƒ t|d ƒ ||ƒ||  ks×J ‚tt| | ƒ||ƒt	dƒ| t	t
ƒ|d |d    ksöJ ‚tt	dƒ| t	t
ƒ|d |d    ||ƒt| | ƒksJ ‚tt| t	|ƒ ƒt|t	|ƒ ƒ ||ƒ|t|d  d|  ƒ d|td	dƒ   ksDJ ‚td||  ||ƒt	dƒd
||| ƒ t
 t|| ƒ d t|| ƒ| || ƒ   t	t
ƒ kswJ ‚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s§J ‚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sÚJ ‚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J ‚d S )Nr   )ru   rw   rª   r«   r<   rA   rB   rM   ra   rJ   rD   r^   )r   r   )r~   ru   rw   r   r   r   r   r	   r   r%   r   r"   r   rV   r1   r'   r   r(   r2   )ru   rw   rª   r«   r<   rA   rD   rD   rE   Útest_cosine_transform  s¢   $
ÿÿ$$ÿÿ$ÿÿÿ8ÿ
ÿÿ
ÿÿ
ÿÿÿÿ"ÿ&ÿ
ÿÿÿ*
ÿ:ÿÿÿÿÿÿ

ÿ&&ÿ
ÿrr­   c                  C   sÒ  t dƒ} t dƒ}t dƒ}t dƒ}tdƒ}td|  | |dƒd| ks#J ‚td| || dƒd|  ks2J ‚td| |  | |dƒd| d  ||d   t| d d ƒ t|d ƒ ks[J ‚td| d  ||d   t| d d ƒ t|d ƒ || dƒ| |  ksƒJ ‚td| |  | ||ƒdd|   ||d   t| d |d  d ƒ t|d |d  ƒ ks´J ‚td| d  ||d   t| d |d  d ƒ t|d |d  ƒ || |ƒ| |  ksäJ ‚t| | t| |  ƒ | ||ƒd|d  | || d	   |d |d  d | td	ƒd    t|td	dƒ ƒ tt	ƒ ks&J ‚td|d  | || d	   |d |d  d | td	dƒ   t|td	dƒ ƒ tt	ƒ || |ƒ| | t| |  ƒ ksgJ ‚d S )
Nr‡   r£   rf   Úmr<   rB   r   rM   ra   )
r   r   r
   r   r1   r"   r   r   r%   r   )r‡   r£   rf   r®   r<   rD   rD   rE   Útest_hankel_transformI  sh   ÿ6ÿ<ÿÿFÿ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J ‚d S r†   )r   r:   r;   rD   rD   rD   rE   Útest_issue_7181e  r   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^   rM   c                      s    t ˆ ttdtffi dddœ¤ŽS )NrT   T)Ú
as_meijergÚneedeval)r   r;   r:   r   rD   ©ÚFrD   rE   Ú<lambda>u  s   ÿz!test_issue_8882.<locals>.<lambda>)r<   r;   r%   r"   r   r   r(   r&   r1   r9   r   rD   rD   r³   rE   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sJ ‚d S )Nzx yTrˆ   )r   r   r"   r   )r:   ÚyrD   rD   rE   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   Úsympy.integrals.laplacer   r   r’   r   r   Ú
sympy.corer   Úsympy.core.numbersr   r   r   r   Úsympy.core.singletonr   Úsympy.core.symbolr   r   Ú(sympy.functions.combinatorial.factorialsr   Ú$sympy.functions.elementary.complexesr    r!   Ú&sympy.functions.elementary.exponentialr"   r#   r$   re   r%   r•   r&   r'   r(   r)   Úsympy.functions.special.besselr*   r+   r,   r-   Ú'sympy.functions.special.delta_functionsr.   r~   r/   r0   Ú'sympy.functions.special.gamma_functionsr1   Úsympy.functions.special.hyperr2   Úsympy.simplify.gammasimpr3   Úsympy.simplify.hyperexpandr4   Úsympy.simplify.trigsimpr5   Úsympy.testing.pytestr6   r7   r8   r9   Ú	sympy.abcr:   r;   r<   r=   r>   r?   rf   rg   rh   rF   rH   rQ   rZ   rk   rn   rt   r   r™   r©   r¬   r­   r¯   r°   r¶   r¸   rD   rD   rD   rE   Ú<module>   sZ   L  ?
`
!
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