
    \hW                     *   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  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JrJ r J!r!  S SK"J#r#  S SK$J%r%  S SK&J'r'  S SK(J)r)  S SK*J+r+  S SK,J-r-  S SK*J.r.J/r/J0r0J1r1J2r2J3r3J4r4J5r5J6r6  S SK7J8r8J9r9J:r:  \" S5      u  r;r<r=\" SSS9u  r>r?r@\" S5      \" S5      srArBS rCS rDS rES rFS rGS  rH\:S! 5       rI\:S" 5       rJS# rKS$ rLS% rMS& rNS' rO\9S( 5       rPS) rQS* rRS+ rSS, rTS- rUS. rVg/)0    )Sum)Add)
DerivativeFunction)Mul)IRationaloopi)S)symbols)	factorial)explog)acoshasech)sqrt)acosasinatancossin)airyai)erf)gamma)	integrate)fps)O)	rational_algorithmFormalPowerSeriesFormalPowerSeriesProductFormalPowerSeriesComposeFormalPowerSeriesInversesimpleDErational_independentexp_rehyper_re)raisesXFAILslowzx y zzn m kT)integerfrc                  J
   S[         S-
  S-  [         S-
  -  -  n [        U [         [        5      S[        * S-
  -  * S-   [        [        S-   5      [        [        5      -  -
  SS4:X  d   eS[         -   [         S-  -   [         S-  -   [         S-
  [         S-
  -  -  n [        U [         [        5      SS[        * S-
  -  -  S-   [         S-   S4:X  d   e[        [
        [        -  [        [         -  -
  [
        [         -  -
  [         S-  -   -  n [        U [         [        5      [
        [        * S-
  -  * [        -  [
        [        -
  -  [        [        * S-
  -  [        -  [
        [        -
  -  -   SS4:X  d   e[         S[         -
  [         S-  -
  -  n [        U [         [        5      b   e[        U [         [        SS9[        S	S5      [        S
5      S-  -   [        * S-
  -  [        S
5      * S-  [        R                  -   -  [        S
5      * S-  [        R                  -
  [        * S-
  -  [        S
5      S-  [        R                  -   -  -   SS4:X  d   eS[         S-  S[         -  -   S-   -  n [        U [         [        5      b   e[        U [         [        SS9[        S	[        -   [        * S-
  -  -  S-  [        S	[        -
  [        * S-
  -  -  S-  -
  SS4:X  d   e[        S[         -   5      n [        U [         [        5      S	[        * -  * [        -  SS4:X  d   e[        [         5      n [        U [         [        5      b   e[        U [         [        SS9[        [        [        * -  -  S-  [        [        * [        * -  -  S-  -
  [        -  SS4:X  d   e[         [        [         5      -  [        S[         S-  -   5      S-  -
  n [        U [         [        5      b   e[        U [         [        SS9[        [        [        * S-   -  -  S-  [        [        * [        * S-   -  -  S-  -
  [        [        S-
  -  -  SS4:X  d   e[        S[         -   S[         -
  -  5      S-  [        [         5      -
  n [        U [         [        5      b   e[        U [         [        SS9S	[        * -  * S-  [        [        [        * -  -  S-  -
  [        [        * [        * -  -  S-  -   [        R                  -   [        -  SS4:X  d   e[        [        [         5      [         [        5      b   eg )N      r      i   Tfull   
   )xr   kr   zymr	   r   r   Halfr   r   r   r   r,   s    V/var/www/auris/envauris/lib/python3.13/site-packages/sympy/series/tests/test_formal.pytest_rational_algorithmr@      s   	a!eaZ1q5!"AaA&
qb1f+	Yq1u-	!<	=q!DE E E 
QA1	!a%AE!23AaA&	Q!a[1	a!eQ'( ( ( 	
QqS1Q3Y1_q!t#$AaA&QK<>a!e
$!qb1f+a-AE)B	CQJK K K 	
QUQT\AaA&...aAD1B?T!WQY&1"q&
17(2+
 G8A:1"q&
)
q'"*qvv

  "#A	'' ' ' 	
QTAaCZ!^AaA&...aAD1
R!VrAv
!	#q"q&QBF);';q&@	@!QGH H H 	AE
AaA&!*q!Q      	QAaA&...aAD1Q!W9/Qqbz\Q.
.!	3Q:; ; ; 	
$q'	CAqDMA%%AaA&...aAD1Q!a[=A
QB1"q&>!1Q 6
6
QU)
	   	QUq1u"T!W,AaA&...aAD11":+/QqA2wY!O
+q1"|q.@
@
&&
!	   c!fa+333    c            
      |   [         n U " / [        5      / :X  d   eU " [        [        5      [        [        5      /[        5      [        [        5      [        [        5      /:X  d   eU " [        S-  [        [        5      [        [        [        5      -  [        S-  /[        5      [        S-  [        S-  -   [        [        [        5      -  [        [        5      -   /:X  d   eU " [        R
                  [        [        [        5      -  [        [        5      [        [        5      [        -  [        [        5      [        [        5      [        /[        5      [        S-   [        [        [        5      -  [        [        5      -   [        [        5      [        -  [        [        5      -   [        [        5      /:X  d   eg )Nr0   r1   r/   )r%   r8   r   r   r   Oner   )ris    r?   test_rational_independentrE   P   s!   	Bb!9??s1vs1v"s1vs1v&6666q!tSVQs1vXq!t,a0	
A1aAhQ'() ) )quuaAhAAq#a&#a&!DaH	
Q#a&3q6!3q6!8c!f#4c!f=> > >rA   c            	         [        [        [        5      [        [        5       H9  n U [        [        5      * [	        [        [        5      [        5      -   S4:X  d   e  O   [        [        [        5      [        [        5       H=  n U [        [        5      [	        [        [        5      [        [        5      -   S4:X  d   e  O   [        [        S[        -   5      [        [        5       HQ  n U [        S-   [	        [        [        5      [        S5      -  [	        [        [        5      [        5      -   S4:X  d   e  O   [        [        [        5      [        [        5       H_  n U [        [	        [        [        5      [        5      -  [        S-  S-
