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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 = | -37573 53225  332    -1093  0     0      -65512 0      0      -69654 |
     | 0      0      0      0      0     65504  0      -80849 46612  0      |
     | 0      -32854 0      0      0     0      -6931  -89955 0      -4829  |
     | 0      0      -63022 0      0     11219  0      87334  6353   23226  |
     | 0      -69168 -19840 54140  0     0      0      0      0      -50659 |
     | 19690  18569  97255  -89923 -3946 0      89479  -59738 -21376 -77582 |
     | 0      0      80104  0      13222 -81715 0      -90348 -46233 -93094 |
     | 78693  28789  0      88627  0     0      -82980 63314  0      0      |
     | 0      70347  26583  21637  0     0      24571  65252  66362  0      |
     | 0      0      6269   0      0     -37905 -36045 10586  0      0      |

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

o2 = (| 0     -37573 0      13712  0      50524  -66605 24193  -39181 -72023
      | 0     0      65504  -15345 -18892 -15345 0      -46612 31267  -15345
      | 0     0      0      -50170 0      -50170 -6931  -39785 -17316 -22145
      | 0     0      11219  35531  -4866  -27491 0      -6353  -21138 -67287
      | 0     0      0      -4812  0      29488  54140  -15028 44516  28157 
      | -3946 19690  -23676 -8230  -9538  3088   -444   31649  53026  246   
      | 13222 0      -2383  595    -4184  1367   0      6567   21244  1599  
      | 0     78693  0      28878  0      38812  5647   -44257 89     10023 
      | 0     0      0      -24720 66362  23500  46208  50193  -2122  -20264
      | 0     0      -37905 14995  37905  21264  -36045 -36045 21264  27533 
     ------------------------------------------------------------------------
     |, | 0 1 0 0  0  -1 0 -1 0  -1 |)
     |  | 0 0 0 -1 0  -1 0 1  -2 -2 |
     |  | 0 0 0 1  0  2  0 0  2  3  |
     |  | 0 0 0 -1 0  0  1 1  -1 0  |
     |  | 1 0 6 7  -3 1  0 -3 6  2  |
     |  | 0 0 1 1  -1 1  0 0  1  1  |
     |  | 0 0 0 -1 0  -1 1 1  -1 -1 |
     |  | 0 0 0 1  0  1  0 0  1  1  |
     |  | 0 0 0 0  1  0  0 -1 1  0  |
     |  | 0 0 0 0  0  0  0 0  0  1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also