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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      -7359  0      0      0      -39511 72344  0      -1264  0     
     | 0      0      28616  -51265 0      0      0      0      -8091  69428 
     | 0      0      0      80038  0      0      0      0      0      -99603
     | 0      0      -35827 0      18982  45761  -17941 0      85907  0     
     | 0      0      0      0      0      0      -18976 -57478 0      0     
     | 0      0      -15944 0      87272  0      0      1008   19092  0     
     | 16535  -99235 0      -68762 0      0      -22413 0      0      -39667
     | 5234   0      0      0      0      28646  0      0      71770  0     
     | -54103 -52827 0      -69716 0      -29518 0      -35571 0      0     
     | 0      79751  58350  0      -34684 -9122  0      0      -71895 0     
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| 0      0      -39511 32833  0      5414   -29364 29364  7359   -8202 
      | 0      28616  0      0      0      20525  -16182 16182  46779  1624  
      | 0      0      0      0      0      0      0      0      -19565 80038 
      | 0      -35827 45761  27820  0      -23501 -3168  22150  -35827 19758 
      | 0      0      0      -18976 -57478 18976  -550   550    0      -18426
      | 0      -15944 0      0      1008   3148   39192  48080  -15944 13044 
      | 16535  0      -16535 -22413 -16535 38948  -15461 15461  -9194  -9549 
      | 5234   0      23412  28646  -5234  19712  5544   -5544  0      -1844 
      | -54103 0      24585  -29518 18532  4933   5089   -5089  -16889 -2326 
      | 0      58350  -9122  -9122  0      4699   -18429 -16255 -21401 6873  
     ------------------------------------------------------------------------
     |, | 1 0 -1 0 -1 1  1  -1 0  -3 |)
     |  | 0 0 0  0 0  0  1  -1 -1 -2 |
     |  | 0 1 0  0 0  1  0  0  1  1  |
     |  | 0 0 0  0 0  0  0  0  1  1  |
     |  | 0 0 0  0 0  0  0  1  0  1  |
     |  | 0 0 1  1 0  -2 -5 5  0  8  |
     |  | 0 0 0  1 0  -1 -3 3  0  4  |
     |  | 0 0 0  0 1  0  1  -1 0  -1 |
     |  | 0 0 0  0 0  1  2  -2 0  -3 |
     |  | 0 0 0  0 0  0  0  0  1  0  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also