
    sgS                        d dl mZmZmZ d dlmZ d dlmZ d dlm	Z	m
Z
 d dlmZmZ d dlmZmZmZmZ d dlmZ d dlmZ  e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 Z#d Z$d Z%d Z&d Z'd Z(d Z)d Z*y)    )Rationaloopi)S)Symbol)explog)rootsqrt)asincossintan)together)limitxc                      ddt         t        d      t        d      z  dz
  z  z  z   j                  t               dk(  sJ y )N         )r   r   )r   r	   leadterm     U/var/www/html/venv/lib/python3.12/site-packages/sympy/series/tests/test_demidovich.pytest_leadtermr      s;    !c!fSVma'(((2215???r   c                     t        | d      S )Nr   r
   r   s    r   root3r          1:r   c                     t        | d      S )N   r   r   s    r   root4r#      r    r   c                      t        dt        dz   z  dt        dz   z  z   dt        z  dt        z  z   z  t        t              dk(  sJ y )Nr   r   r   r   r   r   r   r   r   test_Limits_simple_0r&      s?    !a!e*q1q5z)AqD1a4K8!R@AEEEr   c                  j   t        t        dz   t        dz   z  t        dz   z  t        dz  z  t        t              dk(  sJ t        t        t        dz         t        t              z
  t        t              dk(  sJ t        dt        z  dz
  dt        z  dz   z  dt        z  dz
  z  dt        dz  z  t        z   dz
  z  t        t              dk(  sJ t        t        t	        t        dz  d	z         z  t        t              dk(  sJ t        t        dz   dz  t        dz  dz   z  t        t              dk(  sJ y )
Nr   r   r   r      r"         
   r   r   r   r   r   r   r   r   test_Limits_simple_1r-       s   !a%!a%!a%(A-q"5:::a!etAw&2.!333!A#'AaC!G$acAg.!Q$
Q?BG1LLL5A##Q+q000!a%!QTAX&2.!333r   c                     t        dt        z  t        dz  dz
  z  t        t              dk(  sJ t        t        dz  dt        z  z
  dz   dt        z  dz   z  t        t              t        u sJ t        dt        dz  z  t        z
  dz   t        dz  dt        z  z
  dz   z  t        t              dk(  sJ t        dt        dz  z  dt        z  z
  d	z
  t        t        d	z  dz         z  t        t              dk(  sJ t        dt        z  dz   t        t	        t              z   z  t        t              dk(  sJ t        t        dz  d
t        t        t              z  z   z  t        t              t        u sJ t        t	        t        dz  dz         t        dz   z  t        t              dk(  sJ t        t        t              t        t        t        t        t        t              z         z         z  t        t              dk(  sJ y )Ni  r   r   r   r(   r      r*   r"   r+   r,   r   r   r   test_Limits_simple_2r0   (   s   aA"Ar*a///!Q$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$q47{"3344a<AAAr   c                      t        d      } t        t        t        dz  | dz   t        z  z
  | z   t        dz  | dz  z
  z  t        |             | dz
  d| dz  z  z  k(  sJ y )Nar   r   r   )r   r   r   r   r2   s    r   test_Limits_simple_3ar4   3   sf    sAE1a41q5!)+a/!Q$A+>1EF	
Q1a4  r   c                     t        d      } t        t        | z   dz  t        dz  z
  | z  | d      dt        dz  z  k(  sJ t        ddt        z
  z  ddt        dz  z
  z  z
  t        d      dk(  sJ t        t        dt        z         dz
  t	        dt        z         dz
  z  t        d      t        d      dz  k(  sJ t        t        t              dz
  t        dz
  z  t        d      t        d      dz  k(  sJ t        t        t              dz
  t	        t              dz
  z  t        d	      dk(  sJ t        t	        t              dz
  t        t              dz
  z  t        d      t        d      dz  k(  sJ t        t	        t        dz        dt	        t              z  z
  dz   t        dz
  dz  z  t        d      t        d      d
z  k(  sJ y )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>>>$q'A+a1-q"5:::%(Q,qA.15!QFFF	q!tqqz	!A	%Az11a9<DQKMJ J Jr   c                  @   t        d      } t        t        t              t        |       z
  t        | z
  z  t        |       ddt        |       z  z  k(  sJ t        t        t              dz
  t	        t              dz
  z  t        d      t        dd      k(  sJ t        t        dt        z         t        dt        z
        z
  t        z  t        d      dk(  sJ t        t        t        dz  dt        z  z
  dz         t        z
