
    sg6A                     X   d dl mZ d dlmZ d dlmZmZmZmZ d dl	m
Z
 d dlmZ d dlmZmZ d dlm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mZmZ d dl m!Z! d dl"m#Z#m$Z$ d dl%m&Z'm(Z)m*Z+ d Z,d Z-d Z.d Z/d Z0d Z1d Z2d Z3d Z4d Z5e$d        Z6e$d        Z7d Z8d Z9d Z:d Z;y )!    )Tuple)
Derivative)IRationaloopi)S)symbols)explog)sqrt)cos)gamma)appellf1hypermeijerg)O)xzk)limit)raisesslow)random_complex_numberverify_numericallytest_derivative_numericallyc                  t    t        ddt        dz        } | j                  t              | dz  t        z  k(  sJ y )N    )r   r   diff)ps    [/var/www/html/venv/lib/python3.12/site-packages/sympy/functions/special/tests/test_hyper.pytest_TupleParametersBaser#      s2    b"adA66!9!A    c            	      J   t        t        d        t        ddt              t        t	        dd      t	        d      t              k(  sJ t        ddt              t        dd	t              k(  sJ t        ddt        d
      } | j
                  t	        ddd      k(  sJ | j                  t	        dddd      k(  sJ t        ddt              }|j
                  t	        dd      k(  sJ |j                  t	        ddd      k(  sJ |j                  t        k(  sJ |j                  du sJ t        ddt              }|j
                  t	        dd      k(  sJ |j                  t	        ddd      k(  sJ |j                  t        k(  sJ |j                  du sJ t        t        t	               t	               t              t        t              t              sJ t        t        t        dt	        d      t               z  t        dt        z         t              sJ t        t               t               t               ft               t               ft              }t        |t              sJ t        d      \  }}}}}t        ||f|||ft              j                  t              ||z  ||z  |z  z  t        |dz   |dz   f|dz   |dz   |dz   ft              z  k(  sJ t        t        gg t              j                  t              t!        t        t        gg t              t              k(  sJ ddlm} t         |t              g |t&              g |t(                    t        t        gt&        g |t(                    k(  sJ t        ddt        d
      j*                  t        u sJ y )Nc                  $    t        ddt              S )N   r   )r   r   r   r$   r"   <lambda>ztest_hyper.<locals>.<lambda>   s    eAq!n r$   )r   r'   r'   r'   r   )r   r'   r   )r'   r   r'      r   r'   r*   Fevaluater*   r'   r   r*         r1   r2   T)r1   r*   r2   )r'   r'   z
a1:3, b1:4r   
polar_lift)r   	TypeErrorr   r   r   apbqargumentis_commutativetnr   r   randcplxtdr
   r    r   $sympy.functions.elementary.complexesr4   r   r   func)uha1a2b1b2b3r4   s           r"   
test_hyperrF      s   
9,-q!U5A;a!%DDDDL!,dFA0FFFFiq59A445Aq>!!!445Aq!$$$$fi#A445A;445Aq>!!!::??t###fi#A445A;445Aq>!!!::??t### eEGUWa(#a&!444afeAh++SQZ;;; 		XZ,xz8:.F	KAa8O8 .BBB"bBB<+003
2r"uRx5"q&"q&!1BFBFBF3KQOOP P P !b!!!!$
5!b!3Da(HHHH @*Q-:a=/:a=AqcA3
1&' ' '
 q5166%???r$   c            	      <   ddl m} m}m} ddlm} t               t               t               dz   }}} |t        | |g|gd            t        |      t        |  |z
  |z         z  t        |  |z         t        | |z         z  z  k(  sJ t         |t        ||g|gd            j                         t        ||g|gd      j                         z
        dk  sJ  |t        g g t                    t        t              k(  sJ  |t        g dg t                    t        g dg t              k(  sJ  |t        ddgg gdgdggt                    t        t        dz         k(  sJ  |t        ddgg gg g gt                    t        ddgg gg g gt              k(  sJ y )Nr   )abc)expand_funcr2   r'   绽|=r'   r   r*   )	sympy.abcrH   rI   rJ   sympy.core.functionrK   r;   r   r   absnr   r   r   r   )rH   rI   rJ   rK   rA   rC   c1s          r"   test_expand_funcrS   I   s   !!/XZaBBuaVaS!,-arAvz""E1"q&M%Q-$?@A A A{5"bB434668Bx"q)++-. /167 7 7 uRQ'(CF222uYA./5B3JJJJwA|qcA3Z;<AE