  [	        [        [        5      [        [        5      -  -   S4:X  d   e  O   [        [        [        5      [        [        5      -  [        [        5       H\  n U S[        [        5      -  S[	        [        [        5      5      -  -
  [	        [        [        5      [        [        5      -   S4:X  d   e  O   [        S[        -   S[        -
  -  [        -  [        [        5       HO  n U S[        -  [        [        5      -  [        S-  S-
  [	        [        [        5      [        5      -  -   S4:X  d   e  O   [        [        [        5      [        [        5       HE  n U [        * [        [        5      -  [	        [        [        5      [        [        5      -   S4:X  d   e  g    g )Nr/   r0   )
r$   r   r8   r,   r   r   r   r   nr   )DEs    r?   test_simpleDErI   Z   s^   s1vq!$qtej1q1115555 % s1vq!$adZ!a33Q7777 % s1q5z1a(q1uj1q!44z!A$7JJANNNN ) tAw1%a
1Q4++q!taxAaD!Q9O.OO  	  & s1vc!f}a+a!fqAaD!111JqtQ4JJANNNN , QQ!+Q2ac!A$h!Q$(JqtQ,?!??CCCC 3 vay!Q'qb1g
1Q4A 66:::: (rA   c                  ,   [        [        5      * [        [        [        5      [        5      -   n [        U [        [
        5      [	        [
        5      * [	        [
        S-   5      -   :X  d   e[        [        5      [        [        [        5      [        [        5      -   n [        U [        [
        5      [	        [
        5      [	        [
        S-   5      -   :X  d   e[        [        5      [        [        [        5      [        5      -   [        [        [        5      [        [        5      -   n [        U [        [
        5      [	        [
        5      [	        [
        S-   5      -   [	        [
        S-   5      -   :X  d   e[        [        [        5      [        5      [        [        [        5      [        [        5      -   n [        U [        [
        5      [	        [
        5      [	        [
        S-   5      -   :X  d   e[        [        [        5      [        S5      [        [        [        5      [        S5      -   [        [        [        5      5      -   n [        U [        [
        5      [	        [
        5      [	        [
        S-   5      -   [	        [
        S-   5      -   :X  d   eg )Nr/   r0   r1   r2   )r,   r8   r   r&   r-   r9   ds    r?   test_exp_rerM   t   s   	
1
1Q4##A!Q?qteaAh....	!z!A$1%%A!Q?adQq1uXo---	!z!A$""Z!a%;;A!Q?adQq1uXo!a%88881Q4j1q!44A!Q?adQq1uXo---1Q4AAaD!Q!77*QqT:JJA!Q?adQq1uXo!a%8888rA   c                     [        [        5      [        [        [        5      [        [        5      -   n [        U [        [
        5      [	        [
        5      [
        S-   [
        S-   -  [	        [
        S-   5      -  -   :X  d   e[        * [        [        5      -  [        [        [        5      [        [        5      -   n [        U [        [
        5      [
        S-   [
        S-   -  [	        [
        S-   5      -  [	        [
        5      -
  :X  d   eS[        [        5      -  S[        [        [        5      [        5      -  -
  [        [        [        5      [        [        5      -   n [        U [        [
        5      S[
        -  S-
  [	        [
        S-   5      -  [
        S-   [
        S-   -  [	        [
        S-   5      -  -   S[	        [
        5      -  -   :X  d   eS[        -  [        [        5      -  [        S-  S-
  [        [        [        5      [        5      -  -   n [        U [        [
        5      [
        [	        [
        5      -  S[        -  [	        [
        S-   5      -  -   [
        * S-
  [	        [
        S-   5      -  -   :X  d   e[        S-  S-   [        [        [        5      [        5      -  [        [        S-  S-
  -  [        [        [        5      [        [        5      -  -   n [        U [        [
        5      [
        [
        S-
  -  [
        -   [	        [
        5      -  S[
        -  [
        S-   [
        S-   -  -
  S-   [	        [
        S-   5      -  -   :X  d   e[        S-  S-
  [        [        [        5      [        S5      -  S[        -  [        [        [        5      [        [        5      -  -   [        [        [        5      [        5      -   n [        U [        [
        5      [
        [
        S-
  -  [
        S-
  -  S[
        -  [
        S-
  -  -   [
        -   [	        [
        5      -  [
        * [
        S-   -  [
        S-   -  [	        [
        S-   5      -  -   :X  d   eg )	Nr/   r0   r1   r7   r2   	   (   )r,   r8   r   r'   r-   r9   rG   rK   s    r?   test_hyper_rerR      s2   	!z!A$1%%AAq!!!ac{1QU8'; ;;;;	
1Q4*QqT1a((AAq!QQ!a% 81Q4 ????	!A$:adA&&&AaD!Q)??AAq!	A1QU8q1uq1uoaAh661Q4?@ @ @ 	
!AaDAqD1Hj1q111AAq!	!A$1Qq1uX!a1q5 112 2 2 
BJqtQ''!QUQY-
1Q4A8N*NNAAq!	
AEQ!!q1uq2v&6 6 ;Qq2vYFFG G G Q$(JqtQ*	*QqSAaD!Q1G-G	G	AaD!	
AAq!
