
    sglG                        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
 d dlmZ d dl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mZmZmZmZmZ d d	lmZm Z m!Z! d d
l"m#Z#m$Z$ d dl%m&Z&m'Z'm(Z(m)Z)m*Z* d dl+m,Z, d dl-m.Z. d dl/m0Z0m1Z1m2Z2 d dl3m4Z4m5Z5 d Z6d Z7d Z8d Z9d Z:d Z;d Z<d Z=d Z>d Z?d Z@d ZAd ZBd ZCd ZDd ZEd  ZFe5d!        ZGd" ZHd# ZId$ ZJd% ZKd& ZLd' ZMd( ZNd) ZOd* ZPd+ ZQd, ZRd- ZSd. ZTd/ ZUd0 ZVd1 ZWd2 ZXd3 ZYd4 ZZd5 Z[d6 Z\d7 Z]d8 Z^d9 Z_d: Z`d; Zad< Zbd= Zcd> Zdd? Zed@ ZfdA ZgdB ZhdC ZidD ZjdE ZkdF ZldG ZmdH ZndI ZodJ ZpdK ZqdL ZrdM ZsdN ZtdO ZudP ZvdQ ZwdR ZxdS ZydT ZzdU Z{yV)W    )AccumBounds)
Derivative	PoleError)EIIntegerRationalpi)S)Symbolsymbols)sign)explog)acoshacothasinhatanhcoshcothsinhtanh)ceilingfloorfrac)cbrtsqrt)asincoscotsintan)limit)O)xyz)raisesXFAILc                     t        j                  t         d      t         k(  sJ t        j                  t         d      t        k(  sJ dt         t        z  z  j                  t        d      dt         t        z  z  k(  sJ t        dd      j                  t         d      t        dd      k(  sJ t        j                         t         k(  sJ y )N   n         )r%   nseriesr&   r	        R/var/www/html/venv/lib/python3.12/site-packages/sympy/series/tests/test_nseries.pytest_simple_1r5      s    99Q!!!!99Q!!!!qsGQ!$1Q3///Aq>!!!q!)Xa^;;;99;!r3   c                      t         t        t               z  j                  t         d      t         t        t               z  k(  sJ y )Nr+   r,   )r%   r   r1   r2   r3   r4   
test_mul_0r7      s0    c!fHa1%3q6111r3   c                     t         t        dt         z         z  j                  t         d      t         t        d      z  t         dz  dz  z   t         dz  dz  z
  t         dz  dz  z   t        t         dz        z   k(  sJ t         t        dt         z         z  j                  t         d      t         dz  t         dz  dz  z
  t         dz  dz  z   t        t         dz        z   k(  sJ y )	N   r+   r,   r/      r0      r.   r%   r   r1   r$   r2   r3   r4   
test_mul_1r=      s    c!a%jL!!!q!)Qs1vX1Q->Aa-G	1R.AqD'.   c!a%jL!!	Q " a4!Q$q&=1a46)AadG34 4 4r3   c                      t         dz  j                  t         d      t         dz  k(  sJ dt         z  j                  t         d      dt         z  k(  sJ dt         dz  z  j                  t         d      dt         dz  z  k(  sJ t         t        dd      z  j                  t         d      t         t        dd      z  k(  sJ t        t               dz  j                  t         d      t        t               dz  k(  sJ y )Nr9   r+   r,   r.   r/   )r%   r1   r	   r   r2   r3   r4   
test_pow_0r?   &   s    qD>>!q>!QT)))aC==a= AaC'''adFA#qAv---x1~&&qA&.1hq!n3DEEEGQJQ'DGQJ777r3   c                     dt         z   dz  j                  t         d      t         dz  dt         z  z   dz   k(  sJ t        t               dz   dz  j                  t               dt        t               z  t         z   dz   k(  sJ t        t               t        t               z   dz  j                  t               dt         t	        dd      z  z  t         t	        dd      z  z   t         z   k(  sJ y )Nr.   r9   r+   r,      r/   )r%   r1   r   r   r	   r2   r3   r4   
test_pow_1rB   .   s    UQJQ'1a4!A#:>999 !Wq[1%%a(Ad1gIMA,====!WtAw"++A.!Ax1~4E2E
Xa^
33       r3   c                  p   ddt         z
  z  j                  t         d      dt         z   t         dz  z   t         dz  z   t         dz  z   t        t         dz        z   k(  sJ t         dt         z
  z  j                  t         d      t         t         dz  z   t         dz  z   t         dz  z   t         dz  z   t        t         dz        z   k(  sJ t         dz  dt         z
  z  j                  t         d      t         dz  t         dz  z   t         dz  z   t         dz  z   t         d	z  z   t        t         dz        z   k(  sJ y )
Nr.   r+   r,   r9   r/   r0   rA   r:      r%   r1   r$   r2   r3   r4   test_geometric_1rF   7   s   q1uIqA&!a%!Q$,A*=1*DqAw*NNNNq1uIqA&!ad(QT/AqD*@1a4*G!AqD'*QQQQqD!a%L!!!q!)QTAqD[1a4-?!Q$-F	1.Aw.   r3   c                      t        dt        z         j                  t        d      dt        dz  z   t        dz  dz  z
  t        dz  dz  z   dt        dz  z  d	z  z
  t        t        dz        z   k(  sJ y )
Nr.   r+   r,   r9   r:   r/      r0      r   r%   r1   r$   r2   r3   r4   test_sqrt_1rK   >   sm    A;qA&!ac'AqDF*:QT"W*DqAvcz*QTUVWYZVZT[*[[[[r3   c                     t        t              j                  t        d      dt        z   t        dz  dz  z   t        dz  dz  z   t        dz  dz  z   t        t        dz        z   k(  sJ t        t              j                  t        d	      dt        z   t        dz  dz  z   t        dz  dz  z   t        dz  dz  z   t        dz  d
z  z   t        dz  dz  z   t        dz  dz  z   t        dz  dz  z   t        dz  dz  z   t        dz  dz  z   t        dz  dz  z   t        t        d	z        z   k(  sJ t        dt        z        j                  t        d      t        dt        z        k(  sJ t        ddt        z   z        j                  t        d      t        dt        z
  dt        dz  z  dz  z
  dt        dz  z  dz  z   z  j                         t        t        dz        z   k(  sJ t        dt        z         j                  t        d      t        d      dt        z   t        dz  dz  z   t        dz  dz  z   t        dz  dz  z   z  j                         t        t        dz        z   k(  sJ y )Nr+   r,   r.   r9   r/   rA   r0   r;      x     rD   i  r:   i  	   i 
   i _7    i a   )r   r%   r1   r$   r   expandr2   r3   r4   
test_exp_1rU   B   s@   q6>>!q>!QUQT!V^ad1f%<q!tBw%F1a4%PPPPq6>>!r>"a!ead1fnq!tAv&=1R&G!Q$s(&R	1S'a49' !tEz'*,-qDK'8:;R%-'H	2h'1b5'" " " " qs8A#s1Q3x///q!a%y>!!!q!)	
