
    Цit@                     0   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
  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  S SKJr  S S	KJrJr  S S
KJr  S SKJrJr  S SK J!r!  S SK"J#r#  S SK$J%r%J&r&J'r'J(r(  S r)S r*S r+S r,S r-S r.S r/S r0S r1S r2S r3S r4S r5S r6S r7S r8S r9S  r:S! r;S" r<S# r=S$ r>S% r?S& r@S' rAS( rBS) rCS* rDS+ rES, rFS- rGS. rHS/ rIS0 rJS1 rKS2 rLS3 rMS4 rNS5 rOS6 rPS7 rQS8 rRS9 rSS: rTS; rUS< rVS= rWS> rXS? rYS@ rZSA r[SB r\SC r]SD r^SE r_SF r`gG)H    )Add)Functionexpand)IRationalnanoopi)S)Symbolsymbols)	conjugate	transpose)explog)sqrt)cossin)Integral)OOrder)	unchanged)raises)wxyzc                      [        [        5        [        [        S[        -  [        S5      -  [        S5      -  -  [        5        g )N      )r   r   r   r        \/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/series/tests/test_order.pytest_caching_bugr%      s/     aDa"Q$s1v+c!f
q!r#   c                     [        S5      R                  [        5       :X  d   e[        [        5      R                  [        1:X  d   e[        S[        5      R                  [        1:X  d   e[        [        [        -  5      R                  [        [        1:X  d   e[        [        [        [        5      R                  [        [        1:X  d   eg N   )r   free_symbolssetr   r   r"   r#   r$   test_free_symbolsr+      s    8  CE)))8  QC'''A;##s***1:""q!f,,,Aq>&&1a&000r#   c                  t   [        S5      n [        S[        -  5      [        [        5      :X  d   e[        [        5      S-  [        [        5      :X  d   eS[        [        5      -  [        [        5      :X  d   e[        [        [        5      5      [        [        5      :X  d   e[        [        [        5      [        5      [        [        [        5      [        [        5      :X  d   e[        S5      [        S5      :X  d   e[        [	        [        5      5      [        S[        5      :X  d   e[        [	        S[        -  5      5      R
                  [	        S[        -  5      :X  d   e[        [        [	        S[        -  5      -  5      R
                  [        [	        S[        -  5      -  :X  d   e[        [        U S-  -  5      R
                  [        U S-  -  :X  d   e[        [        U [        SS5      -  -  5      R
                  [        U [        SS5      -  -  :X  d   e[        [        S-  [        -   [        -   [        5      [        S[        5      :X  d   e[        [        S-  [        -   [        -   [        5      [        S[        5      :X  d   e[        [        S 5        [        [        S	 5        g )
Nr      r    ir(   r!   c                  F    [        [        [        5      [        [        5      $ N)r   r   r   r"   r#   r$   <lambda>test_simple_1.<locals>.<lambda>0   s    uSVQ2r#   c                  0    [        [        S[        -
  5      $ Nr-   r   r   r"   r#   r$   r1   r2   1   s    eAq1uor#   )
r   r   r   r   r   exprr   r   
ValueError	TypeError)os    r$   test_simple_1r:   !   s   A1:q!!!8A:q!!!uQx<58###q?eAh&&&q1uQxA!6666:q!!!Q=E!QK'''QqS?3qs8+++3qs8!!Qs1Q3xZ///QqS?1qs8+++Qx1~%&',,Ahq!n4D0EEEEAAq!Qq!W,,,AAq!Qq!W,,,
:23
9-.r#   c                  ^   [        S[        -  5      [        -  [        [        S-  5      :X  d   e[        S[        -  5      [        -  [        S[        5      :X  d   e[        S[        -  5      [        -  [        S[        -  5      -  [        [        S-  [        S[        -  5      -  5      :X  d   e[        S[        -  5      [        -  [        S[        -  5      -  [        [        5      S-  -  R                  [        S-  [        S[        -  5      -  [        [        5      S-  -  :X  d   eg )Nr-   r(   r    )r   r   r   r   r6   r"   r#   r$   test_simple_2r=   4   s    1:a<5A;&&&1:a<5A;&&&1:a<AaC E!Q$s1Q3x-$8888!A#JqLQqS!#a&!)+11QT#ac(]3q62:5MMMMr#   c                  ~   [        [        5      [        -   [        [        5      :X  d   e[        [        5      S-   S[        [        5      -   :X  d   e[        [        5      [        S-  -   [        [        5      :X  d   e[        [        5      S[        -  -   S[        -  [        [        5      -   :X  d   e[        S[        -  5      S[        S-  -  -   S[        S-  -  [        S[        -  5      -   :X  d   e[        [        5      [        S[        -  5      -   [        [        5      [        S[        -  5      -   :X  d   eg Nr-   r(   r   r   r   r"   r#   r$   test_simple_3rA   ;   s    8a<58###8a<1uQx<'''8ad?eAh&&&8ac>QqS58^+++1:!Q$!AqD&51:"55558c!A#h%(S1X"5555r#   c                  T    [        [        5      S-  [        [        S-  5      :X  d   eg r4   r5   r"   r#   r$   test_simple_4rC   D   s     8Q;%1+%%%r#   c                  N   [        [        5      [        [        S-  5      -   [        [        5      :X  d   e[        [        5      [        [        S-  5      -   [        [        S-  5      :X  d   e[        [        5      [        S[        -  5      -   [        S[        -  5      :X  d   eg )Nr-   r(   r5   r"   r#   r$   test_simple_5rF   H   ss    8eAqDk!U1X---8eArEl"eArEl2228eAaCj E!A#J...r#   c                  V   [        [        5      [        [        5      -
