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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      0      -6616  0      -63453 86813  16928 0      0     |
     | -54391 0      -58816 26273  -19484 -30551 0      56128 0      17579 |
     | 0      -234   0      73130  0      98352  0      0     82199  0     |
     | -84164 58218  0      0      42940  -76006 86149  0     0      0     |
     | 0      78564  69776  30866  0      0      -94792 0     0      0     |
     | 99752  0      0      0      -99063 72573  0      0     -93385 0     |
     | -60633 -22724 0      0      -73030 0      -98276 7139  -66557 0     |
     | 0      0      37636  0      -32704 -98415 42271  8716  0      0     |
     | 0      56233  0      0      0      0      0      85865 20833  0     |
     | -65671 -27388 0      -36922 67807  -49111 -10938 0     0      99185 |

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

o2 = (| -10312 -10312 -3696  -10312 -6616  -3696  16928  24320  60912  -70845
      | 13478  -4101  6689   -45338 26273  6689   -39751 -31125 -25288 -58661
      | 8835   8835   17904  8835   73130  17670  234    -35574 -1283  51961 
      | 15278  15278  -27662 15278  0      30556  -15278 -44118 48473  -4226 
      | -22078 -22078 -52944 47698  30866  25620  -8788  27324  -59424 -36112
      | 5678   5678   11356  5678   0      11356  -99063 -22023 -44213 -10145
      | -23390 -23390 -16917 -23390 0      -39641 -43167 -69966 32527  20326 
      | -13648 -13648 19056  23988  0      19056  13648  -62100 -15200 -55371
      | -8799  -8799  12034  -8799  0      68267  29632  5564   26397  3235  
      | 40912  -58273 10027  40912  -36922 -17361 -3990  9470   18993  5236  
     ------------------------------------------------------------------------
     |, | 0  0  0  0  0 0  0  1  -1 -1 |)
     |  | 1  1  1  1  0 2  -1 -3 -3 2  |
     |  | -1 -1 -1 0  0 -1 1  2  3  -1 |
     |  | -1 -1 -2 -1 1 -2 0  4  2  -4 |
     |  | -1 -1 -2 -1 0 -2 1  5  3  -3 |
     |  | 0  0  0  0  0 0  0  0  1  1  |
     |  | 0  0  0  0  0 0  0  0  1  0  |
     |  | -1 -1 -1 -1 0 -1 1  3  3  -2 |
     |  | 1  1  2  1  0 2  0  -4 -3 3  |
     |  | 1  0  1  1  0 1  -1 -2 -2 1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also