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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 = | 71710  0      -93647 69591  -91598 0      -15705 0      27028  77802 
     | 0      0      0      17190  52727  -33224 0      -91689 0      0     
     | 0      60535  0      -58973 -42640 0      40462  0      -8309  0     
     | 0      0      0      -80262 -22274 0      -45264 0      -68340 0     
     | 0      -38578 -73795 -41605 0      67224  0      -88865 0      -54735
     | -56857 0      0      0      -70418 -14592 0      54008  0      0     
     | 98591  0      0      0      0      0      0      -82193 0      -84550
     | 0      74448  0      0      0      30030  55862  -45569 0      -59246
     | 76431  -35301 0      -26402 0      -57869 0      19441  0      0     
     | 0      -26380 -15720 17117  0      0      0      72428  0      24258 
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| -15705 27028  -15875 170    17145 -3931  -33769 38632  35310  -39170
      | 0      0      17190  -17190 56152 -1133  22928  -17167 11499  16057 
      | -20073 -8309  -21966 62428  8910  51190  -39861 526    20239  526   
      | -45264 -68340 -34110 -11154 11240 -424   -11836 -12346 -1020  -12346
      | 38578  0      -3027  3027   -4114 -6607  -10685 19012  -15488 6523  
      | 0      0      0      0      16410 19015  1818   4423   -48798 19015 
      | 0      0      0      0      -2357 6970   -2357  6970   16297  91520 
      | -18586 0      37276  18586  5013  -28565 -20819 1465   -43557 30681 
      | 35301  0      8899   -8899  24759 38804  -33110 -45467 -8854  12402 
      | 26380  0      43497  -43497 5987  4322   -9733  21439  9114   -2819 
     ------------------------------------------------------------------------
     |, | 0  0 0  0  0  1  0  1  2   1  |)
     |  | -1 0 -1 1  -2 -7 -2 -7 -11 -7 |
     |  | 0  0 0  0  1  6  2  6  10  6  |
     |  | 0  0 1  -1 1  2  1  3  4   3  |
     |  | 0  0 0  0  -1 -4 -1 -4 -6  -4 |
     |  | 0  0 0  0  0  3  1  4  6   3  |
     |  | 1  0 2  -1 3  9  2  9  14  9  |
     |  | 0  0 0  0  -1 -3 -1 -3 -5  -3 |
     |  | 0  1 -2 2  -3 -7 -2 -8 -12 -8 |
     |  | 0  0 0  0  1  4  1  4  7   3  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also