
    \h;                     Z   S SK Jr  S SKJr  S SKJrJrJrJr  S SK	J
r
  S SKJrJr  S SKJrJrJr  S SKJrJr  S SKJr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$r$J%r%  S SK&J'r'  \" SSS9u  r(r)r*S r+S r,S r-S r.S r/S r0S r1S r2S r3S r4S r5S r6S r7S  r8\%S! 5       r9g")#    )Sum)Add)IRationaloopi)S)Symbolsymbols)binomial	factorialsubfactorial)	fibonacciharmonic)explog)sqrt)cossin)gamma)	limit_seq)difference_delta)raisesXFAIL)AccumulationBoundszn m kTintegerc                    ^ [         [         S-   -  n U [        -  m[        U 5      S[         -  S-   :X  d   e[        T[         S5      [        S[         -  S-   -  :X  d   e[        [        U4S j5        [        [        U4S j5        g )N            c                     > [        T 5      $ N)dde2s   X/var/www/auris/envauris/lib/python3.13/site-packages/sympy/series/tests/test_limitseq.py<lambda>'test_difference_delta.<locals>.<lambda>   s	    r"v    c                  .   > [        T [        [        5      $ r$   )r%   nr   r&   s   r(   r)   r*      s    r"a}r+   )r-   kr%   r   
ValueError)er'   s    @r(   test_difference_deltar1      sj    	1q5	A	
QBa5AaC!Gb!Q<1acAg;&&&
:~&
:,-r+   c            
      8   [        S[        -  [        S[        45      n [        U [        5      S[        S-   -  :X  d   e[        U [        S5      [	        [        S5       Vs/ s H  nSU[        -   S-   -  PM     sn6 :X  d   e[        S[        -  [        SS[        -  45      n [        U [        5      [	        [        S5       Vs/ s H  nSUS[        -  -   S-   -  PM     sn6 :X  d   e[        [        S[        -  [        S[        45      -  n [        U [        5      S[        S[        -  [        S[        45      -   :X  d   e[        S[        -  [        S[        4[        S[        45      n [        U [        5      [        [        5      :X  d   eg s  snf s  snf )Nr         )r   r.   r-   r%   r   rangemr   r0   is     r(   test_difference_delta__Sumr9      sK   AaC!QAa8q!a%y   aA;#uQx@x!1q519x@AAAAAaC!Q!Aa8seAh?hQAaC!_h?@@@@	C!aAYAa8q3qsQ1I.....AaC!QQ1I&Aa8x{"""  A @s   !F
F
c            
         [         [         [         S-   -  -   n [        U [         5      S[         -  S-   :X  d   e[        U [         S5      S[         -  S-   :X  d   e[         [        S[        -  [        S[         45      -   n [        U [         5      SS[         S-   -  -   :X  d   e[        U [         S5      S[	        [        S5       Vs/ s H  nSU[         -   S-   -  PM     sn6 -   :X  d   eg s  snf )Nr   r    r4   r!      r3   )r-   r%   r   r.   r   r5   r7   s     r(   test_difference_delta__Addr<   .   s    	Aq1uIAa8qsQwaA;!A#'!!!	C!aAYAa8q1a!e9}$$$aA;!c58#D8aAq1uqyM8#DEEEEE#Ds   C)c                  (   S[         -  n [        U [         5      SS[         -  -  :X  d   e[        U [         S5      SS[         -  -  :X  d   eSS[         -  -  n [        U [         5      SSS[         -  -  -  :X  d   e[        U [         S5      SSS[         -  -  -  :X  d   e[         S-  n [        U [         5      [         S-   S-  [         S-  -
  :X  d   e[         [         -  n [        U [         5      [         S-   [         S-   -  [         [         -  -
  :X  d   eg )Nr!   r4   r          r   )r-   r%   r0   s    r(   test_difference_delta__PowrA   8   s    	1Aa8qAvaA;"QT'!!!	AaCAa8r!ac({"""aA;#a!A#h,&&&	1Aa8AzAqD((((	1Aa8AQ'!Q$....r+   c            	      r  ^  [        S[        -  [        5      [        [        S[        -  [        5      [        S[        45      -  m [	        T 5      [        S5      S-  :X  d   e[	        T [        5      T :X  d   eS[        S-  -  S[        S-  -  -   S-   S[        S-  -  S[        -  -   S-
