
    \hJ                        S SK Jr  S SKJrJrJr  S SKJr  S SKJ	r	J
r
  S SKJr  S SKJr  S SKJrJrJr  S SKJr  S S	KJrJr  S S
KJrJr  S SKJrJr  S SKJr  S SK J!r!  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,J-r-J.r.J/r/  S SK0J1r1  S SK2J3r3J4r4J5r5J6r6J7r7J8r8J9r9  S r:S r;S r<S r=S r>S r?S r@S rAS rBS rCS rDS rES  rFS! rGS" rHS# rIS$ rJS% rKS& rLS' rMS( rNS) rOS* rPS+ rQS, rRS- rSg.)/    )Add)
DerivativeFunctiondiff)Mul)IRational)Pow)S)SymbolWildsymbols)Abs)explog)rootsqrt)cossin)factor)O)collectcollect_constfractionradsimprcollect)	unchanged)_unevaluated_Mul)_unevaluated_Addcollect_sqrtfraction_expandcollect_abs)raises)xyzabcdc            
      ,   [        S5      n [        S5      n[        S5      n[        S5      n[        [        SU -  5      5      [        S5      S4:X  d   e[        SSU -   -  5      S[        S5      -   :X  d   e[        SX-   -  5      [        S5      * [        S5      -   :X  d   e[        [        SSU -   U-   -  5      5      [        S5      * [        S5      -   S-   S4:X  d   e[        [        SX-   U-   -  5      5      [        S	5      * S[        S5      -  -   S[        S5      -  -   S
4:X  d   e[        [        SSU -   U-   U-   -  5      5      S[        S5      -  S[        S5      -  -
  S[        S5      -  -
  S[        S5      -  -
  S[        S	5      -  -   S-   S[        S5      -  -   S[        S5      -  -   S4:X  d   e[        [        SX-   U-   U-   -  5      5      S[        S5      -  S[        S5      -  -
  S[        S5      -  -
  S[        S5      -  -
  S[        S5      -  -   S[        S5      -  -   S[        S	5      -  -   S [        S5      -  -   S!4:X  d   e[        SSU S-  -   US-  -   U-   U-   -  5      n[        S"U-  R                  5      S#:X  d   e[        SU-  5      SU-  :X  d   e[        SU-  S$S%9R                  5       SU S-  -   US-  -   U-   U-   :X  d   e[        SU S-  -  5      [        S5      S-  :X  d   e[        SU [        -  U-   U-   U-   -  5      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&[        S5      -  [        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-[        S5      -  [        S-  -  -
  S&[        S	5      -  [        S-  -  -
  S.[        S5      -  [        S-  -  -   S/[        S5      -  [        S-  -  -
  S0[        S5      -  [        S-  -  -
  S1[        S5      -  [        S-  -  -
  S2[        S5      -  [        S-  -  -   S3[        S5      -  [        -  -
  S[        S	5      -  [        -  -
  S4[        S5      -  [        -  -   S5[        S5      -  [        -  -   S6[        S5      -  -
  S7[        S5      -  -   S8[        S5      -  -   S9[        S5      -  -   S#[        S&-  -  S:[        S-  -  -
  S;[        S-  -  -   S<[        S-  -  -
  S=-   -  :X  d   e[        SU [        -  U [        -  -   U-   U-   -  5      [        S5      [        -  [        [        -   S-  -  S[        S5      -  [        -  -
  [        S5      [        -  -   [        S5      [        -  [        [        -   S-  -  -   S[        S5      -  [        -  -
  [        S5      [        -  -   [        S5      [        [        -   S-  -  -
  [        S5      [        [        -   S-  -  -
  S[        S5      -  -
  S[        S5      -  -   S[        S-  -  S&[        S-  -  [        -  -   S
[        S-  -  [        S-  -  -   S$[        S-  -  -
  S&[        -  [        S-  -  -   S-[        -  [        -  -
  S[        S-  -  -   S$[        S-  -  -
  S&-   -  :X  d   e[        SU [        -  U [        -  -   U [        -  -   U [        -  -   -  5      [        S5      S[        -  S[        -  -   S[        -  -   S[        -  -   -  :X  d   e[        SSU [        -  -   U [        -  -   U [        -  -   U [        -  -   -  5      [        S5      [        -  [        S5      [        -  -   [        S5      [        -  -   [        S5      [        -  -   S-
  S[        S-  -  S[        -  [        -  -   S[        -  [        -  -   S[        -  [        -  -   S[        S-  -  -   S[        -  [        -  -   S[        -  [        -  -   S[        S-  -  -   S[        -  [        -  -   S[        S-  -  -   S-
  -  :X  d   e[        [        S-  [        -
  [        [        [        5      -
  -  5      [        [        5      [        -   :X  d   e[        [        S-  [        -
  * [        [        [        5      -
  -  5      [        [        5      [        -   * :X  d   e[        SS[        -
  [        [        -  -   -  5      [        * [        -  S-   [        -   [        S-  S[        -  -
  S-   -  :X  d   e[        S[        * [        -   [        [        [        5      -
  -  -  5      [        * [        [        5      -
  [        [        -
  [        S-  [        -
  -  -  :X  d   eSS[        S5      -  -   [        -  S[        -  S[        [        5      -  -
  -  n[        U5      [        SS[        S5      -  -   -  S[        -  S[        [        5      -  -
  -  :X  d   e[        SU-  5      S>[        -  S?[        S5      -  [        -  -   S?[        [        5      -  -
  S?[        S5      -  [        [        5      -  -   S?[        -  S?[        S-  -  S?[        -  -
  -  -  :X  d   e[        SSS[        S5      -   -  -   5      [        [        R                  S[        S5      -   S@SA9S-   :X  d   e[!        SBS@SC9n[        [        S-  [        S5      [        S-  -  -   [        S5      [        -  U-  -
