
    \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Jr  S SKJr  S SKJr  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  S SKJr  S SKJrJ r J!r!J"r"  S r#S r$g)    )Function)Rationalpi)S)symbols)rfbinomial	factorial)exp)sqrt)	Piecewise)cossin)gamma)	gammasimp)powsimp)simplify)xynkc            
      l    [         n [        [        [        5      5      [        [        5      :X  d   e[        [        [        S-   5      [        -  5      [        [        5      :X  d   e[        [        [        5      [        S-
  -  5      [        [        S-
  5      :X  d   e[        [        [        [        5      -  5      [        [        S-   5      :X  d   e[        [        S-   [        [        S-   5      -  5      [        [        S-   5      :X  d   e[        [        [        [        -   5      [        [        -   -  5      [        [        [        -   S-   5      :X  d   e[        [        [        [        S-   5      -  5      S[        [        5      -  :X  d   e[        [        S-   S-  [        [        S-   5      -  5      [        S-   [        [        S-   5      -  :X  d   e[        [        [        [        5      -  [        [        S-   5      [        S-   -  -   5      [        S-   [        [        S-   5      -  :X  d   e[        [        S[        -  5      [        -  5      [        S[        -  S-   5      S-  :X  d   e[        [        S[        -  5      [        [
        R                  -
  -  5      S[        S[        -  S-
  5      -  :X  d   e[        [        [        5      [        S[        -
  5      -  5      [        [        [        [        -  5      -  :X  d   e[        [        [        5      [        [        * 5      -  5      [        * [        [        [        [        -  5      -  -  :X  d   e[        S[        [        S-   5      -  [        S[        -
  5      -  5      [        [        [        -  5      [        [        -  [        S-   -  [        S-   -  -  :X  d   e[        [        [        S-   5      5      [        [        S-   5      :X  d   e[        [        [        [        5      5      [        [        S-   5      [        [        S-   5      [        [        * [        -   S-   5      -  -  :X  d   e[        [        [        [        5      [        [        [
        R                  -   5      -  [        [        5      -  [        [        [        -   5      -  5      5      SS[        -  S-   -  [        [        5      -  [        S[        -  5      -  [        [        5      -  [        [        [        -   5      -  :X  d   e[        S[        [        5      -  [        [        [        SS5      -
  5      -  [        [        [        SS5      -   5      -  5      SS[        -  [        SS5      -
  -  S[        -  [        S[        -  S-
  5      -  -  :X  d   e[        [        [
        R                  [        S-  -   5      [        S[        S-  -   5      -  [        S[        -   5      -  [        [        5      -  S[        -  -  5      S:X  d   e[        [        [        SS5      5      [        [        SS5      5      -  5      S[        S5      -  [        -  S-  :X  d   e[        [        [        S[        -  5      [        [        5      -  5      5      SS[        -  S-
  -  [        [        [
        R                  -   5      -  [        [        5      -  :X  d   e[        [        5      * [        [        S-   5      -  [        [        S-   5      S-  -   [        [        5      S-  -  n[        U5      [        * :X  d   e[        SU-  5      S[        -  :X  d   e[        [        5      [        [        S-   5      -   [        [        5      -  n[        U5      [        S-   :X  d   e[        SU-  5      S[        S-   -  :X  d   e[        [        5      [        [        S-   5      -   [        [        S-
  5      [        [        5      -   -  [        [        5      -  n[        U5      [        S-  [        -   S-   [        [        S-   5      -  [        S-
  -  :X  d   e[        [        5      * [        [        S-   5      -  [        [        S-   5      S-  -   [        [        5      S-  -  n[        US-  5      [        S-  :X  d   e[        US-  [        [        S-   5      -  5      [        [        [        5      -  :X  d   eU " SS5      U " SS5      -   nX " SS5      -   n[        [        S[        -  5      [        [        5      -  [        [        U-   5      -  [        [        U-   5      -  5      SSS[        -  S-   -  -  SS[        -  S-
  -  -  [        [        5      -  [        S[        -  U " SS5      -   5      -  S-  :X  d   e[        [        S-   [        [        5      -  [        [        5      -  5      [        [        S-   5      [        [        5      -  :X  d   e[        [!        [        [        -   [        5      [        [        [        5      -  5      R                  5       [#        [        [        S-   5      [        [        [        -   [        -   5      -  [        [        S-   5      [        [        [        -   5      -  [        [        * [        -   S-   5      -  -  [        [        * :  4S[        -  [        [        S-   5      -  [        [        * [        -