AEBq!tGAI!Q$q(	)113a1g=> > >q1u:a1%	QQAa!Q$q&(1a472	3;;=!Q$GH H Hr3   c                  B   t        dt        t              z         j                  t        d      t        d      dt        t              z   t        dz  z   t        t              t        z  dz  z   z  j	                         t        t        t              dz        z   k(  sJ y )Nr.   r/   r,   r9   rA   )r   r   r%   r1   rT   r$   r2   r3   r4   test_exp_sqrt_1rW   N   s|    q47{##A#+	QT!Wqs"T!WQYq[0	199;aQ
mKL L Lr3   c                  p   t        t        t        t              z        j                  t        d      dt        t        t              z  z   t        dz  t        t              dz  z  dz  z   t        dz  t        t              dz  z  dz  z   t	        t        dz  t        t              dz  z        z   k(  sJ y Nr0   r,   r.   r9   r/   rA   )r   r%   r   r1   r$   r2   r3   r4   test_power_x_x1rZ   S   s    #a&M""1"*	Ac!fHq!tCFAI~a''!Q$s1vqy.*::Qq!tCFAI~=NNO O Or3   c                  L   t         t         z  j                  t         d      dt         t        t               z  z   t         dz  t        t               dz  z  dz  z   t         dz  t        t               dz  z  dz  z   t        t         dz  t        t               dz  z        z   k(  sJ y rY   )r%   r1   r   r$   r2   r3   r4   test_power_x_x2r\   X   s    qD>>!q>!	Ac!fHq!tCFAI~a''!Q$s1vqy.*::Qq!tCFAI~=NNO O Or3   c                      t        ddt        z  z         j                  t        d      t        t        t              z
  t        dz  dz  z
  t        dz  dz  z   t        dz  dz  z
  t        t        dz        z   k(  sJ y )Nr.   r+   r,   r9   r/   r0   )r   r%   r1   r$   r2   r3   r4   test_log_singular1r^   ]   st    q1Q3w<Q'1s1v:1Q+>Aa+G	1Q,1a4,   r3   c                     ddt         z  t         t        d      t        d      z  z  z   z  } | j                  t         d      t         t        d      t        d      z  dz   z   t         z   t        t         dz        z   k(  sJ y )Nr.   r/   r9   r+   r,   r<   es    r4   test_log_power1rb   b   sl    	QqS1QA''(A99Q!9SVCF]Q%6!7 7! ;a1g EEEEr3   c                      t        d      } ddt        t              z
  z  }|j                  t        d|       dd| z
  z  k(  sJ y )Nlr.   r+   r-   logxr   r   r%   r1   rd   ra   s     r4   test_log_seriesri   g   sA    sA	1s1v:A99Q!!9$1q5	111r3   c                      t        dt        z        } | j                  t        d      t        t               t        d      z   k(  sJ y )Nr+   r,   )r   r%   r1   r`   s    r4   	test_log2rl   m   s9    BqD	A99Q!9Q#b' 1111r3   c                      t        d      } dt        dt        z        z  }|j                  t        d|       d|  t        d      z   z  k(  sJ y )Nrd   r.   rk   r0   re   rg   rh   s     r4   	test_log3rn   r   sH    sA	#bd)A99Q!!9$A2B<(8888r3   c                  z   t        t              } | j                  t        dd      dk7  sJ | j                  t        dd      t        dt              k(  sJ | j                  t        dd      t        t        t              k(  sJ | j                  t        dd      t        t        t        dz  t              z   k(  sJ | j                  t        dd      t        t        t        dz  t              z   k(  sJ | j                  t        dd      t        t        dz  dz  z
  t        t        dz  t              z   k(  sJ t	        t              dz
  t        z  } | j                  t        dd      dt        dz  z   t        dz  dz  z   t        t        dz        z   k(  sJ t        j                  t        dd      t        k(  sJ y )Nr   r.   r9   r/   r0   rA   )r!   r%   r1   r$   r   r`   s    r4   test_series1rp   x   sY   AA99Q1"""99Q11a(((99Q11a(((99Q1Qq!tQZ///99Q1Qq!tQZ///99Q1QT!Va1aj!8888	Q!QA99Q1QqS1a46!1AadG!;;;;99Q1"""r3   c                      t        j                  t         dd      t        dt               k(  sJ t        j                  t         dd      t        t         t               k(  sJ y )Nr   r.   rE   r2   r3   r4   test_series1_failingrr      sD    99Q11a(((99Q11a(((r3   c                      dt         z  j                  t         dd      dt         z  k(  sJ t         dt         z  z   j                  t         dd      t         dt         z  z   k(  sJ y )Nr.   r   r/   )r%   r1   r2   r3   r4   test_seriesbug1rt      sR    aC==Aq!QqS(((!GQ1%QqS000r3   c                     t         dz   dz  j                  t         dd      ddt         z  z
  dt         dz  z  z   dt         dz  z  z
  t        t         dz  t               z   k(  sJ t         dz   dz  j                  t         dd      dt         z
  t         dz  z   t         dz  z
  t        t         dz  t               z   k(  sJ t         dz   dz  j                  t         dd      dk(  sJ t         dz   dz  j                  t         dd      dt         z   k(  sJ t         dz   dz  j                  t         dd      t         dz  dt         z  z   dz   k(  sJ t         dz   dz  j                  t         dd      ddt         z  z   dt         dz  z  z   t        t         dz        z   k(  sJ ddt         z   z  j                  t         dd      dt         z
  t         dz  z   t         dz  z
  t        t         dz  t               z   k(  sJ t         dddt         z  z   z  z   j                  t         dd      ddt         z  z
  d	t         dz  z  z   d
