Integer equivalent aggregation

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Integer equivalent aggregation is a reduction of a system of linear algebraic equations with non-negative integer solutions to a single equation, which is a linear combination of the equations of the system and has the same set of non-negative integer solutions. For example, consider the system:

S = \{ (x,y,z) \in \{0,1\}^3 : x + y = 1 , y + z = 1\}.

By simply adding the equations, we have the equivalent description:

LaTeX: S = \{(x,y,z) \in {0,1}^3: x + 2y + z = 2\}.

Both sets consist of two the points LaTeX: (0,1,0) and LaTeX: (1,0,1).

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