  t        t              t        dd      k(  sJ y )	Nr2   r   r   r   r   r(   r)   )r   r   r   r   r   r   r   r3   s    r   test_Limits_simple_4ar=   F   s    sA$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                      t        t        t        t        dz  dz         t        z
  z  t        t              t	        d      dz  k(  sJ y )Nr   r   )r   r   r   r   r   r   r   r   test_limits_simple_4aar?   N   s7    DANQ&'B/8A;q=@@@r   c                  l    t        t        t        t        dz  dz
        z
  t        t              dk(  sJ y )Nr   r   r   )r   r   r   r   r   r   r   test_Limits_simple_4brA   R   s*    U1a4!8_$a,111r   c                      t        t        dt        t              z         t        z  t        t               dk(  sJ t        t        dt        t              z         t        z  t        t              dk(  sJ y )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                      t        t        t              t        z  t        t              dk(  sJ t        t        t        dt        z        z  t        d      dk(  sJ y )Nr   r   )r   r   r   r   r   r   r   test_boundedrE   \   sD    Q1b!Q&&&3qs8Q"a'''r   c                  r    t        t        dt        z        t        z  dt        z   z  t        d      dk(  sJ y )Nr   r   r   )r   r   r   r   r   r   test_f1arG   a   s.    #ac(1*A&1-222r   c                  z    t        t        dz
  t        dz   z  t        z  t        t              t        d      k(  sJ y )Nr   )r   r   r   r   r   r   r   	test_f1a2rJ   f   s.    1q51q5/A%q"-R888r   c            	         t        d      } t        d      }t        d      }t        d      }t        t        t              t        z  t        d      t        d      dz  k(  sJ t        t        dt        z        t        z  t        d      dk(  sJ t        t        dt        z        t        dt        z        z  t        d      t	        dd      k(  sJ t        t        t
        t        z        t        dt
        z  t        z        z  t        d      t	        d	d      k(  sJ t        t        t        t
        t        z        z  t        t              t
        k(  sJ t        d	t        t              z
  t        dz  z  t        d      t        j                  k(  sJ t        t        t        d	t        z        z  t        t              d	k(  sJ t        t        | t        z        t        |t        z        z
  t        dz  z  t        d      | dz   dz  |dz  dz  z   k(  sJ t        t        t              t        t              z
  t        dz  z  t        d      t        j                  k(  sJ t        t        t        dt        z        z
  t        t        dt        z        z   z  t        d      t	        d	d
       k(  sJ t        d	t        t        t                    z
  t        dz  z  t        d      t	        d	d
      k(  sJ t        t        d	t        t              z         t        d	t        t              z
        z
  t        z  t        d      d	k(  sJ t        d	|t        z  z   t        z  t        t              t        |      k(  sJ t        t        t              t        |      z
  t        |z
  z  t        |      t        |      k(  sJ t        t        t              t        |      z
  t        |z
  z  t        |      t        |       k(  sJ t        t        t        |z         t        t              z
  |z  |d      t        t              k(  sJ y )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                  t    t        t        dz   dt        z  dz   z  t        dz  z  t        t              dk(  sJ y )Nr   r   r   r%   r   r   r   test_f2arQ      s3    1q51Q37#q!t,a4999r   c                      t        t        t        t                    t	        t        t                    z
  t        t              dz  z  t        d      t        dd       k(  sJ y )Nr   r   r      )r   r   r   r   r   r   r   r   r   r   test_f2rT      s[    $AA- "%a&!)-./48@B7GH H Hr   c                  t    t        d      } t        t        | t        z        t        z  t        d      | k(  sJ y )Nr2   r   )r   r   r   r   r3   s    r   test_f3rV      s.    sAac1a#q(((r   N)+sympy.core.numbersr   r   r   sympy.core.singletonr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   r	   (sympy.functions.elementary.miscellaneousr
   r   (sympy.functions.elementary.trigonometricr   r   r   r   sympy.polys.rationaltoolsr   sympy.series.limitsr   r   r   r   r#   r&   r-   r0   r4   r:   r=   r?   rA   rC   rE   rG   rJ   rO   rQ   rT   rV   r   r   r   <module>r_      s    1 1 " $ = A J J . %
 3K@F4B	JEA2
0
(
3
9
:0:H
)r   