t         dz  z  z
  t        t         dz  t               z   k(  sJ dt         z  dz   dz  j                  t         dd      ddt         z  z   dt         dz  z  z   t         dz  z   k(  sJ dddt         z  z   z  j                  t         dd      t         t         dz  z
  t         dz  z   t        t         dz  t               z
  k(  sJ dddt         dz  z  z   z  j                  t         dd      t         dz  t         dz  z
  t        t         dz  t               z   k(  sJ y )Nr.   r   r0   r9   r/   rk   r+   rM   r;   rA   rE   r2   r3   r4   test_series2xrx      s   UbM""1a+q1Q3w1a4/?!AqD&/H1QPQTST:/UUUUUbM""1a+q1uq!t|ad/BQq!tQZ/OOOOUQJ1a(A---UQJ1a(AE111UQJ1a(AqD1Q3JN:::UQJ1a(A!Ga1f,<qAw,FFFFq1uIq!Q'1q51a4<!Q$+>1a4+KKKK1qs7O$$Q1-QqS2ad71BR1W1LqQRTUQUWXz1YYYYqS1WqL!!!Q*a!A#g!Q$.>R.HHHHq1Q3wK  Aq)QAX1_qAqz-IIIIq1QT6zN##Aq!,1q!ta1aj0HHHHr3   c                  .   t        d      } | dz  | t        d       t        d      dz  z  z  z   dz  d| t        d       t        d      dz  z  z  z  d| dz  z  z   z  }|j                         }|j                  | dd      j	                  | d      dk(  sJ y )Nwrk   r/   r9   r   r0   )r   r   rT   r1   subsrz   ra   s     r4   	test_bug2r}      s    sA	
R1	QA 
!#	%&'SVGCFRL,@(A&AAa"gI&M	OA	
A99Q1""1a(A---r3   c                      dt         z   dt         z  z  } | j                  t         d      t        d      t         t        d      z  dz  z
  dt        d      z  t         dz  z  dz  z   t        t         dz        z   k(  sJ y )Nr.   r/   r,   r9   rR   r;   )r%   r1   r   r$   r`   s    r4   test_expr      sj    	
Q!A#A99Q!9A3q6! 3bQi1nR6G G!AqD' QQQQr3   c                  (   t        d      } | dt        t              t        d      t        t              z   z  z
  z  }t        d      }|j                  | dd|      t	        |t        d      z  t        t              t        d      z   z        k(  sJ y )Nrz   r.   r9   logwr   )rf   )r   r   r%   r1   r   )rz   ra   r   s      r4   	test_exp2r      s    sA	AAAQ(()A&>D99	1ad  "4A;AQ#@AB B Br3   c                      dt         z  dt         dz  z  z   dt         z  dt         dz  z  z   z  } | j                  t         d      dt         z
  t         dz  z   t        t         dz        z   k(  sJ y )Nr9   r/   r.   r,   rE   r`   s    r4   	test_bug3r      s`    	
1qAv!a1f%A99Q!9A1qAw 6666r3   c                     d} dt         z  dt         | z  z  z   dt         z  dt         | z  z  z   z  }|j                  t         dd      dt         z
  t         dz  z   t        t         dz        z   k(  sJ t        j                  } dt         z  dt         | z  z  z   dt         z  dt         | z  z  z   z  }|j                  t         dd      dt         z
  t        t               z   t         t        d      dz  z  z   t        t         dz        z   k(  sJ dt        t               z   }|j                  t         dd      dt        t               z   k(  sJ y )Nr9   r/   r.   r   r0   )r%   r1   r$   r   Halfr   pra   s     r4   test_generalexponentr      s   	A	
1qAv!a1f%A99Q1QA!Q$!7777	A	
1qAv!a1f%A99Q1Qa1qtAv;!>1a4!HHHH	DGA99Q1T!W,,,r3   c                      ddt        t              z   z  } | j                  t        dd      dt        z   t        t              z
  t        t              dz  z
  t        t        dz  t              z   k(  sJ y )Nr.   r   r9   r/   rJ   r`   s    r4   test_genexp_xr      s]    	1tAw;A99Q1	AQ$q'1*$qAqz12 2 2r3   c                  n   t        dd      } dt        z  dt        | z  z  z   dt        z  dt        | z  z  z   z  }|j                  t        dd      dt        z   t        dz  z   t        t              z
  t        t	        d      dz  z  z
  t        t	        d      dz  z  z
  t        t        dz        z   k(  sJ y )Nr/   r9   r.   r   r+   )r	   r%   r1   r   r   r$   r   s     r4   test_genexp_x2r      s    AA	
1qAv!a1f%A99Q1QAQ!7!ad1f+!EAaDQRF!SVWXY[\X\V]!]]]]r3   c                      t        d      } d| z  | z  d| z   z  }|j                  | dd      dt        | |       z   k(  sJ |j                  | dd      j                  | d      dk(  sJ y )Nrz   r9   r.   r   )r   r1   r$   r{   r|   s     r4   test_seriesbug2r      sn    sA
A#qAEA99Q1Qq!W,,,99Q1""1a(A---r3   c                      t        d      } t        d| z        | z  }|j                  | dd      dd| dz  z  dz  z
  t        | dz        z   k(  sJ y )Nrz   r9   r   r/   r0   )r   r!   r1   r$   r|   s     r4   test_seriesbug2br      sT    sAAaC
A99Q1Qq!tVAX!Q$!7777r3   c                      t        dd      } t        t        d| z        | z        }|j                  | d      t        d      d| dz  z  dz  z
  d| dz  z  d	z  z
  t	        | dz        z   k(  sJ y )
Nrz   Trealr9   r+   r,   r/   r0   -   r   r   r!   seriesr$   r|   s     r4   test_seriesbug2dr      sq    sAC!HQJA88A8s1v!Q$q01QT6"9<qAwFFFFr3   c                     t        dd      } t        d| z        | z  d| z   z  }|j                  | dd      dt        |       z   k(  sJ |j                  | dd      dd| z  t	        d      z  z   | dz  t        dd      t	        d      dz  z   z  z   t        | dz        z   k(  sJ |j                  | dd      j                  | d      dk(  sJ y )	Nrz   Tr   r9   r.   r   r/   )r   r!   r   r$   r   r	   r{   r|   s     r4   test_seriesbug2cr      s    sA	QqS!q1uA88Aq!AaD(((88Aq!AaCAJ	1hr1oA	)*!+-.q!tW!5 5 5 588Aq!!!!Q'1,,,r3   c                     t        dd      } t        t        d| z        | z        d| z   z  j                  | dd      t        d      | t        d      z  z   t	        | dz  |       z   k(  sJ t        t        t        d| z        | z        d| z   z        j                  | dd      dd| z  t        d      z  z   t	        | dz        z   k(  sJ t        t        d      t	        |       z         j                  | dd      dt	        |       z   k(  sJ dt	        |       z   d| z   z  j                  | dd      dt	        |       z   k(  sJ y )Nr%   Tr   r9   r.   r   )r   r   r!   r   r$   r   r1   r%   s    r4   test_expbug4r      sB   sAAaC