  [        [        5      :X  d   e[        [        5      [        S5      -   [        S5      :X  d   e[        [        5      [        [        S-  5      -   [        [        5      :X  d   e[        S[        -  5      [        S5      -   [        S[        -  5      :X  d   e[        [        5      [        [        S[        -  5      5      -   [        [        S[        -  5      5      :X  d   e[        [        S-  5      [        [        S[        -  5      5      -   [        [        S[        -  5      5      :X  d   e[        [        S-  5      [        [        S[        -  5      5      -   [        [        S[        -  5      5      :X  d   eg )Nr(   r-   r    r<   r@   r"   r#   r$   test_simple_6rH   N   s   8eAh%(***8eAh%(***8eAqDk!U1X---1:a E!A#J...8eC!Ho%s1Q3x888A;s1Q3x(E#ac(O;;;B<%AaC/)U3qs8_<<<r#   c                     S[        S5      -   [        S5      :X  d   eS[        S5      -   [        S5      :X  d   e[        [        S5      -   [        S5      :X  d   eS[        -  [        S5      -   S[        -  [        S5      -   :X  d   eg Nr(   r-   )r   r   r"   r#   r$   test_simple_7rK   X   sv    qt8qtqt8qtqt8qtQ31:1qt###r#   c                     [        [        [        * 5      5      [        [        [        5      5      :X  d   e[        [        S-  [        [        5      -  5      [        [        [        SS5      -  5      :X  d   e[        [        S-  [        [        * S-  * 5      -  5      [        [        [        SS5      -  5      :X  d   e[        [        [        SS5      -  [        [        * S-  5      -  5      [        [        S-  5      :X  d   e[        [        S[        -  [        S-  -  -  5      [        [        [        * [        S-  -  -  5      :X  d   eg )Nr-   r!   r    	   rE   )r   r   r   r   r   r"   r#   r$   test_simple_8rN   _   s    T1"X;!DG*$$$QT$q'\?a8Aq> 12222QT$!ax. !Qq(1a.'8%9999QAtaR!G},-1a4888Q1!}_1qbAaC[=!1111r#   c                     [        [        5      R                  S 5      [        [        S444:X  d   e[        [        5      R                  [        S445      [        [        S444:X  d   e[        [        5      R                  [        S445      [        [        S4[        S444:X  d   e[        [        5      R                  [        S4[        S445      [        [        S4[        S444:X  d   eg Nr   )r   r   as_expr_variablesr   r"   r#   r$   test_as_expr_variablesrR   g   s    8%%d+QF9~===8%%1vi0Q!Q	NBBB8%%1vi0Q!Q!Q8H4IIII8%%1v1v&67AAA?O;PPPPr#   c                  $   [        S[        5      R                  [        S[        5      5      (       d   e[        S[        5      R                  [        S5      5      (       d   e[        S5      R                  [        S[        5      5      SL d   eg )Nr(   F)r   r   containsr"   r#   r$   test_contains_0rU   n   si    A;a,,,,A;a))))8U1a[)U222r#   c                     [        [        5      R                  [        [        5      5      (       d   e[        [        5      R                  [        [        S-  5      5      (       d   e[        [        S-  5      R                  [        [        5      5      (       a   e[        [        5      R                  [        S[        -  5      5      (       a   e[        S[        -  5      R                  [        [        S[        -  5      5      5      (       a   e[        [        5      R                  [        [        S[        -  5      5      5      (       a   e[        S[        -  5      R                  [        [        5      5      (       d   e[        [        S[        -  5      5      R                  [        [        5      5      (       d   e[        [        S[        -  5      5      R                  [        S[        -  5      5      (       d   e[        [        S[        -  5      5      R                  [        [        S[        -  5      5      5      (       d   e[        [        S[        -  5      5      R                  [        [        S[        -  5      5      5      (       d   e[        [        S[        -  5      5      R                  [        [        S[        -  5      5      5      (       a   eg r?   )r   r   rT   r   r"   r#   r$   test_contains_1rW   t   s   8U1X&&&&8U1a4[))))QT{##E!H----Qx  qs,,,,QqSz""5QqS?3333Qx  s1Q3x11111:uQx((((QqS?##E!H----QqS?##E!A#J////QqS?##E#ac(O4444QqS?##E#ac(O4444S1X''c!A#h88888r#   c                  .   [        [        5      R                  [        [        5      5      b   e[        [        5      R                  [        [        [        -  5      5      (       d   e[        [        [        -  5      R                  [        [        5      5      (       d   e[        [        5      R                  [        [        [        -  5      5      (       d   e[        [        5      R                  [        [        S-  [        -  5      5      (       d   eg r4   )r   r   rT   r   r"   r#   r$   test_contains_2rY      s    8U1X&...8U1Q3Z((((1:uQx((((8U1Q3Z((((8U1a46]++++r#   c                     [        [        [        S-  -  5      R                  [        [        S-  [        -  5      5      b   e[        [        S-  [        -  5      R                  [        [        [        S-  -  5      5      b   eg r4   )r   r   r   rT   r"   r#   r$   test_contains_3r[      s`    1a4=!!%1Q-0888Aa=!!%!Q$-0888r#   c            	      <   [        [        S[        S-  -  5      5      R                  [        [	        S[        S-  -  5      5      5      SL d   e[        [	        S[        S-  -  5      5      R                  [        [        S[        S-  -  5      5      5      SL d   eg )Nr(   r-   T)r   r   r   rT   r   r"   r#   r$   test_contains_4r]      sx    Qq!tV&&uS1a4['9:dBBBQq!tV&&uS1a4['9:dBBBr#   c                      [        S[        5      [        S5      ;  d   e[        S5      [        S[        5      ;   d   e[        [        S 5        g )Nr(   c                  h    [        [        [        S-  -  5      [        [        S-  [        -  5      ;   $ r4   r   r   r   r"   r#   r$   r1   test_contains.<locals>.<lambda>   s!    eAadFmuQT!V}<r#   )r   r   r   r8   r"   r#   r$   test_containsrb      s=    A;eAh&&&8uQ{"""
9<=r#   c                  &   [        [        [        -   5      [        [        5      :X  d   e[        S[        -  S[        S-  -  -
  5      [        [        5      :X  d   e[        S[        -   5      [        S[        5      :X  d   e[        SS[        -  -   5      [        S[        -  5      :X  d   e[        [        [        5      S[        [        5      -  -   5      [        [        [        5      S-  S-   [        [        5      -  5      :X  d   e[        [        S[        -  5      [        -   5      [        [        S[        -  5      5      :X  d   e[        [        S[        -  5      S[        S-  -  -   5      [        [        S[        -  5      5      :X  d   eg )Nr    r-   r(      )r   r   r   r   r"   r#   r$   
test_add_1re      s    Q<58###1qAv%(***Q<5A;&&&QqS>U1Q3Z'''
 Q!CF("#uc!fai!mSV-C'DDDDQqSA%AaC/111QqSAaeG#$c!A#h777r#   c                  @   [        [        [        5      5      [        [        S[        -  5      5      -   [        [        [        5      5      :X  d   e[        [        [        5      5      [        [        [        S-  5      5      -   [        [        [        5      5      :X  d   e[        [        [        [        -  5      5      [        [        [        5      [        [        5      -   5      -   [        [        [        5      [        [        5      -   [        [        5      :X  d   eg )Nr-   r    )r   r   r   r   r"   r#   r$   test_ln_argsrg      s    SV9qQqS{"aAi///SV9qQT|#qQy000S1X;3q6CF?++qQ#a&!Q/GGGGr#   c                     [        [        [        -  5      R                  [        [        -  :X  d   e[        [        [        S-  -  5      R                  [        [        S-  -  :X  d   e[        [        [        -  [        5      R                  [        :X  d   e[        [        [        S-  -  [        5      R                  [        S-  :X  d   e[        [        [        -  [        -  5      R                  [        [        -  [        -  :X  d   e[        [        [        -  5      R                  [        [        -  :X  d   e[        [        [        S[        -  5      -  5      R                  [        [        S[        -  5      -  :X  d   e[        [        [        5      [        S[        -  5      -  5      R                  [        [        5      [        S[        -  5      -  :X  d   eg r?   )r   r   r   r6   r   r   r"   r#   r$   test_multivar_0ri      s=   1:??ac!!!1a4=1a4'''1a="""1a4  AqD(((1Q<!A%%%1:??ac!!!3qs8!!Qs1Q3xZ///QAaC!