
    sgB                     P   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;y)"    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                    j                  d      t        d      k(  sJ t        t              t                    j                  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      j%                        t'        dz
        k(  sJ t        d      j%                        t'        dz
        k(  sJ t        d ddz  z
        j%                        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+                         j,                  dfk(  sJ t        ||||
      }|j.                  d u sJ |j0                  d u sJ |j2                  du sJ t        ||      }|j.                  du sJ |j0                  du sJ |j2                  d u sJ t        |||      }|j.                  J |j0                  du sJ |j2                  d u sJ t        |||
      }|j.                  J |j0                  J |j2                  J y )!Nr   xyznTnegativen_nnnonnegativenn_ppositivep_np)nonpositivenp_rreal              d   c                  h    t        t               t                     j                   t              S N)r   r   r   subsr   r   s   f/var/www/html/venv/lib/python3.12/site-packages/sympy/functions/elementary/tests/test_miscellaneous.py<lambda>ztest_Min.<locals>.<lambda>i   #    s3q63q62771=     c                       t        t              S r>   r   r    rD   rA   rB   ztest_Min.<locals>.<lambda>j   
    s1v rD   c                  $    t        t               S r>   rF   r@   s   rA   rB   ztest_Min.<locals>.<lambda>k       s1ay rD   c                  8    t        t        j                         S r>   )r   r	   ComplexInfinityr@   s   rA   rB   ztest_Min.<locals>.<lambda>l   s    s1#4#4a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      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q!9>>S!R   r1:Q###q!9>>q!9>>q":??r1:??q!9>>q!9>>q":??r1:??r2;"r1:q":r2;"r2;"r1:q":r2;"r2;"q!9>>q":??r1:??q!9>>q!9>>q":??r1:??r2;"S"a   q":R###r2;"r2;"q!9>>q":??r1:??r2;"q":??c!!!r3<###r3<###q":??c!!! 5AJJq6Q;;q!9Aq	!!!q!Q<3q!Q<'''q#a)Aq!,,,q#a"+#a)+++q"aAr"a'''r2q>Rq"b!Q"c!Rj000q!Q2r1aR0CAq"4EEEEq!Q?c!Ql***tS$1a(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 	Ar2qA==E!!!u$$$==D   Ar
A==D   t###==E!!!AsBA==   t###==E!!!B1A==   ###==   rD   c                  F
  
 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        
            j                  
d      t        d      k(  sJ t        t        
      t        
            j                  
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
      j!                  
      t#        
dz
        k(  sJ t        
d      j!                  
      t#        
dz
        k(  sJ t        
dz  d
z   d      j!                  
      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%                         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 y )Nr   r   r"   Tr#   r%   r&   r'   r*   r+   r-   r1   r2   r4   r5   r7   r9   r:   r;   r<   c                  h    t        t               t                     j                   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#4#4a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	$BsAq!9>> 5A&&&&&q6Q;;q!9Aq	!!!q!Q<3q!Q<'''q#a)Aq!,,,q#a*Q***q2#r1a C1I---q2#r1"""q!QB3 2 2B1=Q1MMMq!Q?c!Ql***q!a%Q1q5(((tS$1a(C1dO;;;s1vs1v#c!fc!f"5555s1vs1v##Aq)SV333s1vs1v##Aqvv.#aff+===
:=>
:~&
:()
:89q2#rAq!SAY...q2#rAt$At444q!9>>!	!a% 0000q!9>>!	!a% 0000q!tQUA##A&	!IadSAE]*++
AAq!t$q(
)	** * * 	Aq	A335::!Q 	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 ]  }t        j                  |
d      D ]  \  }} |||      j
