# 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:

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