
    ЦiW?                        S SK Jr  S SKJrJrJrJrJrJr  S SK	J
r
  S SKJr  S SKJrJr  S SKJr  S SK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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+J,r,J-r-J.r.J/r/Jr  S SK0J1r1J2r2J3r3   \" SSS9r4\" SSS9r5Sr6S r7\3S 5       r8S r9\3S 5       r:S r;\1S 5       r<S r=\1S 5       r>S r?S r@S rAS  rBS! rCS" rDS# rES$ rFS% rGS& rHS' rIS( rJS) rKS* rLS+ rMS, rNS- rOS. rPS/ rQS0 rRS1 rSS2 rTS3 rUS4 rV\1S5 5       rWS6 rXS7 rYS8 rZS9 r[S: r\S; r]S< r^S= r_\1S> 5       r`S? raS@ rbSA rcSB rdgC)D    )
EulerGamma)EIIntegerRationaloopi)S)Symbol)explog)sqrt)acotatancossinsign)Eierf)digammagammaloggamma)zeta)cancel)coshcothsinhtanh)comparemrvrewritemrv_leadtermgruntzr   )XFAILskipslowxT)realmFc                  2    [         (       d  [        S5        g g )Nr'   )runslowr&        ]/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/series/tests/test_gruntz.py_sskipr0   #   s    7V r.   c                  V   [        [        [        5      [        S[        -  [        [        * 5      -
  5      [        S[        -  5      -
  -  [        [        5      S:X  d   e[        [        [        5      [        S[        -  [        [        * 5      -   [        [        S-  * 5      -   5      [        S[        -  [        [        [        5      * 5      -
  5      -
  -  [        [        5      S:X  d   e[        [        [        [        [        [        * 5      -
  5      SS[        -  -
  -  5      [        [        [        5      5      -
  [        [        5      [        L d   e[        [        [        [        [        [        [        * 5      -   5      5      5      [        [        [        [        5      5      5      -  [        [        5      [        L d   e[        [        [        [        [        5      5      5      [        [        [        [        [        [        [        5      * 5      -
  5      5      5      -  [        [        5      [        L d   e[        [        [        [        [        5      5      5      [        [        [        [        [        [        [        [        5      5      * 5      -
  5      5      5      -  [        [        5      S:X  d   e[        [        [        [        5      5      [        [        [        [        [        [        [        5      5      * 5      -
  5      5      -  [        [        5      S:X  d   e[        [	        [        5      S-  [        [        [	        [        5      5      [	        [	        [        5      5      S-  -  [        [        [	        [	        [        5      5      5      [	        [	        [	        [        5      5      5      S-  -  5      -  5      -  [        [        5      -  [        [        5      S:X  d   e[        [        [	        [        5      -  [	        [        [        [        5      -  [        S-  -
  5      S-  -  [	        [	        [        S-  S[        [        S[        S-  -  [	        [        5      -  5      5      -  -   5      5      -  [        [        5      [        SS5      :X  d   e[        [        [        [        [        * 5      -  [        [        * 5      [        S[        S-  -  [        S-   -  5      -   -  5      [        [        5      -
  [        -  [        [        5      [        S5      * :X  d   e[        S[        -  S[        -  -   S[        -  -  [        [        5      S:X  d   e[        [        [	        [        [	        [        [	        S5      [	        [        5      -  -  5      -  5      -  [        [        5      [        L d   e[        [        [        S[	        [        S-  [        -   5      -  [	        [	        [        5      5      -  5      5      [        [        S[	        [        5      -  [	        [	        [        5      5      -  5      5      -  [        [        5      [        L d   e[        [        [        [        SS5      [        [        S	S
5      -  -  [        SS5      [        [        SS5      -  -  -   S[        S-  -  -   [        SS5      [        [        SS5      -  -  -   5      5      S-  [	        [	        [	        [        SS5      [        [        S	S5      -  -  5      * 5      5      [        S
S5      -  -  [        [        5      [        L d   e[        [        S[        -  [        [        * 5      -  S[        [        5      -  S[        S[        S-  -  [        S-   -  5      -  -   -  5      [        [        5      -