                  sJ |j                  r!|j                  r |||      j                  sDJ |j                  r!|j                  r |||      j                  sJ  |||      j                  J |j                  r!|j                  r |||      j                  sDJ |j                  r!|j                  r |||      j                  sJ  |||      j                  J |j                  r!|j                  r |||      j                  sDJ |j                  r!|j                  r |||      j                  sJ  |||      j                  J |j                  r!|j                  r |||      j                  sJJ |j                  du r%|j                  du r |||      j                  du sJ  |||      j                  J |j                  r!|j                  r |||      j                  sJJ |j                  du r%|j                  du r |||      j                  du sJ  |||      j                  J |j                  r#|j                  r |||      j                  rJ |j                  du r'|j                  du r |||      j                  du rJ  |||      j                  J   y )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      sH   sAs.Asd3AsT"Ast$AsT51AsD!AsAsAs$A1aAq!Q*ESz 42JJuQ/ 3	2DAq q!9$$$$ ~~!..1ay----$$)<)<1ay22221ay--555 }}1ay,,,,Q__1ay....1ay,,444 ||1ay++++Q__1ay....1ay++333 xxAHH1ay''''U"qxx5'81ay''50001ay''/// yyQYY1ay((((e#		U(:1ay((E1111ay((000 zzajj1ay))))u$u)<1ay))U2221ay))111g3	242rD   c                     t        dd      } t        t        |       |       t        |       k(  sJ t        t        |       |       | k(  sJ t	        t        |       |       | k(  sJ t	        t        |       |       t        |       k(  sJ y )Nr   Tr2   )r
   r   r   r   r   r@   s    rA   test_issue_8413r     s|    sA uQxuQx'''wqz1"""uQxq   wqz1+++rD   c                  z   ddl m}  t        dd      }t        dd      }t        dd      t	        d      k(  sJ t        dd      dk(  sJ t        dd	      dt        dd	      z  k(  sJ t        dd	      t        d      k(  sJ t        dd
      dt        dd      z  dz  k(  sJ t        dd      dk(  sJ t        dd      t	        d      t        z  k(  sJ t        dd      dk(  sJ t        | d      t	        |       k(  sJ t        | d      | k(  sJ t        | d	      | t        dd	      z  k(  sJ t        | d	      t        |       k(  sJ t        | d
      | t        dd      z  k(  sJ t        | |      | d|z  z  k(  sJ t        | |       | d|z  z  k(  sJ t        | ||      dd|z  |z  z  | d|z  z  z  k(  sJ y )Nr   r@   r"   Trm   rq   r7   r9      r5   r4   r8   )rN   r   r
   r   r   r   r   r   )r   r"   rq   s      rA   	test_rootr   !  s   sD!AsD!A1:a   1:??1:HQN****1:a   2;!Xa^+A----A;"A;$q'!)###A;"1:a   1:??1:HQN****1:a   2;!Xb!_,,,,1:QqS!!!A2;!bd)###1a=R1Q3q5M!ac(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        ||      }|j                  ddd      dk(  sJ |j                  ddd      dk(  sJ |j                  t        dd      t        t              k(  sJ |j                  ddd      t        d      k(  sJ |j                  t        dd      t        t              k(  sJ y )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T"a[!d1aj[000S!$$$sAsA!QA66#$***66"#q((( 66"#tAw...66#$R00066"#tAw...rD   c            
         t        d      } | st        d       t        d      }t        |t	        t        ||dz
  z        d      d      }t        t              5   || j                  d            dk  sJ 	 d d d        y # 1 sw Y   y xY w)Nnumpyznumpy not installed.r   r7   r   r   )	r   r   r
   r   r   r   r   RuntimeWarningarray)r   r   rM   s      rA   test_issue_11463r   T  s|    '"E#$sAIs1ac7|a0':A 
	( 'R!B&&&' ' 's   B  B	c                     ddl m}  t        d|       j                  t              | t	        |       z  k(  sJ t        d|       j                  t              | t	        | dz
        z  dt	        |  dz         z  z   k(  sJ t        d| dz   d| z        j                  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|       j                  t              | t	        |        z  k(  sJ t        d|       j                  t              | t	        |  dz         z  dt	        | dz
        z  z   k(  sJ t        | |  d      j                  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 y )Nr   r@   r   r7   r8   )rN   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
,   q1"b>!!),	)BqD/)QBF++	)AaC.1q5))	*
Iqb1f
iA.
