
    gB                     R   d dl Zd dlmZ d dlmZ d dlmZmZm	Z	 d dl
mZ d dlmZ d dlmZ d dlmZ d d	lmZ d d
lmZmZ d dlmZmZmZmZmZmZmZ d dlm Z m!Z! d dl"m#Z# d dl$m%Z% d dl&m'Z'm(Z(m)Z) d Z*d Z+d Z,d Z-d Z.d Z/d Z0d Z1d Z2d Z3d Z4d Z5d Z6d Z7d Z8d Z9d  Z:d! Z;dS )"    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                     ddl mm} m} t	          dd          }t	          dd          }t	          dd          }t	          d	d          }t	          d
d          }t	          dd          }t	          dd          }t	          dd          }	t	          dd          }
t          dd          dk    sJ t          t           t                     t           u sJ t          t           |          t           u sJ t          |t                     t           u sJ t          t           |          t           u sJ t          |t                     t           u sJ t          t           d          t           u sJ t          dt                     t           u sJ t          t           |          t           u sJ t          |t                     t           u sJ t          t           |          t           u sJ t          |t                     t           u sJ t          t           t                    t           u sJ t          t          t                     t           u sJ t          ||          |k    sJ t          t
          ||          sJ t          ||          t          ||          k    sJ t          |d          |k    sJ t          d|          |k    sJ t          ||          |k    sJ t          ||          |k    sJ t          ||          |k    sJ t          ||          |k    sJ t          |t                    |k    sJ t          t          |          |k    sJ t          ||          |k    sJ t          |d          |k    sJ t          d|          |k    sJ t          ||          |k    sJ t          ||          |k    sJ t          ||          |k    sJ t          ||          |k    sJ t          |t                    |k    sJ t          t          |          |k    sJ t          dd          dk    sJ t          d|          dk    sJ t          |d          dk    sJ t          d|          dk    sJ t          |d          dk    sJ t          dt                    dk    sJ t          t          d          dk    sJ t          ||          |k    sJ t          t
          ||          sJ t          ||          t          ||          k    sJ t          |t                    |k    sJ t          t          |          |k    sJ t          ||          |k    sJ t          |t                    |k    sJ t          t          |          |k    sJ t          t          t                    t          u sJ t          ||          j        t
          u sJ t          ||          j        t
          u sJ t          ||	          j        t
          u sJ t          ||          j        t
          u sJ t                      t          j
        u sJ t                    k    sJ t          |           t          |           k    sJ t          | |          t          ||           k    sJ t          t          | |                    t          ||           k    sJ t          t          | t                               t          |           k    sJ t          |t          ||||          |k    sJ t          |||          |k    sJ t          |t          d||d          t          |d          k    sJ t          d||t          ||ddd
  
        t          d||          k    sJ t          dd|           t          d|           k    sJ t          ddd||          t          |d          k    sJ t          t
          t                    t                              sJ t          t                    t                              t          t                    t                              k    sJ t          t                    t                                                  d          t          d          k    sJ t          t                    t                                                  t          j                  t          t          j                  k    sJ t!          t"          fd           t!          t"          d            t!          t"          fd           t!          t"          fd           t          d                                        t'          dz
            k    sJ t          d                                        t'          dz