U#VAq!_A3q60AAadAJ0NO O OC!HQJQ!!'1aA!CF
NQq!tW4LM M M s1v!}%%aA.!ad(:::1XQ((Aq1Q1X===r3   c                      t        dt        t              z         j                  t        dd      t        d      t        t        t              z   k(  sJ y )Nr9   r   )r   r$   r%   r1   r2   r3   r4   test_logbug4r     s:    q1Q4x=  Aq)SVa1g-====r3   c                     t        t        dt        z         t        z        j                  t        d      t        d      t        d       t        z  dz  z   dt        d      z  t        dz  z  dz  z   t	        t        dz        z   k(  sJ t        t	        t                    j                  t        dd      dt	        t              z   k(  sJ y )Nr.   r/   r,   r9   rR   r;   r   )r   r   r%   r1   r$   r2   r3   r4   test_expbug5r     s    s1q5z!|$$Q!$,A#a&10Dr#a&yQRTUQU~VXGX0X[\]^`a]a[b0bbbbqt9Q1%QqT111r3   c                      t        t        t                    j                  t        dd      t        t        dz  dz  z
  t        dz  dz  z   dt        dz  z  dz  z
  t        t        dz        z   k(  sJ y )Nr   r:   r/   r+   rQ   rD   i;  r!   r%   r1   r$   r2   r3   r4   test_sinsinbugr     sa    s1v;q!Q'1q!tAv:1R+?!AqD&*+LqQRTUQUw+VVVVr3   c                      t         t        t               dz
  z  } | j                  t         dd      dt         dz  z
  t         dz  dz  z
  t         dz  dz  z   t        t         dz        z   k(  sJ y )Nr.   r   r+   r9   r0   rO   rM   )r%   r   r1   r$   as    r4   test_issue_3258r     s]    	3q6A:A99Q1QqS1a48!3ad2g!=!Q$!GGGGr3   c                      t        dd      } t        | dz        t        dd      z  }|j                  | dd      | | dz  d	z  z
  | d
z  dz  z
  t	        | dz        z   k(  sJ y )Nr%   T)nonnegativer/   r.   r      rD      rS   i  )r   r!   r	   r1   r$   )r%   fs     r4   test_issue_3204r     sg    s%AAqD	8Aq>!A99Q2!ad2g+2d
":Qq"uX"EEEEr3   c                      t        dt        t              z
        } | j                  t        dd      dt        t              dz  z
  t        dz  z
  t        t              dz  dz  z
  t        t        dz        z   k(  sJ y )Nr.   r   r9   r:   r/   rH   )r   r&   r1   r$   )r   s    r4   test_issue_3224r     sb    Qa[A99Q1T!WQY1!4tAwz"}!DqAw!NNNNr3   c                  b   t        d      \  } }t        d      t        d      z  }| d|z   z  }dt        z  t        | d|z   z         t        | | |z  z         z   z  }| t        |       z  t        z  |t        z  z   |dz  dt        z  z  z
  t        |       z   }|j	                  | d      |k(  sJ y )Nzw,ir+   r/   rk   r.   r9   r,   )r   r   r%   r$   r1   )rz   irr   ra   e_sers         r4   test_issue_3463r      s    5>DAqAs1vA	BFA	!c!a!e*oA1H-.ABs1vIaK!A#1ac
*QqT1E99Q!9%%%r3   c                     t        dt        z        j                  t        d      dt        z  dt        dz  z  dz  z
  t        t        dz        z   k(  sJ t        t        t        z         j                  t        d      t        t              t        t              z   k(  sJ t        t        t        z         j                  t        d      t        t              t        t              t        z  z   t        t        dz        z   k(  sJ t        t        t        z         j                  t        d      t        t              t        t              t        z  z   t        t              t        dz  z  dz  z
  t        t              t        dz  z  d	z  z
  t        t              t        dz  z  d
z  z   t        t        dz        z   k(  sJ y )Nr:   r0   r,      r/   r.   r9   r+   rA   r;   )r!   r%   r1   r$   r&   r   r2   r3   r4   test_sinr   )  sR   qs8A#qsSAXaZ'7!AqD''AAAAq1u:a1%Q!A$666q1u:a1%Q#a&():Qq!tW)DDDDq1u:a1%Q#a&():SVAqD[])JAq!tA*Aq!tB*')*1a4*1 1 1 1r3   c                      t        dt        z        t        z  } | j                  t        d      ddt        dz  z  dz  z
  dt        dz  z  d	z  z   t        t        dz        z   k(  sJ y )
Nr:   rA   r,   r   r9   r/   i   r0      r   r`   s    r4   test_issue_3515r   1  s\    AaC
A99Q!9C1HQJad2 =!Q$ GGGGr3   c                     t        t              dz  t        t        t                    t        t              dz  z  t        t              t	        dd      z  t        t              dz  z  z
  z  } | j                  t        d      t	        dd      d	t        dz  z  d
z  z
  dt        dz  z  dz  z
  dt        dz  z  dz  z
  dt        dz  z  dz  z   t        t        dz        z   k(  sJ y )Nr   r9   r.   r/   rP   r,   rk   rM   rD   i   +   r0   i(  ic  rA   i % iy  r:   i )r!   r%   r   r   r	   r1   r$   r`   s    r4   test_issue_3505r   6  s    Ad3q6l3q619,AAs1vqy() 	*A99Q!9R 01QT6#: =