.	// / /rD   c                     ddl m}  ddlm}  | dd      \  }}}}} | d      \  }}}	t	        ||      j                  |       ||||k\  f|df      k(  sJ t	        |||      j                  |       ||||k\  ||k\  z  f|||k\  f|df      k(  sJ t	        ||||      j                  |       ||||k\  ||k\  z  ||k\  z  f|||k\  ||k\  z  f|||k\  f|df      k(  sJ t        ||      j                  |       ||||k  f|df      k(  sJ t        |||      j                  |       ||||k  ||k  z  f|||k  f|df      k(  sJ t        ||||      j                  |       ||||k  ||k  z  ||k  z  f|||k  ||k  z  f|||k  f|df      k(  sJ t	        ||      j                  |       ||||k\  f|df      k(  sJ t        |	||      j                  |       ||	|	|k  |	|k  z  f|||k  f|df      k(  sJ y )Nr   )symbols)	Piecewisez	x y z a bTr2   zvx vy va)sympy.core.symbolr   $sympy.functions.elementary.piecewiser   r   r   r   )
r   r   r   r    r!   rd   bvxvyvas
             rA    test_rewrite_MaxMin_as_Piecewiser   s  s   )>Kd3MAq!Q$JBBq!9Y'9aa[1d)+LLLLq!Q<	*iQ!VQ<O8PSTVW[\V\R]`acg_h.iiiiq!Q?""9-AQ1PQ6?RVW[\V\?];^	
Q!VQ 1a1f+4y2: : : :q!9Y'9aa[1d)+LLLLq!Q<	*iQ!VQ<O8PSTVW[\V\R]`acg_h.iiiiq1a##I.9a!q&QRSVATXY]^X^A_=`	
Q!VQ 1a1f+4y4: : : : r2;y)YB"H~Dz-RRRRr2r?""9-BrbTVh@W;X[]_aeg_gZhkmosjt1uuuurD   c                     ddl m} m} | d|di}t        | |      j	                  |      t        | |      j                  |      j	                         k(  sJ t        | |      j	                  |      t        | |      j                  |      j	                         k(  sJ ddlm} t        d      D ]  }|  |dd	      | |dd	      i}t        | |      j	                  |      t        | |      j                  |      j	                         k(  sJ t        | |      j	                  |      t        | |      j                  |      j	                         k(  rJ  y )
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     sC   "amOq!9???0Aq	'--/0 0 0q!9???0Aq	'--/0 0 0 *2Y 5wtS11gdC6HI1ay$451INN+,2245 	5 51ay$451INN+,2245 	5 5	5rD   c            	         ddl m} m}m} t	        | ||t        | |            t	        | ||      k(  sJ t	        | |t        | ||            t	        | |      k(  sJ t	        | |t        | |            t	        | |      k(  sJ y Nr   rd   r   c)rN   rd   r   r   r   r   r   s      rA   test_issue_12638r     sw    !!q!QAq	"c!Ql222q!SAq\"c!Qi///q!SAY3q!9,,,rD   c                  x    ddl m} m}m} t	        t        | |      t        | ||            t        | |      k(  sJ y r   )rN   rd   r   r   r   r   r   s      rA   test_issue_21399r     s1    !!s1ay#aA,'3q!9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 ]M  } || |||            |k(  sJ  || || ||||                   || || |||                  k(  sJ ||}}O t        |t        ||      t        | ||            t        |t        |t        |t        | |                        k(  sJ y )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     s   ''q#a)!!!q#a)!!!s1ay#a)$As1ay(9999s3q!9c!Qi(--.Aq	3q!93   s1ay#a)Q'3	3q#a),   qA1X AaG}!!!Aa1a$%1a1Q7m)<<<<!1 q#a)SAq\*c	3q#aQ#$/& & & &rD   c            	          ddl m ddlm ddlm} m}m}m} fd} |t        | |              |t        | |              |t        | ||              |t        t        ||       t        ||                   y )Nr   )permutations)Abs)r   r    r!   r   c                 *   | j                   }| j                        }|j                  t        t              rJ  t        t        |                  D ]<  }t        t        ||            }|j                  |      | j                  |      k(  r<J  y r>   )
free_symbolsr   hasr   r   r   lendictzipxreplace)rX   freerd   rl   repsr   r   s        rA   testz!test_rewrite_as_Abs.<locals>.test  sy    ~~IIcN55c?""eCI./ 	8AD!%D::d#qzz$'7777	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 	QOQOQ1SAYAq		"#rD   c                  b   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      j                  t              dk(  sJ t        d
dd      j                  t              dk(  sJ y )Nr5   FevaluateTg      @   r9   r   r7   r   )

isinstancer   r   r   r   r	   rQ   r   r   r   rG   rD   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<<<rD   c                  t    ddl m}  t        d      } | ||      } |j                  |j                   |k(  sJ y )Nr   )Lambdar   )sympy.core.functionr   r
   rO   rT   )r   r   eqns      rA   test_issue_6899r     s6    *sA
A,C388SXX#%%%rD   c                     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 y )
Nr   r   r4   r   r7   r   r8   r9   )rN   r   r    r   r   s     rA   test_Remr     s    q!9>>r1:q":??r2;"q!tQ<3q!tQ<'''s2qzA~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k7  sJ t        ddd	      j                  d
k(  sJ t        d|d	      |k7  sJ t        d|d	      j                  d|fk(  sJ t        d|d	      dk7  sJ t        d|d	      j                  d|fk(  sJ  | d	      5  t        dd      dk7  sJ t        dd      j                  d
k(  sJ t        d|      |k7  sJ t        d|      j                  d|fk(  sJ t        d|      dk7  sJ t        d|      j                  d|fk(  sJ 	 d d d        y # 1 sw Y   y xY w)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!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   4B	GG)<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     % ( . .   " $ ( 6 >K K K = = - > >z!z?"DA2H,38/.
'/$v&5$-5
&"$ 
=&'(rD   