+
    ijD                        ^ RI Ht ^ RIHtHt ^ RIHt ^ RIHtH	t	 ^ RI
Ht ^ RIHt ^ RIHtHt ^ RIHt ^ R	IHt ^ R
IHtHt ^ RIHt ^ RIHtHtHtHtHt ^ RI H!t! ^ RI"H#t# ^ RIH$t$H%t%H&t&H't'H(t(H)t) ^ RIH*t*H+t+H,t,H-t- ^ RI.H/t/ ]!! R4      t0]0Pc                  ]#]#4      R 4       t2]0Pc                  ]#]4      R 4       t2]0Pc                  ]%]$4      R 4       t2]0Pc                  ]%]%4      R 4       t2]0Pc                  ]]%4      R 4       t2]0Pc                  ]]4      R 4       t2]0Pc                  ]$]&4      R 4       t2]0Pc                  ]']4      R 4       t2]0Pc                  ]']%4      R 4       t2]0Pc                  ]']'4      R 4       t2]0Pc                  ]']$4      R 4       t2]0Pc                  ]'])4      R 4       t2]0Pc                  ](]4      R 4       t2]0Pc                  ]-]-4      R  4       t2]0Pc                  ]]4      R! 4       t2]0Pc                  ]*]4      R" 4       t2]0Pc                  ]+]4      R# 4       t2]0Pc                  ]]4      R$ 4       t2]0Pc                  ]]4      R% 4       t2]0Pc                  ]]4      R& 4       t2]0Pc                  ]$])4      R' 4       t2]0Pc                  ]%])4      R( 4       t2]0Pc                  ])]&4      R) 4       t2R* t3]0Pc                  ]$]4      R+ 4       t2]0Pc                  ]%]4      R, 4       t2R-# ).    )_aresame)Lambdaexpand_complex)Mul)ilcmFloat)Eq)S)Dummysymbols)ordered)sign)floorceiling)ComplexRegion)	FiniteSetIntersectionIntervalSetUnion)
Dispatcher)ConditionSet)IntegersNaturalsRealsRangeImageSet	Rationals)EmptySetUniversalSetimageset
ProductSet)numerintersection_setsc                     R # N abs   &&ڀ/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/sets/handlers/intersection.py_r,              c                 l    \        V P                  V P                  \        V P                  V4      4      # r&   )r   sym	conditionr   base_setr(   s   &&r+   r,   r,      s$    q{{LQ,GHHr.   c                     V # r&   r'   r(   s   &&r+   r,   r,           Hr.   c                 2    V \         P                  J d   V # T# r&   )r
   r   r(   s   &&r+   r,   r,   $   s    QZZ1&Q&r.   c                     \        W4      # r&   )r$   r(   s   &&r+   r,   r,   (       Q""r.   c           	      h   VP                   '       Ed@   V P                  '       g<   VP                  '       g*   \        \        V P                  VP                  4      4      # V P                  '       d   VP                  '       d   V P
                  V P                  r2VP
                  VP                  rT\        W$4      p\        W54      p^\        P                  ,          V9   d   \        P                  V9   g2   ^\        P                  ,          V9   d+   \        P                  V9   d   \        V\        ^ 4      4      p\        Wg,          RR7      # VP                  \        P                  4      '       Ed   . p\        R\        RR7      p	V P                  '       gr   V P                    FM  p
\        P                  V
P"                  ^,          9   g   K+  VP%                  V
P"                  ^ ,          4       KO  	  \        V!  p\        W4      # V P                  '       Ed   V P                    F  p
\        P                  V
P"                  ^,          9   d#   VP%                  V
P"                  ^ ,          4       \        P                  V