  [        [        5      S-  -  [        [        5      S:X  d   e[        [        [        [        [        * 5      -  [        [        * 5      [        S[        S-  -  [        S-   -  5      -   -  5      [        [        5      -  [        [        5      S:X  d   e[        [	        [        5      [	        [	        [        5      [	        [	        [        5      5      -   5      [	        [	        [        5      5      -
  -  [	        [	        [        5      [	        [	        [	        [        5      5      5      -   5      -  [        [        5      S:X  d   e[        [        [	        [	        [        [        [	        [        5      [	        [	        [        5      5      -  5      -   5      5      [	        [	        [	        [        [        5      [        -   [	        [        5      -   5      5      5      -  5      [        [        5      [        :X  d   e[        [        [        [        [        [        [        * 5      -   5      5      5      [        [        [        5      5      -  [        [        5      [        L d   eg )N         r      
                  i6      1   -         )r$   r   r(   r   r   r   r   r   r-   r.   r/   test_gruntz_evaluationrE   (   s    #a&#acCGm,s1Q3x78!R@BFFF#a&#acCGmc1a4%j89!c3q6'l*+, -./589: : : #c!c1"g+&AaC01CAK?BG2MMM#c#a#qb'k*+,s3s1v;/??BG2MMM#c#a&k"SSS#a&\1A-B)C%DDR   #c#a&k"SSS#c!f+5F1F-G)H%IIR   #c!f+CCSV,=(=$> ??BG1LLL#a&!)c$s1v,CFa/?"?SQ[)SSV-=,AAB#C D DFJ1gNR   1SV8S3q6AqD1A55QTAc#a1fSVm*<&=$==>?ABCRILTUVXYN[ [ [ 3qaRy#qb'C1a4Q,@"@ABSVKQNR VG$ $ $ 1a4!Q$;!A#&2.!333!CCCF3q6M 23455q"=CCC#c!C1qM/#c!f+567Bs1vIc#a&k123456<?AB B B #c(1a.HRO);;hr1oaQYZ[]_Q`N`>``a"gI&(0R(8HR<L9L(LM N OPQRS!Q8B3C0C!CDDEFQRTUVWXY[]_bde e e 3qs3r7{Ac!fHqQq!tVQU^1D/D$DEFQOFAI "&)*+ + + #aQBiaR3r!Q$wA+?!?@A#a&H!RP   #a&#c!fs3q6{23c#a&kABQ#c#a&k"223567=@AB B B #s3q3s1vc#a&k'9#::;<SQ!c!f!45679 :;<bBEFG G G #c#a#qb'k*+,s3q6{:ArBbHHHr.   c                  H   [        5         [        [        [        [        [        5      SS[        -  -
  -  5      5      [        [        [        [        5      SS[        -  -
  [	        [        5      [	        [        5      * -  -
  -  5      5      -
  [        [
        5      [
        * L d   e[        [        [        [        * S[        [        * 5      -   -  5      5      [        [        * S[        [        * S[        [        * 5      -   -  5      -   -  5      -  [        [        [        * [        [        * S[        [        * 5      -   -  5      -   5      5      -  [        [        * S[        [        * 5      -   -  5      S-  -  [        [        5      -
  [        -   [        [
        5      S:X  d   eg Nr2   r4   )r0   r$   r   r(   r   r   r-   r.   r/   test_gruntz_evaluation_slowrH   a   sU   
H#c#a&!ac'*+,CFA!Gc!fAw.?$?@ABCDErKOQcR R R 3sA2q3r7{+,-c1"a#qb!c1"g+>N:O6O2P.QQQBaRS!W%5!66789!QaR[)*Q./14Q8:;<=>DGHI I Ir.   c                     [        [        [        5      [        S[        -  [        [        * 5      -   5      [        S[        -  [        [        S-  * 5      -   5      -
  -  [        [        5      S:X  d   e[        [        [        [        [        [        5      * 5      -
  5      [        [        5      -
  [        [        [        5      5      -  [        [        S-  5      -  [        [        5      S[        [        5      -  :X  d   e[        [        [        [        5      5      [        [        S[        -  [        [        [        5      * 5      -   5      5      [        [        S[        -  5      5      -
  -  [        [        5      S:X  d   e[        [        [        5      [        [        [        [        * 5      -   5      [        [        5      -
  -  [        [        5      [        L d   e[        [        [        [        [        [        5      5      5      5      [        -  [        [        5      [        [        SS5      5      :X  d   e[        [        [        [        [        [        5      5      5      5      [        -  [        [        5      [        [        SS5      5      :X  d   e[        [        [        [        [        5      5      5      [        [        5      [        L d   e[        [        [        [        5      5      [        [        5      [        L d   e[        [        [        S[        [        5      -  -   5      [        [        5      -
