+
    i                     L    ^ RI Ht ^ RIHt ^ RIHtHt ^ RIHt ^ RI	H
t
 R tR# )    )Rational)	fibonacci)Ssymbols)raiseslinrecc            	        aaaa \        ^^.^^.^R7      R8X  g   Q h\        . R+O. R,O^
R7      R8X  g   Q h\        . R-O^^.^R7      R8X  g   Q h\        . R.O. R/O^R7      ^8X  g   Q h\        . R0O. R1O^FR7      R8X  g   Q h\        ^ .^7,          . R2O,           ^ .^2,          . R3O,           RR7      R8X  g   Q h\        . R0O. R1OR4R7      '       g   Q h\        . R0O. R1OR5R7      '       g   Q h\        ;QJ d&    R \        ^_^s4       4       F  '       d   K   R	M	  R
M! R \        ^_^s4       4       4      '       g   Q h\        ;QJ d&    R \        RR4       4       F  '       d   K   R	M	  R
M! R \        RR4       4       4      '       g   Q h\        P                  \        ^^4      \        ^^4      ^\        ^^	4      \        ^^4      .o^^^\        ^^4      \        ^^4      \        ^^	4      ^.o\        R4      w  oop \        SR,          SR,          ^PR7      \        RR4      8X  g   Q h\        SR,          SR,          ^2R7      \        RR4      8X  g   Q h\        SR,          SR,          ^#R7      \        RR4      8X  g   Q h\        ^ .^<,          \        ^^4      \        ^^4      .,           SRR7      \        RR4      8X  g   Q h\        \        R 4       \        \        VV3R l4       \        \        VV3R l4       \        \        VV3R l4       \        \        VV3R  l4       \        SSV .. R6O^R7      S^,          SS,          ,           SV ,          ,           S,           V ,           8X  g   Q h\        . R7OSSV .^R7      R!S,          R"S,          ,           R#V ,          ,           8X  g   Q h\        . R8OSS.^R7      R$S,          R%S,          ,           8X  g   Q h\        ^ .^2,          . R3O,           SSV .R&R7      R'S,          R(S,          ,           R)V ,          ,           8X  g   Q h\        . ^^.^R7      ^ 8X  g   Q h\        SSV .. R3O^R7      ^8X  g   Q hR*# )9   coeffsinitni*  i  l   X;GD7 l   Y!Hc"6)`ToNR0s(Wm"j  i  l   wN;ELM$xqK a>c              3   ^   "   T F#  p\        ^^.^ ^.VR7      \        V4      8H  x  K%  	  R# 5ir   r   Nr	   r   .0r   s   & c/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/discrete/tests/test_recurrences.py	<genexpr>test_linrec.<locals>.<genexpr>   s2      M=K aV1a&A6)A,F=Ks   +-FTc              3   l   "   T F*  p\        ^^.^^.VR7      \        V^,           4      8H  x  K,  	  R# 5ir   r   r   s   & r   r   r      s7      N=L aV1a&A6)AE:JJ=Ls   24iS  ig  zx y zN   NN   Nl   ua#o[|,VNM,e*iG l	             VvRl   9g9Z
(#l         kr:   NN:Nr   Nl   6Nn&`^W*H
UeX`h"l   EW&G i  l          Pjej~Tl   yk%+Gk& c                  &    \        . RO. RO^R7      # )   r   r            r      r   r   r   r        r   <lambda>test_linrec.<locals>.<lambda>,   s    f,<?VWXr'   c                  <   < \        S R ,          SR,          RR7      # )r   r   '  r   r   abs   r   r(   r)   -   s    fAbE"Gr'   c                  <   < \        S R ,          SR ,          RR7      # )r   r   ir   r,   s   r   r(   r)   .   s    vQrU2&Ir'   c                      < \        SS R R7      # r+   )r   r   )r.   xs   r   r(   r)   /       fQU3r'   c                      < \        S SR R7      # r1   r   )r-   ys   r   r(   r)   0   r3   r'   i i#
 i i|i4.\i  l   `7u)l   <=C^l   x)m Nr$   )r   r   r   r%   )r   r   r   r!   )r   r   r   r   r%   )r   r   r   r    )r   r%   r   r   )r   r   r%   r   )r   r%   r   r+   i )r   r   r   )r   r%   r   )r   r   r   r%   )
r	   allranger   Halfr   r   r   	TypeError
ValueError)zr-   r.   r2   r5   s    @@@@r   test_linrecr<      s:   !Qq!f3u<<<|rBdJJJr2h"=LLLyB?3FFF)CRS S S!R,.aSVi5G4PAB B B )FFFF)FFFF3 M=B2s^M333 M=B2s^M M M M M 3 N=B3_N333 N=B3_N N N N N 
!Q!QHQNHQPQNSA	
Aq(1a.(1a.(1a.!DAgGAq!2QrUb1Q4	66 6 6 2QrUb157LMN N N 2QrUb1F$	&& & & !R8Aq>8Aq>"BBdS13PQR R R 9XY
9GH
:IJ
934
934!Qa8	1!acA!" " "!Qb9q6!8fQh&' ' 'QFb9
XaZ     !R)+1a)tDq>!++nQ.>>? ? ?1a&B/1444!Qa8A===r'   N)sympy.core.numbersr   %sympy.functions.combinatorial.numbersr   
sympy.corer   r   sympy.testing.pytestr   sympy.discrete.recurrencesr	   r<   r&   r'   r   <module>rB      s    ' ; ! ' -4>r'   