# Lattices via sage

I have three questions on lattices:

-Is there a way to obtain the minimal number of generators of a lattices with sage?

-Is there a way to obtain the lattice of all subspaces of a vector space over a finite field with q elements in sage?

-Is there a quick way to obtain all distributive lattices on n points in sage (that is, without filtering them from the set of all posets on n points).

Could you clarify which lattice you mean? A lattice can be a subgroup of the additive group

`R^n`

which is isomorphic to`Z^n`

or a poset with a join and meet operations.