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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 = | 68325  99102 -6170  90499  24262  51288  -7031  0      57708  0      |
     | -80118 0     0      0      2342   0      45031  -5448  69235  0      |
     | -99816 0     0      0      -43752 19895  0      0      -59580 60932  |
     | 0      0     -21213 0      0      0      0      0      6377   -27925 |
     | -71961 0     0      0      61523  0      -55033 -23032 81707  0      |
     | -31845 0     0      28412  0      0      -39315 0      93644  -35375 |
     | 0      0     37178  0      -87050 0      -13603 84992  0      -62849 |
     | -93992 0     34955  83505  0      73499  -7473  0      0      35557  |
     | 0      0     48430  -68454 0      -32647 77161  92876  -71409 -22636 |
     | 0      -3924 0      58258  0      -24432 0      0      -60279 0      |

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

o2 = (| -6170  -35474 63628  -6170  -11212 19456  21675  -13286 36388  -19371
      | 0      -5448  -5448  5448   -8554  -35781 -22558 30333  -779   55927 
      | 0      19895  19895  0      -23857 -457   -22037 61389  -4400  -60932
      | -21213 42426  42426  -21213 42426  7454   -407   -14166 27853  -14501
      | 0      -23032 -23032 23032  15459  -43891 8248   20859  44566  -8969 
      | 0      0      0      0      0      -15914 -35392 -19461 -26441 -3940 
      | 37178  10636  10636  -47814 8578   651    29419  -15686 22311  -46382
      | 34955  3589   3589   34955  3589   29863  32426  -29261 16760  26880 
      | 48430  -36631 -36631 -44446 56245  30242  707    -8432  12713  10905 
      | 0      -20508 -24432 0      -20508 -14681 -36086 14681  40777  0     
     ------------------------------------------------------------------------
     |, | 0 0  0  0  0  1  -1 -1 -2 0  |)
     |  | 0 -1 0  0  -1 -3 4  3  6  0  |
     |  | 1 -2 -2 1  -2 -4 6  3  7  2  |
     |  | 0 0  0  0  0  1  -2 -1 -2 0  |
     |  | 0 0  0  0  1  1  -1 -1 -1 0  |
     |  | 0 1  1  0  1  1  1  -1 0  0  |
     |  | 0 0  0  0  0  0  0  0  0  1  |
     |  | 0 1  1  -1 2  5  -7 -4 -9 -2 |
     |  | 0 0  0  0  0  1  -2 -1 -3 0  |
     |  | 0 0  0  0  0  3  -5 -2 -7 -1 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also