  [        [        5      -  [        S[        -  5      -
  [        -  [        [        5      -  [        [        5      [        SS5      :X  d   e[        [        [        [        S[        [        5      -  -
  5      [        [        5      -
  [        [        5      -   -  [        [        5      [        R                  :X  d   e[        [        [        S[        [        5      -  -   5      [        [        5      -
  [        [        5      -  [        [        5      S:X  d   eg )Nr2   r4   r6   r3   )r$   r   r(   r   r   r   r   r	   r   r   r   r   r   r   r
   Halfr-   r.   r/   test_gruntz_eval_specialrK   l   s    #a&#acCGm,s1Q3adU3C/DDEq"MQRRRR3q3Aw<'(3q61SQ[@3q!t9LRtBxK( ( (#c!f+S1sCF7|);%<!=C!H!MNR  #a&%CG,uQx78!R@BFFF#c''!*-./11b9S"a=QQQQ#c'#a&/*+A-q"5Xb!_9MMMM'''!*-.26"<<<(8A;'B/2555E!aaj.)E!H4c!f<s1Q3xG!f%(0Q8 8 8!uQ58^,uQx7#a&@A1bI66  5QuQxZ(583s1v=q"EJJJr.   c                     [        5         [        [        [        S-   5      [	        S[
        -  5      -  [        [        * 5      [        [        [        R                  -   -  [        [        [        R                  -
  -  S-  -   -  -
  [        [        5      [        L d   e[        [        [        [        [        [        [        [        5      5      5      5      5      5      [        -  [        [        5      S:X  d   eg )Nr2   r4      r   )r0   r$   r   r(   r   r	   r   r
   rJ   r   r   r-   r.   r/   test_gruntz_eval_special_slowrN      s    
H%A,tAbDz)GQQVV_q1qvv:r/AABCDErKNPQ Q Q#c#gggaj&9:;<=a?BG1LLLr.   c            
          [        5         [        [        [        [        [        [        * 5      -
  5      [        S[        -  5      -  5      [        [        [        5      5      -
  [        [
        5      [
        L d   eg Nr2   )r0   r$   r   r   r(   r   r-   r.   r/   ,test_grunts_eval_special_slow_sometimes_failrQ      sL    
H#eAQBK(QqS12Sq]BArJbPPPr.   c            
      
   [        [        [        [        [        [        5      * 5      -
  5      [        [        5      -
  [        [        * 5      -  [        [        [        5      5      -  [        -  [        [        5      S:X  d   eg )Nr3   )r$   r   r(   r   r   r-   r.   r/   test_gruntz_EirS      sT    2a#s1vg,&'"Q%/#qb'9#c!f+EaGBOSUUUUr.   c            	          [        [        [        S5      S-   [        -  5      [	        [        [        [        * 5      -   5      [	        [        5      -
  -  [        [
        5      [        S5      * :X  d   eg )Nr4   r2   )r$   r   r   r(   r   r   r-   r.   r/   test_gruntz_eval_special_failrU      s]     SVaZNtAQBK047:;QDHKAwO O Or.   c                     [        [        [        5      [        [        5      [        L d   e[        [        [        5      [        [        * 5      [        L d   e[        [	        [        5      [        [        5      [        L d   e[        [	        [        5      [        [        * 5      [        * L d   e[        S[        [        5      -  [        [        5      -  [        [        5      [        L d   e[        S[        [        5      -  [        [        5      -  [        [        * 5      S:X  d   e[        S[	        [        5      -  [        [        5      -  [        [        5      [        L d   e[        S[	        [        5      -  [        [        5      -  [        [        * 5      S:X  d   e[        [        [        5      [        [        5      S:X  d   e[        [        [        5      [        [        * 5      S:X  d   e[        [        [        5      [        [        5      S:X  d   e[        [        [        5      [        [        * 5      S:X  d   eg )Nr4   r2   r3   )r$   r   r(   r   r   r   r   r   r-   r.   r/   test_gruntz_hyperbolicrW      s   $q'1b!R'''$q'1rc"b((($q'1b!R'''$q'1rc"rc)))!DG)CF"Ar*b000!DG)CF"As+q000!DG)CF"Ar*b000!DG)CF"As+r111$q'1b!Q&&&$q'1rc"b((($q'1b!Q&&&$q'1rc"b(((r.   c            	      H   [        S[        [        5      S:X  d   e[        [        [        [        5      [        5      S:X  d   e[        [        [        5      [        [        S-  5      [        5      S:X  d   e[        [        [        S-  5      [        [        [        5      5      [        5      S:X  d   e[        S[        [        [        5      5      [        5      S:X  d   e[        [        S[        5      