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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      0      38863  43123  0      93099  80830 0      35257  |
     | 0      -38608 0      0      0      15529  -72800 0     -34067 0      |
     | -79864 61987  0      0      -2792  94899  0      1106  46144  0      |
     | 87626  -31611 0      0      0      0      0      0     0      61259  |
     | 0      0      -60513 -9972  0      0      0      84428 -72650 -59821 |
     | -4065  0      0      83532  -76262 0      -77332 0     -87138 0      |
     | -85255 0      0      0      74347  -18099 0      14600 0      -7478  |
     | 68771  0      23567  -30675 37223  0      0      0     0      -56127 |
     | -56872 50558  -83538 -95946 19940  0      0      0     0      0      |
     | 27477  56214  0      0      0      0      -49287 0     0      0      |

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

o2 = (| -1156  0      0      -12269 25438  -5918  4762   45868  3606   -4762 
      | 0      -38608 15529  38733  -10863 -20070 -34067 24860  -34067 68134 
      | 3898   61987  94899  47250  2393   8604   -37618 -38827 46144  -8526 
      | 0      -31611 0      0      0      -57978 26367  3281   -61259 -26367
      | 33887  0      0      11778  23556  -30451 3825   -7291  37712  8312  
      | -7270  0      0      -9806  -20682 -6869  -401   17419  -3606  87539 
      | -59747 0      -18099 14600  -27048 -23618 -18030 10552  7478   18030 
      | 17019  0      0      0      -37223 -13051 53637  22287  1885   -30070
      | -7532  50558  0      0      -19940 21236  -61748 53584  -12408 -21790
      | 0      56214  0      49287  49287  28737  27477  -20550 0      -27477
     ------------------------------------------------------------------------
     |, | 0  0 0 0  0  -1 1  -1 0  -1 |)
     |  | 0  1 0 0  0  1  0  1  0  0  |
     |  | 1  0 0 0  0  4  -2 5  -1 3  |
     |  | -1 0 0 0  0  -3 2  -4 1  -2 |
     |  | -1 0 0 0  -1 -2 1  -1 0  -1 |
     |  | 0  0 1 0  -1 -1 0  0  0  0  |
     |  | 0  0 0 -1 -1 0  0  1  0  0  |
     |  | 1  0 0 1  2  2  -1 1  0  1  |
     |  | 0  0 0 1  2  -1 1  -4 1  -2 |
     |  | 0  0 0 0  0  1  -1 2  -1 1  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also