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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      0     64152  -18485 7873   0      30481  0      39100 0      |
     | 0      0     0      0      0      -36171 0      0      14494 0      |
     | 76132  0     0      0      0      85671  0      0      0     0      |
     | 0      -1534 0      0      0      0      -91160 -50614 0     0      |
     | 42989  0     0      0      0      0      0      0      87910 -54327 |
     | 0      51166 71801  0      -90603 0      42323  73681  1812  0      |
     | 0      72364 0      0      -23346 -92367 -40150 0      16033 0      |
     | -27981 98933 0      8153   -6831  0      63740  -29398 0     0      |
     | 0      0     -41058 86883  6453   -66810 0      0      0     0      |
     | -67712 10693 0      18968  0      0      -41182 0      0     0      |

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

o2 = (| 39100 -39100 32925  14440  7873   25052  1698   -33317 -6232  -26750
      | 14494 -14494 -14494 -14494 0      -14494 -28988 21805  79781  7311  
      | 0     0      0      0      0      0      0      9539   9539   85671 
      | 0     0      0      0      -50614 0      -52148 0      13136  0     
      | 33583 20744  20744  20744  0      20744  -12839 -17311 8367   -7905 
      | 1812  -1812  -20614 -20614 -16922 69989  11818  -26949 -8262  43040 
      | 16033 -16033 -39379 -39379 -23346 -16033 -6394  18457  -8905  2424  
      | 0     0      -6831  1322   -36229 0      55873  33490  -14516 13662 
      | 0     0      -34605 52278  6453   -41058 -28152 -43425 12879  2400  
      | 0     0      0      18968  0      0      10693  48744  -13824 0     
     ------------------------------------------------------------------------
     |, | 0 0  0  0  0 0  0  -1 -1 0  |)
     |  | 0 0  0  0  0 0  1  0  -2 0  |
     |  | 0 0  1  1  0 1  1  -3 -5 -2 |
     |  | 0 0  0  1  0 0  0  -1 -1 0  |
     |  | 0 0  1  1  1 0  2  -2 -6 -2 |
     |  | 0 0  0  0  0 0  0  1  1  1  |
     |  | 0 0  0  0  0 0  0  0  1  0  |
     |  | 0 0  0  0  1 0  1  0  -2 0  |
     |  | 1 -1 -1 -1 0 -1 -2 4  8  3  |
     |  | 1 -2 -2 -2 0 -2 -3 6  12 5  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also