+
    i                         ^ RI HtHt ^ RIHt ^ RIHt ^ RIHtH	t	H
t
Ht ^ RIHtHtHt ^ RIHt R tR tR	 tR
 tR tR# )    )ZZQQ)DM)DomainMatrix)DMRankErrorDMValueErrorDMShapeErrorDMDomainError)_ddm_lllddm_lllddm_lll_transform)raisesc            
      F   \        . RO. RO. RO. RO.\        4      \        . R	O. R
O. RO. RO.\        4      3\        . RO. RO. RO.\        4      \        . RO. RO. RO.\        4      3\        . RO. RO. RO. RO.\        4      \        . RO. RO. RO. RO.\        4      3.p \        ^^4      pV  EFl  w  r#\        VP                  P                  4       VR7      ^ ,          pWCP                  P                  4       8X  g   Q h\        VP                  P                  4       VR7      pWCP                  P                  4       8X  g   Q h\        VP                  P                  4       VRR7      w  rEWCP                  P                  4       8X  g   Q hVP                  VP                  P                  4       4      VP                  P                  4       8X  g   Q h\        VP                  P                  4       VR7      w  rEWCP                  P                  4       8X  g   Q hVP                  VP                  P                  4       4      VP                  P                  4       8X  g   Q hVP                  P                  VR7      pWCP                  8X  g   Q hVP                  P                  VR7      w  rEWCP                  8X  g   Q hVP                  VP                  4      VP                  8X  g   Q hVP                  P                  4       P                  VR7      pWCP                  P                  4       8X  g   Q hVP                  P                  4       P                  VR7      w  rEWCP                  P                  4       8X  g   Q hVP                  VP                  P                  4       4      VP                  P                  4       8X  g   Q hVP                  VR7      pWC8X  g   Q hVP                  VR7      w  rEWC8X  g   Q hVP                  V4      V8X  d   EKm  Q h	  R# )   deltaTr   return_transformN)r   r   r   r   i@)r   r   r   r   i  )r   r   r   r   i  )r   r   r   r   i  )
      )   r   r   )r      r   r   r   )iir   	   )   4   i  )      r   )"   iFr   )   ir   )   r   is  )r$   r   i   )ir$   7   i  )   i     i  )W   1   i     )i#  +      S   )iCi  iHi!)r   r   r   r   repto_ddmr   matmulr   llllll_transformto_sdm)normal_test_datar   basis_dm
reduced_dmreduced	transforms         a/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/polys/matrices/tests/test_lll.pytest_lllr=   	   s    $###% ')* #"$%' )+,		
  "$  !"$&		
 !"%!# %'( !""(* ,./		
'< q!HE 08<<..0>qA..//1111(,,--/u=..//1111%hll&9&9&;5[_`..//1111 3 3 56*..:O:O:QQQQ.x||/B/B/DER..//1111 3 3 56*..:O:O:QQQQ,,"""/..(((%\\77e7D..(((-???,,%%'++%+8..//1111%\\002@@u@M..//1111 3 3 56*..:O:O:QQQQ,,U,+$$$%33%3@$$$)Z777E !1    c                  J  a \        . RO. RO. RO. RO.\        4      \        . RO. RO. RO. RO.\        4      \        . RO. RO. RO.\        4      .p V  F  o\        \        V3R l4       \        \        V3R l4       \        \        V3R l4       \        \        V3R l4       \        \        V3R l4       \        \        V3R l4       \        \        V3R l4       \        \        V3R l4       \        \        V3R	 l4       \        \        V3R
 l4       K  	  R# )r   c                  J   < \        S P                  P                  4       4      # Nr   r1   r2   	not_basiss   r<   <lambda>+test_lll_linear_dependent.<locals>.<lambda>]   s    HY]]-A-A-C$Dr>   c                  J   < \        S P                  P                  4       4      # rA   )r   r1   r2   rC   s   r<   rE   rF   ^   s    GIMM,@,@,B$Cr>   c                  8   < S P                   P                  4       # rA   r1   r4   rC   s   r<   rE   rF   _   s    IMM$5$5$7r>   c                  T   < S P                   P                  4       P                  4       # rA   r1   r6   r4   rC   s   r<   rE   rF   `   s    IMM$8$8$:$>$>$@r>   c                  $   < S P                  4       # rA   r4   rC   s   r<   rE   rF   a   s    IMMOr>   c                  N   < \        S P                  P                  4       R R7      # T)r   rB   rC   s   r<   rE   rF   b   s    HY]]-A-A-CVZ$[r>   c                  J   < \        S P                  P                  4       4      # rA   )r   r1   r2   rC   s   r<   rE   rF   c   s    $5imm6J6J6L$Mr>   c                  8   < S P                   P                  4       # rA   r1   r5   rC   s   r<   rE   rF   d   s    IMM$?$?$Ar>   c                  T   < S P                   P                  4       P                  4       # rA   r1   r6   r5   rC   s   r<   rE   rF   e   s    IMM$8$8$:$H$H$Jr>   c                  $   < S P                  4       # rA   r5   rC   s   r<   rE   rF   f   s    I$;$;$=r>   N)r   r   r   r   )r   r   r   r   )   r   r   r   )r   rW   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   rW   r      )r   r   )   rX   r   )r   r   rW   )r   r   r   r   )linear_dependent_test_datarD   s    @r<   test_lll_linear_dependentr\   N   s    
O 	 	L 	 	J	" 0	{DE{CD{78{@A{34{[\{MN{AB{JK{=> 0r>   c                  d  a a \         P                  ! R\        4      o \        R^4      \        ^ ^4      \        ^^4      \        ^^4      \        ^d^4      3 F  o\	        \
