
    g;                     n   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!             Z9d"S )#    )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           d S )N            c                  "    t                     S N)dde2s   \/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/series/tests/test_limitseq.py<lambda>z'test_difference_delta.<locals>.<lambda>   s    r"vv     c                  :    t           t          t                    S r$   )r%   nr   r&   s   r(   r)   z'test_difference_delta.<locals>.<lambda>   s    r"a}} r*   )r,   kr%   r   
ValueError)er'   s    @r(   test_difference_deltar0      s    	1q5	A	
QBa55AaC!Gb!Q<<1acAg;&&&&
:~~~~&&&
:,,,,-----r*   c                  n   t          dt          z  t          dt          f          } t          | t                    dt          dz   z  k    sJ t          | t          d          t	          d t          d          D              k    sJ t          dt          z  t          ddt          z  f          } t          | t                    t	          d t          d          D              k    sJ t          t          dt          z  t          dt          f          z  } t          | t                    dt          dt          z  t          dt          f          z   k    sJ t          dt          z  t          dt          ft          dt          f          } t          | t                    t          t                    k    sJ d S )Nr      c                 .    g | ]}d |t           z   d z   z  S r   r,   .0is     r(   
<listcomp>z.test_difference_delta__Sum.<locals>.<listcomp>"   s$    @@@!1q519@@@r*      c                 4    g | ]}d |dt           z  z   d z   z  S )r   r:   r5   r6   s     r(   r9   z.test_difference_delta__Sum.<locals>.<listcomp>%   s(    ???QAaC!_???r*   )r   r-   r,   r%   r   rangemr   r/   s    r(   test_difference_delta__Sumr?      sW   AaC!QAa88q!a%y    aA;;#@@uQxx@@@AAAAAAaC!Q!Aa88s??eAhh???@@@@@	C!aAYAa88q3qsQ1I.......AaC!QQ1I&&Aa88x{{""""""r*   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	          d t          d          D              z   k    sJ d S )Nr   r    r:   r!      r2   c                 .    g | ]}d |t           z   d z   z  S r4   r5   r6   s     r(   r9   z.test_difference_delta__Add.<locals>.<listcomp>5   s$    #D#D#DaAq1uqyM#D#D#Dr*   )r,   r%   r   r-   r   r<   r>   s    r(   test_difference_delta__AddrC   .   s    	Aq1uIAa88qsQwaA;;!A#'!!!!	C!aAYAa88q1a!e9}$$$$aA;;!c#D#D588#D#D#DEEEEEEEEr*   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 d S )Nr!   r:   r          r   )r,   r%   r>   s    r(   test_difference_delta__PowrG   8   s   	1Aa88qAvaA;;"QT'!!!!	AaCAa88r!ac({""""aA;;#a!A#h,&&&&	1Aa88AzAqD(((((	1Aa88AQ'!Q$.......r*   c            	          t          dt          z  t                    t          t          dt          z  t                    t          dt          f          z   t	                     t          d          dz  k    sJ t	           t                     k    sJ dt          dz  z  dt          dz  z  z   dz   dt          dz  z  dt          z  z   dz
  z   t	           t                    t          d          dz  k    sJ t          t                    t          t          t                    t          dt          f          z  t          t          dt          z            dz  z  z   t	           t                    dk    sJ t          t          dz  t          dt          z  t          z  t          dt          f          z  t          dt          f          dt          z  t          z  z   t	           t                    dk    sJ t          t          dt          z  t                    t          dt          z  t                    z  t          dt          f          t          dt          z  t                    t          dt          z  t                    z  z   t	           t                    t          d          dz  k    sJ t          t          t                    dz  t          z  t          ddt          z  f          t          t                    dz  z   t	           t                    t
