
    \h}H                     r   S SK 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JrJr  S SKJrJr  S SKJrJr  S SKJr  S S	KJr  S S
KJr  S SKJrJrJrJr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+J,r,J-r-J.r.J/r/J0r0J1r1J2r2J3r3J4r4  S SK5J6r6  S SK7J8r8  S SK9J:r:  S SK;J<r<  S SK=J>r>J?r?J@r@JArAJBrBJCrCJDrDJErEJFrF  S SKGJHrHJIrIJJrJJKrK  S SKLJMrM  S SKNJOrO  S SKPJQrQJRrRJSrSJTrT  S SKUJVrVJWrW  \" SSS9rXS rY\TS 5       rZS r[\QS 5       r\\QS 5       r]\QS 5       r^S  r_\SS! 5       r`S" raS# rbS$ rcS% rdS& reS' rfS( rgS) rh\SS* 5       riS+ rjg,)-    )Lambda)EIRationaloopi)Eq)S)DummySymbol)Absre)explog)frac)sqrt)	Piecewise)coscotcscsecsintanasinacosatanacotasecacsc)sinhcoshtanhcothsechcschasinhacoshatanhacothasechacsch)gamma)expint)MatrixSymbol)simplify)	function_rangecontinuous_domainnot_empty_inperiodicitylcim	is_convexstationary_pointsminimummaximum)Interval	FiniteSet
ComplementUnion)ImageSet)ConditionSet)XFAILraises_both_exp_powslow)xyaT)realc            
      x	   [        [        [        5      [        [        [        * S-  [        S-  5      5      [        SS5      :X  d   e[        [        [        5      [        [        S[        5      5      [        SS5      :X  d   e[        [        [        5      [        [        S[        5      5      [        [        * [        5      :X  d   e[        [        [        5      [        [        [        S-  [        5      5      [        [        * S5      :X  d   e[        [        S-   [        S-
  -  [        [        SS5      5      [        [        [        * [        SS5      5      [        [        S	S5      [        5      5      :X  d   e[        S[        S-  -  [        [        SS5      5      [        S[        5      :X  d   e[        [        [        5      [        [        SS5      5      [        [        S5      [        S5      5      :X  d   e[        [        [        5      [        -
  [        [        R                  5      [        [        * S5      :X  d   e[        [        S[        -  S-
  5      [        [        SS5      5      [        S[        S5      5      :X  d   e[        [        [        S-
  -  [        S-  [        -
  -
  [        [        R                  5      [        S5      :X  d   e[        [        [        S-
  -  [        S-  [        -
  -
  [        -   [        [        R                  5      [        [        5      :X  d   e[        [        [        5      [        [        [        SS
5      [        S5      5      5      [        [        [        S5      * S5      [        [        S5      5      5      :X  d   e[        [!        [        5      [        [        [        * S5      5      [        SS5      :X  d   e[        [!        [        5      [        [        R"                  5      [        R"                  :X  d   e[        [        [        [        S-  S-   5      -  [        [        R                  5      [        R$                  " SS5      :X  d   e['        [(        S 5        ['        [(        S 5        ['        [(        S 5        ['        [(        S 5        g )N      r                  c                      [        [        [        5      [        [        5      [	        [        5      -
  -  S-  [        -
  [        [
        R                  5      $ NrH   )r0   r   rC   r   r   r
   Reals     V/var/www/auris/envauris/lib/python3.13/site-packages/sympy/calculus/tests/test_util.py<lambda>%test_function_range.<locals>.<lambda>;   s3    AAQ "Q&177*4rW   c                  h    [        [        [        5      [        -   [        [        R                  5      $ N)r0   r   rC   r
   rU   rV   rW   rX   rY   rZ   =   s    A
Aqww* rW   c                  Z    [        [        [        5      [        [        R                  5      $ r\   )r0   r   rC   r
   IntegersrV   rW   rX   rY   rZ   ?   s    A1::*rW   c                  `    [        [        [        5      S-  [        [        R                  5      $ rT   )r0   r   rC   r
   NaturalsrV   rW   rX   rY   rZ   A   s    Aq!QZZ*!rW   )r0   r   rC   r9   r   r   r   r<   r   r   r   r
   rU   r   r:   rD   r   EmptySetopenr@   NotImplementedErrorrV   rW   rX   test_function_rangerd      s   #a&!Xrc!eRT%: 
b!_  #a&!Xa_ 
a^  #a&!Xa_ 
rc2  #a&!XbdB%7 
rc1  1q51q5/1hr1o 
8RC!Q0(8Aq>22NOP P P!QT(AxA 
a_  #a&!Xb!_ 
c"gs1v&' ' '#a&1*a 
rc2  $qsQw-HQN 
aa!" " "!QU)q!tax0!QWW 
q\  !QU)q!tax014a 
q\  #a&!U8B+;Yq\%J 
8SVGQ'3q6):;< < <#a&!Xrc2%6 
b!_  #a&!QZZ0AJJ>>>!DAaL.!QWW5r!9LLLL
 !4 5
 !  !
