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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      62731  0      0      0      -31300 64662  0      0     0      |
     | 34167  -7832  0      24379  79524  59321  0      89589  150   0      |
     | 97460  -68002 0      -29022 0      20444  86790  -66703 52207 0      |
     | 0      -63126 0      1868   40184  12432  0      0      0     -81550 |
     | 0      -7132  69540  0      0      0      -21098 0      0     0      |
     | 0      96744  82248  0      55110  17174  -10035 0      0     0      |
     | -88132 0      -17750 0      69213  52011  0      66323  0     -48528 |
     | 0      13492  -92552 -65461 7261   40276  0      0      0     0      |
     | 0      0      88332  0      -43753 11406  91405  32509  0     0      |
     | -413   99850  -14639 0      0      -37323 0      11159  0     41557  |

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

o2 = (| 0     0      31300  -31300 33231  33231  0      64662  1931   1800  
      | 150   24529  6039   4176   -7009  -16497 33867  -10515 42824  27840 
      | 52207 23185  -5918  -8578  21245  -823   -6954  -3128  19621  14891 
      | 0     1868   -14300 -25884 47644  -32038 0      40184  -19606 -28314
      | 0     0      0      0      -13966 -13966 0      -21098 -13966 62706 
      | 0     0      -17174 -37936 -13733 -13733 0      45075  3441   9707  
      | 0     0      14312  -17202 -28436 11168  -88132 2890   63179  28415 
      | 0     -65461 25185  -32446 26215  -39246 0      7261   1030   18078 
      | 0     0      21103  55159  -40016 -40016 0      15143  -28610 25666 
      | 0     0      48482  -37323 -32129 9841   -413   -11159 -27482 -14609
     ------------------------------------------------------------------------
     |, | 0 0 0  0  0  -1 1  0  -1 -1 |)
     |  | 0 0 0  0  -1 -1 0  0  -1 -2 |
     |  | 0 0 0  0  0  0  0  0  0  1  |
     |  | 0 1 -1 1  -1 0  0  0  0  -3 |
     |  | 0 0 0  -1 2  2  0  1  2  3  |
     |  | 0 0 -1 1  -1 -1 0  0  0  -2 |
     |  | 0 0 0  0  1  1  0  1  1  1  |
     |  | 0 0 1  0  -1 -1 0  -1 -1 0  |
     |  | 1 1 1  0  -4 -2 -2 -3 -2 -3 |
     |  | 0 0 0  0  1  2  0  0  2  3  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also