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The hilbert basis elements must belong to the cone C. |
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== Definition ==
[[File:Hilbert basis.gif|thumb|Hilbert basis visualization. Two rays in the plane define an infinite cone of all the points lying between them. The unique Hilbert basis points of the cone are circled in yellow. Every integer point in the cone can be written as a sum of these basis elements. As you change the cone by moving one of the rays, the Hilbert basis also changes.]]
Given a [[Lattice (group)|lattice]] <math>L\subset\mathbb{Z}^d</math> and a convex polyhedral cone with generators <math>a_1,\ldots,a_n\in\mathbb{Z}^d</math>
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