
    sg;                     `   d dl mZ d dlmZ d dlmZmZmZmZ d dl	m
Z
 d dlmZmZ d dlmZmZmZ d dlmZmZ d dl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% d dl&m'Z'  edd      \  Z(Z)Z*d Z+d Z,d Z-d Z.d Z/d Z0d Z1d Z2d Z3d Z4d Z5d Z6d Z7d  Z8e%d!        Z9y")#    )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                     t         t         dz   z  } | t        z  t        |       dt         z  dz   k(  sJ t        t         d      t        dt         z  dz   z  k(  sJ t        t        fd       t        t        fd       y )N            c                      t               S N)dde2s   S/var/www/html/venv/lib/python3.12/site-packages/sympy/series/tests/test_limitseq.py<lambda>z'test_difference_delta.<locals>.<lambda>   s    r"v     c                  .    t         t        t              S r$   )r%   nr   r&   s   r(   r)   z'test_difference_delta.<locals>.<lambda>   s    r"a} r*   )r,   kr%   r   
ValueError)er'   s    @r(   test_difference_deltar0      sj    	1q5	A	
QBa5AaC!Gb!Q<1acAg;&&&
:~&
:,-r*   c            
      "   t        dt        z  t        dt        f      } t        | t              dt        dz   z  k(  sJ t        | t        d      t	        t        d      D cg c]  }d|t        z   dz   z   c} k(  sJ t        dt        z  t        ddt        z  f      } t        | t              t	        t        d      D cg c]  }d|dt        z  z   dz   z   c} k(  sJ t        t        dt        z  t        dt        f      z  } t        | t              dt        dt        z  t        dt        f      z   k(  sJ t        dt        z  t        dt        ft        dt        f      } t        | t              t        t              k(  sJ y c c}w c c}w )Nr         )r   r-   r,   r%   r   rangemr   r/   is     r(   test_difference_delta__Sumr8      sC   AaC!QAa8q!a%y   aA;#uQx@!1q519@AAAAAaC!Q!Aa8seAh?QAaC!_?@@@@	C!aAYAa8q3qsQ1I.....AaC!QQ1I&Aa8x{"""  A @s    F
 F
c            
         t         t         t         dz   z  z   } t        | t               dt         z  dz   k(  sJ t        | t         d      dt         z  dz   k(  sJ t         t        dt        z  t        dt         f      z   } t        | t               ddt         dz   z  z   k(  sJ t        | t         d      dt	        t        d      D cg c]  }d|t         z   dz   z   c} z   k(  sJ y c c}w )Nr   r    r3   r!      r2   )r,   r%   r   r-   r   r4   r6   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#DaAq1uqyM#DEEEEE#Ds   C"c                     dt         z  } t        | t               ddt         z  z  k(  sJ t        | t         d      ddt         z  z  k(  sJ ddt         z  z  } t        | t               dddt         z  z  z  k(  sJ t        | t         d      dddt         z  z  z  k(  sJ t         dz  } t        | t               t         dz   dz  t         dz  z
  k(  sJ t         t         z  } t        | t               t         dz   t         dz   z  t         t         z  z
  k(  sJ y )Nr!   r3   r          r   )r,   r%   r/   s    r(   test_difference_delta__Powr@   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$....r*   c            	      b    t        dt        z  t              t        t        dt        z  t              t        dt        f      z   t	               t        d      dz  k(  sJ t	         t               k(  sJ dt        dz  z  dt        dz  z  z   dz   dt        dz  z  dt        z  z   dz
  z   t	         t              t        d      dz  k(  sJ t        t              t        t        t              t        dt        f      z  t        t        dt        z        dz  z  z   t	         t              dk(  sJ t        t        dz  t        dt        z  t        z  t        dt        f      z  t        dt        f      dt        z  t        z  z   t	         t              dk(  sJ t        t        dt        z  t              t        dt        z  t              z  t        dt        f      t        dt        z  t              t        dt        z  t              z  z   t	         t              t        d      dz  k(  sJ t        t        t              dz  t        z  t        ddt        z  f      t        t              dz  z   t	         t              t
        j                  dz  k(  sJ t        t         fd       y )	Nr    r   r3   r!   r2   iI iE c                  (    t         t        z        S r$   )r   r5   r?   s   r(   r)   z test_limit_seq.<locals>.<lambda>]   s    yQ/ r*   )r   r,   r   r-   r   r	   r5   r   Oner   r.   r?   s   @r(   test_limit_seqrD   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                     t        dt        z  t        dz  z  t              dk(  sJ t        dt        dz   z  t        dt        z  z   z  t              dk(  sJ t        dt        z  dt        z  z   t        dz   z  t              dk(  sJ t        t        t        t        z        t              dk(  sJ t        t	        dt        z  t        z        t              dk(  sJ t        t
