
    \h                         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Jr  S SKJrJrJrJrJrJrJrJrJr  S rS	 rg
)    )Rationalpi)log)sqrt)erf)GF)ratsimpratsimpmodprime)	xyztabcdec                      S[         -  S[        -  -   [         [        -   [         [        -  -  pX:w  a  [        U 5      U:X  d   eSSS[         -  -   -  SS[         S-   -  -
  pX:w  a  [        U 5      U:X  d   e[         [         [        -   -  [        [         [        -   -  -   SpX:w  a  [        U 5      U:X  d   e[         * [        -
  [        S-  [         [        -   -  -
  [         S-  [         [        -   -  -   S[        -  pX:w  a  [        U 5      U:X  d   e[        [        -  [         -  [        -  [        [        -  [
        -  -   [        [        -  [         -  [        -  -
  [        [        -  [
        -  -
  [        [        -  [         -  [        -  -
  [        [        -  [         -  -
  [        [        -  [
        -  -
  [        [         -  -   [         [        -  [
        -   -  n [        [        -  [        [        -  -
  [        [        -  -
  [        * [        -  [         -  [        [         -  -   [         [        -  [
        -   -  -   [        [        -  [        [        -  -
  [        [        -  -
  [        [        -  [         -  [        [         -  -
  [         [        -  [
        -   -  -
  /nX:w  a  [        U 5      U;   d   e[        [        5      n[        [        [         5      S-
  5      n[        [        [         5      S-   5      nSS[        [         5      -  -
  nX4-  U-  X5-  U-  -
  X5-  [        [         5      -  U-  -   X4-  [        [         5      -  U-  -
  SU-  U-  -   n [        U 5      X4-  S-  X5-  S-  -
  US[        [         5      -  S-
  -  -
  :X  d   eg )N            )r   r   r	   r   r   r   r   r   r   r   r   r   r   r   )fgGABCDs          Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/simplify/tests/test_ratsimp.pytest_ratsimpr"      s   Q319q1uqsmq6gajAo%%a!A#g;Aq1uIq6gajAo%%a!e9q!a%y !q6gajAo%%26AqD!a%L 1a4Q</Aq6gajAo%%	
1Qq1Q3q51Q3q57	"QqSU	*QqSU1W	4qs1u	<qs1u	D	
1
sQw	A	
1qsQqSQBqDFQqSL1Q373	3	
1qsQqSQqSUQqS[1Q373	3	5A 6gajAo%%RACFQJACFQJA	Ac!fHA	AACF
1$qs3q6z!|3ac!e;A1:QQAc!fHqL)99999    c                  f   [         S-  [        -   [         -   n [        [         -
  n[        [         S-  -  [        -
  [         -
  /n[        X-  U[        [         SS9[        S-  * [        [         -  -
  [        -
  [         -
  [        S-  * [        [         -  -   -  :X  d   e[        [         S-  -   S-
  n [        [         S-  -   [         -
  S-
  n[        [         -  S-
  /n[        X-  U[        [         SS9S[         -   [        -
  [         [        -
  -  :X  d   eS[        S-  -  S[        S-  -  -   S[        -  [         -  -   S	[        -  -   S
[         -  -   S-   n S[        S-  -  [         [        S-  -  -
  S[        S-  -  -   S[        -  [         -  -   S[         -  -   S[        -  -   S-   n[        S-  [         S-  -   S-
  /n[        X-  U[        [         SS9SS[         -  -   S[        -  -
  S[         -  S[        -  -
  -  :X  d   e[        [         -  [        -
  S[         -  -
  S-   n [        [         S-  -   S[         -  -
  n[        S-
  [         S-
  /n[        X-  U[        [         SS9[        SS5      :X  d   e[        [        [         S[        -  -
  /SS9[         S-  :X  d   e[        S-  S[        S-  -  -   S[        S-  -  -   S[        S-  -  -   [        -   S[        -  -   [        S-  -   n [        U [        S-   /[	        S5      S9S:X  d   e[        U [        S-   /[	        S5      S9S:X  d   eg )N   lex)orderr   r         r                  %   r      r   )domain)r   r   r
   r   r   )r   r   Fs      r!   test_ratsimpmodprimer4   /   s   	1q1A	AA	
1a4!aA131au5
Q$1q1	!Q$1-. . . 	
AqD1A	AqD1qA	
1q	A131au5	
QQU   	
!Q$AqD1Q3q5 2a4'"Q$.3A	!Q$1a4"QT'!AaCE)BqD02a47"<A	
A1qA131au5	
QqS1Q31qs#$ $ $ 	
!a!A#A	AqD1Q3A	
QAA131au5A   1q1Q3wiu5	!   
A!Q$1a4	!AqD&	(1	,qs	2QW	<A1q1ugbe49991q1ugbe4:::r#   N)sympy.core.numbersr   r   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr   'sympy.functions.special.error_functionsr   sympy.polys.domainsr   sympy.simplify.ratsimpr	   r
   	sympy.abcr   r   r   r   r   r   r   r   r   r"   r4    r#   r!   <module>r=      s+    - 6 9 7 " = / / /!:H;r#   