
    \hlG                        S SK Jr  S SKJrJr  S SKJr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  S SKJrJr  S SKJrJrJrJr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 SK%J&r&J'r'J(r(J)r)J*r*  S SK+J,r,  S SK-J.r.  S SK/J0r0J1r1J2r2  S SK3J4r4J5r5  S r6S r7S r8S r9S r:S r;S r<S r=S r>S r?S r@S rAS rBS rCS rDS rES  rF\5S! 5       rGS" rHS# rIS$ rJS% rKS& rLS' rMS( rNS) rOS* rPS+ rQS, rRS- rSS. rTS/ rUS0 rVS1 rWS2 rXS3 rYS4 rZS5 r[S6 r\S7 r]S8 r^S9 r_S: r`S; raS< rbS= rcS> rdS? reS@ rfSA rgSB rhSC riSD rjSE rkSF rlSG rmSH rnSI roSJ rpSK rqSL rrSM rsSN rtSO ruSP rvSQ rwSR rxSS ryST rzSU r{gV)W    )AccumBounds)
Derivative	PoleError)EIIntegerRationalpi)S)Symbolsymbols)sign)explog)acoshacothasinhatanhcoshcothsinhtanh)ceilingfloorfrac)cbrtsqrt)asincoscotsintan)limit)O)xyz)raisesXFAILc                     [         R                  " [         SS9[         :X  d   e[        R                  " [         SS9[        :X  d   eS[         [        -  -  R                  [        SS9S[         [        -  -  :X  d   e[        SS5      R                  [         SS9[        SS5      :X  d   e[         R                  " 5       [         :X  d   eg )N   n         )r%   nseriesr&   r	        W/var/www/auris/envauris/lib/python3.13/site-packages/sympy/series/tests/test_nseries.pytest_simple_1r5      s    99Q!!!!99Q!!!!qsGQ!$1Q3///Aq>!!!q!)Xa^;;;99;!r3   c                      [         [        [         5      -  R                  [         SS9[         [        [         5      -  :X  d   eg )Nr+   r,   )r%   r   r1   r2   r3   r4   
test_mul_0r7      s0    c!fHa1%3q6111r3   c                     [         [        S[         -   5      -  R                  [         SS9[         [        S5      -  [         S-  S-  -   [         S-  S-  -
  [         S-  S-  -   [        [         S-  5      -   :X  d   e[         [        S[         -   5      -  R                  [         SS9[         S-  [         S-  S-  -
  [         S-  S-  -   [        [         S-  5      -   :X  d   eg )	N   r+   r,   r/      r0      r.   r%   r   r1   r$   r2   r3   r4   
test_mul_1r=      s    c!a%jL!!!q!)Qs1vX1Q->Aa-G	1R.AqD'.   c!a%jL!!	Q " a4!Q$q&=1a46)AadG34 4 4r3   c                     [         S-  R                  [         SS9[         S-  :X  d   eS[         -  R                  [         SS9S[         -  :X  d   eS[         S-  -  R                  [         SS9S[         S-  -  :X  d   e[         [        SS5      -  R                  [         SS9[         [        SS5      -  :X  d   e[        [         5      S-  R                  [         SS9[        [         5      S-  :X  d   eg )Nr9   r+   r,   r.   r/   )r%   r1   r	   r   r2   r3   r4   
test_pow_0r?   &   s    qD>>!q>!QT)))aC==a= AaC'''adFA#qAv---x1~&&qA&.1hq!n3DEEEGQJQ'DGQJ777r3   c                     S[         -   S-  R                  [         SS9[         S-  S[         -  -   S-   :X  d   e[        [         5      S-   S-  R                  [         5      S[        [         5      -  [         -   S-   :X  d   e[        [         5      [        [         5      -   S-  R                  [         5      S[         [	        SS5      -  -  [         [	        SS5      -  -   [         -   :X  d   eg )Nr.   r9   r+   r,      r/   )r%   r1   r   r   r	   r2   r3   r4   
test_pow_1rB   .   s    UQJQ'1a4!A#:>999 !Wq[1%%a(Ad1gIMA,====!WtAw"++A.!Ax1~4E2E
Xa^
33       r3   c                  d   SS[         -
  -  R                  [         SS9S[         -   [         S-  -   [         S-  -   [         S-  -   [        [         S-  5      -   :X  d   e[         S[         -
  -  R                  [         SS9[         [         S-  -   [         S-  -   [         S-  -   [         S-  -   [        [         S-  5      -   :X  d   e[         S-  S[         -
  -  R                  [         SS9[         S-  [         S-  -   [         S-  -   [         S-  -   [         S	-  -   [        [         S-  5      -   :X  d   eg )
Nr.   r+   r,   r9   r/   r0   rA   r:      r%   r1   r$   r2   r3   r4   test_geometric_1rF   7   s   q1uIqA&!a%!Q$,A*=1*DqAw*NNNNq1uIqA&!ad(QT/AqD*@1a4*G!AqD'*QQQQqD!a%L!!!q!)QTAqD[1a4-?!Q$-F	1.Aw.   r3   c                      [        S[        -   5      R                  [        SS9S[        S-  -   [        S-  S-  -
  [        S-  S-  -   S[        S-  -  S	-  -
  [        [        S-  5      -   :X  d   eg )
Nr.   r+   r,   r9   r:   r/      r0      r   r%   r1   r$   r2   r3   r4   test_sqrt_1rK   >   sm    A;qA&!ac'AqDF*:QT"W*DqAvcz*QTUVWYZVZT[*[[[[r3   c                     [        [        5      R                  [        SS9S[        -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        [        S-  5      -   :X  d   e[        [        5      R                  [        S	S9S[        -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S
-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        [        S	-  5      -   :X  d   e[        S[        -  5      R                  [        SS9[        S[        -  5      :X  d   e[        SS[        -   -  5      R                  [        SS9[        S[        -
  S[        S-  -  S-  -
  S[        S-  -  S-  -   -  R                  5       [        [        S-  5      -   :X  d   e[        S[        -   5      R                  [        SS9[        S5      S[        -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   -  R                  5       [        [        S-  5      -   :X  d   eg )Nr+   r,   r.   r9   r/   rA   r0   r;      x     rD   i  r:   i  	   i 
   i _7    i a   )r   r%   r1   r$   r   expandr2   r3   r4   
test_exp_1rU   B   s@   q6>>!q>!QUQT!V^ad1f%<q!tBw%F1a4%PPPPq6>>!r>"a!ead1fnq!tAv&=1R&G!Q$s(&R	1S'a49' !tEz'*,-qDK'8:;R%-'H	2h'1b5'" " " " qs8A#s1Q3x///q!a%y>!!!q!)	