  5      [        S-  [        S5      [        S-  -  -   [        S5      [        -  U-  -
  :X  d   e[        S[        SS[        S5      -  -   5      -  5      [        S5      * [        S5      -   :X  d   e[        S[        SS[        S5      -  -   5      S-  -  5      [        S5      * [        S5      -   S-  * :X  d   e[        [        S[        [        5      -  5      5      [        [        5      [        4:X  d   e[        [        S[        S[        -  S-   5      -  5      5      [        S[        -  S-   5      S[        -  S-   4:X  d   e[        [        S[        S[        S-   -  5      -  5      5      [        S[        -  S-   5      S[        -  S-   4:X  d   e[        SD5      n[        U5      R                  5       SES[#        SS5      -  -  SS[#        SS5      -  -  -
  S-   S[        S5      -  -   :X  d   e[        S[        S5      * S-  [        R                  -
  [        S5      * S-  [        R                  -
  S-  -   -  5      S:X  d   eSF[        S5      -  [        [        S5      S-   5      -  [        S&[        S5      -  S--   5      -  SG[        S5      -  [        SH[        S5      -  S--   5      -  [        [        S5      * S-   5      -  -
  S2[        S5      -  [        SH[        S5      -  S--   5      -  [        [        S5      * S-   5      -  -
  S2[        S5      -  [        [        S5      * S-   5      -  [        S&[        S5      -  S--   5      -  -   S2[        S5      -  [        SH[        S5      -  S--   5      -  [        [        S5      S-   5      -  -   S2[        S5      -  [        [        S5      * S-   5      -  [        S&[        S5      -  S--   5      -  -   S2[        S5      -  [        SH[        S5      -  S--   5      -  [        [        S5      S-   5      -  -   SISJ[        S5      -  -
  S
[        S5      -  [        [        S5      S-   5      -  S([        S5      -  [        [        S5      * S-   5      -  -   S-  -   -  n[        U5      [        R$                  L d   eS[        [        S5      S-  S[        S5      -  -   S[        S5      -  -   S[        S5      -  -   5      -  S-   n[        U5      [        [        S5      S[        S5      -  -   SK[        S5      -  -   SL[        S5      -  -   5      * SM[        SL5      -  SN[        SO5      -  -
  SP[        S5      -  -
  SQ[        S5      -  -
  SR[        S5      -  -   SS-   ST[        S5      -  -   SU[        SK5      -  -   -  SV-  S-   :X  d   e[        S5      [        S5      -
  n[        SUS-  -  5      [        S5      [        S5      -   S-  :X  d   e[        SU* S-  -  5      [        S5      [        S5      -   S-  * :X  d   e[        SU* [        -  -  5      U* [        * -  :X  d   e[        SU[        -  -  5      [        S5      [        S5      -   [        -  :X  d   e[        ['        SS[        S5      -
  -  [        * 5      5      SS[        -  -  S[        S5      -   S[        -  -  -  :X  d   e[)        SS[        S5      -   -  5      n[        U5      [)        [        S5      * S-   5      :X  d   e[        US-  5      [)        [        S5      * S-   5      S-  :X  d   e[        SU-  5      S[)        [        S5      * S-   5      -  :X  d   e[        SU-  5      S[)        [        S5      * S-   5      -  :X  d   e[        [        U[        [        5      -  5      5      [        [        5      [)        [        S5      * S-   5      -  [        4:X  d   eS[        S5      -   n	[        [        U	-  S@SW9[        * [        S5      * S-   -  :X  d   e[        [        [        U	-   -  S@SW9[        [        S-   [        S5      -   -  :X  d   e[        [        [        U	-   -  U	-  S@SW9[        * [        S5      * S-   -  [        S-   [        S5      -   -  :X  d   e[        [        5      [        [        5      -  n[        U5      [+        [        [        5      [        [        5      S[        -  5      :X  d   e[        US@SW9U:X  d   e[        [        [        5      [        [        5      S-  -  5      [+        [        [        5      [        [        S-  5      S[        S-  -  5      :X  d   e[        [        5      [        S-  -  n[        U5      U:X  d   eSXSYKJn
  U
" [        [        S5      S-
  -  [        SXS[        S5      S-   -  45      n[        U5      U
" [        S5      S-   [        -  [        SX[        S5      S-
  45      :X  d   eSXSZKJn  U" [        [        S5      S-
  -  5      n[        U5      U" [        S5      S-   [        -  5      :X  d   eg )[N                           i
         7   =      ]   .   5   G   i*      "   F         i      >         l   N>A      )	max_terms         T   d   t   H   (   i  i  i.     x   i  R   b   v   ;   i'  i  i  i8  i  i  i	   FevaluateAcommutativezE-(2 + 2*sqrt(2) + 4*2**(1/4))/(1 + 2**(3/4) + 3*2**(1/4) + 3*sqrt(2))iih  ii`si      #   i)Ni    i i i iW ivs iW~ iM)symbolicr   )Integral)	FiniteSet)r   r   r   lenargsexpandr'   r(   r)   r*   r%   r$   r   r   r   Halfr   r	   NaNr   r   umulsympy.integrals.integralsrg   
sympy.setsrh   )r2r3r5r7r&   er_   eqbaserrg   rh   s               Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/simplify/tests/test_radsimp.pytest_radsimprz      sN   	aB	aB	aB	aBGAbDM"tAwl2221a"f:
T!W  1bg;	a47  GAq2v{O,-
q'DG	a	#$ $ $GArw|,-.
