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LLL(..., ChangeMatrix => ...) -- also find change of basis matrix

Synopsis

Description

Constructs the change of basis matrix U from the basis A to the basis B. This is an invertible matrix U such thatAU = B.
i1 : A = matrix randomMutableMatrix(10,10,.5,100000)

o1 = | 0      0      0      -9147  0      -83308 -19675 38504  -82503 0     
     | 0      0      0      53183  -46937 0      0      62768  55790  0     
     | 0      0      17083  0      0      64719  -7503  -83852 17780  -2553 
     | 41525  0      -10585 0      7827   0      0      0      -49694 -83644
     | 0      26999  -84433 56414  58880  0      0      0      0      0     
     | -39972 29647  75015  -59891 -18452 0      0      20174  0      0     
     | 50982  -61594 0      84778  -19246 76834  0      -4665  41818  94715 
     | 0      -25719 0      -19920 7107   -87178 69459  -81517 62896  -69962
     | -80235 -18066 -37885 0      0      0      11013  0      387    0     
     | 0      80565  30379  0      -30062 2137   0      0      0      0     
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| -9147  -19675 -9147  0      -53681 0      0      -40155 -21326 -1381 
      | 6246   0      6246   46937  2607   -46937 0      -55790 6978   -12492
      | 17083  -7503  17083  0      8200   17083  0      31933  -59422 -44222
      | -44283 0      -2758  -7827  -39109 -2758  0      49694  49694  -36603
      | 30861  0      30861  -58880 28019  -25553 26999  0      0      -61722
      | 36644  0      -3328  18452  -15124 56563  29647  0      20174  -33316
      | 14550  0      65532  19246  -42960 -19246 -61594 35016  30351  14633 
      | -12813 69459  -12813 -7107  13357  7107   -25719 -11156 -23214 25123 
      | 42350  11013  -37885 0      27259  -37885 -18066 21639  32652  6548  
      | 317    0      317    30062  -30379 317    80565  2137   2137   -634  
     ------------------------------------------------------------------------
     |, | -1 0 0 0  0  0 0 0  0  1  |)
     |  | 0  0 0 0  0  0 1 0  0  0  |
     |  | 1  0 1 0  -1 1 0 0  0  -2 |
     |  | 1  0 1 0  -1 0 0 0  0  -2 |
     |  | 1  0 1 -1 0  1 0 0  0  -2 |
     |  | 0  0 0 0  0  0 0 1  1  0  |
     |  | 0  1 0 0  -1 0 0 2  3  1  |
     |  | 0  0 0 0  0  0 0 0  1  0  |
     |  | 0  0 0 0  1  0 0 -1 -1 0  |
     |  | 0  0 0 0  0  0 0 0  0  1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also