
    \h%                        S SK JrJr  S SKJr  S SKJrJr  S SKJ	r	  S SK
Jr  S SKJr  S SKJr  S SKJr  S S	KJr  S S
KJrJrJr  S SKJrJrJrJr  \R:                  rS rS r S r!S r"S r#S r$S r%S r&S r'S r(S r)S r*g)    )IRational)S)Dummysymbols)log)sqrt)atan)	integrate)Poly)simplify)ratintratint_logpartlog_to_atan)abxtc            
      b   [        [        R                  [        5      S:X  d   e[        [        S5      [        5      S[        -  :X  d   e[        [        [        5      [        S-  S-  :X  d   e[        S[        -  [        5      [        S-  :X  d   e[        S[        -  [        5      [        S-  * :X  d   e[        S[        S-  -  S[        -  -   S-   [        5      [        S-  [        S-  -   [        -   :X  d   e[        R                  n [        S-   n[        X-  [        5      [        [        S-   5      :X  d   e[        X4[        5      [        [        S-   5      :X  d   e[        S-  [        -
  n [        S-
  n[        X-  [        5      [        S-  S-  [        S-  S-  -   :X  d   e[        n [        [        -
  [        [        -   -  n[        X-  [        5      [        [        S-  [        S-  -
  5      S-  :X  d   e[        R                  n [        S-  S-   n[        X-  [        S S9[        [        5      :X  d   e[        X-  [        S	S9[        [        5      :X  d   e[        X-  [        S
S9[        [        [        [        -   5      -  S-  [        [        [        [        -
  5      -  S-  -
  :X  d   e[        S5      n [        S-  S[        S-  -  -
  S[        S-  -  -
  S[        S-  -  -   [        -   S-
  n[        X-  [        5      S[        [        S-   5      -  S[        [        S-
  5      -  -   S[        -  S-   [        S-  S-
  -  -   :X  d   e[        S-  S[        S-  -  -
  S-   n [        S-  S[        S-  -  -
  S[        S-  -  -   S-   n[        X-  [        5      [        [        5      [        [        S-  5      -   [        [        S-  [        SS5      [        S-  -  -
  [        R                  [        S-  -  -   5      -   :X  d   e[        S-  S[        S-  -  -
  S[        S-  -  -
  S[        -  -   S-
  n [        S-  S[        S-  -  -   S[        S-  -  -   S[        S-  -  -   n[        X-  [        5      SS[        -  -   S[        S-  -  -   S[        S-  -  -   S[        -  S[        S-  -  -   [        S-  -   -  [        [        5      -   :X  d   e[        [        S-  U -  [        U-  -  [        5      SS[        -  -
  S[        S-  -  -   S[        S-  -  -
  * SS[        S-  -  -   [        S-  -   -  S[        S5      -  [        [        [        S5      -  S-  5      -  -
  [        R                  [        S-  -  -   S[        S[        S-  -   5      -  -
  :X  d   e[        S-  [        S-  -
  S[        S-  -  -   [        S-  -   [        -
  S-   n [        S-  S[        S-  -  -
  S[        S-  -  -   S[        -  -
  S-   n[        X-  [        5      [        [        R                  [        S-  -  -   [        R                  [        S[        -
  [        S-  -   5      -  -   SS[        -  -
  S[        S-  -  S[        -  -
  S-   -  -   S[        S5      -  [        [        SS5      [        S5      -  S[        -  [        S5      -  S-  -   5      -  S-  -   :X  d   e[        S[        S-  [        -   S-   -  [        5      S[        S5      -  [        [        S5      S-  S[        -  [        S5      -  S-  -   5      -  S-  :X  d   e[        S[        S-  S-   -  [        5      [        S[        -
  [        S-  -   5      * S-  [        S[        -   5      S-  -   [        S5      [        [        S5      * S-  S[        -  [        S5      -  S-  -   5      -  S-  -   :X  d   e[        S[        S-  [        -   S-   -  [        S
S9[        * S[        -  -  [        [        [        -   [        [        -  S[        -  -  -
  5      -  S-  [        S[        -  -  [        [        [        -   [        [        -  S[        -  -  -   5      -  S-  -   :X  d   e[        S[        S-  S-   -  [        S
S9[        S[        -   5      S-  [        SS5      [        S[        -  -  S-  -   [        [        * [        -   [        S[        -  -  S-  -   5      -  -   [        SS5      [        S[        -  -  S-  -
  [        [        * [        -   [        S[        -  -  S-  -
  5      -  -   :X  d   e[        S[        [        [        [        -  -   S-  -  -  [        5      S[        -  S[        -  [        -  -   S[        S-  -  S[        S-  -  [        -  [        -  -   S[        S-  -  [        S-  -  [        S-  -  -   -  [        [        5      [        [        [        -  [        -   5      -
  [        S-  -  -   :X  d   e[        [        S[        S-  -
  -  [        5      [        [        S-  S-
  5      * S-  :X  d   e[        [        * S[        S-  -
  -  [        5      [        [        S-  S-
  5      S-  :X  d   e[        [        S-  SS[        -
  -  -
  R                  [        5      [        5      [        S-  S[        S-
