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Macaulay2 web site
LLLBases
::
LLL(..., ChangeMatrix => ...)
LLL(..., ChangeMatrix => ...) -- also find change of basis matrix
Synopsis
Usage:
(B,U) = LLL(A,ChangeMatrix=>true)
Inputs:
A
,
a
matrix
, over the integers, of size d by n
Outputs:
B
,
a
matrix
, the LLL matrix (also having d rows)
U
,
a
matrix
, the n by n invertible transform matrix
Consequences:
The routine returns a pair of matrices, rather than just one
Description
Constructs the change of basis matrix U from the basis A to the basis B. This is an invertible matrix U such that
AU = B
.
A = matrix randomMutableMatrix(10,10,.5,100000)
(B,U) = LLL(A, ChangeMatrix=>true)
B == A*U
Further information
Default value:
false
Function:
LLL
-- compute an LLL basis
Option name:
ChangeMatrix
-- name for an optional argument
See also
LLLBases
-- lattice reduction (Lenstra-Lenstra-Lovasz bases)