Polynomial inequalities representing polyhedra
classification
🧮 math.MG
math.AGmath.OC
keywords
inequalitiespolynomialn-dimensionalpolyhedraarbitraryboundconeconstructed
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Our main result is that every n-dimensional polytope can be described by at most (2n-1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n-2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities.
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