1a4!QT	')!*,/1HX,=!>@A!Q$!H H H Hr3   c                     t        d      } t        dz  t        t        | t        z         z  t        t        |       z  z
  z  }|j                  t        d      t	        |       t        |       t        z  dz  z
  t	        |       t        dz  z  dz  z
  t        dz  t        |       z  dz  z   t        dz  t	        |       z  d	z  z   t        d
z  t        |       z  dz  z
  t        t        dz        z   k(  sJ t        dz  t        t	        | t        z         z  t        t	        |       z  z
  z  }|j                  t        d      t        |        t	        |       t        z  dz  z
  t        |       t        dz  z  dz  z   t	        |       t        dz  z  dz  z   t        dz  t        |       z  d	z  z
  t        d
z  t	        |       z  dz  z
  t        t        dz        z   k(  sJ y )Nr   rv   rA   r,   r9   r/   r;   r0   rN   r+   rO   )r   r%   r!   r1   r   r$   r   ra   s     r4   test_issue_3501r   =  s   sA	B3q1u:#a&()A99Q!9AQ! 3c!fQTk!m C	1SVB!Ac!fS!)+,a4A;s?!;=>q!tW!E E E E	B3q1u:#a&()A99Q!9Q#a&(1* 4s1vad{1} DAq!tB!Ac!fS!)+,a4A;s?!;=>q!tW!E E E Er3   c                  r   t        dt        z        t        dt        z        z  } | j                  t        d      t        dd      t	        t        dz        z   k(  sJ | j                  t        d      t        dd      dt        dz  z  dz  z
  dt        dz  z  dz  z   t	        t        dz        z   k(  sJ y )	Nr+   r9   r,   rA   #   r0   iI  0   )r!   r%   r1   r	   r$   r`   s    r4   test_issue_3502r   G  s    AaCQqSA99Q!9A1a4 888899Q!9AAqD"SAXb[01QT7:; ; ;r3   c                  
   t        dt        z         dt        z   z  } | j                  t        d      t        d      dz  t        t        d      z  dz  z   t        t        d      z  dz  z
  t	        t        dz        z   k(  sJ y )Nr9   r,   r0   )r!   r%   r1   r   r$   r`   s    r4   test_issue_3503r   N  sj    AE
AEA99Q!9Aq1SV8A: 5#a&
 BQq!tW LLLLr3   c                     t         t        dt         z        z   dz  t         t         t        dt         z        z   z  t         t        dt         z        z   t        dt         z        z  z
  z  } | j                  t         d      t        dd      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 y )Nr/   rv   r9   rD   r,   rk   r0   r+   `   [   i   im+  rA   i  )r%   r!   r1   r	   r$   r`   s    r4   test_issue_3506r   S  s    	
S1XaS1X.!c!A#h,AaC1HHIA99Q!9Q!AqD&)#bAgck1E!Q$Jv4EE!Q$OP P Pr3   c            	      $   t        dd      } t        t        |             j                  | d      t        |       | dz  dz  z
  | dz  d	z  z
  t	        | dz        z   k(  sJ t        |        | t        |        t        t        d| z              z   z  z   t        t        d| z              z   }|j                  | d      t        d      t        d      | z  z   d| dz  z  d
z  z
  d| d
z  z  d
z  z
  d| dz  z  dz  z
  t	        | dz        z   k(  sJ y )Nr%   Tr   r+   r,   r9   rA   r0      r/   r   r   )r%   ra   s     r4   test_issue_3508r   Y  s   sAs1v;a1%Q!Q$q&1a48)Ca1g)MMMM	Q!c!fWs3qs8},--C!H=A88A8AQAadF1H$qAvax/!AqD&);a1gEF F Fr3   c                  \   t         dz  t         dz  t         dz  t        t        t                     z  z
  z  } | j                  t         d      t	        dd      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 y )Nr   r9   rP   r,   r.   r0   r      i  i/  rA   i 	 iq  r:   i )r%   r   r   r1   r	   r$   r`   s    r4   test_issue_3507r   a  s    	BA1T#a&\))*A99Q!9AAb 2ad74</#ad(6/AE!Q$JyDXX[\]^`a]a[bbc c cr3   c                  6   t        t        t                    j                  t        d      t        d      t        dz  t        d      z  dz  z
  t        dz  t        d      z  dz  z
  t        dz  t        d      z  dz  z   t	        t        dz        z   k(  sJ y )Nr+   r,   r.   r9   r0   r:   r;   )r!   r   r%   r1   r$   r2   r3   r4   test_issue_3639r   g  s    s1v;qA&AAc!fQAc!fQ.Ac!fR?!AqD'IJ J Jr3   c                  >   t        t              j                  t        d      t        t        dz  dz  z   t        dz  dz  z   t        t        dz        z   k(  sJ t	        t              j                  t        d      dt        dz  dz  z   t        dz  d	z  z   t        t        dz        z   k(  sJ t        t              j                  t        d      t        t        dz  dz  z
  dt        dz  z  d
z  z   t        t        dz        z   k(  sJ t        t              j                  t        d      dt        z  t        dz  dz  z
  t        dz  z   dt        dz  z  dz  z   t        t        dz        z   k(  sJ t        t              j                  t        d      t        t        dz  dz  z
  dt        dz  z  dz  z   t        t        dz        z   k(  sJ t        t              j                  t        d      t        t        z  dz  t        t        z  z
  dt        z  t        dz  z  dz  z
  t        t        dz  z  dz  z
  t        t        dz        z   k(  sJ t        t              j                  t        d      t        t        dz  dz  z   t        dz  dz  z   t        t        dz        z   k(  sJ t        t              j                  t        d      t         t        z  dz  t        z   t        dz  dz  z   t        dz  dz  z   t        t        dz        z   k(  sJ y )NrA   r,   r/   r+   rN   r.   r9   r0   r;   r   r   i  (   )r   r%   r1   r$   r   r   r   r   r   r
