
    sg                         d dl mZmZ d dl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 d dlmZmZmZ d d	lmZmZ d d
lmZ d dlmZ d dl mZ d dlmZ d dl m!Z! d Z"d Z#d Z$y)    )diffexpand_func)IRationalpi)S)Dummysymbols)catalan)	conjugate)sqrt)betabetaincbetainc_regularized)gamma	polygamma)hyper)Integral)ArgumentIndexError)	unchanged)raisesc            	      
   t        d      \  t        d      } t        t              sJ t        t              sJ t        dd      j                  dk(  sJ t        d      j                  J t        t                    t              t              z  t        z         z  k(  sJ t        t              t              z
        dk(  sJ t        t                    t        t        dz         t        dz         z         j                         k(  sJ t        t                    t              t        d      t        dz         z
  z  k(  sJ t        t                    t              t        d      t        dz         z
  z  k(  sJ t        t                    t        t              t                    k(  sJ t        t        fd	       t              j                  t              t              t              z  t        z         z  k(  sJ t              j                  t              t              d
z  t        d
z        z  k(  sJ t              j                  t              j                  t        | dz
  z  d| z
  dz
  z  z  | ddf            sJ t        t!        dd      t!        dd            t"        j$                  k(  sJ t        t!        dd      t!        dd            dd
t#        d      dz  z  z  t'        t(              z  t        t"        j*                  dz        z  dt        t#        d       dz        z  z  k(  sJ t        t!        dd      t!        dd            ddt-        t!        dd            z  z  k(  sJ t        dd      t"        j.                  k(  sJ t        dd      t"        j.                  k(  sJ t        d
d      t"        j*                  dz  k(  sJ t        t        dz         sJ t        t        d      sJ t        t        d      sJ t        dz         j1                         ddz   z  t-              z  z  k(  sJ t        d      j1                         dz  k(  sJ t        d      j1                         dz  k(  sJ t        t!        dd      t!        dd      d      j1                         t"        j$                  k(  sJ t        d
      t        d
d
      k(  sJ t        d      t              k7  sJ t        d      j1                         t              k(  sJ y )Nzx yt   T   r      c                  :    t               j                  d      S )Nr   )r   fdiff)xys   d/var/www/html/venv/lib/python3.12/site-packages/sympy/functions/special/tests/test_beta_functions.py<lambda>ztest_beta.<locals>.<lambda>$   s    tAqz'7'7':        i
   ii                  d   i'     F)evaluate)r
   r	   r   r   is_realr   r   simplifyr   r   r   r   r   rewriter   dummy_eqr   r   Zeror   r   Oner   ComplexInfinitydoit)r   r    r!   s    @@r"   	test_betar8      s   5>DAqc
AT1a   T1a   2;$&&&1:%%%tAqz"eAhuQx&7a!e&DDDDtAqzDAJ./1444tAqz"k$q!a%.4Aq>2Q&R&[&[&]]]]Q
A$q!*i1o	!QQRU@S.S"TTTTQ
A$q!*i1o	!QQRU@S.S"TTTTT!QZ D1y|$DDDD
:;1:e$aq(9%A,(FFFF7??5!U1Xq[qs%;;;;1:h'00!a!e*AQRUVQVGW:WZ[]^`aYb1cdddb!8B#34>>>b!8B#34A!QKR quuRx0#eQqTE!Gn2DEF F FR (2r"23sCQSUWHX@Y<Y7ZZZZ1:*****1:*****1:r!!!T1a!e$$$T1a   T1a   1q5> Aq!A#wwqz'9$::::1:??!###1:??!###b!8B#3eDIIKqvvUUU7d1aj   E"d1aj000E"'')T!QZ777r$   c            
         t        d      \  } }}}t        t        | |||      sJ t        t        | |d|      sJ t        dddd      j                  dk(  sJ t        ddd|      j                  J t	        t        t
        ddt
        z
  ddt
        z  z               t        t
         ddt
        z   ddt
        z  z
        k(  sJ t        | |dd      j                  t              j                  t        | |      j                  t                    sJ t        ddd|      j                  t              |t        d	d
|      z  k(  sJ t        dddd      j                         dk(  sJ y )N	a b x1 x2r   r   r%   Tr   r(   r   r'   r%   )r
   r   r   r0   r   r   r2   r   r3   r   r   evalfabx1x2s       r"   test_betaincrD   <   sQ   ;'LAq"bWaB+++WaAr***1aB''4///1aB''///WQ1q5!ac'23wr1a!eQQRSTQTW7UUUU1aA&&x099$q!*:L:LX:VWWW1aB''."U7D"5M2MMMM1aA$$&!+++r$   c            
         t        d      \  } }}}t        t        | |||      sJ t        t        | |d|      sJ t        dddd      j                  dk(  sJ t        ddd|      j                  J t	        t        dt
        z  ddt
        z   ddt
        z  z               t        d	t
        z  ddt
        z
  ddt
        z  z
        k(  sJ t        | |dd      j                  t              dk(  sJ t        dd||      j                  t              d|z  t        d
d|      z  d|z  t        d
d|      z  z
  k(  sJ t        dddd      j                         dk(  sJ y )Nr:   r   r   r   r'   Tr   r%   r   r<   r=   r(   )
r
   r   r   r0   r   r   r2   r   r   r>   r?   s       r"   test_betainc_regularizedrF   L   sq   ;'LAq"b(!QB777(!Q2666q!Q+33t;;;q!Q+33;;;(1aQAaC@AEXY[\]Y]_`bcfgbgijmnopmpipEqqqqq!Q*228<AAAq!R,44U;qtE'SWY[D\?\_`ac_cdijqswy{d|_|?||||q!Q*002a777r$   N)%sympy.core.functionr   r   sympy.core.numbersr   r   r   sympy.core.singletonr   sympy.core.symbolr	   r
   %sympy.functions.combinatorial.numbersr   $sympy.functions.elementary.complexesr   (sympy.functions.elementary.miscellaneousr   &sympy.functions.special.beta_functionsr   r   r   'sympy.functions.special.gamma_functionsr   r   sympy.functions.special.hyperr   sympy.integrals.integralsr   r   sympy.core.exprr   sympy.testing.pytestr   r8   rD   rF    r$   r"   <module>rU      sE    3 . . " . 9 : 9 W W D / . 2 % '(8V, 8r$   