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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 = | 0      0      0      0      0      -56390 62598  0     6780   69396  |
     | 51788  -25195 -45986 67213  0      0      0      32546 6653   -34140 |
     | 0      0      27594  -3309  69460  -39238 0      0     -78234 0      |
     | -76588 -28074 0      0      0      0      -30586 75845 0      0      |
     | 7318   -41225 -5872  -2129  -12689 -89871 79552  40383 0      0      |
     | 0      29753  -18524 0      0      0      0      0     -8657  -44637 |
     | -27797 450    259    0      -88978 0      72876  0     0      21408  |
     | 0      -21356 44729  -27692 0      -34401 31061  5086  0      59499  |
     | 71440  0      0      -74587 56323  0      0      0     -62970 -94626 |
     | 54171  0      0      0      0      0      0      47841 90006  70091  |

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

o2 = (| 0      0      6208   44010  37802  -24814 -31576 18070  -18624 -25940
      | -25195 -45986 0      -51461 -9708  6326   18869  17212  16558  4843  
      | 0      27594  30222  -10362 18927  -7428  -31810 -8180  38305  29776 
      | -28074 0      -30586 17682  -2266  -2266  30340  -11130 13150  -9115 
      | -41225 -5872  -23008 -22561 -16900 -30773 -17873 -15872 -2237  -41250
      | 29753  -18524 0      13365  -20954 -22022 -7731  333    -4566  27950 
      | 450    259    -16102 -9878  26361  5471   -5921  -7150  -20085 3887  
      | -21356 44729  -3340  -2202  -6745  -4478  -8567  28827  -19219 38132 
      | 0      0      56323  -11667 32834  -10097 10097  13752  -11822 25419 
      | 0      0      0      14341  1579   21494  -21494 -30226 -12762 3274  
     ------------------------------------------------------------------------
     |, | 0 0 0 1  -2 -2 2  7   -3 6   |)
     |  | 1 0 0 1  -1 -1 0  2   -1 3   |
     |  | 0 1 0 -3 1  3  -3 -9  4  -5  |
     |  | 0 0 0 -2 1  2  -2 -6  3  -4  |
     |  | 0 0 1 -3 5  5  -5 -16 7  -13 |
     |  | 0 0 1 -3 5  5  -4 -14 6  -11 |
     |  | 0 0 1 -4 6  6  -6 -19 8  -15 |
     |  | 0 0 0 0  0  0  0  0   0  1   |
     |  | 0 0 0 -2 2  3  -3 -10 4  -8  |
     |  | 0 0 0 2  -1 -2 2  7   -3 5   |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also