
    \hB                     P   S SK rS SKJr  S SKJr  S SKJrJrJ	r	  S SK
Jr  S SKJr  S SKJr  S SKJr  S S	KJr  S S
KJrJr  S SKJrJrJrJrJrJrJr  S SKJ r J!r!  S SK"J#r#  S SK$J%r%  S SK&J'r'J(r(J)r)  S r*S r+S r,S r-S r.S r/S r0S r1S r2S r3S r4S r5S r6S r7S r8S r9S  r:S! r;g)"    N)	unchanged)Function)IooRational)Pow)S)Symbol)import_module)log)floorceiling)sqrtcbrtrootMinMax	real_rootRem)cossin)	Heaviside)lambdify)raisesskipignore_warningsc                    ^ SSK JmJn Jn  [	        SSS9n[	        SSS9n[	        SSS9n[	        S	SS9n[	        S
SS9n[	        SSS9n[	        SSS9n[	        SSS9n	[	        SSS9n
[        SS5      S:X  d   e[        [        * [        * 5      [        * L d   e[        [        * U5      [        * L d   e[        U[        * 5      [        * L d   e[        [        * U5      [        * L d   e[        U[        * 5      [        * L d   e[        [        * S5      [        * L d   e[        S[        * 5      [        * L d   e[        [        * U5      [        * L d   e[        U[        * 5      [        * L d   e[        [        * U5      [        * L d   e[        U[        * 5      [        * L d   e[        [        * [        5      [        * L d   e[        [        [        * 5      [        * L d   e[        X"5      U:X  d   e[        [
        X(5      (       d   e[        X5      [        X(5      :X  d   e[        US5      U:X  d   e[        SU5      U:X  d   e[        X$5      U:X  d   e[        XB5      U:X  d   e[        X&5      U:X  d   e[        Xb5      U:X  d   e[        U[        5      U:X  d   e[        [        U5      U:X  d   e[        X5      U:X  d   e[        US5      U:X  d   e[        SU5      U:X  d   e[        X5      U:X  d   e[        XH5      U:X  d   e[        X5      U:X  d   e[        Xh5      U:X  d   e[        U[        5      U:X  d   e[        [        U5      U:X  d   e[        SS5      S:X  d   e[        SU5      S:X  d   e[        US5      S:X  d   e[        SU5      S:X  d   e[        US5      S:X  d   e[        S[        5      S:X  d   e[        [        S5      S:X  d   e[        XD5      U:X  d   e[        [
        XF5      (       d   e[        Xd5      [        XF5      :X  d   e[        U[        5      U:X  d   e[        [        U5      U:X  d   e[        Xf5      U:X  d   e[        U[        5      U:X  d   e[        [        U5      U:X  d   e[        [        [        5      [        L d   e[        X#5      R                  [
        L d   e[        XE5      R                  [
        L d   e[        X5      R                  [
        L d   e[        Xg5      R                  [
        L d   e[        5       [        R                  L d   e[        T5      T:X  d   e[        TU 5      [        U T5      :X  d   e[        TX5      [        XT5      :X  d   e[        T[        X5      5      [        XT5      :X  d   e[        T[        U [        * 5      5      [        TU 5      :X  d   e[        U[        X&Xg5      U:X  d   e[        XsU5      U:X  d   e[        U[        SXfS5      [        US5      :X  d   e[        STXb[        X6SSS5
      [        STX#5      :X  d   e[        STSU 5      [        STU 5      :X  d   e[        SSSTXb5      [        UTS5      :X  d   e[        [