QU)QU
ac1q5k
)A
-qt	3"a!e*a!e
aAh	&
'( ( (rA   c                     [        S5      S:X  d   e[        S[        5      S:X  d   e[        S[        SS9S:X  d   e[        S[        SS9S:X  d   e[        S[        -  S[        S-  -  -   5      S[        -  S[        S-  -  -   :X  d   e[        [        S[        -   5      SSS9[        S[        -   5      :X  d   e[        [        S-  [        -   S-   5      n [        U [        5      (       d   eU R
                  [        S-  [        -   S-   :X  d   eU S   S:X  d   eU S   [        S-  :X  d   eU R                  S	5      [        S-  [        -   S-   [        [        S	-  5      -   :X  d   eU R                  5       [        S-  [        -   S-   :X  d   e[        [        S[        -   5      5      n [        U [        5      (       d   eU R
                  [        S[        -   5      :X  d   eU R                  [        [        5      U :X  d   eU S S
 S[        [        S-  * S-  [        S-  S-  [        S	-  * S	-  /:X  d   eU R                  [        5      [        :X  d   eU R                  S5      [        [        S-  S-  -
  [        S-  S-  -   [        S	-  S	-  -
  [        S
-  S
-  -   :X  d   eU R                  R                  S   nU R                  [        SU* -  * [        U-  -  U-  US[         45      :X  d   eU R                  S S9U S S
 p2[#        U5       H  u  pEUS
:X  a    OX4   U:X  a  M   e   [%        [        5      R                  [        5      n [        U [        5      (       d   eU R                  5       [        [        S-  S-  -
  [        S
-  S-  -   [        [        S-  5      -   :X  d   e['        [(        S 5        ['        [*        S 5        g )Nr/   r0   +dir-F)hyperrationalr   r2   r6   r1      r5   rG   x   c                  .    [        [        [        -  5      $ N)r   r;   r8    rA   r?   <lambda>test_fps.<locals>.<lambda>   s    AaCrA   c                      [        [        SS9$ )Nr   rU   )r   r8   r_   rA   r?   r`   ra      s
    s1!}rA   )r   r8   r   
isinstancer    functiontruncater   
polynomialsubsr;   as_leading_termak	variablesinfiniter   r
   	enumerater   r(   NotImplementedError
ValueError)r,   r9   ftsits         r?   test_fpsrs      sZ   q6Q;;q!9>>q!"""q!"""qsQq!tV|!a1f,,,s1q5z73q1u:EEEAqD1HqLAa*++++::AA%%%Q4199Q41a4<<::a=AqD1HqL1QT72222<<>QTAX\)))CAJAa*++++::QU###66!Q<1Ra5QAqD57AqDFQTE!G4444Q1$$$<<?a!Q$q&j1a461AqDF:QT!VCCCC	qA::qbzk!Q$.1Aq":>>>>JJJ"1"6tqyy 
 	A

1Aa*++++::<1q!tAv:1S01QT7::::
 01
:,-rA   c                     [        S[        -  5      S[        -  :X  d   e[        [        S-  [        -   S-   [        S-  -  SS9[        S-  [        -   S-   [        S-  -  :X  d   eS[        S-
  S-  [        S-
  -  -  n [        U [        5      R                  5       [        SS5      [        [        SS5      -  -
  S[        S-  -  S	-  -
  S
[        S-  -  S-  -
  S[        S-  -  S-  -
  S[        S-  -  S-  -
  [	        [        S-  5      -   :X  d   eS[        -   [        S-  -   [        S-  -   [        S-
  [        S-
  -  -  n [        U [        5      R                  5       [
        R                  [        [        SS5      -  -   S[        S-  -  S	-  -   S
[        S-  -  S-  -   S[        S-  -  S-  -   S[        S-  -  S-  -   [	        [        S-  5      -   :X  d   e[        S[        -
  [        S-  -
  -  n [        U [        SS9R                  5       [        [        S-  -   S[        S-  -  -   S[        S-  -  -   S[        S-  -  -   [	        [        S-  5      -   :X  d   eS[        S-  S[        -  -   S-   -  n [        U [        SS9R                  5       [
        R                  [        S-  -
  [        S-  S-  -   [        S-  S	-  -
  [        S-  S	-  -   [	        [        S-  5      -   :X  d   e[        S[        -   5      n [        U [        5      R                  5       [        [        S-  S-  -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        U [        SS9R                  5       [        U [        SS9R                  5       :X  d   e[        U [        S5      R                  5       [        S5      [        SS5      -
  [        S-
  S-  S-  -
  [        S-
  S-  S-  -   [        S-
  S-  S-  -
  [        S-
  S-  S-  -   [        S-  -   [	        [        S-
  S-  [        S45      -   :X  d   e[        U [        SSS9R                  5       [        S5      [        SS5      -
  [        * S-   S-  S-  -
  [        * S-   S-  S-  -
  [        * S-   S-  S-  -
  [        * S-   S-  S-  -
  [        S-  -   [	        [        S-
  S-  [        S45      -   :X  d   e[        [        5      n [        U [        SS9R                  5       [        [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        U [        SSS9R                  5       [        U [        SSS9R                  5       :X  d   e[        U [        SSS9R                  5       [        S5      [        SS5      -
  S[        S-
  S-  -  S-  -
  S[        S-
  S-  -  S-  -   S[        S-
  S-  -  S-  -
  S[        S-
  S-  -  S-  -   [        S-  -   [	        [        S-
  S-  [        S45      -   :X  d   e[        U [        SSSS9R                  5       [        S5      [        SS5      -
  S[        * S-   S-  -  S-  -
  S[        * S-   S-  -  S-  -
  S[        * S-   S-  -  S-  -
  S[        * S-   S-  -  S-  -
  [        S-  -   [	        [        S-
  S-  [        S45      -   :X  d   e[        [        [        5      -  [        S[        S-  -   5      S-  -
  n [        U [        SS9R                  5       [        S-  S-  [        S-  S -  -
  [	        [        S-  5      -   :X  d   e[        S[        -   S[        -
  -  5      S-  [        [        5      -
  n [        U [        SS9R                  S!S"9S[        S-  -  S-  S[        S#-  -  S#-  -   [	        [        S!-  5      -   :X  d   eg )$Nr/   r0   r1   r5   rU   r6   r2         1             iA  @   rZ   q      Tr3      Q   D    )r4   rV         iw  iq  )   i	=     r7   r[      )	r   r8   re   r	   r   r   r=   r   r   r>   s    r?   test_fps__rationalr      s   qs8!1q11$"-!Q$(Q,!Q$1FFFF	a!eaZ1q5!"Aq!9	"a1Xa^+	+bAgai	7"QT'"*	Ds1a4xPR{	R	QT"
Aw
      
QA1	!a%AE!23Aq!9	
!HQN"	"R1WQY	.AqD	;c!Q$hrk	I	QT"
Aw
      	
QUQT\Aq!$((*	AqD1QT6AadF"Qq!tV+a1g56 6 6 	
QTAaCZ!^Aq!$((*	1q!tAv1Q&Aa/!AqD'9: : : 	AE
Aq!9	AqDF
QT!Vad1f$q!tAv-!Q$78 8 8q!$$&#a*;*D*D*FFFFq!Q<  "	Q(1a.	 AEA:b=	0AEA:b=	@
a%!C
q51*T/
*,-aC
023QUQJA2G
HI I I q!QB((*	Q(1a.	 QBFQ;r>	1aR!VaKN	B"q&1S
BFQ;t+
,./c
245q1uqj1a&4I
JK K K 	QAq!$((*a!Q$q&j1a46.AAadG.KKKKq!$A&//1Aqt$--/0 0 0q!QT"++-	a8Aq>	!Aq1uqjLO	3b!a%!mC6G	G	
AEA:c	
AzM%/
023A#
6891q51*q!f8M
NO O O q!QTr*335	a8Aq>	!ArAvkM"$4	4rA26A+~c7I	I	
QBFQ;s	
!a!^E1
245aC
8:;QUQJA:O
PQ Q Q 	
$q'	CAqDMA%%Aq!$((*ad1fq!tBw.>1a4.HHHHQUq1u"T!W,Aq!$((2(.!AqD&(Qq!tVAX2E!R%2PPPPrA   c            
         [        [        5      n [        U [        5      R                  5       [        [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        5      n [        U [        5      R                  5       S[        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        5      n [        U [        5      R                  5       S[        -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        5      n [        U [        5      R                  5       [        [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        [        5      5      n [        U [        5      R                  5       [        [        S-  5      [        [        [        S-  5      -  -