r(QtAwY	47	*B/0 0 0GAq2v{R/012	T"X48	#baj	02d1g:	=48	K

QZ
T!W*
%&(	*+ + + GArw|b0123	T"XDG	#bbk	1CQK	?"T#Y,	N
d1g+
48
$&)$q'k
236	89 9 9 	1r!t8bd?R'",-.A&q(../25551Q3<1Q31Q3"%,,.!bd(RT/B2F2KKKK1bd8Q	  1bdRi"nr)*+	
471a4!DG)AqD.	(1T!W9QT>	9Ad1gIadN	JDGAqD
T"X:ad?
+-.tBxZ1_
=?@bz!Q$
O
T#Y,q!t

 ajAo
.03DGAqD0@
A 	DGAqD
 d2h;q!t+
, /1bk!Q$.>
? 	
$r(
1a4	
 d1g+ad*	
+ .1a[A-=	
>
 	DGAqD

 tAw;q!t+
,
 /2$s)mAqD.@
A 	DGA
 48A
& )+48A
6 9;48A
F 	DI
 47

# &)a[
1 47tAw;
? BDAqDAqDB19B#AqDyB)+/B0	1	2 	2 	2 1bdRTkB&+,-	aAEA:	$q'	!	+d2hqj	84719a	G
F < 
$q'	!
"2hqj
)+/7AEA:+=
>@DQ	J
I A
$q'	
d1gI
&()!Q$1a4(9Bq!tGAqDL(H
1a4)A#ad()T!V)$&'1f)-/1!Q$w)79:);	<= = =
 1bdRTkBqD(2a4/01Q1qsQqS1Q3&'( ( (1a"Q$hAo1,r!t345	aT!WQY	a	*T!WQY	6	:Qq!tVac!e^	!A>!A>!Q$>!"1Q>')*1Q>/121a4>8:;A#a%>@BCAqD&>IKL>M 	NO O O AqD1Hq47{+,Q!  QTAX;DG,-
q'A+  1a!eack?#
AA1qs
Q'( ( (1rAvDG,-.
d1gQA*+, , ,	
QtAwY1Q347?+A1:A$q'	M*AaC!DG)O<<<<1Q3<	A$q'	!	aQi	'!DG)DG*;	;ac1QT6	!D ? 	   1q!d1g+&'AFFBaL51A56 6 6'A1a4$q'!Q$,&a145	1tAwq!t|d1gaik)* * *1T!a$q'k/**+Qx$q'/AAAA1T!a$q'k/*A--.T!WHtAw4F3J2JJJJ GAd1gI&'DGQ<777GAd1Q37mO,-$qsQw-1q1IIIIGAd1a!e9o-./D1qM1Q373KKKK 	
 2 	3A1:"QA%6"61hq!n;L9L"Lq"PSTUYZ[U\S\"\\\\ 1tAwhqj166)d1gXaZ!&&-@1,DDEF!KKK 
d1gd47Q;'	'QtAwY^(<	<DGDDGb))$Qx!|*<<
=DHT"T!W*r/**4a1+==
> 	DGD$q'A&&tAd1gIN';;
< 	DGDDGb))$tAw{*;;	
<
 	DHT47(Q,''QtAwY^(<<
= 	DHT"T!W*r/**4Q!+<<
= @FT!W@48Da1$55
48D$q'A&&')*+@+	,  2;!%% 	
$tAwqy1T!W9$qay01T!W9<
==AA1:	d1g47
"RQZ/
47
 
 	tBx''$s)*;;gd2h>NN
$r(
$T!W_-/679@b9IJR	 %	% ()	)* * * 7T!WD1T1W9$q'DG"3a!77771teaZ< d1gQ&7!%;$;;;;1teaZ< dUqbM1111T1W9$q'DG"3a!777742Q<(1"-.2A,DGqQRs?S2SSSS 	Aq47{OA1:d1gX\****1Q3<3Qx!|,Q....1Q3<1S$q'A.....1Q3<1S$q'A.....GAd1gI&'DGCa
O,CQ+GGGG 	
DGA1Q3'A2Qx!|+<<<<1a!e9u-AEDGO1DDDD1a!e9Q;/	
T!WHqL1q547?+, , , 
aaB2;$tAwQ155552&",,, 4747A:%&$tAwQT
AadF*KKKK 
aAB2;" 3	!T!Wq[/Aq!T!Wq[/#:	;B2;(DGaK?aDGaK5HIIII$	1d1gk?	#B2;)T!Wq[!O4444    c                  
   [        SSS9u  p[        U S-  US-  -
  5      nU [        U-  -   U-
  U [        U-  -   U-   -  n[        U5      [        * U [        U-  -   [        U S-  US-  -
  5      -
  S-  -  SU -  U-  -  :X  d   eg )Nzc pTpositiver,   )r   r   r   r   )r)   psr(   s       ry   test_radsimp_issue_3214r      s    54(DAQTAqD[A	
QqS1q1Q3w{#A1:!Q1WtAqD1a4K'881<<ac!eDDDDr{   c                     [        S5      u  pp#[        SU 5      S:X  d   e[        XU -  -   U 5      U SU-   -  :X  d   e[        X S-  -   U 5      X S-  -   :X  d   e[        U S-  XS-  -  -   U 5      U S-  SU-   -  :X  d   e[        U S-  X-  -   U 5      X-  U S-  -   :X  d   e[        SU S-  -  XS-  -  -   SU -  U-  -   U /5      U S-  SU-   -  SU -  U-  -   :X  d   e[        SU S-  -  XS-  -  -   SU -  U-  -   U/5      SU S-  -  XS-  SU -  -   -  -   :X  d   e[        SU-   U -   S-  R                  5       U 5      SU-   S-  R                  5       U SSU-   S-  -  R                  5       -  -   U S-  SSU-   S-  -  R                  5       -  -   U S-  SSU-   -  R                  5       -  -   U S-  -   :X  d   eX-   n[        XDR                  5      U:X  d   e[        U [	        U 5      -  [        U 5      U-  -   [        U 5      S-  -   SU -  -   U SS9U [	        U 5      -  SU -  -   US-   [        U 5      -  -   :X  d   e[        U [	        U 5      -  [        U 5      U-  -   [        U 5      S-  -   SU -  -   X-  -   X-  [	        U 5      -  -   U SS9U [	        U 5      -  US-   -  SU-   U -  -   US-   [        U 5      -  -   :X  d   eg)	zCollect with respect to Symbolx,y,z,nr0   r,   r-   r3   r2   Nexact)r   r   rk   free_symbolsr   r   )r$   r%   r&   nexprs        ry   test_collect_1r      s:   #JA!1a=AA!GQ AQK///A1Ha!QAX---AqD1T6M1&1a4!a%.888AqD13J#qsQTz111AadFQ!tVOac!e+aS2adAElQqSU6JJJJAadFQ!tVOac!e+aS2a1fqQ$1*~6MMMMa!eai!^++-q1q1uqj5H5H5J	1a!eaZ<


!!6"$%qD!QUQJ,)>)>)@$@6A	1aQi!!6"$%qD6) ) ) ) 5D4**+t3331SV8c!fQh&Q1AaC7$ 
s1vX!^q1uc!fn,- - -1SV8c!fQh&Q1AaC7!#=	CF
T
s1vXq1uQ	)QUCFN:; ; ;r{   c                     [        S5      u  pn[        U [        U5      [        U5      -   -  U[        U5      [        U5      -   -  -   [        U5      [        U5      -   5      X-   [        U5      [        U5      -   -  :X  d   eg)zCollect with respect to a sumza,b,xN)r   r   r   r   )r'   r(   r$   s      ry   test_collect_2r      su    gGA!1c!fs1vo&CFSVO)<<AQUSVc!f_56 6 6r{   c                     [        S5      u  pn[        S5      n[        S5      u  pEpg[        U* S-  XE-  -   U* 5      XE[        SS5      -
  -  :X  d   e[        SXES-  -  -   XE-  5      SXES-  -  -   :X  d   e[        XE-  X-  U-  -   XE-  5      XE-  SU -   -  :X  d   e[        SXE-  -   X-  U-  -   XE-  5      SXE-  SU -   -  -   :X  d   e[        X-  U" U5      -  XU" U5      -  -  -   XC" U5      -  5      X@U-   -  U" U5      -  :X  d   e[        X-  [	        U5      -  X[	        U5      -  -  -   U[	        U5      -  5      X@U-   -  [	        U5      -  :X  d   e[        XS-  -  [	        U5      S-  -  X[	        U5      -  S-  -  -   U[	        U5      -  5      US-  [	        U5      S-  -  X-   -  :X  d   e[        XT-  U-  X-  U-  U-  -   XE-  U-  5      SU -   U-  U-  U-  :X  d   eg)z!Collect with respect to a productza,b,cfr   rN   r0   r,   N)r   r   r   r	   r   )r'   r(   r)   r   r$   r%   r&   r   s           ry   test_collect_3r      s   gGA!A#JA!A2a4!#:r"aXa^);&<<<<Aa4L!#'1qQ$x<777AC!#a%K%a!e444AGac!eOQS)Qa!e_<<<13qt8a1Q4j(!AaD&1QAYqt^CCC13s1v:SV8,aAh71!e9SV;KKKK1T6#a&!)#a3q6Ao5qQx@	1SVQY   13q513q57?ACE*q1uaik!m;;;r{   c                      [        S5      u  pp#[        XU-  -  XU-  -  -   X2-  5      X2-  X-   -  :X  d   e[        XSU-  -  -  XSU-  -  -  -   X2-  5      USU-  -  X-   -  :X  d   eg)zCollect with respect to a powerza,b,c,xr,   Nr   r   )r'   r(   r)   r$   s       ry   test_collect_4r      s~    #JA!1T6AdF?AD)QT15\99911X:ac(
*AD1Q1Xqu5EEEEr{   c                     [        S5      u  pp#n[        US-  US-  -  X1US-  -  S-  -  -   U-   X-  -   XS-  -  U/5      USU -   US-  US-  -  -   -  US-  US-  -  -   USU -   -  US-  US-  -  SU-   -  -   4;   d   e[        SX-   -   X-   S-  -   R                  5       X/5      SU-   USSU-  -   -  -   US-  -   US-  -   :X  d   eg)zCollect with respect to a tuplez	a,x,y,z,nr,   r3   r0   N)r   r   rk   )r'   r$   r%   r&   r   s        ry   test_collect_5r      s    K(MA!1a419qAqD&1},q0136a4D	1q51a4191QT	)	1q5	AqDAIq1u%%I( ( ( ( AK151*,4466!eaQqSk1AqD81a4?@ @ @r{   c                  r    [        S5      n [        U S-  U S-  S-   -  U S-  SS9U S-     U S-  S-   :X  d   eg)z-Unevaluated collect with respect to a productr'   r,   r0   Fr]   Nr   )r'   s    ry   test_collect_pr19431r      sG    A1a4A?AqD59!Q$?AqD1HMMMr{   c            	         [         n [        S5      n[        S5      u  p#nU " U" U5      U5      nU " U" U5      X"5      n[        X5-  XE-  -   U5      X4-   U-  :X  d   e[        X0" XR5      -  X@" XR5      -  -   U5      X4-   U " XR5      -  :X  d   e[        X6-  XF-  -   U5      X4-   U " XR5      -  :X  d   e[        SU" U5      -  SU-  -   U5      SU" U5      -  SU-  -   :X  d   e[        U" U5      U" U5      [	        U" U5      U5      -  -   U[	        U" U5      U5      -  U" U5      -  -   U" U5      R	                  U5      5      X!" U5      -  U" U5      -   U " U" U5      U5      -  U" U5      -   :X  d   e[        U" U5      U" U5      [	        U" U5      U5      -  -   U[	        U" U5      U5      -  U" U5      -  -   U" U5      R	                  U5      SS9X!" U5      -  U" U5      -   U " U" U5      U5      -  U" U5      -   :X  d   e[        SU" U5      -  SU" U5      -  [	        U" U5      U5      -  -   U[	        U" U5      U5      -  U" U5      -  -   U" U5      R	                  U5      SS9SU" U5      -  X!" U5      -  -   U " U" U5      U5      -  SU" U5      -  -   :X  d   eSX%-  -   U-   U" U5      -  n[        UR                  5       U5      XRU" U5      -  SU" U5      -  -   -  SU" U5      -  -   :X  d   eg )Nr   x,a,br.   r-   Tr   r0   )r   r   r   r   r   rk   )Dr   r$   r'   r(   fxfxxru   s           ry   test_collect_Dr      s   AAgGA!	
1Q4B
AaD!-C14!$;#rz1111QrX:!B(
*B/AE1R83CCCC1515="%!%2)99991QqT6AbD="%1Q4!B$6661Q4!A$tAaD!},,qadAqt/CCQqTYYq\R	
1Q4!A$!A$
"QqT)* * *1Q4!A$tAaD!},,qadAqt/CCQqTYYq\Y]^	
1Q4!A$!A$
"QqT)* * *1QqT6AadF4!a=001T!A$]?1Q43GG1ST]ab	
1Q4!AaD&!AaD!*$q1v-. . .	
