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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 = | -37447 0      0      -51473 0      0      0      0      0      -27535
     | 0      -53246 0      65881  0      0      -14722 -12497 54434  46710 
     | 22977  0      -16116 0      4319   20857  0      7342   -14242 0     
     | 0      -12204 64767  91601  35743  0      0      -49416 0      79428 
     | 40143  39290  -27114 88398  0      44696  0      -41834 0      -95201
     | -87550 0      32072  106    -34584 0      92882  -14207 0      18219 
     | -69875 -28131 0      -1574  0      97078  -41972 0      0      0     
     | 0      0      0      94829  0      -19812 0      0      0      0     
     | -84870 0      0      -24373 33290  18589  57957  0      -72191 0     
     | 0      -23412 -41665 0      0      0      31080  0      0      29869 
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| 9912   0      0      9912   9912   -17623 0      -39360 -29448 11825 
      | 11746  0      15906  -16657 -41500 -32130 15906  -21748 -27096 -12003
      | -11012 4319   15695  -19365 -11012 4683   -421   -6327  -23111 25024 
      | 9985   35743  -39550 119    -2219  25455  25217  -13441 12555  29571 
      | 9958   0      318    -32194 49248  -6345  -26796 25715  -3935  -12678
      | -171   -34584 -4700  -9678  -171   13348  27372  -29680 9433   -28264
      | 12457  0      26975  -14518 -15674 -16830 26975  -9164  4449   23005 
      | -19812 0      -19812 0      -19812 -39624 -19812 -4231  -4231  4231  
      | 5812   33290  -1256  7068   5812   4556   -1256  -2381  43588  -16675
      | 8966   0      7668   1298   -14446 -321   -33997 3165   27875  13877 
     ------------------------------------------------------------------------
     |, | -1 0 0 -1 -1 -1 0 -4 -5 4   |)
     |  | 4  0 1 3  5  7  1 20 22 -19 |
     |  | -1 0 0 -1 -1 -1 1 -4 -5 3   |
     |  | 0  0 0 0  0  0  0 1  1  -1  |
     |  | 4  1 2 2  4  6  2 18 19 -19 |
     |  | 1  0 1 0  1  2  1 5  5  -5  |
     |  | 1  0 1 0  1  2  1 5  5  -6  |
     |  | 2  0 2 1  2  4  2 13 13 -14 |
     |  | 4  0 2 2  4  6  2 18 19 -19 |
     |  | 1  0 0 1  1  2  0 5  6  -4  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also