&&#a&QqS/999r#   c                      [        [        S[        -  5      [        S[        -  5      -  5      R                  [        S[        -  5      [        S[        -  5      -  :X  d   eg r'   )r   r   r   r   r6   r"   r#   r$   test_multivar_0ark      sE    QqS#ac("#((C!HS1X,====r#   c                     [        [        [        -   5      R                  [        [        -   :X  d   e[        [        S[        -  -   5      R                  [        [        -   :X  d   e[        [        [        -   5      [        -   R                  [        [        -   :X  d   e[        [        [        -   5      [        S-  -   [        [        [        -   5      :X  d   e[        [        [        -   5      S[        -  -   S[        -  [        [        [        -   5      -   :X  d   e[        [        S-  [        [        -  -   5      R                  [        S-  [        [        -  -   :X  d   eg r?   r   r   r   r6   r"   r#   r$   test_multivar_1rn      s    Q<A%%%QqS>!a%'''!a%L1""q1u---!a%L1a4E!a%L000!a%L1Q31Q3q1u#5555A!!!QTAaCZ///r#   c                      [        [        S-  [        -  [        S-  [        -  -   [        [        5      R                  [        S-  [        -  [        S-  [        -  -   :X  d   eg r4   rm   r"   r#   r$   test_multivar_2rp      sG    Aa!Q$q&!Q',,1QAa???r#   c                      [        [        [        -   5      [        -  [        [        S-  [        [        -  -   [        [        5      :X  d   eg r4   r`   r"   r#   r$   test_multivar_mul_1rr      s1    Q<>U1a4!A#:q!4444r#   c                  T   [        [        5      [        [        5      -   R                  [        [        5      [        [        5      4[        [        5      [        [        5      44;   d   e[        [        5      [        [        5      -   [        [        [        -   5      -   [        [        [        -   5      :X  d   e[        [        S-  [        -  5      [        [        S-  [        -  5      -   R                  [        [        [        S-  -  5      [        [        [        S-  -  5      4[        [        [        S-  -  5      [        [        [        S-  -  5      44;   d   e[        [        S-  [        -  5      [        [        [        -  5      -   [        [        [        -  5      :X  d   eg r4   )r   r   r   argsr"   r#   r$   test_multivar_3ru      s)   !HuQx%%	q58	q58*    8eAhq1u-q1u===!Q$q&ME!Q$q&M)//	qAva1f&	qAva1f&4( ( ( ( !Q$q&ME!A#J&51:555r#   c                      [        SSS9n [        SSS9n[        [        5        [        U 5        [        U5        [        R                  b   eU R                  SL d   eUR                  b   eg )Nr   T)negativer   )complexF)r   r   r   is_positive)r   r   s     r$   test_issue_3468rz      sc    sT"AsD!A 
!H	!H	!H==   ==E!!!==   r#   c                     [         S-   S[         S-  -  -   R                  [         5      S[         S-  -  [        S[         S-  -  5      44:X  d   eSS[         -  -   R                  [         5      S[         -  [        S[         -  5      44:X  d   eS[         -   R                  [         5      S[        S[         5      44:X  d   eS[         S-  -   R                  [         5      S[        S[         5      44:X  d   eS[         S-  -   R                  [         5      S[        S[         5      44:X  d   e[         [         S-  -   R                  [         5      [         [        [         5      44:X  d   eg )Nr(   r!   r-   )r   extract_leading_orderr   r"   r#   r$   test_leading_orderr}      s)   EAadFN11!4!AqD&!AadF)9L8NNNN!G**1-1Q3!A#-1AAAAE((+AaG>>>1H++A.AqAw</AAA1H++A.AqAw</AAA1H++A.Aqt9,>>>r#   c                     [        S[        -   [        S-  -   R                  [        5      5      [        [	        S[        5      4[        S5      [	        S[        5      41:X  d   e[        S[        -  [        [        -  -   [        S-  -   R                  [        5      5      S[        -  [	        [        5      4[        [        -  [	        [        5      41:X  d   eg r?   )r*   r
   r   r|   r   r   r"   r#   r$   test_leading_order2r      s    BA44Q78b!Aq']qT1Q7O=   !bd
QT!88;<!A#qtrT1Q4LA   r#   c                  z    [        [        S-  5      R                  [        5      [        [        S-  5      :X  d   eg r4   )r   r   _eval_as_leading_termr"   r#   r$   test_order_leadtermr      s+    QT7((+qAw666r#   c                     [         [        -  [        [         5      -  [        [         [         SS45      -  n [	        U 5      [	        [         S-  [        -  [         [        5      :X  d   e[	        U [         5      [	        [         S-  5      :X  d   eg rJ   )r   r   r   r   r   )es    r$   test_order_symbolsr      sc    	!CF
8A1ay))AQ41QT!VQ?"""Q7a1gr#   c                      [        [        5      [        L d   e[        [        5      R                  [        5      (       a   eg r0   )r   r   r   rT   r"   r#   r$   test_nanr     s.    S6S==t}}S!!!!!r#   c                      [        S[        5      [        -  [        [        5      :X  d   e[        S[        5      [        -  [        S[        5      :X  d   eg r'   )r   r   r   r"   r#   r$   test_O1r     s<    Q7Q;!A$Q7Q;!Aq'!!!r#   c                     [        [        5      R                  5       S:X  d   e[        [        [        [        5      -  5      R                  5       S:X  d   e[        [        S-  [        [        5      S-  -  5      R                  5       S:X  d   e[        [        [        [        5      -  5      R                  5       S:X  d   e[	        [
