
    sg%                        d dl 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 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mZ d dlmZmZmZmZ ej:                  Zd Zd Z d Z!d Z"d Z#d Z$d Z%d Z&d Z'd Z(d Z)d Z*y)    )IRational)S)Dummysymbols)log)sqrt)atan)	integrate)Poly)simplify)ratintratint_logpartlog_to_atan)abxtc            
      t   t        t        j                  t              dk(  sJ t        t        d      t              dt        z  k(  sJ t        t        t              t        dz  dz  k(  sJ t        dt        z  t              t        dz  k(  sJ t        dt        z  t              t        dz   k(  sJ t        dt        dz  z  dt        z  z   dz   t              t        dz  t        dz  z   t        z   k(  sJ t        j                  } t        dz   }t        | |z  t              t        t        dz         k(  sJ t        | |ft              t        t        dz         k(  sJ t        dz  t        z
  } t        dz
  }t        | |z  t              t        dz  dz  t        dz  dz  z   k(  sJ t        } t        t        z
  t        t        z   z  }t        | |z  t              t        t        dz  t        dz  z
        dz  k(  sJ t        j                  } t        dz  dz   }t        | |z  t        d       t        t              k(  sJ t        | |z  t        d	      t        t              k(  sJ t        | |z  t        d
      t        t        t        t        z         z  dz  t        t        t        t        z
        z  dz  z
  k(  sJ t        d      } t        dz  dt        dz  z  z
  dt        dz  z  z
  dt        dz  z  z   t        z   dz
  }t        | |z  t              dt        t        dz         z  dt        t        dz
        z  z   dt        z  dz   t        dz  dz
  z  z   k(  sJ t        dz  dt        dz  z  z
  dz   } t        dz  dt        dz  z  z
  dt        dz  z  z   dz   }t        | |z  t              t        t              t        t        dz        z   t        t        dz  t        dd      t        dz  z  z
  t        j                  t        dz  z  z         z   k(  sJ t        dz  dt        dz  z  z
  dt        dz  z  z
  dt        z  z   dz
  } t        dz  dt        dz  z  z   dt        dz  z  z   dt        dz  z  z   }t        | |z  t              ddt        z  z   dt        dz  z  z   dt        dz  z  z   dt        z  dt        dz  z  z   t        dz  z   z  t        t              z   k(  sJ t        t        dz  | z  t        |z  z  t              ddt        z  z
  dt        dz  z  z   dt        dz  z  z
   ddt        dz  z  z   t        dz  z   z  dt        d      z  t        t        t        d      z  dz        z  z
  t        j                  t        dz  z  z   dt        dt        dz  z         z  z
  k(  sJ t        dz  t        dz  z
  dt        dz  z  z   t        dz  z   t        z
  dz   } t        dz  dt        dz  z  z
  dt        dz  z  z   dt        z  z
  dz   }t        | |z  t              t        t        j                  t        dz  z  z   t        j                  t        dt        z
  t        dz  z         z  z   ddt        z  z
  dt        dz  z  dt        z  z
  dz   z  z   dt        d      z  t        t        dd      t        d      z  dt        z  t        d      z  dz  z         z  dz  z   k(  sJ t        dt        dz  t        z   dz   z  t              dt        d      z  t        t        d      dz  dt        z  t        d      z  dz  z         z  dz  k(  sJ t        dt        dz  dz   z  t              t        dt        z
  t        dz  z          dz  t        dt        z         dz  z   t        d      t        t        d       dz  dt        z  t        d      z  dz  z         z  dz  z   k(  sJ t        dt        dz  t        z   dz   z  t        d