          j        dz  k    sJ t          t           fd           d S )	Nr    r   r:   r!   r2   iI iE c                  2    t           t          z            S r$   )r   r=   r>   s   r(   r)   z test_limit_seq.<locals>.<lambda>]   s    yQ// r*   )r   r,   r   r-   r   r	   r=   r   Oner   r.   r>   s   @r(   test_limit_seqrK   H   s{   1a3x!Q//!Q;;;AQ<<1Q44!8####Q??a	
1a4!AqD&1	1a4!A#!12AQ??addQh&&&&	!s8A;;Aq	22	2q8AaC==!;K7KLAQ??aAqD3q!tAv1ay)))Aq!955Aa@AQ??a	Xac11a 0 001a)	<	<
1Q3

Xac1--
-
/AQ??ahh.....HQKKN1q!QqSk**Xa[[!^;AQ??aeai''''
:////0000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 d S )	Nr    r   r   r:   r2      )
r   r,   r   r   r   r	   NegativeOner   r   r    r*   r(   test_alternating_signrR   `   s   b1WQT\1%%****bAaC[!ad(+Q//14444acR!Gma!e,a00A5555SAYY""a''''S2a[[!$$))))amAo)1--2222hr1oo)1--2222acAXq!!Q&&&&T!WWacAX%q))Q....QT1Q3(]A&&!++++QAY!A#)1--222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 d S )	NrM   r   r    r   r:   rN   r2   )r   r,   r   r   r   r   rQ   r*   r(   test_accum_boundsrU   n   s   b1Wa  $6r1$=$=====SAYY""&8Q&?&?????SAa[[!^Q''+=a+C+CCCCCQQwYAqD)1--1CB1J1JJJJJQqS!a%[1b1W9,a004Fq!4L4LLLLLLLr*   c                  d   ddl m} m}m} t	          t          d| z  | d|f          t          |          z
  |          t          j        k    sJ t	          t          d| z  | d|f          d|z  z
  |          t          j	        u sJ t	          t          d| z  |           t          t          d|z  |          |d| f          z  |           t          d          dz  k    sJ t	          t          |dz  t          d|z  |z  |d|f          z  |d| f          d| z  | z  z  |           dk    sJ d S )Nr   xyzr   r    r:   r!   )	sympy.abcrX   rY   rZ   r   r   r   r	   
EulerGammaInfinityr   rW   s      r(   test_limitseq_sumr^   v   si   !!!!!!!!!!S1q!Qi((3q661155EEEES1q!Qi((1Q3.22aj@@@@hqsA&&Xac1-=-=1ay)I)II1MMaDD1H   c!Q$QT!VaAY!7!77!QCCa46 "#$ $ $ $ $ $r*   c                      t          t          t                    t          t                    z  t                    t	          d          k    sJ d S )NrM   )r   r   r,   r   r   rQ   r*   r(   test_issue_9308r`      s:    \!__Yq\\1155R@@@@@@r*   c                      t          dd          } t          t          | dz             t          |           z  |                                           t          j        k    sJ d S )Nr,   Tr   r   )r
   r   r   togetherr	   GoldenRatior5   s    r(   test_issue_10382rd      sX    sD!!!AYqs^^IaLL0!44==??1=PPPPPPr*   c                  h    t          t          dd          t          z  t                    dk    sJ d S )NrM   r    r   )r   r   r,   rQ   r*   r(   test_issue_11672rf      s0    Xb!__a'++q000000r*   c                      t          dd          \  } }t          d          }t          t          || z  |d|f                                          || dz   z  z  |          d| dz   z  k    sJ d S )Nzk, nT)positiver=   r   )r   r
   r   r   doit)r-   r,   r=   s      r(   test_issue_14196rj      sy    FT***DAqsASA1ay))..00!a!e*=qAAQAYNNNNNNr*   c                  v    t          dt          z  t          t                    z  t                    dk    sJ d S )Nr2   r   )r   r,   r   rQ   r*   r(   test_issue_16735rl      s2    QT)A,,&**a//////r*   c                      t          dt          t          t          j        dz  z             z  t                    dk    sJ d S )Nr   r    r   )r   r   r,   r	   rJ   rQ   r*   r(   test_issue_19868rn      s:    QuQq[)))1--222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 d S )Nr:   r   r    rO   r!      )r   r,   r   r-   r   r   r	   r   r>   s    r(   test_limit_seq_failrq      s    
!a#amaAY77	7
c(1++a-!Q++
+
-AQ??a 
QTHQqS!$$$q!t+aAY	7	7
ad1fQhAq	
"
"S!A#q)9)9Aq!9%E%E
E
GAQ??addQh&&&& 	
1SAadQ1I&&))QTC1QAq	4J4J-JKAQ??a	!s1a46Aq!9--	-
c!Q$x{{"1a4'!Q33
3
5AQ??a	QT)A,,A%1ac{	3	3
ad1a4i!Q
#
#c)A,,Aqs&D&D
D
FAQ??addRi''''''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,   r=   r-   r0   r?   rC   rG   rK   rR   rU   r^   r`   rd   rf   rj   rl   rn   rq   rQ   r*   r(   <module>r      so   ) ) ) ) ) )       4 4 4 4 4 4 4 4 4 4 4 4 " " " " " " / / / / / / / / X X X X X X X X X X G G G G G G G G = = = = = = = = 9 9 9 9 9 9 ? ? ? ? ? ? ? ? 9 9 9 9 9 9 + + + + + + 8 8 8 8 8 8 . . . . . . . . @ @ @ @ @ @
''4
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