        S 5        g )Nr(   r-   c                  \    [        [        5      [        [        5      -   R                  5       $ r0   r   r   r   getnr"   r#   r$   r1   test_getn.<locals>.<lambda>      1!(:(:(<r#   )r   r   r   r   r   NotImplementedErrorr"   r#   r$   	test_getnr     s    Q499;!Qs1vX;"""QT#a&!)^!!#q(((Qs1vX;"""
 <=r#   c                  t    [        [        S-  5      R                  [        5      [        [        5      :X  d   eg r4   )r   r   diffr"   r#   r$   	test_diffr     s$    QT7<<?ad"""r#   c                  d   [         R                  " 5       b   e[         R                  " 5       [         :X  d   e[        [         5      R                  5       [        [         5      :X  d   e[        [         5      R                  5       S:X  d   e[        [        [         5      -   [        [
        5      -   R                  5       [        [         5      [        [
        5      -   :X  d   e[        [        [         5      -   [        [
        5      -   R                  5       [        :X  d   e[        [        S 5        g )Nr   c                  \    [        [        5      [        [        5      -   R                  5       $ r0   r   r"   r#   r$   r1   test_getO.<locals>.<lambda>   r   r#   )r   getOremoveOr   r   r   r   r   r"   r#   r$   	test_getOr     s    88:;;=AaD;;=AaD   aD>>q   !HqtO!!#qtad{222!HqtO$$&!+++
 <=r#   c                      SSK Jn   [        SU " S[        -  5      -  5      [        S[	        [        5      -  5      :X  d   eg )Nr   digammar(   )'sympy.functions.special.gamma_functionsr   r   r   r   r   s    r$   test_leading_termr   #  s0    ?Qwqs|^!CF(+++r#   c                  >   [        [        5      R                  [        [        5      S5      S:X  d   e[        [        5      R                  [        [        5      [        [        5      :X  d   e[        [        5      R                  [        [        5      [        [        5      :X  d   e[        [        5      R                  [        [        [        -   5      [        [        [        -   [        [        * 45      :X  d   e[	        S5      [        -  R
                  (       d   eg r'   )r   r   subsr   r   is_Powr"   r#   r$   	test_evalr   (  s    8==q1%***8==A%(***8==A%(***8==AE"eAEAr7&;;;;aD!Gr#   c                     [        S5      u  p[        X U5      [        SX5      -   [        SX5      :X  d   e[        XU5      [        SX5      -   [        SX5      :X  d   e[        X-   X5      [        SX5      -   [        SX5      :X  d   e[        SX5      [        X U5      -   [        SX5      :X  d   e[        SX5      [        XU5      -   [        SX5      :X  d   e[        SX5      [        X-   X5      -   [        SX5      :X  d   eg )Nza br(   )r   r   )abs     r$   test_issue_4279r   0  s    5>DAQ1:!Q
"a1j000Q1:!Q
"a1j000QUA>AaJ&!Aq*444Q:!
"a1j000Q:!
"a1j000Q:!%&!Aq*444r#   c                  |   S[        S5      -  [        S5      :w  d   eS[        [        5      -  [        S[        -  5      :w  d   eS[        [        [        [        45      -  [        S[        -  [        [        45      :w  d   e[        S5      n S[        U " [        5      5      -  [        S[        -  5      :w  d   eg )Nr(   f)r   r   r	   r   )r   s    r$   test_issue_4855r   :  s    QqT6QqT>>QqT6QqsVQq1b']?a!aWo---AQqtW9!A#r#   c                     [        SSS9n [        SSS9n[        [        U 5      5      [        [        U 5      5      :X  d   e[        [        U5      5      [        [        U5      5      :X  d   e[        [        U S-  5      5      [        [        U 5      S-  5      :X  d   e[        [        US-  5      5      [        [        U5      S-  5      :X  d   e[        [        U 5      5      [        [        U 5      5      :X  d   e[        [        U5      5      [        [        U5      5      :X  d   e[        [        U S-  5      5      [        [        U 5      S-  5      :X  d   e[        [        US-  5      5      [        [        U5      S-  5      :X  d   eg )Nr   T)realr   )	imaginaryr-   )r   r   r   r   )r   r   s     r$   test_order_conjugate_transposer   C  s:   sAsd#AU1X%	!"5555U1X%	!"5555U1a4[!U9Q<?%;;;;U1a4[!U9Q<?%;;;;U1X%	!"5555U1X%	!"5555U1a4[!U9Q<?%;;;;U1a4[!U9Q<?