P"                  ^,          9   d7   VP%                  \'        \)        W) 4      V
P"                  ^ ,          4      4       \        P                  V
P"                  ^ ,          9   g   K  VP%                  \        ^ 4      4       K  	  \        V!  p\        W4      # R# R# )   T)polarx)clsrealN)is_ComplexRegionr:   r   r   sets
a_interval
b_intervalr
   PiZeror   r   	is_subsetr   r   r   psetsargsappendr   r   )selfotherr1theta1r2theta2new_r_intervalnew_theta_intervalnew_intervalr;   elements   &&         r+   r,   r,   ,   s(   


U[[[ dii!DEE ZZZEKKK$//))5+;+;)"1N!-f!= 1446!aff&6!$$& QVVv%5%*+=+4Q<&9" !B&*, , qwwCU. zzz::66W\\!_, ''Q8 & !,/L44 ZZZ::66W\\!_, ''Q8447<<?* ''2Q(PQ66W\\!_, ''	!5 & !,/L44   r.   c                     V # r&   r'   r(   s   &&r+   r,   r,   [   r4   r.   c                 \   \         ;QJ d>    R  V P                  VP                  R,          ,            4       F  '       d   K   RM3	  RM/! R  V P                  VP                  R,          ,            4       4      '       g   R# V P                  ^ 8X  d   \        P                  # \        \        VP                  V P                  4      4      pW!9  d
   V^,          p\        \        VP                  V P                  4      4      pW19  d
   V^,          p\        V \        W#^,           4      4      # )c              3   8   "   T F  qP                   x  K  	  R # 5ir&   	is_number.0is   & r+   	<genexpr>_.<locals>.<genexpr>b   s     8$7q{{$7   :Nr9   NFTN)allrF   sizer
   r   r   maxinfr   minsupr$   r   )r)   r*   startends   &&  r+   r,   r,   _   s     38AFFQVVBZ$783338AFFQVVBZ$7888 	vv{zz Cquu%&E~

AEE155!
"C
|qQe1W 566r.   c                 ^    \        V \        VP                  \        P                  4      4      # r&   )r$   r   r`   r
   Infinityr(   s   &&r+   r,   r,   s   s    Q

 ;<<r.   c           	        a \         ;QJ d    R  W3 4       F  '       d   K   RM	  RM! R  W3 4       4      '       g   R# V'       g   \        P                  # V '       g   \        P                  # VP                  V P                  8  d   \        P                  # VP                  V P                  8  d   \        P                  # T pVP
                  P                  '       d   VP                  pTpVP
                  P                  '       d   VP                  pVP
                  P                  '       d   V# VP
                  P                  '       d   V # ^ RIH	p R pV! V! V\        R4      4      V! V\        R4      4      ,
          4      w  rgVRJ ;'       d    VRJ pV'       d   \        P                  # VP                  4       ^ ,          p	V! W)4      p
V3R lp\        \        VP                  VP                  4      4      oV! W*4      pVf   \        P                  # V! W:4      pVf   \        P                  # V3R	 lpV! W4      pV! W4      p\        VP                  4      ^ 8  d   VP                  p\        VP                  4      ^ 8  d   VP                  p\!        VP
                  VP
                  4      p\#        VP$                  VP$                  4      p\'        VVS4      # )