   r   r   r   r2   r3   r4   test_hyperbolicr   l  s   7??1?"a!Q$q&j1a48&;a1g&EEEE7??1?"a!Q$q&j1a47&:Qq!tW&DDDD7??1?"a!Q$q&j1QT6"9&<qAw&FFFF7??1?"	!ad2g!a1fSj(1QT723 3 38A#q1a46zAadF2I'=!Q$'GGGG8A#
1Q1qs1a4x{"Qq!tVAX-!Q$78 8 88A#q1a46zAqDF':Qq!tW'DDDD8A#r"uQw{QT!V';ad1f'DqAw'NNNNr3   c                     t        dd      } t        dd      }| dz  | t        d|z  | z
        z  | t        d|z        z  z
  z  }|j                  | d      t        d|z         | t        d|z        z  d	z  z   | d	z  t        d|z        z  d
z  z
  | dz  t        d|z        z  dz  z   t        | dz        z   k(  sJ y )Nrz   Tr   r%   rv   r.   r0   r,   r9   rA   r/   r;   )r   r   r1   r$   )rz   r%   ra   s      r4   test_series2r   y  s    sAsA	B3qsQw<!C!H*,-A99Q!9QqS	Ac!A#hJqL 81a4AaC=? JQPQTRUVWXYVYRZ][]M] ]`abcefbf`g ggggr3   c                     t        dd      } | dz  | dz  t        |       z  | dz  t        |       z  z
  z  }|j                  | d      t	        d      d	z  | d	z  dz  z   d
| dz  z  dz  z   d| dz  z  dz  z   t        | dz        z   k(  sJ y )Nrz   Tr   ir/   r:   r,   r.   r9   rS   r0      i  rA   i^  )r   r"   r!   r1   r   r$   r|   s     r4   test_series3r     s    sA	BAc!fq!tCF{*+A99Q!9
1q!tAv 51a4 Cc!Q$hun TWXYZ\]Y]W^ ^^^^r3   c                     t        d      } t        | dz  t        dz  | dz  z  z   dt        z  | dz  z  z   z  | dz  z  }|j                  | d      j                         j	                         t        ddt        z  z   t        dz  z   z  ddt        dz  z   dt        z  dz  z   z  dz  dt        z  ddt        z  z   t        dz  z   z  fv sJ y )Nrz   r0   r9   r,   r.   rv   )r   r%   r1   removeOrT   r|   s     r4   	test_bug4r     s    sA	1a4!Q$q!t)ac!Q$h&'1,A99Q!9$$&--/Aq1Q3wA~4F	1qs7QqSU?AqsA!Ga"g$5648 8 8 8r3   c                     t        d      } t        d      }t        |        t        d| t        t              z  z         z   dz  | dz  z  t        |        t        dt        | z  z         z   t        |        t        d| t        t              z  z         z   z  | z  t        t        |        t        d| t        t              z  z         z   z  | z  z
  z  }|j                  | d|      t        | z  |z  d| z  z   t	        d|       z   k(  sJ |j                  | d|      t        | z  |z  d| z  z   t        |z  z
  d|z  t        t              z  z   t        t        t              z  |dz  z  z   t	        |       z   k(  sJ y )Nrz   rd   r.   rv   r   re   r9   )r   r   r%   r1   r$   )rz   rd   ra   s      r4   	test_bug5r     sq   sAsA
a&3q1SV8|$	$+AG3s1vgA!G7AwQ3q6\!2264456689CF7A#a&L< 996 	A 99Q!!9$!A!a1g(====99Q!!9$!A!ac(9AaCAJ(F
CF(1a4-)A$)   r3   c                  H   t        t              dt        t              z
  z  j                  t        d      dt        z  t	        t              z   k(  sJ t        t              dz  dt        t              z
  z  j                  t        d      dt	        t              z   k(  sJ y )Nr.   r,   r9   )r!   r%   r   r1   r$   r2   r3   r4   test_issue_4115r     sx    FAAJ((a(0AaC!A$J>>>FAIq3q6z"++A+3q1Q4x???r3   c                  j    t        t        d        t        t        d        t        t        d        y )Nc                  P    t        dt        z        j                  t        dd      S Nr.   r   r+   r!   r%   r   r2   r3   r4   <lambda>ztest_pole.<locals>.<lambda>  s    c!A#hooaA6 r3   c                  V    t        ddt        z  z         j                  t        dd      S r   r   r2   r3   r4   r   ztest_pole.<locals>.<lambda>  s!    c!ac'l11!Q: r3   c                  ^    t         t        dt         z        z  j                  t         dd      S r   )r%   r!   r   r2   r3   r4   r   ztest_pole.<locals>.<lambda>  s!    qQqSz11!Q: r3   )r(   r   r2   r3   r4   	test_poler     s#    
967
9:;
9:;r3   c                     t        t        t                    j                  t        dd      t	        dt              k(  sJ t        t        t                    j                  t        dd      dt	        t              z   k(  sJ t        t        t                    j                  t        dd      dt        z   t	        t        dz        z   k(  sJ t        t        t                    j                  t        dd      dt        z   t        dz  dz  z   t	        t        dz        z   k(  sJ t        t        t                    j                  t        dd      dt        z   t        dz  dz  z   t	        t        dz        z   k(  sJ t        t        t                    j                  t        dd      dt        z   t        dz  dz  z   t        dz  dz  z
  t	        t        dz        z   k(  sJ y )Nr   r.   r9   r/   r0   r+   r:   )r   r!   r%   r   r$   r2   r3   r4   test_expsinbugr     sb   s1v;aA&!Aq'111s1v;aA&!ad(222s1v;aA&!a%!AqD'/999s1v;aA&!a%!Q$q&.1QT7*BBBBs1v;aA&!a%!Q$q&.1QT7*BBBBs1v;aA&!a%!Q$q&.1a46*AAadG*KKKKr3   c                     t        d      } t        |       j                  |       dk(  sJ t        |        j                  |       dk(  sJ t        t        |             j                  |       dk(  sJ t        t        |              j                  |       dk(  sJ t        | dz        j                  |       dk(  sJ t        | dz         j                  |       dk(  sJ t        t	        |             j                  |       dk(  sJ t        t	        |              j                  |       dk(  sJ t        dt        |       z         j                  |       dk(  sJ t        dt        |        z         j                  |       dk(  sJ t        |       j                  | d      dk(  sJ t        |        j                  | d      dk(  sJ t        dd	