AEBq!tGAI!Q$q(	)113a1g=> > >q1u:a1%	QQAa!Q$q&(1a472	3;;=!Q$GH H Hr3   c                  >   [        S[        [        5      -   5      R                  [        SS9[        S5      S[        [        5      -   [        S-  -   [        [        5      [        -  S-  -   -  R	                  5       [        [        [        5      S-  5      -   :X  d   eg )Nr.   r/   r,   r9   rA   )r   r   r%   r1   rT   r$   r2   r3   r4   test_exp_sqrt_1rW   N   s|    q47{##A#+	QT!Wqs"T!WQYq[0	199;aQ
mKL L Lr3   c                  l   [        [        [        [        5      -  5      R                  [        SS9S[        [        [        5      -  -   [        S-  [        [        5      S-  -  S-  -   [        S-  [        [        5      S-  -  S-  -   [	        [        S-  [        [        5      S-  -  5      -   :X  d   eg Nr0   r,   r.   r9   r/   rA   )r   r%   r   r1   r$   r2   r3   r4   test_power_x_x1rZ   S   s    #a&M""1"*	Ac!fHq!tCFAI~a''!Q$s1vqy.*::Qq!tCFAI~=NNO O Or3   c                  H   [         [         -  R                  [         SS9S[         [        [         5      -  -   [         S-  [        [         5      S-  -  S-  -   [         S-  [        [         5      S-  -  S-  -   [        [         S-  [        [         5      S-  -  5      -   :X  d   eg rY   )r%   r1   r   r$   r2   r3   r4   test_power_x_x2r\   X   s    qD>>!q>!	Ac!fHq!tCFAI~a''!Q$s1vqy.*::Qq!tCFAI~=NNO O Or3   c                      [        SS[        -  -   5      R                  [        SS9[        [        [        5      -
  [        S-  S-  -
  [        S-  S-  -   [        S-  S-  -
  [        [        S-  5      -   :X  d   eg )Nr.   r+   r,   r9   r/   r0   )r   r%   r1   r$   r2   r3   r4   test_log_singular1r^   ]   st    q1Q3w<Q'1s1v:1Q+>Aa+G	1Q,1a4,   r3   c                     SS[         -  [         [        S5      [        S5      -  -  -   -  n U R                  [         SS9[         [        S5      [        S5      -  S-   -  * [         -   [        [         S-  5      -   :X  d   eg )Nr.   r/   r9   r+   r,   r<   es    r4   test_log_power1rb   b   sl    	QqS1QA''(A99Q!9SVCF]Q%6!7 7! ;a1g EEEEr3   c                      [        S5      n SS[        [        5      -
  -  nUR                  [        SU S9SSU -
  -  :X  d   eg )Nlr.   r+   r-   logxr   r   r%   r1   rd   ra   s     r4   test_log_seriesri   g   sA    sA	1s1v:A99Q!!9$1q5	111r3   c                      [        S[        -  5      n U R                  [        SS9[        [        5      * [        S5      -   :X  d   eg )Nr+   r,   )r   r%   r1   r`   s    r4   	test_log2rl   m   s9    BqD	A99Q!9Q#b' 1111r3   c                      [        S5      n S[        S[        -  5      -  nUR                  [        SU S9SU * [        S5      -   -  :X  d   eg )Nrd   r.   rk   r0   re   rg   rh   s     r4   	test_log3rn   r   sH    sA	#bd)A99Q!!9$A2B<(8888r3   c                     [        [        5      n U R                  [        SS5      S:w  d   eU R                  [        SS5      [        S[        5      :X  d   eU R                  [        SS5      [        [        [        5      :X  d   eU R                  [        SS5      [        [        [        S-  [        5      -   :X  d   eU R                  [        SS5      [        [        [        S-  [        5      -   :X  d   eU R                  [        SS5      [        [        S-  S-  -
  [        [        S-  [        5      -   :X  d   e[	        [        5      S-
  [        -  n U R                  [        SS5      S[        S-  -   [        S-  S-  -   [        [        S-  5      -   :X  d   e[        R                  " [        SS5      [        :X  d   eg )Nr   r.   r9   r/   r0   rA   )r!   r%   r1   r$   r   r`   s    r4   test_series1rp   x   sY   AA99Q1"""99Q11a(((99Q11a(((99Q1Qq!tQZ///99Q1Qq!tQZ///99Q1QT!Va1aj!8888	Q!QA99Q1QqS1a46!1AadG!;;;;99Q1"""r3   c                      [         R                  " [         SS5      [        S[         5      :X  d   e[         R                  " [         SS5      [        [         [         5      :X  d   eg )Nr   r.   rE   r2   r3   r4   test_series1_failingrr      sD    99Q11a(((99Q11a(((r3   c                      S[         -  R                  [         SS5      S[         -  :X  d   e[         S[         -  -   R                  [         SS5      [         S[         -  -   :X  d   eg )Nr.   r   r/   )r%   r1   r2   r3   r4   test_seriesbug1rt      sR    aC==Aq!QqS(((!GQ1%QqS000r3   c                     [         S-   S-  R                  [         SS5      SS[         -  -
  S[         S-  -  -   S[         S-  -  -
  [        [         S-  [         5      -   :X  d   e[         S-   S-  R                  [         SS5      S[         -
  [         S-  -   [         S-  -
  [        [         S-  [         5      -   :X  d   e[         S-   S-  R                  [         SS5      S:X  d   e[         S-   S-  R                  [         SS5      S[         -   :X  d   e[         S-   S-  R                  [         SS5      [         S-  S[         -  -   S-   :X  d   e[         S-   S-  R                  [         SS5      SS[         -  -   S[         S-  -  -   [        [         S-  5      -   :X  d   eSS[         -   -  R                  [         SS5      S[         -
  [         S-  -   [         S-  -
  [        [         S-  [         5      -   :X  d   e[         SSS[         -  -   -  -   R                  [         SS5      SS[         -  -
