
    QiO                     >   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          Z/ e
ddd          Z0 e	d          Z1d Z2d Z3d Z4d Z5dS )    )IRationaloopizoo)S)DummySymbol)atanh)sqrt)sintan)gamma)hypermeijerg)Integral)O)
elliptic_k
elliptic_f
elliptic_eelliptic_pi)test_derivative_numericallyrandom_complex_numberverify_numerically)zmniT)integerk)r   positivetc                     t          d          t          dz  k    sJ t          t          j                  dt          t	          dd          z  z  t          t	          dd                    dz  z  k    sJ t          d          t          u sJ t          d          t          t	          dd                    dz  dt          dt          z            z  z  k    sJ t          t                    dk    sJ t          t                     dk    sJ t          t          t          z            dk    sJ t          t           t          z            dk    sJ t          t                    dk    sJ t          t                                        t                    t          t                    dt          z
  t          t                    z  z
  dt          z  dt          z
  z  z  k    sJ t          t          t                    t                    sJ t          dd	
          } t          |                                           t          |                                           k    sJ t          dd          }t          |                                          t          |          k    sJ t          t                                        t"                    t          dz  t#          t          j        t          j        ft          j        ft                    z  k    sJ t'          t          t                    t          dz  t#          t          j        t          j        ft          j        ft                    z            sJ t          t                                        t(                    t)          t          j        t          j        fg ft          j        ft          j        fft                     dz  k    sJ t'          t          t                    t)          t          j        t          j        fg ft          j        ft          j        fft                     dz            sJ t          t                                        t                    t          dz  t          t          z  dz  z   dt          z  t          dz  z  dz  z   dt          z  t          dz  z  dz  z   dt          z  t          dz  z  dz  z   dt          z  t          dz  z  dz  z   t/          t          dz            z   k    sJ t          t0                                        t2                                        t3          dt          dt0          t7          t8                    dz  z  z
            z  t8          dt          dz  f                    sJ d S )Nr                  r   FrealTnegative	            i     i           )Kr   r   Halfr   r   r   r   r   r   r   diffEtdr
   	conjugaterewriter   Onetnr   Zeroseriesr   r   r   dummy_eqr   r"   )zizrs     /var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/sympy/functions/special/tests/test_elliptic_integrals.pytest_KrE      sW   Q442a4<<<<QV99"hq!nn,,U8B??-C-CQ-FFFFFFQ443;;;;R55E(1a..))1,aQrT

l;;;;;R55A::::bS66Q;;;;QrT77a<<<<aRU88q====S66Q;;;;Q4499Q<<AaDDAE1Q44</!A#q1u+>>>>>addA;;	%	 	 	 BR55??",,.. 1 11111	d	#	#	#BR55??"%%%%Q44<<	Auafaf%x3334 4 4 4addRT5!&!&!1AE8Q???@@@@@Q44<<  !&!&!2&!&QVI(>CCAEF F F FaddGafaf-r2afY	4JQBOOPQQRRRRRQ44;;q>>RTBqDF]QrT!Q$Ys]:
2ad
3bAe+,.22gadl6.ABDEadGGL L L L L Q44<<!!**4Ac!ffaiK(((1aA,779 9 9 9 9 9 9    c                  4	   t          t          d          t          k    sJ t          dt                    dk    sJ t          t          t          z  dz  t                    t          t          t                    z  k    sJ t          t          t                    dk    sJ t          t          t                     dk    sJ t          t           t                    t          t          t                     k    sJ t          t          t                                        t                    dt          dt          t          t                    dz  z  z
            z  k    sJ t          t          t                                        t                    t          t          t                    dt          z  dt          z
  z  z  t          t          t                    dt          z  z  z
  t          dt          z            ddt          z
  z  t          dt          t          t                    dz  z  z
            z  z  z
  k    sJ t                      } t          t          t          |           t                    sJ t          t          | t                    t                    sJ t          dd          }t          t          |                                          t          t          j                    |                                          k    sJ t          dd	          }t          t          |                                          t          t          j                    |          k    sJ t          t          t                                        t                    t          t          d
z  dt          dz  z  dz  t          dz  z
