All Questions

Suppose I have an ordered basis $\{b_1, \dots, b_n\}$ of a lattice in $\mathbb{R}^n$, but I do not assume that $b_i \in \mathbb{Z}^n$ for all $1 \leq i \leq n$. I would like to perform lattice ...

Let an integer vector be nice when it has only two nonzero components, which sum to zero. So (0, 0, 3, 0, -3) and (-1, 0, 1, 0, 0) are examples of nice vectors in $n=5$ dimensions. Call a lattice ...

Modular inverse is known to be computable by Extended Euclidean algorithm which is the reaping the rewards of computing the GCD of two numbers or proving two numbers are coprime. If we already know ...

Consider the Linear Diophantine in known $a,b,c\in\mathbb Z$ $$ax+by=c.$$ Above can be solve by Extended Euclidean which is not in $NC$ as far as we know. It is clear if Extended Euclidean is in $NC$ ...

Let $\Lambda$ be a lattice with basis, $B$ consisting of vectors $b_i$, so that the elements of $\Lambda$ are of form, $y\in \Lambda \iff y=Bx=\sum_i b_ix_i$ for some $x_i\in\mathbb{Z}$. My questions ...