  [        S-  [        [        S-  5      -  S-  -   [        S-  [        [        S-  5      -  S-  -
  S[        S-  -  [        [        S-  5      -  S-  -   [        S-  [        [        S-  5      -  S-  -
  [	        [        S-  5      -   :X  d   e[        [        [        5      5      n [        U [        5      R                  5       [        [        -   [        [        S-  -  S-  -
  [        [        S-  -  S	-  -
  [	        [        S-  5      -   :X  d   e[        S[        -  5      n [        U [        5      R                  5       [        S-  [        -
  [        S-  S-  -   [        S-  S-  -
  [	        [        S-  5      -   :X  d   e[        [        [        5      -  [        S[        S-  -   5      S-  -
  n [        U [        S
S9R                  5       [        S-  S-  [        S-  S-  -
  [	        [        S-  5      -   :X  d   e[        S[        -   5      n [        U [        S
S9R                  5       [        [        S-  S-  -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S-  -   [	        [        S-  5      -   :X  d   e[        [        S-  5      n [        U [        5      R                  5       S[        SS5      -  [        [        SS5      5      -  S[        -  -  S[        SS5      -  [        S-  -  S[        [        SS5      5      -  -  -
  [	        [        S-  5      -   :X  d   e[        [        5      [        [        5      -  n [        U [        5      R                  5       [        [        S-  -   [        S-  S-  -   [        S-  S-  -
  [	        [        S-  5      -   :X  d   e[        [        5      [        [        5      -  [        -  n [        U [        5      R                  5       S[        -   [        S-  S-  -   [        S-  S-  -
  [        S-  S-  -
  [	        [        S-  5      -   :X  d   e[        [        5      [        [        5      -  n [        U [        5      R                  5       [        S[        S-  -  S-  -
  S[        S-  -  S-  -   [	        [        S-  5      -   :X  d   eg )Nr1   rZ   r6   r\   r/   r0   r2      rv   FrY   r      Z      )r   r8   r   re   r   r   r   r   r   r   r   r   r   r   r	   r   r>   s    r?   test_fps__hyperr      sw   AAq!91q!tAv:1S#81QT7#BBBBAAq!91q!tAv:1R#7!AqD'#AAAAAAq!9	A1QAa!Q$r')AqDH4qAw>? ? ? 	QAq!91q!tAv:1Q#61a4#@@@@DGAq!9	RTQs2a4y[	 1a4BqD	>!#3	3ad3r!t9nQ6F	F	
1a4BqD		"	
 !tC1I~a/
023AqD'
:; ; ; 	E!HAq!91q51QT6!8#3a1fQh#>1a4#HHHHQqS	Aq!92a4!8ad1f#4q!tAv#=!Q$#GGGG	$q'	CAqDMA%%Aq!e$--/1a46AqDG3Ca1g3MMMMAE
Aq!e$--/	AqDF
QT!Vad1f$q!tAv-!Q$78 8 8 	q!tAq!9	
HQN	5!Q0	0!B$	7	
HQN	1a4	5!Q#8!8	9
:<=adG
DE E E 	As1vAq!91q!t8ad1f#4q!tBw#>1a4#HHHHAs1vaAq!91q51a46>AqDG#;ad2g#E!Q$#OOOOAQAq!91qAvax<!AqD&)#;a1g#EEEErA   c                     [         S-  [        [         5      -  n [        U [         5      R                  5       S[         S-  -  SS[         S-  -  -  -
  [	        SS5      -   [         S-  S-  -
  [         S-  S-  -   [        [         S-  5      -   :X  d   e[         S-  [        [         5      -  n [        U [         S	S
9R                  5       [         S-  [         S-  S-  -
  [        [         S-  5      -   :X  d   e[        [        [         5      5      [         -  n [        U [         5      R                  5       [         [         S-  S-  -
  [         S-  S-  -   [         S-  S-  -
  [         S-  S-  -   [        [         S-  5      -   :X  d   e[         S-  [        [        [         5      5      -  n [        U [         5      R                  5       [         S-  [         S-  S-  -
  [         S-  S-  -   [         S-  S-  -
  [        [         S-  5      -   :X  d   eg )Nr/   r2   rZ   r0   r\     选 Fr   r1   r6   r     逝  )	r8   r   r   re   r	   r   r   r   r   r>   s    r?   test_fps_shiftr   ,  s   	2c!fAq!9	!Q$AadFhq#..Ad:QT&[H1QPQT7RS S S 	
1T!WAq!e$--/	1q!tAv!Q$      	DGQAq!9	AqDF
QT"Wq!tCx'!Q$u*4qAw>? ? ? 	
1Sa\Aq!9	1q!tAv1R!Q$s(*Qq!tW45 5 5rA   c                  |   [         [        [         5      -  [        S[         S-  -   5      S-  -
  n [        U [         5      R	                  5       [         S-  S-  [         S-  S-  -
  [        [         S-  5      -   :X  d   e[        [         5      [        [         5      -   [        [         5      -
  [        S[         -   5      -   n [        U [         5      R	                  5       [         S[         S-  -  S-  -
  [         S-  S-  -
  [         S-  S-  -   [        [         S-  5      -   :X  d   eS[         -  [        [         5      -   n [        U [         5      R	                  5       S[         -  [         -   [         S-  S-  -
  [         S-  S-  -   [        [         S-  5      -   :X  d   e[        [         5      [        [         5      -
  S[         S-
  -  -   n [        U [         5      R	                  5       S	[         S-  S-  -
  S
[         S-  -  S-  -
  S[         S-  -  S-  -
  S[         S-  -  S-  -
  [        [         S-  5      -   :X  d   eg )Nr/   r0   r2   r   rZ   r1   r6   r\   rO   r   r   r   w   )	r8   r   r   r   re   r   r   r   r   r>   s    r?   test_fps__Add_exprr   >  s   	$q'	CAqDMA%%Aq!91a46AqDG#3a1g#====AQ#a& 3q1u:-Aq!91qAvax<!Q$q&#81a46#AAadG#KKKK	!c!fAq!91Q37QT!V#3ad3h#>1a4#HHHHAQ!QU)#Aq!9
QT!Va1fQhAqD+c!Q$hsl:Qq!tWDE E ErA   c                     [        [        5      n [        U [        [        5      U :X  d   e[        U [        [        * 5      R	                  5       [        S[        S-  -  [        [        45      :X  d   e[        [        5      n [        U [        [        5      R	                  5       S[        S[        S-  -  [        [        45      -   :X  d   e[        U [        [        * 5      R	                  5       S[        S[        S-  -  [        [        45      -   :X  d   e[        [        5      n [        U [        [        SS9R	                  5       SS[        S-  -  -  SS[        S-  -  -  -   S[        -  -
  [        S-  -   [        S[        S-  -  [        [        45      -   :X  d   e[        U [        [        * SS9R	                  5       SS[        S-  -  -  SS[        S-  -  -  -   S[        -  -
  [        S-  -
  [        S[        S-  -  [        [        45      -   :X  d   e[        S[        -   5      n [        U [        [        5      SS[        S-  -  -  SS	[        S	-  -  -  -
  SS[        S-  -  -  -   SS[        S-  -  -  -
  S[        -  -   [        S[        -  5      -
  [        S[        S-  -  [        [        45      -   :w  d   e[        U [        [        * 5      SS[        S-  -  -  SS	[        S	-  -  -  -
  SS[        S-  -  -  -   SS[        S-  -  -  -
  S[        -  -   [        [        -  -   [        S[        -  5      -
  [        S[        S-  -  [        [        45      -   :w  d   eg )
Nr/   rZ   r5   Tr3   r6   r1   r0   r2   )r   r8   r   r
   re   r   r   r   r   r   r   r>   s    r?   test_fps__asymptoticr   M  s   AAq!R=Aq!bS>""$!AqD&1b'(::::AAq!R=!!#q1Qq!tVaW+='====q!bS>""$QqAv2w-?(????QAq!Rd#,,.