S:X  d   e[        [        [        5      [        [        5      S:X  d   e[        [        [        S-  5      [        [        5      [        5      S:X  d   e[        [        [        [        5      5      [        [        S-  5      [        5      S:X  d   e[        [        [        [        5      5      S[        5      S:X  d   e[        SS[        5      S:X  d   e[        SS[        5      S:X  d   e[        SS[        5      S:X  d   e[        [        [        S-  [        5      S:X  d   e[        [        S-  [        S-  [        5      S:X  d   e[        [        S-  S[        -  [        5      S:X  d   e[        S[        -  [        [        -  [        5      S:X  d   e[        [        [        -  [        * [        5      S:X  d   e[        [        [        5      [        [        * 5      [        5      S:X  d   e[        [        [        * 5      [        S[        -  5      [        5      S:X  d   e[        [        S[        -  5      [        [        5      S-  [        5      S:X  d   e[        [        [        5      S-  [        [        [        [        * 5      -   5      [        5      S:X  d   e[        [        [        5      [        [        [        [        * 5      -   5      [        5      S:X  d   e[        [        [        S-  5      S[        [        S-  5      -  [        5      S:X  d   eg )Nr4   <r2   >r5   =r9   )r    r(   r   r*   r-   r.   r/   test_compare1r\      s   1as"""1c!fa C'''3q63q!t9a(C///3q!t9c#a&k1-4441c#a&k1%,,,1as"""3q61a C'''3q!t9c!fa(C///3s1v;AqD	1-4443s1v;1%,,,1as"""1b!###1b!###1adA#%%%1a4Aq!S(((1a41a C'''1Q31a C'''1a4!Q3&&&3q63r7A&#---3r7C!Ha(C///3qs8SVQY*c1113q619c!c1"g+.2c9993q63q3r7{+Q/36663q!t9aAqD	k1-444r.   c            	      ~   [        [        [        5      [        S-  [        5      S:X  d   e[        [        [        S-  5      [        [        5      S-  [        5      S:X  d   e[        [        [        5      [        [        [        [        * 5      -   5      [        5      S:X  d   e[        [        [        [        [        * 5      -   5      [        [        5      [        5      S:X  d   e[        [        [        [        [        * 5      -   5      [        [        * 5      [        5      S:X  d   e[        [        [        * 5      [        [        5      S:X  d   e[        [        [        [        * 5      [        5      S:X  d   e[        [        [        S[        -  -   5      [        [        5      S:X  d   e[        [        [        [        5      * 5      [        [        5      [        5      S:X  d   e[        [        [        [        [        5      * 5      [        -   5      [        [        [        5      * 5      [        5      S:X  d   eg )Nr7   rZ   r4   r[   rY   r2   r    r   r(   r-   r.   r/   test_compare2r_      s   3q61a4#s***3q!t9c!fai+s2223q63q3r7{+Q/36663q3r7{#SVQ/36663q3r7{#S!Wa0C7773r7Aq!S(((1c1"gq!S(((3q1Q3w<A&#---3Aw<Q+s2223sCF7|a'(#s1vg,:cAAAr.   c                      [        [        [        [        5      5      [        [        [        [        [        5      * 5      -   5      [        5      S:X  d   eg )NrZ   r^   r-   r.   r/   test_compare3ra      s5    3s1v;ASVG$4 5q9S@@@r.   c                  f   [        [        S5      [        5      S:X  d   e[        [        S5      [        5      S:X  d   e[        [        S5      [        5      S:X  d   e[        [        [        5      [        5      S:X  d   e[        [	        [        * 5      [        5      S:X  d   e[        [	        [        5      [        5      S:X  d   e[        [	        [        5      * [        5      S:X  d   e[        SS[        -  -
  [        5      S:X  d   e[        SS[        -  -
  [        5      S:X  d   e[        [        S[        -  5      [        5      S:X  d   e[        [        [        S5      -  [        5      S:X  d   e[        [        S-  [        5      S:X  d   e[        [        S-  [        5      S:X  d   eg )	Nr   r5   r2   r9   r3   r4   r7   )r   r   r(   r   r   r   r   r-   r.   r/   
test_sign1rd      sW   Q1$$$Q1$$$a B&&&A?aQBq   A?aQr!!!AaCq   QqS!"""AaC!!!!GAJ#q(((1a=A1a=Ar.   c                  R   [        [        [        5      S:X  d   e[        [        * [        5      S:X  d   e[        SSS9n [        U [        5      S:X  d   e[        U * [        5      S:X  d   e[        U [        -  [        5      S:X  d   e[        U * [        -  [        5      S:X  d   eg )Nr2   r3   yTpositive)r   r(   r   rf   s    r/   
