+
    i                        ^ RI Ht ^ RIHt ^ RIHtHt ^ RIH	t	H
t
HtHt ]! ^^4      R3R lt]! ^^4      3R lt]! ^^4      3R ltR	# )
    )annotations)floor)ZZQQ)DMRankErrorDMShapeErrorDMValueErrorDMDomainErrorFc           	     X  aaaaaaaaaa \        ^^4      S8  g   S\        ^^4      8  d   \        R4      hV P                  ^ ,          V P                  ^,          8  d   \        R4      hV P                  \
        8w  d   \        R4      hV P                  ^ ,          oV P                  ^,          o^pV P                  4       pV P                  SS3\         4      pV P                  SS3\         4      o\        S4       Uu. uF  p\        ^ ^4      NK  	  upo\        ^^4      oS'       d   V P                  S\
        4      MRpRpV3R loR VVV3R lloR	 VV3R
 lloR R lp	R VVVV3R llp
\        S4       F  pWK,           Uu. uF  p\         P                  ! V\
        4      NK   	  upW[&   \        V4       F{  pV	! WEW34      p VSV,          ,          SV,          V&   \        S4       Uu. uF;  qT,          T,          ST,          T,          Y],          T,          ,          ,
          NK=  	  upY[&   K}  	  V	! WUW34      SV&   K  	  VS8  Ede   S! W3^,
          4      '       g   V
! VSWCV^,
          34       S! V4      '       dC   \        V^,
          RR4       F  pS! W?4      '       d   K  V
! VSWCV34       K!  	  V^,          pK  SV,          V^,
          ,          pSV,          V^,          SV^,
          ,          ,          ,           p SV^,
          ,          V,          pTT,          ST,          T^,
          &   ST,          T,          ST&   TST^,
          &   YC^,
          ,          YC,          uYC&   YC^,
          &   ST^,
          ,          RT^,
           ST,          RT^,
           uST,          RT^,
          % ST^,
          ,          RT^,
          % \        T^,           S4       F  pST,          T,          pST,          T^,
          ,          TT,          ,
          ST,          T&   ST,          T^,
          ,          ST,          T,          ,          T,           ST,          T^,
          &   K  	  S'       d$   Ys^,
          ,          Ys,          uYs&   Ys^,
          &   \        T^,
          ^4      pEKl  \        ;QJ d)    V3R l\        ^S4       4       F  '       d   K   RM	  RM! V3R l\        ^S4       4       4      '       g   Q h\        ;QJ d(    V3R l\        S4       4       F  '       d   K   RM	  RM! V3R l\        S4       4       4      '       g   Q hWG3# u upi u upi   \         d    \        T4      hi ; iu upi   \         d    \        T4      hi ; i)   z!delta must lie in range (0.25, 1)z/input matrix must have shape (m, n) with m <= nzinput matrix domain must be ZZNz-input matrix contains linearly dependent rowsc                :   < \        \        V S,           4      4      # N)r   mfloor)xhalfs   &x/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/polys/matrices/lll.pyclosest_integer!_ddm_lll.<locals>.closest_integer   s    &T"##    c                    V ^8  d   QhRRRR/# )   kintreturnbool )formats   "r   __annotate___ddm_lll.<locals>.__annotate__   s     J JC JD Jr   c                   < SV ,          SSV ,          V ^,
          ,          ^,          ,
          SV ^,
