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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      76588  -34323 -58190 0      0     -47336 27148  |
     | 0     0      0      0      40270  0      99850  0     0      0      |
     | 57764 -73605 -15139 0      -24508 0      70482  69808 0      0      |
     | 0     0      0      61923  0      -13561 0      0     0      4936   |
     | 0     0      -9885  21187  0      0      0      97362 0      -57924 |
     | 0     0      -97989 -13098 0      -32101 0      -4819 0      -20012 |
     | 5572  0      -74461 -34173 0      0      0      0     0      -72185 |
     | -7716 -86814 0      50988  53226  0      0      0     0      -13996 |
     | 0     97006  0      0      -57224 0      -44917 0     -28005 0      |
     | 9170  0      4698   77048  -6730  0      0      0     0      0      |

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

o2 = (| 10854  -15599 -15599 -5143  -47336 8297   18554  26297  -4448  -7870 
      | 0      -1650  -1650  17660  0      -20960 3300   -1650  16010  41920 
      | 0      -21120 36644  -1309  0      -13445 -385   21505  4754   -19229
      | 13561  -946   -946   -14507 0      0      41629  21240  -24078 14507 
      | 0      -16967 -16967 -16967 0      0      7082   31072  15389  16967 
      | 32101  2363   2363   -29738 0      0      -4049  -11412 13682  29738 
      | 0      -2012  3560   -18728 0      -22288 -33445 1284   -24036 7584  
      | 0      6218   -1498  9728   0      -42000 32272  12498  9666   -47522
      | -28005 2274   2274   -25201 -28005 -26261 -4548  -25731 5078   9503  
      | 0      27942  37112  13892  0      -16490 7296   41810  27966  -25502
     ------------------------------------------------------------------------
     |, | 0  -8 -7 -11 0 -4 15 -7 -20 9  |)
     |  | 0  -2 -2 -3  0 -1 4  -2 -5  3  |
     |  | 0  -2 -2 -2  0 0  3  -1 -5  2  |
     |  | 0  1  1  1   0 0  -1 1  2   -1 |
     |  | 0  -5 -5 -7  0 -3 10 -5 -12 6  |
     |  | -1 5  5  6   0 0  -8 3  12  -6 |
     |  | 0  2  2  3   0 1  -4 2  5   -2 |
     |  | 0  0  0  0   0 0  0  0  1   0  |
     |  | 1  0  0  0   1 2  0  1  -1  1  |
     |  | 0  1  1  1   0 0  -1 0  3   -1 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also