
    \h,                        S SK JrJr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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JrJrJr  S SK J!r!J"r"J#r#  S SK$J%r%J&r&  \" S5      r'\" SSS9u  r(r)\" S5      u  r*r+r,S r-S r.S r/\#S 5       r0S r1S r2S r3S r4S r5S r6S r7S r8\"S 5       r9S  r:S! r;S" r<S# r=g$)%    )FunctionLambdaexpand)IRational)Eq)S)Symbolsymbols)rfbinomial	factorial)Abs)sqrt)cossin)factor)rsolversolve_hyperrsolve_polyrsolve_ratio)raisesslowXFAIL)abyzn,kT)integerzC0,C1,C2c                     [        / SQS[        5      S:X  d   e[        / SQS[        5      S:X  d   e[        S[        S-   /[        [        5      S:X  d   e[        SS/[        [        5      [        [        S-  [        -
  S-  -   :X  d   e[        [        * S-
  [        /S[        5      [        [        -  S-
  :X  d   e[        S[        -  S-
  S/S[        -  S-   [        5      S:X  d   e[        SS/[        S-  [        S	-  -   [        5      [        [        S	-  S-  -
  [        S-  S-  -
  [        S-  S
-  -   [        S
-  S
-  -   S[        S-  -  S	-  -   :X  d   eg )Nr!      r   r"   r!                  )r   nC0     W/var/www/auris/envauris/lib/python3.13/site-packages/sympy/solvers/tests/test_recurr.pytest_rsolve_polyr.      sD   {Aq)Q...{Aq)R///AE{Aq)Q...Aw1%q!taxl)::::Q{Aq)RTAX5551q!}acAgq1R777Aw1q!tQ/
QTAX1q 1a4!8+adQh61a4!CD D Dr,   c            	         [        S[        S-  -  [        S-  -   S[        -  -   S-
  S[        S-  -  [        S-  -   S[        -  -
  S[        S-  -  S[        S-  -  -
  S[        -  -
  S-
  S[        S-  -  S	[        S-  -  -   S
[        -  -   S-   /S[        5      n U [        S[        -  S-
  -  [        S-  S-
  -  S-  :X  d   eg )Nr'   r#   r"   r(         	            r   )r   r)   r*   )solutions    r-   test_rsolve_ratior8   !   s    R1Wq!t^ac1A5qAv1}qs7J
1a4"QT'BqD 1$a1fr!Q$w&6A&=&ACDEqJHr1Q37|QTAX.q0000r,   c            	         [        / SQS[        5      [        [        R                  [        R                  [        S5      -  -
  [        -  -  [        [        R                  [        R                  [        S5      -  -   [        -  -  -   [        [        R                  [        R                  [        S5      -  -
  [        -  -  [        [        R                  [        R                  [        S5      -  -   [        -  -  -   4;   d   e[        [        S-  S-
  S[        -  S-
  S/S[        5      [        [        [        S5      [        5      -  [        [        [        S5      * [        5      -  -   [        [        [        S5      [        5      -  [        [        [        S5      * [        5      -  -   4;   d   e[        [        S-  [        -
  S[        -  S-
  S/S[        5      [        [        [        [        5      [        5      -  [        [        [        [        5      * [        5      -  -   [        [        [        [        5      [        5      -  [        [        [        [        5      * [        5      -  -   4;   d   e[        S[        -  [        S-   -  [        S-  * S[        -  -
  S-   [        S-
  /S[        5      [        [        [        5      -  [        S[        -  -  -   :X  d   e[        [        S-   S[        -  S-   * S[        S-  -  S	[        -  -   S
-   -  [        S-   /S[        5      S:X  d   e[        [        * S-
  SS/S[        5      S:X  d   e[        SS/[        [        5      R                  5       [        [        S-  S-  -   [        S-  -
  :X  d   e[        SS/S[        -   [        5      R                  5       [        [        S-  S-  -   [        S-  -   :X  d   e[        SS/S[        [        S-  -   -  [        5      R                  5       [        [        S-  -   [        -
  :X  d   e[        [        * S/S[        5      R                  5       [        [        [        -  -  :X  d   e[        [        * SS/S[        5      R                  5       S[        -  [        -  [        [        S-  -  -  [        [        [        S-  -  -  -   :X  d   e[        / SQS[        5      R                  5       [        [        SS5      [        S5      [        -  S-  -
  [        -  -  [        [        SS5      [        S5      [        -  S-  -   [        -  -  -   :X  d   e[        SS[        -  [        -  S[        -  -
  S/S[        5      S:X  d   eg )Nr    r   r&   r#   r0   r"   r'      3   '   r!   )r"   r"   r"   )r   r)   r*   r	   Halfr   C1r   kr   r   r   r   r   r+   r,   r-   test_rsolve_hyperr@   '   sx   Q*
AFFQVVDG^#a''"affqvvd1g~.E-I*II
AFFQVVDG^#a''"affqvvd1g~.E-I*II/   
 A2a4!8Q/A6
2d1gq>Br47(A..