            k    sJ t          d ddz  z
                                          t'          t          ddz  dz             z              dt'          dz  t          d           z   dz
            z  z
  k    sJ t)          d          }t          ddt           |d          d          z            sJ t          d          }|                                j        dfk    sJ t          ||||
          }|j        d u sJ |j        d u sJ |j        du sJ t          ||          }|j        du sJ |j        du sJ |j        d u sJ t          |||          }|j        J |j        du sJ |j        d u sJ t          |||
          }|j        J |j        J |j        J d S )!Nr   xyznTnegativen_nnnonnegativenn_ppositivep_np)nonpositivenp_rreal              d   c                      t          t                     t                                                    t                    S N)r   r   r   subsr   r   s   o/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py<lambda>ztest_Min.<locals>.<lambda>i   -    s3q663q6622771==     c                  *    t          t                    S r>   r   r    rD   rA   rB   ztest_Min.<locals>.<lambda>j       s1vv rD   c                  .    t          t                     S r>   rF   r@   s   rA   rB   ztest_Min.<locals>.<lambda>k       s1ayy rD   c                  8    t          t          j                   S r>   )r   r	   ComplexInfinityr@   s   rA   rB   ztest_Min.<locals>.<lambda>l   s    s1#4a88 rD   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   rM   emr   s                 @rA   test_MinrZ      su   !!!!!!!!!!sT"""A	t	$	$	$B	$	'	'	'B
D
)
)
)CsT"""A	t	$	$	$B	$	'	'	'B
D
)
)
)CsAq!99>>>>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q!99>>>>S!R     r1::Q####q!99>>>>q!99>>>>q"::????r1::????q!99>>>>q!99>>>>q"::????r1::????r2;;"r1::q"::r2;;"r2;;"r1::q"::r2;;"r2;;"q!99>>>>q"::????r1::????q!99>>>>q!99>>>>q"::????r1::????r2;;"S"a     q"::R####r2;;"r2;;"q!99>>>>q"::????r1::????r2;;"q"::?c!!!!r3<<####r3<<####q"::?c!!!! 55AJq66Q;;;;q!99Aq		!!!!q!Q<<3q!Q<<''''q#a))Aq!,,,,q#a"++#a))++++q"aAr""a''''r2q>>Rq"b!Q""c!Rjj0000q!Q2r1aR00CAq"4E4EEEEEq!Q??c!Qll****tS$1a((C1dOO;;;;S#a&&#a&&)))))s1vvs1vv#c!ffc!ff"5"55555s1vvs1vv##Aq))SVV3333s1vvs1vv##Aqv..#af++====
:====>>>
:~~&&&
:(((()))
:8888999q!99>>!	!a% 0 00000q!99>>!	!a% 0 00000q1"a!A#g##A&&9QQ1q9I9I5I+J+J*J
IacCA2JJ&*++
++, , , , , 	Aq!C!aLL.!!!!! 	Aq		A3355:!Q 	Ar2qA=E!!!!u$$$$=D    Ar

A=D    t####=E!!!!AsBA=   t####=E!!!!B1A=   ###=     rD   c                    
 ddl m
m} m} t	          dd          }t	          dd          }t	          dd          }t	          d	d
          }t	          dd
          }t	          dd          }t          dd          dk    sJ t                      t          j        u sJ t          
          
k    sJ t          
|           t          | 
          k    sJ t          
| |          t          || 
          k    sJ t          
t          | |                    t          || 
          k    sJ t          
t          | t                              t          
|           k    sJ t          |t           ||d          t          |d          k    sJ t          |t           ||          |k    sJ t          d
||t           t          j        ||d	  	        t          d
|          k    sJ t          d
d|           t          d
|           k    sJ t          ||dz   |dz
            d|z   k    sJ t          ddd
||          t          |
d          k    sJ t          t          
          t          
                    t          t          
          t          
                    k    sJ t          t          
          t          
                                        
d          t          d          k    sJ t          t          
          t          
                                        
t          j                  t          t          j                  k    sJ t          t          
fd           t          t          d            t          t          
fd           t          t          d            t          |t           ||d          t          |d          k    sJ t          |t           ||d          t          |d          k    sJ t          d
                              
          t#          
dz
            k    sJ t          
d                              
