Hilbert basis (linear programming): Difference between revisions

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== Definition ==

A set <math>A=\{a_1,\ldots,a_n\}</math> of integer vectors is a Hilbert basis if every integer vector inof its [[convex cone]]

:<math>C=\{ \lambda_1 a_1 + \ldots + \lambda_n a_n \mid \lambda_1,\ldots,\lambda_n \geq 0, \lambda_1,\ldots,\lambda_n \in\mathbb{R}\}</math>

isif alsoevery ininteger itsvector from ''C'' belongs to the [[integer convex cone]]

:<math>\{ \alpha_1 a_1 + \ldots + \alpha_n a_n \mid \alpha_1,\ldots,\alpha_n \geq 0, \alpha_1,\ldots,\alpha_n \in\mathbb{Z}\}</math>