U
    L?hO  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$m%Z&m'Z(m)Z* d dl+m,Z,m-Z-m.Z. e
dddZ/e
ddddZ0e	dƒZ1dd„ Z2dd„ Z3dd„ Z4dd„ Z5dS )é    )ÚIÚRationalÚooÚpiÚzoo)ÚS)ÚDummyÚSymbol)Úatanh)Úsqrt)ÚsinÚtan)Úgamma)ÚhyperÚmeijerg)ÚIntegral)ÚO)Ú
elliptic_kÚ
elliptic_fÚ
elliptic_eÚelliptic_pi)Útest_derivative_numericallyÚrandom_complex_numberÚverify_numerically)ÚzÚmÚnÚiT)ÚintegerÚk)r   ZpositiveÚtc               	   C   s&  t dƒtd kst‚t tjƒdttddƒ  ttddƒƒd  ksFt‚t dƒtksVt‚t dƒttddƒƒd dtdt ƒ  ks„t‚t t	ƒdks”t‚t t	 ƒdks¦t‚t t
t	 ƒdksºt‚t t
 t	 ƒdksÐt‚t tƒdksàt‚t tƒ t¡ttƒdt t tƒ  dt dt   kst‚tt tƒtƒs0t‚tdd	d
} t | ƒ ¡ t |  ¡ ƒksZt‚tddd}t |ƒ ¡ t |ƒks€t‚t tƒ t¡td ttjtjftjftƒ ks´t‚tt tƒtd ttjtjftjftƒ ƒsät‚t tƒ t¡ttjtjfg ftjftjfft ƒd ks"t‚tt tƒttjtjfg ftjftjfft ƒd ƒs\t‚t tƒ t¡td tt d  dt td  d  dt td  d  dt td  d  dt td  d  ttd ƒ ksàt‚t tƒ t¡ tdtdtttƒd   ƒ tdtd fƒ¡s"t‚d S )Nr   é   é   é   éÿÿÿÿé   é   r   F©ÚrealT©Únegativeé	   é€   é   é   iÉ  é €  i  é   é   é   )ÚKr   ÚAssertionErrorr   ÚHalfr   r   r   r   r   r   r   ÚdiffÚEÚtdr	   Ú	conjugateÚrewriter   ÚOneÚtnr   ÚZeroÚseriesr   r   r   Údummy_eqr   r    )ZziZzr© r@   úg/var/www/html/venv/lib/python3.8/site-packages/sympy/functions/special/tests/test_elliptic_integrals.pyÚtest_K   sF    2.<ÿ
0(ÿ
:2ÿÿÿ
ÿ*ÿrB   c               	   C   sV  t tdƒtkst‚t dtƒdks$t‚t tt d tƒtttƒ ksFt‚t ttƒdksXt‚t tt ƒdkslt‚t t tƒt ttƒ ksˆt‚t ttƒ t¡dt	dtt
tƒd   ƒ ks¸t‚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*t‚tƒ } tt t| ƒtƒsFt‚tt | tƒtƒs\t‚tddd}t t|ƒ ¡ t t ¡ | ¡ ƒksŽt‚tddd	}t t|ƒ ¡ t t ¡ |ƒks¼t‚t ttƒ t¡ttd
 dtd  d td    ttd  d  ttd ƒ kst‚t ttƒ t¡ tdt	dtt
tƒd   ƒ tdtfƒ¡sRt‚d S )Nr   r!   r&   r%   r   Fr'   Tr)   r0   r#   é(   é   r2   )ÚFr   r4   r   r   r   r3   r   r6   r   r   r7   Úrandcplxr8   r	   r9   r>   r   r:   r   r?   r    ©ÚrÚmiÚmrr@   r@   rA   Útest_F6   s.    "08.ÿ&">ÿ
&ÿrK   c                  C   s  t tdƒtkst‚t dtƒdks$t‚t tt d tƒtt tƒ ksFt‚t ttƒtksXt‚t tt ƒtkslt‚t dƒtd ks€t‚t dƒdkst‚t tƒtt ks¤t‚t t ƒtks¶t‚t tƒtksÆt‚t t tƒt ttƒ ksât‚t ttƒ 	t¡t
dtttƒd   ƒkst‚t ttƒ 	t¡t ttƒtttƒ dt  ksBt‚t tƒ 	t¡t tƒttƒ dt  ksnt‚tƒ } tt | tƒtƒsŠt‚tt t| ƒtƒs t‚tt tƒtƒs´t‚tddd}t t|ƒ ¡ t t ¡ | ¡ ƒksæt‚t |ƒ ¡ t | ¡ ƒkst‚tddd}t t|ƒ ¡ t t ¡ |ƒks2t‚t |ƒ ¡ t |ƒksLt‚t tƒ t¡td ttd	dƒtjftjftƒ ks„t‚tt tƒtd ttd	dƒtjftjftƒ ƒs¸t‚t tƒ t¡ttjtd