          ,          ,          8  # )r   r   )r   deltag_starmus   &r   lovasz_condition"_ddm_lll.<locals>.lovasz_condition   s5    ayebeAEla&776!a%=HIIr   c               $    V ^8  d   QhRRRRRR/# )r   r   r   jr   r   r   )r   s   "r   r   r   !   s!     % %C %C %D %r   c                <   < \        SV ,          V,          4      S8*  # r   )abs)r   r'   r   r#   s   &&r   mu_small_ddm_lll.<locals>.mu_small!   s    2a58}$$r   c                   V ^8  d   QhRR/# r   rowsztuple[int, int]r   )r   s   "r   r   r   $   s     M M_ Mr   c                j   a aa \        VV V3R  l\        S P                  ^,          4       4       4      # )c              3     <"   T F8  pSS^ ,          ,          V,          SS^,          ,          V,          ,          x  K:  	  R# 5ir   Nr   ).0zr.   r   ys   & r   	<genexpr>-_ddm_lll.<locals>.dot_rows.<locals>.<genexpr>%   s3     L:KQ1T!W:a=1T!W:a=00:Ks   A A)sumrangeshape)r   r4   r.   s   fffr   dot_rows_ddm_lll.<locals>.dot_rows$   s!    L%
:KLLLr   c                   V ^8  d   QhRR/# r-   r   )r   s   "r   r   r   '   s     O O? Or   c                  < S! W^ ,          ,          V^,          ,          4      p\        S4       Uu. uF;  qRV^ ,          ,          V,          WBV^,          ,          V,          ,          ,
          NK=  	  upW#^ ,          &   \        V^,          4       Uu. uF;  qQV^ ,          ,          V,          WAV^,          ,          V,          ,          ,
          NK=  	  upW^ ,          ,          RV^,          % W^ ,          ,          V^,          ;;,          V,          uu&   S	'       d]   \        S4       Uu. uF;  qPV^ ,          ,          V,          W@V^,          ,          V,          ,          ,
          NK=  	  upW^ ,          &   R# R# u upi u upi u upi r1   r8   )
Tr#   r4   r.   rr3   r   mnreturn_transforms
   &&&&  r   
reduce_row_ddm_lll.<locals>.reduce_row'   s   BAwKQ01AFqJAQjmaDG*Q-&777Jq'
NSTXYZT[n ]nDGQ!ak!n2D!D!Dn ]7HT!W
7DG!EJ1XNXDG*Q-!Qjm*;;;XNA1gJ  K ] Os   AE=AF,AFc              3  4   <"   T F  pS! V4      x  K  	  R # 5ir   r   )r2   ir$   s   & r   r5   _ddm_lll.<locals>.<genexpr>T   s     8Kq""Ks   FTc              3  X   <"   T F  p\        V4       F  pS! W4      x  K  	  K!  	  R # 5ir   r>   )r2   rG   r'   r*   s   &  r   r5   rH   U   s#     Bx!qAx~~~xs   '*)r   r	   r9   r   domainr   r
   copyzerosr8   eyeconvert_fromZeroDivisionErrorr   maxall)r   r!   rC   r   r4   y_star_r?   linear_dependent_errorr:   rD   rG   r3   r'   row_dotlnualphabetaxir   r"   r   r$   rA   r#   r*   rB   s   &ff                 @@@@@@@@r   _ddm_lllr\   	   s   	!Qx5ER1X->??wwqzAGGAJLMMxx2~<==	
A	
A	A	AWWaVR F	
!Q	B %a)1bAh)Fa8D(adAL$J J% %MO O 1X56T:TR__Q+T:	qAq1&1G:"VAY.1a JOqRA11a69Q<(???RFI  VaV4q	  a%q5!!q"aQU,A1q5"b)~~q"aQ0 * FAAq1uB1Ia&Q- 77E:a!e}u, 9BqE!a%Lq	D(F1I!F1q5M1uXqtNAD!E(/1!a%y!a%/@"Q%Q-,BqE&1q5M2a!e9Va!e,1q5!_U1Xa5Q<"r'11a!!uQU|beAh6;1a!e %  !"q514aAhAE1A38E!QK83338E!QK888883BuQxB333BuQxBBBBB4KA *4 ;
 % :!"899:R % :!"899:s+   U)$U.U35AVV 3V
V)c                *    \        WR R7      ^ ,          # )Fr!   rC   r\   r   r!   s   &&r   ddm_lllra   Y   s    AU;A>>r   c                    \        WR R7      # )Tr^   r_   r`   s   &&r   ddm_lll_transformrc   ]   s    AT::r   N)
__future__r   mathr   r   sympy.polys.domainsr   r   sympy.polys.matrices.exceptionsr   r   r	   r
   r\   ra   rc   r   r   r   <module>rh      sH    "   & b b Ah M` 1X ?  "!Qx ;r   