JJJwA|b"Xq9:!Qr2h*+ + +r$   c                     ddl m} | j                  |      }|s| S t        |      dk(  sJ | j	                  |j                         |i      S )Nr   Dummyr'   )sympy.core.symbolrV   atomslenxreplacepop)exprsymrV   dums       r"   replace_dummyr_   [   sE    '
**U
Cs8q====#'')S)**r$   c                  f   ddl m}  ddlm} ddlm}m}  |d      }t        t        ddt              j                  |       |       | t        |z   ||      z   |d|      z   |d	|      z  |dt        f      k(  sJ t        d
dt              j                  |       t        d
dt              k(  sJ y )Nr   )SumrU   )RisingFactorial	factorialr   r/   r,   r   r*   rM   )r*   )sympy.concrete.summationsra   rW   rV   (sympy.functions.combinatorial.factorialsrb   rc   r_   r   r   rewriter   r   )ra   rV   rb   rc   _ks        r"   test_hyper_rewrite_sumri   d   s    -'U	sBvvq199#>CArEIbM!OAr$::Ar"#%'BK	11 1 1 GQ'//4i!$% % %r$   c                     t        ddgt              j                  dk(  sJ t        dddgt              j                  t        u sJ t        ddgt              j                  dk(  sJ t        ddgt              j                  t        u sJ t        dd	gt              j                  dk(  sJ t        d
dgt              j                  t        u sJ t        dddgt              j                  dk(  sJ t        g dddgt              j                  dk(  sJ t        ddgddgt              j                  t        u sJ t        g ddgt              j                  dk(  sJ t        dg t              j                  t        u sJ t        ddgdgd      j                  dk(  sJ t        ddgdgd      j                  dk(  sJ t        ddgdgd      j                  dk(  sJ t        ddgdgd      j                  dk(  sJ y )Nr/   r*   r'   r1   rM   r   )r   r'   r   )rd   r'   r   )rd   r   rd   )rd   r   rl   )rd   r'   r*   r   )rd   r   r*   r1   TF)r   r   radius_of_convergencer   convergence_statementr   r$   r"   test_radius_of_convergencero   q   s   !a 66!;;;!Q#99R???QC#99Q>>>QC#99R???bT1%;;q@@@rdA&<<BBB2r(A&<<AAAb!Wa(>>!CCC"a2q'1%;;rAAAbT1%;;q@@@A&<<BBB!Q!a 66$>>>!Q!a 66%???!Q!b!774???!Q!b!775@@@r$   c                     t        t        d        t        t        d        t        ddt              t        t	        dd      t	        d      t	        d      t	        d	      t              k(  sJ t        d
dddt              } | j
                  t	        dd      k(  sJ | j                  t	        ddddd	      k(  sJ | j                  t	        ddd	      k(  sJ | j                  t	        dddd      k(  sJ | j                  t	        ddddddddd	      k(  sJ | j                  t	        ddddd      k(  sJ | j                  t        k(  sJ | j                  dk(  sJ | j                  dk(  sJ | j                  du sJ | j                  du sJ t        g g gt         j"                  gdggd      j                  du sJ t        ddgdgdgd	gt              j                  t         j"                  k(  sJ t%        t        t	               t	               t	        d      t	               t               t'        t              t              sJ t%        t)        t*              t        t	               t	               t	        d      t	        t         j"                        t        dz  dz        z  t-        t              t              sJ t%        t        t	        dd      t	               t	        d      t	        d      t              t/        dt        z         t              sJ t        t0        d        t        t0        d        t        t3               ft3               dt4        z  z   ft	               t3               t3               ft              } t7        | t              sJ t        t	               t3               ft	               t3               t3               ft              } t7        | t              sJ t        t	               t	               t	        t3                     t	        t3               t3                     t              } t7        | t              sJ t9        d      \  }}}}}}}}t        ||f||f||f||ft              j;                  t              t        |dz
