
    \hE                     ^   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  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$J%r%  S SK&J'r'J(r(J)r)J*r*  S SK$J+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$ r?S% r@S& rAS' rBS( rCS) rDS* rES+ rFS, rGS- rHS. rIS/ rJS0 rKS1 rLS2 rMS3 rNS4 rOS5 rPS6 rQS7 rRS8 rSS9 rTS: rUS; rVS< rWS= rXS> rY\+S? 5       rZS@ r[SA r\SB r]SC r^SD r_SE r`SF raSG rbSH rcSI rdSJ regK)L    )Add)Functionexpand)IRationalnanoopi)S)Symbolsymbols)	factorial)	conjugate	transpose)explog)sqrt)cossin)Integral)OOrder)	unchanged)raises)wxyz)XFAILc                      [        [        5        [        [        S[        -  [        S5      -  [        S5      -  -  [        5        g )N      )r   r   r   r        U/var/www/auris/envauris/lib/python3.13/site-packages/sympy/series/tests/test_order.pytest_caching_bugr'      s/     aDa"Q$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$   r%   r&   <lambda>test_simple_1.<locals>.<lambda>2   s    uSVQ2r%   c                  0    [        [        S[        -
  5      $ Nr/   r   r   r$   r%   r&   r3   r4   3   s    eAq1uor%   )
r   r   r   r   r   exprr   r   
ValueError	TypeError)os    r&   test_simple_1r<   #   s   A1:q!!!8A:q!!!uQx<58###q?eAh&&&q1uQxA!6666:q!!!Q=E!QK'''QqS?3qs8+++3qs8!!Qs1Q3xZ///QqS?1qs8+++Qx1~%&',,Ahq!n4D0EEEEAAq!Qq!W,,,AAq!Qq!W,,,
:23
9-.r%   c                  ^   [        S[        -  5      [        -  [        [        S-  5      :X  d   e[        S[        -  5      [        -  [        S[        5      :X  d   e[        S[        -  5      [        -  [        S[        -  5      -  [        [        S-  [        S[        -  5      -  5      :X  d   e[        S[        -  5      [        -  [        S[        -  5      -  [        [        5      S-  -  R                  [        S-  [        S[        -  5      -  [        [        5      S-  -  :X  d   eg )Nr/   r*   r"   )r   r   r   r   r8   r$   r%   r&   test_simple_2r?   6   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_3rC   =   s    8a<58###8a<1uQx<'''8ad?eAh&&&8ac>QqS58^+++1:!Q$!AqD&51:"55558c!A#h%(S1X"5555r%   c                  T    [        [        5      S-  [        [        S-  5      :X  d   eg r6   r7   r$   r%   r&   test_simple_4rE   F   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*   r7   r$   r%   r&   test_simple_5rH   J   ss    8eAqDk!U1X---8eArEl"eArEl2228eAaCj E!A#J...r%   c                  V   [        [        5      [        [        5      -
  [        [        5      :X  d   e[        [        5      [        S5      -   [        S5      :X  d   e[        [        5      [        [        S-  5      -   [        [        5      :X  d   e[        S[        -  5      [        S5      -   [        S[        -  5      :X  d   e[        [        5      [        [        S[        -  5      5      -   [        [        S[        -  5      5      :X  d   e[        [        S-  5      [        [        S[        -  5      5      -   [        [        S[        -  5      5      :X  d   e[        [        S-  5      [        [        S[        -  5      5      -   [        [        S[        -  5      5      :X  d   eg )Nr*   r/   r"   r>   rB   r$   r%   r&   test_simple_6rJ   P   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$   r%   r&   test_simple_7rM   Z   sv    qt8qtqt8qtqt8qtQ31:1qt###r%   c                     [        [        [        * 5      5      [        [        [        5      5      :X  d   e[        [        S-  [        [        5      -  5      [        [        [        SS5      -  5      :X  d   e[        [        S-  [        [        * S-  * 5      -  5      [        [        [        SS5      -  5      :X  d   e[        [        [        SS5      -  [        [        * S-  5      -  5      [        [        S-  5      :X  d   e[        [        S[        -  [        S-  -  -  5      [        [        [        * [        S-  -  -  5      :X  d   eg )Nr/   r#   r"   	   rG   )r   r   r   r   r   r$   r%   r&   test_simple_8rP   a   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$   r%   r&   test_as_expr_variablesrT   i   s    8%%d+QF9~===8%%1vi0Q!Q	NBBB8%%1vi0Q!Q!Q8H4IIII8%%1v1v&67AAA?O;PPPPr%   c                  $   [        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$   r%   r&   test_contains_0rW   p   si    A;a,,,,A;a))))8U1a[)U222r%   c                     [        [        5      R                  [        [        5      5      (       d   e[        [        5      R                  [        [        S-  5      5      (       d   e[        [        S-  5      R                  [        [        5      5      (       a   e[        [        5      R                  [        S[        -  5      5      (       a   e[        S[        -  5      R                  [        [        S[        -  5      5      5      (       a   e[        [        5      R                  [        [        S[        -  5      5      