
    sg}                         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mZ d dlmZmZ  ed      Z ed	      \  ZZZZZd
 Zd Zy)    )Function)Rationalpi)S)symbols)cossin)
DiracDelta	Heaviside)
change_muldeltaintegratefzx_1 x_2 x y zc                     t        t        t              dk(  sJ t        t        t        z  t              dk(  sJ t        t        t        z  t        t              z  t              t        t              t        t        z  fk(  sJ t        t        t        z  t        t              z  t        t              z  t              t        t              t        t        z  t        t              z  fk(  sJ t        t        t              dz  t              t        t              t        t              fk(  sJ t        t        t        t              dz  z  t              t        t              t        t        t              z  fk(  sJ y )N)NN   )r   xyr
        \/var/www/html/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_deltafunctions.pytest_change_mulr      s   a|+++ac1---ac*Q-'+
1qs/CCCCac*Q-'
15q9	A!JqM)*+ + +jmQ&*	A
1&' ' 'a
1q((!,	A*Q-() ) )r   c            
      6   t        t        t              J t        t        t        t              z   t              J t        t        t        d      t              t        t              k(  sJ t	        d      D ]6  } t        t        t        | dz         t              t        t        |       k(  r6J  t        t        t              t              t        t              k(  sJ t        t        t               t              t        t              k(  sJ t        t        t        t
        z
        t              t        t        t
        z
        k(  sJ t        t        t
        t        z
        t              t        t        t
        z
        k(  sJ t        t        t        t              z  t              dk(  sJ t        t        t
        z
  t        t        t
        z
        z  t              dk(  sJ t        t        t              dz  t              t        d      t        t              z  k(  sJ t        t
        t        t              dz  z  t              t
        t        d      z  t        t              z  k(  sJ t        t        t        d      t              t        t        d      k(  sJ t        t
        t        t        d      z  t              t
        t        t        d      z  k(  sJ t        t        t        d      dz  t              t        dd       t        t              z  k(  sJ t        t
        t        t        d      dz  z  t              t
         t        dd      z  t        t              z  k(  sJ t        t        t              t        t              z  t              t        d      t        t              z  k(  sJ t        t        t               t        t              z  t              t        d      t        t              z  k(  sJ t        t        t        dz
        t        t              z  t              t        d      t        t        dz
        z  k(  sJ t        t        dt        z
        t        t              z  t              t        d      t        t        dz
        z  k(  sJ t        t        t        dz  t        z   dz
        t              t        t        dz
        dz  t        t        dz         dz  z   k(  sJ t        t              t        t              t        t        dz  dz
        z   z  t        t              z  t        t        z
  z  }t        |t              t         t        d      t        dt        z         z  t        d      z  dz  t        d      t        dt        z         z  t        d      z  dz  z
  z  t        d      t        dt        z         z  t        d      z  dz  z   t        d      t        dt        z         z  t        d      z  dz  z   z
  dk(  sJ t        t        t        t        z
        z  t        t        t        z
        z  }t        |t              t        t        t        t        z
        z  t        t        t        z
        z  k(  sJ t        t
        dz  z  t        z  t        t
        t        z
        z  t        t
        t        z
        z  t        t        t        z
        z  }t        |t
              t        dz  t        z  t        t        t        z
        dz  z  t        t
        t        z
        z  k(  sJ t        t        dz   t        dt        z        z  t              t        j                  t        t              z  k(  sJ t        t        dz   t        t        t        dd      z  t        dd      z         z  t              t        j                  t        t        t        dd      z         z  k(  sJ t!        d	d
      \  }}}t        t        t        t
        z
        t        t        |z
        z  t        t        |z
        z  t              t        t
        |z
        t        t
        |z
        z  t        t        t
        z
        z  k(  sJ t        t        |z
        t        t        t
        z
        z  t        t        |z
        z  t        t        |z
        z  }t        |t              t        t
        |z
        t        t
        |z
        z  t        t
        |z
        z  t        t        t
        z
        z  k(  sJ t        t        t        z
        t        t        |z
        z  t        t        |z
        z  t        t        t
        z
        z  }t        |t              t        t
        t        z
        t        t
        |z
        z  t        t
        |z
        z  t        t        t
        z
        z  k(  sJ y )Nr   
      r         	   za b cF)commutative)r   r   r
   r   ranger   r   r   r	   r   x_2x_1zr   Halfr   r   )npabcs        r   test_deltaintegrater)      sw   !Q'''!jm+Q/777*Q*A.)A,>>>2Y KjAE2A6*Q:JJJJK*Q-+y|;;;*aR.!,	!<<<*QU+Q/9QU3CCCC*QU+Q/9QU3CCCC!JqM/1-2221q5*QU"33Q71<<<*Q-*A.*Q-	!2LLLL!JqM1,,a0	*Q-	!$% % %*Q*A.*Q2BBBB!Jq!,,a0AjA6F4FFFF*Q*A-q1jA6F5FyQR|5SSSS!Jq!,a//3r*Q:J7J9UV<7WWWW *Q-!A$.2adYq\6IIII*aR.1Q4/3qtil7JJJJ*QU+ad2A6!A$1q5AQ:QQQQ*QU+ad2A6!A$1q5AQ:QQQQ*QTAX\2A6!a%Yq1u-a//0 0 0 	A
1
1a4!8 445c!f<a"fEA!QB3Aya/@(@Q(G(IAyQA&q()) $*AyQA&q($) 	Aya  Q')$* + /00 0 0
 	Jq3w
39 55A!S!Qz!c'':%:9S1W;M%MMMM	!Q$qAE"":a!e#44ZA5FFA!Q1a46*QU*;Q*>#>yQ?O#OOOO1q5*QqS/115)A,9NNNN1q5*Qx1~-=A-N"OOQRS	1x1~-../ / / g51GAq!*QU+Aa!eH4Qq1uX=qA	!a%1q5)AE**+ + + 	
!a%AE""1QU8+Aa!eH4A!Q1QU8Aa!eH#4Qq1uX#=iA>N#NNNN1q5!AE("1QU8+Jq1u,==A!Q:a!e#4Qq1uX#=aAh#F!a%$   r   N)sympy.core.functionr   sympy.core.numbersr   r   sympy.core.singletonr   sympy.core.symbolr   (sympy.functions.elementary.trigonometricr   r	   'sympy.functions.special.delta_functionsr
   r   sympy.integrals.deltafunctionsr   r   r   r!   r    r   r   r"   r   r)   r   r   r   <module>r1      sB    ( - " % ? K ESMO, S!Q	)6r   