2d1gq>Br47(A..;   
 A2a4!8Q/A6
2d1gq>Br47(A..
2d1gq>Br47(A..;   
 	
1a!eq!teackAoq1u-q!58:9Q<"QPQT'8QR R R 	
Q!A#'
Bq!tGbdNR/0!a%8!Q@CDE E E !aQA.!333QA&--/21Q;13DDDDQQ*113rAqDF{QqS7HHHHQA1Hq188:b1a4i!mKKK!Q!$++-AqD888!Q
Aq)002rAgbjQqS6IBqSTUVSVxK6WWWW	1a(//1
HROd1gaik)A--HROd1gaiPQk4QTU3U0UUV V V BqDFQqSL!,a3q888r,   c                  P    [        [        * [        S-   /[        [        5      c   eg )Nr#   )r   r)   r+   r,   r-   test_rsolve_ratio_missedrB   O   s#     !QUQ*666r,   c                 V   ^ ^ [        U U4S j[        [        T 5      5       5       5      $ )z9Compute RHS of recurrence in f(n) with coefficients in c.c              3   j   >#    U  H(  nTU   TR                  [        [        U-   5      -  v   M*     g 7f)N)subsr)   ).0icfs     r-   	<genexpr>"recurrence_term.<locals>.<genexpr>X   s)     <mqtAFF1a!e$$ms   03)sumrangelen)rH   rI   s   ``r-   recurrence_termrO   V   s    <eCFm<<<r,   c            
         [         [         S-   [         S-  [         S-  [         S-  [         [         S-  -   S[         -  S[         S-  -  -   S[         S-  -  -
  S[         S-  -  -   S[         S-  -  -
  /n S	S// S
Q/ SQ[         * S/[         S-  [         -
  S-   S//nU  H  nU H  n[        X25      nUR                  [         5      (       a  [        X4[         5      U:X  d   eUR	                  [         5      (       d  MZ  [        U5      S::  d  Mk  [        X4[         5      R                  [        [        S5      / SQ5      5      R                  5       U:X  a  M   e   M     g)zSome bulk-generated tests.r"   r#   r'   r%      4      r&   r0   )r0   r!   r"   )r!   r"   r"   r!   r"   zC:3)r   r   r   N)r)   rO   is_polynomialr   is_hypergeometricrN   r   rE   zipr   r   )funcscoeffsprH   qs        r-   test_rsolve_bulkr[   [   sB   Q1adAqD!ad(BqD2ad7NQ	1F 5!Q$w5AqD5! #EAw%6!Q!Q$	C
CB FA%Aq!!"1+q000""1%%#a&A+#A!,11#geni2PQXXZ^____  r,   c                      [        [        S-  [        -
  S-   S/[        [        S-  [        -
  S-   -  [        -   S-   [        5      [        :X  d   eg )Nr#   rS   r"   )r   r)   r+   r,   r-   test_rsolve_0_sol_homogeneousr]   l   sG     AB*Aq!tax"},=,AA,EqIQNNNr,   c                  \   [        [        S-   5      [        [        S-   5      -
  [        [        5      -
  n [        S5      [        R                  [        R                  [        S5      -  -   [        -  -  [        S5      [        R                  [        R                  [        S5      -  -
  [        -  -  -
  n[        U [        [        5      5      [        [        R                  [        R                  [        S5      -  -
  [        -  -  [        [        R                  [        R                  [        S5      -  -   [        -  -  -   [        [        R                  [        R                  [        S5      -  -
  [        -  -  [        [        R                  [        R                  [        S5      -  -   [        -  -  -   4;   d   e[        U [        [        5      SS/5      U:X  d   e[        U [        [        5      SSS.5      U:X  d   e[        U [        [        5      [        S5      S[        S5      S05      U:X  d   e[        [        [        5      [        [        S-
  5      -
  [        [        S-
  5      -
  [        [        5      SS/5      U:X  d   e[        [        [        [        5      [        [        S-
  5      [        [        S-