          t#          
dz
            k    sJ t          
dz  d
z   d                              
          d
z  t#          
dz  t          d
dz             z
            z  t#          
t          d
dz            z
  dz             z   k    sJ t          d
          }|                                j        d
fk    sJ t          ||||          }	|	j        du sJ |	j        du sJ |	j        du sJ t          ||          }	|	j        du sJ |	j        du sJ |	j        du sJ t          |||          }	|	j        J |	j        J |	j        J t          |||          }	|	j        J |	j        du sJ |	j        du sJ d S )Nr   r   r"   Tr#   r%   r&   r'   r*   r+   r-   r1   r2   r4   r5   r7   r9   r:   r;   r<   c                      t          t                     t                                                    t                    S r>   )r   r   r   r?   r   r@   s   rA   rB   ztest_Max.<locals>.<lambda>   rC   rD   c                  *    t          t                    S r>   r   r   rG   rD   rA   rB   ztest_Max.<locals>.<lambda>   rH   rD   c                  .    t          t                     S r>   r^   r@   s   rA   rB   ztest_Max.<locals>.<lambda>   rJ   rD   c                  6    t          t          j        d          S )Nr9   )r   r	   rL   rG   rD   rA   rB   ztest_Max.<locals>.<lambda>   s    s1#4a88 rD   F)rN   r   r    r!   r
   r   r	   NegativeInfinityr   r   r   r   r?   rQ   r   rR   rS   r   r"   rT   rU   rV   rW   )r    r!   r"   r%   r&   r*   r-   r1   rX   rY   r   s             @rA   test_Maxrb      s   !!!!!!!!!!sT"""A	t	$	$	$B	$	'	'	'BsT"""A	t	$	$	$BsAq!99>>>> 55A&&&&&q66Q;;;;q!99Aq		!!!!q!Q<<3q!Q<<''''q#a))Aq!,,,,q#a**Q****q2#r1a  C1II----q2#r1""""q!QB3 2B1==Q1MMMMq!Q??c!Qll****q!a%Q1q5((((tS$1a((C1dOO;;;;s1vvs1vv#c!ffc!ff"5"55555s1vvs1vv##Aq))SVV3333s1vvs1vv##Aqv..#af++====
:====>>>
:~~&&&
:(((()))
:88999q2#rAq!!SAYY....q2#rAt$$At4444q!99>>!	!a% 0 00000q!99>>!	!a% 0 00000q!tQUA##A&&	!IadSAE]]*+++
AAq!t$q(
)
)	** * * * 	Aq		A3355:!Q 	Ar1aA=D    t####=E!!!!Ar

A=E!!!!u$$$$=D    Ar1A=   ###=   Ar1A=   t####=E!!!!!!rD   c            
      <   t          dd          } t          ddd          }t          ddd          }t          dd	          }t          d
d          }t          ddd          }t          dd          }t          dd          }t          dd          }t          dd          }	| |||||||||	g
}
t          t          fD ]R}t          j        |
d          D ]7\  }} |||          j        sJ |j        r|j        r |||          j        sJ n5|j        r|j        r |||          j        sJ n |||          j        J |j        r|j        r |||          j        sJ n5|j	        r|j	        r |||          j	        sJ n |||          j        J |j
        r|j
        r |||          j
        sJ n5|j        r|j        r |||          j        sJ n |||          j
        J |j        r|j        r |||          j        sJ n;|j        du r|j        du r |||          j        du sJ n |||          j        J |j        r|j        r |||          j        sJ n;|j        du r|j        du r |||          j        du sJ n |||          j        J |j        r|j        r |||          j        sJ |j        du r |j        du r |||          j        du sJ $ |||          j        J 9Td S )Nr1   Tr2   a)r3   	algebraict)r3   transcendentalq)rationalr*   )
irrationalr"   F)ri   integerirk   o)oddrX   )evenk)primer7   )repeat)r
   r   r   itproductis_realis_algebraicis_transcendentalis_rationalis_irrational
is_integeris_nonintegeris_oddis_evenis_prime)r1   rd   rf   rh   r*   r"   rl   rn   rX   rq   realsextr   r    s                 rA   test_minmax_assumptionsr      s2   sAs...Asd333AsT"""Ast$$$AsT5111AsD!!!AsAsAs$A1aAq!Q*ESz 42 42JuQ/// 3	2 3	2DAq 3q!99$$$$ ~ 6!. 6s1ayy-----$ 6)< 6s1ayy22222s1ayy-555 } 5 5s1ayy,,,,, 5Q_ 5s1ayy.....s1ayy,444 | 4 4s1ayy+++++ 4Q_ 4s1ayy.....s1ayy+333 x 0AH 0s1ayy'''''U""qx5'8'8s1ayy'500000s1ayy'/// y 1QY 1s1ayy(((((e##	U(:(:s1ayy(E11111s1ayy(000 z 2aj 2s1ayy)))))u$$u)<)<s1ayy)U22222s1ayy)1111g3	242 42rD   c                  t   t          dd          } t          t          |           |           t          |           k    sJ t          t          |           |           | k    sJ t	          t          |           |           | k    sJ t	          t          |           |           t          |           k    sJ d S )Nr   Tr2   )r