test_sign2rj      s    1:??A;"sT"A1:??A;"!Q<11a=Br.   c                 L    [        [        X5      S   R                  5       5      $ Nr   )setr!   keys)abs     r/   mmrvrq      s    s1y|  "##r.   c                  @   [        [        [        5      [        1:X  d   e[        [        S[        -  -   [        5      [        1:X  d   e[        [        S-  [        5      [        1:X  d   e[        [        [        5      [        5      [        1:X  d   e[        [        [        5      [        5      [        [        5      1:X  d   e[        [        [        * 5      [        5      [        [        * 5      1:X  d   e[        [        [        S-  5      [        5      [        [        S-  5      1:X  d   e[        [        S[        -  5      * [        5      [        1:X  d   e[        [        [        S[        -  -   5      [        5      [        [        S[        -  -   5      1:X  d   eg rG   )rq   r(   r   r   r-   r.   r/   	test_mrv1rs      s#   1:!AaCs"""1a=QCA?qc!!!A?s1vh&&&QBQBy(((AqD	1#ad),,,QqS	1!$$$A!Ga SQqS\N222r.   c            
         [        [        [        [        [        [        5      * 5      -   5      [        5      [        [        [        5      * 5      1:X  d   e[        [        [        [        [        * 5      -   5      [        5      [        [        [        [        * 5      -   5      [        [        * 5      1:X  d   e[        [        S[        -  [        [        * 5      -   5      [        5      [        [        * 5      1:X  d   eg rP   rq   r   r(   r-   r.   r/   
test_mrv2arv     s    ASVG$%q)c3q6'l^;;;AQBK !$QaR[)93r7(CCCCAaC#qb'M"A&3r7)333r.   c            	          [        [        [        [        [        S-  * 5      -   5      [        5      [        [        S-  * 5      1:X  d   eg )Nr4   ru   r-   r.   r/   
test_mrv2brx     s6    AQTE
N#Q'CAJ<777r.   c                      [        [        [        * S[        S-  -  -   5      [        [        S[        -  -   5      -
  [        5      [        [        S[        -  -   5      [        S[        S-  -  [        -
  5      1:X  d   eg rG   ru   r-   r.   r/   
test_mrv2crz     si    QB1a4K3q1Q3w<',03A!Gc!AqD&1*o/NO O Or.   c                     [        [        [        S-  5      [        [        [        5      -  -   [        [        5      [        -  [        -  -   [        5      [        [        S-  5      1:X  d   e[        [        [        5      [        S[        -  [        [        * 5      -   5      [        S[        -  5      -
  -  [        5      [        [        5      [        [        * 5      1:X  d   e[        [        [        S-  S[        [        S[        S-  -  [        [        5      -  5      5      -  -   5      [        5      [        [        S[        S-  -  [        [        5      -  5      5      1:X  d   e[        [        [        [        [        5      -
  5      [        [        5      -  [        5      [        1:X  d   e[        [        S[        -  [        [        * 5      -
  5      [        S[        -  5      -
  [        [        5      -  [        5      [        [        5      [        [        * 5      1:X  d   e[        S[        [        * [        [        * 5      -   5      -  [        [        5      -
  [        5      [        [        5      [        [        * 5      [        [        [        [        * 5      -
  5      1:X  d   e[        [        [        [        [        [        [        [        5      -  5      -  S-   5      5      [        5      [        [        [        [        5      -  5      1:X  d   e[        [        [        [        [        [        5      S[        -  -   5      5      5      [        5      [        1:X  d   eg )Nr4   r2   r5   )rq   r   r(   r   r-   r.   r/   	test_mrv3r|     sk   AqD	Ac!fH$s1vqy{2A63q!t9+EEEAAaC#qb'M"S1X-.37:1vsA2w6GH H H	1qS1a4A'(((*+,.25c!AqD&Q-6H2I1JK K KAAJA&*qc111	QqS3r7]	c!A#h	&A.37:1vsA2w6GH H H	#qb3r7l
c!f$a)-0VS!Wc!c1"g+>N,OP P PC#aAh-!+,-q1c!CF(m_DDDCCFQqSL)*+Q/A3666r.   c                  h   [         n [        U " U " [        5      U " U " [        5      5      -   5      U " U " [        5      5      -
