4
votes
1answer
225 views

Shortest Non-Zero Vector in Integer Lattices with Given Points

There are two questions related to the shortest non zero vector problem that have left me scratching my head. Please bear with me as I describe the problem. Disclaimer: this is homework. For the ...
1
vote
0answers
90 views

Lattice theory in mathematics and physics

I have undertaken a project examining lattice model and trying to construct algorithm that could work on all lattice (in physical sense, or crystal structure). I notice there is a branch in ...
4
votes
1answer
159 views

Is there an algorithm to find a basis for the lattice $V \cap \Bbb{Z}^n$ given a basis for $V \subseteq \Bbb{Q}^n$?

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 ...
0
votes
1answer
102 views

Lattice Reduction of two matrix

I have two matrices A, B with same number of rows. I want lattice reduction on B. During this reduction, I change rows of A accordingly. That is if i-th row and j-th row in B interchanges, swap i-th ...
0
votes
1answer
172 views

Lattice simplification

Update: There is an answer on same question I posted on Stack Overflow. I'm working on data structure for graph cut algorithm. Problem is to make different cuts on shortest paths. I made data ...
2
votes
0answers
130 views

The $n$-shortest lattice vectors problem in $\mathcal{R}^2$

I am looking for an algorithm to compute the $n$ shortest lattice vectors in $\mathcal{R}^2$. The problem statement is as follows: Given a lattice $L: \{ m \vec{u}+n\vec{v} \} \in \mathcal{R}^2$, a ...