5      (       a   e[        S[        -  5      R                  [        [        5      5      (       d   e[        [        S[        -  5      5      R                  [        [        5      5      (       d   e[        [        S[        -  5      5      R                  [        S[        -  5      5      (       d   e[        [        S[        -  5      5      R                  [        [        S[        -  5      5      5      (       d   e[        [        S[        -  5      5      R                  [        [        S[        -  5      5      5      (       d   e[        [        S[        -  5      5      R                  [        [        S[        -  5      5      5      (       a   eg rA   )r   r   rV   r   r$   r%   r&   test_contains_1rY   v   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 r6   )r   r   rV   r   r$   r%   r&   test_contains_2r[      s    8U1X&...8U1Q3Z((((1:uQx((((8U1Q3Z((((8U1a46]++++r%   c                     [        [        [        S-  -  5      R                  [        [        S-  [        -  5      5      b   e[        [        S-  [        -  5      R                  [        [        [        S-  -  5      5      b   eg r6   )r   r   r   rV   r$   r%   r&   test_contains_3r]      s`    1a4=!!%1Q-0888Aa=!!%!Q$-0888r%   c            	      <   [        [        S[        S-  -  5      5      R                  [        [	        S[        S-  -  5      5      5      SL d   e[        [	        S[        S-  -  5      5      R                  [        [        S[        S-  -  5      5      5      SL d   eg )Nr*   r/   T)r   r   r   rV   r   r$   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      ;   $ r6   r   r   r   r$   r%   r&   r3   test_contains.<locals>.<lambda>   s!    eAadFmuQT!V}<r%   )r   r   r   r:   r$   r%   r&   test_containsrd      s=    A;eAh&&&8uQ{"""
9<=r%   c                  &   [        [        [        -   5      [        [        5      :X  d   e[        S[        -  S[        S-  -  -
  5      [        [        5      :X  d   e[        S[        -   5      [        S[        5      :X  d   e[        SS[        -  -   5      [        S[        -  5      :X  d   e[        [        [        5      S[        [        5      -  -   5      [        [        [        5      S-  S-   [        [        5      -  5      :X  d   e[        [        S[        -  5      [        -   5      [        [        S[        -  5      5      :X  d   e[        [        S[        -  5      S[        S-  -  -   5      [        [        S[        -  5      5      :X  d   eg )Nr"   r/   r*      )r   r   r   r   r$   r%   r&   
test_add_1rg      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_argsri      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 rA   )r   r   r   r8   r   r   r$   r%   r&   test_multivar_0rk      s=   1:??ac!!!1a4=1a4'''1a="""1a4  AqD(((1Q<!A%%%1:??ac!!!3qs8!!Qs1Q3xZ///QAaC!&&#a&QqS/999r%   c                      [        [        S[        -  5      [        S[        -  5      -  5      R                  [        S[        -  5      [        S[        -  5      -  :X  d   eg r)   )r   r   r   r   r8   r$   r%   r&   test_multivar_0arm      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 rA   r   r   r   r8   r$   r%   r&   test_multivar_1rp      s    Q<A%%%QqS>!a%'''!a%L1""q1u---!a%L1a4E!a%L000!a%L1Q31Q3q1u#5555A!!!QTAaCZ///r%   c                      [        [        S-  [        -  [        S-  [        -  -   [        [        5      R                  [        S-  [        -  [        S-  [        -  -   :X  d   eg r6   ro   r$   r%   r&   test_multivar_2rr      sG    Aa!Q$q&!Q',,1QAa???r%   c                      [        [        [        -   5      [        -  [        [        S-  [        [        -  -   [        [        5      :X  d   eg r6   rb   r$   r%   r&   test_multivar_mul_1rt      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 r6   )r   r   r   argsr$   r%   r&   test_multivar_3rw      s)   !HuQx%%	q58	q58*    8eAhq1u-q1u===!Q$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_3468r|      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$   r%   r&   test_leading_orderr      s)   EAadFN11!4!AqD&!AadF)9L8NNNN!G**1-1Q3!A#-1AAAAE((+AaG>>>1H++A.AqAw</AAA1H++A.AqAw</AAA1H++A.Aqt9,>>>r%   c                     [        S[        -   [        S-  -   R                  [        5      5      [        [	        S[        5      4[        S5      [	        S[        5      41:X  d   e[        S[        -  [        [        -  -   [        S-  -   R                  [        5      5      S[        -  [	        [        5      4[        [        -  [	        [        5      41:X  d   eg rA   )r,   r