  |f||f||f||ft              |dz
  t        ||f||f||f||ft              z  z   t        z  k(  sJ t        t        t        gg g g t              j;                  t              t=        t        t        t        gg g g t              t              k(  sJ ddlm }	 t         |	|      g |	|      g |	|      g |	|      g |	t                    t        |g|g|g|g |	t                    k(  sJ dd l!m"}
m#}m$}m%}m&} t        |
g|g|g|gt              jO                  |      t        |z  tQ        ||z
        z  tQ        |
 |z   dz         z  tQ        ||z
        tQ        | |z   dz         z  z  k(  sJ y )!Nc                  "    t        dt              S )Nr'   r   r   r   r$   r"   r(   ztest_meijer.<locals>.<lambda>   s    gam r$   c                  &    t        dddt              S )N)r)   r+   r*   r1   rr   r   r$   r"   r(   ztest_meijer.<locals>.<lambda>   s    glD$B r$   )r/   rt   )ru   )r2   r'   r   r*   r1   r2   r/   r0   )         	   )
               rv   rw   rx   ry   rz   r{   r|   r}   r~   K   rd   TFr   c                  2    t        dt        fdft              S )N)r*   r'   r+   r   r   )r   r   r   r   r$   r"   r(   ztest_meijer.<locals>.<lambda>   s    w~vJ r$   c                  $    t        ddt              S )Nr   )r)   r   )r   r   r   r$   r"   r(   ztest_meijer.<locals>.<lambda>   s    w~~qI r$   za1:3, b1:3, c1:3, d1:3r3   )rH   rI   rJ   ds))r   r5   r   r   r   anr6   aotherbmr7   botherr8   nudeltar9   	is_numberr	   Halfr:   r   r   r   r   r   
ValueErrorr;   r   r<   r
   r    r   r=   r4   rN   rH   rI   rJ   r   r   	integrandr   )grA   rB   rC   rD   rR   c2d1d2plrH   rI   rJ   r   r   s                  r"   test_meijerr      s;   
9+,
9BC><3aU1XuQxq1=> > > 		<1EqIA445A;445Aq!Q''''88uQ1~%%%445Aq!$$$$445Aq!RRR888888uRRR0000::??442::77b==t###;;%Br7affXqcNA.88D@@@Aq6A3aS!,22aff<<< geguwa%'A2>AJJJd2hwuw$Qxqvv1Q@ @ADQL L LgeAqk57E!HeAhB!a%j!   :JK
:IJ 	
QqS 02EGXZ(!	-Aa8O8(*XZ(!	-Aa8O8%
"3hj(*-q	2Aa8O8%,-E%F"BBBBB8b"XBx"b1=BB1E	"q&"Bx"bB8Q	?FGRHr2hR2r(AFF
GHI	JJ J J Aq62r2q)..q17Aq62r2q1156 6 6 FBrF8bfX2x"R&2a5ArdRD2$1./ / / ('A3aS1#q)33A6	1U1q5\%Q
++U1q5\%Q
:K-KLM M Mr$   c                  D   t        g ddgddt        gg t              j                  t              t	        t              t        g ddgddt        gg t              z  dt        g g dddt        dgg t              z  z   k(  sJ t               } d}t        t        t        gg g g |       t              sJ t        t        t        dz  gg g g |       t              sJ t        t        g t        gg g |       t              sJ t        t        g g t        gg |       t              sJ t        t        g g g t        g|       t              sJ t        t        t        g|g|dz   gg |       t              sJ t        t        t        g|dz   g|gg |       t              sJ t        t        t        |gg g |dz   g|       t              sJ t        t        t        |dz   gg g |g|       t              sJ t        dd      }t        t        |dz   g|g|dz
  t        g|g|       t              sJ y )Nr'   r   r   )r'   r'   r'   r2   r*   )r   r   r   r    r   r;   r<   r   )yrH   rI   s      r"   test_meijerg_derivativer      s   21v1ay"a055a8AwrAq6Aq!9b!44
GB	Aq!Q<Q7
7	88 8 8 	
A	Agqc2r2q)1---gq!tfb"b!,a000gb1#r2q)1---gb"qc2q)1---gb"b1#q)1---gqcA3QQ/333gqcAE7QCQ/333gq!fb"q1ugq11555gq!a%j"b1#q11555AAgq1ugsQUAJQ7;;;r$   c                  j   t        g dgdgg t              j                         dt        z  k(  sJ t        dgg g dgt              j                         dt        z  k(  sJ t        g g dgg t              j                         dt        z  k(  sJ t        g g dgt        j
