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LLLBases :: LLL(..., ChangeMatrix => ...)

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      31748  56736 -55496 0      0      0      -80455 -38493 33012  |
     | 0      2981   0     0      0      0      71546  -90668 24734  -85668 |
     | 84195  36101  0     31824  98731  -529   0      0      0      -21064 |
     | -4237  -468   0     0      17868  0      -58021 0      86203  0      |
     | 66381  -58791 0     0      0      85153  -3955  -6139  0      0      |
     | 28516  0      72498 -56232 0      0      -7204  -8383  0      0      |
     | -30334 0      0     0      79496  0      -3949  0      0      0      |
     | -85531 -24224 0     0      0      78891  0      0      0      0      |
     | 0      55135  0     0      -95049 -64284 0      48486  0      0      |
     | 50300  0      0     43487  43444  -31907 90707  -84357 0      -8563  |

              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| 1240  31748  56736 31748  -6721  22683  -21375 32920  -31772 -33012
      | 0     2981   0     2981   10612  2535   -8064  8510   14122  85668 
      | 31824 36101  0     35572  -52888 4211   -21527 17805  52888  21064 
      | 0     -468   0     -468   28182  -19269 -11038 11971  58021  0     
      | 0     -58791 0     26362  -3955  28261  -15948 14049  3955   0     
      | 16266 0      72498 0      -23470 6864   26577  -909   23470  0     
      | 0     0      0     0      -3949  29417  -37315 -71598 3949   0     
      | 0     -24224 0     54667  0      -421   55088  0      0      0     
      | 0     55135  0     -9149  0      38760  577    46563  0      0     
      | 43487 0      0     -31907 38657  -15347 28447  -1477  -38657 8563  
     ------------------------------------------------------------------------
     |, | 0 0 0 0 0  1  -1 0  0  0  |)
     |  | 0 1 0 1 0  3  -2 0  0  0  |
     |  | 1 0 1 0 -1 -5 5  2  1  0  |
     |  | 1 0 0 0 -1 -7 6  3  1  0  |
     |  | 0 0 0 0 0  1  -1 -1 0  0  |
     |  | 0 0 0 1 0  2  -1 0  0  0  |
     |  | 0 0 0 0 1  5  -3 -2 -1 0  |
     |  | 0 0 0 0 0  2  -1 -1 0  0  |
     |  | 0 0 0 0 1  3  -2 -1 0  0  |
     |  | 0 0 0 0 1  3  -2 -1 -1 -1 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also