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      27637 0      0     0      0     0      0      0      1103  |
     | 0      0     0      70260 0      75477 45452  21651  0      96851 |
     | 0      0     0      23354 0      86160 21952  0      0      6625  |
     | -42193 3021  0      51560 -65457 0     0      0      -4944  0     |
     | 0      0     0      0     10271  13806 0      15445  91647  14984 |
     | 0      0     83749  0     0      0     -12003 44867  -53793 0     |
     | 58795  62957 -23430 0     0      0     90482  0      -97198 0     |
     | 0      55852 0      65099 0      0     -13111 0      0      91038 |
     | 0      -6632 -61264 0     21292  0     8714   -49053 0      0     |
     | -7127  0     0      0     0      0     0      -31005 70901  0     |

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

o2 = (| -1103  28740  28740  1103   26534  0      0      -2206  27637  -30946
      | -26591 1783   1783   26591  -26591 45452  21651  8704   -3157  6921  
      | 16729  -18131 -18131 -16729 16729  21952  0      -7396  -1402  10735 
      | -13897 26480  -15713 -51560 31317  18929  0      502    12583  -7658 
      | -4713  14984  14984  14984  -4713  10271  15445  2484   25716  68876 
      | 0      -12003 -12003 0      0      -12003 -38882 32864  32864  -8926 
      | 0      -22946 35849  0      4162   -27108 23430  31687  -22946 16230 
      | -25939 3581   3581   25939  29913  -13111 0      110    -22358 -3471 
      | 21292  2082   2082   0      14660  30006  12211  23537  -25679 163   
      | 0      21381  14254  0      7127   14254  -31005 -23878 -9624  18515 
     ------------------------------------------------------------------------
     |, | 0  -3 -2 0  -1 -2 0  -1 -3 3  |)
     |  | 0  1  1  0  1  0  0  0  1  -1 |
     |  | 0  0  0  0  0  0  -1 0  0  0  |
     |  | 1  -2 -2 -1 1  0  0  3  -1 5  |
     |  | 1  0  0  0  1  1  0  3  1  2  |
     |  | 0  0  0  0  0  0  0  -1 0  -1 |
     |  | 0  1  1  0  0  1  0  1  1  0  |
     |  | 0  0  0  0  0  0  1  1  1  1  |
     |  | 0  0  0  0  0  0  0  0  0  1  |
     |  | -1 1  1  1  -1 0  0  -2 0  -3 |

o2 : Sequence
i3 : B == A*U

o3 = true

Further information

See also