QTB!A188:r"bAaD&1QqT6/&:QqtV&CCCCr{   c                     [         [        -   S-   S-  R                  5       n [        U [         5      [        S-  S[        S-  -  -   S[        -  -   [         S-  -   [         S-  S[        -  S-   -  -   [         S[        S-  -  S[        -  -   S-   -  -   S-   :X  d   e[        U [         [        5      [         S-  S[         S-  -  [        S-   -  -   S[         -  [        S-   S-  -  -   [        S-   S-  -   :X  d   e[        U [         SS9[
        R                  [        S-  S[        S-  -  -   S[        -  -   S-   [         S[        S-  -  S[        -  -   S-   [         S-  S[        -  S-   [         S-  S0:X  d   e[        U [         [        SS9[
        R                  [        S-   S-  [         S[        S-   S-  -  [         S-  [        [        S5      [        S-   5      [         S-  S0:X  d   eg )Nr0   r-   r,   r2   Fr]   )r$   r'   rk   r   r   r   Onern   )r   s    ry   test_collect_funcr     s   
a%!)a!A1a=AqD1QT6MAaC/!Q$6AqsQwG	1QT6AaC<! ! ! ! !1a AqD1QT61q5>$9AaCQ
N$J	
Q
%    1a%(	q!ta1f}qs"Q&	1QT6AaC<!QT1Q37	1a-    1a%0	Az1aQ
l	1d1Q4QAq5* * * *r{   c                     [        S5      u  pp#[        X3U-  -   X2S-  -  -   [        US-  5      -   U5      USU-   US-  -   [        US-  5      -   -  :X  d   e[        X3U-  -   US-  -   [        US-  5      -   U5      USU-   [        US-  5      -   -  US-  -   [        US-  5      -   :X  d   eX-  X-  -   [        US-  -  -   [        US-  -  -   [        US-  5      -   nX U-   -  US-  [        [        -   -  -   [        US-  5      -   n[        XB5      U:X  d   e[        XBSS9U:X  d   e[        X-   5      R                  USS5      n[        U[        U 5      [        U 5      /5      [        U 5      [        U5      R                  USS5      -  [        U 5      [        U5      R                  USS5      -  -   :X  d   e[        U[        U 5      [        U 5      /SS9[        U 5      [        U5      R                  USS5      R                  5       -  [        U 5      [        U5      R                  USS5      R                  5       -  -   [        US-  5      -   :X  d   eg )	Nza,b,x,tr,   r-   r0   F)distribute_order_termr   r6   )	r   r   r   r)   r*   r   seriesr   removeO)r'   r(   r$   tr   gs         ry   test_collect_orderr   (  sQ   #JA!1s7Q!tV#a1g-q1QA1qAw8N5OOOO1s7QT>AadG+Q/	1q51QT7?ad"Qq!tW,- - - 	
ac	AadFQq!tV#a1g-A	q5	AqD!a%L 1QT7*A1=A1u5:::AE
!Q#A1s1vs1v&'As1v}}Q2&&QAaB0G)GGH H H1s1vs1v&eDAs1v}}Q2&..00As1v}}Q2&..00	134QU8	<< < <r{   c                     [        [        S-  [        -  [        [        -  -   [        -   [        -   [        [        -   -  [        5      [        [        S[        -   [        S-  -   -  -   [        [        -   -  :X  d   e[        [        [        S-   [        S-   -  * 5      [        5      [        [        S-   [        S-   -  * 5      :X  d   eg )Nr,   r0   )r   r$   r%   r   r&    r{   ry   test_rcollectr   >  s    QT!Vac\A%)AE2A6	
QA1	A&' ' 'DAEAE?+,a0DAEAE?9K4LLLLr{   c                      [         n [        S5      n[        S5      u  p#nU " U" U5      X"5      n[        X5-  XE-  -   U5      X4-   U-  :X  d   eg )Nr   r   )r   r   r   r   )r   r   r$   r'   r(   r   s         ry   test_collect_D_0r   D  sP    AAgGA!
AaD!-C1515=#&15#+555r{   c                  "   [        S5      u  pp#[        S5      n[        S5      n[        S5      n[        U" U5      X" U5      -  -   U" U5      5      SU -   U" U5      -  :X  d   e[        U" X#5      X" X#5      -  -   U" U5      5      U" X#5      X" X#5      -  -   :X  d   e[        U" X#5      X" X#5      -  -   U" XV5      5      SU -   U" X#5      -  :X  d   e[        U" X#5      X" X#5      -  -   U" XU5      5      U" X#5      X" X#5      -  -   :X  d   e[        U" X"5      X" X"5      -  -   U" XU5      5      SU -   U" X"5      -  :X  d   e[        XS-   U-  -  US-   U-  -   XS-  5      SU -   US-   U-  -  :X  d   e[        XS-   U-  -  US-   U-  -   XQ-  5      XS-   U-  -  US-   U-  -   :X  d   e[        XS-   U-  -  US-   U-  -   US-   U-  5      SU -   US-   U-  -  :X  d   e[        XS-   U-  -  US-   U-  -   XV-  5      SU -   US-   U-  -  :X  d   eg)z4Collect with respect to functions with Wild argumentza b x yr   z.1z.2r0   N)r   r   r   r   )r'   r(   r$   r%   r   w1w2s          ry   test_collect_Wildr   M  sX   #JA!A	dB	dB1Q4!AaD&=!B%(QUAaDL8881Q7QqwY&".!A'AagI2EEEE1Q7QqwY&"	2q1uagoEEE1Q7QqwY&"	2ag!A'	6IIII1Q7QqwY&"	2q1uagoEEE1!eaZ<1q51*,be4QQ
8JJJJ1!eaZ<1q51*,be4	q51*Az!" " "1!eaZ<1q51*,q1urk:	
QQ
  1!eaZ<1q51*,bf5!a%!a%!9KKKKr{   c            
         [        S[        S5      -  S[        -  [        S5      -  -   5      SS[        S5      -  [        -  [        S5      -   -  :X  d   e[        S[        S5      -  S[        -  [        S5      -  -   [        S5      5      S[        S5      -  S[        -  [        S5      -  -   :X  d   e[        [        S5      S[        S5      -   -  [        S5      -   [        [        S5      -  -   5      [        S5      [        S-   [        S5      -   -  [        S5      -   :X  d   e[        S[        -  S[        -  -   S-   S5      [        S[        -  S[        -  -   S-   5      s=:X  a2  [        [        R                  [        S[        [        -   SS9SS9:X  d   e   e[        [        * [        -