  z  z   t          t          dz  z  dz  z   t!          t          dz            z   k    sJ t          t          t                                        t$                                        t%          dt          dt          t          t(                    dz  z  z
            z  t(          dt          f                    sJ d S )Nr   r$   r)   r(   r   Fr*   Tr,   r3   r&   (      r5   )Fr   r   r   r   r6   r   r8   r   r   r9   randcplxr:   r
   r;   r@   r   r<   r   rA   r"   rmimrs      rD   test_FrP   6   s=   Q77a<<<<Q77a<<<<RT!VQ<<1QqTT6!!!!Q88q====Q99>>>>aR88!QxQ77<<??aQ3q6619_ 5 555555Q77<<??a1ggqsAE{3a1ggqsmCAaC!QU)DQs1vvqy[11123 3 3 3 3

Aa1ggq>>a1ggq>>	%	 	 	 BQ881Q[]]BLLNN#C#CCCCC	d	#	#	#BQ881Q[]]B#7#77777Q77>>!	AqD!AqD&)ad"##a1fQh.1a489 9 9 9 Q77??8$$--4Ac!ffaiK(((1a)446 6 6 6 6 6 6rF   c                  |   t          t          d          t          k    sJ t          dt                    dk    sJ t          t          t          z  dz  t                    t          t          t                    z  k    sJ t          t          t
                    t          u sJ t          t          t
                     t          u sJ t          d          t          dz  k    sJ t          d          dk    sJ t          t
                    t          t
          z  k    sJ t          t
                     t
          u sJ t          t                    t          u sJ t          t           t                    t          t          t                     k    sJ t          t          t                                        t                    t          dt          t          t                    dz  z  z
            k    sJ t          t          t                                        t                    t          t          t                    t          t          t                    z
  dt          z  z  k    sJ t          t                                        t                    t          t                    t          t                    z
  dt          z  z  k    sJ t                      } t          t          | t                    t                    sJ t          t          t          |           t                    sJ t          t          t                    t                    sJ t          dd          }t          t          |                                          t          t          j                    |                                          k    sJ t          |                                          t          |                                          k    sJ t          dd          }t          t          |                                          t          t          j                    |          k    sJ t          |                                          t          |          k    sJ t          t                                        t$                    t          dz  t%          t'          d	d          t(          j        ft(          j        ft                    z  k    sJ t/          t          t                    t          dz  t%          t'          d	d          t(          j        ft(          j        ft                    z            sJ t          t                                        t0                    t1          t(          j        t'          d
d          fg ft(          j        ft(          j        fft                      dz  k    sJ t/          t          t                    t1          t(          j        t'          d
d          fg ft(          j        ft(          j        fft                      dz            sJ t          t          t                                        t                    t          t          dz  t          dz   dz  t          dz  z   z  z   t          t          d
z  z  dz  z
  t7          t          dz            z   k    sJ t          t                                        t                    t          dz  t          t          z  dz  z
  d
t          z  t          dz  z  dz  z
  dt          z  t          d
z  z  dz  z
  dt          z  t          dz  z  dz  z
  dt          z  t          dz  z  dz  z
  t7          t          dz            z   k    sJ t          dt          z  t          dz   z                                t                    t          dz  t          t          z  dz  z
  t          t          dz  z  dz  z   d
t          z  t          d
z  z  dz  z
  dt          z  t          dz  z  dz  z
  dt          z  t          dz  z  dz  z
  t7          t          dz            z   k    sJ t          t          t                                        t8                                        t9          t          dt          t          t<                    dz  z  z
            t<          dt          f                    sJ t          t                                        t8                                        t9          t          dt          t          t<                    dz  z  z
            t<          dt          dz  f                    sJ d S )Nr   r$   r)   r   Fr*   Tr,   r'   r&   r(   r3   rH   rI   r5   r%   r/   r1      r2   i  r4      ]   )r9   r   r   r   r   r   r   r   r8   r   r   rJ   r6   rK   r:   r
   r;   r<   r   r   r   r7   r=   r>   r   r?   r@   r   r   rA   r"   rL   s      rD   test_ErU   Q   s   Q77a<<<<Q77a<<<<QrT!VQ<<1QqTT6!!!!Q88s????Q99Q442a4<<<<Q4419999R55AbD====bS66R<<<<S66S====aR88!QxQ77<<??d1qQ{?333333Q77<<??qAww1a01Q377777Q4499Q<<AaDD1Q44K!A#.....