      } t        | dz         j                  |       dk(  sJ y )Nr%   r   rk   r/   r+   r0   r9   rw   T)negativeg      ?r.   )r   r   r   r!   r   r   s    r4   
test_floorr     s   sA8??1"""!9A"$$$Q="a'''aR>  #r)))A;a A%%%!Q$<q!R'''Q="a'''aR>  #q(((SV##A&!+++S!W$$Q'1,,,8??1a A%%%!9Aq!R'''sT"AS>  #q(((r3   c                     t        t              j                  t        d      t        k(  sJ t        t              j                  t        d      dt        z   k(  sJ t        dt        z  dz         j                  t        d      dt        z  k(  sJ t        dt        z  dz         j                  t        d      ddt        z  z   k(  sJ t        t        dz        j                  t        d      t        dz  k(  sJ t        t        dz        j                  t        d      t        dz  k(  sJ t        t        t              dz         j                  t        d      t        t        dz  dz  z
  t        dz  dz  z   t	        t        dz        z   k(  sJ t        t        t              dz         j                  t        d      dt        z   t        dz  dz  z
  t        dz  dz  z   t	        t        dz        z   k(  sJ t        t        t              t
        j                  z         j                  t              t
        j                  t        z   t        dz  dz  z
  t        dz  dz  z   t	        t        dz        z   k(  sJ t        t        d	z        j                  t        d      t	        t        dz        k(  sJ t        dt        z        j                  t              t        d
d      t	        t        dz        z   k(  sJ y )Nr.   cdirrk   r9   r+   r/   rA   rN   r:   r   )r   r%   r   r!   r$   r   r   r   r2   r3   r4   	test_fracr     s`   7>>!!>$)))7>>!">%Q...!a=*ac111!a=+q1Q3w6661:QQ'1a4///1:QR(AqD000A
""11"-QT!Vad3h1F1a41PPPPA
""12".!a%!Q$q&.1a482KaPQSTPTg2UUUUA ''*affqj1a46.AAqDH.LqQRTUQUw.VVVV1:QQ'1QT7222!9A+a"3a1g"====r3   c                     t        t              j                  t              dk(  sJ t        t               j                  t              dk(  sJ t        t        t                    j                  t              dk(  sJ t        t        t                     j                  t              dk(  sJ t        dt	        t              z
        j                  t              dk(  sJ t        dt	        t               z
        j                  t              dk(  sJ t        t              j                  t        d      dk(  sJ t        t               j                  t        d      dk(  sJ y )Nr.   r   r9   r/   rv   )r   r%   r   r!   r   r2   r3   r4   test_ceilingr     s   1:Q1$$$A2;a A%%%3q6?!!!$)))3r7""1%***1s1v:%%a(A---1sA2w;&&q)Q...1:Q"a'''A2;a#r)))r3   c                  ~   t        d      } t        t              j                  t        d      t        k(  sJ t        t               j                  t        d      t        k(  sJ t        t        dz         j                  t        d      t        dz   k(  sJ t        t	        t                    j                  t        d      t        t        dd      t        dz  z  z
  t        t        dz        z   k(  sJ t        t	        t                     j                  t        d      t        t        dd      t        dz  z  z
  t        t        dz        z   k(  sJ t        t        | z
        j                  t        d      |  t        d| z
        z  t        dz
  t        d| z
        z  z   t        d| z
        z   k(  sJ y )Nr   r0   r,   r.   rA   r/   )r   absr%   r1   r!   r	   r$   r   r   s    r4   test_absr     s\   sAq6>>!q>!Q&&&r7??1?"a'''q1u:a1%Q...s1v;qA&!hq!nQT.A*AAadG*KKKKsA2w<Q'1x1~ad/B+BQq!tW+LLLLq1u:a#r$q1u+~QQU8K'KdSTWXSXk'YYYYr3   c                     t        t              j                  t        dd      t        k(  sJ t        t              j                  t        dd      t         k(  sJ t        t        dz         j                  t        dd      dk(  sJ t        t        dz         j                  t        dd      dk(  sJ t        t        dz         j                  t        dd      dk(  sJ t	        t        dz         j                  t        dd      dk(  sJ t        t        t        z         j                  t        dd      t        t        t        z         j                  t        dd      k(  sJ y )	Nr   +)dir-r9   r.   皙@r/   r   r%   r   r   r   r!   r&   r2   r3   r4   test_dirr     s)   q6==A3='1,,,q6==A3='A2---Q<q!-222Q<q!-222S>  A3 /14441s7""1aS"1Q666q1u:Qs+s1q5z/@/@A3/@/OOOOr3   c                     t        t              j                  t        dd      t        k(  sJ t        t              j                  t        dd      t         k(  sJ t        t        dz         j                  t        dd      dk(  sJ t        t        dz         j                  t        dd      dk(  sJ t        t        dz         j                  t        dd      dk(  sJ t	        t        dz         j                  t        dd      dk(  sJ t        t        t        z         j                  t        dd      t        t        t        z         j                  t        dd      k(  sJ y )Nr   r.   r   rk   r9   r   r/   r   r2   r3   r4   	test_cdirr    s)   q6==AA=&!+++q6==AB='A2---Q<q!!,111Q<q!"-222S>  AA .!3331s7""1ab"1Q666q1u:Q+s1q5z/@/@AA/@/NNNNr3   c            	      .   t        d      } t        | t        z        t        z  }|j                  t        dd      j	                         t        dz
