next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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      0      0      0      14735 78124  0      -38596 |
     | 0      96816  69029  0      93860  6587   0     0      0      0      |
     | 11122  12527  -12007 0      0      -44256 95039 -39007 0      0      |
     | -84941 0      -58616 0      0      -42037 0     99550  13719  -3039  |
     | 0      0      22509  -89517 -23477 0      0     -66226 0      -46511 |
     | 0      -22738 0      0      -41064 0      18410 0      0      0      |
     | 0      -75184 0      0      97487  0      0     88000  0      0      |
     | 71091  0      -37481 0      0      -35410 26754 0      8266   0      |
     | 20380  0      0      -4483  12302  0      0     -98618 0      0      |
     | -68765 0      59515  -88645 0      0      59826 0      -44261 0      |

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

o2 = (| 0      0      14735  14735  -9126  -9126  -38596 -35572 5609   -14735
      | 0      6587   9937   6587   16524  -45918 0      16434  -4957  -13174
      | 0      -44256 -33437 50783  17346  -14903 0      6363   16158  4595  
      | 13719  -42037 -6019  -28318 3781   -7078  -3039  -8636  -18817 -42024
      | 0      0      -1487  0      41519  19010  -46511 9283   -3499  0     
      | 0      0      -45392 18410  -26982 -26982 0      -25800 -31310 -18410
      | 0      0      22303  0      22303  22303  0      -17762 -52881 0     
      | 8266   -35410 -10709 -390   13699  -762   0      -20166 919    90359 
      | 0      0      16785  0      21268  21268  0      -42633 21268  20380 
      | -44261 0      14187  15565  -14386 14621  0      -27159 -29329 4192  
     ------------------------------------------------------------------------
     |, | 0 0 0  0 0  0  0 0   0  1  |)
     |  | 0 0 1  0 1  1  0 4   2  0  |
     |  | 0 0 -3 0 -3 -4 0 -10 -5 0  |
     |  | 0 0 -1 0 -2 -2 0 -7  -2 0  |
     |  | 0 0 1  0 1  1  0 2   1  0  |
     |  | 0 1 4  1 5  6  0 20  8  -2 |
     |  | 0 0 1  1 2  2  0 8   3  -1 |
     |  | 0 0 0  0 0  0  0 1   0  0  |
     |  | 1 0 -1 1 3  1  0 12  2  -3 |
     |  | 0 0 0  0 1  1  1 6   1  0  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also