   r   r~   r   r   r$   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                  ~    [        [        S-  5      R                  [        S S5      [        [        S-  5      :X  d   eg rA   )r   r   _eval_as_leading_termr$   r%   r&   test_order_leadtermr      s/    QT7((D!4!Q$???r%   c                     [         [        -  [        [         5      -  [        [         [         SS45      -  n [	        U 5      [	        [         S-  [        -  [         [        5      :X  d   e[	        U [         5      [	        [         S-  5      :X  d   eg rL   )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 r2   )r   r   r   rV   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       $ r2   r   r   r   getnr$   r%   r&   r3   test_getn.<locals>.<lambda>      1!(:(:(<r%   )r   r   r   r   r   NotImplementedErrorr$   r%   r&   	test_getnr     s    Q499;!Qs1vX;"""QT#a&!)^!!#q(((Qs1vX;"""
 <=r%   c                  t    [        [        S-  5      R                  [        5      [        [        5      :X  d   eg r6   )r   r   diffr$   r%   r&   	test_diffr     s$    QT7<<?ad"""r%   c                  d   [         R                  " 5       b   e[         R                  " 5       [         :X  d   e[        [         5      R                  5       [        [         5      :X  d   e[        [         5      R                  5       S:X  d   e[        [        [         5      -   [        [
        5      -   R                  5       [        [         5      [        [
        5      -   :X  d   e[        [        [         5      -   [        [
        5      -   R                  5       [        :X  d   e[        [        S 5        g )Nr   c                  \    [        [        5      [        [        5      -   R                  5       $ r2   r   r$   r%   r&   r3   test_getO.<locals>.<lambda>"  r   r%   )r   getOremoveOr   r   r   r   r   r$   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   2  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   E  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   R  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   \  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"   r0   r/   r>   rG   )r   r   r	   r   r   r   r   r8   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$$a1fq"g(>(C(CTs1SQRV8}TTTTT 1q!A#'{"QG,11QW<<<r%   c                  ^   [        [        [        S45      [        [        [        [        45      -   R                  (       d   e[        [        [        S45      [        [        [        [        45      -   [        [        [        [        45      [        [        [        S45      -   :X  d   e[        [        [        [        [        45      5      [        [        [        [        45      :X  d   e[	        [
        S 5        [	        [
        S 5        [	        [
        S 5        [	        [
        S 5        g )Nr   c                  d    [        [        [        S45      [        [        [        [        45      -  $ rR   r   r   r	   r$   r%   r&   r3   8test_mixing_order_at_zero_and_infinity.<locals>.<lambda>  s    a!Q(8q1b'9J(Jr%   c                  d    [        [        [        [        45      [        [        [        S45      -  $ rR   r   r$   r%   r&   r3   r     s    a!R(9%Aq6:J(Jr%   c                  R    [        [        [        [        [        45      [        5      $ r2   )r   r   r	   r   r$   r%   r&   r3   r     s    eA2w.?(Cr%   c                  H    [        [        [        5      [        [        45      $ r2   r   r$   r%   r&   r3   r     s    eAhB(@r%   )r   r   r	   is_Addr   r   r$   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 rL   )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[        [        5      R                  [        [        [        5      5      [        [        5      :X  d   e[        [        S-  5      R                  [        [        [        [        5      -   5      [        [        S-  5      :X  d   e[        [        [        [        45      R                  [        [        [        [        [        45      5      [        [        [        [        45      :X  d   e[        [        S-  [        [        45      R                  [        [        [        [        [        [        45      -   5      [        [        S-  [        [        45      :X  d   e[        [        [        S-  5      -   R                  [        [        [        [        S-  5      -   5      [        [        [        S-  5      -   :X  d   e[        S-  [        [        S-  5      -   S[        S-  -  -   R                  [        [        [        [        S-  5      -   5      [        [        [        S-  5      -   S-  [        [        S-  5      -   :X  d   e[        S-  [        [        S-  5      -   S-   R                  [        [        [        [        S-  5      -   5      S[        [        S-  5      -   :X  d   e[        [        [        [        45      R                  [        [        [        [        S-  [        [        45      -   5      [        [        S-  [        [        45      :X  d   e[        [        5      R                  SS9R                  [        [        [        5      R                  SS95      R                  5       [        [        S-  S-  -
