In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representation of the object. A classical example is the problem of enumeration of the vertices of a convex polytope specified by a set of linear inequalities:
where A is an m×n matrix, x is an n×1 column vector of variables, and b is an m×1 column vector of constants.
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