c              3      "   T FM  p\         ;QJ d&    R  VP                   4       F  '       d   K   RM	  RM! R  VP                   4       4      x  KO  	  R# 5i)c              3   8   "   T F  qP                   x  K  	  R # 5ir&   rU   )rX   vs   & r+   rZ   _.<locals>.<genexpr>.<genexpr>z   s     /1;;r\   FTN)r]   rF   )rX   rs   & r+   rZ   r[   z   s6     @Ass//sss////s   AA'AFTN)diop_linearc                 H    V P                   WP                  ,          ,           # r&   )rc   step)rl   rY   s   &&r+   <lambda>_.<locals>.<lambda>   s    agg&&(r.   r)   r*   c                 B  < WP                   8X  d   V# \        V P                   V,
          4      S,          p\        WP                   V,           V4      R,          pW0P                   8X  d   M+\        V P                  4      \        V4      8w  d	   W2,          pW09  d   R# V# )   N)rc   r   r   ro   )rJ   csts1ro   s   &&  r+   _first_finite_point_.<locals>._first_finite_point   s{    =H "((Q,$
 1hhmR(,>
 BGG}R(<	r.   c                    < \        V P                  4      S,          pV P                  P                  '       d   \	        WP
                  V4      pV# \	        V P                  W,           V4      pV# r&   )r   ro   rc   	is_finiter   stop)rl   firstrv   rvro   s   &&  r+   _updated_range_.<locals>._updated_range   sW    !&&\$77uffb)B 	 qww
B/B	r.   )r]   r
   r   rb   r`   rc   is_infinitereversed%sympy.solvers.diophantine.diophantinerm   r   as_coeff_Addabsr   ro   r   r_   ra   r|   r   )r)   r*   rJ   rL   rm   eqvavbno_solutiona0ru   rx   rw   s2r   rc   r|   ro   s   &&               @r+   r,   r,   w   s2    3@!@333@!@@@ zzzzuuquu}zzuuquu}zz 
B	xx[[	
B	xx[[ 
xx	xxA 
)B
 Bc
+bU3Z.@@AFB *++tKzz 
	1	B
2
A0 tBGGRWW%&D	R	#B	zzz	R	#B	zzz 
	B		B BGG}q[[BGG}q[[ "((#Erww Dd##r.   c                     V # r&   r'   r(   s   &&r+   r,   r,      r4   r.   c                     V # r&   r'   r(   s   &&r+   r,   r,      r4   r.   c                   a$a%a& ^ RI Hp \        V P                  P                  4      ^8  g0   V P                  P
                  V P                  P                  8w  d   R# V P                  ^ ,          pV\        P                  J Ed   Rp\        V\        4      '       dq   VP                  \        P                  38X  dQ   VP                  P                  pVP                  P                  ^ ,          p\        R4      pVP                  WV4      pM V\        P                  J d   \        R4      ;rdVEe?   V P                  P                  o$V P                  P                  ^ ,          o% \        V! S$V,
          S%X3RR7      4      p\        T4      ^ 8X  d   \        P"                  # \$        ;QJ d    R T 4       F  '       g   K   RM	  RM! R T 4       4      '       d   \        T4      ^8X  dn   T^ ,          w  rTP&                  w  p
S$P                  S%TP                  T
S%4      4      P)                  4       p\+        \-        S%T4      \        P                  4      # R# \/        T$T%3R lT 4       !  # V\        P0                  8X  EdO   ^ R	IHpHo& V&3R
 lpV P                  P                  pV P                  P                  ^ ,          o%\        S%P8                  RR7      pVP                  S%V4      pVP;                  4       w  pp\=        V4      pVP                  VS%4      pVP                  VS%4      pVP&                  p\-        S%V4      pVP>                  '       d   MVVP>                  RJ d   \        P"                  # VS%08w  d   R# W=! \@        PB                  ! \E        V4      4      S%4      ,          pW=! V! V4      S%4      ,          p\+        