Hilbert basis (linear programming): Difference between revisions

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:<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>
 
if every integer vector from ''C'' belongs to the integer convex cone of A:
 
:<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 convex cone of the others.
 
== References ==