        [        T5      [        T5      5      (       d   e[        [        T5      [        T5      5      [        [        T5      [        T5      5      :X  d   e[        [        T5      [        T5      5      R                  TS5      [        S5      :X  d   e[        [        T5      [        T5      5      R                  T[        R                  5      [        [        R                  5      :X  d   e[!        ["        U4S j5        [!        ["        S 5        [!        ["        U4S j5        [!        ["        U4S j5        [        ST5      R%                  T5      ['        ST-
  5      :X  d   e[        TS5      R%                  T5      ['        ST-
  5      :X  d   e[        ST* SST-  -
  5      R%                  T5      ['        T[        SST-  S-   5      -   5      * S['        ST-  [        ST* 5      -   S-
  5      -  -
  :X  d   e[)        S5      n[        SS[        U" S5      S5      -  5      (       d   e[        ST5      nUR+                  5       R,                  ST4:X  d   e[        X'X:5      nUR.                  S L d   eUR0                  S L d   eUR2                  SL d   e[        Xg5      nUR.                  SL d   eUR0                  SL d   eUR2                  S L d   e[        XeU5      nUR.                  b   eUR0                  SL d   eUR2                  S L d   e[        XFU
5      nUR.                  b   eUR0                  b   eUR2                  b   eg )!Nr   xyznTnegativen_nnnonnegativenn_ppositivep_np)nonpositivenp_rreal              d   c                  h   > [        [        T 5      [        T 5      5      R                  T [        5      $ N)r   r   r   subsr   r   s   k/var/www/auris/envauris/lib/python3.13/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py<lambda>test_Min.<locals>.<lambda>i   !    s3q63q62771=    c                       [        [        5      $ r>   r   r    rE   rA   rB   rC   j       s1vrE   c                  $   > [        [        T 5      $ r>   rG   r@   s   rA   rB   rC   k       s1ayrE   c                  8   > [        [        R                  T 5      $ r>   )r   r	   ComplexInfinityr@   s   rA   rB   rC   l   s    s1#4#4a8rE   fF)	sympy.abcr   r    r!   r
   r   r   r   funcr	   Infinityr   r   r   r?   Halfr   
ValueErrordiffr   r   r"   argsis_positiveis_nonnegativeis_negative)r    r!   r"   r%   r&   r)   r*   r-   r.   r0   r1   rN   emr   s                 @rA   test_Minr[      s   !!sT"A	t	$B	$	'B
D
)CsT"A	t	$B	$	'B
D
)CsAq!9>>sRC=RCsA;2#q2#;2#sB<B3rB3<B3sA;2#q2#;2#sB<B3rB3<B3sA;2#q2#;2#sB<B3rB3<B3q9>>S!    r:Q###q!9>>q!9>>q:??r:??q9>>q9>>q":??r1:??r;"r1:q":r;"r;"r:q:r2;"r2;"q!9>>q":??r1:??q!9>>q!9>>q":??r1:??r;"S"    q:R###r2;"r2;"q9>>q":??r1:??r2;"q:??c!!!r<###r<###q:??c!!! 5AJJq6Q;;q!9Aq	!!!q!<3qQ<'''q#a)A!,,,q#a"+#a)+++q"aA"a'''rq>Rq"b!"c!Rj000q!Q2raR0CAq4EEEEq!Q?c!Ql***tS$1(C1dO;;;S#a&#a&))))s1vs1v#c!fc!f"5555s1vs1v##Aq)SV333s1vs1v##Aqvv.#aff+===
:=>
:~&
:()
:89q!9>>!	!a% 0000q!9>>!	!a% 0000q1"a!A#g##A&9QQ1q9I5I+J*J
IacCA2J&*+
++, , , , 	Aq!C!aL.!!!! 	Aq	A335::!Q 	A2A==E!!!u$$$==D   A
A==D   t###==E!!!ABA==   t###==E!!!B1A==   ###==   rE   c                  H
  ^
 SSK Jm
Jn Jn  [	        SSS9n[	        SSS9n[	        SSS9n[	        S	SS
9n[	        SSS
9n[	        SSS9n[        SS5      S:X  d   e[        5       [        R                  L d   e[        T
5      T
:X  d   e[        T
U 5      [        U T
5      :X  d   e[        T
X5      [        XT
5      :X  d   e[        T
[        X5      5      [        XT
5      :X  d   e[        T
[        U [        5      5      [        T
U 5      :X  d   e[        U[        * X5S5      [        US5      :X  d   e[        U[        * X55      U:X  d   e[        ST
XR[        * [        R                  X5S5	      [        ST
U5      :X  d   e[        ST
SU 5      [        ST
U 5      :X  d   e[        XwS-   US-
  5      SU-   :X  d   e[        SSST
XR5      [        UT
S5      :X  d   e[        [        T
5      [        T
5      5      [        [        T
5      [        T
5      5      :X  d   e[        [        T
5      [        T
5      5      R                  T
S5      [        S5      :X  d   e[        [        T
5      [        T
5      5      R                  T
[        R                  5      [        [        R                  5      :X  d   e[        [        U
4S j5        [        [        S 5        [        [        U
4S j5        [        [        S 5        [        U[        * X5S5      [        US5      :X  d   e[        U[        * X5S5      [        US5      :X  d   e[        ST
5      R!                  T
5      [#        T
S-
  5      :X  d   e[        T
S5      R!                  T
5      [#        T
S-
  5      :X  d   e[        T
S-  ST
-   S5      R!                  T
5      ST
-  [#        T
S-  [        ST
S-   5      -
  5      -  [#        T
[        ST
S-  5      -
  S-   5      -   :X  d   e[        ST
5      nUR%                  5       R&                  ST
4:X  d   e[        XVX'5      n	U	R(                  SL d   eU	R*                  SL d   eU	R,                  SL d   e[        X#5      n	U	R(                  SL d   eU	R*                  SL d   eU	R,                  SL d   e[        X#U5      n	U	R(                  b   eU	R*                  b   eU	R,                  b   e[        X$U5      n	U	R(                  b   eU	R*                  SL d   eU	R,                  SL d   eg )Nr   r   r"   Tr#   r%   r&   r'   r*   r+   r-   r1   r2   r4   r5   r7   r9   r:   r;   r<   c                  h   > [        [        T 5      [        T 5      5      R                  T [        5      $ r>   )r   r   r   r?   r   r@   s   rA   rB   test_Max.<locals>.<lambda>   rD   rE   c                       [        [        5      $ r>   r   r   rH   rE   rA   rB   r^      rI   rE   c                  $   > [        [        T 5      $ r>   r`   r@   s   rA   rB   r^      rK   rE   c                  6    [        [        R                  S5      $ )Nr9   )r   r	   rM   rH   rE   rA   rB   r^      s    s1#4#4a8rE   F)rO   r   r    r!   r
   r   r	   NegativeInfinityr   r   r   r   r?   rR   r   rS   rT   r   r"   rU   rV   rW   rX   )r    r!   r"   r%   r&   r*   r-   r1   rY   rZ   r   s             @rA   test_Maxrd      s   !!sT"A	t	$B	$	'BsT"A	t	$BsAq!9>> 5A&&&&&q6Q;;q!9Aq	!!!q!<3qQ<'''q#a)A!,,,q#a*Q***q2#ra C1I---q2#r"""q!QB3 2 2B1=Q1MMMq!Q?c!Ql***qa%Q1q5(((tS$1(C1dO;;;s1vs1v#c!fc!f"5555s1vs1v##Aq)SV333s1vs1v##Aqvv.#aff+===
:=>
:~&
:()
:89q2#rq!SAY...q2#rt$At444q!9>>!	!a% 0000q!9>>!	!a% 0000q!tQUA##A&	!IadSAE]*++
AAq!t$q(
)	** * * 	Aq	A335::!Q 	A1A==D   t###==E!!!A
A==E!!!u$$$==D   A1A==   ###==   A1A==   t###==E!!!rE   c            
         [        SSS9n [        SSSS9n[        SSSS9n[        SSS	9n[        S
SS9n[        SSSS9n[        SSS9n[        SSS9n[        SSS9n[        SSS9n	XX#XEXgX/
n
[        [        4 GH}  n[        R                  " U
SS9 GH_  u  pU" X5      R
                  (       d   eUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOQUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOU" X5      R                  b   eUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOQUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOU" X5      R                  b   eUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOQUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOU" X5      R                  b   eUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOKUR                  SL a'  UR                  SL a  U" X5      R                  SL d   eOU" X5      R                  b   eUR                  (       a+  UR                  (       a  U" X5      R                  (       d   eOKUR                  SL a'  UR                  SL a  U" X5      R                  SL d   eOU" X5      R                  b   eUR                  (       a-  UR                  (       a  U" X5      R                  (       d   eGM  UR                  SL a)  UR                  SL a  U" X5      R                  SL d   eGMJ  U" X5      R                  c  GM`   e   GM     g )Nr1   Tr2   a)r3   	algebraict)r3   transcendentalq)rationalr*   )
irrationalr"   F)rk   integerirm   o)oddrY   )evenk)primer7   )repeat)r
   r   r   itproductis_realis_algebraicis_transcendentalis_rationalis_irrational
is_integeris_nonintegeris_oddis_evenis_prime)r1   rf   rh   rj   r*   r"   rn   rp   rY   rs   realsextr   r    s                 rA   test_minmax_assumptionsr      s   sAs.Asd3AsT"Ast$AsT51AsD!AsAsAs$A1qQ*ESzJJuQ/DA q9$$$$ ~~!..1y----$$)<)<1y22221y--555 }}1y,,,,Q__1y....1y,,444 ||1y++++Q__1y....1y++333 xxAHH1y''''U"qxx5'81y''50001y''/// yyQYY1y((((e#		U(:1y((E1111y((000 zzajj1y))))u$u)<1y))U2221y))111g 0 rE   c                     [        SSS9n [        [        U 5      U 5      [        U 5      :X  d   e[        [        U 5      U 5      U :X  d   e[	        [        U 5      U 5      U :X  d   e[	        [        U 5      U 5      [        U 5      :X  d   eg )Nr   Tr2   )r
   r   r   r   r   r@   s    rA   test_issue_8413r     s|    sA uQxuQx'''wqz1"""uQxq   wqz1+++rE   c                     SSK Jn   [        SSS9n[        SSS9n[        SS5      [	        S5      :X  d   e[        SS5      S:X  d   e[        SS	5      S[        SS	5      -  :X  d   e[        SS	5      [        S5      :X  d   e[        SS
5      S[        SS5      -  S-  :X  d   e[        SS5      S:X  d   e[        SS5      [	        S5      [        -  :X  d   e[        SS5      S:X  d   e[        U S5      [	        U 5      :X  d   e[        U S5      U :X  d   e[        U S	5      U [        SS	5      -  :X  d   e[        U S	5      [        U 5      :X  d   e[        U S
5      U [        SS5      -  :X  d   e[        X5      U SU-  -  :X  d   e[        X* 5      U SU-  -  :X  d   e[        XU5      SSU-  U-  -  U SU-  -  -  :X  d   eg )Nr   r@   r"   Tro   rs   r7   r9      r5   r4   r8   )rO   r   r
   r   r   r   r   r   )r   r"   rs   s      rA   	test_rootr   !  s   sD!AsD!A1:a   1:??1:HQN****1:a   2;!Xa^+A----A;"A;$q'!)###A;"1:a   1:??1:HQN****1:a   2;!Xb!_,,,,:QqS!!!2;!bd)###a=R1Q3q5M!ac(2222rE   c                     [        SS5      S:X  d   e[        SS5      [        SS5      :X  d   e[        SS5      n [        U 5      U :X  d   e[        SS5      nUS-  n[        SS5      n[        X-   U-   5      SU-   U-   :X  d   e[        [        SS5      5      [        SS5      * :X  d   e[        S	S5      S
:X  d   e[        S5      n[        S5      n[        XE5      nUR                  SSS.5      S:X  d   eUR                  SSS.5      S:X  d   eUR                  [        SS.5      [        [        5      :X  d   eUR                  SSS.5      [        S5      :X  d   eUR                  [        SS.5      [        [        5      :X  d   eg )Nr   r8   ir5   r6   r   r7   g       g       r   r"   )r   r"      )r   r   r
   r?   r   r   r   )r1   r1r2r3r   r"   gs          rA   test_real_rootr   =  sz   Rr!!!S!S!,,,RAQ<1	b!B	QB	b!BRWr\"b2gl222T"a[!d1aj[000S!$$$sAsA!A66#$***66"#q((( 66"#tAw...66#$R00066"#tAw...rE   c            
      ,   [        S5      n U (       d  [        S5        [        S5      n[        U[	        [        XS-
  -  5      S5      S5      n[        [        5         U" U R                  S5      5      S:  d   e S S S 5        g ! , (       d  f       g = f)Nnumpyznumpy not installed.r   r7   r   r   )	r   r   r
   r   r   r   r   RuntimeWarningarray)r   r   rN   s      rA   test_issue_11463r   T  sq    '"E#$sAIs1c7|a0':A 
	(R!B&&& 
)	(	(s   B
Bc                     SSK Jn   [        SU 5      R                  [        5      U [	        U 5      -  :X  d   e[        SU 5      R                  [        5      U [	        U S-
  5      -  S[	        U * S-   5      -  -   :X  d   e[        SU S-   SU -  5      R                  [        5      SU -  [	        SU -  5      -  [	        U S-
  5      -  U S-   [	        U * S-   5      -  [	        U S-   5      -  -   :X  d   e[        SU 5      R                  [        5      U [	        U * 5      -  :X  d   e[        SU 5      R                  [        5      U [	        U * S-   5      -  S[	        U S-
  5      -  -   :X  d   e[        X * S5      R                  [        5      U [	        SU -  5      -  [	        U * S-
  5      -  U [	        SU -  5      -  [	        U S-
  5      -  -
  S[	        U * S-   5      -  [	        U S-   5      -  -
  :X  d   eg )Nr   r@   r   r7   r8   )rO   r   r   rewriter   r   r@   s    rA    test_rewrite_MaxMin_as_Heavisider   a  s   q!9Y'1Yq\>999q!9Y'1Yq1u-=+=	)QBF
,   q!A#qs##I.	!IacN9QU++	
Q	1"q&!!)AE"22	33 3 3 q!9Y'1Yr]?:::q!9Y'1YrAv->+>	)AE
,   q"b>!!),	)BqD/)QBF++	)AaC.1q5))	*
Iqb1f
iA.
.	// / /rE   c                     SSK Jn   SSKJn  U " SSS9u  p#pEnU " S5      u  pxn	[	        XV5      R                  U5      U" XUU:  4US45      :X  d   e[	        X#U5      R                  U5      U" X"U:  X$:  -  4X3U:  4US45      :X  d   e[	        X#XV5      R                  U5      U" XUU:  XR:  -  XS:  -  4XfU:  Xc:  -  4X"U:  4US45      :X  d   e[        XV5      R                  U5      U" XUU:*  4US45      :X  d   e[        X#U5      R                  U5      U" X"U:*  X$:*  -  4X3U:*  4US45      :X  d   e[        X#XV5      R                  U5      U" XUU:*  XR:*  -  XS:*  -  4XfU:*  Xc:*  -  4X"U:*  4US45      :X  d   e[	        Xx5      R                  U5      U" XwU:  4US45      :X  d   e[        XU5      R                  U5      U" XU:*  X:*  -  4XwU:*  4US45      :X  d   eg )Nr   )symbols)	Piecewisez	x y z a bTr2   zvx vy va)sympy.core.symbolr   $sympy.functions.elementary.piecewiser   r   r   r   )
r   r   r   r    r!   rf   bvxvyvas
             rA    test_rewrite_MaxMin_as_Piecewiser   s  sN   )>Kd3MA!$JBBq9Y'9aa[1d)+LLLLqQ<	*i!V<O8PST[\V\R]`acg_h.iiiiqQ?""9-AQ16?RVWV\?];^	
!V 11f+4y2: : : :q9Y'9aa[1d)+LLLLqQ<	*i!V<O8PST[\V\R]`acg_h.iiiiqa##I.9aq&QVATXYX^A_=`	
!V 11f+4y4: : : : r;y)Y"H~Dz-RRRRrr?""9-Brbh@W;X[]eg_gZhkmosjt1uuuurE   c                     SSK Jn Jn  U SUS0n[        X5      R	                  US9[        X5      R                  U5      R	                  5       :X  d   e[        X5      R	                  US9[        X5      R                  U5      R	                  5       :X  d   eSSKJn  [        S5       H  nX" SS	5      X" SS	5      0n[        X5      R	                  US9[        X5      R                  U5      R	                  5       :X  d   e[        X5      R	                  US9[        X5      R                  U5      R	                  5       :X  a  M   e   g )
Nr   r   r    r8   r   )r?   )randint   r<   r;   )
rO   r   r    r   evalfr?   r   sympy.core.randomr   range)r   r    fixed_test_datar   rn   random_test_datas         rA   test_issue_11099r     s.   "amOq9???0A	'--/0 0 0q9???0A	'--/0 0 0 *2YwtS11gdC6HI1y$45INN+,2245 	5 51y$45INN+,2245 	5 5	 rE   c            	          SSK Jn JnJn  [	        XU[        X5      5      [	        XU5      :X  d   e[	        X[        XU5      5      [	        X5      :X  d   e[	        X[        X5      5      [	        X5      :X  d   eg Nr   rf   r   c)rO   rf   r   r   r   r   r   s      rA   test_issue_12638r     se    !!qQA	"c!l222qSq\"c!i///qSY3q9,,,rE   c                  t    SSK Jn JnJn  [	        [        X5      [        XU5      5      [        X5      :X  d   eg r   )rO   rf   r   r   r   r   r   s      rA   test_issue_21399r     s+    !!s1y#aA,'3q9444rE   c                  r   SSK Jn JnJnJnJn  [        S[        SU5      5      S:X  d   e[        S[        SU5      5      S:X  d   e[        [        X#5      [        X$5      5      [        U[        X45      5      :X  d   e[        [        [        X5      [        X45      5      R                  5      [        X5      [        X45      1:X  d   e[        [        X#5      [        X$5      U5      [        U[        U[        X45      5      5      :X  d   e[        [        pe[        S5       HF  nU" X&" X#5      5      U:X  d   eU" X&" X5" X!U5      5      5      U" X&" X5" X5      5      5      :X  d   eXepeMH     [        U[        X#5      [        XU5      5      [        U[        U[        U[        X5      5      5      5      :X  d   eg )Nr   )vwr   r    r!   r9   r7   r   )rO   r   r   r   r    r!   r   r   setrU   r   )r   r   r   r    r!   ABrn   s           rA   test_instantiation_evaluationr     s   ''q#a)!!!q#a)!!!s1y#a)$As1y(9999s3q9c!i(--.A	3q93   s1y#a)Q'3	3q#a),   q1XAaG}!!!Aa1$%1a1Q7m)<<<<1  q#a)Sq\*c	3q#aQ#$/& & & &rE   c            	         ^^ SSK Jm  SSKJm  SSKJn JnJnJn  UU4S jnU" [        X5      5        U" [        X5      5        U" [        XU5      5        U" [        [        X05      [        X5      5      5        g )Nr   )permutations)Abs)r   r    r!   r   c                 8  > U R                   nU R                  T5      nUR                  [        [        5      (       a   eT" [        [        U5      5      5       H=  n[        [        X5      5      nUR                  U5      U R                  U5      :X  a  M=   e   g r>   )