  S	[         S-  -  -   S
[         S-  -  -
  [        [         S-  [         5      -   :X  d   eS[         -  S-   S-  R                  [         SS5      SS[         -  -   S[         S-  -  -   [         S-  -   :X  d   eSSS[         -  -   -  R                  [         SS5      [         [         S-  -
  [         S-  -   [        [         S-  [         5      -
  :X  d   eSSS[         S-  -  -   -  R                  [         SS5      [         S-  [         S-  -
  [        [         S-  [         5      -   :X  d   eg )Nr.   r   r0   r9   r/   rk   r+   rM   r;   rA   rE   r2   r3   r4   test_series2xrx      s   UbM""1a+q1Q3w1a4/?!AqD&/H1QPQTST:/UUUUUbM""1a+q1uq!t|ad/BQq!tQZ/OOOOUQJ1a(A---UQJ1a(AE111UQJ1a(AqD1Q3JN:::UQJ1a(A!Ga1f,<qAw,FFFFq1uIq!Q'1q51a4<!Q$+>1a4+KKKK1qs7O$$Q1-QqS2ad71BR1W1LqQRTUQUWXz1YYYYqS1WqL!!!Q*a!A#g!Q$.>R.HHHHq1Q3wK  Aq)QAX1_qAqz-IIIIq1QT6zN##Aq!,1q!ta1aj0HHHHr3   c                  0   [        S5      n U S-  U [        S5      * [        S5      S-  -  -  -   S-  SU [        S5      * [        S5      S-  -  -  -  SU S-  -  -   -  nUR                  5       nUR                  U SS5      R	                  U S5      S:X  d   eg )Nwrk   r/   r9   r   r0   )r   r   rT   r1   subsrz   ra   s     r4   	test_bug2r}      s    sA	
R1	QA 
!#	%&'SVGCFRL,@(A&AAa"gI&M	OA	
A99Q1""1a(A---r3   c                      S[         -   S[         -  -  n U R                  [         SS9[        S5      [         [        S5      -  S-  -
  S[        S5      -  [         S-  -  S-  -   [        [         S-  5      -   :X  d   eg )Nr.   r/   r,   r9   rR   r;   )r%   r1   r   r$   r`   s    r4   test_expr      sj    	
Q!A#A99Q!9A3q6! 3bQi1nR6G G!AqD' QQQQr3   c                  $   [        S5      n U S[        [        5      [        S5      [        [        5      -   -  -
  -  n[        S5      nUR                  U SSUS9[	        U[        S5      -  [        [        5      [        S5      -   -  5      :X  d   eg )Nrz   r.   r9   logwr   )rf   )r   r   r%   r1   r   )rz   ra   r   s      r4   	test_exp2r      s    sA	AAAQ(()A&>D99	1ad  "4A;AQ#@AB B Br3   c                      S[         -  S[         S-  -  -   S[         -  S[         S-  -  -   -  n U R                  [         SS9S[         -
  [         S-  -   [        [         S-  5      -   :X  d   eg )Nr9   r/   r.   r,   rE   r`   s    r4   	test_bug3r      s`    	
1qAv!a1f%A99Q!9A1qAw 6666r3   c                     Sn S[         -  S[         U -  -  -   S[         -  S[         U -  -  -   -  nUR                  [         SS5      S[         -
  [         S-  -   [        [         S-  5      -   :X  d   e[        R                  n S[         -  S[         U -  -  -   S[         -  S[         U -  -  -   -  nUR                  [         SS5      S[         -
  [        [         5      -   [         [        S5      S-  -  -   [        [         S-  5      -   :X  d   eS[        [         5      -   nUR                  [         SS5      S[        [         5      -   :X  d   eg )Nr9   r/   r.   r   r0   )r%   r1   r$   r   Halfr   pra   s     r4   test_generalexponentr      s   	A	
1qAv!a1f%A99Q1QA!Q$!7777	A	
1qAv!a1f%A99Q1Qa1qtAv;!>1a4!HHHH	DGA99Q1T!W,,,r3   c                      SS[        [        5      -   -  n U R                  [        SS5      S[        -   [        [        5      -
  [        [        5      S-  -
  [        [        S-  [        5      -   :X  d   eg )Nr.   r   r9   r/   rJ   r`   s    r4   test_genexp_xr      s]    	1tAw;A99Q1	AQ$q'1*$qAqz12 2 2r3   c                  p   [        SS5      n S[        -  S[        U -  -  -   S[        -  S[        U -  -  -   -  nUR                  [        SS5      S[        -   [        S-  -   [        [        5      -
  [        [	        S5      S-  -  -
  [        [	        S5      S-  -  -
  [        [        S-  5      -   :X  d   eg )Nr/   r9   r.   r   r+   )r	   r%   r1   r   r   r$   r   s     r4   test_genexp_x2r      s    AA	
1qAv!a1f%A99Q1QAQ!7!ad1f+!EAaDQRF!SVWXY[\X\V]!]]]]r3   c                      [        S5      n SU -  U -  SU -   -  nUR                  U SS5      S[        X 5      -   :X  d   eUR                  U SS5      R                  U S5      S:X  d   eg )Nrz   r9   r.   r   )r   r1   r$   r{   r|   s     r4   test_seriesbug2r      sl    sA
A#qAEA99Q1QqW,,,99Q1""1a(A---r3   c                      [        S5      n [        SU -  5      U -  nUR                  U SS5      SSU S-  -  S-  -
  [        U S-  5      -   :X  d   eg )Nrz   r9   r   r/   r0   )r   r!   r1   r$   r|   s     r4   test_seriesbug2br      sT    sAAaC
A99Q1Qq!tVAX!Q$!7777r3   c                      [        SSS9n [        [        SU -  5      U -  5      nUR                  U SS9[        S5      SU S-  -  S-  -
  SU S-  -  S	-  -
  [	        U S-  5      -   :X  d   eg )