  U " U " [        5      U " U " U " [        5      5      5      -   5      -  U " [        5      -  [        5      [        1:X  d   e[        [        [        [        [        [        [        [        5      -  5      -  S-   5      5      [        [        [        [        [        5      S[        -  -   5      5      5      -
  [        5      [        [        [        [        5      -  5      1:X  d   eg rP   )r   rq   r(   r   )lns    r/   	test_mrv4r   )  s    	BBqEBr!uI%&BqE2Br!ur"RU)}7L4MMbQReS#  C#aAh-!+,-CCFQqSL8I4J0KKQO	Qs1vX  r.   c                 (    [        U S   U S   X5      $ Nr2   r   )r"   )ro   rp   cs      r/   mrewriter   1  s    1Q41q$$r.   c                     [        [        5      n [        [        U [        5      [        [        5      S[        -  [        * 4:X  d   e[        [        S-  5      n [        [        U [        5      [        [        5      S[        -  [        S-  * 4:X  d   e[        [        S[        -  -   5      n [        [        U [        5      [        [        5      S[        -  [        * S[        -  -
  4:X  d   eS[        [        * [        [        * 5      -   5      -  [        [        5      -
  n [        [        U [        5      [        [        5      S[        [        [        5      -  -  S[        -  -
  [        * 4:X  d   eg rG   r   r(   r   r!   r*   es    r/   test_rewrite1r   5  s   AAC1Iq!$1qb	111AqD	AC1Iq!$1q!te444A!GAC1Iq!$1qb1Q3h777	#qb3r7l
c!f$AC1Iq!$Ac!fH!);aR(@@@@r.   c                  <   [        [        5      [        [        [        [        5      5      5      -  n [        U [        5      [        [        5      1:X  d   e[	        [        U [        5      [        [        5      S[        -  [        [        5      -  [        * 4:X  d   eg rP   )r   r(   r   rq   r   r!   r*   r   s    r/   test_rewrite2r   @  sg    As3s1v;A1:#a&!!!C1Iq!$1SVaR(8888r.   c            	         [        [        * S[        S-  -  -   5      [        [        S[        -  -   5      -
  n [        [        U [        5      [        [        5      S[        -  [        [        S[        -  S[        S-  -  -   5      -  -   [        * S[        -  -
  4[        S[        -  [        S[        -  [        S-  -   5      -  -
  [        S-  [        -
  44;   d   eg )Nr2   r4   r3   r6   r   r   s    r/   test_rewrite3r   H  s    QB1a4K3q1Q3w<'AC1Iq!$"Q$3	!a1f4 2 +rAaCx*!#$qs3qsQW}+='=#=q2w{"K)M M M Mr.   c            	         [        [        S[        -  5      * [        5      S:X  d   e[        S[        [        * [        [        * 5      -   5      -  [        [        5      -
  [        5      S:X  d   e[        [        S[        -  [        [        * 5      -
  5      [        S[        -  5      -
  [        [        5      -  [        5      [        S[        -  5      * S4:X  d   eg )Nr2   )r3   r   r   )r#   r   r(   r-   r.   r/   test_mrv_leadterm1r   O  s    QqS	1%000#qb3r7l++c!f4a8GCCC	QqS3r7]	c!A#h	&A.38;AaCy!nE E Er.   c            	          [        [        [        [        5      [        -   5      [        -
  [        [        [        5      [        [        5      -   5      -  [        [        5      -  [        5      S:X  d   eg )N)r2   r   )r#   r   r   r(   r-   r.   r/   test_mrv_leadterm2r   V  sN    SVaZ1,c#a&3q6/.BB3q6I1M  r.   c                     [        [        [        * [        [        * 5      [        [        * [        [        5      -  5      -  -   5      [        5      [        [        * [        [        [        5      -  -
  5      1:X  d   e[	        [        [        * [        [        * 5      [        [        * [        [        5      -  5      -  -   5      [        5      [        [        * 5      S4:X  d   eg rl   )rq   r   r(   r   r#   r-   r.   r/   test_mrv_leadterm3r   \  s    QBaRaRAY//0!4aR!CF(]9K8LLLLQBaRaRAY!778!<aR!LLLr.   c                     [        [        [        [        5      [        L d   e[        [        [        [        * 5      [        * L d   e[        [        * [        [        5      [        * L d   e[        [        S-  [        [        * 5      [        L d   e[        [        S-  * [        [        5      [        * L d   e[        [        [        [        5      -  [        SSS9S:X  d   e[        S[        -  [        [        5      S:X  d   e[        [	        [        5      [        [        5      [        L d   e[        [	        [        5      * [        [        5      [        * L d   e[        [	        [        5      [        -  [        [        5      [        L d   e[        S[        -  [	        [        * 5      -
