lattice - Maple Help

lattice

find a reduced basis of a lattice

 Calling Sequence lattice(lvect) lattice(lvect, integer)

Parameters

 lvect - list of vectors or a list of lists

Description

 • Important: The lattice function has been deprecated. Use the superseding function IntegerRelations[LLL] instead.
 • The lattice function finds a reduced basis (in the sense of Lovasz) of the lattice specified by the vectors of lvect using the LLL algorithm.
 • If the lattice is generated by vectors with integer coefficients and the option integer is specified, then the reduction is performed using only integer arithmetic. This version is sometimes faster than the default version, which uses rational arithmetic.
 • This function requires that the dimension of the subspace generated by the vectors equals the number of vectors.

Examples

Important: The lattice function has been deprecated. Use the superseding function IntegerRelations[LLL] instead.

 > $\mathrm{lattice}\left(\left[\left[1,2,3\right],\left[2,1,6\right]\right]\right)$
 Warning, lattice is obsolete, use IntegerRelations:-LLL
 $\left[\left[{0}{,}{-3}{,}{0}\right]{,}\left[{1}{,}{-1}{,}{3}\right]\right]$ (1)
 > $\mathrm{lattice}\left(\left[\left[1,2,3\right],\left[2,1,6\right]\right],'\mathrm{integer}'\right)$
 $\left[\left[{0}{,}{-3}{,}{0}\right]{,}\left[{1}{,}{-1}{,}{3}\right]\right]$ (2)
 > $\mathrm{lattice}\left(\left[\left[1,2,3\right],\left[-1,0,1\right],\left[0,1,1\right]\right]\right)$
 $\left[\left[{-1}{,}{0}{,}{1}\right]{,}\left[{0}{,}{1}{,}{1}\right]{,}\left[{0}{,}{-1}{,}{1}\right]\right]$ (3)

References

 Lenstra, A. K.; Lenstra, H. W.; and Lovasz, L. "Factoring Polynomials with Rational Coefficients." Mathematische Annalen, (December 1982): 515-534.