  5      -   5      [        [        5      SS/5      U:X  d   eU R                  [         [        [        [        U [        [        5      5      R                  [        [        5      5      5      R                  5       S:X  d   e[        S-
  [        [        S-   5      -  [        S-  S[        -  -   S-
  [        [        S-   5      -  -
  S[        -  [        S-   -  [        [        5      -  -   n [        [        [        5      -  [        S[        -  -  -   nS[        [        5      -  SS[        -  -  -   n[        U [        [        5      5      U:X  d   e[        U [        [        5      / 5      U:X  d   e[        U [        [        5      0 5      U:X  d   e[        U [        [        5      SS/5      U:X  d   e[        U [        [        5      SSS.5      U:X  d   e[        U [        [        5      [        S5      S[        S5      S05      U:X  d   eU R                  [         [        [        [        U [        [        5      5      R                  [        [        5      5      5      R                  5       S:X  d   e[        [        5      [        [        S-
  5      -
  S-
  n [        U [        [        5      [        S5      S05      S[        -  :X  d   e[        U [        [        5      [        S5      S05      S[        -  S-   :X  d   e[        U [        [        5      [        S5      S[        S5      S05      b   eU R                  [         [        [        [        U [        [        5      5      R                  [        [        5      5      5      R                  5       S:X  d   eS[        [        S-
  5      -  [        [        5      -
  S-
  n [        U [        [        5      [        S5      S05      S[        -  * S-  [        R                  -   :X  d   e[        U [        [        5      [        S5      S05      S[        -  S-  [        R                  -   :X  d   e[        U [        [        5      [        S5      S05      SS[        -  -  S-  [        R                  -   :X  d   eU R                  [         [        [        [        U [        [        5      5      R                  [        [        5      5      5      R                  5       S:X  d   e[        [        5      S[        -  [        [        S-
  5      -  -
  n [        U [        [        5      5      [        [        [        5      -  :X  d   eU R                  [         [        [        [        U [        [        5      5      R                  [        [        5      5      5      R                  5       S:X  d   e[        [        5      S[        -  [        [        S-
  5      -  -
  S-
  n [        U [        [        5      5      b   eS[        [        S-
  5      -  S[        -
  [        [        5      -  [        -  -   n [        U [        [        5      [        S5      S05      S[        S-
  -  [        -  :X  d   e[        U [        [        5      [        S5      S05      S[        S-
  -  [        -  S-  :X  d   e[        U [        [        5      [        S5      S05      S[        S-
  -  [        -  S-  :X  d   eU R                  [         [        [        [        U [        [        5      5      R                  [        [        5      5      5      R                  5       S:X  d   e[        S-
  [        S-
  -  [        [        S-   5      -  [        S-   [        S-   -  [        [        5      -  -
  n [        U [        [        5      [        S5      S[        S	5      S
05      [        [        S-