                  gt              j                         dt        z  k(  sJ t        g g t        j
                  gdgt              j                         dt        z  k(  sJ t        ddgg dgdgt              j                         t        u sJ y )Nr'   r   r   r1   )r   r   
get_periodr   r	   r   r   r   r$   r"   test_meijerg_periodr      s   2sQCQ'224"<<<A3BQ'224"<<<2rA3A&113qt;;;
BaffXq"",*,!B$7 7 7
B1#q"",*,!B$7 7 7Aq62sQC+668B>>>r$   c                     ddl m}   | dt        z  t        z        t        z  }t        }t        g g |      j                  |k(  sJ t        dgg |      j                  |k(  sJ t        dgdg|      j                  |k(  sJ t        ddgdg|      j                  |k(  sJ t        ddgdg | dt        z  t        z              j                  dk(  sJ y )Nr   	exp_polarr   r'   )&sympy.functions.elementary.exponentialr   r   r   r   r   r8   )r   rH   rI   s      r"   test_hyper_unpolarifyr      s    @!B$q&!A	AR$$)))!b!%%***!qc1&&!+++!Q!a ))Q...!Q!i"Q/099Q>>>r$   c                  h	   ddl m} m}m}m}m}m}m}m}m	}m
}	m}
m} ddlm ddlm} t#        d      \  } G fdd|       } ||      j%                  d       |dt'        |      d	kD  fd
f      k(  sJ  | t(        t*        z        |z        j%                  d       |dt'        |      d	kD  fd
f      k(  sJ  | dt(        z  t*        z        |z        j%                  d       |t'        |      d	kD  fd
f      k(  sJ  | dt(        z  t*        z        |z        j%                  d       |t'        |      d	kD  fd
f      k(  sJ  | dt(        z  t*        z        |z        j%                  d       |dz  t'        |      d	kD  fd
f      k(  sJ  | dt(        z  t*        z        |z        j%                  d       |dz  t'        |      d	kD  fd
f      k(  sJ  ||      j%                  d      k(  sJ  | t(        t*        z        |z        j%                  d      k(  sJ fd}t-        d	d       | ||      t/        t0        j2                  d	gt-        dd      g|      |      sJ  | ||      t/         gg |      |      sJ  | ||      t/        t0        j2                  z
  gdz  g|      |      sJ  | ||      | t/        d	d	gdg|      z  |      sJ  | ||      t/        t0        j2                  t0        j2                  gt-        dd      g|      |      sJ  | ||      t/        d	d	gt-        dd      g|      |      sJ  | ||      t/         t0        j2                  z
  gt0        j2                  g|      |      sJ  | ||      d|z  dz  d	z   z  t/         t0        j2                  z
   gt0        j2                  g|      j5                  |      z  |      sJ  | |	|      | dz  t/        t-        dd      d	d	gddg|      z  |      sJ  | |
|      t/         gt0        j2                  g|      |      sJ  | ||      dz  |z  t/        d	z
  d	z   gt-        dd      g|      z  |      sJ y )Nr   )HyperRepHyperRep_atanhHyperRep_power1HyperRep_power2HyperRep_log1HyperRep_asin1HyperRep_asin2HyperRep_sqrts1HyperRep_sqrts2HyperRep_log2HyperRep_cosasinHyperRep_sinasinr   )	Piecewisez	a b c d zc                   ^    e Zd Ze fd       Zefd       Zefd       Zefd       Zy)test_hyperrep.<locals>.myrepc                     S Nr   )clsr   rH   s     r"   _expr_smallz(test_hyperrep.<locals>.myrep._expr_small       Hr$   c                     S r   r   )r   r   rI   s     r"   _expr_small_minusz.test_hyperrep.<locals>.myrep._expr_small_minus  r   r$   c                     |z  S r   r   )r   r   rQ   rJ   s      r"   	_expr_bigz&test_hyperrep.<locals>.myrep._expr_big      Q3Jr$   c                     |z  S r   r   )r   r   rQ   r   s      r"   _expr_big_minusz,test_hyperrep.<locals>.myrep._expr_big_minus	  r   r$   N)__name__
__module____qualname__classmethodr   r   r   r   rH   rI   rJ   r   s   r"   myrepr      sQ    		 
	 
	 
	 
	 
	 
	 
	r$   r   nonrepr'   Tr   r*   r1   r2   nonrepsmallc           