   r   r   r   r   r@   s    rA   test_issue_8413r     s    sA uQxxuQxx''''wqzz1""""uQxxq    wqzz1++++++rD   c                  v   ddl m}  t          dd          }t          dd          }t          dd          t	          d          k    sJ t          dd          dk    sJ t          dd	          dt          dd	          z  k    sJ t          dd	          t          d          k    sJ t          dd
          dt          dd          z  dz  k    sJ t          dd          dk    sJ t          dd          t	          d          t          z  k    sJ t          dd          dk    sJ t          | d          t	          |           k    sJ t          | d          | k    sJ t          | d	          | t          dd	          z  k    sJ t          | d	          t          |           k    sJ t          | d
          | t          dd          z  k    sJ t          | |          | d|z  z  k    sJ t          | |           | d|z  z  k    sJ t          | ||          dd|z  |z  z  | d|z  z  z  k    sJ d S )Nr   r@   r"   Trm   rq   r7   r9      r5   r4   r8   )rN   r   r
   r   r   r   r   r   )r   r"   rq   s      rA   	test_rootr   !  sN   sD!!!AsD!!!A1::a    1::????1::HQNN*****1::a    2;;!Xa^^+A-----A;;"A;;$q''!)####A;;"1::a    1::????1::HQNN*****1::a    2;;!Xb!__,,,,,1::QqS!!!!A2;;!bd)####1a==R1Q3q5M!ac(2222222rD   c                     t          dd          dk    sJ t          dd          t          dd          k    sJ t          dd          } t          |           | k    sJ t          dd          }|dz  }t          dd          }t          ||z   |z             d|z   |z   k    sJ t          t          dd                    t          dd           k    sJ t          d	d          d
k    sJ t          d          }t          d          }t          ||          }|                    ddd          dk    sJ |                    ddd          dk    sJ |                    t          dd          t          t                    k    sJ |                    ddd          t          d          k    sJ |                    t          dd          t          t                    k    sJ d S )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   =  s   Rr!!!!S!S!,,,,RAQ<<1	b!B	QB	b!BR"Wr\""b2gl2222T"a[[!!d1ajj[0000S!$$$$sAsA!QA66##$$****66""##q(((( 66""##tAww....66##$$R000066""##tAww......rD   c            
      l   t          d          } | st          d           t          d          }t          |t	          t          ||dz
  z            d          d          }t          t                    5   ||                     d                    dk     sJ 	 d d d            d S # 1 swxY w Y   d S )Nnumpyznumpy not installed.r   r7   r   r   )	r   r   r
   r   r   r   r   RuntimeWarningarray)r   r   rM   s      rA   test_issue_11463r   T  s    '""E %#$$$sAIs1ac7||a00'::A 
	(	( ' 'qR!!B&&&&&' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 's   6%B))B-0B-c                     ddl m}  t          d|                               t                    | t	          |           z  k    sJ t          d|                               t                    | t	          | dz
            z  dt	          |  dz             z  z   k    sJ t          d| dz   d| z                                t                    d| z  t	          d| z            z  t	          | dz
            z  | dz   t	          |  dz             z  t	          | dz             z  z   k    sJ t          d|                               t                    | t	          |            z  k    sJ t          d|                               t                    | t	          |  dz             z  dt	          | dz
            z  z   k    sJ t          | |  d                              t                    | t	          d| z            z  t	          |  dz
            z  | t	          d| z            z  t	          | dz
            z  z
  dt	          |  dz             z  t	          | dz             z  z
  k    sJ d S )Nr   r@   r   r7   r8   )rN   r   r   rewriter   r   r@   s    rA    test_rewrite_MaxMin_as_Heavisider   a  st   q!99Y''1Yq\\>9999q!99Y''1Yq1u-=-=+=	)QBF

,    q!A#qs##I..	!IacNN9QU+++	
Q	1"q&!!!)AE"2"22	33 3 3 3 q!99Y''1Yr]]?::::q!99Y''1YrAv->->+>	)AE

,    q1"b>>!!),,	)BqD//)QBF+++	)AaC..1q5)))	*
Iqb1f
iA..