      t         dt        z  z  t        t        t        z   t        t        z  dt        z  z  z
        z  dz  t        dt        z  z  t        t        t        z   t        t        z  dt        z  z  z         z  dz  z   k(  sJ t        dt        dz  dz   z  t        d
      t        dt        z         dz  t        dd      t        dt        z  z  dz  z   t        t         t        z   t        dt        z  z  dz  z         z  z   t        dd      t        dt        z  z  dz  z
  t        t         t        z   t        dt        z  z  dz  z
        z  z   k(  sJ t        dt        t        t        t        z  z   dz  z  z  t              dt        z  dt        z  t        z  z   dt        dz  z  dt        dz  z  t        z  t        z  z   dt        dz  z  t        dz  z  t        dz  z  z   z  t        t              t        t        t        z  t        z         z
  t        dz  z  z   k(  sJ t        t        dt        dz  z
  z  t              t        t        dz  dz
         dz  k(  sJ t        t         dt        dz  z
  z  t              t        t        dz  dz
        dz  k(  sJ t        t        dz  ddt        z
  z  z
  j                  t              t              t        dz  dt        dz
  z  z   k(  sJ t        t              }t        dt        dz  dz   z  t        t              |k(  sJ t        dt        dz  dz   z  t        d      |k(  sJ t        dt        dz  dz   z  t        t              |k(  sJ t               }t        d|dz  dz   z  ||      t        |      k(  sJ y )Nr                  realTF$                        	      1   )symbolr   )r   r   Zeror   Oner   r   r
   r   r   Halfr	   halfr   diffr   )fgansds       [/var/www/html/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_rationaltools.pytest_ratintr6      sh
   !&&!!!!!A$?ac!!!!Q<1a46!!!!A#q>QT!!!"Q$?q!te###!AqD&1Q3,"A&!Q$A+/999	A	AA!a%s1q5z)))1a&!AE
***	1qA	AA!A#q>QT!Vad1f_,,,	A	
QQA!A#q>SA1-a////	A	1qA!A#qt$Q///!A#qt$Q///!A#qu%3q1u:a!CAJ,q.)HHHH	"A	1qAv!Q$1a4'!+a/A!A#q>
3q1u:#a!e*$1q1a4!8'<<= = = 	
1qAvA	1qAv!Q$"A!A#q>Q$q!t*tAaC(1a.A*=$=q!t$KLLM M M 	
1r!Q$w1a4!A#%)A	1qAv1a4!AqD&(A!A#q>	
QqS1QT6	AadF	"QqS1QT6\AqD%89CFBC C C 1a46AaC.!$
r!t)a1f
r!Q$w
&'Qq!tVad):;	$q'	$qay{##	$&'ffQTk	245c!ad(mO	DD D D 	
1q!ta1fq!t#a'!+A	1qAv!Q$1$q(A!A#q>	AFF1a4K!&&QUQT\!222a!A#g!Q$1r@Q5RR
47
4QQ/!A#d1g+a-?@@C	DD D D !QTAX\"A&	$q'	$tAwqy1Q3tAw;q=011!34 4 4 !QTAX,"	QUQT\	1s1q5z!|+d1gdDG8<A#d1g+a-<  7! /!!"/# 	## # # !QTAX\"AE2	
1d7
3tax$q&D.011!3	!T'	#dQha4/002	33 3 3 !QTAX,.#a!e*Q,	"a1QW9Q;	&TEAI!T'	!,C(DD3E	"a1QW9Q;	&TEAI!T'	!,C(DD3E E E E
 !QAaC!|^$a(	
1qs1uqAv!Q$q
*Qq!tVAqD[A-==>FS1q\!1a4B( 	(( ( ( !QAX,"s1a4!8}nQ&66661"a!Q$h-#s1a4!8}Q6661Q3AE?((+Q/1Q3AE?BBB
q'C!QTAX,!,333!QTAX,#.#555!QTAX,!,333 	A!QTAX,!,Q777    c                  z   t        t        t        dz  dz
  t        t              t        t        dz  dz
  t              t        dt        z  dz   t              fgk(  sJ t        t        dz  t        dz  dz
  t        t              t        t        dz  dz
  t              t        dt        z  dz   t              fgk(  sJ y )Nr   r'   r   r   r   r   )r   r   r   r    r7   r5   test_ratint_logpartr;   t   s    !QTAXq!,
q!tax
T"Q$(A.	/01 1 1!Q$1q!Q/
q!tax
T"Q$(A.	/01 1 1r7   c                  n    t        dt        dz  dz   z  t              t        t        dz        dz  k(  sJ y )Nr   r   r%   r    )r   r   r
   r:   r7   r5   test_issue_5414r=   {   s/    !QTBY-#tAaCy{222r7   c                     t        dt        dz  t        dz  z   z  t              t         t	        t         t        z  t        z         z  dz  t        t	        t        t        z  t        z         z  dz  z   t        z  k(  sJ y )Nr   r   )r   r   r   r   r   r:   r7   r5   test_issue_5249r?      sm    	1a4!Q$;!"3r!tax= 0 2Qs1Q37|^A5E EqHI I Ir7   c            