  | dt        d| dz  z  dz         z  z  t        d| z        dz  z
  z  t        d| z        dz  z   k(  sJ y )Nr   r0   r9   r,   ir.   rH   )r   r   r%   r   r   r   r   s     r4   test_issue_3504r    s    sAQqS	!A88AqA8&&(	
QAd3q!t8a<(()D1IbL89D1IaKGH H Hr3   c                     t        d      \  } }dd| t        z  z   z  }|j                  t        dd      d| t        z  z
  | dz  t        dz  z  z   | dz  t        dz  z  z
  | dz  t        dz  z  z   t        t        dz        z   k(  sJ dd| |z   t        z  z   z  }|j                  t        dd      dt        |  |z
  z  z   t        dz  | |z   dz  z  z   t        t        dz        z   k(  sJ y )Nza,br.   r   r+   r9   r/   r0   )r   r%   r   r$   )r   br   s      r4   test_issue_4441r    s    5>DAq	1qs7A88Aq!AaC!Q$q!t) 3ad1a4i ?	1QT	!adG!   	1Aqy=A88Aq!ArAvJ
Q$Az/!adG!$ $ $ $r3   c                     t        t              j                  t        t        dz  d      j	                         t         dz  t        dz  z   dt        t        dz  z
  z  z
  k(  sJ t        t              j                  t        t        d      j	                         t         dz  t        dz  z   dt        t        z
  z  z   k(  sJ t        t        t              t        dt        z        z  t        t        dz        t        d      k(  sJ y )Nr9   r/   r,   rA   r.   r0   rk   )r"   r%   r   r
   r   r    r#   r   r2   r3   r4   test_issue_4329r	    s    q6==BqDA=&..0	A!aRTl"# # #q6==B!=$,,.	
1r!taRj ! ! !QQqS!1bd+s2w666r3   c                     t        t        t        dz  z         j                  d      t        t              k(  sJ t        t        t        dz  z         j                  d      t        t        t        dz        z   k(  sJ dt        z   dz  j                  t        d      t        dz  dt        z  z   dz   k(  sJ ddt        z  z   j                         ddt        z  z   k(  sJ t	        t        t              j                         t              j                         dt        z   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 y )	Nr9   r.   r,   rA   r/   r0   r;   r+   )r   r%   r   r$   r   r   doitr2   r3   r4   test_issue_5183r    s%   q1a4x=!$!,,,q1a4x=!$AadG333UQJqA&!Q$1*q.888!GQqS(((c!fmmoq)..0	A1QAa!Q$r')AadG34 4 4r3   c                     t        d      } dt        dz  | dz  z   dz  z  j                  t        t        | z  d      t         d| dz  z  t         | z  t        z   z  z  dd| dz  z  t         | z  t        z   dz  z  z  z
  t	        dt        t        | z  f      z   k(  sJ dt        dz  | dz  z   dz  z  j                  t        t        | z  d      dd| dz  z  z  t        d| dz  z  t         | z  t        z   z  z  z
  dd| dz  z  t         | z  t        z   dz  z  z  z
  t	        t         | z  t        z   t        t        | z  f      z   k(  sJ y )	Nr   r.   r9   r   )x0r-   r0   r/   rH   )r   r%   r1   r   r$   r   s    r4   test_issue_5654r    s`   sAq!tAqDy1n%%aAaC1%5	
AadFQBqD1HAadFQBqD1Hq=$8!99Aa!QqSNJK K Kq!tAqDy1n%%aAaC1%5Bq!tG	
AadFQBqD1H	:!"AadFQBqD1Hq=$8!9::<=qbdQhAaC<Q:R R R Rr3   c                     t        t        t        z         j                  t        dd      } t        t        t        z   t        z         j                  t        dd      }| j                  t        t        t        z         |}}||z
  j                         j                         j                         dk(  sJ t        t        t        z         j                  t        dd      } t        t        t        z   t        z         j                  t        dd      }|j                  t        dt        di      | j                  t        d      k(  sJ y )Nr   r.   r9   r/   )	r   r%   r'   r   r&   r{   rT   r   simplify)sxsxys1s2s       r4   test_issue_5925r  !  s    	a!e		Aq!	$B
q1uqy/
 
 Aq
)CWWQABG%%'002a777	a!e		Aq!	$B
q1uqy/
 
 Aq
)C88Qq!AJ2771a=000r3   c                      t        t        dz        j                  t        dd      dt        dz  z   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 y )
Nr/   r      r.   rA   r9   rP   rM   r;   )r   r%   r1   r$   r2   r3   r4   
test_exp_2r  ,  sh    q!t9Q2&!ad(QT!V*;ad1f*Dq"uRx*ORSTUWYTYRZ*ZZZZr3   N)|sympy.calculus.utilr   sympy.core.functionr   r   sympy.core.numbersr   r   r   r	   r
   sympy.core.singletonr   sympy.core.symbolr   r   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   r   %sympy.functions.elementary.hyperbolicr   r   r   r   r   r   r   r   #sympy.functions.elementary.integersr   r   r   (sympy.functions.elementary.miscellaneousr   r   (sympy.functions.elementary.trigonometricr   r   r    r!   r"   sympy.series.limitsr#   sympy.series.orderr$   	sympy.abcr%   r&   r'   sympy.testing.pytestr(   r)   r5   r7   r=   r?   rB   rF   rK   rU   rW   rZ   r\   r^   rb   ri   rl   rn   rp   rr   rt   rx   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r	  r  r  r  r  r2   r3   r4   <module>r)     s   + 7 < < " / 5 = f f f F F A O O %     .248 \	HL
O
O

F
22
9# ) )
1
I .R
B7
	-2^.8G->>2WH
FO
&1H
HE;M
PFcJ

Oh_8@
<L)(>*ZPOH$74R1[r3   