%;;;;r#   c                     [        SSS9n [        X [        -  -   [        5      [        S[        5      :X  d   eX [        -  -   [        [        5      -  [        [        5      :X  d   eU [        -  [        [        5      -  [        [        S-  [        5      :X  d   e[        S[        [        5      -   U -  U -  [        -  5      X -  [        -  [        [        S-  [        5      -   :X  d   e[        X -  [        [        5      -   [        -  5      X -  [        -  [        [        S-  [        5      -   :X  d   e[        U [        [        5      -   U -  [        -  5      X -  [        -  [        [        S-  [        5      -   :X  d   eg )NAF)commutativer(   r-   )r   r   r   r   )r   s    r$   test_order_noncommutativer   P  s$   s&AqS!a+++!GU1Xq)))aCq>U1a4^+++1uQx<"1$Q&'13q55Aq>+AAAA13q>1$%Qq!tQ)????1uQx<"1$%Qq!tQ)????r#   c                  h    S[         S-  -   S-  [        [         5      -  [        [         5      :X  d   eg )Nr(   r-   i'  )r   r   r"   r#   r$   test_issue_6753r   Z  s*    1HuQqT!QqT)))r#   c                  `   [        S[        -   [        [        45      [        [        [        [        45      :X  d   e[        S[        -  [        [        45      [        [        [        [        45      :X  d   e[        [        [        [        45      S-  [        [        [        [        45      :X  d   eS[        [        [        [        45      -  [        [        [        [        45      :X  d   e[        [        [        [        [        45      [        [        45      [        [        [        [        45      :X  d   e[        [        [        [        [        45      [        [        45      [        [        [        [        4[        [        45      :X  d   e[        S[        [        45      [        S[        [        45      :X  d   e[        [        S-  [        -   [        -   [        [        45      [	        [        S-  [        [        45      :X  d   e[        [        S-  [        -   [        -   [        [        45      [	        [        [        [        45      :X  d   e[        S[        -  [        [        45      [        -  [        [        S-  [        [        45      :X  d   e[        S[        -  [        [        45      [        -  [        S[        [        45      :X  d   e[        S[        -  [        [        45      [        -  [        S[        -  5      -  [        [        S-  [        S[        -  5      -  [        [        45      :X  d   e[        S[        -  [        [        45      [        -  [        S[        -  5      -  [        [        5      S-  -  [        [        S-  [        S[        -  5      -  [        [        5      S-  -  [        [        45      :X  d   e[        [        [        [        45      S[        -  -   S[        -  [        [        [        [        45      -   s=:X  a  [        [        [        [        45      :X  d   e   e[        [        [        [        45      S-   S[        [        [        [        45      -   s=:X  a  [        [        [        [        45      :X  d   e   e[        [        [        [        45      [        -   [        [        [        [        [        45      -   s=:X  a  [        [        [        [        45      :X  d   e   e[        [        [        [        45      [        S-  -   [        S-  [        [        [        [        45      -   :X  d   e[        S[        -  [        [        45      S[        S-  -  -   S[        S-  -  [        S[        -  [        [        45      -   s=:X  a"  [        S[        -  [        [        45      :X  d   e   e[        [        [        [        45      [        S[        -  5      -   [        S[        -  5      [        [        [        [        45      -   :X  d   e[        [        [        [        45      S-  [        [        S-  [        [        45      :X  d   e[        [        [        [        45      [        [        S-  [        [        45      -   [        [        S-  [        [        45      :X  d   e[        [        [        [        45      [        [        S-  [        [        45      -   [        [        [        [        45      :X  d   e[        [        [        [        45      [        S[        -  [        [        45      -   [        [        [        [        45      :X  d   e[        [        [        [        45      [        [        [        [        45      -