Nrz   Trealr9   r+   r,   r/   r0   -   r   r   r!   seriesr$   r|   s     r4   test_seriesbug2dr      sq    sAC!HQJA88A8s1v!Q$q01QT6"9<qAwFFFFr3   c                     [        SSS9n [        SU -  5      U -  SU -   -  nUR                  U SS5      S[        U 5      -   :X  d   eUR                  U SS5      SSU -  [	        S5      -  -   U S-  [        SS5      [	        S5      S-  -   -  -   [        U S-  5      -   :X  d   eUR                  U SS5      R                  U S5      S:X  d   eg )	Nrz   Tr   r9   r.   r   r/   )r   r!   r   r$   r   r	   r{   r|   s     r4   test_seriesbug2cr      s    sA	QqS!q1uA88Aq!AaD(((88Aq!AaCAJ	1hr1oA	)*!+-.q!tW!5 5 5 588Aq!!!!Q'1,,,r3   c                     [        SSS9n [        [        SU -  5      U -  5      SU -   -  R                  U SS5      [        S5      U [        S5      -  -   [	        U S-  U 5      -   :X  d   e[        [        [        SU -  5      U -  5      SU -   -  5      R                  U SS5      SSU -  [        S5      -  -   [	        U S-  5      -   :X  d   e[        [        S5      [	        U 5      -   5      R                  U SS5      S[	        U 5      -   :X  d   eS[	        U 5      -   SU -   -  R                  U SS5      S[	        U 5      -   :X  d   eg )Nr%   Tr   r9   r.   r   )r   r   r!   r   r$   r   r1   r%   s    r4   test_expbug4r      sB   sAAaC
U#VAq!_A3q60AAadAJ0NO O OC!HQJQ!!'1aA!CF
NQq!tW4LM M M s1v!}%%aA.!ad(:::1XQ((Aq1Q1X===r3   c                      [        S[        [        5      -   5      R                  [        SS5      [        S5      [        [        [        5      -   :X  d   eg )Nr9   r   )r   r$   r%   r1   r2   r3   r4   test_logbug4r     s:    q1Q4x=  Aq)SVa1g-====r3   c                     [        [        S[        -   5      [        -  5      R                  [        SS9[        S5      [        S5      * [        -  S-  -   S[        S5      -  [        S-  -  S-  -   [	        [        S-  5      -   :X  d   e[        [	        [        5      5      R                  [        SS5      S[	        [        5      -   :X  d   eg )Nr.   r/   r,   r9   rR   r;   r   )r   r   r%   r1   r$   r2   r3   r4   test_expbug5r     s    s1q5z!|$$Q!$,A#a&10Dr#a&yQRTUQU~VXGX0X[\]^`a]a[b0bbbbqt9Q1%QqT111r3   c                      [        [        [        5      5      R                  [        SS5      [        [        S-  S-  -
  [        S-  S-  -   S[        S-  -  S-  -
  [        [        S-  5      -   :X  d   eg )Nr   r:   r/   r+   rQ   rD   i;  r!   r%   r1   r$   r2   r3   r4   test_sinsinbugr     sa    s1v;q!Q'1q!tAv:1R+?!AqD&*+LqQRTUQUw+VVVVr3   c                      [         [        [         5      S-
  -  n U R                  [         SS5      S[         S-  -
  [         S-  S-  -
  [         S-  S-  -   [        [         S-  5      -   :X  d   eg )Nr.   r   r+   r9   r0   rO   rM   )r%   r   r1   r$   as    r4   test_issue_3258r     s]    	3q6A:A99Q1QqS1a48!3ad2g!=!Q$!GGGGr3   c                      [        SSS9n [        U S-  5      [        SS5      -  nUR                  U SS5      X S-  S	-  -
  U S
-  S-  -
  [	        U S-  5      -   :X  d   eg )Nr%   T)nonnegativer/   r.   r      rD      rS   i  )r   r!   r	   r1   r$   )r%   fs     r4   test_issue_3204r     se    s%AAqD	8Aq>!A99Q2!d2g+2d
":Qq"uX"EEEEr3   c                      [        S[        [        5      -
  5      n U R                  [        SS5      S[        [        5      S-  -
  [        S-  -
  [        [        5      S-  S-  -
  [        [        S-  5      -   :X  d   eg )Nr.   r   r9   r:   r/   rH   )r   r&   r1   r$   )r   s    r4   test_issue_3224r     sb    Qa[A99Q1T!WQY1!4tAwz"}!DqAw!NNNNr3   c                  Z   [        S5      u  p[        S5      [        S5      -  nU SU-   -  nS[        -  [        U SU-   -  5      * [        X U-  -   5      -   -  nU* [        U 5      -  [        -  U[        -  -   US-  S[        -  -  -
  [        U 5      -   nUR	                  U SS9U:X  d   eg )Nzw,ir+   r/   rk   r.   r9   r,   )r   r   r%   r$   r1   )rz   irr   ra   e_sers         r4   test_issue_3463r      s    5>DAAs1vA	BFA	!c!a!e*oA1H-.ABs1vIaK!A#1ac
*QqT1E99Q!9%%%r3   c                     [        S[        -  5      R                  [        SS9S[        -  S[        S-  -  S-  -
  [        [        S-  5      -   :X  d   e[        [        [        -   5      R                  [        SS9[        [        5      [        [        5      -   :X  d   e[        [        [        -   5      R                  [        SS9[        [        5      [        [        5      [        -  -   [        [        S-  5      -   :X  d   e[        [        [        -   5      R                  [        SS9[        [        5      [        [        5      [        -  -   [        [        5      [        S-  -  S-  -
  [        [        5      [        S-  -  S	-  -
  [        [        5      [        S-  -  S
-  -   [        [        S-  5      -   :X  d   eg )Nr:   r0   r,      r/   r.   r9   r+   rA   r;   )r!   r%   r1   r$   r&   r   r2   r3   r4   test_sinr   )  sR   qs8A#qsSAXaZ'7!AqD''AAAAq1u:a1%Q!A$666q1u:a1%Q#a&():Qq!tW)DDDDq1u:a1%Q#a&():SVAqD[])JAq!tA*Aq!tB*')*1a4*1 1 1 1r3   c                      [        S[        -  5      [        -  n U R                  [        SS9SS[        S-  -  S-  -
  S[        S-  -  S	-  -   [        [        S-  5      -   :X  d   eg )
Nr:   rA   r,   r   r9   r/   i   r0      r   r`   s    r4   test_issue_3515r   1  s\    AaC
A99Q!9C1HQJad2 =!Q$ GGGGr3   c                     [        [        5      S-  [        [        [        5      5      [        [        5      S-  -  [        [        5      [	        SS5      -  [        [        5      S-  -  -
  -  n U R                  [        SS9[	        SS5      S	[        S-  -  S
-  -
  S[        S-  -  S-  -
  S[        S-  -  S-  -
  S[        S-  -  S-  -   [        [        S-  5      -   :X  d   eg )Nr   r9   r.   r/   rP   r,   rk   rM   rD   i   +   r0   i(  ic  rA   i % iy  r:   i )r!   r%   r   r   r	   r1   r$   r`   s    r4   test_issue_3505r   6  s    Ad3q6l3q619,AAs1vqy() 	*A99Q!9R 01QT6#: =
