The chiral reservation of the lattice basis before and after lattice reduction.

[hongyi-zhao]

Suppose A is the original lattice, and B is the result obtained by lattice reduction. If I want to retain the chirality of the bases before and after the lattice reduction, aka, Det[A] == Det[B]. I'm not sure whether this is possible.

See here for the related discussion.

Regards, Zhao

[malb]

Lattice reduction is multiplication by an unimodular transformation matrix and thus leaves the determinant unchanged.

[hongyi-zhao]

By convention, an unimodular matrix M is a square integer matrix having determinant +1 or -1, as described below:

This does not seem to be consistent with your above statement.

[malb]

Flip the sign of a row then.