okay, I shall add a reduced_basis attribute which gets improved using LLL 
reduction et al.

On Friday 04 Apr 2014 13:35:05 John Cremona wrote:
> This is not sso different from the situation with (say) finite abelian
> groups, where the user might start with 2 generators of orders 2 and 3
> and internally you work with one generator of order 6.  Now th object
> has .use_defined_gens() and some sort of .canonical_gens().
> 
> For lattices, one could agree never to change the basis returned by
> L.basis(), but store other bases (with respective transformations)
> which would be accessed by L.LLL_basis() etc.  After all, LLL is not a
> "lattice reduction algorithm" -- it does not change the lattice! --
> but it as "lattice basis reduction" algorithm.
> 
> It hardy seems necessary to have a separate class for lattice bases though.
> 
> John
> 
> On 4 April 2014 11:36, Volker Braun <vbraun.n...@gmail.com> wrote:
> > On Friday, April 4, 2014 11:19:11 AM UTC+1, Martin Albrecht wrote:
> >> existing one. However, in my case it would seem natural to improve the
> >> basis
> >> during the lifetime of an object.
> > 
> > IMHO that is always going to cause tears later on as the end-user isn't
> > going to be aware that this modified all references to the lattice. The
> > only downside of returning new objects is memory, and I'm pretty sure
> > your problem runs of CPU before RAM. If you don't like that your lattice
> > has a built-in basis then you could return new BasisOfLattice (say)
> > objects.
> > 
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