  -  [        S-
  -  :X  d   e[        U [        [        5      [        S5      S[        S	5      S05      [        * [        S-
  -  [        S-
  -  S[        -  -  :X  d   eU R                  [         [        [        [        U [        [        5      5      R                  [        [        5      5      5      R                  5       S:X  d   e[        [        [        [        S-   5      [        [        [        5      -  5      [        [        5      [        S5      [        05      R                  5       [        [        -  :X  d   e[        [        [        5      [        [        [        S-
  5      -  -
  [        [        5      [        S5      [        [        5      [        [        -   -  [        S5      [        [        [        -
  -  05      R                  5       [        [        S-  S-   -  [        [        [        5      * [        -  -  -
  :X  d   eS[        S-  -  S[        -  -   S-
  [        [        S-
  5      -  S	[        S-  -  S[        -  -
  S-   [        [        5      -  -   n [        U [        [        5      [        S5      [!        S[        -  S-   S5      05      nSS[        -  -  [        -  S[        -  S-
  S-  -  S[        -  S-   -  S-  n[#        [%        USS95      U:X  d   e[        [        [        5      [        [        [        S-   5      [        [        S-
  5      -   -  S-  -   [        [        5      5      n['        U5      S:X  d   e[        [        S-   [        [        5      -  [        [        5      5      b   e[        [        S-   [        [        5      -  [        S-   [        [        S-   5      -  -   [        S-   [        [        S-   5      -  -   [        [        5      5       b   e[        [        [        5      [        [        S-   5      -   S[        -  -   S[        -  -   [        [        5      5      S[        -  [        -  S[        -  S-  -
  S[        -  S	-  -
  :X  d   eg )Nr#   r"   r&   r   )r   r"   r'   r(   r%      ir!   i    rS   r3   T)funcz@C0*((-sqrt(1 - a**2) - 1)/a)**n + C1*((sqrt(1 - a**2) - 1)/a)**n)r   r)   r   r	   r=   r   r*   r>   r   rE   r   r?   simplifyr   r   r   r   r   r   str)rI   hgynsols        r-   test_rsolveri   r   s   	!a%1QU8ad"AQ!&&a.(1,,
q'166AFF47N*Q.
.	/A !QqT?
AFFQVVDG^#a''"affqvvd1g~.E-I*II
AFFQVVDG^#a''"affqvvd1g~.E-I*II   
 !QqTAq6"a'''!QqTqQ<(A---!QqTAaD!QqT1-.!333!A$1q5/Aa!eH,adQF;q@@@"QqT1QU8aAh./11v>!CCC66!VAva133Aq9:;DDF!KKK	
Q!a%AqD1Q3JNAa!eH44qsAE{1Q47GGA
9Q<"QT'!A
9Q<!AqD& A!QqT?a!QqT2!###!QqT2!###!QqTAq6"a'''!QqTqQ<(A---!QqTAaD!QqT1-.!33366!VAva133Aq9:;DDF!KKK	!qQx!A!QqTAaD!9%1,,,!QqTAaD!9%1q000!QqTAaD!QqT1-.66666!VAva133Aq9:;DDF!KKK	!AE(
QqTAA!QqTAaD!9%!Q$q166)9999!QqTAaD!9%Aa!&&888!QqTAaD!9%1a4AFF)::::66!VAva133Aq9:;DDF!KKK	!qs1QU8|A!QqT?b1o---66!VAva133Aq9:;DDF!KKK	!qs1QU8|aA!QqT?"""	!AE(
a!eQqT\!^#A!QqTAaD!9%QUA555!QqTAaD!9%QUAa777!QqTAaD!9%QUAa77766!VAva133Aq9:;DDF!KKK	
QQ!a% AEAE?1Q4#77A!QqTAaD!QqT2./1a!e9a!e3DDDD	1Q4!A$1Q4%'+,"a!e*a!e*<bAY*FG G G 66!VAva133Aq9:;DDF!KKK"Qq1uXq1v&!qtQi8AACq!tKKK!A$1QqS6/!A$qT47AE?AaD!QU)466>hj!aL1tAwh]?*+ + + 
QTBqD2	qQx'1QT6BqD=1+<ad*BBA	1Q4!A$1q! 45	6B
ac(1*acAg\
!1Q37
+B
.C&$'(C///
11QU8aAh./111Q4
8Cs8YYYY1q5!A$,!%---AE1Q4<1q5!AE("22a!eQq1uX5EEqtL   !A$1q5/AqD(1a4/162'"*q!tAv:MPQSTPTUVPV:VVVVr,   c                     ^  [        S5      m [        [        S 5        [        [        U 4S j5        [        [        U 4S j5        [        [        S 5        [        [        U 4S j5        [        [        S 5        g )Nxc                  t    [        [        [        5      [        [        S-   5      -
