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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 = | -85259 0      11672  -75408 -91831 24077  -32439 -18985 0      0     
     | -997   0      99908  0      84294  -71649 -90766 -99610 -43682 0     
     | 0      -56260 0      74751  0      0      59018  -61255 0      -66632
     | 0      -65717 0      17684  0      0      66850  -90838 0      -65644
     | 0      72521  83604  -46619 0      52895  18046  50664  0      -35903
     | 79701  0      91344  0      0      60366  0      66056  -99919 -33047
     | 0      46489  48947  -22990 -4193  0      -82780 -39960 0      -77505
     | 0      55234  -65513 12784  -33495 61629  0      -90693 3136   0     
     | 64435  -45485 0      -79740 79257  79496  -75085 -21021 -85572 -14782
     | 0      34277  0      21081  19580  -27030 0      0      32197  30006 
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| 16857  -85259 -6572  -57903 -85259 -648   -27378 43587  35749  -12281
      | -39988 -997   85291  13642  -44679 -9948  -25866 -67752 -15423 54125 
      | 5361   0      0      74751  0      5361   23868  53486  -10372 -15749
      | -49093 0      0      17684  0      -49093 -73227 40685  73     25267 
      | 16305  0      0      6276   0      -36590 28865  -13247 28075  25112 
      | -20809 79701  -79701 -19335 -20218 98445  48195  -37431 18744  70468 
      | -15257 0      -4193  -27183 0      -11064 7904   43280  -75047 -59452
      | 21567  0      -33495 40918  3136   -9703  3071   11929  -55982 5829  
      | 13896  64435  14822  14578  -21137 5150   -9933  -41811 24627  -5093 
      | 27144  0      19580  13631  32197  2397   -19462 51194  896    43519 
     ------------------------------------------------------------------------
     |, | 0  1 -1 -1 1 1  -2 3  0  2  |)
     |  | -1 0 0  0  0 -1 1  -3 -1 -1 |
     |  | 1  0 0  0  0 1  -1 3  1  2  |
     |  | 1  0 0  1  0 1  1  1  0  0  |
     |  | 0  0 1  1  0 -1 1  -2 0  -1 |
     |  | 2  0 0  1  0 1  0  3  1  1  |
     |  | -1 0 0  0  0 -1 0  -2 0  0  |
     |  | 0  0 0  0  0 0  1  -1 0  -1 |
     |  | 2  0 0  0  1 1  -2 6  1  2  |
     |  | 1  0 0  0  0 1  -1 2  1  2  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also