        V V3R l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       \	        \
        V V3R l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       K  	  R# )r   c                  2   < \        S P                  SR 7      # r   r   r1   dummy_matrixwrong_deltas   r<   rE   &test_lll_wrong_delta.<locals>.<lambda>l   s    Xl.>.>k%Rr>   c                  2   < \        S P                  SR 7      # r_   r   r1   ra   s   r<   rE   rd   m   s    W\-=-=[%Qr>   c                  <   < S P                   P                  SR 7      # r_   rI   ra   s   r<   rE   rd   n   s    \%5%5%9%9%9%Lr>   c                  X   < S P                   P                  4       P                  SR 7      # r_   rK   ra   s   r<   rE   rd   o   s"    \%5%5%<%<%>%B%B%B%Ur>   c                  (   < S P                  SR 7      # r_   rM   ra   s   r<   rE   rd   p   s    \%5%5K%5%Hr>   c                  4   < \        S P                  SR R7      # )Tr   r`   ra   s   r<   rE   rd   q   s    Xl.>.>kdh%ir>   c                  2   < \        S P                  SR 7      # r_   r   r1   ra   s   r<   rE   rd   r   s    %6|7G7G{%[r>   c                  <   < S P                   P                  SR 7      # r_   rR   ra   s   r<   rE   rd   s   s    \%5%5%C%C+%C%Vr>   c                  X   < S P                   P                  4       P                  SR 7      # r_   rT   ra   s   r<   rE   rd   t   s#    \%5%5%<%<%>%L%LS^%L%_r>   c                  (   < S P                  SR 7      # r_   rV   ra   s   r<   rE   rd   u   s    \%?%?k%?%Rr>   Nr   r   r   )r   onesr   r   r   r   ra   s   @@r<   test_lll_wrong_deltarr   i   s    $$VR0L2q	2a8R1Xr!QxCL|RS|QR|LM|UV|HI|ij|[\|VW|_`|RS Mr>   c                    a  \         P                  ! R\        4      o \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R	 l4       \        \        V 3R
 l4       R# )rZ   c                  .   < \        S P                  4      # rA   r`   wrong_shape_matrixs   r<   rE   &test_lll_wrong_shape.<locals>.<lambda>z   s    *<*@*@!Ar>   c                  .   < \        S P                  4      # rA   rf   ru   s   r<   rE   rw   {   s    );)?)?!@r>   c                  8   < S P                   P                  4       # rA   rI   ru   s   r<   rE   rw   |   s    !3!7!7!;!;!=r>   c                  T   < S P                   P                  4       P                  4       # rA   rK   ru   s   r<   rE   rw   }   s    !3!7!7!>!>!@!D!D!Fr>   c                  $   < S P                  4       # rA   rM   ru   s   r<   rE   rw   ~   s    !3!7!7!9r>   c                  2   < \        S P                  R R7      # rO   r`   ru   s   r<   rE   rw      s    *<*@*@SW!Xr>   c                  .   < \        S P                  4      # rA   rl   ru   s   r<   rE   rw      s    !23E3I3I!Jr>   c                  8   < S P                   P                  4       # rA   rR   ru   s   r<   rE   rw      s    !3!7!7!E!E!Gr>   c                  T   < S P                   P                  4       P                  4       # rA   rT   ru   s   r<   rE   rw      s    !3!7!7!>!>!@!N!N!Pr>   c                  $   < S P                  4       # rA   rV   ru   s   r<   rE   rw      s    !3!A!A!Cr>   N)rZ   r   )r   rq   r   r   r	   ru   s   @r<   test_lll_wrong_shaper   x   s    %**626
<AB
<@A
<=>
<FG
<9:
<XY
<JK
<GH
<PQ
<CDr>   c                    a  \         P                  ! R\        4      o \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R l4       \        \        V 3R	 l4       \        \        V 3R
 l4       R# )r   c                  .   < \        S P                  4      # rA   r`   wrong_domain_matrixs   r<   rE   'test_lll_wrong_domain.<locals>.<lambda>   s    (+>+B+B"Cr>   c                  .   < \        S P                  4      # rA   rf   r   s   r<   rE   r      s    '*=*A*A"Br>   c                  8   < S P                   P                  4       # rA   rI   r   s   r<   rE   r      s    "5"9"9"="="?r>   c                  T   < S P                   P                  4       P                  4       # rA   rK   r   s   r<   rE   r      s    "5"9"9"@"@"B"F"F"Hr>   c                  $   < S P                  4       # rA   rM   r   s   r<   rE   r      s    "5"9"9";r>   c                  2   < \        S P                  R R7      # rO   r`   r   s   r<   rE   r      s    (+>+B+BUY"Zr>   c                  .   < \        S P                  4      # rA   rl   r   s   r<   rE   r      s    "34G4K4K"Lr>   c                  8   < S P                   P                  4       # rA   rR   r   s   r<   rE   r      s    "5"9"9"G"G"Ir>   c                  T   < S P                   P                  4       P                  4       # rA   rT   r   s   r<   rE   r      s    "5"9"9"@"@"B"P"P"Rr>   c                  $   < S P                  4       # rA   rV   r   s   r<   rE   r      s    "5"C"C"Er>   Nrp   )r   rq   r   r   r
   r   s   @r<   test_lll_wrong_domainr      s    &++FB7
=CD
=BC
=?@
=HI
=;<
=Z[
=LM
=IJ
=RS
=EFr>   N)sympy.polys.domainsr   r   sympy.polys.matricesr   !sympy.polys.matrices.domainmatrixr   sympy.polys.matrices.exceptionsr   r   r	   r
   sympy.polys.matrices.lllr   r   r   sympy.testing.pytestr   r=   r\   rr   r   r    r>   r<   <module>r      s;    & # : b b I I 'B8J?6TEGr>   