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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 = | -67970 0      44301  -68267 0      25894  0      0      0      66716 
     | 14401  0      0      30668  80177  -45447 0      0      0      -11650
     | 50461  0      0      0      -57465 0      0      -18314 0      0     
     | 0      -72635 0      -11955 -95656 0      0      38968  -20917 49605 
     | 0      47613  -44675 95811  0      85633  65382  26593  -71961 0     
     | 0      0      0      0      -22109 0      -98420 6648   64446  0     
     | 0      0      0      0      -70181 48525  0      0      82541  0     
     | -25727 0      -1301  0      0      79523  56231  -68329 48101  0     
     | -61211 0      -70707 0      46050  -87944 -21154 0      -35813 0     
     | -43021 -21610 0      0      -20187 0      -69062 0      49592  34686 
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| 0      44301  -23966 5856   0      22712  -66716 15059  -27445 -8907 
      | 0      0      30668  -12205 0      -27917 11650  -28027 64465  2641  
      | 0      0      0      -25318 18314  50461  0      -36453 0      175   
      | -72635 0      -11955 39857  -38968 -11075 23030  -4443  16733  -782  
      | 47613  -44675 51136  -37659 -26593 -3523  -47613 -674   3599   -43758
      | 0      0      0      -15461 -6648  0      0      -54202 -33974 -33524
      | 0      0      0      -21656 0      0      0      43312  34016  -39229
      | 0      -1301  -1301  -11931 68329  -24426 0      -29537 24809  1488  
      | 0      -70707 -70707 38309  0      9496   0      34146  30977  20406 
      | -21610 0      0      -41598 0      -29945 -13076 9393   15216  50473 
     ------------------------------------------------------------------------
     |, | 0 0 0 1  0  1  0  -3 0  -3 |)
     |  | 1 0 0 -1 0  1  -1 1  0  0  |
     |  | 0 1 1 -2 0  -1 0  3  0  4  |
     |  | 0 0 1 -2 0  -1 0  2  1  3  |
     |  | 0 0 0 1  0  0  0  -2 0  -2 |
     |  | 0 0 0 1  0  0  0  -2 -1 -2 |
     |  | 0 0 0 0  0  0  0  1  1  0  |
     |  | 0 0 0 1  -1 0  0  0  0  -2 |
     |  | 0 0 0 0  0  0  0  0  1  -1 |
     |  | 0 0 0 0  0  1  -1 -2 1  -2 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also