  [        [        [        [        45      :X  d   e[        [        [        [        45      [        S[        [        45      -   [        [        [        [        45      :X  d   e[        [        [        [        45      [        [        S-  [        [        45      -   [        [        S-  [        [        45      :X  d   e[        S[        -  [        [        45      [        S[        [        45      -   [        S[        [        45      :X  d   e[        [        [        [        45      [        [        S[        -  5      [        [        45      -   [        [        [        [        45      :X  d   e[        [        S-  [        [        45      [        [        S[        -  5      [        [        45      -   [        [        S-  [        [        45      :X  d   e[        [        S-  [        [        45      [        [        S[        -  5      [        [        45      -   [        [        S[        -  5      [        [        45      :X  d   e[        [        [        5      [        [        45      R                  [        S[        [        5      -  [        [        45      R                  s=:X  a  [        [        5      :X  d   e   e[        [        [        -  [        [        45      R                  [        S[        [        -  -  [        [        45      R                  s=:X  a$  [        [        [        [        5      -  5      :X  d   e   e[        S[        -  SS[        -  S-   -  -
  [        [        45      R                  [        S-  :X  d   eg )Nr(   r    r.   r-   r<   rE   )r   r   r	   r   r   r   r   r6   r"   r#   r$   test_order_at_infinityr   ^  s   QB E!aW$55551q"g%Ar7"3333QGQ%Ar7"3333uQB  E!aW$5555q1b'"QG,a!R0AAAAq1b'"QG,a!R1b'0JJJJQGa!R 1111AA2w'1QTAr7+;;;;AA2w'1QB=8881q"gq E!Q$B$88881q"gq E!aW$55551q"gq QqS)U1a4AaC=1b'-JJJJ1q"gq QqS)#a&!)3uQT#ac(]3q6SU:=UXY[]W^7____QGqs"acE!aW,=&=Rq1b'ARRRRRRQGq Aa!R(9$9NU1q"g=NNNNNNQGq Aa!R(9$9NU1q"g=NNNNNNQGq!t#q!teA2w.?'????1q"g1a4'1QT6E!A#2w4G+G^5QRSTQTWXZ\V]K^^^^^^QGs1Q3x'3qs8eA2w6G+GGGGQGa5A2w#7777QGuQTAr733uQTAr77KKKKQGuQUQG44a!R8IIIIQGuQqS1b'22eA2w6GGGGQGuQB00E!aW4EEEEQGuQB00E!aW4EEEEQGuQTAr733uQTAr77KKKK1q"gq1b'!22eA2w6GGGGQGuS1X2w775QG;LLLLA2w%AaC1b'"::eAqD1b'>RRRRBB 5QqSAr7#;;uS1XPQSUw?WWWW Q!R!&&%#a&1b'*B*G*GQ3q6QQQQQA2w$$a1fq"g(>(C(CTs1SQRV8}TTTTT 1q!A#'{"QG,11QW<<<r#   c                  ^   [        [        [        S45      [        [        [        [        45      -   R                  (       d   e[        [        [        S45      [        [        [        [        45      -   [        [        [        [        45      [        [        [        S45      -   :X  d   e[        [        [        [        [        45      5      [        [        [        [        45      :X  d   e[	        [
        S 5        [	        [
        S 5        [	        [
        S 5        [	        [
        S 5        g )Nr   c                  d    [        [        [        S45      [        [        [        [        45      -  $ rP   r   r   r	   r"   r#   r$   r1   8test_mixing_order_at_zero_and_infinity.<locals>.<lambda>  s    a!Q(8q1b'9J(Jr#   c                  d    [        [        [        [        45      [        [        [        S45      -  $ rP   r   r"   r#   r$   r1   r     s    a!R(9%Aq6:J(Jr#   c                  R    [        [        [        [        [        45      [        5      $ r0   )r   r   r	   r   r"   r#   r$   r1   r     s    eA2w.?(Cr#   c                  H    [        [        [        5      [        [        45      $ r0   r   r"   r#   r$   r1   r     s    eAhB(@r#   )r   r   r	   is_Addr   r   r"   r#   r$   &test_mixing_order_at_zero_and_infinityr     s    !aVuQB008888QFeA2w//5QG3DuQQRTUPVGW3WWWWq1b'"#uQB'8888  JK
 JK
 CD
 @Ar#   c                  T   [        [        [        S45      [        S[        S45      :X  d   e[        S[        -  S-
  [        S45      [        [        S-
  [        S45      :X  d   e[        [        * S-   [        S45      [        [        S-
  [        S45      :X  d   e[        [        S-
  [        S45      S-  [        [        S-
  S-  [        S45      :X  d   e[        [        S-
  [        S45      [        [        S-
  [        S45      -
  [        [        S-
  [        S45      :X  d   eg rJ   )r   r   r   r"   r#   r$   test_order_at_some_pointr     s    QFuQA////1q1a&!U1q51a&%9999!a!Q E!a%!Q$8888QA"eQUQJA&????QA!AEAq6"22eAEAq66JJJJr#   c                     S[        [        5      -   R                  [        S[        -  5      S[        S[        -  [        [        45      -   :X  d   eS[        [        5      -   R	                  [        S5      S:X  d   e[        [        [        S-  5      -   [        -  R	                  [        S5      S:X  d   e[        [        S-  5      R                  [        [
        S-
  5      [        [
        S-
  S-  [
        S45      :X  d   e[        S[        S-  -  [        S45      R                  [        [
        S-
  5      [        S[
        S45      :X  d   eg )Nr(   r   r-   
   r    )r   r   r   r	   limitr   r"   r#   r$   test_order_subs_limitsr     s   aLq!A#&!eAaC!R.A*AAAAaL1%***q!t_a&&q!,111A;Aq1u%AzAq6)BBBBAqD1a&!&&q!a%0E!aV4DDDDr#   c                      [        [        5      R                  [        SS5      [        S5      [        [        S-