1a4!QT	')!*,/1HX,=!>@A!Q$!H H H Hr3   c                     [        S5      n [        S-  [        [        U [        -   5      -  [        [        U 5      -  -
  -  nUR                  [        SS9[	        U 5      [        U 5      [        -  S-  -
  [	        U 5      [        S-  -  S-  -
  [        S-  [        U 5      -  S-  -   [        S-  [	        U 5      -  S	-  -   [        S
-  [        U 5      -  S-  -
  [        [        S-  5      -   :X  d   e[        S-  [        [	        U [        -   5      -  [        [	        U 5      -  -
  -  nUR                  [        SS9[        U 5      * [	        U 5      [        -  S-  -
  [        U 5      [        S-  -  S-  -   [	        U 5      [        S-  -  S-  -   [        S-  [        U 5      -  S	-  -
  [        S
-  [	        U 5      -  S-  -
  [        [        S-  5      -   :X  d   eg )Nr   rv   rA   r,   r9   r/   r;   r0   rN   r+   rO   )r   r%   r!   r1   r   r$   r   ra   s     r4   test_issue_3501r   =  s   sA	B3q1u:#a&()A99Q!9AQ! 3c!fQTk!m C	1SVB!Ac!fS!)+,a4A;s?!;=>q!tW!E E E E	B3q1u:#a&()A99Q!9Q#a&(1* 4s1vad{1} DAq!tB!Ac!fS!)+,a4A;s?!;=>q!tW!E E E Er3   c                  j   [        S[        -  5      [        S[        -  5      -  n U R                  [        SS9[        SS5      [	        [        S-  5      -   :X  d   eU R                  [        SS9[        SS5      S[        S-  -  S-  -
  S[        S-  -  S-  -   [	        [        S-  5      -   :X  d   eg )	Nr+   r9   r,   rA   #   r0   iI  0   )r!   r%   r1   r	   r$   r`   s    r4   test_issue_3502r   G  s    AaCQqSA99Q!9A1a4 888899Q!9AAqD"SAXb[01QT7:; ; ;r3   c                     [        S[        -   5      S[        -   -  n U R                  [        SS9[        S5      S-  [        [        S5      -  S-  -   [        [        S5      -  S-  -
  [	        [        S-  5      -   :X  d   eg )Nr9   r,   r0   )r!   r%   r1   r   r$   r`   s    r4   test_issue_3503r   N  sj    AE
AEA99Q!9Aq1SV8A: 5#a&
 BQq!tW LLLLr3   c                     [         [        S[         -  5      -   S-  [         [         [        S[         -  5      -   -  [         [        S[         -  5      -   [        S[         -  5      -  -
  -  n U R                  [         SS9[        SS5      S[         S-  -  S	-  -   S
[         S-  -  S-  -   S[         S-  -  S-  -   [	        [         S-  5      -   :X  d   eg )Nr/   rv   r9   rD   r,   rk   r0   r+   `   [   i   im+  rA   i  )r%   r!   r1   r	   r$   r`   s    r4   test_issue_3506r   S  s    	
S1XaS1X.!c!A#h,AaC1HHIA99Q!9Q!AqD&)#bAgck1E!Q$Jv4EE!Q$OP P Pr3   c            	         [        SSS9n [        [        U 5      5      R                  U SS9[        U 5      U S-  S-  -
  U S-  S	-  -
  [	        U S-  5      -   :X  d   e[        U 5      * U [        U 5      * [        [        SU -  5      5      -   -  -   [        [        SU -  5      5      -   nUR                  U SS9[        S5      [        S5      U -  -   SU S-  -  S
-  -
  SU S
-  -  S
-  -
  SU S-  -  S-  -
  [	        U S-  5      -   :X  d   eg )Nr%   Tr   r+   r,   r9   rA   r0      r/   r   r   )r%   ra   s     r4   test_issue_3508r   Y  s   sAs1v;a1%Q!Q$q&1a48)Ca1g)MMMM	Q!c!fWs3qs8},--C!H=A88A8AQAadF1H$qAvax/!AqD&);a1gEF F Fr3   c                  X   [         S-  [         S-  [         S-  [        [        [         5      5      -  -
  -  n U R                  [         SS9[	        SS5      [         S-  S-  -   S[         S-  -  S	-  -   S
[         S-  -  S-  -   S[         S-  -  S-  -   [        [         S-  5      -   :X  d   eg )Nr   r9   rP   r,   r.   r0   r      i  i/  rA   i 	 iq  r:   i )r%   r   r   r1   r	   r$   r`   s    r4   test_issue_3507r   a  s    	BA1T#a&\))*A99Q!9AAb 2ad74</#ad(6/AE!Q$JyDXX[\]^`a]a[bbc c cr3   c                  2   [        [        [        5      5      R                  [        SS9[        S5      [        S-  [        S5      -  S-  -
  [        S-  [        S5      -  S-  -
  [        S-  [        S5      -  S-  -   [	        [        S-  5      -   :X  d   eg )Nr+   r,   r.   r9   r0   r:   r;   )r!   r   r%   r1   r$   r2   r3   r4   test_issue_3639r   g  s    s1v;qA&AAc!fQAc!fQ.Ac!fR?!AqD'IJ J Jr3   c                     [        [        5      R                  [        SS9[        [        S-  S-  -   [        S-  S-  -   [        [        S-  5      -   :X  d   e[	        [        5      R                  [        SS9S[        S-  S-  -   [        S-  S	-  -   [        [        S-  5      -   :X  d   e[        [        5      R                  [        SS9[        [        S-  S-  -
  S[        S-  -  S
-  -   [        [        S-  5      -   :X  d   e[        [        5      R                  [        SS9S[        -  [        S-  S-  -
  [        S-  -   S[        S-  -  S-  -   [        [        S-  5      -   :X  d   e[        [        5      R                  [        SS9[        [        S-  S-  -
  S[        S-  -  S-  -   [        [        S-  5      -   :X  d   e[        [        5      R                  [        SS9[        [        -  S-  [        [        -  -
  S[        -  [        S-  -  S-  -
  [        [        S-  -  S-  -
  [        [        S-  5      -   :X  d   e[        [        5      R                  [        SS9[        [        S-  S-  -   [        S-  S-  -   [        [        S-  5      -   :X  d   e[        [        5      R                  [        SS9[        * [        -  S-  [        -   [        S-  S-  -   [        S-  S-  -   [        [        S-  5      -   :X  d   eg )NrA   r,   r/   r+   rN   r.   r9   r0   r;   r   r   i  (   )r   r%   r1   r$   r   r   r   r   r   r
