o
    GZŽhO  ã                   @   s  d dl mZ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 d dl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 d dlmZmZm Z!m"Z# d dl$m%Z&m'Z(m)Z* d dl+m,Z,m-Z-m.Z. e
dddZ/e
ddddZ0e	dƒZ1dd„ Z2dd„ Z3dd„ Z4dd„ Z5dS )é    )ÚIÚRationalÚooÚpiÚzoo)ÚS)ÚDummyÚSymbol)Úatanh)Úsqrt)ÚsinÚtan)Úgamma)ÚhyperÚmeijerg)ÚIntegral)ÚO)Ú
elliptic_kÚ
elliptic_fÚ
elliptic_eÚelliptic_pi)Útest_derivative_numericallyÚrandom_complex_numberÚverify_numerically)ÚzÚmÚnÚiT)ÚintegerÚk)r   ZpositiveÚtc               	   C   s  t dƒtd ks
J ‚t tjƒdttddƒ  ttddƒƒd  ks#J ‚t dƒtu s+J ‚t dƒttddƒƒd dtdt ƒ  ksBJ ‚t tƒdksJJ ‚t t ƒdksSJ ‚t t	t ƒdks]J ‚t t	 t ƒdkshJ ‚t tƒdkspJ ‚t t
ƒ t
¡tt
ƒdt
 t t
ƒ  dt
 dt
   ksJ ‚tt t
ƒt
ƒs–J ‚tdd	d
} t | ƒ ¡ t |  ¡ ƒksªJ ‚tddd}t |ƒ ¡ t |ƒks¼J ‚t t
ƒ t¡td ttjtjftjft
ƒ ksÕJ ‚tt t
ƒtd ttjtjftjft
ƒ ƒsìJ ‚t t
ƒ t¡ttjtjfg ftjftjfft
 ƒd ksJ ‚tt t
ƒttjtjfg ftjftjfft
 ƒd ƒs(J ‚t t
ƒ t
¡td tt
 d  dt t
d  d  dt t
d  d  dt t
d  d  dt t
d  d  tt
d ƒ ksjJ ‚t tƒ t¡ tdtdtttƒd   ƒ tdtd fƒ¡s‹J ‚d S )Nr   é   é   é   éÿÿÿÿé   é   r   F©ÚrealT©Únegativeé	   é€   é   é   iÉ  é €  i  é   é   é   )ÚKr   r   ÚHalfr   r   r   r   r   r   r   ÚdiffÚEÚtdr	   Ú	conjugateÚrewriter   ÚOneÚtnr   ÚZeroÚseriesr   r   r   Údummy_eqr   r    )ZziZzr© r?   úd/var/www/auris/lib/python3.10/site-packages/sympy/functions/special/tests/test_elliptic_integrals.pyÚtest_K   sF   2.:ÿ.(
ÿ:2ÿÿÿ
ÿ*ÿrA   c               	   C   sL  t tdƒtks	J ‚t dtƒdksJ ‚t tt d tƒtttƒ ks#J ‚t ttƒdks,J ‚t tt ƒdks6J ‚t t tƒt ttƒ ksDJ ‚t ttƒ t¡dtdtt	tƒd   ƒ ks\J ‚t ttƒ t¡t
ttƒdt dt   t ttƒdt   t	dt ƒddt  tdtt	tƒd   ƒ   ks”J ‚tƒ } tt t| ƒtƒs¡J ‚tt | tƒtƒs«J ‚tddd}t t|ƒ ¡ t t ¡ | ¡ ƒksÃJ ‚tddd	}t t|ƒ ¡ t t ¡ |ƒksÙJ ‚t ttƒ t¡ttd
 dtd  d td    ttd  d  ttd ƒ ksJ ‚t ttƒ t¡ tdtdtt	tƒd   ƒ tdtfƒ¡s$J ‚d S )Nr   r!   r&   r%   r   Fr'   Tr)   r0   r#   é(   é   r2   )ÚFr   r   r   r   r3   r   r5   r   r   r6   Úrandcplxr7   r	   r8   r=   r   r9   r   r>   r    ©ÚrÚmiÚmrr?   r?   r@   Útest_F6   s.   "08.
