
    gS                     
   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*dS )    )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                       t                     dk    sJ d S )N         )r   r   )r   r	   leadterm     ^/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/series/tests/test_demidovich.pytest_leadtermr      sK    !c!ffSVVma'(((2215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 d S )Nr   r   r   r   r   r   r   r   r   test_Limits_simple_0r&      sK    !a!e*q1q5z)AqD1a4K8!R@@AEEEEEEr   c                     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 d S )
Nr   r   r   r      r"         
   r   r   r   r   r   r   r   r   test_Limits_simple_1r-       s-   !a%!a%!a%(A-q"55::::a!etAww&2..!3333!A#'AaC!G$acAg.!Q$
Q?BGG1LLLL5A###Q++q0000!a%!QTAX&2..!333333r   c                     t          dt          z  t          dz  dz
  z  t          t                    dk    sJ t          t          dz  dt          z  z
  dz   dt          z  dz   z  t          t                    t          u sJ t          dt          dz  z  t          z
  dz   t          dz  dt          z  z
  dz   z  t          t                    dk    sJ t          dt          dz  z  dt          z  z
  d	z
  t          t          d	z  dz             z  t          t                    dk    sJ t          dt          z  dz   t          t	          t                    z   z  t          t                    dk    sJ t          t          dz  d
t          t          t                    z  z   z  t          t                    t          u sJ t          t	          t          dz  dz             t          dz   z  t          t                    dk    sJ t          t          t                    t          t          t          t          t          t                    z             z             z  t          t                    dk    sJ d S )Ni  r   r   r   r(   r      r*   r"   r+   r,   r   r   r   test_Limits_simple_2r0   (   s   aA"Ar**a////!Q$1*q.1Q37+Q33r9999!AqD&1*q.1a4!A#:>2Ar::a????!AqD&1Q3,"DANN2Ar::a????!A#'AaL)1b11Q6666ArAd1ggI~&2.."4444q!tax!a%(!R00A5555aa$q477{"3"33444a<<AAAAAAr   c                      t          d          } t          t          t          dz  | dz   t          z  z
  | z   t          dz  | dz  z
  z  t          |                     | dz
  d| dz  z  z  k    sJ d S )Nar   r   r   )r   r   r   r   r2   s    r   test_Limits_simple_3ar4   3   s}    sAE1a41q5!)+a/!Q$A+>1EEFF	
Q1a4     r   c                  x   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 d S )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7!QU)aQTl*Q22b8888$q1u++/E!a%LL1$45q!<<AMMMM$q''A+A&1--!Q>>>>$q''A+a1-q"55::::%((Q,qA.155!QFFFF	q!tqqz	!A	%Az11a9 9<DQKKMJ J J J J Jr   c                     t          d          } t          t          t                    t          |           z
  t          | z
  z  t          |           ddt          |           z  z  k    sJ t          t          t                    dz
  t	          t                    dz
  z  t          d          t          dd          k    sJ t          t          dt          z             t          dt          z
            z
  t          z  t          d          dk    sJ t          t          t          dz  dt          z  z
  dz             t          z
  t          t                    t          dd          k    sJ d S )	Nr2   r   r   r   r   r(   r)   )r   r   r   r   r   r   r   r3   s    r   test_Limits_simple_4ar=   F   s   sA$q''DGG#a!e,a33q!DGG)}DDDD$q''A+a1-q!44AFFFF$q1u++QU+Q.155::::adQqSj1n%%)1b11Xb!__DDDDDDr   c                      t          t          t          t          dz  dz             t          z
  z  t          t                    t	          d          dz  k    sJ d S )Nr   r   )r   r   r   r   r   r   r   r   test_limits_simple_4aar?   N   sG    DANNQ&'B//8A;;q=@@@@@@r   c                      t          t          t          t          dz  dz
            z
  t          t                    dk    sJ d S )Nr   r   r   )r   r   r   r   r   r   r   test_Limits_simple_4brA   R   s8    U1a4!8__$a,,111111r   c                  4   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 d S )Nr   r   )r   r	   r   r   r   r   r   r   test_Limits_simple_4crC   W   sn    QQZ"As++q0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 d S )Nr   r   )r   r   r   r   r   r   r   test_boundedrE   \   sZ    Q1b!!Q&&&&3qs88Q""a''''''r   c                      t          t          dt          z            t          z  dt          z   z  t          d          dk    sJ d S )Nr   r   r   )r   r   r   r   r   r   test_f1arG   a   s<    #ac((1*A&1--222222r   c                      t          t          dz
  t          dz   z  t          z  t          t                    t          d          k    sJ d S )Nr   )r   r   r   r   r   r   r   	test_f1a2rJ   f   s<    1q51q5/A%q"--R888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 d S )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FF1H,,,,QqS!Q""a''''QqS#ac(("Aq))Xa^^;;;;RT3qtAv;;&1--!Q????3r!t99a$$****!c!ff*ad"Aq))QV33333qs88Q##q((((#ac((S1XX%q!t+Q22q!teAg1Q6FFFFF#a&&3q66/1a4'A..!&8888!c!A#hh,S1XX.155(1a..HHHH!d3q66ll"AqD(!Q//8Aq>>AAAA$q3q66z""T!c!ff*%5%55q8!Q??1DDDD!ac'Aq"%%Q////#a&&3q66/AE*Aq11SVV;;;;#a&&3q66/AE*Aq11c!ffW<<<<#a!e**s1vv%q(!Q//3q66999999r   c                      t          t          dz   dt          z  dz   z  t          dz  z  t          t                    dk    sJ d S )Nr   r   r   r%   r   r   r   test_f2arQ      s?    1q51Q37#q!t,a44999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 d S )Nr   r   r      )r   r   r   r   r   r   r   r   r   r   test_f2rT      s    $A A-- "%a&&!)-./4 48@B7GH H H H H Hr   c                      t          d          } t          t          | t          z            t          z  t          d          | k    sJ d S )Nr2   r   )r   r   r   r   r3   s    r   test_f3rV      s>    sAac1a##q((((((r   N)+sympy.core.numbersr   r   r   sympy.core.singletonr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   r	   (sympy.functions.elementary.miscellaneousr
   r   (sympy.functions.elementary.trigonometricr   r   r   r   sympy.polys.rationaltoolsr   sympy.series.limitsr   r   r   r   r#   r&   r-   r0   r4   r:   r=   r?   rA   rC   rE   rG   rJ   rO   rQ   rT   rV   r   r   r   <module>r_      s
   1 1 1 1 1 1 1 1 1 1 " " " " " " $ $ $ $ $ $ = = = = = = = = A A A A A A A A J J J J J J J J J J J J . . . . . . % % % % % %
 F3KK@ @ @    F F F4 4 4B B B  	J 	J 	JE E EA A A2 2 2
0 0 0
( ( (
3 3 3
9 9 9
: : :0: : :H H H
) ) ) ) )r   