VV4      # \        V\F        4      '       Ed   ^ RI$H%pH&pH'p V P                  P                  pV P                  P                  ^ ,          o%RRppVPP                  VPR                  ppVPT                  '       d   TpMTpV! WPV                  S%4      w  ppV! WPX                  S%4      w  pp \Z        ;QJ d    R VV 3 4       F  '       d   K   RM	  RM! R VV 3 4       4      '       Ed   VS%8X  d$   \        V4      ^8X  d   VP\                  ^ ,          pVS%8X  d$   \        V 4      ^8X  d   V P\                  ^ ,          p\$        ;QJ d    R VV3 4       F  '       g   K   RM	  RM! R VV3 4       4      '       d   R# \        P"                  p!\Z        ;QJ d    R VV3 4       F  '       d   K   RM	  RM! R VV3 4       4      '       d,   VV8  d   TTpp\G        VVVV4      p"VP_                  V"4      p!MmVPa                  \        P0                  4      '       dI   V! VS%\        P0                  4      p#\        V!\        \b        34      '       g   V#P_                  V4      p!MR# V!\        P"                  J d   \        P"                  # \        V!\d        4      '       d1   V!Pf                  \        Ph                  Jd   \/        \        V!4      !  p!V!e   \+        \-        S%V4      V!4      # R# R# R#   \        \         3 d     R# i ; i)r   )diophantineNmT)symspermutec              3   H   "   T F  q F  q"P                   x  K  	  K  	  R # 5ir&   )free_symbols)rX   tuplss   &  r+   rZ   r[      s     Dt!^^t^    "Fc              3   V   <"   T F  pSP                  SV^ ,          4      x  K   	  R# 5i)r   N)subs)rX   r   fnns   & r+   rZ   r[   )  s#     "CU2771ad#3#3Us   &))denomssolve_linearc           
         < . pV  FW  pS! V^ V.4      w  rEWA8X  d   VP                  \        V4      4       K2  VP                  \        V\        V^ 4      4      4       KY  	  \	        V!  # )r   )rG   r   r   r	   r   )exprsr0   solsrY   r;   xisr   s   &&    r+   _solution_union_.<locals>._solution_union.  s`     D%aSE28KK	#/KKS"Q( ;<  $<r.   )r=   )invert_realinvert_complexsolvesetc              3   B   "   T F  p\        V\        4      x  K  	  R # 5ir&   )
isinstancer   rW   s   & r+   rZ   r[   l  s     :Az!Y''s   c              3   (   "   T F  qR J x  K
  	  R # 5ir&   r'   rW   s   & r+   rZ   r[   w  s     9&89&8s   c              3   8   "   T F  qP                   x  K  	  R # 5ir&   )is_realrW   s   & r+   rZ   r[   }  s     9&899&8r\   )5sympy.solvers.diophantiner   lenlamda	variables	signature	base_setsr
   r   r   r   exprr   r   list	TypeErrorNotImplementedErrorr   anyr   expandr!   r   r   r   sympy.solvers.solversr   r   nameas_real_imagr   is_zeror   	make_argsr#   r   sympy.solvers.solvesetr   r   r   	left_open
right_openr   r`   rb   r]   rF   	intersectrD   r   r   r^   rf   )'rH   rI   r   r2   gmvarr   solnssolnsolmtr   r   r   fn_f_reimifreelamr   r   r   new_infnew_sup	new_lopen	new_ropeninverterg1h1g2h2	range_setrP   	solutionsr   r   r   s'   &&                                  @@@r+   r,   r,      s5   5 	DJJ  !A%zz##tzz';';;~~a H 1::eX&&5??qzzm+K!!B++''*Cc
ABajj 3ZA>B

$$Q'A[b1vtLM 5zQzz!DDDDDDu:?!&qJD,,DQ771dii1o6==?D#F1dOQZZ@@ "CU"CDD>
	  JJOOJJ  #166%VVAr]"BBWWR^WWR^Qm::: ZZ5 ::qc\ eBi(!- -H 	OF1Iq11X&&	E8	$	$	6 	6 JJOOJJ  #$0@0@9	999"H%H!YY*B!YY*B3:"b:333:"b:::Qwr7a< ggajGQwr7a< ggajG
 s9w&89sss9w&8999 

Is9w&89sss9w&8999 W$'.WG')YO$..|<	??177++ (Aqww 7I%i(L1IJJ$-$7$7$>	AJJ&zz!Iu--)..

