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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 = | -3829  -93610 15395  0      -27137 0      -94395 0      649    91894 
     | 73073  0      0      77035  0      0      50537  0      -59324 0     
     | 0      377    0      0      0      63303  0      0      0      -43978
     | 0      -76363 0      0      0      -75694 72483  0      -75796 0     
     | 0      0      0      5711   98017  0      34241  -73284 10852  0     
     | 0      91874  0      0      -47622 0      -99311 0      -96323 7309  
     | 3174   -75718 -94163 -19497 0      -40114 30389  0      28325  0     
     | -74016 19605  98094  -28954 -34188 -87664 0      0      0      0     
     | 0      -99750 59855  0      4750   35333  46170  45308  -76746 52182 
     | 0      0      0      81009  0      -16640 12897  -83857 0      0     
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| -48167 24859  -14429 29909  33738  -2693  49080 3611   2698   -12687
      | 20077  -16115 -37210 15786  19748  45401  18903 -9036  29019  -29348
      | -24276 24276  -34178 -9902  -9902  9902   29227 19804  14853  43499 
      | -7091  7091   -31008 -23917 -23917 23917  20706 -24649 -38264 21438 
      | 7594   22850  22240  14646  20357  16772  -4164 34484  -36519 -24002
      | 3114   -50736 10680  7566   7566   40056  43298 36557  -9855  6998  
      | -12886 -9785  -38850 -22790 -45461 -186   9586  18365  2168   -34743
      | -15791 26665  -2565  -60790 -15728 -16130 -6464 13376  6677   -6614 
      | 32171  17887  21792  -10379 -10379 -25132 8437  -20662 -15962 -33462
      | 14850  -17698 -2568  -17418 63591  -57895 25067 21939  -20826 -14290
     ------------------------------------------------------------------------
     |, | 1  -2 12  12  11  -8 -8 -23 -16 26  |)
     |  | 1  -1 3   2   2   -2 -2 -4  -3  4   |
     |  | 0  0  3   3   3   -2 -2 -6  -4  7   |
     |  | -2 3  -17 -15 -14 12 11 30  22  -34 |
     |  | -2 3  -14 -12 -12 11 9  25  18  -28 |
     |  | 1  -1 5   4   4   -4 -3 -8  -6  9   |
     |  | 2  -2 9   7   7   -7 -6 -15 -11 16  |
     |  | -2 3  -16 -14 -14 12 10 28  21  -32 |
     |  | 0  0  1   1   1   -1 -1 -2  -1  2   |
     |  | 2  -2 8   6   6   -6 -5 -12 -9  12  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also