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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 = | 60843  51276  -63047 0      0     -36161 54256  0      45092  0      |
     | -83923 0      -59975 0      0     87563  0      -15734 32341  0      |
     | 67497  -55031 -21632 -42340 0     -86628 0      -5193  0      0      |
     | 0      0      15949  0      78457 0      0      0      0      -98130 |
     | 89017  80343  85498  0      -3037 -42938 5583   0      0      10940  |
     | -85463 0      -71311 -20622 0     0      -90274 0      0      16570  |
     | 0      -26197 -16806 -84066 0     -14485 -94523 0      0      86472  |
     | 0      30783  0      -16496 -6438 -34631 78441  0      48750  -69024 |
     | 0      24893  0      2802   0     0      0      71758  0      0      |
     | 0      -38626 -86463 35120  26004 0      0      0      -55191 -92700 |

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

o2 = (| -15518 0     0      0      9164   9334   45092  -36331 9164   -71638
      | -35981 0     -15734 0      -32341 52588  32341  -13100 -32341 5713  
      | 19131  0     -5193  -42340 0      30707  0      -37848 42340  46923 
      | -19673 78457 0      0      -19673 19673  0      -19673 0      -3489 
      | -32593 -3037 0      0      13486  -47750 0      10395  5583   16904 
      | 11759  0     0      -20622 -73704 -11759 0      -37271 -69652 27905 
      | 6434   0     0      -84066 -8051  19763  0      39361  -10457 -28353
      | -11140 -6438 0      -16496 -45771 29107  48750  -1055  46187  33621 
      | 0      0     71758  2802   0      46865  0      19289  -2802  27576 
      | -11505 26004 0      35120  -11505 -5060  -55191 -9989  20071  -40842
     ------------------------------------------------------------------------
     |, | -1 0 0 0 0  1  0 -1 0  2  |)
     |  | 0  0 0 0 0  -1 0 1  0  -2 |
     |  | 0  0 0 0 0  0  0 0  0  1  |
     |  | 0  0 0 1 0  0  0 -2 -1 2  |
     |  | 1  1 0 0 1  -1 0 1  0  -4 |
     |  | -1 0 0 0 0  1  0 0  0  1  |
     |  | 1  0 0 0 1  -1 0 2  1  -4 |
     |  | 0  0 1 0 0  1  0 0  0  1  |
     |  | -1 0 0 0 -1 2  1 -3 -1 5  |
     |  | 1  0 0 0 1  -1 0 1  0  -3 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also