 !  
 !! "rW   c                      [        [        [        5      S-  [        S[        -  5      S-  -   S-   [        [        R                  5      [        S[        5      :X  d   eg )NrH   rK   rJ   )r0   r   rC   r
   rU   r9   r   rV   rW   rX   test_function_range1rf   E   sB    #a&!)c!A#hk1A5q!''BhqQSnTTTrW   c                     [        [        [        5      [        [        SS[        -  5      5      [        SS[        -  5      :X  d   e[        [        [        5      [        [        SS[        -  5      5      [        [        S[        S-  SS5      [        [        S-  [        [        SS5      -  SS5      [        [        [        SS5      -  S[        -  SS5      5      :X  d   e[        [        [        5      [        [        SS[        -  5      5      [        [        R                  " S[        5      [        R                  " [        S[        -  5      5      :X  d   e[        [        S-
  [        S-
  S-  -  [        [        R                  5      [        [        [        * SSS5      [        S[        SS5      5      :X  d   e[        [        [        5      [        S[        -  S-
  5      -   [        [        R                  5      [        [        SS5      [        SS5      :X  d   e[        S[        [        S-
  5      -  [        [        R                  5      [        S[        SS5      :X  d   e[        S[        -  S-
  [        [        R                  5      [        [        R                  " [        * S5      [        R                  " S[        5      5      :X  d   e[        S[        S-  S-
  -  S-   [        [        R                  5      [        [        R                  " [        * S5      [        R                  " SS5      [        R                  " S[        5      5      :X  d   e[        [        S-   [        -  [        [        R                  5      [        S	[        5      :X  d   e[        [        S-   [        S-  -  [        [        R                  5      [        S	[        5      :X  d   e[        [        [        -  [        [        R                  5      [        S[        5      :X  d   e[        [        S-   [        [        S-  5      -  [        [        R                  5      [        [        R                  " S	S5      [        R                  " S[        5      5      :X  d   e[        [        [        [        5      S-  S-   5      [        [        R                  5      n U R!                  S[        -  S-  5      (       a   eU R!                  S
5      (       d   e[#        SSSS9n[        [        SU-  -  [        [        R                  5      [        S[        5      :X  d   e[%        S5      n[        S[        [        5      -  [        [        R                  5      R'                  [)        [        R                  [        [+        [-        USU-  [        -  [        -   5      [        R.                  5      [+        [-        USU-  [        -  5      [        R.                  5      5      5      5      (       d   e[        [        [        5      [1        [        5      -   [        [        R                  5      [        R                  :X  d   e[        [3        [        5      [        [        R                  5      [        S	S5      :X  d   e[        S[5        [        [        5      5      -  [        [        R                  5      [        R                  " [7        S	5      [8        5      :X  d   e[        [;        [        5      [=        [        5      -   [        [        R                  5      [        R                  :X  d   e[        [?        [        5      [A        [        5      -   [        [        R                  5      [        R                  :X  d   e[        [C        [        5      [E        [        5      -   [        [        R                  5      [        R                  :X  d   e[        [G        [        5      [        [        R                  5      [        S[        5      :X  d   e[        [I        [        5      [        [        R                  5      [        R                  " S	S5      :X  d   e[        [I        [        5      [G        [        5      -   [        [        R                  5      [        RJ                  :X  d   e[        [M        [        5      [        [        R                  5      [        RN                  " SS5      :X  d   e[        [Q        [        5      [        [        R                  5      [        [        R                  " [        * S	5      [        R                  " S[        5      5      :X  d   e[        [S        [        5      [        [        R                  5      [        [        [        * S	5      [        S[        5      5      :X  d   e[        [U        [        5      [        [        R                  5      [        [        [        * S	5      [        S[        5      5      :X  d   e[V        [X        [Z        4 Ho  n[        U" [        5      [        [        R                  5      [        [        R                  " [        * S5      [        R                  " S[        5      5      :X  a  Mo   e   [        []        [        5      [        [        R                  5      R!                  S5      S:X  d   e[        S[7        [        5      [        -
