
    g%                         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*dS )    )IRational)S)Dummysymbols)log)sqrt)atan)	integrate)Poly)simplify)ratintratint_logpartlog_to_atan)abxtc            
         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
                      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 d S )Nr                  realTF$                        	      1   )symbolr   )r   r   Zeror   Oner   r   r
   r   r   Halfr	   halfr   diffr   )fgansds       d/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/integrals/tests/test_rationaltools.pytest_ratintr6      s   !&!!!!!!A$$??ac!!!!!Q<<1a46!!!!!A#q>>QT!!!!"Q$??q!te####!AqD&1Q3,"A&&!Q$A+/9999	A	AA!a%s1q5zz))))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$$$Q////!A#qu%%%3q1u::a!CAJJ,q.)HHHHH	"A	1qAv!Q$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$KLLLM M M M 	
1r!Q$w1a4!A#%)A	1qAv1a4!AqD&(A!A#q>>	
QqS1QT6	AadF	"QqS1QT6\AqD%89CFFBC C C C 1a46AaC.!$$
r!t)a1f
r!Q$w
&'Qq!tVad):;	$q''	$qay{###	$&'fQTk	245c!ad(mmO	DD D D D 	
1q!ta1fq!t#a'!+A	1qAv!Q$1$q(A!A#q>>	AF1a4K!&QUQT\!2!222a!A#g!Q$1r@Q5RR
477
4QQ/!A#d1gg+a-?@@@C	DD D D D !QTAX\"A&&	$q''	$tAwwqy1Q3tAww;q=0111!34 4 4 4 !QTAX,""	QUQT\		1s1q5zz!|+d1ggdDGG8<A#d1gg+a-<  7! 7! /!!"/# 	## # # # !QTAX\"AE222	
1d7
3tax$q&D.0111!3	!T'	#dQha4/0002	33 3 3 3 !QTAX,...#a!e**Q,	"a1QW9Q;	&TEAI!T'	!,C(D(DD3E	"a1QW9Q;	&TEAI!T'	!,C(D(DD3E E E E E
 !QAaC!|^$a((	
1qs1uqAv!Q$q
*Qq!tVAqD[A-==>FFS1q\\!1a4B( 	(( ( ( ( !QAX,""s1a4!8}}nQ&666661"a!Q$h-##s1a4!8}}Q66661Q3AE?((++Q//1Q3AE?BBBB
q''C!QTAX,!,,,3333!QTAX,#...#5555!QTAX,!,,,3333 	A!QTAX,!,,,Q777777    c                     t          t          t          dz  dz
  t          t                    t          t          dz  dz
  t                    t          dt          z  dz   t                    fgk    sJ t          t          dz  t          dz  dz
  t          t                    t          t          dz  dz
  t                    t          dt          z  dz   t                    fgk    sJ d S )Nr   r'   r   r   r   r   )r   r   r   r    r7   r5   test_ratint_logpartr;   t   s    !QTAXq!,,
q!tax

T"Q$(A..	/01 1 1 1!Q$1q!Q//
q!tax

T"Q$(A..	/01 1 1 1 1 1r7   c                      t          dt          dz  dz   z  t                    t          t          dz            dz  k    sJ d S )Nr   r   r%   r    )r   r   r
   r:   r7   r5   test_issue_5414r=   {   s=    !QTBY-##tAaCyy{222222r7   c                  6   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 d S )Nr   r   )r   r   r   r   r   r:   r7   r5   test_issue_5249r?      s    	1a4!Q$; !"3r!tax== 0 2Qs1Q37||^A5E EqHI I I I I Ir7   c            
         t          dd          \  } }}t          t          | ||z  t          dz  z  | dz  z   || z  z   z  t                              t	          |           t          t	          |          t	          |          z  t          z  t	          |           t	          | |z             z  z            z  t	          |          t	          |          z  t	          | |z             z  z  k    sJ d S )Nza,b,cTpositiver   )r   r   r   r   r	   r
   )r   r   cs      r5   test_issue_5817rD      s    g---GAq!F1ac!Q$hAo!34a8899QT Awwq''$q1u++-/ 0 0 	015aaa!e1L	NN N N N N Nr7   c                  z    t          d          } t          d| dz  dz   z            t          |           k    sJ d S )Nur   r   )r   r   r
   )rF   s    r5   test_issue_5981rG      s>    AQ1q\""d1gg------r7   c                      t          dd          \  } }}}t          || |z  |z   z  |          || z  |t          | |z  |z             z  | dz  z  z
  k    sJ d S )Nza b c xTrA   r   )r   r   r   )r   r   rC   r   s       r5   test_issue_10488rI      sm    i$///GAa!Q!AYq!!QqS1S1q\\>!Q$+>%>>>>>>>r7   c                     t          dd          } t          | t          dz  | dz  z   z  t                    t          t          | z            k    sJ t          dt          dz  | dz  z   z  t                    t          t          | z            | z  k    sJ t          dd| dz  t          dz  z  z   z  t                    t          | t          z            | z  k    sJ d S )Nr   Tnonzeror   r   r   r   r   r
   r   s    r5   "test_issues_8246_12050_13501_14080rO      s    T"""AQ1q!t_a((D1II5555Q1q!t_a((D1IIaK7777QAqDAI&**d1Q3iik999999r7   c            
      R   t          dd          \  } }t          t          dz  dz   | dz  z
  t          dz  dz   |dz  z   z  t                    t          |dz  | dz  z   t          t          t	          |dz  dz             z            z  t	          |dz  dz             z  z
  k    sJ d S )Nzk a0Tr   r   r   )r   r   r   r
   r	   )ka0s     r5   test_issue_6308rS      s    F&&&EAradQhAo1q2q5(891==	RUQT\4$r1uqy// 12224A	??BBC C C 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 d S )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IIqAv$6	67 7 7 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 d S )NQQ)domainr   r   EX)r   r   r   r.   r	   r
   r   )r1   r2   fg_anss      r5   test_log_to_atanr[      s    QVQt,,,d47719a.M.M.MqAtAd1ggIaKMDGGAI-...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 d S )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6	#a&&1SA!a((((4774Q	!d1gg4 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      s   , , , , , , , , " " " " " " . . . . . . . . 6 6 6 6 6 6 9 9 9 9 9 9 9 9 9 9 9 9 / / / / / / & & & & & & , , , , , , M M M M M M M M M M                        v_8 _8 _8D1 1 13 3 3I I I
N N N. . .? ? ?
: : :C C C7 7 7( ( (" " " " "r7   