Another thought about standard forms for temperament mappings

We want (for dimensions above linear temperaments) a standard form of the mapping so as to be able to calculate generator steps. Perhaps taking Hermite form first, and then doing a Minkowski reduction on the non-octave part of the lattice (excluding the first column) would be a good plan. The reduction could be with regard to the weighted distance function Paul likes. The problem with it all is that it's hard to compute; an LLL reduction would be much easier. Anyone care to weigh in on this?

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...>
wrote:
> We want (for dimensions above linear temperaments) a
>standard form of the mapping so as to be able to calculate
>generator steps. Perhaps taking Hermite form first, and then
>doing a Minkowski reduction on the non-octave part of the
>lattice (excluding the first column) would be a good plan. The
>reduction could be with regard to the weighted distance
>function Paul likes. The problem with it all is that it's hard to
>compute; an LLL reduction would be much easier. Anyone care
>to weigh in on this?

what about the TM reduction?