  [        [        5      S:X  d   e[        [        S[        -  -   [        [        5      [        L d   eg )Nr4   r   +dirr2   )r$   r(   r   r   r   r-   r.   r/   test_limit1r   b  sd   !Qr!!!!Q###1"a###!Q$B32%%%1a4%BB3&&&!CF(Aqc*a///!A#q""""#a&!R B&&&3q6'1b!bS(((#a&(Ar"b(((!A#QB-B'1,,,!ac'1b!R'''r.   c                     [        [        [        -  [        SSS9S:X  d   e[        [        [        5      S-
  [        -  [        S5      S:X  d   e[        SS[        -  -   [        [        5      S:X  d   e[        [        S[        -  5      * [        [        5      S:X  d   e[        [        [        [        * 5      -   [        [        5      [        L d   e[        [        [        [        S-  * 5      -   [        [        5      [        L d   e[        [        [        [        [        5      * 5      -   [        [        5      [        L d   e[        SS[        -  -   [        [        * 5      -
  [        [        5      S:X  d   eg )Nr   r   r   r2   r3   r4      )r$   r(   r   r   r-   r.   r/   test_limit2r   q  s   !Q$1#&!+++3q6A:q.!Q'1,,,!ac'1b!Q&&&3qs8)Q#r)))!c1"g+q"%+++!c1a4%j.!R(B...!c3q6'l"Ar*b000"qs(S!W$a,222r.   c            	         [        S5      n [        [        [        S[	        [        5      -   5      -
  [        [
        5      S:X  d   e[        [        [        U [	        [        5      -   5      -
  [        [
        5      S:X  d   e[        [	        [        5      S[	        [        5      -   -  [        [
        5      S:X  d   e[        [	        [        5      U [	        [        5      -   -  [        [
        5      S:X  d   eg )Nro   r2   r   )r   r$   r(   r   r   r   )ro   s    r/   test_limit3r   |  s    sA!c!c!f*o%q"-222!c!c!f*o%q"-222#a&!c!f*%q"-222#a&!c!f*%q"-222r.   c                      [        S[        -  S[        -  -   S[        -  -  [        [        5      S:X  d   e[        SS[        -  -  SS[        -  -  -   [        -  [        S5      S:X  d   eg )Nr5   r7   r2   r   r$   r(   r   r-   r.   r/   test_limit4r     s_    1a4!Q$;!A#&2.!3331qs8a!A#h&*Aq1Q666r.   c            
         [        [        * S[        [        * 5      -   -  5      n [        U 5      [        [        * SU -   -  5      -  [        [        [        * U -   5      5      -  U S-  -  [        [        5      -
  [        -   n[        U[        5      SU -  [        [        * 5      [        [        5      [        [        U -
  5      [        [        SU -   -  5      1:X  d   eg rG   )r   r(   rq   )hexprs     r/   test_MrvTestCase_page47_ex3_21r     s    QBCGAq6#qb!a%j/!#c1"q&k"221a47#a&@1DDa=QqS#qb'3q63q1u:s1a!e9~NNNNr.   c                  8   [        S5      n [        [        [        -  [        [        5      [        [        -  :X  d   e[        U [        -  [        -  [        [        5      U [        -  [        -  :X  d   e[        U S-  [        -  [        -  [        [        5      U [        -  [        -  :X  d   e[        U S-  [        [        5      -  [        -  [        [        5      R                  5       R                  [        5      [        U 5      [        -  [        -  :X  d   eg )Nrf   r5   )	r   r$   r   r(   r   r   simplifyr"   _signri   s    r/   test_gruntz_Ir     s    sA!A#q"2%%%!A#a%B1Q3r6)))!A#a%'1b!QqSV+++!A#c!f*Q,2&//199%@E!HQJrMQQQr.   c                  |    [        [        S-   S[        [        S-   5      -  -  [        [        5      [        :X  d   eg rP   )r$   r(   r   r   r   r-   r.   r/   test_issue_4814r     s.    1q5Ac!a%jL)1b1Q666r.   c            	         [        S[        [        5      -  [        [        5      S:X  d   e[        S[	        [        5      -  [        [        5      S:X  d   e[        [        [        5      [	        [        5      -  [        [        5      [        L d   e[        [        [        [        5      5      [        [        5      -  [        [        5      [        L d   e[        [        [        5      [        S5      S:X  d   e[        [        [        SS5      S[        -  -   5      [        [        5      [        [        SS5      5      :X  d   e[        [        [        [        -  5      [        [        [        5      5      -  [        [        5      S:X  d   e[        [        [        [        [        5      5      5      [        [        5      -  [        [        5      [        L d   eg )Nr2   r   r5   r4   r:   )r$   r   r(   r   r   r   r   r   r-   r.   r/   test_intractabler     s6   !E!H*a$)))!HQK-B'1,,,%(8A;&2."444#eAh-a(!R0B666%(Aq!Q&&&%A1,-q"5x1~9NNNN#ad)CaM)1b1Q666#eE!Ho&s1v-q"5;;;r.   c            