AadFa1a4j 1Q3&A-!AqD&1b'0BBC C Cq!bSt$--/
AadFa1a4j 1Q3&A-!AqD&1b'0BBC C C 	AE
Aq!R=	Qq!tVq!AqD&z	!AqAvJ	.AadF	;ac	AC!H	L	
1QT6Ar7	
   q!bS>	Qq!tVq!AqD&z	!AqAvJ	.AadF	;ac	AAbD	H	RT
qAv2w'
() ) )rA   c                  	   [        [        [        5      5      [        -  n [        U [        5      R	                  5       S[        [        5      -  [        [        5      S-  -
  [        [        SS5      -  S-  -   [        [        SS5      -  S-  -
  [        [        SS5      -  S	-  -   [        [        S
S5      -  S-  -
  [        [        SS5      -  S-  -   [        [        S-  5      -   :X  d   e[        [        [        5      5      [        -  n [        U [        5      R	                  5       [        [        SS5      -  [        [        SS5      -  S-  -
  [        [        SS5      -  S-  -   [        [        S
S5      -  S-  -
  [        [        SS5      -  S	-  -   [        [        S-  5      -   :X  d   e[        [        [        5      5      [        S-  -  n [        U [        5      R	                  5       [        [        SS5      -  [        [        SS5      -  S-  -
  [        [        R                  -  S-  -   [        [        SS5      -  S-  -
  [        [        SS5      -  S
-  -   [        [        SS5      -  S-  -
  [        [        S
S5      -  S-  -   [        [        SS5      -  S-  -
  [        [        S-  5      -   :X  d   e[        [        [        5      5      n [        U [        5      R	                  5       R                  5       S[        S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        [        5      -   [        [        SS5      -  S-  -   [        [        SS5      -  S-  -   [        [        SS5      -  S-  -   [        [        S
S5      -  S	-  -   [        [        SS5      -  S-  -   [        [        S-  5      -   :X  d   e[        [        [        5      5      [        -  n [        U [        5      R	                  5       R                  5       [        [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        [        SS5      -  -   [        [        SS5      -  S-  -   [        [        SS5      -  S-  -   [        [        S
S5      -  S-  -   [        [        SS5      -  S	-  -   [        [        S-  5      -   :X  d   eg )Nr/   rZ   r1   r0   r\   r6   r   r   r   rP   i ar   l    LQf r5      r   r   r   r2   r   i _7 )r   r   r8   r   re   r	   r   r   r   r=   r   expandr>   s    r?   test_fps__fractionalr   e  s   DGqAq!9	
47T!WQY	HQN!23!6	6	
HQN	4	
 "#Xa^"3F":
;	
HQN	8	#
$&'"a&8&C
DFG1g
NO O O
 	DGqAq!9	
HQN	QA.q0	01hq!n3DS3H	H	
HQN	4	
 "#Xb!_"4V";
<>?1g
FG G G 	T!W1Aq!9	
HRO	a"a02	2QYq[	@	
HQN	1	
 (1a.02
356A5Fr5I
J	
HQN	2	
 !8B? 22 5
689!Q$
@A A A
 	DGAq!9&&(	
QqS1a47	QT#X	%1U
	2QT'\	ADG	K	
HQN	1	
 (1a.04
578(1a.7H7M
N	
HQN	6	!
"$%xA$6x$?