Aa1ggq>>a1ggq>>addA;;	%	 	 	 BQ881Q[]]BLLNN#C#CCCCCR55??",,.. 1 11111	d	#	#	#BQ881Q[]]B#7#77777R55??"%%%%Q44<<2a4Q/H15(TU)V)V"VVVVVaddRT5(2q//16!:QUHaHHHIIIIIQ44<<  	168Aq>>*B/16)afY1G!	L	LLQNO O O OaddWqvx1~~6;qvi!&=SVWUWXXXYZZ[[[[[Q77>>!	AqD1a4%(QrT/""Qq!tVAX-!Q$78 8 8 8Q44;;q>>RTBqDF]QrT!Q$Ys]:	"QT	#Bq!tE)*,/F1a4K,>?AB1a4I I I I IQqS!A#Y<<q!!
1r!tAv1a4	!AbDAIaK/"R%1*S.@2b5A:c>QTUVWYZVZT[T[[\ \ \ \ Q77??8$$--a!CFFAI+o&&Aq	224 4 4 4 4Q44<<!!**a!CFFAI+o&&Ar!t557 7 7 7 7 7 7rF   c                     t          dt          t                    t          t          t                    k    sJ t          dt          t                    t          t          t                    t	          dt          t          t                    dz  z  z
            t          t                    z  t          t          t                    z
  dt          z
  z  z   k    sJ t          t          t          t          z  dz  t                    t          t          t          t                    z  k    sJ t          t          t          d          t          t	          t          dz
            t          t                    z            t	          t          dz
            z  k    sJ t          t          t          t                    t          t          t                    t          dt          t                    z
  t          t                    t	          dt          t          t                    dz  z  z
            z  z   k    sJ t          t          t          t                    dk    sJ t          t           t          t                    dk    sJ t          t          t          t                    dk    sJ t          t          t          t                     dk    sJ t          dt                    t          t                    k    sJ t          dt                    t          u sJ t          t          d          t          dt	          dt          z
            z  z  k    sJ t          dd          t           u sJ t          dd          t          u sJ t          t          t                    t          t                    dt          z
  z  k    sJ t          t          t           t                    t          t          t          t                     k    sJ t          dd          t          dd          }} t          | t          |                                          t          |                                 t          j                    |                                          k    sJ t          dd	
          t          dd	
          }}t          |t          |                                          t          |t          j                    |          k    sJ t          t          t                                                    t          t          j                    t          j                              k    sJ t          t          t          t                                        t                    t          t          t                    t          t          z
  t          t          t                    z  t          z  z   t          dz  t          z
  t          t          t          t                    z  t          z  z   t          t	          dt          t          t                    dz  z  z
            z  t          dt          z            z  ddt          t          t                    dz  z  z
  z  z  z
  dt          t          z
  z  t          dz
  z  z  k    sJ t          t          t          t                                        t                    dt	          dt          t          t                    dz  z  z
            dt          t          t                    dz  z  z