  -  [        [        R                  5      [)        [        R                  [_        [        [a        [        * [7        [        5      -   S5      [        R                  5      5      :X  d   e[        [c        [        S-  5      [        [        SS	5      5      [        [        R                  " S[        S5      * 5      [        R                  " [        S5      * S	5      [        R                  " [        S5      * [        S5      * 5      5      :X  d   e[        [c        [        5      [        [        R                  5      [)        [        R                  [        R.                  5      :X  d   e[e        [f        S 5        [e        [f        S 5        [        [        [i        [        5      -   [        [        R                  5      [        R                  :X  d   eg )Nr   rH   FTrK   rJ   rQ   rI   rM   d)evenzeronc                  Z    [        S[        S-  S-   -  [        [        R                  5      $ NrJ   rH   )r1   rC   r
   	ComplexesrV   rW   rX   rY   (test_continuous_domain.<locals>.<lambda>   s!    ):	1a46
Aq{{*$rW   c                  R    [        [        [        5      [        [        SS5      5      $ )NrL   r   )r1   r,   rC   r9   rV   rW   rX   rY   rp      s    ):a!Xb^*%rW   )5r1   r   rC   r9   r   r   r<   r   r   rb   r
   rU   r   r   r   Ropencontainsr   r   dummy_eqr;   r=   r   r^   r   r   r   r   r   r    r!   r"   r$   r   r&   r'   r(   ra   r*   Lopenr)   r   r   r#   r+   r%   r   r>   r	   r   r@   rc   r,   )domainri   rl   fs       rX   test_continuous_domainrx   J   s   SVQAbD(9:hq!B$>OOOOSVQAbD(9:hq"Q$t,hr!tRA=NPTVZ.[r(1a.(!B$e<	>> > > SVQAbD(9:eahmmB"5?7 7 7 7a!eq1uqj11agg>hsAtT*HQD$,GHI I ISVc!A#'l2Aqww?!QT401 1 1QtAE{]Aqww78Ar4QU;VVVVQqS1Wa1hmmRC#X]]1b%9:; ; ;Q1q\A-q!'':hmmRC$hmmB&:HMM!R<PQR R RacBY1773xB7GGGGacRT]Aqww78B;KKKKQT1agg.(1b/AAAacC1I-q!'':er1x}}Q3?5 5 5 5s3q619q=11agg>FqtAv&&&&??1sE*AQ1Xq!''2hq"oEEEc
AQs1vXq!''2;;J	xq!A#b&2+ 6

Cq!A#b& 11::>@=A B B B B SVc!f_a9QWWDDDT!Wa1Xb!_DDDQtCF|^Q8HNN3r7TU<VVVVT!WT!W_a9QWWDDDT!WT!W_a9QWWDDDT!WU1X-q!'':aggEEEU1Xq!''2hq"oEEEU1Xq!''2hmmB6JJJJU1XeAh.177;qzzIIIU1Xq!''2hnnQ6JJJJU1Xq!''2erc2a 476 6 6 6T!Wa1U"b8Ar?6, , , ,T!Wa1U"b8Ar?6, , , ,E4  1q!''2eMM2#q!8==B#779 9 	9 9 ! T!Wa1::1=FFFQA
^Q8J	aQBQK!3QWW==? ? ? ?T!Q$ZHRO<b47(#X]]DG8R%@tAwha)A+ + + + T!Wa1Z	6   
 !$ %
 !% &Qr]Aqww7177BBBrW   c                      [        [        [        [        5      -   [        S:  4[        [        5      S45      n [	        U [        [
        R                  5      [
        R                  :X  d   eg )Nr   T)r   r   r   rC   r1   r
   rU   )	acot_conts    rX   test_continuous_domain_acotr{      sF    2d1g:qs+d1gt_=IY1773qww>>>rW   c                      [        [        [        5      [        [        R                  5      R                  S5      S:X  d   eg )NrI   F)r1   r,   rC   r
   rU   rs   rV   rW   rX   test_continuous_domain_gammar}      s,    U1Xq!''2;;B?5HHHrW   c                      [        [        S-
  S[        -
  -  [        [        R                  5      [        R
                  " S[        5      :X  d   eg )NrH   rJ   )r1   rC   r
   rU   r9   rb   r   rV   rW   rX    test_continuous_domain_neg_powerr      s4    acQqS\1agg6(--2:NNNNrW   c                     [        [        [        S[        -  5      R                  [	        SSSS5      5      [        5      [	        [
        R                  SSS5      :X  d   e[        [        [        [        S-  5      R                  [	        SS5      5      [        5      [        [	        [        S5      * S5      [	        SS5      5      :X  d   e[        [        [        S-  [        -   [        5      R                  [	        SS5      5      [        5      [        [	        [        S5      * S-  [
        R                  -
  S5      [	        S[        SS5      [        S5      S-  -   5      [	        SS5      5      :X  d   e[        [        [        [        S-
  -  5      R                  [
        R                  5      [        5      [        [