  -  m [	        T [        5      [        S5      S-  :X  d   e[        [        5      [        [        [        5      [        S[        45      -  [        [        S[        -  5      S-  -  -  m [	        T [        5      S:X  d   e[        [        S-  [        S[        -  [        -  [        S[        45      -  [        S[        45      S[        -  [        -  -  m [	        T [        5      S:X  d   e[        [        S[        -  [        5      [        S[        -  [        5      -  [        S[        45      [        S[        -  [        5      [        S[        -  [        5      -  -  m [	        T [        5      [        S5      S-  :X  d   e[        [        [        5      S-  [        -  [        SS[        -  45      [        [        5      S-  -  m [	        T [        5      [
        R                  S-  :X  d   e[        [        U 4S j5        g )	Nr    r   r4   r!   r3   iI iE c                  (   > [        T [        -  5      $ r$   )r   r6   r@   s   r(   r)    test_limit_seq.<locals>.<lambda>]   s    yQ/r+   )r   r-   r   r.   r   r	   r6   r   Oner   r/   r@   s   @r(   test_limit_seqrF   H   s   1a3x!Q/!Q;;AQ<1Q4!8###Q?a	
1a4!AqD&1	1a4!A#!12AQ?adQh&&&	!s8A;Aq	2	2q8AaC=!;K7KLAQ?aAqD3q!tAv1ay))Aq!95Aa@AQ?a	Xac11a 001a)	<
1Q3
Xac1-
-
/AQ?ah....HQKN1q!QqSk*Xa[!^;AQ?aeeai'''
:/0r+   c                     [        S[        -  [        S-  -  [        5      S:X  d   e[        S[        S-   -  [        S[        -  -   -  [        5      S:X  d   e[        S[        -  S[        -  -   [        S-   -  [        5      S:X  d   e[        [        [        [        -  5      [        5      S:X  d   e[        [	        S[        -  [        -  5      [        5      S:X  d   e[        [
        R                  S-  [        -  [        5      S:X  d   e[        [        SS5      [        -  [        5      S:X  d   e[        [        S-  [        -  [        5      S:X  d   e[        [        [        5      [        S-  [        -  -  [        5      S:X  d   e[        [        S-  [        S-  [        -  -  [        5      S:X  d   e[        [        [        S-   -  [        S-  [        -  -   [        5      S:X  d   eg )	Nr    r   r   r4   r3      )
r   r-   r   r   r   r	   NegativeOner   r   r    r+   r(   test_alternating_signrM   `   s   b1WQT\1%***bAaC[!ad(+Q/1444acR!Gma!e,a0A555SAY"a'''S2a[!$)))ammAo)1-222hr1o)1-222acAXq!Q&&&T!WacAX%q)Q...QT1Q3(]A&!+++QAY!A#)1-222r+   c                      [        S[        -  [        5      [        SS5      :X  d   e[        [        [        [        -  5      [        5      [        SS5      :X  d   e[        [        [        [        -  S-  5      S-  [        5      [        SS5      :X  d   e[        SS[        -  -  [        S[        -  -   -  [        5      [        SS5      :X  d   e[        S[        -  [        S-   -  SS[        -  -  -   [        5      [        SS5      :X  d   eg )	NrH   r   r    r   r4   rI   r3   )r   r-   r   r   r   r   rL   r+   r(   test_accum_boundsrP   n   s    b1Wa $6r1$====SAY"&8Q&????SAa[!^Q'+=a+CCCCQQwYAqD)1-1CB1JJJJQqS!a%[1b1W9,a04Fq!4LLLLr+   c                     SSK Jn JnJn  [	        [        SU -  U SU45      [        U5      -
  U5      [        R                  :X  d   e[	        [        SU -  U SU45      SU-  -
  U5      [        R                  L d   e[	        [        SU -  U 5      [        [        SU-  U5      USU 45      -  U 5      [        S5      S-  :X  d   e[	        [        US-  [        SU-  U-  USU45      -  USU 45      SU -  U -  -  U 5      S:X  d   eg )Nr   xyzr   r    r4   r!   )	sympy.abcrS   rT   rU   r   r   r   r	   