.	// / / / / /rD   c                      ddl m}  ddlm}  | dd          \  }}}}} | d          \  }}}	t	          ||                              |           ||||k    f|df          k    sJ t	          |||                              |           ||||k    ||k    z  f|||k    f|df          k    sJ t	          ||||                              |           ||||k    ||k    z  ||k    z  f|||k    ||k    z  f|||k    f|df          k    sJ t          ||                              |           ||||k    f|df          k    sJ t          |||                              |           ||||k    ||k    z  f|||k    f|df          k    sJ t          ||||                              |           ||||k    ||k    z  ||k    z  f|||k    ||k    z  f|||k    f|df          k    sJ t	          ||                              |           ||||k    f|df          k    sJ t          |	||                              |           ||	|	|k    |	|k    z  f|||k    f|df          k    sJ d S )Nr   )symbols)	Piecewisez	x y z a bTr2   zvx vy va)sympy.core.symbolr   $sympy.functions.elementary.piecewiser   r   r   r   )
r   r   r   r    r!   rd   bvxvyvas
             rA    test_rewrite_MaxMin_as_Piecewiser   s  sB   ))))))>>>>>>GKd333MAq!Q$$JBBq!99Y''99aa[1d)+L+LLLLLq!Q<<	**iiQ!VQ<O8PSTVW[\V\R]`acg_h.i.iiiiiq!Q??""9--AQ1PQ6?RVW[\V\?];^	
Q!VQ 1a1f+4y2: 2: : : : :q!99Y''99aa[1d)+L+LLLLLq!Q<<	**iiQ!VQ<O8PSTVW[\V\R]`acg_h.i.iiiiiq1a##I..99a!q&QRSVATXY]^X^A_=`	
Q!VQ 1a1f+4y4: 4: : : : : r2;;y))YYB"H~Dz-R-RRRRRr2r??""9--BrbTVh@W;X[]_aeg_gZhkmosjt1u1uuuuuuurD   c                  n   ddl m} m} | d|di}t          | |                              |          t          | |                              |                                          k    sJ t          | |                              |          t          | |                              |                                          k    sJ ddlm} t          d          D ]}|  |dd	          | |dd	          i}t          | |                              |          t          | |                              |                                          k    sJ t          | |                              |          t          | |                              |                                          k    sJ d S )
Nr   r   r    r8   r   )r?   )randint   r<   r;   )
rN   r   r    r   evalfr?   r   sympy.core.randomr   range)r   r    fixed_test_datar   rl   random_test_datas         rA   test_issue_11099r     s   "amOq!99???00Aq		''--//0 0 0 0q!99???00Aq		''--//0 0 0 0 *)))))2YY 5 5wwtS111ggdC6H6HI1ayy$4551IINN+,,22445 5 5 51ayy$4551IINN+,,22445 5 5 5 5	5 5rD   c            	      R   ddl m} m}m} t	          | ||t          | |                    t	          | ||          k    sJ t	          | |t          | ||                    t	          | |          k    sJ t	          | |t          | |                    t	          | |          k    sJ d S Nr   rd   r   c)rN   rd   r   r   r   r   r   s      rA   test_issue_12638r     s    !!!!!!!!!!q!QAq		""c!Qll2222q!SAq\\""c!Qii////q!SAYY3q!99,,,,,,rD   c                      ddl m} m}m} t	          t          | |          t          | ||                    t          | |          k    sJ d S r   )rN   rd   r   r   r   r   r   s      rA   test_issue_21399r     s[    !!!!!!!!!!s1ayy#aA,,''3q!99444444rD   c                     ddl m} m}m}m}m} t          dt          d|                    dk    sJ t          dt          d|                    dk    sJ t          t          ||          t          ||                    t          |t          ||                    k    sJ t          t          t          ||          t          ||                    j	                  t          ||          t          ||          hk    sJ t          t          ||          t          ||          |          t          |t          |t          ||                              k    sJ t          t          }}t          d          D ]g} || |||                    |k    sJ  || || ||||                               || || |||                              k    sJ ||}}ht          |t          ||          t          | ||                    t          |t          |t          |t          | |                                        k    sJ d S )Nr   )vwr   r    r!   r9   r7   r   )rN   r   r   r   r    r!   r   r   setrT   r   )r   r   r   r    r!   