        R                  [        S5      5      :X  d   e[        [        [        [        S-
  -  5      R                  [
        R                  5      [        5      [        [
        R                  [        S5      5      :X  d   e[        [        [        S-  S	[        -  -
  S-   [        S-
  -  5      R                  [
        R                  5      [        5      [        [
        R                  [        S5      5      :X  d   e[        [        S	S[        [        S-
  -  5      R                  [	        SS	5      5      [        5      [	        [        * [        5      :X  d   e[        [        S[        [        S-
  -  5      R                  [	        SS	5      5      [        5      [	        [        S	5      S-  S5      :X  d   e[        [        [        [        S-  S-
  -  5      R                  [
        R                  5      [        5      [        [
        R                  [        SS5      5      :X  d   e[        [        [        [        S-  5      R                  [        [	        SS	SS5      [	        SS
5      5      5      [        5      [        [	        [        S
5      * S5      [	        [        S	5      * SSS5      [	        SS	SS5      [	        SS
5      5      :X  d   e[        [        S5      R                  [	        S	S5      5      [        5      [
        R                  :X  d   e[        [        [        S-  [        S-   -  5      R                  [	        S[        5      5      [        5      [        [	        SSSS5      [	        S[        5      5      :X  d   e[        [         S 5        [        [         S 5        [        ["        S 5        g )NrH   rJ   TFrI   rQ      rh   rK   rM   c                       [        [        5      $ r\   )r2   rC   rV   rW   rX   rY   #test_not_empty_in.<locals>.<lambda>   s    |ArW   c                  6    [        [        SS5      [        5      $ )Nr   rJ   )r2   r9   rC   rV   rW   rX   rY   r      s    |HQNA>rW   c                      [        [        [        5      R                  [        R
                  5      [        [        5      $ r\   )r2   r:   rC   	intersectr
   rU   rE   rV   rW   rX   rY   r      s     <	! 6 6qww ?AFrW   )r2   r:   rC   r   r9   r
   Halfr<   r   r   rU   r;   rE   r   ra   r@   
ValueErrorrc   rV   rW   rX   test_not_empty_inr      s.   	!QqS)33HQ44OPRSTD%() ) )	!QT*44Xa^DaHhQx$hq!n56 6 6	!Q$(A.88!QH!LhRy{QVV+R0q(2q/DHQJ67!Q	II I I 	!QU),66qww?C177IaL)* * *	!QU),66qww?C177IaL)* * *	1a4!A#:>AE":;EEaggNPQR177IaL)* * *	!Q1q5	2<<Xa^LaP"b  	!QAY/99(1a.I1M1a  	!QTAX,/99!''BAF177Ib!,-. . .	!QT*44U8Aq$PT;U;CAq>6K LMNPhQx$hQxT4&Hq!T4((1a.	:: : : 	!..x1~>BajjPPP	!Q$A,/99(1b/JANhr2tU+Xa_=> > >
:./
:>?
FHrW   c                  N  ^ [        [        S[        -  5      [        5      [        :X  d   e[        S[	        S[        -  5      -  [        5      [        S-  :X  d   e[        [        [        5      S-  [        5      S[        -  :X  d   e[        S[	        S[        -  5      -  [        5      [        S-  :X  d   e[        [	        [        5      [        [        5      -  [        5      S[        -  :X  d   e[        [        [        5      [	        [        5      -  [        5      S[        -  :X  d   e[        [	        [        5      [        [        5      -  [        5      S[        -  :X  d   e[        [        S[        -  5      [        S[        -  5      -  [        -
  [        5      [        S-  :X  d   e[        [	        [        5      [        [        5      -   [        5      [        :X  d   e[        [        [        5      [        S[        -  5      -
  [        5      S[        -  :X  d   e[        [        [        5      S-
  [        5      S[        -  :X  d   e[        [        S[        -  5      [        [        5      [        [        5      -  -   [        5      [        :X  d   e[        [        [        [        5      5      [        5      S[        -  :X  d   e[        [        [        S[        -  5      5      [        [        S[        -  5      5      -
  [        5      [        :X  d   e[        [        S[        -  5      [        [	        [        5      [        S[        -  5      -
  5      -  [        5      [        :X  d   e[        [        [        [        5      [        S[        -  5      -
  5      [        5      S[        -  :X  d   e[        [	        [        S[        -  5      5      [        5      [        :X  d   e[        S[	        [        5      S-  -  [        5      [        :X  d   e[        [        [        S-  5      [        5      S:X  d   e[        [        [        5      S-  [        5      S[        -  :X  d   e[        [	        S[        -  S-
  S-  5      [        5      [        SS5      :X  d   e[        [        S5      [        S-   -  [        -   S-  [        5      S[        S5      S-   -  :X  d   e[        [        S-  S-   [        -  [        5      b   e[        [        [        [        5      5      [        5      S[        -  :X  d   e[        [        [        5      S-  [        [        5      S-  -   [        5      [        R                   L d   e[        [	        [        5      [        5      [        R                   L d   e[        [        [        5      ["        [        [        5      -  -   [        5      S[        -  :X  d   e[        [        [        S[        -  5      -
  [        5      [        :X  d   e[        [        [        5      [        5      b   e[        [        ["        [        -  5      [        5      S[        -  :X  d   e[        [        ["        [$        -  5      [$        5      S[        -  :X  d   e[        [        [$        5      [$        5      b   e[        [        [        [        [$        5      ["        [        S[$        -  5      -  -   5      SS9[$        5      S[        -  :X  d   e[        [        [        [        S[$        -  5      ["        [        [$        5      -  -   5      SS9[$        5      S[        -  :X  d   e[        [        [        [$        5      5      [$        5      S[        -  :X  d   e[        [        S["        -  [$        -  5      [$        5      [        :X  d   e[        [        [$        ["        [        [$        5      -  -   5      [$        5      b   e[        [        [        [$        S-  5      [        [$        5      -   5      [$        5      S[        -  :X  d   e[        [        [        5      [        5      b   e[        [        [        5      [        [        5      -  [        5      b   e[        [        [        5      [        -  [        5      b   e[        ['        [        ['        [        [        5      5      5      5      [        5      [        :X  d   e[)        S [
        [        [        [        [        [        4 5       5      (       d   e[        ['        [        [	        [        5      5      5      [        5      [        :X  d   e[        ['        [        [        [        5      [	        [        5      -   5      5      [        5      S[        -  :X  d   e[        [        [        5      [        R*                  :  [        5      S[        -  :X  d   e[        [        S:  [        5      b   e[        [        S-  [        S-  -
  S-   [        5      b   e[        ['        [        5      [        5      b   e[        ['        [        S-  S-
  5      [        5      b   e[        [        S-  S-   S-  [        5      b   e[        [,        [        -  S-  [        5      b   e[        [        [/        S[        5      5      [/        S[        5      -  [        5      b   e[1        S	[        S
:  4[        S-  [        S:*  4[        [        5      S45      n [        U [        5      b   e[3        SSS5      m[5        [6        U4S j5        [5        [6        U4S j5        [5        [6        U4S j5        [5        [6        U4S j5        g )NrH   rh   rQ   rK   rJ   F)evaluatec              3   v   #    U  H/  n[        [        U" [        5      5      [        5      [        :H  v   M1     g 7fr\   )r3   r   rC   r   ).0rw   s     rX   	<genexpr>#test_periodicity.<locals>.<genexpr>   s,      ' 9&1{3qt9a(B. 9&s   79r   rI   Tmc                  .   > [        [        T 5      T 5      $ r\   r3   r   r   s   rX   rY   "test_periodicity.<locals>.<lambda>   s    CFA(>rW   c                  4   > [        [        T S   5      T 5      $ N)r   r   r   r   s   rX   rY   r      s    C$L!(DrW   c                  4   > [        [        T 5      T S   5      $ r   r   r   s   rX   rY   r      s    CFAdG(DrW   c                  :   > [        [        T S   5      T S   5      $ r   r   r   s   rX   rY   r      s    C$L!D'(JrW   )r3   r   rC   r   r   r   r   rD   r   r   r   r   r   r   r   r
   Zeror   rE   r   allr   r   r-   r   r.   r@   rc   )pr   s    @rX   test_periodicityr      s!   s1Q3x#r)))C!H}a(BqD000s1vqy!$",,,q#ac({A&"Q$...s1vc!f}a(AbD000s1vA'+qt333s1vc!f}a(AbD000s1Q3xAaC(1,a0BqD888s1vA*b000s1vAaC(!,"444s1vz1%2---s1Q3x#a&Q-/3r999s3q6{A&!B$...s3qs8}s3qs8}4a8B>>>s1Q3xCFS1X$5 66:b@@@s3q6C!H,-q1QrT999s3qs8}a(B...qQ{A&",,,s1Q3x#q(((s1vax#qt+++sAaCE19~q)Xa^;;;Q1a1,a0AaOCCC1Q!|Q'///s2a5z1%2---s1vqy3q619,a0AFF:::s1vq!QVV+++s1v#a&(!,"444q3qs8|Q'2---s1vq!)))s1Q3x#qt+++s1Q3x#qt+++s1vq!)))s3s1v#ac(
23eDaHAbDPPPs3s1Q3x!CF(23eDaHAbDPPPs3q6{A&!B$...s1Q3q5z1%+++s1qQx<(!,444s3qs8c!f,-q1QrT999s1vq!)))s1vs1v~q)111s1vqy!$,,,s3s3q6{+,a0B666 'S#sC9& ' ' ' ' 's3s1v;'+r111s3s1vA/0!4"<<<s1v*ad222q1ua (((q!tad{Q*222s1vq!)))s1a4!8}a(0001q!|Q'///1ax#+++s6!Q<(15q9AAA1a"f+1a1f~A~>Aq!$$$S!QA
 >?