2R%tI7	$q!i88u 
%O 23  s   ([ [! [!c                     \        VP                  4      \        V P                  4      8w  d   \        P                  # \	        R  \        V P                  VP                  4       4       !  # )c              3   H   "   T F  w  rVP                  V4      x  K  	  R # 5ir&   )r   )rX   rY   js   &  r+   rZ   r[     s     G3F41A3Fr   )r   rF   r
   r   r"   zipr?   r(   s   &&r+   r,   r,     sD    
166{c!&&k!zzG3qvvqvv3FGHHr.   c                 f   \         P                  \         P                  3pV \        V!  8X  dJ   V P                  V P
                  rCVP                  '       g   W29   g   VP                  '       g   WB9   d   V# V P                  V4      '       g   R # RpV P                  VP                  8:  Ed]   VP                  V P                  8:  EdA   V P                  VP                  8  d   VP                  pVP                  pEM[V P                  VP                  8  d   V P                  pV P                  pEM&V P                  p\        V P                  VP                  4      '       g   VP                  P                  \        4      '       d3   V P                  P                  \        4      '       g   VP                  pM}V P                  P                  \        4      '       d3   VP                  P                  \        4      '       g   V P                  pM&\        \        W.4      4      ^ ,          P                  pV P                  ;'       g    VP                  pV P                  VP                  8  d   V P                  pV P                   p	EM[V P                  VP                  8  d   VP                  pVP                   p	EM&V P                  p\        V P                  VP                  4      '       g   VP                  P                  \        4      '       d3   V P                  P                  \        4      '       g   VP                  pM}V P                  P                  \        4      '       d3   VP                  P                  \        4      '       g   V P                  pM&\        \        W.4      4      ^ ,          P                  pV P                   ;'       g    VP                   p	W,
          ^ 8X  d   V'       g	   V	'       d   RpMRpV'       d   \         P"                  # \        XXXX	4      # )NFT)r
   NegativeInfinityrf   r   leftrightr   _is_comparablerc   rd   r   r   hasr   r   r   r   r   )
r)   r*   inftylrl   emptyrc   r   rd   r   s
   &&        r+   r,   r,     s    

*EHevvqww1999
aiii1:H AEww!%%AGGquu,77QWWGGEIWWqwwGGEIGGEAGGQWW-- 77;;u%%aggkk%.@.@GGEWW[[''E0B0BGGE
 !!0399E22q{{I55155=%%CJUUQUU]%%CJ %%CAEE155))5599U##AEEIIe,<,<%%CUUYYu%%aeeii.>.>%%Cwu~.q155C55J;!jEzzE3	:66r.   c                 "    \         P                  # r&   )r
   r   r(   s   &&r+   r,   r,     s    ::r.   c                     V# r&   r'   r(   s   &&r+   r,   r,     r4   r.   c                 J    \        V P                  VP                  ,          !  # r&   )r   	_elementsr(   s   &&r+   r,   r,     s    q{{Q[[022r.   c                 t     \        V  Uu. uF  q"V9   g   K  VNK  	  up!  # u upi   \         d     R # i ; ir&   )r   r   )r)   r*   els   && r+   r,   r,     s<    5"1W225665 s   	( ##( ( 77c                     R # r&   r'   r(   s   &&r+   r,   r,     r-   r.   c                     V # r&   r'   r(   s   &&r+   r,   r,     r4   r.   c                     V # r&   r'   r(   s   &&r+   r,   r,     r4   r.   c                     V # r&   r'   r(   s   &&r+   r,   r,     r4   r.   c                 T    VP                   \        P                  J d!   VP                  \        P                  J d   V # \        \        V P                  \        VP                  4      4      \        VP                  4      ^,           4      p\        W!4      #   \         d     R# i ; i)rs   N)_infr
   r   _suprf   r   r_   r`   r   r   r   r   r$   
ValueError)r)   r*   r   s   && r+   _intlike_intervalr     sv    66Q'''AFFajj,@H#aeeWQVV_-uQWW~/AB && s   =B  AB B'&B'c                     \        W4      # r&   r   r(   s   &&r+   r,   r,     r7   r.   c                     \        W4      # r&   r   r(   s   &&r+   r,   r,     r7   r.   N)4sympy.core.basicr   sympy.core.functionr   r   sympy.core.mulr   sympy.core.numbersr   r   sympy.core.relationalr	   sympy.core.singletonr
   sympy.core.symbolr   r   sympy.core.sortingr   $sympy.functions.elementary.complexesr   #sympy.functions.elementary.integersr   r   sympy.sets.fancysetsr   sympy.sets.setsr   r   r   r   r   sympy.multipledispatchr   sympy.sets.conditionsetr   r   r   r   r   r   r   r   r    r!   r"   sympy.simplify.radsimpr#   r$   registerr,   r   r'   r.   r+   <module>r     s   % 6  * $ " . & 5 > . K K - 0  H H ( 23  L,7 8 L#.I /I Hh/ 0 Hh/' 0' Hh/# 0# M3/,5 0,5\ He, - E8,7 -7& E8,= -= E5)o$ *o$d E8, - E9- . Hc*` +`F J
3I 4I Hh/A7 0A7F Hc* + L#. / Iy13 23 Is+ , C% & Hi0 1 Hi0 1 Iu- . Hh/# 0# Hh/# 0#r.   