@BCAqD'
JK K K
 	DGQAq!9&&(	
QT!Vad2g	1S	(1a4:	58Aq>8I	I	
HQN	1	
 (1a.04
578(1a.7H7M
N	
HRO	F	"
#%&q!tW
-. . .rA   c                     [        SS[        -  -   5      n [        U [        5      [        [        5      * [        -   [        S-  S-  -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :w  d   e[        U [        SS9[        [        5      * [        -   [        S-  S-  -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :w  d   eg )	Nr/   r0   r1   r2   r6   rZ   Fr   )r   r8   r   r   r>   s    r?   !test_fps__logarithmic_singularityr     s    A!GAq!9	Q!ad1fq!tAv%1Q.Aa7!AqD'AB B Bq!e$	Q!ad1fq!tAv%1Q.Aa7!AqD'AB B BrA   c                      [        [        5      n [        U [        5      [        S5      [        [        5      -
  [        S-  S-  -
  S[        S-  -  S-  -
  [	        [        S-  5      -   :X  d   eg )Nr0   r2   r1   r{   rZ   )r   r8   r   r   r   r>   s    r?   &test_fps__logarithmic_singularity_failr     sV    aAq!9AQ!Q$q&01QT6"9<qAwFFFFrA   c                  >   [         [        -  [        [         S-  5      -  n [        U [         5      R	                  S5      [         [        S-   -  [         [        S-   -  S-  -
  [        [         [        S-   -  [         5      -   :X  d   e[         [        -  [        S[         -   5      -  n [        U [         5      nUR                  R                  S   nUR                  [        SU* -  * [         U[        -   -  -  U-  US[        45      :X  d   e[         S-
  [        -  [        S[         -   5      -  n [        U [         S5      R	                  5       [         S-
  [        -  [        S5      -  [         S-
  [        S-   -  S-  -   [         S-
  [        S-   -  S-  -
  [         S-
  [        S-   -  S	-  -   [         S-
  [        S
-   -  S-  -
  [         S-
  [        S-   -  S-  -   [        [         S-
  [        S-   -  [         S45      -   :X  d   e[         [        S-
  -  [        [         5      -  n [        U [         5      R	                  5       [         [        S-
  -  [         [        -  S-  -
  [         [        S-   -  S-  -   [        [         [        S
-   -  [         5      -   :X  d   e[         [        S-
  -  [        [         5      -  [         [        -  [        [         5      -  -   n [        U [         5      R	                  5       [         [        S-
  -  [         [        S-   -  -   [         [        S-   -  S-  -   [         [        -  -   [         [        S
-   -  S-  -   [         [        S-   -  S-  -   [        [         [        S-   -  [         5      -   :X  d   e[         [        -  [        [         5      -  n [        U [         [        5      R	                  5       [         [        S-
  -  * S-  [         [        S-
  -  S-  -   [         [        -  [        S-  S[         -  -
  -  -   [        S[         -  [        * -  [         S-  -  [         [        45      -   :X  d   e[         [        S-  -  [        [         5      -  n [        U [         5      R	                  5       [         [        S-  -  [         [        S-  S-   -  S-  -
  [         [        S-  S
-   -  S-  -   [        [         [        S-  S-   -  [         5      -   :X  d   e[         [        [         -   -  [        [         5      -  n [        U [         5      R	                  5       [         [         [        -   S-   -  [         [         [        -   S-   -  S-  -
  [         [         [        -   S-   -  S-  -   [        [         [         [        -   S-   -  [         5      -   :X  d   eg )Nr0   rv   rZ   r/   r   r5   r1   r~   r   r2   r   r6   r   r   <   r\   )r8   rG   r   r   re   r   r   ri   rj   rk   r   r
   r   r   r   r   r<   )r,   fpr9   s      r?   test_fps_symbolicr     s   	1SAYAq!9a AAJQUA$=!a!e*a@P$PPPP	1SQZA	QB
A;;raRj[QU#Q&Ar
34 4 4 
Q
3q1u:Aq!Q<  "
a%!CF	a!eq1u-a/	/1q5AE2B22E	EQRSVWRWHXY[H[	[
a%1q5	#	
!"Q!a% 0 5
6891q5AE:JQPQF8S
TU U U 	
AE
3q6Aq!9	
QUad1f	q1q5z"}	,qQUQ/?	?A A A 	
AE
3q6AqDQK'Aq!9	
QUa!a%j	 1q1u:a<	/!Q$	6	
QUB
QUB
')*1q1u:q)9
:; ; ; 	
1T!WAq!R=!!#
a!e*QQUA	%1bdQqSj(9	9	
AaCA2;q!taW	%
&' ' ' 	
AaCQAq!9	AaC1qsQw<>!A!aLO3aAaC!Ga6HHI I I 	
AE
3q6Aq!9	AEAIQUQY))AA	N3,>>1q1uqy>STAUUV V VrA   c                      [         [        [         5      -  [        S[         -  5      -  n [        U [         5      R	                  5       S[         S-  -  S[         S-  -  -   [         S-  S-  -
  [         S-  -
  [        [         S-  5      -   :X  d   eg )Nr0   r1   r2   r6   rZ   )r8   r   r   r   re   r   r>   s    r?   test_fps__slowr     sp    	#a&QqSAq!91QT6AadF?QT!V#;ad#BQq!tW#LLLLrA   c                    ^ [        [        [        5      5      [        [        [        5      5      smn TU -   nUR                  [        [        5      [        [        5      -   :X  d   eUR                  5       S[        -   [        S-  S-  -
  [        S-  S-  -
  [        S-  S-  -   [        S-  S-  -   [        [        S-  5      -   :X  d   eTS-   nUR                  [        [        5      S-   :X  d   eUR                  5       S[        -   [        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eSU -   nUR                  [        [        5      S-   :X  d   eUR                  5       S[        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eT[        -   [        T[        5      :X  d   eU R                  5       * S	[        S-  S-  -   [        S-  S-  -
  [        [        S-  5      -   :X  d   eTT-
  [        R                  L d   eTU -
  nUR                  [        [        5      [        [        5      -
  :X  d   eUR                  5       S	[        -   [        S-  S-  -   [        S-  S-  -
  [        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eTS-
  nUR                  [        [        5      S-
  :X  d   eUR                  5       S	[        -   [        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eSU -
  nUR                  [        [        5      * S-   :X  d   eUR                  5       [        S-  S-  [        S-  S-  -
  [        [        S-  5      -   :X  d   e[        [        U4S
 j5        [        [        U4S j5        TS-  nUR                  S[        [        5      -  :X  d   eUR                  5       S[        -  [        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eSU -  nUR                  S[        [        5      -  :X  d   eUR                  5       SS[        S-  -  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eTU -  [        TU 5      :X  d   eT[        -  [        T[        5      :X  d   eTR                  5       nUR                  [        [        5      :X  d   eUR                  5       S[        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eU R                  5       nUR                  [        [        5      * :X  d   eUR                  5       [        * [        S-  S-  -   [        S-  S-  -
  [        [        S-  5      -   :X  d   eU R                  5       R                  5       nUR                  [        [        5      * :X  d   eUR                  5       S	[        S-  S-  -   [        S-  S-  -
  [        [        S-  5      -   :X  d   e[        [        [        [        5      5      5      nUR                  5       nUR                  5       R!                  5       SS[        [        5      -  -  [        R"                  -   [        S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        S-  S-  -   [        [        5      S-  -   [        [%        SS5      -  S-  -   [        [%        SS5      -  S-  -   [        [%        SS5      -  S-  -   [        [%        SS5      -  S-  -   [        [%        SS5      -  S-  -   [        [        S-  5      -   :X  d   eTR'                  [        SS45      [        S5      * S-   :X  d   e['        T[        SS45      [        S5      * S-   :X  d   e['        T[        5      nUR                  [        [        5      * :X  d   eUR                  5       S	[        S-  S-  -   [        S-  S-  -
  [        [        S-  5      -   :X  d   eU R'                  [        5      nUR                  [        [        5      :X  d   eUR                  5       [        [        S-  S-  -
  [        S-  S-  -   [        [        S-  5      -   :X  d   eg )Nr/   r0   r1   rZ   r2   r   r6   r\   r5   c                  8   > T [        [        [        5      SS9-   $ )Nr5   rU   r   r   r8   f1s   r?   r`   &test_fps__operations.<locals>.<lambda>  s    rCAB$77rA   c                  8   > T [        [        [        5      SS9-   $ )Nr/   x0r   r   s   r?   r`   r     s    rCA1$55rA   rQ   rv   r      i`'  i  i *0   i  r   i ; rP   i n r   i 9r   )r   r   r8   r   rd   re   r   r   r   Zeror(   rn   r   diffr   r   r   r=   r	   r   )f2fsumfsubfmfdf3fir   s          @r?   test_fps__operationsr     sw   Q[#c!f+FB7D==CFSVO+++==?	A1QAa!Q$r')AqDH4qAw>? ? ? 6D==CFQJ&&&==?a!ead1fnq!tCx7!AqD'AAAAr6D==CFQJ&&&==?a!Q$q&j1a472Qq!tW<<<<Fs2qz!!!KKM>R!Q$q&[1a472Qq!tW<<<<G7D==CFSVO+++==?