  -  -   :X  d   e[        [        5      n[        S[        S-  S-   -  [        [        S9U:X  d   e[        S[        S-  S-   -  [        SS9U:X  d   e[        S[        S-  S-   -  [        [        S9U:X  d   e[        5       n[        SUS-  S-   -  X3S9[        U5      :X  d   eg )Nr                  realTF$                        	      1   )symbolr   )r   r   Zeror   Oner   r   r
   r   r   Halfr	   halfr   diffr   )fgansds       `/var/www/auris/envauris/lib/python3.13/site-packages/sympy/integrals/tests/test_rationaltools.pytest_ratintr6      sP
   !&&!!!!!A$?ac!!!!Q<1a46!!!!A#q>QT!!!"Q$?q!te###!AqD&1Q3,"A&!Q$A+/999	A	AA!%s1q5z)))1&!AE
***	1qA	AA!#q>QT!Vad1f_,,,	A	
QQA!#q>SA1-a////	A	1qA!#qt$Q///!#qt$Q///!#qu%3q1u:a!CAJ,q.)HHHH	"A	1qAv!Q$1a4'!+a/A!#q>
3q1u:#a!e*$1q1a4!8'<<= = = 	
1qAvA	1qAv!Q$"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!#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$q(A!#q>	AFF1a4K!&&QUQT\!222a!A#g!Q$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$h-#s1a4!8}Q6661Q3AE?((+Q/1Q3AE?BBB
q'C!QTAX,!,333!QTAX,#.#555!QTAX,!,333 	A!QTAX,,Q777    c                  ~   [        [        [        S-  S-
  [        [        5      [        [        S-  S-
  [        5      [        S[        -  S-   [        5      4/:X  d   e[        [        S-  [        S-  S-
  [        [        5      [        [        S-  S-
  [        5      [        S[        -  S-   [        5      4/:X  d   eg )Nr   r'   r   r   r   r   )r   r   r   r    r7   r5   test_ratint_logpartr;   t   s    !QTAXq!,
q!tax
T"Q$(A.	/01 1 1!Q$1q!Q/
q!tax
T"Q$(A.	/01 1 1r7   c                  p    [        S[        S-  S-   -  [        5      [        [        S-  5      S-  :X  d   eg )Nr   r   r%   r    )r   r   r
   r:   r7   r5   test_issue_5414r=   {   s/    !QTBY-#tAaCy{222r7   c                     [        S[        S-  [        S-  -   -  [        5      [        * [	        [        * [        -  [        -   5      -  S-  [        [	        [        [        -  [        -   5      -  S-  -   [        -  :X  d   eg )Nr   r   )r   r   r   r   r   r:   r7   r5   test_issue_5249r?      sm    	1a4!Q$;!"3r!tax= 0 2Qs1Q37|^A5E EqHI I Ir7   c            
      r   [        SSS9u  pn[        [        XU-  [        S-  -  U S-  -   X-  -   -  [        5      5      [	        U 5      [        [	        U5      [	        U5      -  [        -  [	        U 5      [	        X-   5      -  -  5      -  [	        U5      [	        U5      -  [	        X-   5      -  -  :X  d   eg )Nza,b,cTpositiver   )r   r   r   r   r	   r
   )r   r   cs      r5   test_issue_5817rD      s    g-GA!F1c!Q$hAo34a89QTAwq'$qu+-/ 0 	015aaae1L	NN N Nr7   c                  `    [        S5      n [        SU S-  S-   -  5      [        U 5      :X  d   eg )Nur   r   )r   r   r
   )rF   s    r5   test_issue_5981rG      s.    AQ1q\"d1g---r7   c                      [        SSS9u  pp#[        X0U-  U-   -  U5      X0-  U[        X-  U-   5      -  U S-  -  -
  :X  d   eg )Nza b c xTrA   r   )r   r   r   )r   r   rC   r   s       r5   test_issue_10488rI      sO    i$/GAQ!AYq!QS1Sq\>!Q$+>%>>>>r7   c                  n   [        SSS9n [        U [        S-  U S-  -   -  [        5      [        [        U -  5      :X  d   e[        S[        S-  U S-  -   -  [        5      [        [        U -  5      U -  :X  d   e[        SSU S-  [        S-  -  -   -  [        5      [        U [        -  5      U -  :X  d   eg )Nr   Tnonzeror   r   r   r   r   r
   r   s    r5   "test_issues_8246_12050_13501_14080rO      s    T"AQ1q!t_a(D1I555Q1q!t_a(D1IaK777QAqDAI&*d1Q3ik999r7   c            
         [        SSS9u  p[        [        S-  S-   U S-  -
  [        S-  S-   US-  -   -  [        5      [        US-  U S-  -   [        [        [	        US-  S-   5      -  5      -  [	        US-  S-   5      -  -
  :X  d   eg )Nzk a0Tr   r   r   )r   r   r   r
   r	   )ka0s     r5   test_issue_6308rS      s    F&EAadQhAo1q2q5(891=	RUQT\4$r1uqy/ 1224A	?BBC C Cr7   c                      [        SSS9n [        S[        S-  U S-  -   S-  -  [        5      [        SU S-  -  SU S-  -  [        S-  -  -   -  [        [        U -  5      SU S-  -  -  -   :X  d   eg )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                  ,   [        [        [        R                  -   [        SS9[        [	        S5      S-  [        SS9pS[        S[	        S5      -  [        -  S-  [	        S5      S-  -   5      -  n[        X5      U:X  d   e[        X5      U* :X  d   eg )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.MqtAd1gIaKMDGAI-..Fq&&&q'''r7   c            	      "   S[         -  S-   [         S-  [         -   S-   -  S[         -  -   n [        U [         5      [        [         S-  [         S-  -   [         -   5      :X  d   e[        S[         -  S-   [         S-  S[         -  -   S-   -  S[         -  -   [         5      S[        [         5      -  S[        [         S-  S[         -  -   S-   5      -  -   [        S5      [	        [        S5      [         -  S-  [        S5      -   5      -  S-  -
  :X  d   eg )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   