free_symbolsr   hasr   r   r   lendictzipxreplace)rY   freerf   rn   repsr   r   s        rA   test!test_rewrite_as_Abs.<locals>.test  st    ~~IIcN55c??""eCI./AD%D::d#qzz$'7777 0rE   )	itertoolsr   $sympy.functions.elementary.complexesr   rO   r   r    r!   r   r   r   )r   r    r!   r   r   r   r   s        @@rA   test_rewrite_as_Absr     sQ    &8$$8 	QOQOQ1SYA		"#rE   c                  0   [        [        SSS9[        5      S:X  d   e[        [        SSS9[        5      S:X  d   e[        [	        SSSS9[        5      S:X  d   e[        SSS9[        S[
        R                  SS9:X  d   e[        SSS9[        S[        SS5      SS9:X  d   e[	        SS	SS9[        S[
        R                  SS9:X  d   e[	        SSS	SS9R                  [        5      S:X  d   e[        S
SSS9R                  [        5      S:X  d   eg )Nr5   FevaluateTg      @   r9   r   r7   r   )

isinstancer   r   r   r   r	   rR   r   r   r   rH   rE   rA   test_issue_14000r     s   d1u-s3t;;;d3/5===d2q51374???E"c!QVVe&DDDDe$C!Q%(PPPP1u%Q)GGGGAq5)--c2d:::RU+//4<<<rE   c                  t    SSK Jn   [        S5      nU " X5      nUR                  " UR                  6 U:X  d   eg )Nr   )Lambdar   )sympy.core.functionr   r
   rP   rU   )r   r   eqns      rA   test_issue_6899r     s2    *sA
,C88SXX#%%%rE   c                  &   SSK Jn Jn  [        SS5      S:X  d   e[        SS5      S:X  d   e[        SS5      S:X  d   e[        SS5      S:X  d   e[        U S-  U5      [        U S-  U5      :X  d   e[        [        SS5      S-   S5      S	:X  d   eg )
Nr   r   r4   r   r7   r   r8   r9   )rO   r   r    r   r   s     rA   test_Remr     s    q!9>>r1:q":??r2;"q!tQ<3q!tQ<'''s2qzA~q!Q&&&rE   c                     SSK Jn   [        SSS9n[        SS5      S:X  d   e[        SS5      R                  S:X  d   e[        SU5      U:X  d   e[        SU5      R                  S:X  d   e[        SU5      S:X  d   e[        SU5      R                  S:X  d   e[        SSS	S9S:w  d   e[        SSS	S9R                  S
:X  d   e[        SUS	S9U:w  d   e[        SUS	S9R                  SU4:X  d   e[        SUS	S9S:w  d   e[        SUS	S9R                  SU4:X  d   eU " S	5         [        SS5      S:w  d   e[        SS5      R                  S
:X  d   e[        SU5      U:w  d   e[        SU5      R                  SU4:X  d   e[        SU5      S:w  d   e[        SU5      R                  SU4:X  d   e S S S 5        g ! , (       d  f       g = f)Nr   r   r*   Tr+   r9   r   rH   F)r9   r   )sympyr   r
   r   rU   r   )r   r*   s     rA   test_minmax_no_evaluater     s   sT"Aq!9>>q!9>>Rq!9>>q!9>>Rq!9>>q!9>>Rq!e$)))q!e$))V333q!e$)))q!e$))aV333q!e$)))q!e$))aV333	%1ayA~~1ay~~'''1ayA~~1ay~~!Q'''1ayA~~1ay~~!Q''' 
s   +BG
G)<r   rv   sympy.core.exprr   r   r   sympy.core.numbersr   r   r   sympy.core.powerr   sympy.core.singletonr	   r   r
   sympy.externalr   &sympy.functions.elementary.exponentialr   #sympy.functions.elementary.integersr   r   (sympy.functions.elementary.miscellaneousr   r   r   r   r   r   r   (sympy.functions.elementary.trigonometricr   r   'sympy.functions.special.delta_functionsr   sympy.utilities.lambdifyr   sympy.testing.pytestr   r   r   r[   rd   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rH   rE   rA   <module>r      s     % ( . .   " $ ( 6 >K K K = = - > >z!z?"DA2H,38/.
'/$v&5$-5
&"$ 
=&'(rE   