ABrl   s           rA   test_instantiation_evaluationr     sj   ''''''''''''''q#a))!!!!q#a))!!!!s1ayy#a))$$As1ayy(9(99999s3q!99c!Qii((-..Aq		3q!993    s1ayy#a))Q''3	3q#a)), ,    qA1XX  qAAaGG}}!!!!qAAa1a$$%%1aa11Q77mm)<)<<<<<!1q#a))SAq\\**c	3q#aQ##$$/& /& & & & & & &rD   c            	      H   ddl m ddlm ddlm} m}m}m} fd} |t          | |                      |t          | |                      |t          | ||                      |t          t          ||           t          ||                               d S )Nr   )permutations)Abs)r   r    r!   r   c                 j   | j         }|                               }|                    t          t                    rJ  t          t          |                              D ]M}t          t          ||                    }|	                    |          | 	                    |          k    sJ Nd S r>   )
free_symbolsr   hasr   r   r   lendictzipxreplace)rX   freerd   rl   repsr   r   s        rA   testz!test_rewrite_as_Abs.<locals>.test  s    ~IIcNN55c??"""eCII..// 	8 	8AD!%%D::d##qzz$'7'777777	8 	8rD   )	itertoolsr   $sympy.functions.elementary.complexesr   rN   r   r    r!   r   r   r   )r   r    r!   r   r   r   r   s        @@rA   test_rewrite_as_Absr     s    &&&&&&888888$$$$$$$$$$$$8 8 8 8 8 8 	DQOOODQOOODQ1DSAYYAq			"	"#####rD   c                     t          t          dd          t                    dk    sJ t          t          dd          t                    dk    sJ t          t	          ddd          t                    dk    sJ t          dd          t          dt
          j        d          k    sJ t          dd          t          dt          dd          d          k    sJ t	          dd	d          t          dt
          j        d          k    sJ t	          ddd	d                              t                    dk    sJ t          d
dd                              t                    dk    sJ d S )Nr5   FevaluateTg      @   r9   r   r7   r   )

isinstancer   r   r   r   r	   rQ   r   r   r   rG   rD   rA   test_issue_14000r     su   d1u---s33t;;;;d3///55====d2q51113774????E"""c!QVe&D&D&DDDDDe$$$C!Q%(P(P(PPPPP1u%%%Q)G)G)GGGGGAq5)))--c22d::::RU+++//44<<<<<<rD   c                  r    ddl m}  t          d          } | ||          } |j        |j         |k    sJ d S )Nr   )Lambdar   )sympy.core.functionr   r
   rO   rT   )r   r   eqns      rA   test_issue_6899r     sP    ******sA
&A,,C38SX#%%%%%%rD   c                  h   ddl m} m} t          dd          dk    sJ t          dd          dk    sJ t          dd          dk    sJ t          dd          dk    sJ t          | dz  |          t          | dz  |          k    sJ t          t          dd          dz   d          d	k    sJ d S )
Nr   r   r4   r   r7   r   r8   r9   )rN   r   r    r   r   s     rA   test_Remr     s    q!99>>>>r1::q"::????r2;;"q!tQ<<3q!tQ<<''''s2qzzA~q!!Q&&&&&&rD   c                     ddl m}  t          dd          }t          dd          dk    sJ t          dd          j        dk    sJ t          d|          |k    sJ t          d|          j        dk    sJ t          d|          dk    sJ t          d|          j        dk    sJ t          ddd	          dk    sJ t          ddd	          j        d
k    sJ t          d|d	          |k    sJ t          d|d	          j        d|fk    sJ t          d|d	          dk    sJ t          d|d	          j        d|fk    sJ  | d	          5  t          dd          dk    sJ t          dd          j        d
k    sJ t          d|          |k    sJ t          d|          j        d|fk    sJ t          d|          dk    sJ t          d|          j        d|fk    sJ 	 d d d            d S # 1 swxY w Y   d S )Nr   r   r*   Tr+   r9   r   rG   F)r9   r   )sympyr   r
   r   rT   r   )r   r*   s     rA   test_minmax_no_evaluater     s   sT"""Aq!99>>>>q!99>Rq!99>>>>q!99>Rq!99>>>>q!99>Rq!e$$$))))q!e$$$)V3333q!e$$$))))q!e$$$)aV3333q!e$$$))))q!e$$$)aV3333	% ( (1ayyA~~~~1ayy~''''1ayyA~~~~1ayy~!Q''''1ayyA~~~~1ayy~!Q'''''( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (s   BG??HH)<r   rt   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   rZ   rb   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rG   rD   rA   <module>r      s       % % % % % % ( ( ( ( ( ( . . . . . . . . . .             " " " " " " $ $ $ $ $ $ ( ( ( ( ( ( 6 6 6 6 6 6 > > > > > > > >K K K K K K K K K K K K K K K K K K = = = = = = = = = = = = = = - - - - - - > > > > > > > > > >z! z! z!z?" ?" ?"DA2 A2 A2H, , ,3 3 38/ / /.
' 
' 
'/ / /$v v v&5 5 5$- - -5 5 5
& & &"$ $ $ 
= 
= 
=& & &' ' '( ( ( ( (rD   