 DE
 DE
 JKrW   c            	      
   [        [        [        5      [        SS9[        :X  d   e[        [	        [        5      [        [        5      -   [        SS9S[        -  :X  d   e[        [        [        5      [        5      S[        -  :X  d   e[        [	        [        [        -  5      [        5      S[        -  [        [        5      -  :X  d   e[        [        [        [        [        5      5      5      [        5      [        :X  d   eg )NT)checkrH   )
r3   r   rC   r   r   r   r   rD   absr   rV   rW   rX   test_periodicity_checkr     s    s1vq-333s1vA6!B$>>>s1vq!QrT)))s1Q3x#qtCF{222s3s1v;'+r111rW   c                      [        [        R                  [        S5      [        S5      /5      S:X  d   e[        [        S-  [        S-  [        /5      [        :X  d   e[        S[        -  [        S-  /5      S[        -  :X  d   e[        [        R                  S[        -  /5      b   e[        [        S5      S[
        -  -   [
        S-  [        SS5      -   [        R                  [
        -   /5      [        S5      S[
        -  -   :X  d   eg )NrH   rK      rQ   rJ   )r4   r
   r   r   Oner   r   rV   rW   rX   	test_lcimr   	  s    1qt$%***Ar!tR !R'''2r!t2%%%"&&&1!QqS8Aq>115519=>!A$1*LLLrW   c                  b   [        S[        -  [        [        R                  " S[        5      S9S:X  d   e[        S[        -  [        [        [        * S5      S9S:X  d   e[        [        S-  [        [        S[        5      S9S:X  d   e[        S[        S-  -  [        [        R
                  " S[        5      S9S:X  d   e[        S[        S-  -  [        [        R                  " [        * S5      S9S:X  d   e[        [        [        5      [        5      S:X  d   e[        [        S-  [        S-  -   [        [        5      S:X  d   e[        [        [        5      [        [        5      -   [        5      S:X  d   e[        S	[        S-  -  S[        S-  -  -
  [        [        5      S:X  d   eg )
NrJ   r   )rv   TFrH   rK   rI   rO   )
r5   rC   r9   rb   r   ru   rr   r   rD   r   rV   rW   rX   test_is_convexr     sK   QqS!HMM!R$89TAAAQqS!HbS!$45>>>QT1Xa_5===Qq!tVQx~~a'<=EEER1WasA(>?4GGGSVQ5(((QT!Q$Y1%---SVc!f_a(E111Qq!tVa1f_a+u444rW   c                     [        [        [        5      [        [        [        * S-  [        S-  5      5      [        * S-  [        S-  1:X  d   e[        [        [        5      [        [        R
                  " S[        S-  5      5      [        R                  L d   e[        [        [        5      [        5      [        R                  L d   e[        [        [        5      [        [        5      -  [        [        S[        5      5      [        S-  [        [        SS5      -  1:X  d   e[        [        [        5      [        [        S[        5      5      S[        1:X  d   e[        [        S-   [        S-
  -  [        5      [        [        SS5      5      :X  d   e[        [        S-   [        S-
  -  [        [        SS5      5      [        R                  L d   e[        [        S-  S-   [        S-
  -  [        5      S[        S5      -
  S[        S5      -   1:X  d   e[        [        S-  S-   [        S-
  -  [        [        SS5      5      S[        S5      -   1:X  d   e[        [        S-  [        S-  -   S[        S-  -  -
  [        [        R                  5      [        S	S[        SS5      5      :X  d   e[        [        [        5      [        5      [        R                  L d   e[        [!        [        5      [        -
  [        [        R                  5      S
1:X  d   e[        [        [        5      [        [#        [        SS5      [        SS5      5      5      S[        * [        1:X  d   e[        [$        [        [        R                  5      [        R                  :X  d   e[        [$        [        [        R                  5      [        R                  :X  d   eg )NrH   r   rQ   rK   rI   rL   rM   rN   rh   rJ   rP   )r6   r   rC   r9   r   rr   r
   ra   r   r   r   r   r:   r   rU   r   r   r<   rD   rV   rW   rX   test_stationary_pointsr     s+   SVQ"Q1(= 
c!eRT]  c!fa2a4)@ 
ZZ  SVQ 
ZZ  SVCF]Ax2 
dBx1~%&' ' 'SVQB 
W  acAaC[! 
