
    \hS                        S SK JrJr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  S SKJrJrJrJr  S SKJr  S SKJr  \" S	5      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#S r$S r%S r&S r'S r(S r)S r*g)    )Rationaloopi)S)Symbol)explog)rootsqrt)asincossintan)together)limitxc                      SS[         [        S5      [        S5      -  S-
  -  -  -   R                  [         5      S:X  d   eg )N         )r   r   )r   r	   leadterm     Z/var/www/auris/envauris/lib/python3.13/site-packages/sympy/series/tests/test_demidovich.pytest_leadtermr      s;    !c!fSVma'(((2215???r   c                     [        U S5      $ )Nr   r
   r   s    r   root3r          1:r   c                     [        U S5      $ )N   r   r   s    r   root4r#      r    r   c                      [        S[        S-   -  S[        S-   -  -   S[        -  S[        -  -   -  [        [        5      S:X  d   eg )Nr   r   r   r   r   r   r   r   r   test_Limits_simple_0r&      s?    !a!e*q1q5z)AqD1a4K8!R@AEEEr   c                  t   [        [        S-   [        S-   -  [        S-   -  [        S-  -  [        [        5      S:X  d   e[        [        [        S-   5      [        [        5      -
  [        [        5      S:X  d   e[        S[        -  S-
  S[        -  S-   -  S[        -  S-
  -  S[        S-  -  [        -   S-
  -  [        [        5      S:X  d   e[        [        [	        [        S-  S	-   5      -  [        [        5      S:X  d   e[        [        S-   S-  [        S-  S-   -  [        [        5      S:X  d   eg )
Nr   r   r   r      r"         
   r   r   r   r   r   r   r   r   test_Limits_simple_1r-       s   !a%!a%!a%(A-q"5:::a!etAw&2.!333!A#'AaC!G$acAg.!Q$
Q?BG1LLL5A##Q+q000!a%!QTAX&2.!333r   c                     [        S[        -  [        S-  S-
  -  [        [        5      S:X  d   e[        [        S-  S[        -  -
  S-   S[        -  S-   -  [        [        5      [        L d   e[        S[        S-  -  [        -
  S-   [        S-  S[        -  -
  S-   -  [        [        5      S:X  d   e[        S[        S-  -  S[        -  -
  S	-
  [        [        S	-  S-   5      -  [        [        5      S:X  d   e[        S[        -  S-   [        [	        [        5      -   -  [        [        5      S:X  d   e[        [        S-  S
[        [        [        5      -  -   -  [        [        5      [        L d   e[        [	        [        S-  S-   5      [        S-   -  [        [        5      S:X  d   e[        [        [        5      [        [        [        [        [        [        5      -   5      -   5      -  [        [        5      S:X  d   eg )Ni  r   r   r   r(   r      r*   r"   r+   r,   r   r   r   test_Limits_simple_2r0   (   s   aA"Ar*a///!Q$1*q.1Q37+Q3r999!AqD&1*q.1a4!A#:>2Ar:a???!AqD&1Q3,"DAN2Ar:a???!A#'AaL)1b1Q666ArAd1gI~&2."444q!tax!a%(!R0A555aa$q47{"3344a<AAAr   c                      [        S5      n [        [        [        S-  U S-   [        -  -
  U -   [        S-  U S-  -
  -  [        U 5      5      U S-
  SU S-  -  -  :X  d   eg )Nar   r   r   )r   r   r   r   r2   s    r   test_Limits_simple_3ar4   3   sf    sAE1a41q5!)+a/!Q$A+>1EF	
Q1a4  r   c                     [        S5      n [        [        U -   S-  [        S-  -
  U -  U S5      S[        S-  -  :X  d   e[        SS[        -
  -  SS[        S-  -
  -  -
  [        S5      S:X  d   e[        [        S[        -   5      S-
  [	        S[        -   5      S-
  -  [        S5      [        S5      S-  :X  d   e[        [        [        5      S-
  [        S-
  -  [        S5      [        S5      S-  :X  d   e[        [        [        5      S-
  [	        [        5      S-
  -  [        S	5      S:X  d   e[        [	        [        5      S-
  [        [        5      S-
  -  [        S5      [        S5      S-  :X  d   e[        [	        [        S-  5      S[	        [        5      -  -
  S-   [        S-
  S-  -  [        S5      [        S5      S
-  :X  d   eg )Nhr   r   r   r   r*   r"   @   	   )r   r   r   r   r   r   r#   )r6   s    r   test_Limits_simple_3br:   :   s   sA1q51*q!t#Q&1-1a4777!QU)aQTl*Q2b888$q1u+/E!a%L1$45q!<AMMM$q'A+A&1-!Q>>>$q'A+a1-q"5:::%(Q,qA.15!QFFF	q!tqqz	!A	%Az11a9<DQKMJ J Jr   c                  H   [        S5      n [        [        [        5      [        U 5      -
  [        U -
  -  [        U 5      SS[        U 5      -  -  :X  d   e[        [        [        5      S-
  [	        [        5      S-
  -  [        S5      [        SS5      :X  d   e[        [        S[        -   5      [        S[        -
  5      -
  [        -  [        S5      S:X  d   e[        [        [        S-  S[        -  -
  S-   5      [        -
  [        [        5      [        SS5      :X  d   eg )	Nr2   r   r   r   r   r(   r)   )r   r   r   r   r   r   r   r3   s    r   test_Limits_simple_4ar=   F   s    sA$q'DG#a!e,a3q!DG)}DDD$q'A+a1-q!4AFFF$q1u+QU+Q.15:::adQqSj1n%)1b1Xb!_DDDr   c                      [        [        [        [        S-  S-   5      [        -
