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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     39300  0      0      -39658 -13219 0      85615  98252  0      |
     | 0     3120   65667  0      -32893 -16796 0      -50348 0      -64931 |
     | 0     0      0      0      0      61934  -86822 -16216 0      -8580  |
     | 0     0      -53867 -50703 0      61     0      0      0      0      |
     | 0     0      0      0      -32821 73029  -12693 -51654 86437  0      |
     | 0     -22340 96680  -2063  8746   -91564 0      -98344 0      0      |
     | 0     0      0      73533  0      0      -34072 0      81668  0      |
     | 74880 -51202 68030  0      0      -31184 -25579 0      -92236 -83641 |
     | 60971 0      0      0      0      91501  0      -84825 0      84684  |
     | 0     -40284 38164  0      0      0      36117  0      -12682 88048  |

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

o2 = (| -39658 39300  39300  0      -358   0      19294  1203   33941  -70610
      | -32893 3120   3120   0      35894  0      -36013 19247  -15123 35344 
      | 0      0      0      0      0      -86822 0      -29410 16308  32524 
      | 0      0      0      -50703 -53867 0      50703  56909  3103   6267  
      | -32821 0      0      0      -32821 -12693 53616  -36864 -48310 -17451
      | 8746   -22340 -22340 -2063  83086  0      33149  51065  -33417 -51308
      | 0      0      0      73533  0      -34072 8135   25937  25937  17802 
      | 0      -51202 23678  0      16828  -25579 -41034 -39518 -2672  -53346
      | 0      0      60971  0      0      0      0      -13493 -6817  17037 
      | 0      -40284 -40284 0      -2120  36117  27602  -11715 26449  967   
     ------------------------------------------------------------------------
     |, | 0 0 1 0 0 0 0  0  0  -1 |)
     |  | 0 1 1 0 1 0 -1 0  0  0  |
     |  | 0 0 0 0 1 0 0  -2 -1 -2 |
     |  | 0 0 0 1 0 0 -1 1  1  2  |
     |  | 1 0 0 0 1 0 1  -4 -3 -5 |
     |  | 0 0 0 0 0 0 0  -2 -1 -1 |
     |  | 0 0 0 0 0 1 0  -1 -1 -1 |
     |  | 0 0 0 0 0 0 0  -1 0  -1 |
     |  | 0 0 0 0 0 0 1  -1 -1 -2 |
     |  | 0 0 0 0 0 0 0  1  1  1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also