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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 = | 53009  -85384 0      -53000 0      -24879 94613  0      28302 65613  |
     | 0      0      0      0      51812  17086  45348  -7633  0     0      |
     | 0      0      32794  23877  12713  0      -53467 0      72312 94550  |
     | 0      0      0      0      0      -29172 39629  0      0     0      |
     | -18148 0      0      0      0      7355   -2362  0      0     0      |
     | 42571  65385  -97438 -46152 -59795 -19988 -81166 92570  0     36009  |
     | 0      -78969 0      -94631 0      -43974 0      0      37165 0      |
     | -37956 0      0      0      0      0      0      -87707 0     0      |
     | 0      0      -33888 0      0      -4860  -34845 0      0     0      |
     | 61547  93686  33646  95317  0      0      -78282 0      0     -18843 |

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

o2 = (| 1284   32384  -1504  27447  1284   -2568  2359   27837  27740  -26456
      | 41190  0      -34726 13482  -10622 21244  21244  5720   24848  8709  
      | -12338 -8917  28444  -4595  7743   17308  48463  5742   -10337 30793 
      | -10457 0      -29172 8258   -10457 20914  20914  -4398  -16516 6059  
      | -4993  0      7355   -17341 -4993  9986   9986   -44668 16534  -21527
      | 2296   -14099 -10301 -13063 -35347 -26744 23364  1796   7724   -10296
      | -10055 -15662 14694  23864  -10055 20110  -1393  -8345  -11765 1710  
      | 0      0      0      0      0      0      0      0      -37956 -49751
      | 5817   33888  29028  -17394 -28071 22254  -11634 10734  -32988 4917  
      | -21075 -32015 -13172 -8504  12571  8504   21676  22987  30056  -17485
     ------------------------------------------------------------------------
     |, | 0  0  0  0  0  0  0  0   1  -1  |)
     |  | 0  -1 -1 0  0  0  1  -1  1  -1  |
     |  | 1  -1 -1 3  2  -3 -2 7   -4 6   |
     |  | -1 1  1  -2 -1 2  1  -4  2  -3  |
     |  | 2  0  -1 3  1  -2 -2 8   -5 7   |
     |  | -1 0  1  -3 -1 2  2  -8  6  -7  |
     |  | -1 0  0  -2 -1 2  2  -6  4  -5  |
     |  | 0  0  0  0  0  0  0  0   0  1   |
     |  | -4 0  2  -8 -4 8  7  -22 14 -18 |
     |  | 2  0  -1 4  2  -4 -3 11  -7 9   |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also