  [        [        5      5      $ Nr"   )r   r   r)   r?   r+   r,   r-   <lambda>$test_rsolve_raises.<locals>.<lambda>   s    vadQq1uXoqt<r,   c                  p   > [        [        [        5      [        [        S-   5      -
  T " [        5      5      $ rm   r   r   r)   rk   s   r-   rn   ro      s     vadQq1uXoqt<r,   c                  p   > [        [        [        5      T " [        S-   5      -
  [        [        5      5      $ rm   rq   rr   s   r-   rn   ro      s     vadQq1uXoqt<r,   c                      [        [        [        5      [        [        5      [        [        S-   5      -  -
  [        [        5      5      $ rm   )r   r   r)   r   r+   r,   r-   rn   ro      s)    vadT!WQq1uX-=&=qtDr,   c                     > [        [        [        5      [        [        S-   5      -
  [        [        5      T " S5      S05      $ )Nr"   r   rq   rr   s   r-   rn   ro      s*    vadQq1uXoqtadAYGr,   c                      [        [        [        5      [        [        S-   5      -   S[        -  -   [        [        5      -   [        [        5      5      $ )Nr"   r#   )r   r   r)   r   r+   r,   r-   rn   ro      s1    vadQq1uXo1&<s1v&EqtLr,   )r   r   
ValueErrorrr   s   @r-   test_rsolve_raisesrx      sN    A
:<=
:<=
:<=
:DE
:GH
:LMr,   c            	         [        [        S-   5      [        [        S-   5      -
  [        [        5      S-  -   n [        U [        [        5      5      S[        * S-   -  [        -  [        -  S[        * -  [        -  -   :X  d   e[        U [        [        5      [        S5      S[        S5      S05      SS[        -
  -  [        -  :X  d   eg )Nr#   r"   r%   r   )r   r)   r   r>   r*   rI   s    r-   test_issue_6844r{      s    	!a%1QU8ad1f$A!QqT?a1"q&k"nQ.aR;;;;!QqTAaD!QqT1-.!a!e*Q,>>>r,   c                     [        SSS9n [        SSS9n[        [        5      SU -  [        U5      -  [        [        S-
  5      -  -
  U S-  [        [        S-
  5      -  -   n[	        U[        [        5      5      [
        U [        U5      [        [        [        U5      5      -  -
  -  [        -  -  [        U [        U5      [        [        [        U5      5      -  -   -  [        -  -  -   :X  d   eg )NrT)positivetheta)realr#   r"   )
r
   r   r)   r   r   r*   r   r   r   r>   )r}   r   rI   s      r-   test_issue_18751r      s    sT"A7&E	!q1us5z!Aa!eH,,q!taAh>A!QqT?
As5zAc#e*o--.22RCJ3sSXz?IZ<Z9[^_8_5__` ` `r,   c                     [        [        [        S-   5      [        [        S-   5      -
  [        [        S-   5      -
  [        [        5      -   [        [        5      5      S[        -  [        -  [        -   [
        [        -  -   :X  d   e[        [        [        S-   5      S[        [        S-   5      -  -   S[        [        S-   5      -  -   [        [        5      -   [        [        5      5      R                  5       S[        -  [        -  S[        -  [        -  [        -  -
  S[        -  [
        -  [        S-  -  -
  :X  d   e[        [        [        5      S[        [        S-
  5      -  -
  S[        [        S-
  5      -  -   S[        [        S-
  5      -  -
  [        [        5      / SQ5      SS[        -  -  [        -
  S-
  :X  d   e[        [        [        S-   5      S[        [        S-   5      -  -