xA'( ( (a!ea!e_a"a 
ZZ  ad1fqs^Q 
$q'k1tAw;'( ( (ad1fqs^QA 
$q'k]  QTAqD[1QT611agg 
r1hq!n-. . .SVQ 
ZZ  SVaZAGG 
S  SVQhq!nhr2>N(O 
"b\  Q177 
WW  Q1::.!**<<<rW   c                  |
   [        [        [        5      [        5      [        R                  L d   e[        [        [        5      [        [        SS5      5      [        S5      :X  d   e[        [        [        5      [        5      [        L d   e[        [        [        5      [        [        [        * S-  [        S-  5      5      [        R                  L d   e[        [        [        5      [        [        5      -  [        [        R                  5      [        R                  :X  d   e[        [        [        [        5      [        [        5      -  [        [        [        [        SS5      -  [        [        SS5      -  5      5      5      [        S5      S-  :X  d   e[        [        S-   [        S-
  -  [        5      [        L d   e[        [        S-   [        S-
  -  [        [        SS5      5      [        S	5      :X  d   e[        [        S-   [        S-
  -  [        [        SS5      5      [        SS
5      :X  d   e[        [        [        S-  * [        S-  -
  [        S-  -   S-   [        5      5      S[        S5      -  S-  [        SS5      -   :X  d   e[        [        [        5      [        [        [        * S5      5      [        S5      :X  d   e[        [!        [        5      [        -
  [        [        R                  5      [        R"                  L d   e[        [        [        5      [        [%        [        SS5      [        SS5      5      5      [        R                  L d   e[        [        [        5      [        [        5      -
  [        [        R                  5      [        S5      :X  d   e[        [&        [        [        R                  5      [&        :X  d   e[        [)        [*        S-  [*        -   5      [*        [        SS5      5      S:X  d   e[        [)        S[*        S-  -  S[*        -  -   5      [*        [        SS5      5      S:X  d   e[        [)        S[*        -  S[*        S-  -  S-   -  5      [*        [        SS5      5      S:X  d   e[        [        [        [        S-  S-   5      -  [        [        R                  5      S:X  d   e[-        [.        S 5        [-        [.        S 5        [-        [.        S 5        [-        [.        S 5        [-        [.        S 5        [-        [.        S 5        g )Nr   rJ   rQ   rK   rO   rM   rH   rL      rN   
   )   i   i+  r   rP   <      i     c                  Z    [        [        [        5      [        [        R                  5      $ r\   )r8   r   rC   r
   ra   rV   rW   rX   rY   test_maximum.<locals>.<lambda>U      A1:: >rW   c                  l    [        [        [        [        5      5      [        [        R
                  5      $ r\   )r8   r   r   rC   r
   ra   rV   rW   rX   rY   r   V      CFQ

 CrW   c                  n    [        S[        S-  [        S-  -   S-   -  [        [        R                  5      $ rn   )r8   rC   rD   r
   ra   rV   rW   rX   rY   r   W  &    1a4!Q$;?(;Q

 KrW   c                  N    [        [        [        5      [        [        5      5      $ r\   )r8   r   rC   rV   rW   rX   rY   r   X      AA 7rW   c                  h    [        [        [        5      [        [        -  [        R
                  5      $ r\   )r8   r   rC   rD   r
   ra   rV   rW   rX   rY   r   Y      A!QZZ @rW   c                  P    [        [        [        5      [        R                  5      $ r\   )r8   r   rC   r
   r   rV   rW   rX   rY   r   Z      A 6rW   )r8   r   rC   r
   r   r9   r   r   r   r   rU   r   r/   r   r   r   r   NegativeOner<   rD   r   rE   r@   r   rV   rW   rX   test_maximumr   =  s   3q61&&&3q61hq!n-Q7773q61###3q61hs1ubd34===3q6#a&=!QWW-777GCF3q6M1hr(1a.7H"XVWYZ^J[.\] 
!WQY  AaC!A#;"b(((AaC!A#;8B?3qu<<<AaC!A#;8B?3x1~EEEGQTE!Q$Jq!tOB.2 
R[_xc223 3 33q61hsA./3q69993q6A:q!''*amm;;;3q61eHQNHR4DE 
UU  3q6#a&=!QWW-a8881a!Q&&&3q!tax=!Xa^4:::3r!Q$wA~&8Aq>:cAAA3r!tQq!tVaZ()1hq!n=DDD1T!Q$q&\>1agg.!333
:>?