   r   r   r   r2   r3   r4   test_hyperbolicr   l  s   7??1?"a!Q$q&j1a48&;a1g&EEEE7??1?"a!Q$q&j1a47&:Qq!tW&DDDD7??1?"a!Q$q&j1QT6"9&<qAw&FFFF7??1?"	!ad2g!a1fSj(1QT723 3 38A#q1a46zAadF2I'=!Q$'GGGG8A#
1Q1qs1a4x{"Qq!tVAX-!Q$78 8 88A#q1a46zAqDF':Qq!tW'DDDD8A#r"uQw{QT!V';ad1f'DqAw'NNNNr3   c                  r   [        SSS9n [        SSS9nU S-  U [        SU-  U -
  5      -  U [        SU-  5      -  -
  -  nUR                  U SS9[        SU-  5      * U [        SU-  5      -  S	-  -   U S	-  [        SU-  5      -  S
-  -
  U S-  [        SU-  5      -  S-  -   [        U S-  5      -   :X  d   eg )Nrz   Tr   r%   rv   r.   r0   r,   r9   rA   r/   r;   )r   r   r1   r$   )rz   r%   ra   s      r4   test_series2r   y  s    sAsA	B3qsQw<!C!H*,-A99Q!9QqS	Ac!A#hJqL 81a4AaC=? JQPQTRUVWXYVYRZ][]M] ]`abcefbf`g ggggr3   c                     [        SSS9n U S-  U S-  [        U 5      -  U S-  [        U 5      -  -
  -  nUR                  U SS9[	        S5      S	-  U S	-  S-  -   S
U S-  -  S-  -   SU S-  -  S-  -   [        U S-  5      -   :X  d   eg )Nrz   Tr   ir/   r:   r,   r.   r9   rS   r0      i  rA   i^  )r   r"   r!   r1   r   r$   r|   s     r4   test_series3r     s    sA	BAc!fq!tCF{*+A99Q!9
1q!tAv 51a4 Cc!Q$hun TWXYZ\]Y]W^ ^^^^r3   c                     [        S5      n [        U S-  [        S-  U S-  -  -   S[        -  U S-  -  -   -  U S-  -  nUR                  U SS9R                  5       R	                  5       [        SS[        -  -   [        S-  -   -  SS[        S-  -   S[        -  S-  -   -  S-  S[        -  SS[        -  -   [        S-  -   -  4;   d   eg )Nrz   r0   r9   r,   r.   rv   )r   r%   r1   removeOrT   r|   s     r4   	test_bug4r     s    sA	1a4!Q$q!t)ac!Q$h&'1,A99Q!9$$&--/Aq1Q3wA~4F	1qs7QqSU?AqsA!Ga"g$5648 8 8 8r3   c                     [        S5      n [        S5      n[        U 5      * [        SU [        [        5      -  -   5      -   S-  U S-  -  [        U 5      * [        S[        U -  -   5      -   [        U 5      * [        SU [        [        5      -  -   5      -   -  U -  [        [        U 5      * [        SU [        [        5      -  -   5      -   -  U -  -
  -  nUR                  U SUS9[        U -  U-  SU -  -   [	        SU 5      -   :X  d   eUR                  U SUS9[        U -  U-  SU -  -   [        U-  -
  SU-  [        [        5      -  -   [        [        [        5      -  US-  -  -   [	        U 5      -   :X  d   eg )Nrz   rd   r.   rv   r   re   r9   )r   r   r%   r1   r$   )rz   rd   ra   s      r4   	test_bug5r     sq   sAsA
a&3q1SV8|$	$+AG3s1vgA!G7AwQ3q6\!2264456689CF7A#a&L< 996 	A 99Q!!9$!A!a1g(====99Q!!9$!A!ac(9AaCAJ(F
CF(1a4-)A$)   r3   c                  @   [        [        5      S[        [        5      -
  -  R                  [        SS9S[        -  [	        [        5      -   :X  d   e[        [        5      S-  S[        [        5      -
  -  R                  [        SS9S[	        [        5      -   :X  d   eg )Nr.   r,   r9   )r!   r%   r   r1   r$   r2   r3   r4   test_issue_4115r     sx    FAAJ((a(0AaC!A$J>>>FAIq3q6z"++A+3q1Q4x???r3   c                  j    [        [        S 5        [        [        S 5        [        [        S 5        g )Nc                  P    [        S[        -  5      R                  [        SS5      $ Nr.   r   r+   r!   r%   r   r2   r3   r4   <lambda>test_pole.<locals>.<lambda>  s    c!A#hooaA6r3   c                  V    [        SS[        -  -   5      R                  [        SS5      $ r   r   r2   r3   r4   r   r     s    c!ac'l11!Q:r3   c                  ^    [         [        S[         -  5      -  R                  [         SS5      $ r   )r%   r!   r   r2   r3   r4   r   r     s    qQqSz11!Q:r3   )r(   r   r2   r3   r4   	test_poler     s#    
967
9:;
9:;r3   c                     [        [        [        5      5      R                  [        SS5      [	        S[        5      :X  d   e[        [        [        5      5      R                  [        SS5      S[	        [        5      -   :X  d   e[        [        [        5      5      R                  [        SS5      S[        -   [	        [        S-  5      -   :X  d   e[        [        [        5      5      R                  [        SS5      S[        -   [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        [        5      5      R                  [        SS5      S[        -   [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        [        5      5      R                  [        SS5      S[        -   [        S-  S-  -   [        S-  S-  -
  [	        [        S-  5      -   :X  d   eg )Nr   r.   r9   r/   r0   r+   r:   )r   r!   r%   r   r$   r2   r3   r4   test_expsinbugr     sb   s1v;aA&!Aq'111s1v;aA&!ad(222s1v;aA&!a%!AqD'/999s1v;aA&!a%!Q$q&.1QT7*BBBBs1v;aA&!a%!Q$q&.1QT7*BBBBs1v;aA&!a%!Q$q&.1a46*AAadG*KKKKr3   c                     [        S5      n [        U 5      R                  U 5      S:X  d   e[        U * 5      R                  U 5      S:X  d   e[        [        U 5      5      R                  U 5      S:X  d   e[        [        U * 5      5      R                  U 5      S:X  d   e[        U S-  5      R                  U 5      S:X  d   e[        U S-  * 5      R                  U 5      S:X  d   e[        [	        U 5      5      R                  U 5      S:X  d   e[        [	        U * 5      5      R                  U 5      S:X  d   e[        S[        U 5      -   5      R                  U 5      S:X  d   e[        S[        U * 5      -   5      R                  U 5      S:X  d   e[        U 5      R                  U S5      S:X  d   e[        U * 5      R                  U S5      S:X  d   e[        SS	S