QAa!Q$q& 1a47*QT#X5!Q$?@ @ @ 6D==CFQJ&&&==?b1fq!tAvo1S81QT7BBBBr6D==SVGaK'''==?ad1fq!tBw.1a48888
:78
:56	aB;;!CF(""";;=AaC!Q$q&L1a472Qq!tW<<<<	
RB;;!CF(""";;=A!Q$qL1a461AadG;;;;GB###Fs2qz!!!	B;;#a&   ;;=A1QJAb01QT7::::	B;;3q6'!!!;;=QBAaK!Q$s(2Qq!tW<<<<		B;;3q6'!!!;;=BAaK!Q$r'1AadG;;;;	Sa\	B	B;;=!	
Ad1gI	!B$	&Ac	1AqDJ	>Af	L	
Ah
a
#%&A%6r%9
:<=x1~<Md<R
S	
HQN	5	 
!#$hq!n#4W#<
=?@(2q/?QR[?[
\ 
1a4
   <<Aq	"s1vgk111R!Q#Aw{222	2q	B;;3q6'!!!;;=BAaK!Q$r'1AadG;;;;	aB;;#a&   ;;=A1QJAc1AadG;;;;rA   c                    ^^ [        [        [        5      5      [        [        [        5      5      [        [	        [        5      5      smp[        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        TR                  U [        5      m[        T[        5      (       d   e[        TR                  [        5      (       d   e[        TR                  [        5      (       d   eTR                  [        [        5      :X  d   eTR                  [        [        5      :X  d   eTR                  [        [        5      [        [        5      -  :X  d   eTR!                  S5      [        [        S-  -   [        S-  S-  -   :X  d   eTR#                  S5      [        [        S-  -   [        S-  S-  -   [%        [        S-  5      -   :X  d   eTR'                  S5      [        [        S-  -   [        S-  S-  -   :X  d   e[        [(        U4S j5        [        [(        U4S	 j5        [        [(        U4S
 j5        [        [(        U4S j5        TR                  U[        5      R!                  S5      [        S[        S-  -  S-  -
  :X  d   eTR                  U[        5      R#                  S5      [        S[        S-  -  S-  -
  [%        [        S-  5      -   :X  d   eg )Nc                  J   > T R                  [        [        5      [        5      $ r^   )productr   r8   r   s   r?   r`   #test_fps__product.<locals>.<lambda>      rzz#a&!4rA   c                  \   > T R                  [        [        [        5      SS9[        S5      $ Nr5   rU   r2   r   r   r   r8   r   s   r?   r`   r         rzz#c!f"*=q!DrA   c                  \   > T R                  [        [        [        5      SS9[        S5      $ Nr/   r   r2   r   r   s   r?   r`   r         rzz#c!f*;QBrA   c                  ^   > T R                  [        [        [        5      5      [        S5      $ Nr2   )r   r   r   r;   r8   r   s   r?   r`   r         rzz#c!f+q!<rA   r2   r0   r1   c                  &   > T R                  S5      $ Nr6   
_eval_termfprods   r?   r`   r   !      (8(8(;rA   c                     > T R                   $ r^   rk   r   s   r?   r`   r   "  	    rA   c                  .   > T R                  [        5      $ r^   _eval_derivativer8   r   s   r?   r`   r   #      (>(>q(ArA   c                  .   > T R                  [        5      $ r^   r   r8   r   s   r?   r`   r   $      (:rA   )r   r   r8   r   r   r(   rn   r   rc   r!   ffpsr    gfpsr,   grd   _eval_termsre   r   rf   rm   )r   r   r   r   s     @@r?   test_fps__productr     s,   SVc#a&k3s1v;JB
:45
:DE
:BC
:<=JJr1Ee56666ejj"34444ejj"3444477c!f77c!f>>SVc!f_,,,Q1q!t8ad1f#4444>>!AqD1a46 1AadG ;;;;A!ad(QT!V"3333
 ;<
 67
 AB
 :;::b!((+q1QT6!8|;;;::b!%%a(A!Q$qL1QT7,BBBBrA   c                  `
  ^ ^^^ [        [        [        5      5      [        [        [        5      5      [        [	        [        5      5      sm mm[        [        U 4S j5        [        [        U 4S j5        [        [        U 4S j5        [        [        U 4S j5        [        [        U U4S j5        [        [        UU4S j5        T R                  T[        5      m[        T[        5      (       d   e[        TR                  [        5      (       d   e[        TR                  [        5      (       d   eTR                  [        [        5      :X  d   eTR                  [        [        5      :X  d   eTR                  [        [        [        5      5      :X  d   eTR!                  S5      S[        -   [        S	-  S	-  -   [        S
-  S-  -
  [        S-  S-  -
  :X  d   eTR#                  5       S[        -   [        S	-  S	-  -   [        S
-  S-  -
  [        S-  S-  -
  [%        [        S-  5      -   :X  d   eTR#                  S5      S[        -   [        S	-  S	-  -   [        S
-  S-  -
  [%        [        S-  5      -   :X  d   e[        [&        U4S j5        [        [&        U4S j5        [        [&        U4S j5        [        [&        U4S j5        T R                  T[        5      R#                  S
5      S[        -   [        S	-  S	-  -   [%        [        S
-  5      -   :X  d   eT R                  T[        5      R#                  S5      S[        -   [        S	-  S	-  -   [        S
-  S-  -
  [        S-  S-  -
  [        S-  S-  -
  [        S-  S-  -   [%        [        S-  5      -   :X  d   eT R                  T[        5      R#                  S5      S[        -   [        S	-  S	-  -   [        S
-  S-  -
  [        S-  S-  -
  [%        [        S-  5      -   :X  d   eTR                  T[        5      R#                  S
5      [        [        S-  S-  -
  [%        [        S
-  5      -   :X  d   eTR                  T[        5      R#                  S5      [        [        S-  S-  -
  [        S-  S-  -   S[        S-  -  S-  -
  [%        [        S-  5      -   :X  d   eTR                  T[        5      R#                  S5      [        [        S-  S-  -
