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I have done some reading about integer points in polyhedra, and in one of the books I have come across the definition: "Let $f$,$g$ be polyhedra. $f$ $\equiv$ $g$ modulo polyhedra with lines provided the difference $f-g$ is a linear combination of indicators of polyhedra with lines."

My problem is that I just cannot understand what the meaning of "modulo polyhedra with lines". I know that it somehow makes polyhedra containing lines irrelevant for us, because we don't really care about them when trying to determine the number of integer points in polyhedra. Can anyone explain this to me using a language that isn't just a quote from the definition? I really need your help. Thanks in advance.

Kris
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A. Barvinok gives a precise definition of this in page 14 of their notes Lattice Points, Polyhedra, and Complexity:

Definition 2. We say that a polyhedron $P$ contains a line if there are points $x$ and $y$ such that $y\neq 0$ and $x + ty\in P$ for all $t\in\mathbb{R}$. [...]

user347489
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