  S[        [        5      -  -   [        [        5      [        S5      S[        S5      S	[        S5      S
05      S
[        -  S[        -  -   :X  d   eg )Nr'   r#   r"   r!   r&   r%   )r"   r'   r6   r   r6   r0   )r   r   r)   r>   r*   C2r   r+   r,   r-   test_constant_namingr      s   !AaC&1QqS6/AacF*QqT11Q48R!GBJObQRd<RRRR!AaC&1QqS6/!AacF(*1Q4/16==?B72:QSVWPWXZPZ[\P\C\`bef_fgi_ijkmnjn_nCnnnn!A$1QU8#a!a%j01Qq1uX:=ad7KqQRTUQUvXYz\]~]]] !AaC&1QqsV8#a!f,adQqT!QqT!QqT"4MNSUXYRY\]^_\_R____r,   c                     [        [        5      S[        [        S-   5      -  -   S[        [        S-   5      -  -
  S[        [        S-   5      -  -
  S[        [        S-   5      -  -   S[        [        S	-   5      -  -   S[        [        S
-   5      -  -
  S[        [        S-   5      -  -
  [        [        S-   5      -   n [        U [        [        5      5      c   eg )N   r"   i  r#   iD  r'   i  r%   r&   r(      r6   )r   r)   r   rz   s    r-   test_issue_15751r      s    	!r!AE({S1q5\)D1q5M9D1q5MIDQRSTWXSXQYMY\_`abcfgbg`h\hhkmnopqtupunvkvvyz{|  @A  |A  zB  	BA!QqT?&&&r,   c            
         S[        [        5      -  S[        [        S-   5      -  -   S[        [        S-   5      -  -   S[        [        S-   5      -  -   n [        U [        [        5      5      n[        SS	[	        S5      S-  -  -  S
-  SS[        S5      [        -  -   SS[        S5      -  -   [	        S5      S-  -  -  -   S[        S5      [        -  -
  -  SS[        S5      -  -   [	        S5      S-  -  -  S-  -   S[        S5      [        -  -
  SS[        S5      -  -   [	        S5      S-  -  -  -  [        -  -  [        SS	[	        S5      S-  -  -  S
-  SS[        S5      [        -  -
  SS[        S5      -  -   [	        S5      S-  -  -  -   S[        S5      [        -  -   -  SS[        S5      -  -   [	        S5      S-  -  -  S-  -   S[        S5      [        -  -   SS[        S5      -  -   [	        S5      S-  -  -  -  [        -  -  -   [        SS	[	        S5      S-  -  -  S
SS[        S5      -  -   [	        S5      S-  -  -  -  [	        S5      S-  -
  SS[        S5      -  -   [	        S5      S-  -  S-  -   [        -  -  -   nX:X  d   eUR                  [        S[        S[        S[        S05      R                  5       n[        US-   5      S:  d   eg )Nir%   r"   r(   r#   .   r'   V   r2   E   ir!   iln i  i#  i^     i  i      gYB?gvIh%<=)r   r)   r   r*   r	   r   r   r>   r   rE   evalfabs)rI   rh   expectedes       r-   test_issue_17990r      s   AaD1Qq1uX:!AE(
*R!a%[8A
AaD/CBrAaDF|OB&#d1gai&T$ZCQ46B# 1# +#%&a]*45:Sd^5K	
1a5** DGAIDJ(>!A$q&'IIK   BrAaDF|OB&#d1gai&4	dL CtAvB 1 +!"T!WQY*016T$Z1G	
1a1** DGAIDJ(>!A$q&'IIK   3rAaDF|#RT$Z)?1Q46(J%JK	!RDdO+qtAv6s:;=>? ??H ??"aQAq!,-335Aq$$%---r,   c                  (   [        S5      n U " [        S-   5      U " [        S-   5      -
  U " [        S-   5      -
  U " [        5      -   n[        X" [        5      5      S[        -  [        -  [        -   [
        [        -  -   :X  d   eU " [        S-   5      SU " [        S-   5      -  -   SU " [        S-   5      -  -   U " [        5      -   n[        X " [        5      5      S[        -  [        -  S[        S-   -  [        -  [        -  -   S[        S-   -  [
        -  [        S-  -  -   :X  d   e[        U " [        5      SU " [        S-
  5      -  -
  SU " [        S-
  5      -  -   SU " [        S-
  5      -  -
