next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

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 = | 60055  -98738 -58609 -76012 -19949 18649  -5533  0      0      -53997
     | 0      7577   2317   0      0      -65326 0      53285  -20733 0     
     | 0      0      0      42630  -35628 0      99102  0      -58594 0     
     | 0      -25582 0      0      -94596 -45074 -68246 2207   43084  27925 
     | -36807 -21383 0      0      -3840  96043  0      13039  0      51999 
     | 92820  -86761 -47256 0      0      92662  -50448 0      0      91588 
     | 59846  -44622 0      -35925 -42027 0      15670  -46430 0      0     
     | 0      0      -47447 -76702 0      0      526    6509   -45817 72814 
     | 0      -87106 -57334 -31858 0      0      -7688  0      0      -82809
     | 0      0      0      83710  0      -88050 -1645  -51391 -66891 0     
     ------------------------------------------------------------------------
     |
     |
     |
     |
     |
     |
     |
     |
     |
     |

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

o2 = (| -19316 610    40129  -58609 0      -58835 20180  -57532 -3846  -79072
      | 31756  37016  -5260  2317   53285  14     -5260  -17790 -3824  8720  
      | 4880   4880   0      0      0      -48834 -35628 -15964 29424  -3446 
      | 4405   -21177 25582  0      2207   -1477  -69014 17502  -28837 5691  
      | 31689  -26501 21383  0      13039  -29234 17543  -21383 -47884 54454 
      | -18076 35239  39505  -47256 0      -22342 39505  7751   39798  47978 
      | 3041   18265  44622  0      -46430 23114  2595   -80547 -46612 41825 
      | -19924 27523  -47447 -47447 6509   2720   -47447 -27625 2054   57766 
      | 26381  -3391  29772  -57334 0      -6782  29772  -4296  41959  -13564
      | 19514  19514  0      0      -51391 23528  0      16819  -32203 -25494
     ------------------------------------------------------------------------
     |, | -1 0  0  0 0 -1 0  0  0  -2 |)
     |  | -2 -1 -1 0 0 -2 -1 1  0  -4 |
     |  | 1  0  1  1 0 0  1  -2 -3 0  |
     |  | 0  0  0  0 0 0  0  1  1  0  |
     |  | 1  1  0  0 0 2  1  0  1  3  |
     |  | -1 -1 0  0 0 -2 0  0  -1 -3 |
     |  | 1  1  0  0 0 2  0  0  2  4  |
     |  | 0  0  0  0 1 -1 0  0  0  -1 |
     |  | 1  1  0  0 0 3  0  1  3  5  |
     |  | 1  1  0  0 0 2  0  0  1  4  |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also