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 in its [[convex cone]]
 
:<math>\{ \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>
 
is also in its [[integer 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>
 
and no vector from ''A'' belongs to the integer cone of the others.
 
== References ==