  [        S-  S-  -   [%        [        S-  5      -   :X  d   eg )Nc                  J   > T R                  [        [        5      [        5      $ r^   )composer   r8   r   s   r?   r`   #test_fps__compose.<locals>.<lambda>-  r   rA   c                  \   > T R                  [        [        [        5      SS9[        S5      $ r   r   r   r   r8   r   s   r?   r`   r   .  r   rA   c                  \   > T R                  [        [        [        5      SS9[        S5      $ r   r   r   s   r?   r`   r   /  r   rA   c                  ^   > T R                  [        [        [        5      5      [        S5      $ r   )r   r   r   r;   r8   r   s   r?   r`   r   0  r   rA   c                  0   > T R                  T[        5      $ r^   r   r8   )r   r   s   r?   r`   r   2      rzz"a0rA   c                  0   > T R                  T[        5      $ r^   r   )r   r   s   r?   r`   r   3  r   rA   rZ   r/   r0   r2   rv   r6   r   c                  &   > T R                  S5      $ r   r   fcomps   r?   r`   r   @  r   rA   c                     > T R                   $ r^   r   r   s   r?   r`   r   A  r   rA   c                  .   > T R                  [        5      $ r^   r   r   s   r?   r`   r   B  r   rA   c                  .   > T R                  [        5      $ r^   r   r   s   r?   r`   r   C  r   rA   r   r   r   r1   r7   i;  )r   r   r8   r   r   r(   rn   r   rc   r"   r   r    r   r,   r   rd   r   re   r   rm   )r   r   r   r   s   @@@@r?   test_fps__composer   *  s   SVc#a&k3s1v;JBB
:45
:DE
:BC
:<=
:01
:01JJr1Ee56666ejj"34444ejj"3444477c!f77c!f>>SQ[(((Q1q51a46>AqDF#:QT"W#DDDD>>q1uq!tAv~1Q6Ab@1QT7JJJJ>>!A1QAa 7!AqD' AAAA
 ;<
 67
 AB
 :;::b!%%a(AEAqDFNQq!tW,DDDD::b!%%a(	A1QAa!Q$r')AqDH4q!tBw>1a4HI I I::b!%%a(	A1QAa!Q$r')AadG34 4 4 ::b!%%a(A1QJ1a4,@@@@::b!%%a(A1QJAb,@1QT6#:,MPQRSUVRVPW,WWWW::b!%%a(A1QJAb,@1QT7,JJJJrA   c                  t  ^^ [        [        [        5      5      [        [        [        5      5      [        [	        [        5      5      smp[        [        U4S j5        U R                  [        5      m[        T[        5      (       d   e[        TR                  [        5      (       d   e[        [        U4S j5        TR                  [        [        5      :X  d   eTR                  [        [        * 5      :X  d   eTR                  S5      S[        -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S	-  -   :X  d   eTR                  5       S[        -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S	-  -   [        S-  S
-  -
  [!        [        S-  5      -   :X  d   eTR                  S5      S[        -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S	-  -   [!        [        S-  5      -   :X  d   e[        ["        U4S j5        [        [        U4S j5        [        ["        U4S j5        [        ["        U4S j5        [        ["        U4S j5        U R                  [        5      R                  S5      S[        -
  [        S-  S-  -   [        S-  S-  -
  [        S-  S	-  -   [        S-  S
-  -
  [        S-  S-  -   [        S-  S-  -
  [!        [        S-  5      -   :X  d   eUR                  [        5      R                  5       S[        S-  S-  -   S[        S-  -  S	-  -   [!        [        S-  5      -   :X  d   eUR                  [        5      R                  S5      S[        S-  S-  -   S[        S-  -  S	-  -   S[        S-  -  S-  -   [!        [        S-  5      -   :X  d   eg )Nc                  .   > T R                  [        5      $ r^   )inverser8   r   s   r?   r`   #test_fps__inverse.<locals>.<lambda>S  s    rzz!}rA   c                     > T R                   $ r^   )r   finvs   r?   r`   r   X  s	    tyyrA   r6   r/   r0   r1   rZ   r2   r   r\   c                  &   > T R                  S5      $ r   r   r   s   r?   r`   r   `  s    (:rA   c                     > T R                   $ r^   )r   r   s   r?   r`   r   a  s	    tvvrA   c                     > T R                   $ r^   r   r   s   r?   r`   r   b  s	    rA   c                  .   > T R                  [        5      $ r^   r   r   s   r?   r`   r   c  s    (=(=a(@rA   c                  .   > T R                  [        5      $ r^   r   r   s   r?   r`   r   d  s    q(9rA   rv   r   r   r   =   )r   r   r8   r   r   r(   rn   r   rc   r#   r   r    r,   rd   r   re   r   rm   )r   r   r   r   s     @@r?   test_fps__inverser  P  s   SVc#a&k3s1v;JB
:,-::a=Dd45555dii!23333
:()66SV==CG###A!a%!Q$q&.1a46"9AqDG"CCCC==?a!ead1fnq!tAv51R?!Q$s(JQqRStWTTTT==q1uq!tAv~1Q6Ab@1QT7JJJJ
 :;
:~&
 56
 @A
 9:::a=!!!$	A1QAa!Q$r')AqDH4q!tCx?!Q$t)KaPQSTPTgUV V V ::a=!!#q1a46zAadF2I'=!Q$'GGGG::a=!!!$AqDF
Qq!tVBY(>AqD(LqQRTUQUw(VVVVrA   N)Wsympy.concrete.summationsr   sympy.core.addr   sympy.core.functionr   r   sympy.core.mulr   sympy.core.numbersr   r	   r
   r   sympy.core.singletonr   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr   &sympy.functions.elementary.exponentialr   r   %sympy.functions.elementary.hyperbolicr   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   r   r   r   r   sympy.functions.special.besselr   'sympy.functions.special.error_functionsr   'sympy.functions.special.gamma_functionsr   sympy.integrals.integralsr   sympy.series.formalr   sympy.series.orderr   r   r    r!   r"   r#   r$   r%   r&   r'   sympy.testing.pytestr(   r)   r*   r8   r;   r:   rG   r<   r9   r,   r-   r@   rE   rI   rM   rR   rs   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r_   rA   r?   <module>r     s6   )  6  4 4 " % > = @ 9 Q Q 1 7 9 / #  I I I 5 4
'
1a
'4
(1a}hsm1/4d>49"(4&.R 0Q 0Qf ,F ,F^5$E)0.>B G G
#VLM
O<bC8#KLWrA   