        j                  dz  t        z  t              dk(  sJ t        t        dd      t        z  t              dk(  sJ t        t        dz  t        z  t              dk(  sJ t        t        t              t        dz  t        z  z  t              dk(  sJ t        t        dz  t        dz  t        z  z  t              dk(  sJ t        t        t        dz   z  t        dz  t        z  z   t              dk(  sJ y )	Nr    r   r   r3   r2      )
r   r,   r   r   r   r	   NegativeOner   r   r    r*   r(   test_alternating_signrK   `   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                     t        dt        z  t              t        dd      k(  sJ t        t        t        t        z        t              t        dd      k(  sJ t        t        t        t        z  dz        dz  t              t        dd      k(  sJ t        ddt        z  z  t        dt        z  z   z  t              t        dd      k(  sJ t        dt        z  t        dz   z  ddt        z  z  z   t              t        dd      k(  sJ y )	NrF   r   r    r   r3   rG   r2   )r   r,   r   r   r   r   rJ   r*   r(   test_accum_boundsrN   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                     ddl m} m}m} t	        t        d| z  | d|f      t        |      z
  |      t        j                  k(  sJ t	        t        d| z  | d|f      d|z  z
  |      t        j                  u sJ t	        t        d| z  |       t        t        d|z  |      |d| f      z  |       t        d      dz  k(  sJ t	        t        |dz  t        d|z  |z  |d|f      z  |d| f      d| z  | z  z  |       dk(  sJ y )Nr   xyzr   r    r3   r!   )	sympy.abcrQ   rR   rS   r   r   r   r	   
EulerGammaInfinityr   rP   s      r(   test_limitseq_sumrW   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"#$ % $r*   c                  z    t        t        t              t        t              z  t              t	        d      k(  sJ y )NrF   )r   r   r,   r   r   rJ   r*   r(   test_issue_9308rY      s(    \!_Yq\115R@@@r*   c                      t        dd      } t        t        | dz         t        |       z  |       j                         t        j
                  k(  sJ y )Nr,   Tr   r   )r
   r   r   togetherr	   GoldenRatio)r,   s    r(   test_issue_10382r]      sA    sD!AYqs^IaL0!4==?1==PPPr*   c                  P    t        t        dd      t        z  t              dk(  sJ y )NrF   r    r   )r   r   r,   rJ   r*   r(   test_issue_11672r_      s"    Xb!_a'+q000r*   c                      t        dd      \  } }t        d      }t        t        || z  |d|f      j	                         || dz   z  z  |      d| dz   z  k(  sJ y )Nzk, nT)positiver5   r   )r   r
   r   r   doit)r-   r,   r5   s      r(   test_issue_14196rc      s_    FT*DAqsASA1ay)..0!a!e*=qAQAYNNNr*   c                  \    t        dt        z  t        t              z  t              dk(  sJ y )Nr2   r   )r   r,   r   rJ   r*   r(   test_issue_16735re      s$    QT)A,&*a///r*   c                  v    t        dt        t        t        j                  dz  z         z  t              dk(  sJ y )Nr   r    r   )r   r   r,   r	   rC   rJ   r*   r(   test_issue_19868rg      s-    QuQq[))1-222r*   c            	         t        t              dz  t        dt        t              z  t        dt        f      z  t        t        t        t              t        z  t        dt        f      z  z  } t	        | t              dk(  sJ t        dt        z  t        dt        z  t              z  t        dz  z  t        dt        f      t        dt        z  t        z  dz  t        dt        f      t        t        dt        z  t              t        dt        f      z  z  } t	        | t              t        d      dz  k(  sJ t        dz  t        dt        z  t        dz  z  t        dt        f      dz  z  dt        z  t        dt        z  t        z  t        dt        f      z  z  } t	        | t              dk(  sJ t        t              t        dt        z  t        z  t        dt        f      z  t        t        dt        z  t        t              z  t        dz  z  t        dt        f      z  z  } t	        | t              dk(  sJ t        dt        z  t        t              z  t        dz  z  t        ddt        z  f      t        dt        z  t        dz  z  t        dt        f      t        t        t              t        ddt        z  f      z  z  } t	        | t              t        d      dz  k(  sJ y )Nr3   r   r    rH   r!      )r   r,   r   r-   r   r   r	   r   r?   s    r(   test_limit_seq_failrj      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,   r5   r-   r0   r8   r;   r@   rD   rK   rN   rW   rY   r]   r_   rc   re   rg   rj   rJ   r*   r(   <module>ry      s    )  4 4 " / X X G = 9 ? 9 + 8 . @
'4
(1a.#F/ 103M%AQ
1O03 ( (r*   