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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      -54577 38239  0      0      0      -97883 0      -89292 |
     | 99020 -11664 0      63949  0      81708  11497  -29031 0      0      |
     | 7927  0      0      97682  0      -7890  0      99296  0      0      |
     | 28315 0      -68597 89605  0      0      0      0      0      92362  |
     | 59223 0      0      0      59773  0      -97195 38501  0      0      |
     | 0     49168  63660  0      0      -4485  -69338 90970  0      0      |
     | 0     0      0      -95768 0      0      0      0      -46325 0      |
     | 0     0      -3130  62900  0      87599  7238   0      0      75208  |
     | 0     0      0      -77123 0      0      31429  0      -46610 45210  |
     | 0     75675  0      0      -37623 -47130 60344  0      0      -59398 |

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

o2 = (| 0      0      0      0      -26968 -54577 0     0      19221  19018 
      | 0      -11664 -167   0      -11272 11497  99020 -28976 22544  -57615
      | 0      0      0      0      -6276  0      7927  -15817 12552  77203 
      | 0      0      0      0      47589  -68597 28315 -28315 65781  -4491 
      | 59773  59773  22351  0      -21272 22351  -550  550    -17229 17779 
      | 0      49168  -20170 0      -40835 -5678  0     44683  18010  -18010
      | 0      0      0      -46325 3118   0      0     0      -52561 49443 
      | 0      0      7238   0      30959  4108   0     87599  16420  46480 
      | 0      0      31429  -46610 -16097 31429  0     0      30794  -14697
      | -37623 38052  60773  0      -9507  -14902 37623 -9078  -2761  -34862
     ------------------------------------------------------------------------
     |, | 0 0 0 0 0  0 1  -1 0  -1 |)
     |  | 0 1 1 0 0  0 0  1  0  0  |
     |  | 0 0 0 0 -2 1 0  0  3  -3 |
     |  | 0 0 0 0 -1 0 0  0  2  -1 |
     |  | 1 1 2 0 -1 2 -1 1  1  0  |
     |  | 0 0 0 0 1  0 0  1  -2 2  |
     |  | 0 0 1 0 0  1 0  0  0  0  |
     |  | 0 0 0 0 1  0 0  0  -2 2  |
     |  | 0 0 0 1 2  0 0  0  -3 1  |
     |  | 0 0 0 0 0  0 0  0  1  -1 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also