Normal to a set of integer vectors

Question

Given a set of $i$ integer vectors resting in $d$ space (with $i$ < $d$), how do you find a normal to the set of vectors while keeping all of the computations in $\mathbb{Z}$?

Answer 1

You are looking for a solution of a system of linear Diophantine equations: $$AX = 0$$ where $A$ is a matrix of your integer vectors, and $X$ - the normal vector you want to find.

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