      8   [        [        S[        [        [        5      5      -  [        [
        5      S[        [        5      [        [        R                  5      -   -  -
  5      S:X  d   e[        S[        [        5      -  [        [
        * 5      [
        * L d   eg r   )
r   r$   r   r   r(   r   r	   r
   rJ   r   r-   r.   r/   test_aseries_trigr     st    &3tAw<B/B#aff+%&' (+,- - -!DG)Q$+++r.   c                      [        [        [        [        [        [        [        5      -  5      5      -  [        [        5      [        L d   eg )N)r$   r(   r   r   r   r-   r.   r/   test_exp_log_seriesr     s/    !CAc!fH&&2."444r.   c                      [        [        S-  [        -   S-   S[        -  [        S-  -   -  S[        -  -  [        [        5      S:X  d   eg )Nr:   r2   r4   r3   r   r-   r.   r/   test_issue_3644r     s?    AqD1HqL1a4!Q$;/2a48!R@AEEEr.   c                      [        SSSS9n U S-   [        U S-   -  -  [        U S-   -  S-
  -  [        [        S-
  -  -
  n[        U[        S5      R                  5       U S-  :X  d   eg )NnT)integerrh   r2   r4   )r   r(   r$   r   )r   rs     r/   test_issue_6843r     sg    sD40A	
QAE
AAJN+aQi7A!Q?##%1,,,r.   c                      [        [        [        S[        -  5      -
  [        [        5      [        R
                  :X  d   eg rP   )r$   r(   r   r   r
   r   r-   r.   r/   test_issue_4190r     s)    !eAaCj.!R(ALL888r.   c                  
   [        S5      n [        SSS9n[        S5      n[        SSS9n[        SSS9nS	U -  X-
  S
-   -  XX-
  S
-   -  -   -  U-  US
-
  X U-
  S	-   -  XX-
  S
-   -  -   -  U-  -  -   U -
  X-  U -
  -  nUR                  X"S
-   5      n[        UR                  X$5      U [        5      S
:X  d   e[        UR                  X#5      U [        5      R	                  5       S	US
-   -  U-   S
-
  US
-   US
-   -  -  :X  d   eg )Nr   r   Trg   r   pr*   )negativer4   r2   )r   subsr$   r   r   )r   r   r   r   r*   r   s         r/   test_issue_5172r     s.   sAsT"AsAsT"AsT"AqS!%!)_aQUQY-/014	
QEAIquqyM 12Q6679:;=>TAXGD99QAD$))A/1b)Q...$))A/1b)224	
QUa!	a!eq1u--. . .r.   c                      [        S[        [        5      -  [        S5      S:X  d   e[        [        [        [        5      -  [        S5      S:X  d   eg r   )r$   r   r(   r-   r.   r/   test_issue_4109r     s@    !E!H*a#q(((!E!H*a#q(((r.   c                      [        [        S[        [        * 5      -  5      [        S-  -  [        S5      [        S[        -  5      :X  d   eg )Nr4   r   )r$   r   r   r(   r   r-   r.   r/   test_issue_6682r     s9    #aA2h-1$a+s1Z</@@@@r.   c                  ~    SSK Jn   [        [        [        * -  [        SSS9[
        U " S[        * -  5      -  :X  d   eg )Nr   r   -r   r3   )sympy.functionsr   r$   r(   r	   r   r   s    r/   test_issue_7096r     s4    $!bS&!QC(BtRB3K/@,@@@@r.   c                      [        [        5      SS[        -  -   [        S-  -  -  n [        [        5      n[	        U [        [
        5      U:X  d   e[	        SU -  [        [
        5      SU-  :X  d   eg rG   )r   r(   r   r   r$   r   )eqanss     r/   test_issue_24210_25885r     s_    	Q1Q3A	B
q'C"a###!B$2!C%'''r.   N)e
sympy.corer   sympy.core.numbersr   r   r   r   r   r	   sympy.core.singletonr
   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   r   r   $sympy.functions.elementary.complexesr   r   'sympy.functions.special.error_functionsr   r   'sympy.functions.special.gamma_functionsr   r   r   &sympy.functions.special.zeta_functionsr   sympy.polys.polytoolsr   %sympy.functions.elementary.hyperbolicr   r   r   r   sympy.series.gruntzr    r!   r"   r#   r$   sympy.testing.pytestr%   r&   r'   r(   r*   r,   r0   rE   rH   rK   rN   rQ   rS   rU   rW   r\   r_   ra   rd   rj   rq   rs   rv   rx   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/   <module>r      s   ! @ @ " $ = 9 K K > = N N 7 ( H H	 	 2 2 3T
3T 
 5I 5IpI K K&M Q QV O O)5@
BA $	348O7%A9MEM(337 O OR7<,5F-9 . .)
AA(r.   