         t        | j                  d      |t        dd      t        dd      t        j                  t        j                        syt        | j                  d      j                   t        t        z        z        j                  t              | j                   t        t        z        z        j                  d      t        dd      t        dd      t        j                  t        j                        sy| j                   t        t        z        z        j                  d      }t        |j                  d      j                         |j                  d      j                         z
        d	kD  ryfd
}dD ]  } || dt        z  t        z  |z  t        t        z  dz        } || dt        z  t        z  |z  t        t        z  z   t         t        z  dz        }t        ||      s y || dt        z  t        z  |dz   z  t         t        z  dz        } || dt        z  t        z  |z  t        t        z  z   t        t        z  dz        }t        ||      r y y)z2 Test that func is a valid representation of hyp. r   rd   r   r   Fr   g     ?g?rL   c                     | j                   |      z        j                  d      }|j                   |      z        j                  t              S )Nr   )subsrg   replacer   )r>   rH   rI   rvr   r   s       r"   dosubsz(test_hyperrep.<locals>.t.<locals>.dosubs-  sL    1il1n-55h?B771il1n-55iEEr$   )	r   r'   r   r*   r1   rd   rl   rk   r'   T)r:   rg   r   r	   r   r   r   r   r   r   rP   rQ   )	r>   hypr   r\   r   rQ   expr1expr2r   s	     `     r"   tztest_hyperrep.<locals>.t  s    $,,}-sAROxA!&&AFFLLL',,9QrT?1$&&-gi&=IIa1R4*+33MBXb!_Q166QVV	M
 yyIadOA-.66x@tyyI&((*TYYq)-D-F-F-HHIEQ	F 1 	A41R1R462E41RAbD1"R%':EeUA&41RQ!Bq9E41RAbD!B$q&9EeUA&	 r$   rl   )sympy.functions.special.hyperr   r   r   r   r   r   r   r   r   r   r   r   r   r   $sympy.functions.elementary.piecewiser   r
   rg   rP   r   r   r   r   r	   r   r    )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rH   rI   rJ   r   r   s                   @@@@@r"   test_hyperrepr      s   , , , ,
 A>K(MAq!Q    8H%As1vz?QI)NNNN1R4"#++H51c!fqj/At9-. . .1Q3r6"1$%--h71c!fqj/At9-. . .1Q3r6"1$%--h71c!fqj/At9-. . .1Q3r6"1$%--h71Q3A
#aY/0 0 01Q3r6"1$%--h71Q3A
#aY/0 0 08M*a///1R4"#++M:a???D 	AA^AqvvqkHQN3CQ GKKK_Q"EA2$A$6:::_Q"E1a!&&j/AaC5!$DaHHH]1r%AQ"77;;;^Aqvvqvv&6!Q8H! LaPPP^Aq!fx1~.> BAFFF_Q"EA2qvvz*:QVVHa$H!LLL_Q"T1Q37^EA2;"3affXqAFFqII1N N N]1r!tE8Aq>1a*@1a&!$LLaPPPa#UQB7QVVHa%@!DDDa#QqSU5!a%Q(1a.AQST+U%UWXYYYr$   c                  8   ddl m}  ddlm} ddlm} t               }t         | t        t        z  t        z        z  }t        t        g |dz   dz  gg|dz  g| dz  |dz   dz  gg|dz  dz        z  } |||      }dD ]h  }d	D ]a  }t        ||z
  j                  t        |t        |i
            dk  sJ t        ||z
  j                  t        |t        | i
            dk  raJ  j d}	|j                  t        |      }dD ]  }dt        dd      ddt        dd      ddfD ]r  }t        ||z
  j                  t        |t        ||	z   |||	z
  i
            dk  sJ t        ||z
  j                  t        |t        | |	z   || |	z
  i
            dk  rrJ   t        dd | t         t        z        dz        t        dd | t        t        z        dz        z   dt!        t              z  z  }
|
t        t#        d      z  z
  j                  d      dk(  sJ y )Nr   r   )besseli)lr'   r   r1   )      ?      ?)g        g?g333333?r   g?r'   g/$@g.@)r   rL   gvIh%<=r   r*   g      ?g      ?g      ?r   ))r   r   ))r   r   r   r   T)chop)r   r   sympy.functions.special.besselr   rN   r   r;   r   r   r   r   r   rP   rQ   r   r   r   r   )r   r   r   rH   argr   r   x_k_epsr\   s              r"   test_meijerg_evalr   K  si   @6
A
Iad1f
