Gomory group

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The group associated with the corner polyhedron problem:

LaTeX: 
\left\{v \in \mathbb{Z}^n :  \sum_j r(A_j)v_j = r(b),\; v \ge 0 \right\},

where LaTeX: v corresponds to the nonbasic variables and LaTeX: r(d) is the remainder, LaTeX: d\!\mod |B|, where LaTeX: |B| is the determinate of the basis, LaTeX: B. The idea is that the nonbasic value chosen in this group, together with the basic levels imputed by the equations LaTeX: Ax=b, yields an integer solution (but a basic level might be negative).


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