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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      7972  45170  0      0      49313  75233  0      -76837 |
     | 0      0      76699 20626  -33686 0      23952  81068  0      0      |
     | 0      -64211 0     0      -98526 0      92096  -39365 -53457 0      |
     | 72161  0      23973 1599   0      -87312 -22021 0      0      -7687  |
     | 0      73580  29016 0      -73940 0      0      -99275 88363  0      |
     | -83816 0      0     0      -43418 0      35164  52987  8291   0      |
     | 0      26767  0     0      0      -35874 0      0      0      17284  |
     | 0      0      0     0      -7187  0      -25899 -50365 0      -39092 |
     | 66245  0      0     54892  0      -80273 -48401 0      0      0      |
     | 44216  0      0     -36900 86596  0      51838  0      -33691 -13571 |

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

o2 = (| 0      7972  45170  22091  -49615 0      22091  -67261 76837  -26536
      | 0      76699 20626  17429  -27163 0      17429  -38055 0      9720  
      | 10754  0     -10754 -5050  -33329 -64211 5704   15804  0      37985 
      | 0      23973 1599   46589  11015  0      31438  39124  7687   -33975
      | 14783  29016 -14783 19229  24760  73580  34012  -4446  0      35122 
      | 8291   0     -8291  12589  4030   0      -62936 -4298  0      9986  
      | -26767 0     26767  26767  -27143 26767  -35874 -17660 -17284 26391 
      | 0      0     0      -43178 -29000 0      -43178 43178  39092  21365 
      | 0      0     54892  11353  20519  0      -2675  14028  0      64058 
      | -33691 0     -3209  -5480  29270  0      5045   8689   13571  12327 
     ------------------------------------------------------------------------
     |, | 0  0 0  1  -1 0 2  -1 0  -2 |)
     |  | -1 0 1  1  -3 1 0  -2 0  -1 |
     |  | 0  1 0  -1 1  0 -1 1  0  2  |
     |  | 0  0 1  -1 1  0 -1 0  0  3  |
     |  | 0  0 0  -1 2  0 -1 1  0  2  |
     |  | 0  0 0  0  -1 0 1  -1 0  -1 |
     |  | 0  0 0  0  1  0 0  0  0  1  |
     |  | 0  0 0  1  -1 0 1  -1 0  -2 |
     |  | 1  0 -1 0  3  0 1  1  0  0  |
     |  | 0  0 0  0  1  0 0  0  -1 1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also