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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      -24972 62567  -35890 0     0      -41145 0      0      -43832 |
     | 0      -71951 -8910  0      0     87882  913    35690  0      66215  |
     | 0      32697  0      0      0     0      -99392 0      -23546 0      |
     | 71693  0      0      0      56314 -18398 0      0      -18614 0      |
     | 0      0      -41722 0      42093 0      0      0      46091  83753  |
     | -33586 0      0      -41516 0     0      39185  -55108 0      0      |
     | 0      0      0      0      0     0      0      0      0      47772  |
     | 38182  0      26632  -17853 56515 74377  -96509 -3742  0      -53753 |
     | -57821 0      80659  0      0     0      76698  0      -49661 60787  |
     | 0      -35816 82232  0      -4958 17333  0      86157  0      -80455 |

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

o2 = (| -35890 -9213  -15759 -26677 -14628 0     16333  10918  -19309 0     
      | 0      -44600 -27351 44600  -18132 0     -10537 -36261 -19417 0     
      | 0      -23546 56243  23546  7850   0     1301   32697  -33998 23546 
      | 0      -18614 18614  3235   -9273  56314 -12360 0      -3019  18614 
      | 0      4369   -4369  37724  -38157 42093 433    0      -42093 -46091
      | -41516 -27924 27924  19994  7867   0     -27861 -13592 33523  0     
      | 0      0      0      0      47772  0     -47772 0      0      0     
      | -17853 -5332  5332   5812   19942  56515 48623  14111  -8501  0     
      | 0      30998  -30998 26823  -4980  0     -21843 0      18877  49661 
      | 0      -3925  -31891 -1033  -5790  -4958 -11660 50341  36816  0     
     ------------------------------------------------------------------------
     |, | 0 0  0  -1 3  0 -2 0  1  0  |)
     |  | 0 0  1  0  4  0 -3 1  2  0  |
     |  | 0 1  -1 -1 1  0 0  0  0  0  |
     |  | 1 2  -2 -1 -3 0 4  -1 -2 0  |
     |  | 0 0  0  1  -3 1 2  0  -1 0  |
     |  | 0 0  0  0  2  0 -1 0  1  0  |
     |  | 0 0  0  0  1  0 -1 0  1  0  |
     |  | 0 -1 1  1  1  0 -2 1  1  0  |
     |  | 0 1  -1 -1 1  0 0  0  0  -1 |
     |  | 0 0  0  0  1  0 -1 0  0  0  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also