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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      -30910 -19080 -13091 0      0      -52433 0      0     |
     | 0      0      37701  -29974 54312  -86088 -51314 8881   0      0     |
     | 0      -19628 -30051 47341  -66028 40413  -14538 0      0      -6884 |
     | 0      0      0      0      0      0      99704  0      0      0     |
     | -32414 0      15661  0      0      0      0      -75063 0      0     |
     | 62824  50912  51912  -26343 0      -72707 0      0      -18873 0     |
     | -60121 79769  0      0      0      0      0      0      0      93850 |
     | 34989  -2663  0      -92490 16221  0      0      0      -26098 0     |
     | -40116 8003   -22755 -76308 0      49863  -66780 94616  76351  0     |
     | 0      -56630 -491   -10151 43978  20575  -23394 -89297 0      0     |

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

o2 = (| -30910 -30910 -17819 0      13091  0      0      -1261  0      -52433
      | 37701  -48387 -16611 0      31776  0      0      -13363 -51314 8881  
      | -30051 10362  48721  12744  38359  12744  -6884  -8264  -14538 12744 
      | 0      0      0      0      0      0      0      0      99704  0     
      | 15661  15661  15661  0      0      -32414 -32414 -48075 0      -75063
      | 51912  -20795 1000   -50912 2922   -6961  43951  16608  -18873 -32039
      | 0      0      14081  14081  14081  -46040 33729  19648  0      14081 
      | 0      0      -13558 2663   -39656 11554  8891   -70041 -26098 28761 
      | -22755 27108  -30758 -8003  18485  28232  36235  -9315  9571   10262 
      | -491   20084  12161  56630  -7923  56630  0      -22312 -23394 -32667
     ------------------------------------------------------------------------
     |, | 0 0 0  0  0  1  1 1  0 0  |)
     |  | 0 0 -1 -1 -1 -1 0 1  0 -1 |
     |  | 1 1 1  0  0  0  0 -1 0 0  |
     |  | 0 0 0  0  0  0  0 1  0 0  |
     |  | 0 0 -1 0  -1 0  0 1  0 0  |
     |  | 0 1 0  0  -1 0  0 0  0 0  |
     |  | 0 0 0  0  0  0  0 0  1 0  |
     |  | 0 0 0  0  0  0  0 0  0 1  |
     |  | 0 0 0  0  1  1  1 1  1 -1 |
     |  | 0 0 1  1  1  1  1 0  0 1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also