  -  [        [        5      [	        S5      S-  :X  d   eg )Nr   r   )r   r   r   r   r   r   r   r   test_limits_simple_4aar?   N   s7    DANQ&'B/8A;q=@@@r   c                  n    [        [        [        [        S-  S-
  5      -
  [        [        5      S:X  d   eg )Nr   r   r   )r   r   r   r   r   r   r   test_Limits_simple_4brA   R   s*    U1a4!8_$a,111r   c                      [        [        S[        [        5      -   5      [        -  [        [        * 5      S:X  d   e[        [        S[        [        5      -   5      [        -  [        [        5      S:X  d   eg )Nr   r   )r   r	   r   r   r   r   r   r   test_Limits_simple_4crC   W   sT    QQZ"As+q000QQZ"Ar*a///r   c                      [        [        [        5      [        -  [        [        5      S:X  d   e[        [        [        S[        -  5      -  [        S5      S:X  d   eg )Nr   r   )r   r   r   r   r   r   r   test_boundedrE   \   sD    Q1b!Q&&&3qs8Q"a'''r   c                  t    [        [        S[        -  5      [        -  S[        -   -  [        S5      S:X  d   eg )Nr   r   r   )r   r   r   r   r   r   test_f1arG   a   s.    #ac(1*A&1-222r   c                  |    [        [        S-
  [        S-   -  [        -  [        [        5      [        S5      :X  d   eg )Nr   )r   r   r   r   r   r   r   	test_f1a2rJ   f   s.    1q51q5/A%q"-R888r   c            	         [        S5      n [        S5      n[        S5      n[        S5      n[        [        [        5      [        -  [        S5      [        S5      S-  :X  d   e[        [        S[        -  5      [        -  [        S5      S:X  d   e[        [        S[        -  5      [        S[        -  5      -  [        S5      [	        SS5      :X  d   e[        [        [
        [        -  5      [        S[
        -  [        -  5      -  [        S5      [	        S	S5      :X  d   e[        [        [        [
        [        -  5      -  [        [        5      [
        :X  d   e[        S	[        [        5      -
  [        S-  -  [        S5      [        R                  :X  d   e[        [        [        S	[        -  5      -  [        [        5      S	:X  d   e[        [        U [        -  5      [        U[        -  5      -
  [        S-  -  [        S5      U S-  * S-  US-  S-  -   :X  d   e[        [        [        5      [        [        5      -
  [        S-  -  [        S5      [        R                  :X  d   e[        [        [        S[        -  5      -
  [        [        S[        -  5      -   -  [        S5      [	        S	S
5      * :X  d   e[        S	[        [        [        5      5      -
  [        S-  -  [        S5      [	        S	S
5      :X  d   e[        [        S	[        [        5      -   5      [        S	[        [        5      -
  5      -
  [        -  [        S5      S	:X  d   e[        S	U[        -  -   [        -  [        [        5      [        U5      :X  d   e[        [        [        5      [        U5      -
  [        U-
  -  [        U5      [        U5      :X  d   e[        [        [        5      [        U5      -
  [        U-
  -  [        U5      [        U5      * :X  d   e[        [        [        U-   5      [        [        5      -
  U-  US5      [        [        5      :X  d   eg )Nmnr6   r2   r   r   r   r(   r   r"   )r   r   r   r   r   r   r   r   r   Halfr   r   r   )rL   rM   r6   r2   s       r   test_f1brO   k   s*   sAsAsAsAQ1a CF1H,,,QqS!Q"a'''QqS#ac("Aq)Xa^;;;RT3qtAv;&1-!Q???3r!t9a$***!c!f*ad"Aq)QVV3333qs8Q#q(((#ac(S1X%q!t+Q2q!teAg1Q6FFFF#a&3q6/1a4'A.!&&888!c!A#h,S1X.15(1a.HHH!d3q6l"AqD(!Q/8Aq>AAA$q3q6z"T!c!f*%55q8!Q?1DDD!ac'Aq"%Q///#a&3q6/AE*Aq1SV;;;#a&3q6/AE*Aq1c!fW<<<#a!e*s1v%q(!Q/3q6999r   c                  v    [        [        S-   S[        -  S-   -  [        S-  -  [        [        5      S:X  d   eg )Nr   r   r   r%   r   r   r   test_f2arQ      s3    1q51Q37#q!t,a4999r   c                      [        [        [        [        5      5      [	        [        [        5      5      -
  [        [        5      S-  -  [        S5      [        SS5      * :X  d   eg )Nr   r   r      )r   r   r   r   r   r   r   r   r   r   test_f2rT      s[    $AA- "%a&!)-./48@B7GH H Hr   c                  v    [        S5      n [        [        U [        -  5      [        -  [        S5      U :X  d   eg )Nr2   r   )r   r   r   r   r3   s    r   test_f3rV      s.    sAac1a#q(((r   N)+sympy.core.numbersr   r   r   sympy.core.singletonr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   r	   (sympy.functions.elementary.miscellaneousr
   r   (sympy.functions.elementary.trigonometricr   r   r   r   sympy.polys.rationaltoolsr   sympy.series.limitsr   r   r   r   r#   r&   r-   r0   r4   r:   r=   r?   rA   rC   rE   rG   rJ   rO   rQ   rT   rV   r   r   r   <module>r_      s    1 1 " $ = A J J . %
 3K@F4B	JEA2
0
(
3
9
:0:H
)r   