  5      [        S[        [        -   SS9:X  d   e[        S[        -  S[        -  -
  S[        -  -
  S5      [        S[        [        -
  [        -
  SS9:X  d   e[        S[        -  S[        -  -
  S[        -  -
  S	5      [        S[        -  [        S	[        [        -   SS95      :X  d   e[        S
S[        S5      -  -   5      [        -  [        S[        S5      -   5      [        -  -   S-  n [        U S-   5      S[        [        S5      S-   5      -  [        S5      [        -  [        -   -  S-   :X  d   e[        [        [        -   [        S-  -   [        S-  -   5      [        [        -   [        [        R                  [        [        -   SS9-   :X  d   eg )Nr,   r-   r3   r.   r0   Fr]   r1   rb   r8   )r   r   r'   r$   r%   r   r   r   r   r&   r   r    r(   rl   rv   s    ry   test_collect_constr   `  s   47QqSa[01	1T!W9Q;a !" " "47QqSa[0$q':	$q'	AaCQK     a!d1g+.a81T!W9DEQQa!DG+, , , 1qsQ*acAaCi!m$BAEE3q!a%%05AB B B B B !a CAEE$BBBB1qsQqS!,Aq1uqy5)* * *1qsQqS"-1c"a!ee<=> > > rAd1gI~
q
 4DG#4Q#6
6	9BQ	$tAw{
T!WQY]+a/0 0 0 Q1qs*+q1us1661q5SX7Y/YYYYr{   c                  R   [        S5      n U " [        5      R                  [        5      nU " [        5      U-   U " [        5      U-  -   n[        U[	        S5      5      U " [        5      US-   -  U-   :X  d   eU " [        5      U " [        5      U-  -   [        U-  U " [        5      -  -   n[        X!5      [        U " [        5      -  U " [        5      -   U-  U " [        5      -   :X  d   e[        X " [        5      5      [        U-  U-   S-   U " [        5      -  :X  d   eU " [        5      U-   U " [        5      U-  -   n[        X " [        5      U/5      U " [        5      SU-   -  U-   :X  d   e[        X!U " [        5      /5      USU " [        5      -   -  U " [        5      -   :X  d   eg )Nr   wr0   )r   r$   r   r   r   )r   r   ru   s      ry   test_issue_13143r   |  s\   A	
11B	!r	AaDGA1d3i AaD"q&MB$6666	!qtBw2ad"A1>a!fqtmR/!A$66661ad"r	Aqt3333	!r	AaDGA1qtRj!QqT1r6]R%777711Q4j!RQqT]QqT%9999r{   c                  |   [        [        [        S[        -  -  -  [        [        S[        -  -  -  -   [        [        -  5      [        [        -   [        [        -  S-  -  :X  d   e[        [        SS[        -  -  -  [        SS[        -  -  -  -   S[        -  5      [        [        -   S[        -  S-  -  :X  d   eg )Ng       @r,   )r   r'   r%   r$   r(   r   r{   ry   test_issue_6097r     s    1QQZ<!AAJ,.15!a%!Q$9LLLL1QQZ<!AAJ,.15!a%!Q$9LLLLr{   c                     [         [        -   [        -  [         -  n U R                  SS9[        U 5      s=:X  a#  [         [        -  [        S-  -   [         -  :X  d   e   eU R                  5       [        [        S-  [         -  -   :X  d   eg )NT)fracr,   )r$   r%   rk   r!   r   s    ry   test_fraction_expandr     sl    
a%1B99$9?2#6H1Q3A:q.HHHHH99;!ad1f*$$$r{   c                  ,   [        [        S5      u  pn[        SSS9n[        [        R                  5      S:X  d   e[        U 5      U S4:X  d   e[        SU -  5      SU 4:X  d   e[        X-  5      X4:X  d   e[        U S-  5      U S4:X  d   e[        X-  U-  5      X-  U4:X  d   e[        XU-  -  5      XU-  4:X  d   e[        SUS-  -  5      SUS-  4:X  d   e[        XS-  -  5      XS-  4:X  d   e[        U S-  S-   U-  5      U S-  S-   U4:X  d   e[        XS-   -  US-  -  5      XS-   -  US-  4:X  d   e[        [        U * 5      S	S
9[        U * 5      S4:X  d   e[        SX-   -  S-  S	S
9S[        SX-   SS94:X  d   e[        X-  U-  5      X-  U4:X  d   e[        XS-  -  U-  5      XS-  -  U4:X  d   e[        SS	S9n[        [        U5      5      S[        U* 5      4:X  d   e[        [        U* 5      5      [        U* 5      S4:X  d   e[        SS	S9n[        [        U* 5      [        U5      -  S	S
9[        U* 5      [        U5      -  S4:X  d   e[        SS[        R                  SS9n[        U5      S:X  d   e[        US	S
9[        SSSS9S4:X  d   e[        SS[        R                  [        R                  [        SSSS9SS9n[        U5      S:X  d   e[        US	S
9[        SSSS9[        SSSSS94:X  d   eg )Nxyzr_   Fr`   )r0   r,   r0   r,   r/   Tr   r]   r1   r   )negativer   r}   )r0   r3   )
mapr   r   r   rl   r   r   r   r   r
   )r$   r%   r&   r_   r   r   ms          ry   test_fractionr     sR   &% GA!s&AAFFv%%%A;1a&   AaC=QF"""AC=QF"""AaC=QF"""ACE?qsAh&&&AsGaC(((AadF1a4y(((AdFa4y(((QTAXqL!adQh]222A1uIadN#q5	1a4'8888CG4(S!WaL888QYM.1c!QUe6T2UUUUACE?qsAh&&&AeGAI1U7A,...d#ACF3r7|+++CGaR!,,,d#ACGCFN$/CGCFNA3FFFFAq!&&5)AA;&   AT"s1a%'@!&DDDDAq!&&!&&#ae"<uMAA;&   AT"A&Aq!e(DEF F Fr{   c                      [        S5      u  pp#nUS-  U-  X0S-  -  -   U-  R                  5       n[        XPS-  U-  U/5      U:X  d   eg )NzaA Re a b Dr-   )r   rk   r   )aARer'   r(   r   ru   s         ry   test_issue_5615r     sW    m,OBA!