  [        S45      -   :X  d   eg )Nr   r(   )r   r   seriesr   r"   r#   r$   test_issue_9351r     s9    q6==B"c"ga"fq"g0F&FFFFr#   c                      [        S5      [        S5      -  [        S5      :X  d   e[        S5      [        S5      -  [        S5      :X  d   eg r'   )r   r"   r#   r$   test_issue_9192r     s>    Q4!9!Q41:1r#   c                      [        [        [        [        5      -  [        [        5      -   [        [        45      [        [        [        [        5      -  [        [        45      :X  d   eg r0   )r   r   r   r   r	   r"   r#   r$   test_issue_9910r     s?    Qs1vXAB(AaAhB,@@@@r#   c                      [        S5       V s/ s H  n [        U -  PM     nn UR                  [        [        S-  5      5        [	        U6 R                  [        S5      [        S5      :X  d   eg s  sn f )Ni  i  r(   )ranger   appendr   r   r   )ils     r$    test_performance_of_adding_orderr     sX    T{#{!A{A#HHQq$wZ7<<!!$$$ 	$s   A0c                  (   [         S-  [         S-  -   [         S-  -   [        [         S-  [         [        45      -   R                  5       [         S-  [         S-  -   [         S-  -   [        [         S-  [         [        45      -   [         S	-  4:X  d   e[         S
-  [        [         S-  [         [        45      -   R                  (       d   e[        [         S-  [         [        45      R                  [         S
-  5      SL d   e[        [         [         [        45      R                  [        [         [         S45      5      b   e[        [         [         S45      R                  [        [         [         [        45      5      b   e[        [        S 5        g )Nr<   r   i   r!      r-      r    Fr   c                  Z    [        [        S-  5      R                  [        [        -  5      $ )Nr    )r   r   rT   r   r"   r#   r$   r1   "test_issue_14622.<locals>.<lambda>  s    !Q$(8(8A(>r#   )r   r   r	   as_numer_denomr   rT   r   r   r"   r#   r$   test_issue_14622r     s4   Ga"gB'!AGaW*==MMO	1q!tadQq!taW--q!tT5 5 5 5qD1QTAr7##++++QTAr7$$QT*e333QB=!!!A1v,/777QA<  1q"g/777
 >?r#   c                     [        S[        S-  -  S[        S-  -  -   [        [        * 45      [        S[        S-  -  [        [        * 45      :X  d   e[        S[        S-  -  [        [        5      -   [        [        * 45      [        S[        S-  -  [        [        * 45      :X  d   e[        S[        S-  -  [        [        * 5      -   [        [        * 45      [        [        [        * 5      [        [        * 45      :X  d   e[        S[        -  [        [        45      R	                  [        [        * 5      [        S[        -  [        [        * 45      :X  d   eg )Nr(   r-   r   r   )r   r   r	   r   r   r"   r#   r$   test_issue_15539r     s   Qq!tVa1f_q2#h'1Qq!tVa"X+>>>>Qq!tVc!f_q2#h'1Qq!tVa"X+>>>>Qq!tVc1"gB3x(Ac1"gB3x,@@@@QqS1b'?A2&!BqD1rc(*;;;;r#   c                  2    [        [        S5      (       d   eg rP   )r   r   r"   r#   r$   test_issue_18606r     s    UAr#   c                  `    [        [        [        5      5      R                  S5      (       d   eg r4   )r   r   r   rT   r"   r#   r$   test_issue_22165r     s!    SV9a    r#   c            	      
   [        [        [        -  S[        -  -   [        [        45      [        [        [        [	        [        5      -  5      [        [        45      :X  d   e[        [        [        -  [        S-  -   [        [        45      [        [        [        [	        [        5      -  5      [        [        45      :X  d   e[        [        [        -  S[        S-  -  -   [        [        45      [        [        [        [	        [        5      -  5      [        [        45      :X  d   e[        S[        -  S[        -  -   [        [        45      [        [        [        [	        S5      -  5      [        [        45      :X  d   eg )Nr-   r(   r    )r   r   r	   r   r   r"   r#   r$   test_issue_23231r     s     QTAqD[1b'"aAc!fH2w&????QTAqD[1b'"aAc!fH2w&????QTAadF]QG$#aAh-!R(AAAAQTAqD[Ar7#qQs1vXB'@@@@r#   c                      [        [        [        [        5      -  S-   [        [        45      [        [        [        [        45      :X  d   eg r'   )r   r   r   r	   r"   r#   r$   test_issue_9917r     s1    Qs1vX\Ar7#qQG}444r#   N)asympy.core.addr   sympy.core.functionr   r   sympy.core.numbersr   r   r   r	   r
   sympy.core.singletonr   sympy.core.symbolr   r   $sympy.functions.elementary.complexesr   r   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   sympy.integrals.integralsr   sympy.series.orderr   r   sympy.core.exprr   sympy.testing.pytestr   	sympy.abcr   r   r   r   r%   r+   r:   r=   rA   rC   rF   rH   rK   rN   rR   rU   rW   rY   r[   r]   rb   re   rg   ri   rk   rn   rp   rr   ru   rz   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r"   r#   r$   <module>r      s[    2 9 9 " / G = 9 ? . ' % '    "1/&N6&/=$2Q39,9
C
>8H:>0@56!?7"
"
>#>,
5
<@**=X	BKEG
A%
@<!A5r#   