  [        S	-  S-  -   S[        S
-  -  S-  -
  [        [        S-  5      -   :X  d   e[        [        5      R                  SS9R                  [        [        [        5      R                  SS95      R                  5       S[        S-  S-  -
  S	[        S-  -  S-  -   S[        S-  -  S-  -
  [        [        S-  5      -   :X  d   e[        [        5      R                  [        [        S[        -  [        [        45      5      [        S[        -  [        [        45      :X  d   eg )Nr*   r   r/   
   r"   rG      )nr#      i;        %      i  )r   r   r   r	   limitr   r   r   seriesr   r   r$   r%   r&   test_order_subs_limitsr     se   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D Q499Q!1%%%QT7<<1qt8$!Q$///QB=a1q"g/1QB=@@@QTAr7  A!aW$56!AqD1b':JJJJ!Q$KaQq!tW-Qq!tW<<<qD1QT7NQq!tV#))!Q1a4[9a!AqD'kR=PSTUVXYUYSZ=ZZZZqD1QT7NQ$$QAadG4AadGCCCQB=aQq!taW%5!56!AqD1b':JJJJq6==1=""1SV]]Q]%78??AQAaZRSUVRVWYRYEY\]^_ab^b\bcf\fEfijklnokoipEppppq6==1=""1SV]]Q]%78??AQAaZRSTUWXTXRXY[R[E[^`abdeae^efi^iEilmnoqrnrlsEssssQ499Q!A#2w(AacAr7O;;;r%   c                      [        [        S-  5      R                  [        [        [        S-  * 5      5      [        [        S[        S-  -  5      [        [        * 45      :X  d   e[        [        S 5        g )Nr"   r/   r>   c                  h    [        [        5      R                  [        [        S[        -  5      5      $ r)   )r   r   r   r$   r%   r&   r3   4test_order_failing_due_to_solveset.<locals>.<lambda>  s    !		!QqsV(<r%   )r   r   r   r   r	   r   r   r$   r%   r&   "test_order_failing_due_to_solvesetr     sR    QT7<<31u:&!C1a4L1rc(*CCCC
 <=r%   c                      [        [        5      R                  [        SS5      [        S5      [        [        S-
  [        S45      -   :X  d   eg )Nr   r*   )r   r   r   r   r$   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$   r%   r&   test_issue_9192r     s>    Q4!9!Q41:1r%   c                      [        [        [        [        5      -  [        [        5      -   [        [        45      [        [        [        [        5      -  [        [        45      :X  d   eg r2   )r   r   r   r   r	   r$   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<<!!$$$ 	$s   A0c                  (   [         S-  [         S-  -   [         S-  -   [        [         S-  [         [        45      -   R                  5       [         S-  [         S-  -   [         S-  -   [        [         S-  [         [        45      -   [         S	-  4:X  d   e[         S
-  [        [         S-  [         [        45      -   R                  (       d   e[        [         S-  [         [        45      R                  [         S
-  5      SL d   e[        [         [         [        45      R                  [        [         [         S45      5      b   e[        [         [         S45      R                  [        [         [         [        45      5      b   e[        [        S 5        g )Nr>   r!   ir   r#   r   r/   r   r"   Fr   c                  Z    [        [        S-  5      R                  [        [        -  5      $ )Nr"   )r   r   rV   r   r$   r%   r&   r3   "test_issue_14622.<locals>.<lambda>  s    !Q$(8(8A(>r%   )r   r   r	   as_numer_denomr   rV   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 rR   )r   r   r$   r%   r&   test_issue_18606r     s    UAr%   c                  `    [        [        [        5      5      R                  S5      (       d   eg r6   )r   r   r   rV   r$   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%   c            	      2   [        S[        -  [        [        5      -   [        [        45      [        [        [        5      [        [        45      :X  d   e[        S[        -  [        [        5      -   [        [        -  -   [        [        45      [        [	        [        [        [        5      -  5      [        [        45      :X  d   e[        [        [        [        5      -   [        [        45      [        [        [        5      [        [        45      :X  d   eg r6   )r   r   r   r	   r   r   r$   r%   r&   test_issue_22836r     s    QTIaL 1b'*a	!q"g.FFFFQTIaL 1a4'!R1Qs1SV8}q"g5NNNNQ12w'1Yq\Ar7+CCCCr%   N)fsympy.core.addr   sympy.core.functionr   r   sympy.core.numbersr   r   r   r	   r
   sympy.core.singletonr   sympy.core.symbolr   r   (sympy.functions.combinatorial.factorialsr   $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<   r?   rC   rE   rH   rJ   rM   rP   rT   rW   rY   r[   r]   r_   rd   rg   ri   rk   rm   rp   rr   rt   rw   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   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!?@"
"
>#>,
5
<@**=X	BK<. > >
G
A%
@<!A5Dr%   