  z  z  k    sJ t          t          t          t                                        t                    t          t          t                    t          dz
  z  t          t          t          t                    z   t          t          dt          z            z  dt          dz
  z  t	          dt          t          t                    dz  z  z
            z  z  z
  dt          t          z
  z  z  k    sJ t          t          t                                        t                    t          t                    t          t          z
  t          t                    z  t          z  z   t          dz  t          z
  t          t          t                    z  t          z  z   dt          t          z
  z  t          dz
  z  z  k    sJ t          t          t                                        t                    t          t                    t          dz
  z  t          t          t                    z   dt          t          z
  z  z  k    sJ t          t          t          t                                        t                    t          t          dz  t          dz  t          dz  z   z  z   t          dz  dt          dz  z  dz  t          t          z  dz  z   t          dz  z
  t          dz  dz  z   t          dz  z
  z  z   t'          t          dz            z   k    sJ t          t          t          t                                        t*                                        t+          ddt          t          t.                    dz  z  z
  t	          dt          t          t.                    dz  z  z
            z  z  t.          dt          f                    sJ t          t          t                                        t*                                        t+          ddt          t          t.                    dz  z  z
  t	          dt          t          t.                    dz  z  z
            z  z  t.          dt          dz  f                    sJ d S )Nr   r)   r$   r'   r   Fr*   r   Tr,   r&   r5   r3   rH   
   rI   rS   )Pr   r   rJ   r   r   r   r9   r   r   r   r   r   r6   r   r
   r;   r8   r@   r   r<   r   rA   r"   )nirN   nrrO   s       rD   test_Pr[      sO   Q1::1a    Q1::1a	a!CFFAI+o		s1vv	%!Q	/!a%89 9 9 9 9Q"Q??a!Qi''''Q1::tAE{{3q661224A;;>>>>>Q1::1a1Q1::-AtA#a&&!)O7L7L0LLLLLLRA;;!bS!Q<<1Q2;;!QB3<<1Q77add????Q77c>>>>Q77b!DQKK-(((((Q77rc>>>>R88r>>>>Q77addAEl""""QA;;1Q1::+%%%%Ce$$$fSu&=&=&=BRB<<!!##	",,..!+--889 9 9 9C$'''sT""" 	BRB<<!!##qQ[]]B'?'?????Q77!AKMM1;=="A"AAAAAQ1::??1!Aq''QUAaGGOA,="=	
A1Q1::a# "#Dc!ffaiK* % % #QqS#"#$a!CFFAI+o#6#8#8:;QU)QU:K"M M M M M Q1::??1DQs1vvqy[$9$91qQ{?$K!LLLLLQ1::??1!Aq''1q5/AaAJJ">	#ac((
Aq1uId1qQ{?3334#578!a%y"B B B B BQ77<<??qttq1uaddl1n4	
A1Q771  !a%y!a%02 2 2 2 2Q77<<??qttQU|a1gg51q5	BBBBB Q1::Q1q!tQqS1Q3Y'7#7	1a1fRi!A#b& 1R4'!Q$q&01R478$9;<QT77$C C C C C Q1::h''00Q3q6619_d1qQ{?&;&;;<q!QiHHJ J J J JQ77??8$$--Q3q6619_d1qQ{?&;&;;<q!RTlKKM M M M M M MrF   N)6sympy.core.numbersr   r   r   r   r   sympy.core.singletonr   sympy.core.symbolr	   r
   %sympy.functions.elementary.hyperbolicr   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   'sympy.functions.special.gamma_functionsr   sympy.functions.special.hyperr   r   sympy.integrals.integralsr   sympy.series.orderr   *sympy.functions.special.elliptic_integralsr   r6   r   rJ   r   r9   r   rX   sympy.core.randomr   r:   r   rK   r   r>   	sympy.abcr   r   r   r   jr"   rE   rP   rU   r[    rF   rD   <module>rk      s   9 9 9 9 9 9 9 9 9 9 9 9 9 9 " " " " " " - - - - - - - - 7 7 7 7 7 7 9 9 9 9 9 9 ? ? ? ? ? ? ? ? 9 9 9 9 9 9 : : : : : : : : . . . . . .            8 8 8 8 8 8 8 8 8 8 8 8@ @ @ @ @ @ @ @ @ @          
F3
F3t,,,	E#JJ9 9 9@6 6 66-7 -7 -7^5M 5M 5M 5M 5MrF   