         t        dd      \  } }}t        t        | ||z  t        dz  z  | dz  z   || z  z   z  t                    t	        |       t        t	        |      t	        |      z  t        z  t	        |       t	        | |z         z  z        z  t	        |      t	        |      z  t	        | |z         z  z  k(  sJ y )Nza,b,cTpositiver   )r   r   r   r   r	   r
   )r   r   cs      r5   test_issue_5817rD      s    g-GAq!F1ac!Q$hAo!34a89QTAwq'$q1u+-/ 0 	015aaa!e1L	NN N Nr7   c                  ^    t        d      } t        d| dz  dz   z        t        |       k(  sJ y )Nur   r   )r   r   r
   )rF   s    r5   test_issue_5981rG      s.    AQ1q\"d1g---r7   c                      t        dd      \  } }}}t        || |z  |z   z  |      || z  |t        | |z  |z         z  | dz  z  z
  k(  sJ y )Nza b c xTrA   r   )r   r   r   )r   r   rC   r   s       r5   test_issue_10488rI      sY    i$/GAa!Q!AYq!QqS1S1q\>!Q$+>%>>>>r7   c                  n   t        dd      } t        | t        dz  | dz  z   z  t              t        t        | z        k(  sJ t        dt        dz  | dz  z   z  t              t        t        | z        | z  k(  sJ t        dd| dz  t        dz  z  z   z  t              t        | t        z        | z  k(  sJ y )Nr   Tnonzeror   r   r   r   r   r
   r   s    r5   "test_issues_8246_12050_13501_14080rO      s    T"AQ1q!t_a(D1I555Q1q!t_a(D1IaK777QAqDAI&*d1Q3ik999r7   c            
         t        dd      \  } }t        t        dz  dz   | dz  z
  t        dz  dz   |dz  z   z  t              t        |dz  | dz  z   t        t        t	        |dz  dz         z        z  t	        |dz  dz         z  z
  k(  sJ y )Nzk a0Tr   r   r   )r   r   r   r
   r	   )ka0s     r5   test_issue_6308rS      s    F&EAradQhAo1q2q5(891=	RUQT\4$r1uqy/ 1224A	?BBC C Cr7   c                      t        dd      } t        dt        dz  | dz  z   dz  z  t              t        d| dz  z  d| dz  z  t        dz  z  z   z  t        t        | z        d| dz  z  z  z   k(  sJ y )Nr   TrK   r   r   r    r   rM   rN   s    r5   test_issue_5907rU      s|    T"AQ1q!ta''+	
AadFQq!tVAqD[ 	!D1IqAv$6	67 7 7r7   c                  :   t        t        t        j                  z   t        d      t        t	        d      dz  t        d      }} dt        dt	        d      z  t        z  dz  t	        d      dz  z         z  }t        | |      |k(  sJ t        ||       | k(  sJ y )NQQ)domainr   r   EX)r   r   r   r.   r	   r
   r   )r1   r2   fg_anss      r5   test_log_to_atanr[      s    QVVQt,d4719a.MqAtAd1gIaKMDGAI-..Fq!&&&q!'''r7   c            	         dt         z  dz   t         dz  t         z   dz   z  dt         z  z   } t        | t               t        t         dz  t         dz  z   t         z         k(  sJ t        dt         z  dz   t         dz  dt         z  z   dz   z  dt         z  z   t               dt        t               z  dt        t         dz  dt         z  z   dz         z  z   t        d      t	        t        d      t         z  dz  t        d      z         z  dz  z
  k(  sJ y )Nr   r   r   r    r   r#   )r   r   r   r	   r
   )es    r5   test_issue_25896r^      s     
1q1a4!8a< 1Q3&A!Q<3q!tad{Q////1Q37QTAaCZ!^,qs2A6	#a&1SA!a(((474Q	!d1g4 , ,! 	!" " "r7   N)+sympy.core.numbersr   r   sympy.core.singletonr   sympy.core.symbolr   r   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr	   (sympy.functions.elementary.trigonometricr
   sympy.integrals.integralsr   sympy.polys.polytoolsr   sympy.simplify.simplifyr   sympy.integrals.rationaltoolsr   r   r   	sympy.abcr   r   r   r   r.   r/   r6   r;   r=   r?   rD   rG   rI   rO   rS   rU   r[   r^   r:   r7   r5   <module>rj      sv    , " . 6 9 9 / & , M M    vv_8D13I
N.?
:C7("r7   