Cwa!eQYK(AaC5A2a4!a%2C*Dc1fQhOOEAsOE  H; 	HB((q"an(=>FFF((q"a"o(>?%GGG	HH CJJq!E JAdHQNCM 	JB((ArCxBH= ) ? @BGH H H((AsSy!bS3Y? ) A BDIJ J J	JJ L"5y!B7G7IJl$71R49JKL
DH*D 2c!f9T*a///r$   c                  "   t        d      \  } }t        dt        dd      t        dd      f| dz        j                  |       dd| dz  z  d	z  z   d
| dz  z  dz  z   t	        | dz        z   k(  sJ t        dt        dd|      z  |d      dk(  sJ y )Nzk, xr)   r1   r*   r2   r   r'   ry      Q   i`  rv   r   )r
   r   r   seriesr   r   )r   r   s     r"   test_limitsr   k  s    6?DAqAA7A>EEaHqAvby=2ad74<'!AqD'12 2 2 5q))1a0A555r$   c            	         t        d      \  } }}}}}t        | |||||      t        | |||||      k(  sJ t        | |||||      t        | |||||      k(  sJ t        | |||t        j                  t        j                        t        j                  u sJ t        | |||t        j                  t        j                  d      }|j
                  t        u sJ |j                         t        j                  u sJ y )Nza b1 b2 c x yFr-   )r
   r   r	   ZeroOner>   doit)rH   rC   rD   rJ   r   r   fs          r"   test_appellf1r   t  s     1Ar2q!QAr2q!Q'8Ar2q!Q+GGGGAr2q!Q'8Ar2q!Q+GGGGAr2q!&&!&&1QUU:::BAqvvqvv>A66X668quur$   c                     ddl m}  t        d      \  }}}}}}} | t        ||||||      |      ||z  t        |dz   ||dz   |dz   ||      z  |z  k(  sJ  | t        ||||||      |      ||z  t        |dz   ||dz   |dz   ||      z  |z  k(  sJ  | t        ||||||      |      dk(  sJ  | t        ||||||      |      t	        t        ||||||      |      k(  sJ y )Nr   )r    za b1 b2 c x y zr'   )rO   r    r
   r   r   )r    rH   rC   rD   rJ   r   r   r   s           r"   test_derivative_appellf1r     s*   (#$56Ar2q!QBAq!,a0AbD!a%RRSVUVYZUZ\]_`9a4abc4ccccBAq!,a0AbD!a%RRSVUVYZUZ\]_`9a4abc4ccccBAq!,a0A555BAq!,a0ZBPRTUWXZ[@\^_5````r$   c                  N   t        d      \  } }}}t        ddt        dz        j                  t        dd       dt        dz  dz  z   t        dz  d	z  z   t        d
z  dz  z   t	        t        dz        z   k(  sJ t        t              j                  t        dd       t        | |f| |ft              j                  t        dd       k(  sJ t        | |f||ft              j                  t        dd       t        | |f||ft              t	        t        dz        z   k(  sJ t        t        d       dz  t        d      dz  fddt        z  t        dz   z        j                  t              dt        z
  t        dz  dz  z   dt        dz  z  dz  z
  dt        dz  z  dz  z
  dt        dz  z  dz  z
  t	        t        d
z        z   k(  sJ t        dz  t        t        d       dz  t        d      dz  fddt        z  t        dz   z        z  j                  t              t        dz  t        t        z  dz  z
  t        t        dz  z  dz  z   dt        z  t        dz  z  dz  z
  dt        z  t        dz  z  dz  z
  dt        z  t        dz  z  dz  z
  t	        t        d
z        z   k(  sJ y )Nza1 b1 a2 b2r/   rM   r   rw   r'   r*   r1      rv   ih  r)      @   ]   r2   rx      )
r
   r   r   _eval_nseriesr   r   r   r	   nseriesr   )rA   rC   rB   rD   s       r"   test_eval_nseriesr     s|   ]+NBBA&44Q4@	AqDF
QT"Wq!tCx'!AqD'12 2 2q6!D)r2hR!$221a>? ? ?"bB8Q'55aDAr2hR!$qAw./ / /1Q4%'1Q46"D!A#q1u+6>>qA	A1Q1a4!Bq!tGBJ.AqD;a1gEF F FqD1a1a($!QU<<EEaH
1r!tAv1a4	!AbDAIaK/"R%1*S.@2b5A:c>QTUVWYZVZT[[\ \ \r$   N)<sympy.core.containersr   rO   r   sympy.core.numbersr   r   r   r   sympy.core.singletonr	   rW   r
   r   r   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   'sympy.functions.special.gamma_functionsr   r   r   r   r   sympy.series.orderr   rN   r   r   r   sympy.series.limitsr   sympy.testing.pytestr   r   sympy.core.randomr   r;   r   r:   r   r<   r#   rF   rS   r_   ri   ro   r   r   r   r   r   r   r   r   r   r   r   r$   r"   <module>r      s    ' * 4 4 " % = 9 8 9 D D     % -' '+@\+$+
%A&@MF<(?? VZ VZr 0 0>6a\r$   