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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      0      0      65733 97122  75624  54458  0      |
     | 0      0      -65094 -44518 7057   0     89527  0      34557  65921  |
     | 0      57235  -57685 97338  27036  77388 -40920 -426   32535  -93544 |
     | 29641  -41248 0      0      97945  0     0      -97106 0      0      |
     | 73767  0      0      0      0      0     -15072 -23211 59443  -8484  |
     | 0      0      14928  26267  0      0     0      0      -19005 38815  |
     | 0      50977  0      0      0      -5042 -74180 -73539 50386  -37631 |
     | -59032 0      0      0      -92487 0     0      46850  -98701 0      |
     | 33322  0      0      -84530 -61079 -9806 -12343 0      84827  0      |
     | 0      0      0      0      0      0     -78646 0      -58135 0      |

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

o2 = (| 0      0      65733  9891   -11275 32773  11794  23069  42664  -42664
      | 0      -65094 0      7057   -9961  34394  14509  10951  -10124 -33567
      | 57235  -57685 20153  6457   -4750  -36194 8831   64     -16670 20014 
      | -41248 0      41248  -40409 11607  44251  7765   11607  -23214 11607 
      | 0      0      0      -23211 -14324 22463  -22060 -7736  73019  -7736 
      | 0      14928  0      0      7262   7666   38411  19810  33933  46077 
      | 50977  0      -56019 -17520 4451   45885  -66587 30916  -22612 35958 
      | 0      0      0      -45637 -39669 -7181  13149  -39669 -19363 -39669
      | 0      0      -9806  -51273 -23219 10876  7372   54042  -30526 -20682
      | 0      0      0      0      -58135 -20511 -37624 20511  -20511 20511 
     ------------------------------------------------------------------------
     |, | 0 0 0  0  -1 1  -2 -1 2  -1 |)
     |  | 1 0 -1 1  -1 2  -4 -1 2  -1 |
     |  | 0 1 0  0  0  1  -1 0  1  0  |
     |  | 0 0 0  0  1  -1 2  0  0  1  |
     |  | 0 0 0  1  0  0  -1 0  0  0  |
     |  | 0 0 1  -1 -1 1  0  1  0  0  |
     |  | 0 0 0  0  0  1  -1 -1 1  -1 |
     |  | 0 0 0  1  0  -1 0  0  0  0  |
     |  | 0 0 0  0  1  -1 2  1  -1 1  |
     |  | 0 0 0  0  0  0  1  1  0  1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also