  S-   5      -  [        [        S-   5      [        [        * [        -   S-   5      -  [        [        * [        -
  [        -
  S-   5      -  -  S	45      :X  d   e[%        S
SS9u  pE[        X-  U-  5      [        U5      U-  U-  :X  d   e[        [        S[        -  5      [        [        5      -  [        [        * U " SS5      -
  5      -  5      SS[        -  S-   -  * [        [        5      -  SS[        -  S-   ['        [        [        -  5      -  -  -  :X  d   e[        [        [        5      [        [        U " SS5      -   5      -  [        [        U " SS5      -   5      -  [        [        U " SS5      -  5      -  5      SSS[        -  S-   -  -  SS[        -  [
        R                  -
  -  -  [        [        5      -  [        [        U " SS5      -  [
        R                  -   5      -  S-  :X  d   e[        [        [        SS5      5      [        [        SS5      5      -  5      S:X  d   e[        [        [        S-   [        [
        R                  -   5      5      [        [        S-   5      [        [        U " SS5      -   5      [        [        * [        -   U " SS5      -   5      -  -  :X  d   e[        [        [        S-   [        S-   5      5      [        [        S-   5      [        [        S-   5      [        [        * [        -   S-   5      -  -  :X  d   e[        [        S[        5      5      [        [        [        -  5      [        [        -  -  :X  d   e[        [        [        SS5      -   5      [        [        U " SS5      -   5      -  n[        U5      U:X  d   e[        [        S[        -  [
        R                  -   5      [        S[        -  U " SS5      -
  5      -  5      SS[        -  U " SS5      -
  -  S[        -  S-
  -  [        S[        -  U " SS5      -   5      -  [        [        5      -  :X  d   e[%        SS	S9u  pg[        [)        U5      5      n[        U5      U:X  d   e[        US-   5      n[        U5      U:X  d   e[        US-   5      [        US-   5      [        U* U-   S-   5      -  -  n[        U5      U:X  d   e[%        SS	S	S9n[        [        U* S-   5      5      [        U* S-   5      :X  d   eg )N               TzA BF)commutative   g       @g      @r      zi m)integerp)r$   positive)r   r   r   r   r   r   Halfr   r   r
   r   r	   r   r   r   r   r   r   r   r   r   )	ReabABimr%   s	            [/var/www/auris/envauris/lib/python3.13/site-packages/sympy/simplify/tests/test_gammasimp.pytest_gammasimpr1      s   A U1X%(***U1q5\!^$a000U1Xq1u%&%A,666QuQxZ E!a%L000a!eU1q5\)*eAEl:::U1q5\1q5)*eAEAI.>>>>QuQU|^$%(
222a!eaZa!e,-!a%q1u1EEEEQuQxZ%A,A"667	
Qa!e   U1Q3Z\"eAaC!GnQ&6666U1Q3ZQVV,-51q>1AAAAU1XeAEl*+r#bd)|;;;U1XeQBi'(RC3r!t9,====QuQU|^E!a%L01BqD	2a4Q<Q'() ) ) Yq1u%&%A,666Xa^$a!eeAEl5!a!#4456 6 6 9aq166z""58+E!a%L8: ;	BqD1Hd2huQqSz)%(25Q<?@ @ @ QuQxZa(1a.&8 99%HQPQN@R:SST	AaC(1a. !1R4acAg#678 8 8affqslE!ac'N*5Q<7R@AEGJKL L LU8B?+E(2q/,BBCr$q'zRT}UVVVV9U1Q3Za012	AaC!GU1qvv:&&tBx/0 0 0 (5Q<	%A,/	158Q;>AQ<A2QqS>RT!!!	qE!a%L	 %(*AQ<1q5   QqS>QAY&&&	qE!a%L	 5Q<%(#:;E!HDAQ<AqD1HqL%A,6A>>>>
(5Q<	%A,/	158Q;>AQT?ad"""QT%A,&'1U1X:555	!Q!Aq'A	AaGAU1Q3Za(q1u5eAElB 
q1Q37|^A1qM)$r(251qAw3GGIJ J J a!eYq\)%(23uQU|E!H7LLLLRAq\(1a.01::<		q1ueAEAI&	&a!eU1q5\(A%QQR
BS(S	TVW[\Z\V\]
qq1u	eQBFQJ/	/q1ueQBFQJ>O1OPUWXVX[\V\_`V`cdVdPe1e	fhlmAo o o o 5e,DAQSUy|A~a//// U1Q3Za(rAaG|)<<=	
QqS1Wd2hAaC!GSAY#6 78: : :aq1Q7{##E!a1g+$66uQqAwY7GGI	!acAg,q2a4!&&=))$r(251Q7QVV9K3LLQNP P P
 U8Aq>*5!Q+@@AQFFF Xa!eQZ01U1q5\	q1Q7{	E1"q&1Q7"23	365 5 5 5Xa!eQW-.a!eeAGnUA26A:%6678 8 8 Xa^$BqD	2a4(8888a(1a. !%AaG"44AQ<1U1Q3<(qsQq!W})==>	AaC!Aq'MAaC!G$U1Q31a=%99$r(BC C C 5D)DAc!fAQ<1a!eAQ<1a!eeAEl5!a!#445AQ<1TD1AUA26]#uaR!V}444    c                     [        S5      " [        5      n [        [        [        5      -   n[	        U5      n[	        UR                  [        U 5      5      R                  U [        5      U:X  d   e[	        UR                  [        [        [        5      5      5      R                  [        [        5      [        5      U:X  d   eS[	        SU-  5      -  U:X  d   e[	        U R                  [        U5      5      R                  S   U:X  d   eg )Nfr   r   )r   r   r   r   r   subsr   args)fxeqanss      r0   test_issue_22606r:   w   s    	#q	B	
U1XB
B-CRWWQ^$))"a0C777RWWQA'(--c!fa8C???Yqt_###RWWQ^$))!,333r2   N)%sympy.core.functionr   sympy.core.numbersr   r   sympy.core.singletonr   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr   r	   r
   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   (sympy.functions.elementary.trigonometricr   r   'sympy.functions.special.gamma_functionsr   sympy.simplify.gammasimpr   sympy.simplify.powsimpr   sympy.simplify.simplifyr   	sympy.abcr   r   r   r   r1   r:    r2   r0   <module>rJ      sA    ( - " % N N 6 9 : ? 9 . * ,    b5J4r2   