:CD
:KL
:78
:@A
:67rW   c                  V   [        [        [        5      [        5      [        R                  L d   e[        [        [        5      [        [        SS5      5      [        S5      :X  d   e[        [        [        5      [        5      [        * L d   e[        [        [        5      [        [        [        * S-  [        S-  5      5      [        R                  L d   e[        [        [        5      [        [        5      -  [        [        R                  5      [        SS5      :X  d   e[        [        [        [        5      [        [        5      -  [        [        [        [        SS5      -  [        [        SS5      -  5      5      5      [        S5      * S-  :X  d   e[        [        S-   [        S-
  -  [        5      [        SS5      :X  d   e[        [        S-   [        S-
  -  [        [        S	S
5      5      [        SS5      :X  d   e[        [        S-  [        S-  -
  [        S-  -   S-   [        5      [        S5      :X  d   e[        [        [        5      [        [        S[        5      5      [        S5      :X  d   e[        [        [        5      [        -
  [        [        R                  5      [        * L d   e[        [        [        5      [        [!        [        S
S5      [        SS5      5      5      [        R                  L d   e[        [        [        5      [        [        5      -
  [        [        R                  5      [        S5      * :X  d   e[        ["        [        [        R                  5      ["        :X  d   e[        [        [        [        S-  S-   5      -  [        [        R                  5      S:X  d   e[%        [&        S 5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        g )NrJ   rQ   rI   rH   rK   rO   rM   irL   r   rP   r   rh   r   c                  Z    [        [        [        5      [        [        R                  5      $ r\   )r7   r   rC   r
   ra   rV   rW   rX   rY   test_minimum.<locals>.<lambda>p  r   rW   c                  l    [        [        [        [        5      5      [        [        R
                  5      $ r\   )r7   r   r   rC   r
   ra   rV   rW   rX   rY   r   q  r   rW   c                  n    [        S[        S-  [        S-  -   S-   -  [        [        R                  5      $ rn   )r7   rC   rD   r
   ra   rV   rW   rX   rY   r   r  r   rW   c                  N    [        [        [        5      [        [        5      5      $ r\   )r7   r   rC   rV   rW   rX   rY   r   s  r   rW   c                  h    [        [        [        5      [        [        -  [        R
                  5      $ r\   )r7   r   rC   rD   r
   ra   rV   rW   rX   rY   r   t  r   rW   c                  P    [        [        [        5      [        R                  5      $ r\   )r7   r   rC   r
   r   rV   rW   rX   rY   r   u  r   rW   )r7   r   rC   r
   r   r9   r   r   r   r   rU   r   r/   r   r   r   r<   rD   r@   r   rV   rW   rX   test_minimumr   ]  s   3q61...3q61hq!n-Q7773q61"$$$3q61hs1ubd34EEE3q6#a&=!QWW-"a@@@GCF3q6M1hr(1a.7H"XVWYZ^J[.\] 
1gXaZ  AaC!A#;"hsA&6666AaC!A#;8B?3xAFFF1a419QT>"$a(AbE1113q61hr2./3r7:::3q6A:q!''*rc1113q61eHQNHR4DE 
]]  3q6#a&=!QWW-$q'9991a!Q&&&1T!Q$q&\>1agg."444
:>?
:CD
:KL
:78
:@A
:67rW   c                      [        [        S5      [        S-
  -  S[        [        S-  S-   5      -  -  [        5      [        S5      S-  :X  d   eg )NrK   rJ   rH   )r8   r   rC   rV   rW   rX   test_issue_19869r   x  sH    DGQUOQtAqD1H~%56:!WQY  rW   c                      [        [        5      n [        U [        [        R                  5      [        S[        SS5      :X  d   eg )Nr   FT)r   rE   r0   r
   rU   r9   r   )rw   s    rX   test_issue_16469r   }  s1    AA!Q(HQE4,HHHHrW   c                      [        [        [        [        -  [        S-  [
        R                  S-  -   -  5      [        5      S:X  d   eg )NrQ   rH   rO   )r3   r   r   r   rC   r
   r   rV   rW   rX   test_issue_18747r     s5    s2a41qvvax0115:::rW   c                      [        [        5      [        S-  :  R                  5       [        R
                  " S[        S5      S-  5      :X  d   eg )NrK   rI   rJ   rH   )r   rC   r   as_setr9   rr   r
   rV   rW   rX   test_issue_25942r     s8    GbdN""$r1Q46(BBBBrW   N)ksympy.core.functionr   sympy.core.numbersr   r   r   r   r   sympy.core.relationalr	   sympy.core.singletonr
   sympy.core.symbolr   r   $sympy.functions.elementary.complexesr   r   &sympy.functions.elementary.exponentialr   r   #sympy.functions.elementary.integersr   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   (sympy.functions.elementary.trigonometricr   r   r   r   r   r   r   r   r   r   r   r   %sympy.functions.elementary.hyperbolicr    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   'sympy.functions.special.gamma_functionsr,   'sympy.functions.special.error_functionsr-   "sympy.matrices.expressions.matexprr.   sympy.simplify.simplifyr/   sympy.calculus.utilr0   r1   r2   r3   r4   r5   r6   r7   r8   sympy.sets.setsr9   r:   r;   r<   sympy.sets.fancysetsr=   sympy.sets.conditionsetr>   sympy.testing.pytestr?   r@   rA   rB   	sympy.abcrC   rD   rE   rd   rf   rx   r{   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   rV   rW   rX   <module>r      s]   & 7 7 $ " - : = 4 9 :F F F F: : : : 9 : ; ,F F F E D ) 0 C C 
3T$"N U U=C@ ? ? I I O OHB DL DLN2M	5=@8@86
I
 ; ;CrW   