
    \h}                         S SK Jr  S SKJrJr  S SKJr  S SKJr  S SK	J
r
Jr  S SKJrJr  S SKJrJr  \" S5      r\" S	5      u  rrrrrS
 rS rg)    )Function)Rationalpi)S)symbols)cossin)
DiracDelta	Heaviside)
change_muldeltaintegratefzx_1 x_2 x y zc                  
   [        [        [        5      S:X  d   e[        [        [        -  [        5      S:X  d   e[        [        [        -  [        [        5      -  [        5      [        [        5      [        [        -  4:X  d   e[        [        [        -  [        [        5      -  [        [        5      -  [        5      [        [        5      [        [        -  [        [        5      -  4:X  d   e[        [        [        5      S-  [        5      [        [        5      [        [        5      4:X  d   e[        [        [        [        5      S-  -  [        5      [        [        5      [        [        [        5      -  4:X  d   eg )N)NN   )r   xyr
        a/var/www/auris/envauris/lib/python3.13/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            
      l   [        [        [        5      b   e[        [        [        [        5      -   [        5      b   e[        [        [        S5      [        5      [        [        5      :X  d   e[	        S5       H8  n [        [        [        U S-   5      [        5      [        [        U 5      :X  a  M8   e   [        [        [        5      [        5      [        [        5      :X  d   e[        [        [        * 5      [        5      [        [        5      :X  d   e[        [        [        [
        -
  5      [        5      [        [        [
        -
  5      :X  d   e[        [        [
        [        -
  5      [        5      [        [        [
        -
  5      :X  d   e[        [        [        [        5      -  [        5      S:X  d   e[        [        [
        -
  [        [        [
        -
  5      -  [        5      S:X  d   e[        [        [        5      S-  [        5      [        S5      [        [        5      -  :X  d   e[        [
        [        [        5      S-  -  [        5      [
        [        S5      -  [        [        5      -  :X  d   e[        [        [        S5      [        5      [        [        S5      :X  d   e[        [
        [        [        S5      -  [        5      [
        [        [        S5      -  :X  d   e[        [        [        S5      S-  [        5      [        SS5      * [        [        5      -  :X  d   e[        [
        [        [        S5      S-  -  [        5      [
        * [        SS5      -  [        [        5      -  :X  d   e[        [        [        5      [        [        5      -  [        5      [        S5      [        [        5      -  :X  d   e[        [        [        * 5      [        [        5      -  [        5      [        S5      [        [        5      -  :X  d   e[        [        [        S-
  5      [        [        5      -  [        5      [        S5      [        [        S-
  5      -  :X  d   e[        [        S[        -
  5      [        [        5      -  [        5      [        S5      [        [        S-
  5      -  :X  d   e[        [        [        S-  [        -   S-
  5      [        5      [        [        S-
  5      S-  [        [        S-   5      S-  -   :X  d   e[        [        5      [        [        5      [        [        S-  S-
  5      -   -  [        [        5      -  [        [        -
  -  n[        U[        5      [        * [        S5      [        S[        -   5      -  [        S5      -  S-  [        S5      [        S[        -   5      -  [        S5      -  S-  -
  -  [        S5      [        S[        -   5      -  [        S5      -  S-  -   [        S5      [        S[        -   5      -  [        S5      -  S-  -   -
  S:X  d   e[        [        [        [        -
  5      -  [        [        [        -
  5      -  n[        U[        5      [        [        [        [        -
  5      -  [        [        [        -
  5      -  :X  d   e[        [
        S-  -  [        -  [        [
        [        -
  5      -  [        [
        [        -
  5      -  [        [        [        -
  5      -  n[        U[
        5      [        S-  [        -  [        [        [        -
  5      S-  -  [        [
        [        -
  5      -  :X  d   e[        [        S-   [        S[        -  5      -  [        5      [        R                  [        [        5      -  :X  d   e[        [        S-   [        [        [        SS5      -  [        SS5      -   5      -  [        5      [        R                  [        [        [        SS5      -   5      -  :X  d   e[!        S	S
S9u  p#n[        [        [        [
        -
  5      [        [        U-
  5      -  [        [        U-
  5      -  [        5      [        [
        U-
  5      [        [
        U-
  5      -  [        [        [
        -
  5      -  :X  d   e[        [        U-
  5      [        [        [
        -
  5      -  [        [        U-
  5      -  [        [        U-
  5      -  n[        U[        5      [        [
        U-
  5      [        [
        U-
  5      -  [        [
        U-
  5      -  [        [        [
        -
  5      -  :X  d   e[        [        [        -
  5      [        [        U-
  5      -  [        [        U-
  5      -  [        [        [
        -
  5      -  n[        U[        5      [        [
        [        -
  5      [        [
        U-
  5      -  [        [
        U-
  5      -  [        [        [
        -
  5      -  :X  d   eg )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)      sn   !Q'''!jm+Q/777*Q*A.)A,>>>2YjAE2A6*Q:JJJJ *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1GA!*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   