Q$q&1U7
B	&&(A11uRxm$)))r{   c                      SSK Jn Jn  SSKJn  U " U" SSS5      R
                  6 R                  R                  n[        U" U5      R                  5       5      S:  d   e[        U" [        U5      5      5      S:  d   eg )Nr   )PolygonRegularPolygon)denom)r   r   r0   r.   g-q=)sympy.geometry.polygonr   r   sympy.simplify.radsimpr   verticescentroidr$   absr   r   )r   r   r   r$   s       ry   test_issue_5933r     sf    @,1-667@@BBAuQxzz|u$$$uWQZ !E)))r{   c                  ,  ^^ [        SSS9u  mm[        S5      u  p[        [        UU4S j5        [        X-  XS-   -  -   T5      X-  XS-   -  -   :X  d   e[        X-  XS-   -  -   TT-  -   TT-  -   U5      USU -  S-   -  TT-  -   TT-  -   :X  d   eg )Nza bFr`   zx yc                  .   > [        T T-  TT -  -   T 5      $ )N)r   )r'   r(   s   ry   <lambda>"test_issue_14608.<locals>.<lambda>  s    71Q319a#8r{   r0   r,   )r   r#   AttributeErrorr   )r$   r%   r'   r(   s     @@ry   test_issue_14608r     s    5e,DAq5>DA
>8913aC=!$a1g55513aC=1Q3&1,a0AqsQwK!A#4E!4KKKKr{   c            	      p   [        [        5      [        [        5      -   n [        U 5      U :X  d   e[	        [
        [        [        5      [        [        5      5      (       d   e[        [        [        -  5      n[        U[        5      (       d   e[        [        [        5      [        [        5      -  5      U:X  d   e[        S[        [        [        5      [        [        5      -  5      -   5      S[        U5      -   :X  d   e[        SSS9n[        U[        SU-
  5      -  5      R                  SL d   eg )Nr0   r   Tr}   )r   r$   r%   r"   r   r   r   
isinstancer   r   is_commutative)r   ansr   s      ry   test_collect_absr     s    AQAq>QS#a&#a&))))
ac(Cc3s1vc!f}%,,,q3s1vc!f}--.!c#h,>>> 	sT"AqQqSz"11T999r{   c                  l    [        S[        -  S-  5      n [        U [        [        5      5      U :X  d   eg )Nr-   r3   )r   r$   r   r   s    ry   test_issue_19149r     s,    	QqSUB2s1v"$$$r{   c                      [        S5      u  pU S-  US-   -  SSU-  -   U -  -   n[        X S-  SU -  4SS9nX0S-  US-   SU -  SSU-  -   0:X  d   eg )Nza, br,   r0   r/   Fr]   r   )r'   r(   r   	collecteds       ry   test_issue_19719r     sp    6?DAa41q5>Q1WaK'D!tQqSkE:IAq1uac1qs73333r{   c                     [        S[        [        [        S-  5      -   -  5      S[        [        [        S-  5      -   -  :X  d   e[        S[        [        [        S-  5      -
  -  5      S[        [        [        S-  5      -
  -  :X  d   eg )Nr0   r,   )r   r$   r   r   r{   ry   test_issue_21355r     sl    1a$q!t*n%&!Qad^*<<<<1a$q!t*n%&!Qad^*<<<<r{   N)Tsympy.core.addr   sympy.core.functionr   r   r   sympy.core.mulr   sympy.core.numbersr   r	   sympy.core.powerr
   sympy.core.singletonr   sympy.core.symbolr   r   r   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   r   (sympy.functions.elementary.trigonometricr   r   sympy.polys.polytoolsr   sympy.series.orderr   r   r   r   r   r   r   sympy.core.exprr   r   rn   r   r    r!   r"   sympy.testing.pytestr#   	sympy.abcr$   r%   r&   r'   r(   r)   r*   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{   ry   <module>r      s     < <  ,   " 5 5 4 = A ? (   X X % 30 0 ' ) ) )P5dE;06<*F@ND,*&<,M6L&Z8:M
%(FV**L:%4=r{   