This might be a stupid/very simple question, but since I can't quite seem to come up with a nice trick I will ask it anyway.
Assume that we have a vectorspace $V \subseteq \mathbb{Q}^n$ given in the form of a basis $b_1,\ldots, b_k \in \mathbb{Q}^n$ [EDIT: $V$ was originally assumed to be real, but since the question becomes unreasonably hard in this case, I am assuming $V \subseteq \mathbb{Q}^n$] . With this information I would like to find a basis for the lattice $L= V\cap \mathbb{Z}^n$ Does there exist an efficient algorithm for finding such a basis?
EDIT: In light of Sean Eberhard's answer below an algorithm which would solve the problem in the generality originally stated, i.e. for $V$ any real subspace, is clearly far too optimistic. Hence allow me to modify the question by adding the assumption that $b_1,\ldots, b_k \in \mathbb{Q}^n$, i.e. that in fact $V\subseteq \mathbb{Q}^n$.
EDIT 2: $V$ should be a proper subspace, since the answer is trivial otherwise, as pointed out below (my original labelling of the basis elements meant that Chris Eagles remark below answered my question as stated). Hope the problem has now been given in a way making it feasible without being trivial...