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Computational Number Theory is for explicit calculations or algorithms involving anything of interest to number theorists.

11 votes
1 answer
2k views

Best way to find a closest vector in a lattice

Let $v_1,\dotsc,v_n$ be linearly independent vectors in $\mathbb{R}^n$, and let $\Lambda=\bigoplus_{i=1}^n \mathbb{Z}v_i$. The question is, given a vector $w$ in $\mathbb R^n$, find the element $v$ o …
12 votes
1 answer
1k views

How many LLL reduced bases are there?

For a given $n$-dimensional lattice embedded inside $\mathbb R^n$ along with a given inner product, how many distinct LLL-reduced bases are there? In this question, a lattice is the set of all $\math …