EulerGammaInfinityr   rR   s      r(   test_limitseq_sumrY   v   s   !!S1q!Qi(3q6115EEES1q!Qi(1Q3.2ajj@@@hqsA&Xac1-=1ay)II1MaD1H  c!Q$QT!VaAY!77!QCa46"#$ % $r+   c                  |    [        [        [        5      [        [        5      -  [        5      [	        S5      :X  d   eg )NrH   )r   r   r-   r   r   rL   r+   r(   test_issue_9308r[      s(    \!_Yq\115R@@@r+   c                      [        SSS9n [        [        U S-   5      [        U 5      -  U 5      R                  5       [        R
                  :X  d   eg )Nr-   Tr   r   )r
   r   r   togetherr	   GoldenRatio)r-   s    r(   test_issue_10382r_      sA    sD!AYqs^IaL0!4==?1==PPPr+   c                  R    [        [        SS5      [        -  [        5      S:X  d   eg )NrH   r    r   )r   r   r-   rL   r+   r(   test_issue_11672ra      s"    Xb!_a'+q000r+   c                      [        SSS9u  p[        S5      n[        [        X -  USU45      R	                  5       XS-   -  -  U5      SU S-   -  :X  d   eg )Nzk, nT)positiver6   r   )r   r
   r   r   doit)r.   r-   r6   s      r(   test_issue_14196re      sY    FT*DAsAS1ay)..0!!e*=qAQAYNNNr+   c                  ^    [        S[        -  [        [        5      -  [        5      S:X  d   eg )Nr3   r   )r   r-   r   rL   r+   r(   test_issue_16735rg      s$    QT)A,&*a///r+   c                  x    [        S[        [        [        R                  S-  -   5      -  [        5      S:X  d   eg )Nr   r    r   )r   r   r-   r	   rE   rL   r+   r(   test_issue_19868ri      s-    QuQq[))1-222r+   c            	         [        [        5      S-  [        S[        [        5      -  [        S[        45      -  [        [        [        [        5      [        -  [        S[        45      -  -  n [	        U [        5      S:X  d   e[        S[        -  [        S[        -  [        5      -  [        S-  -  [        S[        45      [        S[        -  [        -  S-  [        S[        45      [        [        S[        -  [        5      [        S[        45      -  -  n [	        U [        5      [        S5      S-  :X  d   e[        S-  [        S[        -  [        S-  -  [        S[        45      S-  -  S[        -  [        S[        -  [        -  [        S[        45      -  -  n [	        U [        5      S:X  d   e[        [        5      [        S[        -  [        -  [        S[        45      -  [        [        S[        -  [        [        5      -  [        S-  -  [        S[        45      -  -  n [	        U [        5      S:X  d   e[        S[        -  [        [        5      -  [        S-  -  [        SS[        -  45      [        S[        -  [        S-  -  [        S[        45      [        [        [        5      [        SS[        -  45      -  -  n [	        U [        5      [        S5      S-  :X  d   eg )Nr4   r   r    rJ   r!      )r   r-   r   r.   r   r   r	   r   r@   s    r(   test_limit_seq_failrl      s=    
!a#amaAY7	7
c(1+a-!Q+
+
-AQ?a 
QTHQqS!$$q!t+aAY	7
ad1fQhAq	
"S!A#q)9Aq!9%E
E
GAQ?adQh&&& 	
1SAadQ1I&))QTC1QAq	4J-JKAQ?a	!s1a46Aq!9-	-
c!Q$x{"1a4'!Q3
3
5AQ?a	QT)A,A%1ac{	3
ad1a4i!Q
#c)A,Aqs&D
D
FAQ?adRi'''r+   N):sympy.concrete.summationsr   sympy.core.addr   sympy.core.numbersr   r   r   r   sympy.core.singletonr	   sympy.core.symbolr
   r   (sympy.functions.combinatorial.factorialsr   r   r   %sympy.functions.combinatorial.numbersr   r   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   'sympy.functions.special.gamma_functionsr   sympy.series.limitseqr   r   r%   sympy.testing.pytestr   r   !sympy.calculus.accumulationboundsr   r-   r6   r.   r1   r9   r<   rA   rF   rM   rP   rY   r[   r_   ra   re   rg   ri   rl   rL   r+   r(   <module>r{      s    )  4 4 " / X X G = 9 ? 9 + 8 . @
'4
(1a.#F/ 103M%AQ
1O03 ( (r+   