dƒfg ftjftjfft ƒ d ksüt‚tt tƒttjtd
dƒfg ftjftjfft ƒ d ƒs<t‚t ttƒ t¡ttd td  d td    ttd
  d  ttd ƒ kst‚t tƒ t¡td tt d  d
t td  d  dt td
  d  dt td  d  dt td  d  ttd ƒ kst‚t dt td  ƒ t¡td tt d  ttd  d  d
t td
  d  dt td  d  dt td  d  ttd ƒ ks t‚t ttƒ t¡ tt
dtttƒd   ƒtdtfƒ¡sÜt‚t tƒ t¡ tt
dtttƒd   ƒtdtd fƒ¡st‚d S )Nr   r!   r&   r   Fr'   Tr)   r$   r#   r%   r0   rC   rD   r2   r"   r,   r.   é¯   r/   i¹  r1   é   é]   ) r7   r   r4   r   r   r   r   r   r   r6   r   r   rE   r3   rF   r8   r	   r9   r:   r   r   r   r5   r;   r<   r   r=   r>   r   r   r?   r    rG   r@   r@   rA   Útest_EQ   sf    ".2,&"84.ÿ
@<ÿ
2ÿÿÿ
ÿjÿ
"ÿ
&ÿrO   c               
   C   s  t dttƒtttƒkst‚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sft‚t t	t
t d tƒt
t t	tƒ ksŒt‚t t	tdƒttt	d ƒttƒ ƒtt	d ƒ ksÀt‚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st‚t tttƒdkst‚t t ttƒdks6t‚t t	ttƒdksLt‚t t	tt ƒdksdt‚t dtƒttƒks|t‚t dtƒtkst‚t t	dƒtdtdt	 ƒ  ks´t‚t ddƒt ksÊt‚t ddƒtksÞt‚t t	t	ƒtt	ƒdt	  ksþt‚t t	t tƒt t	ttƒ ks t‚tdddtddd } }t | t|ƒ ¡ t |  ¡ t ¡ | ¡ ƒksht‚tdd	d
tdd	d
 }}t |t|ƒ ¡ t |t ¡ |ƒks¨t‚t t	tƒ ¡ t t	 ¡ t ¡ ƒksÎt‚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svt‚t t	ttƒ t¡dtdtttƒd   ƒdt	ttƒd     ks¾t‚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s4t‚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”t‚t t	tƒ t¡ttƒtd  t t	tƒ dt	t   ksÐt‚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sPt‚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¡s¦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d fƒ¡sþt‚d S )Nr   r&   r!   r$   r   Fr'   r   Tr)   r#   r2   r0   rC   é
   rD   rM   )ÚPr   r   rE   r4   r   r   r   r7   r   r   r   r
   r   r3   r   r	   r9   r6   r>   r   r:   r   r?   r    )ÚnirI   ÚnrrJ   r@   r@   rA   Útest_P€   s~    0ÿ
&4H$ "ÿ


ÿ&&.ÿÿ
ÿÿÿþH,2ÿ
ÿ(ÿÿ<*>ÿ
ÿ:ÿ
>ÿrT   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   rE   r   r7   r   rQ   Zsympy.core.randomr   r8   r   rF   r   r<   Z	sympy.abcr   r   r   r   Újr    rB   rK   rO   rT   r@   r@   r@   rA   Ú<module>   s&    /