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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      -96531 98109  78565  18054  -36473 0      57221 
     | 0      -26071 0      -91444 19798  0      0      16545  -64546 24306 
     | 86301  99881  0      42514  0      -17739 0      -33767 0      53870 
     | 0      49021  0      -53223 0      0      -82400 0      0      17608 
     | 0      0      -88446 0      22466  -51916 1676   0      0      0     
     | 0      -12388 11460  -69785 0      0      0      92863  0      0     
     | 0      29820  21163  -61975 -34867 0      0      -29485 0      0     
     | 0      -82840 -74166 0      -39402 0      -32315 0      -14587 -53810
     | -30516 66748  0      0      0      -25777 -8622  0      12095  0     
     | 0      -48487 0      0      0      65884  -98461 -41055 11266  -14208
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| 752    -752   -7899  -32989 -32666 -16656 -24232 30747  27226  14543 
      | -35832 -28714 10798  -6290  -19153 -15951 20459  -3747  -7779  -27359
      | 4589   -4589  -36267 3836   -29298 11695  42175  -12584 -15258 -3114 
      | -5160  5160   33460  -15852 -21411 -29657 47265  -12367 24815  -19256
      | 11582  -11582 -27688 5222   -43514 -17244 -5222  -1064  12646  -15826
      | 13632  -13632 26178  -26178 -928   -13790 13790  -11302 24934  42679 
      | 295    -295   11024  23843  -18751 28890  5977   19386  -19091 32200 
      | 8081   -22668 5783   -20191 -5983  -20156 5748   10523  -56252 27457 
      | -7424  19519  -3662  34178  24137  -20475 20475  36111  -13019 9378  
      | -24857 36123  679    -14887 -2921  16450  -30658 -41320 2255   21874 
     ------------------------------------------------------------------------
     |, | -7  7   -11 10  1  10  -10 -4 -4 13  |)
     |  | -2  2   -3  3   1  2   -2  0  -2 4   |
     |  | -5  5   -7  7   1  7   -7  -3 -2 8   |
     |  | 2   -2  3   -3  0  -3  3   1  1  -4  |
     |  | -10 10  -15 14  2  13  -14 -5 -5 17  |
     |  | 4   -4  6   -6  0  -6  6   3  1  -6  |
     |  | 1   -1  1   -1  0  -1  1   1  0  -1  |
     |  | 2   -2  3   -3  0  -3  3   1  1  -3  |
     |  | 2   -1  2   -2  -1 -1  1   0  2  -2  |
     |  | 16  -16 24  -23 -4 -21 22  7  10 -29 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also