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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      39785  -49570 -95452 0      0      0      57092  -78192
     | 0      -61642 -56184 10497  0      0      0      0      0      -4682 
     | 0      0      0      30291  0      75333  -32475 0      -53023 0     
     | -67306 0      0      0      0      76931  57179  -26471 -82604 0     
     | 73362  0      -86578 0      0      -50002 -82961 0      0      0     
     | -1920  0      0      0      0      -25211 0      0      0      0     
     | 86157  29735  54600  -13975 0      0      33787  0      -93180 -24542
     | 0      0      0      97656  37195  0      0      0      -84705 -98930
     | 0      93291  62459  -25533 0      -49503 0      65320  -75909 0     
     | 59174  0      0      0      0      0      -42265 79577  53311  0     
     ------------------------------------------------------------------------
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              10        10
o1 : Matrix ZZ   <--- ZZ
i2 : (B,U) = LLL(A, ChangeMatrix=>true)

o2 = (| -45882 -39785 -32310 -39785 -26213 -4666  5597   -7975  2425   -34188
      | -10497 -5458  5815   56184  10854  39934  3544   -12768 8448   -1914 
      | -30291 -32475 30291  -32475 28107  29284  -20296 26930  -16799 -20296
      | 0      57179  0      30708  30708  -21627 22456  42208  -13158 22456 
      | 0      3617   0      3617   3617   2365   -41306 -8347  3268   45272 
      | 0      0      0      0      0      1920   21371  -3840  -42742 21371 
      | 13975  8922   -38517 -20813 -43570 30641  -25464 -6759  -27493 -50329
      | -60461 0      -38469 0      21992  40721  25255  3263   22902  25255 
      | 25533  30832  -25533 2861   45086  23086  -30629 -29066 -34885 203   
      | 0      -42265 0      37312  37312  14310  -2354  39911  -26511 -2354 
     ------------------------------------------------------------------------
     |, | 0  0  0  0  0  -1 2   2  -4  2   |)
     |  | 0  1  0  0  1  -3 4   4  -7  5   |
     |  | 0  -1 0  -1 -1 2  -3  -3 5   -4  |
     |  | -1 0  1  0  2  -4 10  8  -18 10  |
     |  | 1  0  -1 0  -2 4  -10 -8 19  -10 |
     |  | 0  0  0  0  0  0  -1  0  2   -1  |
     |  | 0  1  0  1  1  -3 6   5  -10 6   |
     |  | 0  0  0  1  1  0  1   1  -2  1   |
     |  | 0  0  0  0  0  -1 1   1  -1  1   |
     |  | 0  0  1  0  1  -2 5   4  -10 5   |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also