Verify that a point is inside a lattice I am wondering if there's a polynomial time algorithm that, given a lattice $\Lambda$ with basis $\mathbf{B}$ and a point $x$ in space, it tells you whether $x$ is in $\Lambda$ or not!
If you compute a base of a the dual lattice, and then check that the inner product of the point and the vector if this base are all integers:
To compute this base it's $\mathbf{B}(\mathbf{B}^{T}\mathbf{B})^{-1}$:
https://cseweb.ucsd.edu/classes/wi12/cse206A-a/LecDual.pdf