9n [        U S-   5      R                  U 5      S:X  d   eg )Nr%   r   rk   r/   r+   r0   r9   rw   T)negativeg      ?r.   )r   r   r   r!   r   r   s    r4   
test_floorr     s   sA8??1"""!9A"$$$Q="a'''aR>  #r)))A;a A%%%!Q$<q!R'''Q="a'''aR>  #q(((SV##A&!+++S!W$$Q'1,,,8??1a A%%%!9Aq!R'''sT"AS>  #q(((r3   c                     [        [        5      R                  [        SS9[        :X  d   e[        [        5      R                  [        SS9S[        -   :X  d   e[        S[        -  S-   5      R                  [        SS9S[        -  :X  d   e[        S[        -  S-   5      R                  [        SS9SS[        -  -   :X  d   e[        [        S-  5      R                  [        SS9[        S-  :X  d   e[        [        S-  5      R                  [        SS9[        S-  :X  d   e[        [        [        5      S-   5      R                  [        SS9[        [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        [        5      S-   5      R                  [        SS9S[        -   [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        [        5      [
        R                  -   5      R                  [        5      [
        R                  [        -   [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        S	-  5      R                  [        SS9[	        [        S-  5      :X  d   e[        S[        -  5      R                  [        5      [        S
S5      [	        [        S-  5      -   :X  d   eg )Nr.   cdirrk   r9   r+   r/   rA   rN   r:   r   )r   r%   r   r!   r$   r   r   r   r2   r3   r4   	test_fracr     s`   7>>!!>$)))7>>!">%Q...!a=*ac111!a=+q1Q3w6661:QQ'1a4///1:QR(AqD000A
""11"-QT!Vad3h1F1a41PPPPA
""12".!a%!Q$q&.1a482KaPQSTPTg2UUUUA ''*affqj1a46.AAqDH.LqQRTUQUw.VVVV1:QQ'1QT7222!9A+a"3a1g"====r3   c                     [        [        5      R                  [        5      S:X  d   e[        [        * 5      R                  [        5      S:X  d   e[        [        [        5      5      R                  [        5      S:X  d   e[        [        [        * 5      5      R                  [        5      S:X  d   e[        S[	        [        5      -
  5      R                  [        5      S:X  d   e[        S[	        [        * 5      -
  5      R                  [        5      S:X  d   e[        [        5      R                  [        S5      S:X  d   e[        [        * 5      R                  [        S5      S:X  d   eg )Nr.   r   r9   r/   rv   )r   r%   r   r!   r   r2   r3   r4   test_ceilingr     s   1:Q1$$$A2;a A%%%3q6?!!!$)))3r7""1%***1s1v:%%a(A---1sA2w;&&q)Q...1:Q"a'''A2;a#r)))r3   c                  l   [        S5      n [        [        5      R                  [        SS9[        :X  d   e[        [        * 5      R                  [        SS9[        :X  d   e[        [        S-   5      R                  [        SS9[        S-   :X  d   e[        [	        [        5      5      R                  [        SS9[        [        SS5      [        S-  -  -
  [        [        S-  5      -   :X  d   e[        [	        [        * 5      5      R                  [        SS9[        [        SS5      [        S-  -  -
  [        [        S-  5      -   :X  d   e[        [        U -
  5      R                  [        S5      U * [        SU -
  5      -  [        S-
  [        SU -
  5      -  -   [        SU -
  5      -   :X  d   eg )Nr   r0   r,   r.   rA   r/   )r   absr%   r1   r!   r	   r$   r   r   s    r4   test_absr     s\   sAq6>>!q>!Q&&&r7??1?"a'''q1u:a1%Q...s1v;qA&!hq!nQT.A*AAadG*KKKKsA2w<Q'1x1~ad/B+BQq!tW+LLLLq1u:a#r$q1u+~QQU8K'KdSTWXSXk'YYYYr3   c                     [        [        5      R                  [        SSS9[        :X  d   e[        [        5      R                  [        SSS9[        * :X  d   e[        [        S-   5      R                  [        SSS9S:X  d   e[        [        S-   5      R                  [        SSS9S:X  d   e[        [        S-   5      R                  [        SSS9S:X  d   e[	        [        S-   5      R                  [        SSS9S:X  d   e[        [        [        -   5      R                  [        SSS9[        [        [        -   5      R                  [        SSS9:X  d   eg )	Nr   +)dir-r9   r.   皙@r/   r   r%   r   r   r   r!   r&   r2   r3   r4   test_dirr    s)   q6==A3='1,,,q6==A3='A2---Q<q!-222Q<q!-222S>  A3 /14441s7""1aS"1Q666q1u:Qs+s1q5z/@/@A3/@/OOOOr3   c                     [        [        5      R                  [        SSS9[        :X  d   e[        [        5      R                  [        SSS9[        * :X  d   e[        [        S-   5      R                  [        SSS9S:X  d   e[        [        S-   5      R                  [        SSS9S:X  d   e[        [        S-   5      R                  [        SSS9S:X  d   e[	        [        S-   5      R                  [        SSS9S:X  d   e[        [        [        -   5      R                  [        SSS9[        [        [        -   5      R                  [        SSS9:X  d   eg )Nr   r.   r   rk   r9   r   r/   r   r2   r3   r4   	test_cdirr    s)   q6==AA=&!+++q6==AB='A2---Q<q!!,111Q<q!"-222S>  AA .!3331s7""1ab"1Q666q1u:Q+s1q5z/@/@AA/@/NNNNr3   c            	      *   [        S5      n [        U [        -  5      [        -  nUR                  [        SSS9R	                  5       [        S-
  U S[        SU S-  -  S-   5      -  -  [        SU -  5      S-  -
  -  [        SU -  5      S-  -   :X  d   eg )Nr   r0   r9   r,   ir.   rH   )r   r   r%   r   r   r   r   s     r4   test_issue_3504r    s    sAQqS	!A88AqA8&&(	
QAd3q!t8a<(()D1IbL89D1IaKGH H Hr3   c                     [        S5      u  pSSU [        -  -   -  nUR                  [        SS5      SU [        -  -
  U S-  [        S-  -  -   U S-  [        S-  -  -
  U S-  [        S-  -  -   [        [        S-  5      -   :X  d   eSSX-   [        -  -   -  nUR                  [        SS5      S[        U * U-
  -  -   [        S-  X-   S-  -  -   [        [        S-  5      -   :X  d   eg )Nza,br.   r   r+   r9   r/   r0   )r   r%   r   r$   )r   br   s      r4   test_issue_4441r    s    5>DA	1qs7A88Aq!AaC!Q$q!t) 3ad1a4i ?	1QT	!adG!   	1qy=A88Aq!ArAvJ
Q$z/!adG!$ $ $ $r3   c                     [        [        5      R                  [        [        S-  SS9R	                  5       [        * S-  [        S-  -   S[        [        S-  -
  -  -
  :X  d   e[        [        5      R                  [        [        SS9R	                  5       [        * S-  [        S-  -   S[        [        -
  -  -   :X  d   e[        [        [        5      [        S[        -  5      -  [        [        S-  5      [        S5      :X  d   eg )Nr9   r/   r,   rA   r.   r0   rk   )r"   r%   r   r
   r   r    r#   r   r2   r3   r4   test_issue_4329r
    s    q6==BqDA=&..0	A!aRTl"# # #q6==B!=$,,.	
1r!taRj ! ! !QQqS!1bd+s2w666r3   c                     [        [        [        S-  -   5      R                  SS9[        [        5      :X  d   e[        [        [        S-  -   5      R                  SS9[        [        [        S-  5      -   :X  d   eS[        -   S-  R                  [        SS9[        S-  S[        -  -   S-   :X  d   eSS[        -  -   R                  5       SS[        -  -   :X  d   e[	        [        [        5      R                  5       [        5      R                  5       S[        -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        [        S-  5      -   :X  d   eg )	Nr9   r.   r,   rA   r/   r0   r;   r+   )r   r%   r   r$   r   r   doitr2   r3   r4   test_issue_5183r    s%   q1a4x=!$!,,,q1a4x=!$AadG333UQJqA&!Q$1*q.888!GQqS(((c!fmmoq)..0	A1QAa!Q$r')AadG34 4 4r3   c                     [        S5      n S[        S-  U S-  -   S-  -  R                  [        [        U -  SS9[        * SU S-  -  [        * U -  [        -   -  -  SSU S-  -  [        * U -  [        -   S-  -  -  -
  [	        S[        [        U -  45      -   :X  d   eS[        S-  U S-  -   S-  -  R                  [        [        U -  SS9SSU S-  -  -  [        SU S-  -  [        * U -  [        -   -  -  -
  SSU S-  -  [        * U -  [        -   S-  -  -  -
  [	        [        * U -  [        -   [        [        U -  45      -   :X  d   eg )	Nr   r.   r9   r   )x0r-   r0   r/   rH   )r   r%   r1   r   r$   r   s    r4   test_issue_5654r    s`   sAq!tAqDy1n%%aAaC1%5	
AadFQBqD1HAadFQBqD1Hq=$8!99Aa!QqSNJK K Kq!tAqDy1n%%aAaC1%5Bq!tG	
AadFQBqD1H	:!"AadFQBqD1Hq=$8!9::<=qbdQhAaC<Q:R R R Rr3   c                     [        [        [        -   5      R                  [        SS5      n [        [        [        -   [        -   5      R                  [        SS5      nU R                  [        [        [        -   5      Up2X#-
  R                  5       R                  5       R                  5       S:X  d   e[        [        [        -   5      R                  [        SS5      n [        [        [        -   [        -   5      R                  [        SS5      nUR                  [        S[        S05      U R                  [        S5      :X  d   eg )Nr   r.   r9   r/   )	r   r%   r'   r   r&   r{   rT   r   simplify)sxsxys1s2s       r4   test_issue_5925r  !  s    	a!e		Aq!	$B
q1uqy/
 
 Aq
)CWWQAG%%'002a777	a!e		Aq!	$B
q1uqy/
 
 Aq
)C88Qq!AJ2771a=000r3   c                      [        [        S-  5      R                  [        SS5      S[        S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S	-  -   [        [        S-  5      -   :X  d   eg )
Nr/   r      r.   rA   r9   rP   rM   r;   )r   r%   r1   r$   r2   r3   r4   
test_exp_2r  ,  sh    q!t9Q2&!ad(QT!V*;ad1f*Dq"uRx*ORSTUWYTYRZ*ZZZZr3   N)|sympy.calculus.utilr   sympy.core.functionr   r   sympy.core.numbersr   r   r   r	   r
   sympy.core.singletonr   sympy.core.symbolr   r   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   r   %sympy.functions.elementary.hyperbolicr   r   r   r   r   r   r   r   #sympy.functions.elementary.integersr   r   r   (sympy.functions.elementary.miscellaneousr   r   (sympy.functions.elementary.trigonometricr   r   r    r!   r"   sympy.series.limitsr#   sympy.series.orderr$   	sympy.abcr%   r&   r'   sympy.testing.pytestr(   r)   r5   r7   r=   r?   rB   rF   rK   rU   rW   rZ   r\   r^   rb   ri   rl   rn   rp   rr   rt   rx   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r
  r  r  r  r  r2   r3   r4   <module>r*     s   + 7 < < " / 5 = f f f F F A O O %     .248 \	HL
O
O

F
22
9# ) )
1
I .R
B7
	-2^.8G->>2WH
FO
&1H
HE;M
PFcJ

Oh_8@
<L)(>*ZPOH$74R1[r3   