ÿ$ >
ÿ&ÿrJ   c                  C   s  t tdƒtks	J ‚t dtƒdksJ ‚t tt d tƒtt tƒ ks#J ‚t ttƒtu s,J ‚t tt ƒtu s6J ‚t dƒtd ks@J ‚t dƒdksHJ ‚t tƒtt ksRJ ‚t t ƒtu s[J ‚t tƒtu scJ ‚t t tƒt ttƒ ksqJ ‚t ttƒ t¡t	dtt
tƒd   ƒks‡J ‚t ttƒ t¡t ttƒtttƒ dt  ksŸJ ‚t tƒ t¡t tƒttƒ dt  ks´J ‚tƒ } tt | tƒtƒsÁJ ‚tt t| ƒtƒsËJ ‚tt tƒtƒsÔJ ‚tddd}t t|ƒ ¡ t t ¡ | ¡ ƒksìJ ‚t |ƒ ¡ t | ¡ ƒksúJ ‚tddd}t t|ƒ ¡ t t ¡ |ƒksJ ‚t |ƒ ¡ t |ƒksJ ‚t tƒ t¡td ttd	dƒtjftjftƒ ks:J ‚tt tƒtd ttd	dƒtjftjftƒ ƒsTJ ‚t tƒ t¡ttjtd
dƒfg ftjftjfft ƒ d ksvJ ‚tt tƒttjtd
dƒfg ftjftjfft ƒ d ƒs–J ‚t ttƒ t¡ttd td  d td    ttd
  d  ttd ƒ ksÀJ ‚t tƒ t¡td tt d  d
t td  d  dt td
  d  dt td  d  dt td  d  ttd ƒ ksJ ‚t dt td  ƒ t¡td tt d  ttd  d  d
t td
  d  dt td  d  dt td  d  ttd ƒ ksHJ ‚t ttƒ t¡ tt	dtt
tƒd   ƒtdtfƒ¡sfJ ‚t tƒ t¡ tt	dtt
tƒd   ƒtdtd fƒ¡s…J ‚d S )Nr   r!   r&   r   Fr'   Tr)   r$   r#   r%   r0   rB   rC   r2   r"   r,   r.   é¯   r/   i¹  r1   é   é]   )r6   r   r   r   r   r   r   r   r5   r   r   rD   r3   rE   r7   r	   r8   r9   r   r   r   r4   r:   r;   r   r<   r=   r   r   r>   r    rF   r?   r?   r@   Útest_EQ   sf   ",0*$"84.
ÿ@<
ÿ2ÿÿÿ
ÿj
ÿ"
ÿ&ÿrN   c               
   C   sì  t dttƒtttƒksJ ‚t dttƒtttƒtdtttƒd   ƒttƒ tttƒ dt   ks3J ‚t tt	t
 d tƒt	t ttƒ ksFJ ‚t ttdƒtttd ƒttƒ ƒttd ƒ ks`J ‚t tttƒtttƒt dttƒ ttƒtdtttƒd   ƒ  ksƒJ ‚t tttƒdksJ ‚t t ttƒdks˜J ‚t tttƒdks¢J ‚t ttt ƒdks­J ‚t dtƒttƒks¸J ‚t dtƒtu sÁJ ‚t tdƒt
dtdt ƒ  ksÒJ ‚t ddƒt u sÜJ ‚t ddƒtu såJ ‚t ttƒttƒdt  ksôJ ‚t tt tƒt tttƒ ksJ ‚tdddtddd} }t | t|ƒ ¡ t |  ¡ t ¡ | ¡ ƒks)J ‚tdd	d
tdd	d
}}t |t|ƒ ¡ t |t ¡ |ƒksIJ ‚t ttƒ ¡ t t ¡ t ¡ ƒks\J ‚t tttƒ t¡tttƒtt tttƒ t  td t t tttƒ t  ttdtttƒd   ƒ tdt ƒ ddtttƒd      dtt  td   ks°J ‚t tttƒ t¡dtdtttƒd   ƒdtttƒd     ksÔJ ‚t tttƒ t¡tttƒtd  t tttƒ ttdt ƒ dtd  tdtttƒd   ƒ   dtt   ksJ ‚t ttƒ t¡ttƒtt ttƒ t  td t t ttƒ t  dtt  td   ks?J ‚t ttƒ t¡ttƒtd  t ttƒ dtt   ks]J ‚t tttƒ t¡ttd td td    td dtd  d tt d  td  td d  td    ttd ƒ ksJ ‚t tttƒ t¡ tddtttƒd   tdtttƒd   ƒ  tdtfƒ¡sÈJ ‚t ttƒ t¡ tddtttƒd   tdtttƒd   ƒ  tdt
d fƒ¡sôJ ‚d S )Nr   r&   r!   r$   r   Fr'   r   Tr)   r#   r2   r0   rB   é
   rC   rL   )ÚPr   r   rD   r   r   r   r6   r   r   r   r
   r   r3   r   r	   r8   r5   r=   r   r9   r   r>   r    )ÚnirH   ÚnrrI   r?   r?   r@   Útest_P€   s~   0
ÿ&4F""
ÿ

ÿ&&.ÿÿ
ÿÿÿþH,2ÿ
ÿ(ÿÿ<*>ÿ
ÿ:
ÿ>ÿrS   N)6Zsympy.core.numbersr   r   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r	   Z%sympy.functions.elementary.hyperbolicr
   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   Z'sympy.functions.special.gamma_functionsr   Zsympy.functions.special.hyperr   r   Zsympy.integrals.integralsr   Zsympy.series.orderr   Z*sympy.functions.special.elliptic_integralsr   r3   r   rD   r   r6   r   rP   Zsympy.core.randomr   r7   r   rE   r   r;   Z	sympy.abcr   r   r   r   Újr    rA   rJ   rN   rS   r?   r?   r?   r@   Ú<module>   s(     /