  U " [        5      U " S5      SU " S5      SU " S5      S	05      SS[        -  -  [        -
  S-
  :X  d   e[        U " [        5      SU " [        S-
  5      -  -
  [        -
  U " [        5      U " S5      S05      SS[        -  -  [        -
  S-
  :X  d   eg )
Nr   r'   r#   r"   r!   r&   r%   r   r6   )r   r)   r   r>   r*   r   )r   eqeq2s      r-   test_issue_8697r     s   A	
1q5Aa!eH	qQx	'!A$	.B"adQwrzBA5555
AE(QqQxZ
!Aa!eH*
,qt
3C3!!GBJ"Ar)!++rQUmB.>q!t.CCD E D !A$1QU8#a!a%j01Qq1uX:=A$1q!A$1Q43589!Q$
QG G G !A$1QU8#a'1!ay9Qq!tVaZ!^KKKr,   c            	         [        [        5      [        [        S-
  5      -
  S[        [        S-
  5      -  -
  S[        -  -
  n [        U [        [        5      5      S[        -  [        -  S[        -  [        -  -   [        -
  [        SS5      -
  :X  d   e[        U [        [        5      [        S5      S[        S5      S05      S[        -  * S-  SS[        -  -  -   [        -
  [        SS5      -
  :X  d   e[        S[        [        5      -  [        [        S-   5      -   [        -   S-
  [        [        5      5      S[        -  [        -  [        -   :X  d   eg )Nr"   r#   r!   r&   r   r0   )r   r)   r   r*   r>   r   rz   s    r-   test_diofantissue_294r     s   	!qQx!Aa!eH*$qs*A!QqT?rAgbj1a472Q6!QGGGG!QqTAaD"adA./b1WHQJ1a44G45568@A5G H H H "QqT'Aa!eH$q(1,ad3q!tBw{BBBr,   c            
      @   [        S5      n [        [        U " [        5      SU " [        S-
  5      -  [        -   5      U " [        5      5      S[        -  [        -  [        -
  S-
  :X  d   e[        [        U " [        S-   5      SU " [        5      -  [        S-  -   S-   5      U " [        5      5      S[        -  [        -  [        S-  -
  S[        -  -
  S-
  :X  d   e[        [        U " [        S-   5      SU " [        5      -  [        S-  -   S-   5      U " [        5      U " S5      S05      SS[        -  -  S-  [        S-  -
  S[        -  -
  S-
  :X  d   e[        [        U " [        5      SU " [        S-
  5      -  S[        S-  -  -   5      U " [        5      5      S[        -  [        -  S[        S-  -  -
  S[        -  -
  S	-
  :X  d   e[        [        U " [        5      SU " [        S-
  5      -  [        S-  -   5      U " [        5      5      S[        -  [        -  [        S-  -
  S[        -  -
  S
-
  :X  d   e[        [        U " [        5      SU " [        S-
  5      -  [        -   5      U " [        5      U " S5      S05      SS[        -  -  [        -
  S-
  :X  d   eg )NrI   r#   r"   r%   r   r   r'   rS   r2   r(   )r   r   r   r)   r*   rz   s    r-   test_issue_15553r      s"   A"QqT1Qq1uX:>*AaD1QT"Wq[1_DDD"Qq1uXq1v1}q011Q48AqDGadNQqS<PST<TTTT"Qq1uXq1v1}q011Q4!A$CqAvaxRSUVRVYZ[\Y\G\_`G````"QqT1Qq1uX:!Q$./16!Q$r'AadF:JRPQT:QTV:VVVV"QqT1Qq1uX:1,-qt41R!Q$18Lq8PPPP"QqT1Qq1uX:>*AaD1Q4)<!Q$
QNNNr,   N)>sympy.core.functionr   r   r   sympy.core.numbersr   r   sympy.core.relationalr   sympy.core.singletonr	   sympy.core.symbolr
   r   (sympy.functions.combinatorial.factorialsr   r   r   $sympy.functions.elementary.complexesr   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   sympy.polys.polytoolsr   sympy.solvers.recurrr   r   r   r   sympy.testing.pytestr   r   r   	sympy.abcr   r   r   r)   r?   r*   r>   r   r.   r8   r@   rB   rO   r[   r]   ri   rx   r{   r   r   r   r   r   r   r   r+   r,   r-   <module>r      s    : : , $ " / N N 4 9 ? ( P P 4 4 SMud#1Z 
B
D1%9P 7 7=
`"OZWzN?`` ' '
. LCOr,   