# LLL Demonstration

# WORK IN PROGRESS

This is a demo of the LLL algorithm. You can check the debug box to step through the algorithm to see exactly how LLL works.**Set**\(k=2\).

**While**\(k\leq n\)

**For**\(j\) from \(k-1\) down to \(1\)

**Set**\(\vec{v}_k=\vec{v}_k-\lfloor \mu_{k,j} \rceil \vec{v}_j\)

**EndFor**

**If**\( \|\vec{v}_k^*\|^2\geq (\delta-\mu_{k,k-1}^2)\|v_{k-1}^*\|^2 \):

**Set**\(k=k+1\)

**Else**

**Swap**\(\vec{v}_k\) and \(\vec{v}_{k-1}\)

**Set**\(k=\max(k-1,2)\)

**EndIf**

**EndWhile**

**Output**LLL-reduced basis \(\{\vec{v}_1,\cdots ,\vec{v}_n\}\)

Orthogonality Defect:

Number of lattice points rendered per direction:

LLL \(\delta\):

k=; Current step:

Gram-Schmidt Coefficient Matrix: